Laboratory works in colloid chemistry 9786010446564

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AL-FARABI KAZAKH NATIONAL UNIVERSITY

LABORATORY WORKS IN COLLOID CHEMISTRY

Almaty «Qazaq University» 2020

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UDC 544.7 (075.8) LBC 24.6 я73 L 11 Recommended by the Academic Council of the Faculty of Chemistry and Chemical Technology and Editorial and Publishing Council of al-Farabi KazNU (Protocol No.3 dated 13.03.2020) Reviewers: doctor of Chemical Science, professor K.Zh. Abdiyev doctor of Chemical Science, professor G.A. Mun Authors: K.B. Musabekov, S.M. Tazhibayeva, K.I. Omarova, A.K. Kokanbayev, S.Sh. Kumargaliyeva, A.O. Adilbekova Zh.B. Ospanova, O.A. Esimova, M.Zh. Kerimkulova

L 11

Laboratory works in colloid chemistry / K.B. Musabekov, S.M. Tazhibayeva, K.I. Omarova, [et al.]. – Almaty: Qazaq University, 2020. – 126 p. ISBN 978-601-04-4656-4 The manual presents the guidelines for laboratory works on the main sections of colloid chemistry: surface phenomena, adsorption of surfaceactive substances, molecular-kinetic properties of dispersed systems, stability and coagulation of colloids, lyophilic and lyophobic disperse systems. The manual is intended for students and undergraduates of chemical and chemical-technological specialties.

DC 544.7 (075.8) LBC 24.6 я73 ISBN 978-601-04-4656-4

© Musabekov K.B., Tazhibayeva S.M., Omarova K.I., [et al.], 2020 © Al-Farabi KazNU, 2020

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PREFACE The manual "Laboratory works in colloid chemistry" has been designed for students of chemical and chemical-technological specialties of higher educational institutions. The manual is the result of long-term experience of teachers of colloid chemistry at the department of analytical, colloidal chemistry and technology of rare elements of al-Farabi Kazakh National University. The purpose of the manual is to study surface phenomena, methodology and properties of dispersed systems. The manual contains laboratory works on all major items of colloid chemistry: surface phenomena (adsorption at the liquid-gas interface, solid-liquid, surface wetting, surface modification), molecular-kinetic properties of dispersed systems (sedimentation analysis of suspensions), lyophilic system for determining the critical concentrations of micelle formation of surface-active substances, stability of lyophobic systems (study of coagulation and stabilization of sols, preparation of emulsions and foam), electrical properties of disperse systems (determination of the electro-kinetic potential by electrophoresis method). To help students, each laboratory work contains brief theoretical information and questions for self-control. The practicum is compiled taking into account prerequisites according to the curriculum of the students (higher mathematics, physics, inorganic chemistry, organic chemistry). Therefore special methods of measurement and processing of graphs and tables are not considered in the manual. Methodical textbook is based on the experience of teachers of department of analytical, colloid chemistry and technology of rare elements. The authors hope that the textbook "Laboratory works in colloid chemistry" will help the students to gain deeper understunding of same questions of Colloid Chemistry. Any comments and suggestions of the readers will be gratefully accepted.

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1. ADSORPTION FROM SOLUTIONS Adsorption is a spontaneous redistribution of system components between the surface layer and the volume of the phase. Desorption (Гі) and related changes in surface tension (dσ) and chemical potentials (dμі) of the system components are related to each other by the Gibbs fundamental adsorption equation:  dσ   Г i dμ i ,

(1.1)

where Гі is an excess of components in the surface layer (per unit surface) in comparison with the initial concentration; μі is the chemical potentials of the components. Taking into account that μ = μо + RTlnai , a dμi = RTlnai, we obtain Гi  

dа i  dσ 

  RT  da i 

(1.2)

At low concentrations of adsorbate in a binary solution, a can be replaced by с and the relation (1.2) becomes the widely used Gibbs adsorption equation: Гi  

dс  dσ   , RT  dс 

(1.3)

where с is the equilibrium concentration of adsorbate in the solution. In the Gibbs adsorption equation (1.3), the effect of the nature of the substances on adsorption is reflected by the derivative dσ . This dс

derivative also determines the sign of Gibbs adsorption. Thus, the quantity

dσ can serve as a characteristic of the behavior of subdс

stances during adsorption. To eliminate the effect of concentration on the derivative, take its limiting value as с → 0. This value was called surface activity by P.A. Rehbinder: 4

 dσ  Г  RT    dc   c0  C  c0

(1.4)

g  

Surface activity is the most important adsorption characteristic of substances, which determines many of their properties and applications. Units for measuring surface activity in SI (The International System of Units) are J · m/mol or N · m2/mol, and also in Gibbs (erg · cm/mol). The equation (1.4) shows that the more the surface tension decreases with the concentration of the adsorbed substance, the greater the surface activity of this substance is. The physical meaning of surface activity is that it represents the force that holds the substance on the surface and is calculated per unit of Gibbs adsorption. Surface activity can be calculated graphically by the surface tension isotherm. To do this, draw a tangent to the curve before intersection with the ordinate axis, the negative tangent of the adjacent angle of this tangent is the surface activity (Fig. 1).

ІІ о

∆

∆С2

С2

Fig. 1.1. Dependence of the surface tension on the concentration of the aqueous solution: I – butyric acid, II – sodium sulfate

Surface activity, like Gibbs adsorption, can be positive and negative. Its absolute value and sign depend on the nature of both the adsorbed substance and the medium (solvent). If the surface tension 5

at the interface decreases with increasing concentration of the substance, such a substance is called surface-active. For such substances g > 0,

d dc

< 0 and Г > 0

Substances that increase the surface tension at the interface with increasing concentration are called surface-inactive. For them g < 0,

d dc

> 0 and Г < 0

Negative Gibbs adsorption Г < 0 means that the concentration of the adsorbed substance in the volume is larger than in the surface layer. With an increase in the concentration of the surface-inactive substance in the volume, its concentration in the surface layer increases more slowly. As a result, with an increase in the concentration of the surface inactive substance in the volume, the Gibbs adsorption value is negative (Figure 1.1). The term "surfactants" is generally applied to specific substances having very high surface activity with respect to water, which is a consequence of their special structure. The surfactant molecules have a non-polar (hydrocarbon) part and a polar part, represented by the functional groups –СООН, –NH2, –O–, –SO2OH, etc. Hydrocarbon radicals are pushed out of the water to the surface, and their adsorption is Г > 0. The surfactant type of conventional soaps (sodium oleate) at a concentration of 10-6 mol/cm3 (1 mol/l) reduces σ of water at 298K from 72.5·10-3 to 30·10-3 J/m2, which gives g = 4 ∙ 10 Gibbs. This means that for a certain thickness of the surface layer, the surfactant concentration is 3·104 times (i.e. tens of thousands of times) higher than the surfactant concentration in the solution volume. An example of surface-inactive substances with respect to water is inorganic salts, which are strongly hydrated. They interact with water more than molecules of water between themselves. As a consequence, they have a negative adsorption Г < 0. When adding inorganic salts to water, the surface tension increases. But due to the fact 6

that adsorption is negative, the increase in concentration in the surface layer lags behind its growth in volume. Therefore, the surface tension of the solution with increasing concentration of surface-inactive substances grows very slowly. The value of adsorption depends on the nature of the adsorbing surface, the nature of adsorbent, its concentration, temperature, etc. The dependence of adsorption on the concentration of the adsorbed substance in the volume at constant temperature is called the adsorption isotherm. The analytical expression for the isotherm of monomolecular adsorption at low concentrations of adsorbate is the Langmuir equation: A  A

Kc 1  Kc

,

(1.5)

where A∞ is the limiting value of adsorption (monolayer capacity); K is the equilibrium constant of the adsorption process, expressed in terms of the ratio of adsorption and desorption rates. The relation of the Gibbs adsorption equation (1.3) to the Langmuir equation (1.5) for the surfactant gives Shishkovsky's equation showing the change in the surface tension of the solution (two-dimensional pressure π) with the concentration of dissolved surfactant in volume: π  σ 0  σ  A  RTln(1  Kc) ,

(1.6)

where σ0 is the surface tension of the pure solvent; A∞ is the limit number of moles of surfactants per 1 cm2 (limit adsorption). A joint solution of the Gibbs (1.3) and Shishkovsky (1.6) equations for highly active surfactants gives an expression for the twodimensional pressure in the surface layer (π) equal to the difference in surface tension of the solvent and solution: π  σ 0  σ  A  RT or πS M  RT ,

where SM is the surface occupied by 1 mole of surfactant. 7

(1.7)

This equation is valid only in the region of dilute surfactant solutions. The equation of Gibbs, Langmuir and Shishkovsky from experimental data on the surface tension of solutions allows us to: 1) calculate the adsorption of surfactants at the interface between the solution and air; 2) determine the characteristics of the surface monomolecular layer-limiting adsorption, thickness, linear dimensions of surfactant molecules. The most accessible for experimental measurement of surface tension are liquid-gas and liquid-liquid systems. The σ (c) dependence determined in this way, in accordance with the Gibbs equation, makes it possible to calculate the adsorption of the surfactant at the interphase boundaries. For solids, the existing methods for determining surface tension are very few, laborious and not very accurate. Therefore, adsorption on solids can be measured directly from the difference between the initial and equilibrium concentrations of the surfactant solution. Methods for measuring surface tension The existing methods for determining surface tension are divided into 3 main groups: 1. Static methods – method of capillary uplift; – methods of a recumbent drop (bubble) and a hanging drop; – measurement of the curvature of the liquid interface; – method of balancing a ring, plate and other solid in the surface layer (Wilhelm); – method of balancing the barrier, etc. These methods make it possible to measure σ with a fixed interfacial surface in equilibrium with the volume and not changing during the measurement. 2. Semi-static methods – The method of greatest pressure formation of bubbles and droplets; – The method of tearing off the ring or frame; – The method of weighing and counting drops is the stalagmometric method. 3. Dynamic methods 8

– method of capillary waves; – method of oscillating jets and drops. Dynamic methods are complex in hardware design. In addition, in the case of solutions, in particular surfactant solutions, a certain time is required to establish equilibrium in the surface layer. For practical purposes, static and semi-static methods are more often used to measure the equilibrium values of the surface tension of liquids. In this laboratory practice, it is proposed to use two fairly common semi-static methods for measuring the surface tension of solutions: the method of maximum bubble pressure and the stalagometric method. Method of maximum bubble pressure (Rebinder's method) It is known that in the presence of a curved phase interface (for example, a gas bubble in a liquid or a drop of oil in water) some additional internal pressure arises. This so-called capillary pressure is directed from the liquid side and tends to reduce the surface of the bubble, compresses it. The value of the capillary pressure is determined by the nature of the liquid (the value of the surface tension) and depends on the curvature of the surface. According to Laplace's law for a gas bubble or a droplet of liquid having a spherical shape, in addition, the internal pressure is expressed as ΔP  

2σ R

,

(1.8)

where R is the radius of curvature of the surface. The center of curvature can be inside the liquid (positive curvature) and outside the liquid (negative curvature). For a plane surface R = ∞. According to equation (1.8), for a flat surface, for a convex surface and for a concave surface ∆P < 0. When a thin glass capillary is lowered into the water, a curved surface (meniscus) is formed as a result of wetting. The pressure below this surface is lower than the pressure at the flat surface. As a result, there is a buoyant force that lifts the liquid in the capillary until the weight of the column balances the acting force. There is a quantitative dependence of the height Һ, the radius of curvature of the surface R, the radius of the tube r, the boundary angle θ and the boundary tension σ of the sheared layer, called the Jurin equation: 9

h

2σ cosθ



rg p 1  p g

(1.9)

,

where − is the difference in density of two bulk phases. If p1 ≫ pg, then p can be neglected in this case. In the case of non-wetting cosθ < 0, according to equation (1.9), h < 0, i.e. the liquid level should drop. In the case of complete wetting (cosθ = 1), a simplified expression is obtained, which is used in practice for small edge angles: h 

2σ rgp g

(1.10)

,

The equation (1.9) provides the basis for the experimental measurement of surface tension by the method of the greatest bubble pressure. To find σ, you need to measure the pressure that must be applied in order to form an air bubble from the capillary with radius r lowered into the liquid being examined. To form a bubble, it is necessary to overcome the capillary pressure ΔP  2σ on the surface R

of the bubble that is concave from the liquid side. As the pressure increases, this bubble grows, changing its shape and radius of curvature. In Fig. 1.2 it is shown that at the beginning (position 1) the bubble has a large radius of curvature and its surface is almost flat. In this case Р < ΔP. Then the radius of curvature decreases, the gas bubble becomes more and more convex. At R = r (position 2), the pressure inside the capillary is equal to the internal pressure Р = ΔP and reaches its maximum value. Under these conditions, the pressure on the walls of the bubble on the liquid side is equal to the gas phase. With further increase in pressure, the radius of curvature again begins to increase, the pressure from the side of the bubble wall falls, it cannot balance the air pressure inside the bubble, so the bubble comes to an unstable state – it rapidly expands and breaks away from the capillary.

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2 r

1 2 3 Fig. 1.2. Formation of an air bubble in the capillary

The scheme of the Rehbinder instrument for measuring the surface tension is shown in Fig. 1.3. The test solution is poured into the cell (1) to a level at which the tip (2) only touches the surface, slightly lifting the liquid. The depth of immersion of the capillary should be close to zero in order to exclude the difficultly of taking hydrostatic pressure into account. Excess fluid is taken with a capillary. The measuring cell is connected by a branch pipe (3) with an aspirator (4) and a micromanometer (5). The pressure gauge (5) is set using the adjusting feet in a horizontal position (according to the level of the macromanometer). The arm of the micromanometer (6) with the measuring tube (7) is set to the position corresponding to K = 0.3. Rotating the level control of the manometric liquid (8), set the meniscus in the manometer tube to zero. The aspirator (4) is filled with water to the indicated mark and tightly closed with a stopper. The three-way valve (9) rotates clockwise until it stops. Slowly opening the aspirator tap and carefully draining the water from it, create a vacuum in the system. The amount of pressure in the capillary is recorded by raising the liquid in the measuring tube (7)

3 1

4 9

2

8

7

6

5

Fig. 1.3. A scheme for measuring surface tension by the method of maximum bubble pressure. 1 – a measuring cell; 2 – a pipette with a capillary; 3 – a branch pipe; 4 – an aspirator; 5 – a liquid manometer

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As the pressure increases, the air bubble grows, changing its shape and radius of curvature. The moment of separation of the bubble from the capillary is fixed by the maximum rise of the liquid in the measuring tube. The air bubble, piercing the surface layer, bursts. At this point, the pressure drops, and the manometric liquid begins to drop. But then, due to the formation of a new bubble, it rises again. Thus, the level of the manometric liquid fluctuates all the time. Gradually adjusting the opening degree of the aspirator crane, it is achieved that air bubbles from the capillary tip slip into the solution one by one at an interval of 20-30 seconds. If the level of the manometric liquid for 2-3 minutes shows a constant pressure, it is considered steady, and the readings are recorded in the log. In order not to determine the radius of the capillary, this method of measuring surface tension is used as a relative method. So for two liquids with surface tension σ1 and σ2 when determining the pressure with the same capillary tip, we get: 2 = (r/2)P2

σ1 = (r/2)P1;

(1.11)

By dividing these two equations by each other, we get: σ1 σ2



P1 P2



h1 h2

,

(1.12)

where h1 and h2 are the heights of liquids in a manometric tube, from which: σ1  σ 2

h1 h2

(1.13)

Before measurements, the cell, capillary pipette and solution flasks should be thoroughly washed with chrome mix and distilled water. Beginning with pure water and passing to solutions of increasing concentration, determine the maximum pressure at which an air bubble from the capillary end of the pipette will flow. Each measurement is repeated at least 3 times, the average value is recorded, and then the surface tension is calculated from formula (1.13). 12

Stalagmometric method The measurement of surface tension by this method is based on the fact that, at the moment of detachment of the droplet from the lower end of the vertical tube, the weight of the drop g is balanced by the surface tension F (Fig. 4a), which acts along the circumference of the neck of the drop and prevents its detachment. At the moment of detachment of the droplet in the first approximation, we can assume that: q  F  2ππrσ ,

(1.14)

where r is the internal radius of the capillary. Usually, droplet separation does not occur along the line of the inner perimeter of the capillary of a stalagmometric tube of radius r, but occurs in the neck of a drop having a smaller radius. Therefore, for a more accurate determination of σ, the value should be multiplied by a certain coefficient, depending on the ratio of the volume of the drop V to the cube of the tube radius k = f(V/r3). It has been shown experimentally that this coefficient does not change very much with a change in the volume of drops, even if it changes by1000 times. For drops that differ comparatively little in volume, this coefficient can be assumed to be the same.

А 1 Б

2 Fig. 1.4. The structure of the stalagmometer: 1 – an expansion; 2 – a capillary opening; Tags – A, B

13

Since at the moment of detachment F = q, determining the weight of the droplet g formed, it is possible to calculate the surface tension of the fluid σ. To determine the weight of a drop, use a stalagmometer, which is a glass tube with an expansion in the middle, ending with a capillary below (Fig. 1.4). The tube usually has a horizontal elbow portion into which the capillary is soldered so that the liquid drips more slowly. The stalagmometric tube is filled with the test liquid to a certain volume V and the number of drops n emanating from a given volume bounded by two labels is measured. The weight of the droplet is calculated by the equation: q

vρρ n

,

(1.15)

where ρ is the density of the solution; g is the acceleration of gravity. Obviously, if the drop is separated, the equality must be observed. K2π2π 

vρρ n

(1.16)

In connection with the difficulty in determining the radius of the capillary r and, respectively, the value of the coefficient K, the surface tension of the solutions is determined by comparing the data on the outflow of the liquid and liquid under investigation with a known surface tension from the stalagmometer. Writing equation (1.16) for both liquids, dividing the first of these equations by the second and reducing the constant values, we obtain the formula for calculating: σ x  σ st

p x  n st , p st  n x

(1.17)

where the subscript x refers to the parameters of the liquid under study, and the subscript st to the parameters of the liquid with known surface tension. The average number of drops from the 3-5 measurements is taken as the value of n. The measurements are carried out under condi14

tions of slow droplet formation, about 1-3 drops per minute. The flow rate of the liquids is kept constant and adjusted by means of a screw clamp located at the top of the stalagmometric tube. Before starting work to remove impurities from the capillary, the gel tube is washed several times with a chrome mixture and water.

1.1 Determination of the specific surface area of solid adsorbent The purpose of the work: obtaining isotherms of surface tension of surfactant solutions at the boundary with air; calculating the cross-sectional area and the axial length of the surfactant molecule in the saturated adsorption layer; determination of the limiting adsorption of surfactants from an aqueous solution on coal; calculation of the specific surface of the adsorbent under study. Devices and tableware: a device for measuring surface tension, scales, flasks with a capacity of 50 ml, funnels and filter paper, pipettes for 25 ml. Reagents: activated carbon, solutions of propyl, and butyl and isoamyl alcohols, acetic, propionic, butyric acid. The order of the work: The work can be divided into two parts. In the first part of the study, the dependence of the surface tension of surfactant solutions (surfactants) on concentration is determined on the basis of adsorption at the solution-air interface, the cross-sectional area and the axial length of the surfactant molecule in the saturated monomolecular adsorption layer. In the second part of the work on changing the surface tension of the surfactant solution in contact with the solid phase, the adsorption of this substance from the solution on a solid adsorbent is determined and the specific surface of the adsorbent is calculated. To perform the work, 6 surfactant solutions of 50 ml are prepared by successive dilutions (as instructed by the teacher) in flasks carefully washed by chrome mixture and then by distilled water. Since the equilibrium adsorption of surfactants on the coal is achieved after 1.5-2 hours, it is necessary to prepare the experiments on 15

adsorption on coal in advance. Activated carbon is preliminarily grinded in a mortar and 6 samples per 1 g are taken. The samples are placed in flasks with surfactant solutions (25 ml each), stirred for 10 minutes and allowed to stand until the measurement begins (not less than 1.5 hours). Then the students begin to perform the first part of the work – measurements of surface tension in pure (without coal) aqueous surfactant solutions. Measurement of surface tension is carried out by the method of maximum bubble pressure or by a stalagmometric method. Measurements begin with water and pass to solutions of increasing concentration. Calculate the surface tension of the solutions by formulas (1.13) and (1.17) and plot the scale σ = f(с) on a large scale 18 x 24 cm, which also serves as a calibration curve for determining the equilibrium surfactant concentrations after adsorption on coal. From the dependence σ = f (c), according to the Gibbs equation, adsorption of Г is calculated for various surfactant concentrations. You can use the graphical method. To the curve σ = f (c), tangents are constructed at different points and continued to the intersection with the ordinate axis (Fig. 1.5).

Г = f(с)

B Z B1

= f(с) 0

C

C1

Fig. 1.5. Dependence of the surface tension σ = f(c) and Gibbs adsorption Г = f(с) on the concentration of the aqueous surfactant solution

16

Through the points in which the tangents are constructed, the lines parallel to the abscissa axis are drawn also up to their intersection with the ordinate axis. The length of the segment Z along the ordinate axis between the tangent line and the horizontal line drawn through the same point is Сdσ/dc. Substituting the value of Z in the Gibbs equation (1.3), we obtain:

z

Г

(1.18)

RT

in this way, the values of Γ are calculated for those concentrations for which tangential lines are constructed on the curve σ = f(c) at the corresponding points. Their values are plotted on the graph and an adsorption isotherm Г = f (c) is obtained (Fig. 1.5). Neglecting the difference between the adsorption A and the Gibbs adsorption Г for surfactants, we can assume Γ ≈ A. The Langmuir equation (1.5) calculates the value of the limiting adsorption Г and the constant K. For this we use the graphical method that transforms the Langmuir equation into the equation of the straight line: с Г 1 Г



Kc  1 KГ 



 a  const

c Г

с Г 1

KГ



1 KГ 

 b  const

 ac  b

(1.19)

(1.20)

(1.21)

To find Г  , plot the values of the concentration C on the abscissa axis, and C/Г on the ordinate axis and connect the resulting points with the straight line (Fig. 1.6).

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C/Г

φ b C Fig. 1.6. Adsorption isotherm in the coordinates of the linear form of the Langmuir equation

The cotangent of the angle φ formed by this line with the of the abscissa axis is equal Г, and the segment of ordinates cut off by the line is equal to b = 1/К Г . Whence, substituting, K is determined. Knowing the value, calculate the cross-sectional area (s) and the axial length (δ) of the surfactant molecule according to the formulas:

s

1 , Г N A

(1.22)

where ΝA is the Avogadro number and δ  Г

M, ρ

(1.23)

where M is the molecular weight; ρ is the density of the surfactant. In the second part of the work, after the adsorption equilibrium is established (1.5-2 hours), the surfactant solutions are separated from the coal by filtration and the surface tension is determined. 18

Then, the equilibrium concentration of the solutions is determined from the surface tension isotherms (the calibration curve) obtained in the first part of the work. For each concentration, adsorption of surfactants on carbon is calculated by the formula: A

c0  ce V , m

(1.24)

where m is the sample of coal, kg, V is the volume of the solution from which adsorption takes place, m3, Co is the initial concentration of surfactant, kmole/m3, Cе is the equilibrium concentration of surfactant, kmole/m3. The limiting value of adsorption of surfactants on activated carbon A∞ is determined graphically, starting from the straightened adsorption isotherm of Langmuir С/A = f(С). Then, knowing the crosssectional area of the adsorbed molecules calculated in the first part of the work, calculate the specific surface area of the activated carbon, expressing it in m2/kg: Ssp  A  sN A ,

(1.25)

where A∞ is the value of the limiting adsorption per unit area of the activated carbon, mole/kg, s is the area occupied by one surfactant molecule in the saturated adsorption layer at the boundary f/g, m2, ΝA is the Avogadro number (ΝA = 6.02 · 1023 mole-1). The textbook briefly describes the method of measuring surface tension, provides a diagram of the device, details all calculations related to work. The results obtained are recorded in Tables 1.1 and 1.2; the following graphs are plotted: σ  f(C0 ) ; Г  f(C0 ) ; C0 Г

 f(C0 ) ;

Ce  f(Ce ) A

19

Table 1.1 No. of flasks

Adsorption at the boundary f/g Со, kmole/m3

The highest pressure of the bubble P, mm, or the number of drops

σ f/g, J/m2

Г f/g, kmol/m2

Со/Г

1 . . . . . 6 Table 1.2 No. of flasks

Adsorption at the boundary f/g The highest pressure of the bubble is P, mm, or the number of drops

σ f/g, J/m2

Сe, kmol/m3

A f/h, kmol/m2

Сe/A

1 . . . . . 6

In addition to working with this surfactant (alcohols, acids), it is necessary to record the surface tension isotherms   f (C ) for the other two members of the homologous series of surfactants (alcohols or acids) in the same way (excluding adsorption on carbon only), as instructed by the teacher. On one plot, three surface tension isotherms are constructed for each surfactant and it is checked whether the Traube rule is satisfied for the solutions of these surfactants.

20

1.2 Investigation of adsorption on fabric The purpose of the work: study of adsorption of dyes on fabric, getting acquainted with the principles of working with a photocolorimeter, determination of the limiting adsorption of the dye; calculation of the specific surface of the adsorbent under study. Devices and tableware: measuring flasks with a capacity of 100 ml (6 pcs.); cups with a capacity of 100 ml (6 pcs.); a glass rod; measuring cylinders for 50 ml; tweezers; analytical scales; calorimeter. Reagents: cloth; dye solution of the initial concentration; The order of the work: From the initial solution, 5 solutions of such concentrations are prepared in volumetric flasks, that each subsequent solution is twice as dilute as the previous solution. Of the prepared solutions, including the original, take a measuring cylinder of 25 ml of the solution and transfer to the cups. Six pieces of fabric of the same texture and size (approximately 2х5 cm) are weighed on analytical scales, fixing the weight of each shred separately. Suspended pieces of tissue are moistened with distilled water and placed in dye solutions. Dye the fabric for 30 minutes, periodically mixing the contents of the glass with a glass rod. While the solutions are dyeing, determine the optical density of the solutions remaining in the measuring flasks with the help of a photocolorimeter FEK-56M or KFK. The light filter with which the research is conducted is indicated by the teacher. From the data obtained, a calibration curve A = f (C1) is constructed. After this time, the pieces of tissue from the solutions are removed. Then, using a photocolorimeter, the optical density of each dye solution is again determined using the curve of the dependence A = f (C1). As a calibration with respect to the known optical density of solutions after dyeing (adsorption of the dye on the tissue), the concentrations (C2) corresponding to it are found. To do this, from the point corresponding to the A2 value of the solution after adsorption, a straight line parallel to the axis of abscissa is drawn up before crossing with the calibration curve. From the point of intersection, the perpendicular to the abscissa is drawn. The amount of adsorption of the dye is calculated by the formula: a

C1  C 2 m

21

V ,

(1.26)

where C1 is the concentration of the dye in g/L before adsorption; C2 is the concentration of the dye in g/L after adsorption; V is the volume of the solution from which adsorption was carried out, in liters; m is the mass of the adsorbent, in grams The obtained data are recorded in the form of the Table: Table 1.3 No.

С1

A1 before adsorption

A2 after adsorption

С2

a

An adsorption isotherm is constructed a = f(С2) Using the Langmuir equation, the maximum adsorption of amax is determined by the graphical method, for which the Langmuir equation is transformed into the equation of the straight line: C 1 C   a a max  K a max

The graph is plotted in coordinates:

(1.27)

C  f(C) a

The cotangent of the slope of this line to the axis of abscissa is the value of amax, i.e. amax = ctg . 1.3 Adsorption of acetic acid from aqueous solutions by activated carbon "Particles on the surface of solids, like the liquid molecules of the surface layer, have an unbalanced part of the force field directed toward the other phase. Therefore, solids, like liquids, have a significant reserve of free surface energy, which they seek to reduce due to the adsorption of substances that lower the surface tension. However, methods for direct measurement of surface tension for solids are not 22

known, which prevents the application of the basic Gibbs thermodynamic equation having universal value. Conventional solid adsorbents – clays, coal, silica gel, ion exchangers – are porous bodies or finely divided powders. These adsorbents are permeated with a very large number of capillaries and cracks, so it is difficult to determine their specific surface area. The adsorption value is therefore measured from the difference in the concentration of the adsorbed substance in the solution before and after adsorption, and the adsorption is expressed by the number of moles of the adsorbed substance, not per unit of surface, but per unit mass of the adsorbent." From all of the above, it follows that good adsorbents must have a highly developed surface, inherent to porous bodies and highly disperse powders. In 1913 A.V. Dumanskiy showed that when the particles of a dispersed phase are grinded, the total interface increases rapidly (Fig. 1.7), and together with it the supply of free surface energy also increases, which has a great influence on the properties of the disperse system. A measure of the reserve of free surface energy of a unit of separation area is the surface tension at the interface.

Fig. 1.7.

Thus, the reserve of free surface energy of the entire disperse system (A) will be:

A  S σ ,

(1.28)

where S is the area of the interface, and σ is the surface tension at the interface. 23

It is convenient to take the specific surface as a measure of the phase separation area, i.e. the surface, which a unit volume of the dispersed phase, has S cm 2  σ cm 3

S0 

(1.29)

How the specific surface area is related to the size and shape of the particles can be demonstrated by the following simple examples. 1. Take 1 cm3 of solid matter in the form of a cube. The length of its edge will be denoted by the letter "a", equal to 1 cm. The specific surface of the cube will be equal to: S0 

6a 2 a



2

6 1

 6 cm 2 /cm 3

1

(1.30)

We will cut it into all smaller regular identical cubes. First, we divide each edge of the cube in half, then a = ½ cm. The degree of grinding or the degree of dispersion according to Dumansky, as a reciprocal of the size of the particle diameter, will be equal to Д

1 a



1 12

2

(1.31)

In this case, 8 cubes will be obtained. The number of them will be denoted by the letter "n". The total surface of all the cubes obtained is equal to: S = 6a2n. Specific surface, i.e. the surface of 1 cm3 can be found by determining the total surface of all the cubes obtained from 1 cm3 by cutting S0 

S V

6a 2 n



V

61/2   23



6a 2 n 1

61/2   8 2



1

2



1

 6  2  12 cm 2 /cm 3

24



(1.32)

Then, we divide each edge of all the cubes obtained once again in half, while the length of the edge of the newly obtained cubes will be equal to a = 1/4, and their number n = 64, the dispersion Д = 1/1/4 = 4. Specific surface area: S0 

6a 

2



n

V

6  1/4   64 2



1

 6  1/4   4 3  6  4  24 cm 2 /cm 3

(1.33)

2

Thus, the specific surface in this case will grow as grinding proceeds, obeying the equation: S0 = 6D. The same ratio between the specific surface and the degree of dispersion, one can get in a simpler way, dividing the surface area of one cube obtained by cutting by its volume, i.e. referring it to unit volume S0 

S V



6a 2 a

3

 6

1

(1.34)

 6D

a

Using this formula, it is easy to calculate the specific surface area of a powder with cubic particles of any degree of dispersion. The results of this calculation for clarity are given in Table 1.4. Table 1.4 Dependence of the specific surface on the degree of dispersion Edge length of the cube a, сm

Specific surface area

Dispersion D

1 a

S0 

S V



 m /cm 

6a 2 a3

 6  D cm 2 /cm 3 2

3

1

2

3

1

1

6 сm2/сm3

10-1

10

60 сm2/сm3

10-2

102

600 сm2 = 0.06 m2/сm3

10-3

103

6000 сm2 = 0.6 m2/сm3

10-4

104

60000 сm2 = 6 m2

25

 or

1

2

10-5

105

10-6

106

10-7

107

10-8

108

3 m2

60 600 m2 6000 m2

The world of colloids is the world of large

f

S0  0

Table 1.4 shows that the specific surface increases rapidly with increasing degree of dispersion. It is especially large in colloid-dispersed systems and the reserve of specific free surface energy (Us) reaches its maximum values. When switching to molecular or ion-dispersed systems, the physical interface between the dispersed phase and the dispersion medium disappears, the system becomes homogeneous and does not have a reserve of free surface energy (Us). 1. For particles of spherical shape, the relationship between the specific surface and the degree of dispersion will be as follows: S0 

S V



4ππ 2 3  , 4 πr 3 r 3

(1.35)

where r is the radius of particles. We pass from the radius to the diameter or the diameter of the particle a = 2r, then S0 

3 r



23 a



6 a

 6

1 a

 6D

(1.36)

But for a sphere of volume 1 cm3, V = 4/3πr3 = 1 cm3, the radius is 1 3 3 r3 3 3  0,62 cm 4 π 4π 4  3,14 3

26

(1.37)

The specific surface of such a ball of volume 1cm3 will be equal to S0 

3 r



6



a

6

 4,86 cm 2 /cm 3

1,24

(1.38)

When it is crushed into identical particles of a spherical shape with a diameter "a", the specific surface will grow: S 0  4,86 

1 a

 4,86  D

(1.39)

2. For particles of cylindrical shape-fibers, the relation between the specific surface and the dispersion: S 0, cylinder



2  rl  2  r 2



πr 2 1

2  r 1  r  πr 2 1



2 1  r  rl

,

(1.40)

where S0,cylinder is the surface area equal to the sum of the area of the lateral surface and the area of the bases. For highly elongated fibers, the area of the base of the cylinder is very small in comparison with the area of the lateral surface and can be neglected. Then S 0, cylinder 

2  rl πr 2 1



2 r

(1.41)

We pass from the radius to the diameter a = 2r and obtain S 0, cylinder 

2 2 4 1    4  4D a r 2 a

(1.42)

3. For particles having the shape of thin plates or films, the ratio S0 and D will be: S 0, plate 

S V



2lP  2lh  2Ph lPh

(1.43)

The quantities 2lh and 2Ph can be neglected, since they are insignificant for very thin plates in comparison with the area 2lP. 27

Then S0 

S V



2lP 2Ph



2 h

 2

1 h

 2D

(1.44)

If h is the minimum parameter, then the degree of dispersion found as D  1 will be maximal. h

From the last two examples it is clear that in the case of onesided dispersion, for example, in the preparation of polymer films, blowing a soap bubble, making synthetic fibers, dispersing solutions, we obtain particles with very different parameters. To calculate the specific surface in such cases, take the minimum particle size or the maximum degree of dispersion. It can be seen from the examples given that, depending on the shape of the particles, the coefficient before D in the equation connecting the specific surface with the dispersion varies, and in general, including for irregularly shaped particles, we can write S 0  K  D , where K is a coefficient depending on forms of particles. Thus, the specific surface of disperse systems strongly depends both on the shape of the particles and on their size. The purpose of the work: establish a quantitative dependence of the adsorption of activated carbon of acetic acid on the concentration of the solution. Draw an adsorption isotherm. From the results obtained, determine the constants in the equation of the Bedekker – Freundlich isotherm. Using the Langmuir isotherm, calculate the value of the active specific surface of the adsorbent. The order of the work. In order for each student to work independently and the results of his work were objective, in each laboratory, laboratory technicians prepare initial solutions of acetic acid of their concentration, which periodically changes and remains only known to the teacher and laboratory assistant. From these solutions, as instructed by the teacher, students dilute their original solutions, the concentration of which is determined by titration. Starting the work, the student receives a burette from the laboratory assistant for 50 ml, pipettes for 5, 10 and 50 ml, a graduated 28

cylinder for 100 ml. 3 cups per 100-150 ml for titration and 12 cones per 100-150 ml. All dishes are thoroughly washed. 6 wash flasks are put in a drying oven. The remaining 6 cones are numbered as follows: 1', 2'; 3', 4', 5' and 6'. In them 100 ml of initial solutions of acetic acid are prepared for adsorption. The concentration of these solutions will later be determined by titration, so they are prepared by dilution using a graduated cylinder. The concentration of each next solution should be twice less than the previous one. Solutions are prepared at the direction of the teacher and their compositions can be, for example, the following: Table 1.5

No. of solution ml of acetic acid

1

2

3

4

5

100

50

25

12

6

3

0

50

75

88

94

97

ml of water

6

or others, at the instruction of the teacher. The composition of the solutions is recorded in Table 1.6, starting with the most diluted. Table 1.6 Composition and concentration of initial solutions

No. of solution

Composition of solution

Acetic acid, ml

Solution taken for titration, ml

water, ml

Volume for titration with 0.1 NaOH solution, ml

exp.

6 5 4 3 2 1

29

average

Concentration of solutions before adsorption С, mole/l

Give solutions to stand, and during this time on the technical scales weigh (on watch glasses or glossy paper), six samples of 1g of activated carbon. Dry the flasks from the drying cabinet, cool them, number 1, 2, 3, 4, 5, 6 and use for adsorption. In these dry flasks, beginning with the most dilute and gradually passing to all the concentrated ones, pour the pipette, previously rinsing it with a small amount of this solution, to 50.0 ml of previously prepared stock solutions. From the flask 6' is poured into the flask 6, from the flask 5', into the flask 5, etc. The drying of the flasks is necessary in order that they do not change when the initial solutions are cast. The residues of the original solutions are retained to determine their concentration by titration. Then, into the flasks, into which 50 ml of the initial solutions were added, approximately at the same time prepared samples coal are poured out, the solutions are shaken well and, after recording the time, left to stand for 1.5-2 hours until the adsorption equilibrium is established. From time to time the solution is shaken. While adsorption is in progress, the concentration of the remainning "С’" starting solutions is determined by titration. Titration begins with the most dilute solution, repeating it at least 3 times. Titrate with a 0.1 N alkali solution in the presence of phenolphthalein. Aliquots for titration in dilute solutions (№ 6', 5', 4' and 3') take 10 ml, for concentrated (2' and 1') – 5 ml. The results of titration are recorded in Table 1.6. Calculate the concentration of the initial solutions "С’" and record the results in the same table. Then proceed to determine the concentration of acetic acid in solutions after adsorption. The last 10 min before this, solutions are not shaken to allow coal to settle. Carefully remove the transparent solution by pipetting, avoiding the adsorbent entering it, and titrate the same aliquots with the same alkali as before. Titration is again started from the diluted solution. If the adsorbent is a highly dispersed, poorly settling powder, the solutions after adsorption are filtered through pleated filters into dry flasks. To avoid errors due to adsorption of the acid with a filter, it is first saturated with a small amount (3-5 ml) of the filtered solution, and all the filtrate from this portion of the solution is discarded. The results of the titration are recorded in Table 1.7. 30

Table 1.7 Concentration of acetic acid after adsorption of "C"

No. of solution

Taken for titration of solution, ml

Volume for titration of 0,1 N alkali, ml exp.

6

5

5

5

4

10

3

10

2

10

1

10

Concentration after adsorption of C, gmol/l

average

After the titration is complete, the used coal from all the flasks is transferred to one flask and handed over to a laboratory technician for regeneration. Wash used dishes, put in order the workplace and proceed to calculations. First, calculate the concentration of solutions after the adsorption of "С". We will call it the equilibrium concentration. The calculations are recorded in a notebook, and the results are recorded in Table 1.7. Then the concentration of solutions is calculated by decreasing the adsorption (C'-C) by the amount of adsorbed acetic acid with activated carbon according to the formula: x m



C  C1 1000

V,

(1.45)

where X is the amount of adsorbed acetic acid in gmol/l; m is the amount of adsorbent, g; (C'-C) is a decrease in the concentration of С  С1 is a decrease in the concentration of acetic acid in gmol/l, 1000 acetic acid in 1 ml of the solution; υ is the volume of the solution of acetic acid taken for adsorption, in this case 50 ml.

31

The calculations are recorded in the notebook, and the results are recorded in Table 1.8 No. Concentration of of the initial sosolutions, lugmol/l, C tion

Concentration of solutions after adsorption gmol/l, С1

c-с1 = x

lgС1

x m,

lg x m

С1/Г/

gmol/l

1 2 3 4 5 6

Based on the obtained results, an isotherm of adsorption is constructed, plotting the equilibrium concentration of C, gmol/l, on the abscissa axis and the amount of adsorbed matter x/m, gmol/l on the ordinate axis. X/m

C Fig. 1.8.

In order to establish the relationship between the amount of adsorbed matter and its equilibrium concentration in the solution, in practice a simple equation, empirically found by Bedecker and carefully checked by Freudlich, called the Freundlich isotherm, is often used: X

m

 aC

32

1

n

(1.46)

where X is the amount of the adsorbed substance; m is the amount of adsorbent, g; С is the equilibrium concentration of adsorbent in solution; a and n are constants. Adsorption proceeds on the surface of the adsorbent. Consequently, the amount of adsorbed material depends on the surface area of the adsorbent. In the Freundlich equation, however, it is related to the mass of the adsorbent, with which it is only indirectly related. The constant "a" in the equation gives the relationship between the surface size and the mass of the adsorbent. In addition, it is known that adsorption processes exhibit some chemical mechanisms. Thus, non-polar adsorbents adsorb nonpolar substances better, and polar ones better adsorb polar substances. The constant n characterizes connection between the adsorbate and the adsorbent. In order to use Freundlich's isotherm, it is necessary to determine the constants in it. It is convenient to find them graphically. For this, the logarithmic isotherm is transformed into the equation of a straight line: lg X

m

 lga 

1 lgC n

(1.47)

Find the logarithms of the experimentally determined x/m and "C", record them in Table 1.8 and plot the graph, laying lg x/m on the ordinate axis, and lgC on the abscissa axis, as shown in Fig. 1.9. /m lg X X/m

II II II 00 --lglgCC

lg C lg C III III

aа

в IV IV

44 lg X/m X /m -- lg

Fig. 1.9.

33

Depending on the units in which we express the concentration and the amount of the adsorbed substance, we obtain the straight line I, II or III on the graph. Under our conditions, when the concentration is expressed in gmol/l, and the amount of adsorbent in gmol/g, we obtain line IV. When plotting a plot on coordinate axes, it is convenient to take the same scale. If the equation is applied and the results obtained are correct, then all points lie on the straight line. This serves as a test both for the correctness of the results obtained and for the fact that the process we are investigating is adsorption. Based on the properties of the equation of the straight line, the segment cut by the continuation of the straight line IV from the ordinate axis (OB) will be equal to lga. Hence we find "a". From the tables of logarithms, we find a number whose mantissa is 0.4 or 0.4000. It is equal to 251. We take into account the characteristic, then a = 0.0251 or 2.51 x 10-2. The constant 1/n will be equal to the tangent of the slope (φ) of our straight line tgφ, which is easily found from the ratio of the legs b / a. In our graph it is 1/4. The found values of a and 1/n are substituted in the equation of the Freundlich isotherm, for example X

m

 aC

1

n

= 2,51х10-2хС1/4 11



lga  1,6 lg a   1,6  2,4

1 в 1  tg   n a 4

To verify the correctness of the constants found, let us take an arbitrary concentration "C" in the interval used in this paper and calculate the amount of adsorption x / m for it by equation (1.47). Put the results on the graph (Fig. 1.9) and see if the point gets on our isotherm. In our examples, all quantities are taken arbitrarily, and hence the constants calculated from them cannot serve as a basis for evaluating the correctness of the results obtained in the paper. Here we complete the analysis of the Freundlich isotherm and proceed to determination of the value of the active specific surface of our adsorbent, activated carbon. 34

a. Determination of the active surface area of activated carbon. The determination of the active specific surface S' of the adsorbent is based on the theory of the "thin" monomolecular Langmuir adsorption layer. For calculations the Langmuir isotherm equation is used.  Моль  ,   А  С  см 2  С

Г  Г

(1.48)

where: Г is the amount of adsorbed substance at a given concentration in a solution per 1 cm2 of adsorbent surface, gmol/cm2; Г  is the maximum amount of adsorbed material, also per 1 cm2, when all adsorption centers are occupied, i.e. when the whole monomolecular layer is filled, gmol/cm2; C is the equilibrium concentration of adsorbent in solution; gmol/l; A is a constant. Find in the textbooks its physical meaning. We rewrite this equation for 1g of an adsorbent having a surface. S0 ,

cm2 m 2 g

kg

Г  S0  Г   S0

S0 ,

C AC

,

gmol

(1.49)

g

ГS0  Г Г  S0  Г Г  Г 

S0 ,

С

mol

АС

g

Г '

(1.50)

, cm2  m 2 

Г





The constants Г and "A" in the Langmuir isotherm are conveniently determined by the graphical method proposed by P.A. Rehbinder on the basis of an experimentally determined adsorption isotherm. We transform the equation as follows into the equation of the straight line

35

ГА  С  Г С

ГА  С Г  С А С С    Г  Г Г  Г Г Г Г

or С Г



А Г 



1 Г 

(1.51)

С

This equation is analogous to the equation of the straight line: y = a + kx. In order to find the value, a graph is plotted, plotting along the abscissa "C", and along the ordinate axis С/Г'. Г', as can be seen from the equation, is the amount of adsorbed substance per adsorbent at a concentration C, i.e. the value x/m found by us earlier. From Table 1.8 we take the equilibrium concentrations "C" and the corresponding x/m, and calculate

С С . We record the values  Г X m

obtained in the same table and the plot, plotting on the abscissa axis an independent variable (in this case, the equilibrium concentration of "C"), and along the ordinate function, С/Г

φ

∆С/Г'

∆С

в

0 С5

С4

С3 С2

С1

С

Fig. 1.10.

i.e

C С .  Г X m

Through most points we draw a straight line (Fig. 1.10).

Continuing it to the intersection with the ordinate axis, we find the 36

А in the equation. The tangent of Г 

segment OB, equal to the constant

the slope of the straight line will be equal to I/ Г' or ctg  Г . Using the graph for each pair of points lying on the line, calculate and find the mean value ctg 

С  С2 ΔC  Г  1 C С С 1 Δ  2 Г Г1 Г2

For some grades of coal in the region of low concentrations, a straight line is obtained, rising steeper than at high concentrations. The values of Г' found at these concentrations are overestimated and the active specific surface of the coal found by them differs greatly from that given in the literature. The results close to the literature are obtained in the region of average concentrations (from 0.05 to 0.5n) of solutions. In the equation S 0 

Г  , in addition to the found Г', there is also Г

the quantity Г – the limiting amount of adsorbed acetic acid per 1cm2 of the surface of the coal. For solids, especially powders and porous bodies, it is difficult to prepare a sample with an ideally smooth surface that could be measured. Therefore, as a standard, a really perfectly smooth liquid surface is taken, which is all equally active with respect to adsorption. At high concentrations of the solution, the surface is completely covered by the adsorbed substance, and "Г" reaches the limiting value " Г". The quantity Г is usually found from the Gibbs isotherm: Г

Сdσ RTdC

(1.52)

R is the universal gas constant equal to 8.313 x 107 erg/mole, T is the absolute temperature, σ is the surface tension, dyne/cm or erg/cm, C is the concentration of the solution, mol/l. Based on the measurement of the surface tension of acetic acid solutions of different concentrations, the amount of adsorbed mate37

rial per 1 cm2 of the surface of solution G is calculated from the Gibbs isotherm; according to the obtained data, a graph of the dependence of "Г" on "C" is plotted (Fig. 1.11). Г

Г∞

Г(с)

(с) Fig. 1.11.

By this curve, building an asymptote to it, one finds the limiting amount of adsorbed acetic acid per 1 см2 - Г. Substitute this value into the equation and find the value of the active surface of the adsorbent. A.V. Dumansky in his book "Colloids" gives a value for Г aqueous solutions of acetic acid, equal to Г   3,8  10 10

gMol cm 2

Thus, the value of the active specific surface area of the activated carbon will be: S '0 

Г ' mid 3,8  10 10

 

, cm 2 m 2

Report form. The report should contain the title and description of the purpose of the work, brief theoretical information, a description of the progress of work, a table of experimental data, charts of the adsorption isotherm (on millimeter paper), the results of calculations, the conclusion on the work done. 38

Control questions 1. Give the definition of: adsorption, adsorbent, adsorb, adsorbate. 2. What are the features of adsorption at the solid-liquid phase interface? 3. How can we determine the constants in the Freindlich equation if experimental data on adsorption have been obtained in a certain range of concentrations? 4. What characteristics differ physical adsorption from chemisorption?

39

2. INFLUENCE OF SURFACE-ACTIVE SUBSTANCES ON WETTING AND ADHESION The wetting phenomenon occurs with the participation of three volume phases separated by three surface layers. A definite value of the surface tension is characteristic of each interface: σsg, σsl, σlg. The ratio determines the conditions for the coexistence of bulk phases, the phase equilibrium conditions and the behavior of the liquid on the surface of a solid: 1) If σsg > σsl, then a spontaneous flowing of the liquid occurs – a surface with a larger free energy is replaced by a surface with a lower free energy, i.e. reduction in the energy reserve of the system. At the values of (σsg – σsl) approximately equal to σlg, the spreading of the droplet stops (Fig. 2.1, a). The condition for unlimited spreading (full wetting) is the inequality (σsg – σsl) > σlg. 2) If σsg < σsl, the spreading of the drop along the surface of the solid does not occur (Fig. 2.1, b). b

a

a-wetting b-non-wetting Fig. 2.1. Behavior of a drop on a solid surface

The measure of wetting is the equilibrium wetting angle . The angle  is defined as the angle between the tangent drawn from the point of contact of the three phases to the surface of the drop and the surface of the solid. The wetting angle is measured towards the liquid phase. The following condition is satisfied in the equilibrium state: σs-g – σs-l = σl-g · cosθ 40

(2.1)

from here cosθ =

σsg  σsl σlg

(2.2)

Equation (2.2) determines the wetting conditions and is a mathematical expression of Young's law. For σsg > σsl, cosθ > 0, θ < 90° (wetting condition), while the surface of a solid is called lyophilic (when wetted with water, hydrophilic). In the case when σsg < σsl, cosθ < 0, θ > 90º (non-wetting condition) and the surface of a solid is called lyophobic (when water is hydrophobic). Materials with a hydrophilic surface include, for example, quartz, glass, metal oxides. Materials with a hydrophobic surface include metals in which the surface is not oxidized, most polymers, as well as all organic materials (teflon, polystyrene) are insoluble in water and possess low dielectric permittivity. The quantities σsg and σsl, entering equation 2.2 are usually unknown and it is difficult to predict the wetting angle for a real surface. Therefore, it is advisable to consider molecular forces (adhesion and cohesion forces) and their work, which determines the values of the surface tension at three interfaces and, correspondingly, the value of the wetting angle. The forces of cohesion (coalescence) reflect the forces of interaction between molecules within one homogeneous phase. The forces of adhesion (adherence) show the interaction between molecules of different phases. The work of cohesion is defined as the work necessary to break a homogeneous volume phase and is referred to a unit area: Wс = 2σl-g

(2.3)

Two new LG surfaces are formed as a result of rupture of a single volume phase (for example, water). The adhesion work, per unit area, is the work of rupturing the interfacial surface layer. In this case, two new different surfaces and energy gain are formed as a result of disappearance of the free energy of the initial interphase boundary. The adhesion work for the SL interface is: 41

Wa = σl-g + σs-g – σl-g

(2.4)

or, taking Young's equation into account, we obtain the Dupree equation: Wa = σl-g (1+ cos)

(2.5)

The wetting ability of liquids and their adhesive interaction with solids are largely determined by the nature of the substances that make up the contacting phases. Comparison of Eqs. (2.3) and (2.5) shows that high adhesion between phases can be realized only when the ratio is σs-g > σl-g or Wa > 0.5Wc. Under conditions of complete non-wetting, Wa = 0, for Wa = W, the cracks become unbounded. The Wa-Wc difference is called the spreading coefficient. The work of liquid for wetting the solid surface is calculated by the equation Wwet. = σl-g · cosθр

(2.6)

The nature of the surface of a solid, and therefore the nature of its contact with the wetting liquid can be changed by modifying the surface. Wetting can be controlled by surfactants. The degree of change in the wetting angle depends on the nature and concentration of the surfactant, and the nature of the solid surface. For hydrophilic surfaces, an increase in in the surfactant concentration first causes an increase in the contact angle, whereas a further increase in the concentration results in a decrease in the contact angle. Such a change in the contact angle is associated with adsorption of surfactant molecules on the surface of a solid. In the case of a hydrophilic surface, the adsorbed surfactant molecules are oriented by their polar groups towards the surface, and the hydrocarbon ends into the aqueous phase. There is a hydrophobization of the hydrophilic surface, and consequently an increase. With a further significant increase in the surfactant concentration in the solution, a second layer of adsorbed surfactant molecules facing each other with non-polar radicals can form on the surface, and the surface becomes hydrophilic again (Fig. 2.2 a). 42

a

b

Fig. 2.2. Orientation scheme for diphilic surfactant molecules at the solid-liquid interface: a) hydrophilic surface; b) a hydrophobic surface

With increasing surfactant concentration in the case of hydrophobic surfaces (teflon, paraffin), the edge angle decreases due to the adsorption of surfactants on the surface and orientation of their molecules by polar radicals to the surface, and, by polar groups in the aqueous phase (Fig. 2.2 b), and surface hydrophilization of teflon occurs. Wetting isotherms for hydrophobic surfaces are similar to the surface tension isotherms of this surfactant. The typical isotherms for wetting solid surfaces of different nature are shown in Fig. 2.3. cosθ 1 1 0,5 3 1

2

3

-0,5

4

2

5

lgC

4

-1 Fig. 2.3. Isotherms of wetting hydrophilic (1,2) and hydrophobic (3,4) surfaces with surfactant solutions

2.1 Investigation of wetting of the solid surface and determination of adhesion work Purpose of the work: To study adhesion and the effect of surfactants on wetting of solid surfaces. 43

Reagents and apparatus: Surfactant solutions, distilled water, hydrophilic and hydrophobic plates (quartz, teflon, Al, etc.), a device for determining the edge angles (horizontal microscope with goniatric nozzle and special movable table), apparatus (stalagmometer, Rebinder's method) for determining surface tension of the liquid, injectors, filter paper, chemical flasks and glass beakers with a capacity of 50 ml. Procedure: Prepare solutions of surfactants of the following concentrations: 1·10-5; 1·10-4; 1·10-3; 1·10-2; 1·10-1%. As a surfactant, take one of the following substances as instructed by the teacher; sodium lauryl sulfate (SLS), sodium oleate, bromide cetyl trimethyl ammonium bromide, OP-7, OP-10, etc. Boil quartz and teflon plates before work for an hour in a solution of soda, rinse with distilled water, then treat with a hot solution of freshly prepared chrome mixture, rinse again with distilled water and dry in a vacuum desiccator. Place the dried plate (quartz or teflon) in a cuvette, put a drop of 0.05 ml of a surfactant solution of the appropriate concentration on its surface, close the cuvette with a lid to prevent evaporation of the liquid. Measuring the contact angle of wetting Measure the contact angle of wetting with a horizontal microscope with a goniatric nozzle and a special movable table. For each HMS concentration use a separate plate and put at least 5-6 drops of the same size on its surface. Measure the contact angle for each drop and calculate the average value of θ. The effect of gravity will make a noticeable error in the value of the edge angle when the droplet size is changed, especially when it increases. Measure the contact angle 5 minutes after the formation of the drop. To determine the work of wetting and the work of adhesion, first determine the surface tension of solutions using a stalagmometer. The values of the surface tension must be substituted in formulas (2.6) and (2.2) and calculate the adhesion work and wetting work. Record the results in the form of table 2.1:

44

Table 2.1

Concentation of SAS, %

Droplet No.

θº

θaverage

cos θ

σ, J m2

Wa , J m2

Ww , J m2

Report on work: 1) Construct a wetting isotherm (cosθ – lgC) and describe obtained results in the work book. 2) Calculate the work of wetting by equation 2.6. The value of σlg of solutions is determined by the stalagmometric method. Construct a graph (Ww – Csurf). 3) Calculate the work of adhesion Wa by equation 2.2, construct the graph (Wa – Сsurf). 2.2 Determination of unknown concentration of surfactant by the wetting isotherm Purpose of the work: to determine the unknown concentration of surfactant by the wetting isotherm. Equipment and reagents: Device for determining the contact angle of wetting, solutions of surfactants (or polyelectrolytes) in the concentration range 1·10-5; 1·10-4; 1·10-3; 1·10-2; 1·10-1 %, metal plates (aluminum). The order of the work Take surfactant or polyelectrolyte as directed by the teacher. Prepare solutions of surfactants (or polyelectrolytes) in the concentration range 1·10-5; 1·10-4; 1·10-3; 1·10-2; 1·10-1 %. As a metal plate, take aluminum plates. On the cleaned and dried surface of the plates put a drop, with a volume of 0.05 ml, a solution of surfactant or PE, and measure the wetting angle by using a horizontal microscope with a goniatric nozzle and a special movable table. For each solution, apply at least 3-4 drops of the same size. All results should be written down in the form of a table (see work 2.1, Table 2.1) 45

Construct a wetting isotherm (cosθ – lgC) and describe the obtained dependence in the workbook. Then, get from the laboratory assistant a solution of surfactant (or PE) with an unknown concentration, measure the wetting angle and determine its concentration by the wetting isotherm. 2.3 Determination of the wetting contact angle by measuring droplet parameters Purpose of the work: To study the effect of surfactants on wetting of solid surfaces and adhesion. Reagents and equipment: Surfactant solutions, distilled water, hydrophilic and hydrophobic plates (quartz, teflon, Al, etc.), device for determining the contact angle (microscope), device for determining surface tension of liquid (stalagmometer), syringes, filter paper, chemical flasks and glass beakers for 50ml. The order of the work Prepare solutions of surfactants and polyelectrolytes (PE) of the following concentrations: 1·10-5; 1·10-4; 1·10-3; 1·10-2; 1·10-1 %. Take the plate by instruction of the teacher. The cosine of the contact angle θ, included in the formulas for calculating the work of adhesion and wetting, is found from the main parameters of a drop of liquid applied to a solid surface: the height h and the diameter of the base d (Fig. 2.4). С

С h h A

B

A

Fig. 2.4. A diagram explaining the change of the contact angle

46

B

The values of cosθ are calculated by the equation: cos θ 

(d/2)

2

 h2

(d/2)

2

 h2

(2.6)

For d / 2 < h, we can use a simpler formula: cosθ  1 

h d/2

(2.7)

Parameters of droplets h and d are measured using an installation, the main parts of which are a cathetometer, a measuring cell-cuvette and a lighting device that provides a contrast image of the drop and the studied surface. To measure the diameter of the drop base, the crosspiece of the eyepiece – micrometer is moved along the vertical by rotating the micrometer screw of the cathetometer, and the crosshair is combined with the image of the plate (the drop-surface of the plate interface). Rotating the eyepiece – micrometer drum, lead to the center of the crosshair to the left extreme point of the drop (point A in Fig. 2.4) and the number of divisions n1 corresponding to its position in the eyepiece – micrometer is counted along the micrometer scales. Then, rotating the drum counterclock-wise, combine the crosshair with the right extreme point of the drop (point B, Fig. 2.4), fixing its position on the micrometer scales (n2). Calculate the difference Δn  n 2  n 1 that determines the diameter of the base of the drop d. When determining the droplet height, the eyepiece crosshair is initially combined with the middle of the drop base by moving it to the position of the drum corresponding to the division (n1 + n2) / 2. Then, the eyepiece-micrometer is rotated around the tube to 90 degrees, and with the help of the drum, the center of the crosshair is brought to the top of the drop (point C, Fig. 2.4). Record the reading on the scale of the micrometer. After this, the crosshair is combined with the image of the liquid – plate surface interface by rotating the drum. The height is found from the difference in readings (n1 – n2). Measurements of angles and surface tension for each surfactant con47

centration are carried out 3 times and the obtained values are found as the arithmetic mean. The experimental and calculated data are recorded in Table 2.2. Table 2.2

Surfactant concentration %

Drop No.

θº

Θaverage

cos θ

σ, J/m2

Wa , J/m2

Wl , J/m2

Control questions 1. What is adhesion and wetting? 2. What parameters are used to quantify them? 3. How does the nature of solids and liquids affect wetting and adhesion? 4. What are hydrophilic and hydrophobic surfaces? (give examples) 5. How can we affect the wetting phenomena? 6. How can the hydrophobization or hydrophilization of the surface be explained? 7. What methods of defining the contact angle do you know?

48

3. DETERMINATION OF CRITICAL CONCENTRATION OF MICELLE FORMATION OF SURFACTANTS Micelle formation in solutions of surfactants. Typical representatives of lyophilic disperse systems are micellar dispersions of surfactant, which besides separate molecules contain colloidal particles – the associates of surfactant molecules with a high degree of association m (m is the degree of association, m = 20-100). When spherical micelles are formed in a polar solvent – water – hydrocarbon chains of surfactants are combined in a compact core and hydrated polar groups turn into water. Due to hydrophilicity of the outer shell, shielding the hydrocarbon core from water, σ on the boundary of the micelle environment is reduced to a value less than σcr (σ < σcr), which determines the thermodynamic stability of micellar systems for macrophase of surfactant. Micellar systems discover the inherent properties of colloidal systems: light scattering, increased viscosity, etc. The ability of surfactants to form micelles is determined by the optimum ratio of hydrophilic and hydrophobic parts, so-called hydrophilic-lypophilic balance (HLB). Micelle forming surfactants include sodium, potassium, ammonium salts of fatty acids with long hydrocarbon radical C12-20 and other ionic and nonionic synthetic detergents. In the tendency of surfactants to form micelles a significant role is played by the ability of polar groups to shield the hydrocarbon core from contact with water. This ability is determined not only by the size of polar groups, but also by their nature, the nature of the interaction with the solvent, in particular, hydration. With the decrease in the degree of aggregation, the size of micelles is reduced, and, consequently, increases the portion of the substance on the interface of micelles with the solution, thus, the degree of shielding of the hydrocarbon core by the polar groups should reduce. In other words, the fragmentation of micelles is responsible for the increase in surface tension with decreasing size of micelles. Therefore, the presence of micelles of spherical shape with a certain optimal degree of association m, which corresponds to particles of colloidal dimensions with a radius r, close to the length of the hydrocarbon chains lm, is thermodynamically advantageous. 49

The formation of micelles with higher degrees of association m (with dimensions r > lm), while maintaining the spherical shape, is thermodynamically not profitable because it must be accompanied by the occurrence of polar groups in the volume of the micelles. Therefore, the values of m are increased not due to increasing the size of the spherical micelles, and by changing of their shape – transition to asymmetric structure. The maximum of possible concentration at which colloidal surfactants are in an aqueous solution in the molecular (ionic) form is called the critical concentration of micelle formation (CCM) (10-5-10-3 mol/l). Micelles are characterized by the aggregation number (number of molecules in the micelle) and micellar mass (the sum of the molecular masses of molecules that form a micelle). From the point of the thermodynamics, the moving force of micelle formation is hydrophobic interactions: hydrocarbon parts of the dipolar molecules are pushed out from the aquatic environment to avoid as far as possible the contact with water. Consequently, the micelles are formed whose core consists of a liquid hydrocarbons (tightly packed hydrocarbon chains) and the outer part – of the polar groups. Micelle formation is a spontaneous process, as the change of Gibbs potential: ΔG = ΔH – TΔS < 0. Change of H is negligible, the main contribution has entropy – TΔS. The removal of the hydrocarbon chains of diphilic molecules from water and their inclusion in the micelle destroy the structure of water, as a result the entropy of the system increases. The mechanism of micelle formation. With increasing concentration the surfactant chemical potential, expressing the tendency of removal of component from the solution, increases. At low concentrations of surfactant ions come to the surface of the solution, reducing the free energy of the system. Soon the surface layer is saturated. Then, when the concentration increases, the system removes hydrocarbon radicals from water into the liquid "pseudophase" – micelle – separating it from water by a hydrophilic shell (Fig. 3.1). This phenomenon leads to a gain of energy of 1.08 RT (~2000 joules) for each CH2-group, which is the work of adsorption at the interface water/ air 50

(3000 joules). The longer the chain, the bigger the payout energy and the lower the concentration of surfactant required for the formation of micelles. Thus, the CCM decreases with increasing length of the hydrocarbon radical of the surfactants.

b

a

d

c

Fig. 3.1. The state of the surfactant molecules at the interface of water/gas (a, b, c) and in solution (d)

The value of CCM depends on several factors: 1. The CCM decreases with increasing molecular mass of the hydrocarbon chains of the surfactant. 2. Temperature effect: a) for ionic surfactant CCM increases with increasing temperature due to disaggregating action of the thermal motion of molecules. However, this effect is weakened by hydrophobic interactions, accompanied by an increase in the entropy of the system. b) for nonionic surfactants, the CCM decreases with increasing temperature because with increasing temperature the hydrogen bonds between the ether oxygen atom and water molecules are destroyed, oxyethylenic chains are dehydrated and their mutual repulsion preventing aggregation decreases. Micelle formation in a non-aqueous environment. In non-polar organic solvents with low dielectric permeability ε of a polar group diphilic molecules become lyophobic, as a result, associates are formed in which the core is formed from the polar groups and hydrocarbon radicals are in the non-aqueous environment. These units are referred as "reverse micelles". 51

Ionic surfactants do not dissociate in them. Polar core is formed by the forces of dipole-dipole interaction between ion pairs, and hydrogen bonds are also possible . Surfactants that form micelles in non-polar solvents, are insoluble in water: the balance of hydrophilic and an oleophilic properties of molecules is strongly shifted in the direction of oleophilithy. The degree of aggregation of m is less than in direct micelles. The core of the micelles consists of polar groups smaller than hydrocarbon radicals. Therefore, the degree of shielding of the core, required for thermodynamic stability of the micelles, is achieved at lower degrees of association. The aggregates in these mixtures are present at low surfactant concentration in solution (10-6-10-7 mole/l). In the formation of micelles a significant role is played by the polarity of the solvent. It is necessary that the environment was a "good solvent" only for the hydrocarbon radicals. In environments equally related to both parts of diphilic surfactant molecules, micelle formation does not occur and surfactants show their true solubility. Solubilization in solutions of surfactants. The inclusion in the micelles of the third component, insoluble or poorly soluble in the dispersion medium, is called solubilization. A substance that dissolves in solutions of surfactant, is called solubilizate. There is direct solubilization (in the aqueous dispersions of surfactants) and backward solubilization (in the hydrocarbon systems Fig. 3.2).

a

b

Fig. 3.2. Solubilization of polar (a) and non-polar (b) organic molecules in micelles of surfactants

It is shown that the solubility of octane in water is small and is ~0,0015%. However, in 10% sodium oleate 2% of octane can be dissolved. Quantitatively, the ability of solubilization can be characterized by the relative solubilization, S is the ratio of the number of moles of the solubilizing substance Nsol to the number of moles of surfactant in micellar state Nmic 52

S = Nsol/Nmic

(3.1)

With increasing surfactant concentration up to the region of forming anisodiametric micelles there is a sharp increase in S, as a result anisodiametric micelles again transform into spherical. At the solubilization process the molecular weight of micelles increases not only due to the inclusion of molecules of solubilisate, but also due to the increase of the number of surfactant molecules in the micelle, because the increase of hydrophobicity of the core requires increase of the amount of surfactant molecules to maintain balance. At solubilization in lamellar micelles the organic matter enters the interior of the micelle, is located between the hydrocarbon radicals of the surfactant molecules and pushing the layers of molecular chains. At solubilization of polar organic substances, including surfactants, not able to forming micelles, solubilized molecules are included in the structure of micelles. 3.1 Determination of critical concentration of micelle formation by the method of solubilization Solubilizing ability of surfactants is often estimated using an oleophilic dye (e.g., Sudan III, orange OT). These dyes are practically insoluble in water, soluble in the hydrophobic part of the micelle, coloring the solution. The color intensity is higher, the greater the amount of colloid-solute substance (dye). Determination of the content of solubilizing dye is based on measuring of the optical density D of solution. Molar solubilizing ability Sm of the surfactant solution is calculated as the ratio of the obtained values of S to the surfactant concentration: Sm= S/Cpowder ,

(3.2)

where C is the concentration of the surfactant in the solution, mol/l. By the curve of the concentration dependence of the optical density D = f(C) of solubilizing solutions it is possible to determine the CCM, extrapolating the initial portion of the curve to the intersection with the axis of concentration. The work purpose: Determination of the dependence of the molar solubilization of oil-soluble dye on surfactant concentration; determination of CCM by the method of solubilization. 53

Apparatus and reagents: For the work required: photocolorimeter, conical flasks with stoppers 50 ml capacity, funnel for filtering, burettes or graduated pipettes, filter paper, solutions of surfactants of 0.01 M dye (e.g., Sudan III). The order of execution of work. In conical flasks prepare 8 solutions of surfactants by successive dilution of the initial solution. In each of the prepared surfactant solutionы add 5-10 mg of the dye (on the tip of a scalpel). The flask is stoppered, the mixture is stirred ин intense shaking, incubated for 40-60 minutes and filtered through a paper filter. Using photoelectrocolorimeter measure the optical density D of each solution starting from the solution with a minimum concentration at a specific filter (for solution of Sudan used filter No. 3, λ = 540 nm). Find the molar solubilizing ability of solutions of surfactants by the calibration curve D = f(C) for the dye solution in an organic solvent, e.g., benzene, toluene. The results are recorded in Table 3.1. Table 3.1

The concentration of the surfactant solution g/L mol/L

Optical density D

Dav

S

Sm

Plot the graph of dependencies D and Sm on the surfactant concentration. Determine the CCM by extrapolation of the initial areas of dependencies on the concentration axis (Fig. 3.3). Sm

D

CCM

C

CCM

C

Fig. 3.3. Determination of CCM by solubilization of dye in micelles of surfactants

54

Report: 1. Plot the results of the experiment as the graph of dependencies D = f(CSAS). 2. Determine by formula the values of Sm, plot the graph of Sm = f(CSAS). 3. By extrapolating the initial sections of the curves find the values of CCM. 3.2 Determination of critical concentration of micelle formation by the surface tension Measurement of surface tension by this method is based on the fact that at the time of separation of the drop from the lower end of the vertical tube the weight of the drop q is equal to the surface force F which acts along the circumference of the neck of the drop and prevents its separation. At the time of separation of the drop at the first approximation we can assume that q = F = 2πrσ ,

(3.3)

where r is the internal radius of the capillary. Typically, the droplet detachment does not occur along the line of the inner perimeter of stalagmometer capillary tube of radius r, but along the neck of the drop, having a smaller radius. Therefore, for more accurate determination of the σ, the value should be multiplied by some coefficient depending on the ratio of the drop volume ν to the cube of the tube radius, K = f(ν/r3). It is shown experimentally that this ratio is not changing very much when you change the volume drops even 1000 times. For drops, relatively little different in volume, this ratio can be considered the same as at the time of separation F = q, then, by determining the weight of the formed drops of q, we can calculate surface tension of the liquid σ. To determine the weight of the drop stalagmometer is used, which is a glass tube with an extension in the middle, ending at the bottom of the capillary (Fig. 1.4). The tube usually has a horizontal crankshaft, in which the capillary is soldered for the fluid drip slowly. Stalagmometric tube is filled with the investigated liquid of a certain volume ν, and the number of drops n arising from this volume, bounded by two marks, is measured. The weight of each drop is calculated according to the equation: 55

q = νρg/n ,

(3.4)

where ρ is the density of fluid; g is the acceleration of free fall. Obviously, when the drop falls there should be the equality: K2πrσ = νρg/n ,

(3.5)

Because of complexity of determination of the radius of the capillary r and, accordingly, the value of the coefficient K, surface tension of solutions is found by comparing the data on flowing out of the test liquid from stalagmometer and the liquid with known surface tension. Writing the equation (3.5) for both liquids, dividing the first of these equations by the second and reducing the constant values, we get the formula for calculation: σх = σst ρх nst / ρst nx ,

(3.6)

where the subscript x refers to the parameters of the test liquid, and the index st to the parameters of the liquid with known surface tension. The value n is the average number of drops in five measurements. The rate is measured in terms of the slow formation of droplets approximately 1-3 drops per minute. The velocity of the liquid outflow is kept constant and adjusted using the screw terminal located in the upper part of the stalagmometer tube. Before work to remove contaminants from the stalagmometer capillary tube it is washed several times with chromic mixture and water. The order of execution of work: stalagmometer is fixed in the tripod in vertical position and the liquid is sucked so that it is above the top of the label (in this case, the tube should be free of air bubbles), then the liquid is allowed to flow out of the capillary. When the liquid level coincides exactly with the top mark, start counting drops; stop counting drops when the fluid level reaches the bottom mark. The experiment is repeated several times and the average value of the observed counts is taken (the discrepancy between the individual measurements must be no more than 1-2 drops).

56

The results of experiments are recorded in Table 3.2: Table 3.2

СSAS, mol/L

Nst

nx

σx

According to the obtained results it is necessary to plot the curve of dependence σ = f(C) and to determine the CCM graphically as shown in Fig. 3.4.

Fig. 3.4. Dependence of surface tension of surfactant solutions on their concentration

Report: 1. Plot the results of the experiment as the graph of dependencies σ = f(CSAS). 2. By extrapolating the initial portion of the curve, find the value of CCM. 3.3 Determination of critical concentration of micelle formation by the conductometric method Depending on the concentrations of the solutions semicolloids can be in the molecular (or ionic) or in a micellar state. The concentration at which semicolloids transfer from the molecular state in the micelle state is called the critical concentration of micelle formation (CCM). 57

It is known that the equivalent conductivity when the degree of dissociation is equal to1, depends only on the ion mobility of the electrolyte λ∞ = U+v ,

(3.7)

where "U" and "v" are the mobility of cations and anions, respectively. Observing the dependence of equivalent conductivity on solution concentration of ionic semicolloids, we can see the transition of a true solution into a micellar. As micelles are formed and increase in size the mobility of the particles decreases, which decreases the equivalent conductivity. This decline continues until the micelle is completely formed and a constant value of mobility is set. In addition, in parallel to the enlargement process, the process of blocking charges also reduces the conductivity of the solution. Thus, the moment of transition of the curve from falling to the constancy will correspond to the completion of the formation of micellar system. The curve of dependence of the equivalent conductivity of ion polycolloid on its concentration decreases sharply in the initial region, which corresponds to the condition of the solution with a predominance of ions. In the section BC the micelles dominate, the curve segment CD indicates the almost complete transition of the system in the micellar state. The equivalent conductivity can be expressed through the electrical conductivity in the form: λ = 1000ωæ,

(3.8)

where ω is the dilution in liter equal to the reciprocal of concentration 1/C (N). Specific conductivity is determined by the resistance of the liquid column with a height of 1 cm between electrodes of area 1 cm2. But as the determination of conductivity is carried out in the vessel with the liquid column, which is not equal to the geometrically correct cubic centimeter, then the correction K is introduced; it is found for a known conductivity of a solution of potassium chloride of a certain concentration. Then: 58

K = æKCl . RKCl

(3.9)

Hence, for the investigated solution with the resistance æ = K/Rx

(3.10)

λ = 1000 æ0 ω = 1000 Kω æ

(3.11)

But since æ = 1/R, where R is the resistance of a column of electrolyte in the vessel, then after substitution we obtain an expression for equivalent conductivity, convenient for calculations. λ

1000Kω

(3.12)

R

Suppose, for example, we measure the conductivity of solution = 0.02 N. The dilution ω = 1: 0. 02 = 50 L. The resistance in this case was equal to 320 Ohms. The constant of the instrument of 0.8. Then 0,8 * 50 * 1000  125. by equation (3.12): λ  320 The order of execution of work

3 4

5

2 1

8 9 n

7

10

6

Fig. 3.5. Conductivity cell with a reochord bridge R-38: 1 – a power switch; 2 – a socket for bridge switching; 3 – an indicator light; 4 – resistance switch of the reference leg; 5 – a burette with the solution; 6 – an electrolytic cell; 7 – a magnetic stirrer; 8 – terminals for connecting the electrolytic cell; 9 – a handle the reochord to regulate the ratio of the shoulders; 10 – a correction of zero of the galvanometer; 11 – the switch of the sensitivity of the galvanometer

59

The resistance of the liquid column is measured using reochord bridge R-38, (Fig. 3.5) Alternating current voltage as 127 and 220 volts is switched through the power socket 2 in position of switch 1 on the sign  . When you turn on the instrument signal lamp 3 lights. The electrodes of the container filled with the test fluid are connected to terminal 8, the switch of the shoulder 4 is set to the "zero setting" and the switch of the galvanometer 11 in position "right". Rotating the corrector handle 10 set the arrow of the galvanometer in position "0". By the switch of the comparison shoulder 4 different resistors are successively introduced and by turning the crank of the reochord 9, equilibration of the bridge is achieved. At the moment of balance, the galvanometer is set to "0". On the limb of reochord the ratio of the shoulders "m" is read. The sought resistance will be R = mR0, where R0 is the resistance of the comparison shoulder 4. Test liquid is poured into the vessel 6 with two platinum electrodes, the conductors sealed in the tubes are connected to the terminals. A certain amount of the subject liquid using a pipette is introduced into the vessel, making sure that the fluid covers the electrodes, and make measurements. For diluting the solution by half, remove from the vessel with a pipette (the pipette should be taken to spray on a thin stalk), half of the volume of the liquid, then add as much distilled water. EXAMPLE: Conductometric method is used to study micelle formation in aqueous solutions of sodium stearate – C17H35COONa. Since sodium stearate is soluble in water only at high temperatures, the measurement was carried out at 90 °C .The initial concentration C = 0.25 g-EQ/l. At first, the instrument constant was determined for 0.02 N KCl, whose specific conductivity is 0.002768. The resistance of KCl solution is equal to 270, then K = 0.002768 · 270 = 0.747. Solution with the initial concentration was placed in the vessel with a volume of 60 ml, after the resistance measurement 30 ml was taken by a pipette and 30 ml of water was added. The resistance value was used to determine the equivalent conductivity of solutions according to formula 3.8. The results of observation are recorded in table 3.3 and depicted in graphs. 60

Тable 3.3

С 10-2 l/g EQ 25 12.5 6.25 3.12 1.56 0.78 0.39 0.2

l/g EQ

m

R0, Оm

R, Оm

cm-1·Оm-1

4 8 16 32 64 128 256 500

1.15 1.68 1.8 2.05 3.65 6.2 7.8 0.125

100 100 100 100 100 100 100 100

115 168 180 205 365 620 780 1250

25 34 64 114 128 150 200 300

According to this data, the CMC of sodium stearate = 3.5 · 10-2 g-EQ Control questions: 1. How does the length of the hydrocarbon radical of the surfactant affect the value of CCM? 2. How does CCM change when you add electrolyte to the surfactant solution? 3. How does the entropy of the system during the formation of micelles of surfactant change? 4. How does the CCM of nonionic surfactants change? 5. How does temperature affect the phase state of surfactant? 6. What methods can be used to determine the value of CCM? 7. What is the mechanism of formation of micelles of surfactant? 8. Define the concepts of "solubilization," "solubilised", "solubilizer"? 9. Give examples of application of solubilization.

61

4. SEDIMENTATION ANALYSIS OF SUSPENSIONS Colloidal systems are microheterogeneous systems characterized by three main features: the degree of dispersion, heterogeneity and aggregative stability, i.e. instability. The degree of dispersion is characterized by the fineness of the dispersed phase particles. The size of colloidal particles varies from 1 nm to 100 nm. At grinding of particles of dispersed phase, the total surface area and the free surface energy increase. The free surface energy equals to E = σS, where S is the surface area of the dispersed phase, and σ is the surface tension of the dispersed phase at the interface with dispersion medium. The specific surface area S0 is taken as a characteristic of interfacial area, i.e. surface per a unit of volume of a dispersed phase. S0 

S V

,

(4.1)

where S is the total surface area, V is the total volume of the dispersed phase, cm3. The volume of powders is difficult to determine experimentally. Therefore, an effective specific surface area is often used, i.e. the surface area per unit of mass of a dispersed phase particle. S0 

S0 ps

,

(4.2)

where ps is the density of the substance forming the dispersed phase. Colloidal disperse systems are characterized by high specific surface area and high free surface energy. A large reserve of free surface energy has a strong influence on many properties of colloidal systems. So, they have maximum chemical reactivity, adsorption and catalytic activity, plasticity, mechanical strength, etc.

62

The degree of dispersion is a value inversely proportional to the size of particle diameter: D

1 , d

(4.3)

where d is the average particle diameter. Since the colloidal properties are determined by the reserve of free surface energy related to the specific area, Wolfgang Ostwald proposed to take the specific surface area S0 as a measure of dispersion. The dispersion and the specific surface area are related as follows: they have the same unit of measurement [cm-1], but they differ numerically, because S0 depends on the shape of the particles. Thus, for particles of the cubic form S0 

S V



6a 2 a3



6 a

6

1 a

 6D ,

(4.4)

where a is the length of cube edge. For particles of another shape, the coefficient before D is different. Generally, a ratio is defined as follows: S0 = k · D

(4.5)

Since the properties of colloidal systems depend on the particle size, grinding is widely used to obtain a product with the desired properties. Researchers show great interest. The methods of determination of the dispersion degree both for fine disperse and coarse disperse systems are of interest for researches. The methods of the dispersion degree determination are termed as dispersion analysis, but these methods for fine disperse systems differ significantly from those for coarse disperse systems. For coarse disperse systems, the sedimentation analysis based on the measurement of the settling rate is the most reliable method. 4.1 Sedimentation analysis by Figurovsky In 1936 Professor of the Department of Colloid Chemistry of Moscow State University N.A. Figurovsky developed the theory and 63

methodology of a simple method of sedimentation analysis. He proposed the original sedimentation balance of a very simple construction to weigh the suspension sediment. Figurovsky's balance (Fig. 4.1) represents an elastic, gradually thinning bar (spire) made from glass, quartz or other material not possessing residual deformation. The bar has a hook for a pan immersed in the cylinder with suspension. Suspension is settled on the pan, leading to the deflection of the bar playing the role of the balance beam. According to Hooke's law, the deflection of an elastic bar is proportional to the load. Consequently, the deflection of the bar can determine the weight of the sediment on the pan. If the balance is graded, then the sediment weight in grams can be immediately determined from the deflection of the balance beam. But Figurovsky showed that it is possible to carry out the analysis without graduation of the balance, if the weight of the sediment is expressed proportionally to units of the scale deflection of the balance beam. So, after immersing the pan of Figurovsky's balance into a properly mixed suspension, the deflection of the beam is determined on the scale through the certain intervals of time. Then, the sedimentation curve is plotted as a function of suspension weight on time. This curve is analyzed graphically by plotting the tangents, representing the weights of the fractions in % from the weight of the powder sample. On the sedimentation curve (Fig. 4.2), the weight of the sediment P1 when the total first fraction τ1 = H/U1 is completely settled is equal to the segment OD1. The weight of the first fraction is equal to the segment OE1, cut off from the axis of ordinates by the tangent to the curve at point B1.

Fig. 4.1. Scheme of Figurovsky balance

64

The weight of the first fraction in % of the total powder weight is defined as: F1 

ОЕ1 ODn

,

where ODn is the weight of sediment when the entire suspension is completely settled. At time τ2, when the second fraction settles, the sediment weight will be equal to the segment OD2; and the weight of the fully settled first and second fractions in it will be equal to the segment OE2, cut off from the y-axis by the tangent to the curve at the point B2. Then the weight of the second fraction in % is: F2 

OE 2 - ОЕ 1 OD n

 100%

How to determine the radius of particles of the fraction, if we do not know its weight in grams? Figurovsky used the Svedberg method, i.e. he defined the constant of sedimentation rate, and along it finds the radius of the part by the equation: τ

CU

How to determine the sedimentation rate of a polydisperse suspension? Figurovsky solved the problem very simply. For the whole fraction settling, i.e. for the particles on the surface of the suspension had time to settle, they must pass way H from the surface of the liquid to the bottom of the pan. One can measure easily this distance by a ruler, but it should not change during the experiment. For this purpose, a bar is taken which bends for 1-2 mm, when suspension is completely settled and the pan is immersed in suspension into a depth of 20-30 cm. Under such conditions, when the suspension is completely settled, the path is increased by approximately 0.5-1% and it can be considered almost constant. In order to improve the accuracy of determining the deflection of the balance beam, a horizontal microscope is used. 65

Bn

Dn

D2

B2

D1

B1

τn

τ1 τ2 Fig. 4.2.

After dividing the path H by time τ, during which the fraction has settled, we find the constant rate, and along it the radius of the particles in this fraction. u1 

H τ

, r1  Ku 1

(4.3)

The sedimentation analysis according to Figurovsky method is carried out as follows. A sufficiently wide cylinder is used, because the pan immersed should not touch the walls. 1 liter or ½ liter of distilled water is poured into the cylinder. The pan is immersed into a cylinder with water and hanged to a balance beam. The pan is immersed in water at a depth of 20-30 cm, not touching the bottom 2-3 cm and walls of cylinder. The position of the cylinder on the table is marked with chalk to put it on this place at an unexpected displacement. Then the horizontal microscope is placed so that the scale and the end of the bar are seen clearly. The zero of the scale and the end of the beam should be located at the bottom, because at the suspen66

sion settling, the balance beam will lower and we will observe the reverse image by means of microscope. After this, the pan is taken out carefully without moving the cylinder and the microscope from their positions. The desired sample of the powder is weighed by means of technical balances. The sample of powder to be tested is weighed on scales to make a 0.5% suspension from it. The experimental results are recorded in Table 4.1, which is prepared preliminary. A sample of weighed powder is placed into the cylinder and mixed carefully with a special stirrer for 2-3 minutes. The pan is immersed quickly, but carefully. When the convection currents in the liquid and the bar oscillation die out, but not later than 15-30 seconds after immersion of the cup, mark the position of the end of the bar on the scale of the microscope and immediately turn on the stopwatch. This count is taken as the beginning of the experiment, i.e. for the zero point. Then, without stopping the stopwatch, observe the increase in the weight of the sediment first every 30 seconds, and then the time intervals gradually increase. When the weight of the sediment practically does not change and the suspension brightens, without shifting anything, carefully determine the distance from the surface of the liquid to the bottom of the pan H, which is the distance that the settling particles passed. It determines the settling rate and the radius of the particles. Processing of experimental results Based on the results of the experiment, a settling curve P = f(τ) is plotted on a large scale on a 20 x 15 millimeter-sized paper, plotting the time τ along the abscissa axis, and the weight of the sediment along the ordinate axis in units of the scale of the microscope P. On the same graph, the sedimentation curve of the suspension in the presence of an electrolyte is drawn. Comparing the rate of increase in the weight of the sediment, we conclude how the electrolyte affects the stability of the suspension. Further, the settling curve obtained in the absence of the electrolyte is analyzed graphically by the Oden method, i.e. 810 points are chosen on the settling curve, where the greatest bending is observed, and by the "mirror method" tangents are drawn to them. The first point is taken in the end of a straight line 67

segment on the settling curve, where it departs from the straight line drawn along it from the origin. In Fig. 4.3 this point is B1, it corresponds to the time τmin, by which the largest particles with rmax have settled. For the end point take the point Bm, where the curve goes to a straight line parallel to the abscissa axis. This point corresponds to the time τmax, when the settling of the smalllest particles with rmin ended. Thus, in our suspension there are particles with radius range from rmax to rmin. P B5 Bm

ε5 ε5

B4 B3

D2 ε3

B2

ε2 ε1

B1

τmin rmax

τmin rmax

Fig. 4.3.

If the powder was not subjected to special fractionation before the analysis, then the suspension will contain particles of all possible sizes in the range of radius from rmax to rmin. Accordingly, in each fraction there will be particles of not one specific radius, but some interval of radii. Having selected 8-10 points on the settling curve, we thus mentally divide the suspension into 8-10 fractions. To determine the weight of these fractions in the sediment, draw tangents to the selected points and extrapolate them to the intersection with the ordinate axis; the segments cut by them will characterize the weights of the completely settled fractions. 68

First, we draw a tangent to a point B1 corresponding to time τ1. All the particles that during this time τ1 

A will pass the path from U1

the surface of the suspension to the bottom of the pan, i.e. will have time to settle will be the first fraction F1. Its weight in the sediment will be equal to OE1, cut off by the tangent from the ordinate axis in units of the scale of the microscope, and in % of the total powder weight it will be equal to F1 % 

OE1  100. OD n

The particle size of this fraction is found from the settling rate u1 

H cm r  τ1 sec 1

9 η u1  2 (d T  d ж )  g

Κu 1

(4.4)

It is convenient to carry out calculations logarithmically lg r1 = 1/2 (log K + lg u1)

(4.5)

The viscosity of water at t0 is found in the reference book. Thus, the first fraction includes particles with radius less than rmax and greater than r1. The values found are F1%; they are recorded into Table 4.2. Similarly, we find the characteristics for the second fraction Q2 %, the sedimentation of which has ended by the time point τ2 

H . u2

The tangent drawn to the point B2 cuts the segment OE2 from the ordinate axis, equal to the weight in the sediment of the fully settled first and second fractions. Let's express it in percentages and denote as Q2%: Q 2  F1  F2 

69

OE 2 OD m

 100

Hence the weight of the second fraction is: F2 = Q2 – F1. The sedimentation rate of the particles of this fraction will be equal: u2 

H cm τ 2 sec

, r2 

Κu 2

(4.6)

This fraction includes particles with radius from τ1 up to τ2. Obtained data τ2, Q2 %; F2 %; U2 is recorded in Table 4.2. Similarly, we perform calculations for all fractions and record the results in the Table. Complete the sedimentation analysis by plotting the mass distribution curves of the suspension in terms of particle sizes, i.e. by their radius. The distribution curves make the analysis results more visible. There are the integral and differential distribution curves. Firstly, we plot an integral distribution curve. Integral distribution curve In other words, it is the cumulative or accumulative curve, which shows the dependence on the radius of the total number of particles with dimensions exceeding the radius ri. To plot the integral curve of the distribution, plot along the ordinate axis the weight of all the fractions Qi% that have completely settled by the given instant. This is the constant part in the entire sediment at a given time. n

Pi  Q i   i 1

dp τi dτ

We put along the abscissa axis the minimum radius of particles, i.e. the radius of the particles of the smallest of the completely settled fractions, and the curve shown in Fig. 4.4 is obtained. Thus, in constructing this curve, the data of the second and fifth columns of Table 4.2 are used. Our curve Q1 = F1 here includes particles with radius from rmax to r1; Q2 = F1 + F2, this includes particles with radius from rmax to r2, and so on. The inflection point on this curve corresponds to the radius of the particles, which are the most in the given suspension, i.e. the most probable particle size.

70

Q, % Q5 Q4 Qb dQ = F Qa Q3 Q2 Q1 r3

r4 rв rа r3 r2

r1 rmax r

Fig. 4.4.

Since

Q  f(r) 

P P  , τ r

the integral curve is the curve of the first

derivatives of the sedimentation curve. An important feature of the integral distribution curve is that it can quickly determine the percentage of any fractions of interest in a given suspension. To determine the percentage of the fraction of interest one can choose the necessary radius on the abscissa axis (in Fig. 4.4, these are ra and rb), continue the lines to the intersection with the curve; from the intersection points draw the lines parallel to the abscissa axis till crossing with the ordinate axis (points Qa and Qb in Fig. 4.4). The difference Qb – Qa = dQ = F% gives us the weight of the fraction of interest in % of the weight of the whole suspension. The integral distribution curve can be used to draw a differential distribution curve. The results of sedimentation analysis are characterized well by means of differential distribution curve. Differential distribution curve "The differential distribution curve shows the change of a substance weight with the change of the particle radius per unit near the given radius value". Before drawing the differential distribution curve let us return once more to the sedimentation curve. From Fig. 4.5 it is seen that the weight of the fraction in the first approximation is proportional to the interval of the radius of particles in the fraction; F = F(r) · ∆r, where F(r) is the distribution function and it is equal to the weight of the fraction per unit of radius interval. 71

Fig. 4.5.

F(r) F(r)2

r2

r1

r

Fig. 4.6.

If we know the distribution function, then we can represent the weight of the fraction graphically with the area of the rectangle (Fig. 4.6), where F(r) is the ordinate, and the radii r1 and r2 are abscissas. Thus, the physical meaning of the distribution function is the fraction weight per unit of radius: the analytical meaning is the density of probable appearance of a given value of a random variable. F  Q i 1  Q i  ΔQ  Q; F(r) 

F Δr



Q r

The distribution function is the first derivative of the integral curve. Using the integral curve ΔQ , one can calculate the distribution Δr

function for constructing the differential distribution curve (Fig. 4.7). 72

As Q  P , then

F(r) 

r

Q  P  2P  ( ) 2 r r r r

the distribution

function is the second derivative of the sedimentation curve.

Fig. 4.7.

In practice, to plot the differential distribution curve, first one should find the distribution function for experimental results: F (r) =

F%

ri  ri 1

and write it in column 7 of the Table. Then,

using found F(r) and radii, represent the weight of each fraction by the area of the rectangle in the graph. By connecting the midpoints of the rectangle by a smooth curve, we obtain the differential distribution curve shown in Fig. 4.8. F(r) F(r)4

F(r)5 F(r)3 F(r)2 F(r)6

F5

F7

F(r)1

F3

F4

F6

F2 F1

r7

r6

r5

r4

r3

Fig. 4.8.

73

r2

r1

r

"The area limited by the differential curve and the abscissa axis gives the total weight fraction of particles of all sizes (100%), and the area bounded by two radii ri and ri+1 is the percentage in the suspension of particles with radii from ri to ri+1."The distribution curve usually has one maximum corresponding to the weight of the largest fraction and the most probable particle size in the suspension. The curve of a monodisperse suspension has a sharp maximum, while for a polydisperse suspension the maximum is small and the curve is low-sloped (Fig. 4.9 and 4.10). If the powder is obtained by joint breaking of two minerals of different hardness, then there is a distribution curve for each of them. The soft mineral has more fine particles, while the solid mineral has larger particles. The total distribution curve obtained experimentally will have two max which show polydispersity and polyminerality. F(r)

r Fig. 4.9.

F(r)

r Fig. 4.10.

According to A.P. Rehbinder, "Dispersion of a suspension can be characterized by a single value of the effective specific surface, i.e. the surface of all the particles contained in 1g of precipitate". 74

As it is shown above, the specific surface of spherical particles is equal to: S0 

4ππ2



4 3 πr 3

and the effective specific surface is

S '0 

3

(4.7)

r 3 rp

, where ρ is the density

of the dispersed phase. Since each fraction contains particles of different radii, the effective specific surface is calculated for particles of average radius: raver. 

ri  ri 1 2

; S'  0 i

(

3 ri  ri 1 2

 )d

6

(4.8)

(ri  ri 1 )d

Thus, we find the effective specific surface for all fractions and put their values into the eighth column of the Table. S0 – is the specific effective surface of 1 gram of this fraction. However, in the suspension there is not one gram of it, but some quantity equal to F, therefore the percentage of the surface of the particles of this fraction in the total surface of the entire suspension will be equal to: ΔS'0 i



S '0

i

100

 Fi % 

6

F%

(ri  ri 1 )d 100

 0,06

F% (ri  ri 1 )d

(4.9)

The values of found ∆S0 are recorded the 9-th column of the Table. They show which fraction has the largest surface and, therefore, has the greatest effect on the adsorption, catalytic and other properties of this powder. The total effective surface of the entire suspension will be equal to the sum of all ∆S0 rmax rmax F% см 2 S '0   ΔS '0  0,06  , rmin rmin (ri  ri 1 )d г

75

(4.10)

Since we calculate by the formula for spherical particles, the data on the specific surface area obtained by us are approximate and relative, but in fact, in crushing the particles of various shapes are obtained, and their surface will be larger than that of the particles of the spherical shape. In addition, the particles have cracks and micropores, the surface of which is also not taken into account. Thus, the apparent or "geometric" surface calculated by us is much smaller than the true surface. The described method of weight sedimentation analysis by Figurovsky allows us to use very simple equipment to obtain rather accurate and detailed information easily and quickly about the size of the particles and the amount of investigated powder or suspension. But this method has its drawbacks. Firstly, we cannot take into account the largest particles which settle down before we begin to determine the weight of the sediment by means of sedimentation curve. It is difficult to take into account the smallest particles whose sedimentation can last for many hours. Usually the experiment ends without waiting for the complete settling of the suspension. Secondly, Figurovsky uses the approximate Oden equation to describe the sedimentation curve. This equation is solved by an approximate graphic method. The graphical method has become widely used for constructing distribution curves because of its simplicity and clarity. But it is not objective enough, which can lead to errors, especially when processing the sloping part of the settling curve. Other authors propose to use in the sedimentation analysis equations for the real settling curves with rude approximation and to solve these equations not graphically but by an analytical method. One of the simplest analytical methods is the method proposed by N.N. Tzyurupa for slow settling suspensions. According to this method, the sedimentation curve is described by the equation: m  Qm

τ  Qmα , τ  τo

(4.11)

where Qm and о are some constants of dimension m and , respectively. The physical meaning of the constant will be clear if we suppose τ → . In this case, τ/(+τ0) → 1 and m → Qm. Thus, Qm characterizes the amount of powder which settles during an infinitely large time interval. 76

If 100% is taken as the amount of powder settled for a specific finite period of time, then Qm should be greater than 100%. At τ = τ0 m = Qm/2, therefore τ0 is sometimes called the "halftime sedimentation". The total amount of powder settled at time τ is:  dm   τ  dτ  τ

(4.12)

m  Q

Or  dm   τ  dτ  τ

(4.13)

Qm  m  

Substituting m and dm/dτ in (4.13), in accordance with equation (4.11), it is obtained: 

2

   Q m  a 2  τ  τ0  τ

Q  Q m 

(4.14)

The value of α can be expressed in terms of particle sizes: τ

a

τ  τ0



r02 r02

 r2

.

(4.15)

Where ro  KH/τ o Thus: 

Q  Q m  a 2  Q m 



   r 

r02 r02

(4.16)

2

Equation (4.16) is an analytic expression of the integral distribution curve. The equation of the differential distribution curve can be obtained by differentiating equation (4.16) with respect to r: F

dQ dr

 4Q m



r02

r  r04 r

2



3



4Q m

77

r0

a 1  a   a 2 

4Q m r0

ε

(4.17)

The values of α2 and ε as a function of r/r0 are shown in Table 4.3. Table 4.3

r/r0

α2

ε

r/r0

α2

ε

r/r0

α2

ε

0.1

0.980

0.097

0.6

0.541

0.239

1.4

0.114

0.054

0.2

0.925

0.177

0.7

0.451

0.209

1.6

0.079

0.036

0.3

0.842

0.232

0.8

0.372

0.182

1.8

0.056

0.023

0.4

0.743

0.255

0.9

0.305

0.155

2.0

0.040

0.016

0.45

0.692

0.260

1.0

0.250

0.125

2.5

0.019

0.007

0.5

0.640

0.256

1.2

0.168

0.083

3.0

0.010

0.003

By the equations for the integral and differential distribution functions, it is possible to determine the values of the three fundamental radii characterizing the polydisperse system. The minimum radius can be obtained from equation (4.16) with Q = 100%:



rmin.  ro 0,1  Q m  1



1/2

(4.18)

Differentiating the equation (4.17) with respect to r and equating the derivative to zero (for the maximum value of the function), we can obtain the value of the most probable radius: (4.19)

rн  ro / 2,24

The maximum value of the radius is: rmax =3r0 ,

(4.20)

at which the value of the distribution function F is  0.01 from its maximum value. If the degree of half-dispersion P is determined by the ratio of the maximum radius to the minimum one, then in accordance with (4.20) and (4.18): P

r max. rmin.



0,1  78

3



Qm 1

1/2

(4.21)

Thus, the degree of polydispersity depends only on Qm, and the value of the most probable radius characterizing the total dispersion of the system depends only on r0. This allows us to consider r0 as a coefficient characterizing the dispersion, and Qm – as a coefficient characterizing polydispersity. From (4.16) it follows that the percentage of any fraction is equal to



ΔQ 1  Q 1  Q 2  Q m  a 22  Q m  a 12  Q m a 22  a 12



(4.22)

Thus, the method of sedimentation analysis of N.N. Tzyurupa consists in the determination of two coefficients: r0 and Q m. To find these values, the sedimentation equation (6) is written as: τ/m  τ 0 /Q m  τ/Q m

(4.23)

In the coordinates τ/m – τ (4.23) is the equation of a straight line. The cotangent of the slope of the straight line to the axis τ is equal to Qm, and the segment cut off on the ordinate axis equals to τ0/Qm. The constant τ0 is determined by the equation ro  KH/τ o for τ = τ0. In order to calculate the constant K, we need the data on the viscosity and density of the liquid phase and the density of the powder substance. We apply the equations (4.16) and (4.17) using constant value to draw the integral and differential distribution curves. Table 4.1 Form for recording of experimental results Sedimentation analysis of powder ________________________ Date:___________ TC of the room, ρS – density of the suspension, ρL – density of the medium,  – viscosity of the dispersion medium Time intervals 1 30  

Time from the beginning of the experiment 2 0 30 1 130 … … 5

Position of the bar on the microscope scale 3 a0 a1 a2 a3 … … a10

79

The weight of the precipitate in units of the microscope scale 4 a1 – a0 a2 – a0 a3 – a0 a3 … … a10 – a0

1 1

2

3

5

10

2 6 7 8 9 10 12 14 16 18 20 23 26 29 32 35 40 45 50 55 60 70 80 90

80

3 a11 a12 a13 … …

4 a11 – a0 a12 – a0 a13 – a0 … …

… … …

… … …

81

Q2 = F1+F2

τ2

-//-

F Fi = Qi- Qi1

F Fm = Qmax- Qi

-//-

-//-

Qi = F1 + F2 +…Fi

Qmax = F1 + F2 +…Fm

-//-

-//-

τi

τmax

-//-

Q3 = F1 + F2 + F3

τ3

F3 = Q3- Q2

F2 = Q2- F1

F1

Q1 = F1

τ1

3 -

2

1

F%

τmin

Q%

τ, sec 5

r3  Ku 3

H τ3

H τ max

rmin  Ku min

ri  Kui

H ui  τi u min 

-//-

-//-

-//-

-//-

r2  Ku 2

H τ2

u2  u3 

r1  Ku1

rirmin

ri-1-ri

-//-

-//-

r2-r3

r1-r2

rmaxr1

-

6

Ku , cm Δr, cm

rmax  Ku max

r

H τ1

H  , τ min

4

H , cm/s τ

u1 

u max

u

F% r

F3 % r2  r3

Fr m 

Fmax % r2  rmin

F% Fr i  i ri 1  ri

-//-

-//-

Fr 3 

F2 % r1  r2

F1 % rmax  r1

Fr 2 

Fr 1 

-

7

F(r) =

6

-//-

-//-

6

r2  r2  p

S0 m 

6

ri  rmin  p

6 S0i  ri 1  ri  p

S 03 

6

r1  r2  p

rmax  r1  p

S02 

S01 

-

8

S0, cm2

The parameters of the suspension obtained as a result of sedimentation analysis

S 0 min 

S 0i 

S02 

S02 

S01 

 F2 %

 F2 %

 F1 %

S 0 min  Fm % 10 0

S 0i  Fi % 10 0

-//-

-//-

10 0

S 02

10 0

S 02

10 0

S 01

-

9

ΔS0, cm2

Table 4.2

4.2 Sedimentation analysis of suspensions on torsion scales The sedimentation analysis can also be carried out using the torsion balance. When using the torsion balance (Fig. 4.11), first of all, it is necessary to check the correctness of the set up of the scale. Then check the equilibrium position of the balance as follows: remove the metal cup, the weight of 500 mg is weighted instead of a cup; then moving the level of the arrester 1 to the right, release the balance beam and, using the handle 2, set the pointer of arrow 3 to the end position, to the scale division 500 of the scale. The balance is in equilibrium when the equilibrium pointer 5 is against the vertical line of equilibrium on the scale.

500

2

1000

3

6

5

1

H

Fig. 4.11. Scheme of torsion balance

If you set the pointer arrow 3 to the digit of scale 500 (at a weight of 500 mg), the equilibrium pointer 5 is not against the vertical line, it is brought to this position by means of screw 4. After this, the balance is again locked by moving the lever to the left. In a glass cylinder with millimeter divisions pour distilled water to a level 1-2 cm 82

below the edge of the cylinder, set on the right side of the device and immerse the glass or metal cup in the water, suspending it on the balance rod pull 6. It should be ensured that there are no air bubbles on the cup, and the cylinder is set in such a position that the cup is symmetrical with respect to the cylinder walls. Then release the lock of the balance (move lever 1 to the right) and balance the balance by moving the handle 2 of arrow pointer 3 counterclockwise until the pointer of equilibrium 5 that has moved to the left is again against the vertical line. Record the count on the scale of the balance – this figure corresponds to the initial count of the experiment, i.e. the weight of the cup without sediment in water. On the millimeter scale on the walls of the cylinder determine the height of the column H of the liquid above the cup (the distance from the bottom of the cup to the water level in the cylinder), expressing it in cm. Then, the balance is locked (lever 1 is moved to the left). The volume of water poured into the cylinder is measured and a 0.8% suspension of finely divided quartz or calcium carbonate is prepared directly in the cylinder. The weight required for this is calculated and weighed on the scales. The prepared suspension in the cylinder is thoroughly mixed with a special disk agitator. Moving the disk up and down for 2-3 minutes, the particles of the suspension are uniformly distributed throughout the volume. Without stopping mixing, put the cylinder on the right side of the device and, removing the mixer, quickly immerse the cup in the suspension, suspending it to the balance rod pull 6. Simultaneously with the immersion of the cup, start the stopwatch and release the lock of the balance (lever 1 move to the right). Due to settling of the suspension particles on the cup, the equilibrium pointer 5 moves to the right. The first count is done in 10 seconds from the beginning of the experiment. The handle 2 smoothly moves the pointer 3 (which was stopped at the initial position) in the counterclockwise direction until the balance is balanced (i.e., before the balance pointer 5 is set against the line). The speed of the process of sedimentation of the polydisperse suspension is greatest at the beginning of the experiment, therefore at the beginning the counts are taken after 10-30 seconds, then gradually the intervals between the counts are increased, at the end of the experiment the readings are carried out after 10-15 minutes. 83

As the sediment accumulates on the cup, the equilibrium pointer shifts to the left and returns to the equilibrium position at each count with the handle 2. It is necessary to bring the balance to equilibrium, directly before the start of the countdown. Readings on the scale of balance using the arrow 3 are made only when the balance is in equilibrium: they are proportional to the weight of the sediment that has settled on the cup at a given time. The experiment is conducted for 1-1.5 hours until the settling process ends and the next two counts, taken in 10-15 minutes, give identical or very close values. After the measurement is completed, you have to lock the balance (move lever 1 to the left), set the pointer arrow 3 to 0 of the scale, remove and wash the cup and cylinder. The results (scale and time readings) are recorded in a table. Calculate the differences between each sample P on the scale of weights and the initial readout P0 – these differences are proportional to the weight of the sediment on the balance pan. On a millimeter paper, on a large scale, the sedimentation of the suspension is plotted, plotting the time from the beginning of the experiment in seconds along the abscissa axis, and along the ordinate axis – the difference in readings. Further calculation is carried out in the same way as when working with Figurovsky's sedimentometer. Control questions: 1. What are the specific features of colloidal systems? 2. What is the measure of the heterogeneity and degree of fragmentation of disperse systems? 3. What are the main methods used to determine the particle size and for which disperse systems do they apply? 4. What is the sedimentation constant and what does it characterize? 5. What is the peculiarity of the Figurovsky method used to determine the particle size? 6. What is the purpose of the integral and differential curves for the particle size distribution? 7. How does the form of the distribution curves change as the polydisperse system approaches monodisperse? 8. What are the specific features of N.N. Tzurupa's tangential and analytical method used to process the results of sedimentation analysis? 9. How can we carry out a sedimentation analysis of coarsely dispersed systems using torsion scales?

84

5. ELECTRO-KINETIC PHENOMENA Electrophoresis refers to electro-kinetic phenomena associated with a relative displacement of the phases of a dispersed system under the action of an electric current. For the first time these phenomena (electro-osmosis and electrophoresis) were discovered in 1808 by Professor Reuss, a professor at Moscow University. Later, in the second half of the nineteenth century, inverse phenomena were discovered, called the flow potential (Quinnke) and the settling potential (Dorn), in which the appearance of an electric field was observed when the external phases were displaced rlative to each other under the action of external mechanical forces. Electro-kinetic phenomena are a consequence of the formation of a double electric layer at the boundary of a dispersed phase with a dispersion medium. Particles of the dispersed phase of free-dispersion systems with a liquid dispersion medium (sols, suspensions, emulsions) in most cases have DEL. There are three mechanisms for the formation of DEL on interphase surfaces: 1. Dissociation of surface functional groups belonging to one of the phases. 2. The preferential adsorption of ions of a single charge sign from the volume of one phase on the surface of the other. 3. Orientation of polar molecules at the interphase boundary. The resulting electric layer is called double, because it consists of two layers of charges of the opposite sign. One layer is located on the interphase surface, which has the potential φ0. The ions that form this layer are called potential-determining. The charge of this layer is compensated by the charge of the second layer of ions, called counter ions. One part of the counter ions is retained at the surface due to electrostatic and adsorption interactions, forming an adsorption layer (the Helmholtz layer). The other part of the counter ions is in the solution adjacent to the surface and forms a diffuse layer (the Guy layer) because of their participation in the thermal motion (Fig. 5.1).

85

φ φ0

φδ

ζ φδ/e

δ

λ

x

Fig. 5.1. Diagram of the structure of a double electric layer

The thickness of the adsorption layer δ is taken equal to the diameter of the counter ions. A layer of potential-determining ions together with the counter ion layer adjacent to it form an electric capacitor, in which the potential changes linearly. The potential φδ, corresponding to the interface between the adsorption and diffuse layers is called the potential of the diffuse layer. The change in this potential in the direction of decrease of the diffuse layer is described by the following equation:

   е  æх

(5.1)

where x is the distance from the beginning of the diffuse part of the DES; æ is the reciprocal of the thickness of the diffuse layer. It follows from (5.1) that the thickness of the diffuse layer, denoted by λ = 1/æ, is the distance at which the potential φδ decreases by a factor of e. In accordance with the Guy-Chapman theory, the thickness of the diffuse layer is calculated by the following relationship: 86

λ = 1/æ =

1 εε 0 RT ; I   c0i zi2 , 2 2 i 2F I

(5.2)

where ε0 is the electric constant, ε is the relative permittivity of the dispersion medium; F is the Faraday constant; I is the ionic strength; c0i and zi are the concentration and charge of the i-th ion. As can be seen from equation (5.2), the parameters of the dispersion system are influenced by the thickness of the diffuse layer, the temperature, the dielectric constant and the ionic strength of the dispersion medium. For any electro-kinetic phenomenon, the motion of the dispersed phase relative to the dispersion medium leads to a violation of the integrity of the DEL. For example, in the case of electrophoresis, the directed motion of a dispersed phase to one of the electrodes (cathode or anode) causes separation of the adsorption layer from the diffusion along the sliding plane. There is no exact location of the sliding plane, it is generally assumed that it passes along the boundary between these two layers or can be somewhat shifted to the region of the diffusive part of the DEL (Fig. 5.1). The potential on the sliding surface is called the electro-kinetic potential or the ξ potential (the zeta potential). It can be determined experimentally either by the speed of movement of the dispersed phase in the electric field or by the speed of the dispersion medium in porous bodies, since the relative rate of phase displacement depends on the magnitude of the electro-kinetic potential. According to the Guy-Chapman theory for x = 1, we can write:

ζ   x  l   δ e  χl   δ e  l/λ

(5.3)

As can be seen from equation (5.3), the magnitude of the electrokinetic potential is determined by the potential of the diffuse layer φδ and its thickness λ. It follows that such parameters of the system as the temperature, the dielectric constant of the medium, and the ionic force will also affect the value of z potential. Depending on the type of electrolyte to be introduced into the dispersion medium, it is possible not only to change the thickness of the diffusion layer and the value of the electrokinetic potential, but also to change the sign of the charge of the z 87

potential. Electrolytes, introduction of which into the dispersion medium causes compression of the diffuse part of the DEL, i.e., a decrease in the value of λ by increasing the ionic strength, are called indifferent. Indifferent electrolytes do not change the potential of the surface φ0. In contrast, non-indifferent electrolytes change the surface potential due to the specific adsorption of ions in the Helmholtz layer. For electrophoresis, the electrokinetic potential can be calculated by the Helmholtz-Smoluchowski equation:

ζ

η  ue , [V] εε0

(5.4)

where η is the viscosity of the dispersion medium (Pa·s), ε is the relative permittivity of the medium (for water at 18 °C ε = 81), ε0 is the electric constant (8.85 × 10-12 F/m), and ue is the electrophoretic mobility of sol particles. It should be noted that equation (5.4) was obtained in the assumption that the thickness of the diffusion layer is much smaller than the particle radius r. In the case of non-observance of this condition, i.e. λ ≥ r, the mobility of particles undergoes changes under the action of an electric field. This is due to the appearance of relaxation effects and electrophoretic inhibition. The first is due to the violation of the symmetry of the diffuse layer around the particle, which arises from the motion of the phases in the opposite direction, which, on the whole, leads to a decrease in the effective value of uef and ζ-potential. The second effect is also related to the ionic atmosphere: a counter flow of counter ions creates additional friction that prevents the particle from moving. In addition, additional complications may arise when calculating the ζ-potential by electrophoresis data when the particles of the dispersed phase have a pronounced anisometric structure (for example, a rod-like shape). 5.1 Determination of the electro-kinetic potential of sols by the macro-electrophoresis method The method of macro-electrophoresis makes it possible to determine the values of ζ-potentials of particles in ultra-micro-heterogeneous systems. In macro-electrophoresis, the velocity of the 88

separation of the sol-contact liquid interface is determined, which is the dispersion medium of the sol, or an electrolyte solution whose electrical conductivity is equal to the electrical conductivity of the sol. Objective: determination of the magnitude and sign of the electrokinetic potential of sol particles by the macro-electrophoresis method. Instruments and equipment: Electrophoresis unit, 100 and 250 ml conical flasks, 1 and 5 ml pipettes, 50 ml measuring cylinder. Reagents: Solutions: 1% and 2% FeCl3; 1.5% – KMnO4; 1% Na2S2O3; saturated sulfur solution in acetone; 0.1% – K4Fe (CN)6; 2% alcohol solution of rosin. First, as instructed by the teacher, the sol is prepared. Solutions of sols are obtained by the following methods: Preparation of iron hydroxide sol The hydrolysis method is often used to produce heavy metal hydroxide sols. For example, ferric chloride reacts with water according to the equation: FeCl3 + 3H2O = Fe (OH)3 + 3HCl The hydrolytic equilibrium resulting from the reaction depends on the concentration and temperature. With increasing temperature and increasing dilution, the degree of hydrolysis increases. This is used in the preparation of the iron hydroxide sol according to the method described. 85 ml of distilled water is heated to a boiling point in a conical flask. Without removing the flask from the tile, 15 ml of 2% ferric chloride are added dropwise to the boiling water. After a few minutes of boiling, a red-brown iron hydroxide sol is obtained by hydrolysis. When cooled, the reaction proceeds in the opposite direction, so the sol obtained is recommended to be still hot for dialysis. The structure of the micelle of the obtained sol can be represented as follows: {m ((Fe (OH)3)n FeO+(n-x) Cl-}z +xClPreparation of sol manganese dioxide by reduction Boil water is pipetted with 5 ml of a 1.5% solution of potassium permanganate and diluted with distilled water to 50 ml. Then 0.5-1 ml of a 1% solution of sodium thiosulfate is injected dropwise into the flask until a cherry red sol of manganese dioxide is obtained. 89

Preparation of sulfur sol To 50 ml of water, 1 ml of a saturated (without heating) sulfur solution in acetone (from a dropper) is added while agitating. A bluish white sol forms in the water with negatively charged particles. Preparation a sol of Berlin azure a) production of a negatively charged sol of Berlin azure: 25 ml of a 0.1% solution of K4Fe(CN)6 is diluted with water to 125 ml and 0.85 ml of a solution of FeCl3 is added dropwise by heating. b) production of a positively charged sol of Berlin azure: 3 ml of a 1% solution of FeCl3 is diluted with water to 100 ml and 8.5 ml of a 0.1% solution of K4Fe(CN)6 is added. Preparation of rosin sol 5-10 ml of 2% alcohol rosin solution dropwise with vigorous shaking to 100 ml of distilled water, resulting in a milky white, fairly stable sol. The order of the work The electro-kinetic potential is determined by electrophoresis in the following way: the electrophoresis analyzer is a wide U-shaped tube to which a narrow tube with a funnel is soldered, which serves to fill the instrument with the investigated sol (Fig. 5.2). 6 4

5

8

7

10

2

1 9

3 a

b

Fig. 5.2. Scheme of the device for carrying out macro-electrophoresis. 1 – a thermostat; 2 – a cell; 3 – platinum electrodes; 4 – terminals from platinum electrodes for the reference measurement; 5 – a special pipette; 6 – a three-way crane; 7 – a rubber stopper; 8 – salt bridge; 9 – test tubes with a saturated solution of copper sulfate; 10 – a copper electrode

90

Work with this device starts with pouring a little sol into the narrow tube through the funnel with a closed tap. Slightly opening the tap, fill the gap of the tap with the sol, making sure that there are no air bubbles in the slit and that the sol does not get into the narrow part of the U-shaped tube. The tap is closed and the narrow tube is filled with the sol, and the U-shaped tube with distilled water or other side liquid. In the electrophoretic U-shaped tube, a colloidal solution is introduced. If you do this carefully and slowly, a sharp boundary between the sol and the lateral fluid is obtained in the U-shaped tube. Then electrolytes connected to a constant current source are introduced, and the rate of descent of the colored boundary in the other part is observed. As soon as the level of the colored liquid column reaches the zero point of the calibration, turn on the stopwatch or notice by the watch with the second hand, for how long the painted border will move, for example for 5 mm. Measuring with a flexible wire, the distance between the electrodes (the ends of the agar siphons immersed in the side liquid) determine the average value of the potential gradient H (electric field strength) (V/m):

Н

V(V) , l(m)

(5.5)

where V is the applied voltage in volts. The value must be measured 5 – 6 times and the average value is taken. L is the distance between the electrodes (m). The electrophoretic mobility is calculated from the equation:

ue 

S τH



Sl τV

,

(5.6)

where S, (m) is the shift of the sol-contact liquid interface in time τ (s). Knowing uef it is possible to calculate the value of the electro-kinetic potential ζ by the equation (5.4), expressed in volts. 91

To convert the water viscosity values to the SI system use the following 1 poise = 0.1 Pa·s = 0.1 (m·N/M) · s, (H2O) – 0.01 poise (0.001 Pa·s) The results are written according to the following scheme in Table 5.1: Time τ, s

Distance traveled by sol, S, m

Voltage V, V

Length L, sм

Gradient of potential Н, (V/m)

Electrical speed Ue, м2/V·s

Electrokinetic potential ζ, V

Control questions: 1. What are the mechanisms for the formation of a double electric layer (DEL)? 2. What is the structure of DEL by modern theoretical concepts? 3. Explain the essence of electro-kinetic phenomena. 4. What is the electro-kinetic potential? By what methods can it be determined? 5. Write the Helmholtz-Smoluchowski equation for the ζ potential for electrophoresis. 6. What measured value is used to determine electrophoretic mobility for macro-electrophoresis?

92

6. STABILITY AND COAGULATION OF DISPERSE SYSTEMS The main colloid-chemical characteristic is dispersion, i.e. fragmentation of substance. Colloidal chemistry studies dimensions from larger than simple molecules to those visible to the naked eye (from 10-7 to 10-2 cm). The quantitative measure of dispersion is the specific surface, (S0), determined by the ratio:

So 

S , V

(6.1)

where S and V are the total surface and the volume of the dispersed phase (DP). For particles having the cubic form: So 

6l 2 l

3



6 l

,

(6.2)

where l is the length of the edge of the cube. At l = 1 cm, So = 6 cm2, and at l = 10-6 cm, So = 6 · 106 = 600 m2. Thus, when dispersion increases, the specific surface S0 also increases, reaching significant values. As S0 grows, the fraction of molecules at the interface between the phases will increase, which, according to the energy state, are "special" i.e. different from molecules in the bulk of the phase. The fraction of special molecules is f = 6 / n, where n is the number of molecules on the edge. More precisely, the following equation is proposed for a cube:

f



2 n 2  n  2n  n  2 n3

2



(6.3)

At a sufficiently high dispersion, the fraction of "special" molecules decreases, since the fraction of bulk molecules decreases, and disappears completely at n = 2. The value of S0 loses its physical meaning. 93

Surface "special" molecules have excess free energy, which accumulates when the work on breaking the bonds in the process of dispersion is performed. Thus, colloidal systems are characterized by an excess of surface (free) energy, therefore, they are thermodynamically unstable. At the same time, stability means the ability to keep the degree of dispersion and the uniform distribution of the dispersed phase in the medium unchanged in time. Since coarsening of the particles leads to a decrease in the surface energy, then in the limit, the colloids tend to an equilibrium state corresponding to the separation of the system into two phases with a minimum interface. (Such an equilibrium state can practically never occur). The problem of stability – the problem of the "life and death" of disperse systems – is one of the most important and complex. When considering stability, it is necessary to distinguish between the stability of lyophilic colloids and lyophobic colloids. Lyophilic colloids – molecular colloids, as well as lyophilic suspenoids (clays, soaps) – disperse spontaneously forming thermodinamically stable systems. We have indicated above that the surface (free) energy increases with dispersing. For lyophilic systems, the free energy (F) decreases:

ΔF  ΔU  TΔΔ < 0

(6.4)

This expression is a criterion of lyophilicity (Rehbinder et al.). The increase in entropy in the dispersion process usually contributes to a decrease in F, since the system comes to a more uniform distribution of the dispersed phase in the medium (ΔSmixing > 0). The balance of internal energy ΔU during the dispersion process consists of the energy spent on breaking molecular bonds with the formation of a new surface (cohesion work Wc) and the gain resulting from the interfacial solvation interaction (adhesion work Wa). For lyophilic systems, Wa > Wc, which means that the internal energy of the system decreases as a result of the dispersion (ΔU < 0). Here one can also see similarity of the processes of dispersion and dissolution, since dissolution, for example of crystals, is determined by the ratio of the solvation energy Wa and the destruction energy of the crystals Wc, taking into account the entropy of mixing. 94

Lyophobic colloids are characterized by a binding energy inside the dispersed phase much greater than the energy of interfacial interaction (Wc >> Wa) and this difference is not compensated by the entropy factor:

ΔF  ΔU  TΔΔ > 0

(6.5)

In this case, the dispersion does not occur spontaneously, but requires expense of external work. Lyophobic systems are thermodynamically unstable and have a significant surface tension at the interphase boundary (Wa – min). Thus, for lyophobic systems the stability problem is of paramount importance. Despite the thermodynamic instability, many lyophobic systems exist in a non-stable state for a very long time. Peskov introduced the idea of different types of stability: sedimentation and aggregation. Sedimentation stability is stability of the dispersed phase with respect to the gravity force. Violation of sedimentation resistance can be caused by: 1) settling of particles in coarsely dispersed systems; 2) isothermal distillation of small particles into large particles followed by settling of the latter; 3) loss of aggregative stability as a result of coalescence of particles (coagulation) under the influence of various factors Aggregative stability is the ability of dispersed system to keep dispersity and individuality of particles of a dispersed phase. The loss of aggregative stability as a result of coagulation leads to the destruction of the disperse system. What are the reasons that cause coagulation of colloidal particles? Numerous observations indicate a variety of reasons that cause coagulation. The influence of heat and cold, electromagnetic fields, hard radiation, mechanical effects, chemical agents lead to coagulation. All these effects destroy the energy barrier that prevents the particles from converging, and the metastable system passes into a more stable state, corresponding to the separation of the system into two phases with a minimum interface. Of all the factors that cause coagulation, the focus is on the action of electrolytes. 95

Coagulant action of electrolytes. All electrolytes without exception cause coagulation. The effect of electrolytes on the stability of lyophobic colloids can be summarized as follows: 1. Coagulation occurs at a certain critical concentration Cd of electrolytes, called the coagulation limit. 2. Coagulation is caused by an ion whose charge sign is opposite to the charge of a colloidal particle, i.e. counterion. 3. The coagulating effect of ions increases with their valency. 4. For ions of the same charge, the coagulating action increases with increasing size of the ions. The coagulation limit strictly depends on the valence of the counterion. It was found that for monovalent counterions, the coagulation limits are between 25 and 100 millimoles, for divalent – 0.52 millimoles, for trivalent in the range of 0.01-0.1 millimoles per liter. This regularity is known, as Schulze-Hardy rule, which does not establish a direct proportional relationship between the valence of the ion and its coagulating ability. The coagulating force increases much more rapidly than valence. For the As2S3 sol, Schulze found the following ratio for 1, 2 and 3 valence cations: 1: 20: 350. Other researchers found other ratios. This is due to the difficulty of obtaining the same sol with the same characteristics. Ions with the same valence, although they are close in coagulation capacity, still have different actions. For monovalent ions, we can write the following lyotropic series. Li+  Na+  K+  NH4+ It is known that the influence of electrolytes, according to the Schulze-Hardy rule, is established not only for coagulation limit, but also for electrokinetic phenomena and in general for all phenomena in which the double electric layer (DEL) plays a major role. Thus, the value of the ζ potential decreases with increasing concentration of the electrolyte and the valence of the counterion. Therefore, in many early works the stability of colloidal systems was related to the value of the ζ potential and it was assumed that a certain critical min value of ζ (~ 30 mV) corresponds to the coagulation limit, below which coagulation occurs. But it turned out that in many cases the value of the ζ-potential corresponding to the beginning of the 96

coagulation differs from 30 mV. In addition, not always a decrease in the value of the ζ-potential caused coagulation, but, on the contrary, increased stability of disperse systems. This led to the question of existence of a simple connection between the ζ-potential and stability. However, the DEL parameters play a major role in estimating stability, particularly, in determining the electrostatic repulsion forces acting between the dispersed particles. Repulsive forces do not determine the boundaries of stability, they should be considered in conjunction with the forces of attraction (van der Waals forces). The theory of stability developed by Derjagin and Landau considers the process of coagulation as a result of combined action of van der Waals attraction forces and electrostatic repulsive forces between particles. Depending on the balance of these forces between particles in a thin interlayer of liquid there occurs either a positive "disjoining pressure", preventing interaction, or a negative one, which leads to thinning of the interlayer and contact between particles. Forces of attraction. The conception of attraction forces between two neutral atoms was introduced by Van der Waals to explain the properties of real gases and liquids. Therefore, the forces of attraction are called van der Waals forces, which consist of three components: 1) dipole-dipole interaction force (Keezom force); 2) induction interaction (Debye force); 3) dispersion interaction (London force). The existence of the first two types of interaction supposes the presence of a constant dipole moment of interacting molecules or at least an induced dipole moment. These two types of forces are determined by the magnitude of the dipole moment and polarizability (the ability of the electron shells to deform under the action of an external electric field) of molecules. Tolstoy and his co-workers showed (1955) that the dispersed particles can also have an electric dipole structure that arises as a result of spontaneous unipolar orientation of single dipoles of the medium (H2O, OH-) adsorbed on their surface or as a result of orientation of the polar groups of particles of that substance. With the help of various electro-optical methods, the existence of a rigid dipole moment (thousands and millions of debyes) in many colloids, including viruses and bacteria, was proved. However, between the nonpolar molecules, the determining forces are the predominant dispersion forces (forces of London), 97

which are caused by a typical quantum-mechanical effect, and in all cases, except the extremely polar molecules (for example H2O, NH3), they are stronger than the Debye and Keezoma effect. Dispersion forces are caused by the fluctuation of electrons as they rotate around the nucleus of atoms. Electron fluctuations lead to the appearance of an oscillating dipole moment, which leads to attraction of two nonpolar molecules. For colloidal particles, which are conglomerates of atoms, due to the summation of interatomic interactions, the attractive forces of dispersed particles must be much greater than the attractive forces of individual molecules and atoms. There are two ways of calculating the interaction energy. De Beer and Hamaker proceeded from the additivity of atomic forces of attraction (the so-called microscopic theory). Lifshitz chose a macroscopic method of consideration, in which the London force is not expected to be additive. Later Renne and Niiber established that with the help of a microscopic theory one can obtain results that coincide with the macroscopic theory by introducing a correction factor that takes into account non-additivity. For colloidal particles, only dispersion forces are adding additively, whereas the orientational and inductive effects of individual molecules are largely mutually compensated. Calculation of the interaction of two plates (per 1 cm2) gives the equation: A 48π8 2

Ua  

(6.6)

For the interaction of two spherical particles Ua  

Ar , 12H

(6.7)

where Ua is the energy of attraction of two particles, A is Hamaker's constant, H is the distance between particles, r is the radius of particles. According to Hamaker theory, A = 2 n2β, where n is the number of atoms per unit volume of the particle, β  98

3 h  ν o2  α 2 , where h is 4

the Planck constant, o is the electron rotation frequency, and α is the polarizability of molecules. The main difference of forces of attraction between colloidal particles from those of the molecules is their relatively slow weakening with distance, i.e. their large range of action. The so-called long-range interaction is characteristic of colloidal particles. Forces of repulsion. The repulsion that occurs between dispersed particles is a consequence of their identical charge. It is impossible to estimate this repulsion on the basis of the Coulomb law, since the charge on the particle surface is neutralized by the charge of counterions and repulsion occurs as a result of overlapping of double electrical layers of particles. When the DEL is closed, the forces acting from the inner plates of both colloidal particles to the ions located between the approaching surfaces will not be completely shielded by the outer plates. Such a change in forces disrupts the statistical equilibrium that existed before the overlapping of the ionic atmospheres, and causes charge redistribution. Electrical equilibrium of the system also disrupts, resulting in unbalanced forces of electrical nature. The concentration of ions in the overlapping zone will be different from that in the other points of electrolyte surrounding the particles, which causes the appearance of additional forces of osmotic nature. The calculation of the energy of ion-electrostatic interaction was carried out by Deryagin and Frumkin, and was subsequently confirmed by Fervey and Overbeck. The concept of disjoining pressure, which is formed in a thin interlayer of liquid between approaching particles, was introduced into theory and theoretically substantiated by Deryagin. The disjoining pressure (P) represents the pressure difference ΔP in a thin layer of liquid and pressure P0 in the bulk liquid phase in equilibrium with the interlayer. Developed by Deryagin's school, modern concepts allow us to distinguish four main components of the disjoining pressure: a) electrostatic, caused by mutual overlapping of the DEL (positive contribution); b) molecular, due to van der Waals forces of attraction (negative contribution); 99

c) adsorption, which occurs at overlapping of molecular adsorption layers, which creates an osmotic flow towards the interlayer and leads to repulsion; d) structural, associated with the formation of boundary layers of a solvent with a special structure (positive contribution). Relation between the disjoining pressure equation and the electrical parameters of the DEL is written as: н

П    ρ  d i

(6.8)

0

where  is the bulk density of a charge, i is the potential of the plane of greatest approximation.  and  are determined using the theory of DEL. By the value of Π, we can calculate the electrostatic component (the repulsive energy Urep) of two particles 

U rep  2  П  dH

(6.9)

H/2

For the case of constancy of , a symmetric binary electrolyte, we obtain the equation: U rep 

64c o RT χ

 γ 2  e  2χχ

(6.10)

where C0 is the concentration of electrolyte, and χ is inverse to the thickness of the diffuse part of DEL. χ  1/δ  z  F 8  π  c o /ε  RT , γ 

expi /2  1

expi /2  1

Hence, the repulsive energy is a function of concentration (C0), valence (z), thickness of the DEL (), and the repulsion decreases with increasing c0 and z, and decreasing i. 100

The total forces of particle interaction. Stability of disperse systems depends on the sign and magnitude of the total interaction energy due to the addition of the ion-electrostatic repulsive energy and van der Waals attraction energy. According to the equation, the total interaction energy of the two plates is expressed by the equation: U  U rep  U a 

64c o RT χ

 γ 2  e  2χχ 

A' H2

(6.11)

The sign of U cannot be immediately predicted from the form of the equation. Considering the dependence of the energy of repulsion and attraction on H, we note that for Urep it has an exponential character, while for Ua it is power dependence. This means that when Н  0Urep  const, and Ua  ∞ (without considering the repulsive forces of the electron shells). Consequently, at small distances, attractive forces prevail. At large distances, gravity forces also prevail, because the power function decreases much more slowly than the exponential function.

Fig. 6.1. Curves of potential energy as a function of the distance between particles. 1 – forces of attraction; 2 – repulsive forces; 3 – total forces of interaction.

At medium distances repulsion for small  (i.e., dilute solutions) and large i and  can predominate. In this case, a potential barrier and two minima ("holes") appear on the curve U (H). A typical example of such curve constructed from equation (6.11) for given values of the constants is shown in Fig. 6.1. 101

Whether the repulsive forces will prevail over the forces of attraction depends on the numerical values of the constants, which determine the forces of attraction and repulsion. The distances between particles, on which the maxima and minima appear, by the order of magnitude should be the same as the thickness of the DEL, which determines the radius of action of repulsive forces. It should be noted that in most cases encountered in practice, there is no need to take into account the lag effect for London forces, since it appears at distances > 1000Å. In colloidal systems, the thickness of DEL has smaller values. The total interaction energy is determined by the concentration and valence of the electrolyte ions, the surface potential, and the value of the Hamaker constant. As the concentration of the electrolyte increases, the height of the barrier (Umax) decreases, disappears at a certain concentration, and the particles are allowed to stick together unhindered. An increase in the value of the Hamaker constant reduces the height of the barrier at constant potential and concentration. With increasing surface potential up to a certain value (~ 100 mV), repulsive forces, hence, Umax also increase. General analysis of the stability problem. The possibility that particles closely approach each other is determined by the height of the energy barrier and the depth of the holes. There are three typical cases that characterize a certain state of stability of the system. 1. The height of the barrier and the depth of the secondary minimum are small (< kT). In this case, particles approach due to the kinetic energy to the smallest possible distance with a decrease in the interaction energy to a depth of the primary minimum. Coagulation occurs due to the short-range interaction of particles. Disperse systems in this state are unstable and subjected to rapid coagulation with the formation of large aggregates. Coagulation in this case is irreversible. Rapid coagulation of disperse systems is achieved by the addition of electrolytes. 2. The height of the barrier is large (>> kT), and the depth of the secondary minimum is small (> kT). In this case, regardless of the 102

height of the barrier, the so-called long-range interaction of particles occurs. The distance corresponding to the second minimum is about 10-2 nm. A flexible connection is established – two particles can neither break up, nor approach closely and continue to exist as a pair. Other particles can join (also at great distances) this pair with formation of triples and more complex aggregates. Aggregation in the secondary minimum differs from aggregation in the primary minimum in that at such a long-range interaction the particles keep their individuality, and the entire system preserves its dispersion and specific surface area. In addition, the difference related to the depth of the secondary minimum (1kT < U < 10kT) is that aggregates formed during long-range interaction can easily decay, i.e. there is an equilibrium sol – aggregate. At a sufficient concentration of particles, long-range interaction can lead to conversion of the sol to a structured system. As the number of particles in the aggregate increases, the depth of the second minimum increases, thus contributing to collective interactions. It is established that in many cases periodic colloidal structures (PCS) are formed, possessing long-range order and representing quasi-crystalline formations. The main advantage of the DLVO theory is the justification of the Schulze-Gardi rule, which is considered as criterion for testing the theory of stability. When the coagulation limit is reached, the height of the Umax barrier approaches zero and the whole particle collision is effective (rapid coagulation). The analysis of stability of disperse systems shows that the boundary conditions for rapid coagulation in terms of Deryagin's theory can be written as 1) Umax = 0 and 2) dUmax/dH = 0Umax is the maximum energy (see Fig. 6.2). U Hк H

Fig. 6.2. The potential energy of interaction between two plates is C = Ck.

103

These conditions express a decrease in the height of the energy barrier to zero. The first condition, when substituting in (6.11) the values of Ck, Zk, Hk, corresponding to the coagulation limit, gives 64  C к  RT χк

 γ2  e

 2χ к H к

A'



(6.12)

H к2

Differentiating (6.12) with respect to H and equating the derivative to zero for U = Umax, according to the second condition, we get: 64  С к  RT  γ 2  e

 2χ к H к



A'

(6.13)

H 3к

Dividing (6.12) by (6.13), we obtain: Нк = 1/к

(6.14)

Thus, for C = Ck, the maximum potential energy of the system is reached when the plates approach each other at a distance equal to twice the thickness of the diffuse layer. Substituting (6.14) into (6.13) and taking into account that, χ к  z  F 8  π  Ск /ε  RT we find: 3/2

2

64  С к  RT  γ  e

2

'

A 

 8π  3/2  A'z  F   Cк  ε  RT 

χ 3к

3

3

or 3 С1/2 к  z  const

(6.15)

Consequently CК 

Const z

104

6



B z6

(6.16)

This expression represents Deryagin's "sixth-degree law" and establishes the dependence of the coagulating ability of the ion (Vk = 1/Sk) on the charge of the z ion. It follows that for single-, double-, and triple charged ions the ratio is 1: 64: 729 and agrees well with the Schulze-Hardy rule. Based on the theory of the double layer and taking into account the forces of attraction an expression for the criteria for the stability of sols was obtained: nz6 = const ,

(6.17)

where n is the number concentration of particles; z is the valence of counter-ions. To fix particles in the second minimum, the DLVO theory leads to a value of the exponent equal to 2.5, which coordinates well with many experimental data on long-range interaction.

6.1 Determination of coagulation thresholds for sols of manganese dioxide and iron hydroxide Purpose of the work: 1. Determine the coagulation thresholds of the sol (Fe(OH)3, MnO2, etc.) with electrolytes with different charge of the coagulating ion and find the dependence of the coagulation capacity on the valence of the coagulation ion (SchulzeGardi rule). Check the implementation of the Deryagin's law of the sixth degree. Instruments and reagents: Photocolorimeter FEK-56M; tubes with a capacity of 20 ml; a 250 ml conical flask; graduated pipettes; solutions of ferric chloride, potassium permanganate, sodium thiosulfate, sodium chloride (4 n), calcium chloride (0.01 n), aluminum chloride (0.001 n), or sodium chloride (4 n), sodium sulfate (0.01 n), and potassium hexacyanoferrate (0.001 n). Procedure: According to the known methods (see Chapter 5), a sol (MnO2, Fe(OH)3) is obtained at the instruction of the teacher. 105

MnO2 sol has a negative charge, therefore, cations will coagulate with it, and the Fe(OH)3 sol is positively charged, it is coagulated by anions. The work on the determination of the coagulation thresholds of sol by electrolytes consists of a series of successive determinations of the smallest concentrations of electrolytes that cause coagulation. First series of experiments Six clean tubes are numbered with pencil. Measure 10 ml of the initial NaCl solution in the first test tube and 9 ml of distilled water into the remaining tubes. 1 ml of solution is transferred from the first test tube to the second and mixed well. Then, transfer 1 ml of solution from the second test tube, into the third. After mixing 1 ml of solution from the third test tube, transfer it to the fourth tube. Transfer 1 ml of solution from the fourth into the fifth. Pour out 1 ml of solution from the fifth tube. The sixth tube remains with clean water and serves as a control sample after the addition of the sol. 1 ml of the sol (MnO2 for NaCl, CaCl2, AlCl3) or Fe(OH)3 (for NaCl, Na2SO4, K3Fe(CN)6) is pipetted into all six tubes, thoroughly mixed, the time is noted and is allowed to stand for 15 minutes. The NaCl concentration decreases in the resulting row of tubes by 10 times from the first to the fifth. If C0 denotes the initial concentration of NaCl, the NaCl concentration in the tube with the serial number "n" can be determined by the formula: Cn1 = C0 10n-1, g-eq./l

(6.18)

Calculate the concentration of NaCl in each tube and then record in Table 6.1 Table 6.1

No.

Concentration

1

2

3

4

5

6 (contr)

С (NaCl), g-eq./l

At the end of the time, mark the table with a "+" sign, where there is coagulation, and with a "-" sign, where it doesn't occur. The minimum concentration of Cn, where coagulation is observed, is approximately the threshold of coagulation and serves as the initial one for a more accurate determination in the second series of experiments. 106

Second series of experiments Pour out solutions from all tubes, except the sixth. Prepare 50 ml of a solution of Cn concentration from the initial solution of Co by pipetting the required amount of solution into a clean cone (50 ml) and bring it to the mark. Make a series of four tubes and measure consistently 8, 6, 4, 2 ml of solution Cn and add up to 9 ml of distilled water. Then add 1 ml of sol, mix and leave for 15 minutes. Write in table 6.2, where the composition of the solution in each tube is written and the results of the experiment: Table 6.2

No. 1 2 3

Volume V NaCl, ml V H2O, ml V золь, ml

1 8 1 1

2 6 3 1

3 4 5 1

4 2 7 1

5 (contr) 9 1

The concentration of solutions is calculated by the formula: Cn =

Cn 10

 C1исх

(6.19)

Mark the test tubes with a "+" sign where there is coagulation. The minimum concentration, where the coagulation occurred, is considered as the threshold of coagulation. If a coagulation threshold is required to be determined even more accurately, then a third series of experiments is carried out by analogy with the second. Similarly, two series of experiments with solutions of CaCl2 and AlCl3 for the MnO2 sol; Na2SO4 and K3Fe(CN)6 and for the Fe(OH)3 sol are carried out. The coagulation thresholds found in the second series of experiments, and the coagulation capacity of the cations (anions) are compared and recorded in Table 6.3. The least coagulating ability is possessed by that cation (anion), for which the coagulation threshold is the greatest. Table 6.3

Cation (Anion)

С – coagulation threshold

107

Coagulation ability

The less is the coagulation threshold compared to the first, the more is the coagulation ability of another cation (anion). Thus, we will get the coagulating ability of the sodium ion of the calcium ion

С Na  С

C Na

, of the aluminum ion

CAl2

Сa 2 

manganese dioxide sol and, similarly, of the chloride ion sulfate ion

CCl Cso2

, of the hexacyanoferrate ion

4

CCl CFeCN  2

C Na  C Na 

,

, – for the CCl CCl

, of the

– for the iron

6

hydroxide sol. It is necessary to make conclusions whether the Schulze-Gardi rule applies to this sol based on the obtained data. It's possible to check from the values of the coagulation threshold, whether the value rule is satisfied (Deryagin criterion), Ск = const/z6 – and if there following relation is observed: Vk' : Vk'' : Vk''' = 1 : 64 : 729

Write the formulas of the micelle of the sol of manganese dioxide and iron hydroxide. 6.2. Synthesis of hydrosol of iron hydroxide, study of its coagulation and stabilization Stability of the system can be infinitely increased when introducing low- and high-molecular surfactants into the sol. The stabilizing effect of surfactants is associated with adsorption on the surface of particles. Long-chain surfactants, and in particular macromolecules of high molecular weight substances (HMS), carrying their own solvate layers, form adsorption-solvate layers of great length and density, which overlap not only the first but also in many cases the second potential well. According to Rebinder, in the case of adsorption, HMS adsorption-solvate should be considered as lyophilic film jelly (gel-like structured layer). Such layers possess resistance to shear, elasticity, high viscosity and create a "structural-mechanical barrier" that prevents contact of particles. Structuring occurs as a 108

result of orientation of molecules and lateral cohesion – hydrophobic interaction of nonpolar groups, formation of hydrogen bonds, dipoledipole attraction between adjacent adsorbed molecules. The strength of adsorption-solvate layers increases with time, reaching a limiting value in a few hours because of small diffusion coefficients and slow orientation of macromolecules at the interface. It is necessary that the surface tension on the outer surface of the adsorption-solvate layer is small and does not increase sharply to the surface of the particle to stabilize the sols. If this condition is not met, coagulation occurs by adhering the adsorption layers. The ability of the HMS to form adsorption-solvate layers on the surface of particles is called a protective action. Stabilized sols often acquire the properties of a protective colloid, for example, in terms of the -potential. Protection of disperse systems is used in the manufacture of medicines. Bactericidal preparations protargol and kollargol are sols of metallic silver, stabilized with proteins. They form a very fine powder, spontaneously "dissolved" in water with the formation of a highly dispersed sol when evaporated. Bactericidal properties are not screened by the protein coat and extend to the aqueous medium surrounding the particles. Zygmondi proposed the so-called "golden number" to describe the protective effect of the HMS, which refers to the number of mg of HMS added to 10 ml of red gold sol to prevent it from becoming blue when 1 ml of 10% NaCl solution is introduced into the system. Ag, Fe(OH)3 etc. are sometimes used instead of gold sol (correspondingly, it is said "silver", "iron", etc. number). Purpose of the work: Objective: to determine the coagulation thresholds of the sol and to study its dependence on the charge of the coagulating ion; determination of the protective number of the stabilizer. Instruments and reagents: photocolorimeter FEK-56 M, electric tiles. Conical flask with a capacity of 250 ml. Test tubes with a capacity of 20 ml. Pipettes, 2% of ferric chloride solution (III). 0.00125 M of sodium sulfate, 0.5 M of sodium acetate, 0.01% of gelatin. Procedure: 20 ml of ferric chloride is poured to prepare the hydrosol of Fe(OH)3 in a flask with 500 ml of boiling distilled water. The resulting reddish – brown sol is cooled to room temperature. Next, the coagulation of the iron hydroxide sol is investigated when sodium sulfate and sodium acetate solutions are added there by measuring the optical density of the resulting systems. 109

In 10 tubes pour 10 ml of sol, water and electrolyte (solution of Na2SO4 or CH3COONa) in the following volumes (for Na2SO4 1-7 tubes): Table 6.4

No. of tube

1

Volume of water, ml Volume of electrolyte, ml

2

3

4

5

6

7

8

9

10

10.0

9.5 9.25 9.0 8.0 7.0 6.0 5.5 5.25 5.0

0

0.5 0.75 1.0 2.0 3.0 4.0 4.5 4.75 5.0

Determination of the optical density (D) is carried out on a photocolorimeter FEK-56 M. The FEK-56 M device has 4 filters: neutral, green, blue and red. A schematic diagram of the device is shown in Fig. 6.3. The light beam from the light source 1, passing through the light filter 2, falls on the prism 3, which divides the light beam into two streams. Reflecting from the mirrors 4, the parallel light rays pass through the cuvettes 5 and 11, fall on the mirrors 7 and 9 and then go to the photocells 8. In the course of the right light beam, two cuvettes (one with the sol, the other with the dispersion medium) can be installed in series. 1 2 3

4

5

11

10 9

6 8

Fig. 6.3. The optical scheme of the FEK-56 M device: 1 – a light source; 2 – a light filter; 3 – a prism; 4, 7, 9 – deflecting mirrors; 5, 11 – cuvettes; 6, 10 – sliding diaphragms; 8 – photocells.

110

The sliding diaphragm 6, located along the right ray of light, changes its area when the associated drum rotates, and thereby changes the intensity of the light flux incident on the right photocell. The sliding diaphragm 10, located along the path of the left ray, serves to attenuate the intensity of the light flux incident on the left photocell. When the intensities of both light fluxes are equal, the arrow of the recording microammeter is in the zero position. The right light beam is a measuring light, the left one is a compensating beam. The procedure for working on the FEK-56 M device is as follows. The photoelectrocolorimeter is turned on and all measurements are made after 30 minutes. Set the electrical zero of the device, for which use the handle on the top panel of the device to overlap the light rays by the curtain (handle in the right position) and by the handle "zero" on the left panel, set the microammeter needle to "0". A cuvette filled with a dispersion medium is placed on the path of the left light beam. Two cuvettes are placed in the right cuvette holder: one with the dispersion medium, the other with the system under study (sol), and by the rotation of the handle on the right panel of the instrument, a cuvette with a sol is placed on the path of the right light beam. Indices of the right and left drums are set to "0" on the scale of optical density (printed in red numerals). Then the shutter, overlapping the light rays, is transferred to the "open" position. Due to the absorption or scattering of light by the system under investigation (in this case, scattering), the light flux of lower intensity will fall on the right photocell than on the left photocell, and the microampermeter arrow is returned to "0" (equalize the intensities of both light fluxes). Then, a cuvette with a dispersion medium is placed along the right ray by turning the handle on the right panel of the device. In this case, the needle of the microampermeter, set to "0" shifts as the photometric equilibrium is again violated (the dispersion medium is more transparent and the intensity of the light flux incident on the right photocell increases). Rotation of the right drum achieves the initial zero position of the arrow and the value of the optical density of the system under investigation is counted on the scale of the right drum. The cuvette with the test solution is washed after each measurement of the optical density and rinsed with distilled water. The obtained data is recorded in Table 6.5. 111

Table 6.5 Results of studying of coagulation of the iron hydroxide sol by the optical method

Optical density, A

Volume of the electrolyte, ml

Na2SO4

CH3COONa

The electrolyte is introduced into each sample of the sol 2-4 minutes before the measurement of its optical density. Measure the optical density of the sol in each sample using a photocolorimeter and a light filter No. 8 or No. 9. The obtained data is recorded in Table 6.5. A dependence graph A  f(Vel ) for CH3COONa and Na2SO4 is obtained, and threshold volumes of electrolyte Vc which cause rapid coagulation are found. The value of the coagulation threshold Cc is recorded according to the formula:

Сc 

Сel  Vc , V

where Сel is the concentration of the introduced electrolyte, mol/l; V is the volume of the sol, ml. Compare the found values of Cc for Na2SO4 and CH3COONa, explain them in accordance with the Schulze-Gardi rule and the Deryagin-Landau law. The protective number of the polymer, gelatin, relative to the ferric hydroxide sol is then determined. For this, 10 samples are prepared by pouring in the tubes sol and solutions in the following volume and sequence: Table 6.6

No. of tube Volume of sole, ml Volume of water, ml Volume of gelatin solution, ml

1 2 3 4 5 6 7 8 9 10 10 10 10 10 10 10 10 10 10 10 Up to 20 ml, taking into the account the volume of sol, gelatin and electrolyte 5

4

3.5

112

3.0

2.5

2.0

1.5

1.0

0.5

0

The total volume of samples should be the same and equal 20 ml as in case of studying coagulation. Electrolyte-coagulator is added 10-15 minutes after the introduction of gelatin. The optical density of the sol is measured 3-5 minutes after the electrolyte is introduced. The value of A is written in Table 6.7 Table 6.7

No. of tube

Volume of gelatin solution, ml

Optical density, A

A graph of the dependence A = f (Vst) is obtained. The volume of gelatin solution Vgel necessary to prevent coagulation of the sol is found and the value of S is calculated by the formula: S = Cst · Vgel / V The value of Vgel corresponds to the volume of the stabilizer in the ash containing the electrolyte threshold volume, at which the lower horizontal section appears on the curve of the dependence A = f(Vst) (Fig. 6.4)

Fig. 6.4. Dependence of optical density D on a) the volume of electrolyte-coagulator Vel; b) the volume of the stabilizer Vst. Control questions: 1. What is meant by the stability of disperse systems? 2. What are the reasons for the difference in the stability of lyophilic and lyophobic systems?

113

3. What kinds of resistance are known in accordance with the classification of Peskov? 4. What is the process of coagulation and what are the causes that cause the coagulation of disperse systems? 5. Which ion causes coalescence of the sols and what characteristics of the ion determine its coagulability? 6. What is the regularity of the Schulze-Gardi rule? 7. When does the alternation of coagulation and stability zones occur? 8. What is the difference between attractive forces acting between individual molecules and colloidal particles? 9. What are the causes of appearance of repulsive forces between colloidal particles? 10. What are the causes of the disjoining pressure? 11. What is the reason for the loss of stability of the disperse system during neutralization coagulation? 12. What determines the form of potential interaction curves for particles? 13. What is the feature of long-range interaction of dispersed particles? 14. What does Deryagin's "law of the sixth degree" establish?

114

7. FORMATION AND PROPERTIES OF LYOPHOBIC DISPERSE SYSTEMS 7.1 Preparation of emulsions and study of their properties There are two basic types of emulsions – the dispersion of oil in water (o/w) and the dispersion of water in oil (w/o). The first refer to the direct-type emulsions, the second – to the inverse emulsion. Depending on the content of the dispersed phase, the emulsions are classified into dilute (the content of the dispersed phase is less than 1% by volume), concentrated (up to 74% of the volume) and highly concentrated (over 74% of the volume). Emulsions are typically lyophobic disperse systems (with the exception of spontaneously occurring "critical" emulsions). The loss of their aggregative stability can be caused by isothermal distillation or coagulation (coalescence of droplets) and it is usually accompanied by the loss of sedimentation stability (stratification of the system). As a measure of stability of emulsion, it is possible to take the time of existence of a certain volume of the emulsion before its complete stratification. Stability of emulsion is increased by introducing of a stabilizator (an emulsifier) into the system, the role of which is played by electrolytes, surfactants and high-molecular compounds. The aggregative stability of emulsions is determined by the same factors that cause the resistance to coagulation of other lyophobic disperse systems. Diluted emulsions can be fairly stable in the presence of such weak emulsifiers as electrolytes. The stability of these emulsions is mainly caused by the presence of a double electrical layer on the particles of the dispersed phase. The stability of concentrated and highly concentrated emulsions is in most cases determined by the action of a structural-mechanical barrier in the formation of adsorption layers of the emulsifier. Usually, formed interphase adsorption layers cause a smooth change in the properties of the transition zone at the interface of the two liquid phases, increasing the lyophilicity of the particles of the dispersed phase. The strongest stabilizing effect is produced by high-molecular compounds and colloid surfactants (soaps, nonionic surfactants) whose adsorption layers have a gel-like structure and are strongly hydrated. 115

The type of emulsion formed during the mechanical dispersion significantly depends on the relation of the volumes of phases. The liquid that has a larger volume usually becomes a dispersion medium. In dispersing with an equal volume of two liquids emulsions of both types are formed, but survives the one that has a higher aggregate stability and is determined by the nature of the emulsifier. The ability of an emulsifier to provide stability of one or another type of emulsion is determined by the energy of its interaction with the polar and nonpolar media, which can be characterized by a semi-empirical characteristic – the number of the hydrophilic-lipophilic balance (HLB) of surfactants. Surfactants that have low HLB values (2-6) are more soluble in organic solvents and stabilize the emulsion w/o, whereas surfactants with HLB = 12-18 dissolve better in water and stabilize o/w emulsion. Alkaline salts of fatty acids of average molecular weight always give emulsions of o/w type, and salts of divalent metals, for example magnesium, give emulsions of w/o type. With a gradual increase in concentration of divalent ions in the emulsion of o/w type, which is stabilized by soap with a cation of a singly charged metal, the emulsion is converted and transits into an emulsion of the w/o type. A special case is the stabilization of emulsions by highly disperse powders. Such stabilization is possible with limited selective wetting of powders (when the contact angle θ is greater than 0°, but less than 180°). In this case, the powders stabilize the phase that is poorly wetted. Thus, hydrophilic chalk "armors" the oil phase and does not allow the oil droplets to coalesce in the aqueous dispersion medium. In this case, the contact angle, which characterizes selective wetting, in explaining the stabilization of emulsions by fine – dispersed powders is an analog of HLB of surfactant molecules. In practice, the type of emulsions is determined by the following methods. By dilution method, the drop of emulsion is introduced into a test tube with water. If the drop is evenly dispersed in the water, it is an emulsion of o/w. The drop of emulsion w/o will not be dispersed in water. According to the method of coloring the continuous phase, several crystals of a water-soluble dye, for example, methyl orange or methylene blue, color the emulsion of o/w evenly throughout the volume. The emulsion of w/o type is evenly colored throughout the volume by a liposoluble dye. The type of emulsions can 116

also be determined from its electrical conductivity (conductivity method). High values of electrical conductivity indicate that the dispersion medium is a polar liquid, and the emulsion refers to the o/w type. Small values of the electrical conductivity indicate the formation of a reverse emulsion (type w/o). The purpose of work: obtaining an emulsion, determining its type and studying its stability; obtaining a reverse emulsion. Devices and reagents: Device for obtaining an emulsion, stopwatch, cylinder with divisions; various solutions of surfactants with a concentration of 10-2 M. The order of implementation of work: The surfactant solutions are prepared by diluting the initial solution (0.01 M) according to the following records (Table 7.1): Table 7.1

Number of the flask

1

2

3

4

5

The volume of the surfactant solution, ml

0.5

1

1.5

2

2.5

The volume of water, ml

4.5

4

3.5

3

2.5

Concentrations of the obtained surfactant solutions are calculated. In a ceramic beaker pour 5 ml of surfactant solution (from the flask No.1) and add 5 ml of oil. Then an emulsion is obtained by setting or shaking for 5 min. Immediately after preparation, the emulsion is poured in the amount of 10 ml into a test tube with fissions and the time of separation into two phases is determined. The rest of the emulsion is transferred to a flask and its type is determined. The stability of the emulsion is determined by the amount of the separated dispersed phase. After the end of emulsification, the test tube with the emulsion is installed in a rack and the stopwatch is started. The amount of exfoliating oil (or water) at the time τ before complete stratification into two phases is fixed. Measurements are made at first every minute, then after 5-10 minutes. The results of measurements are recorded in Table 7.2: 117

Table 7.2

Counting time, s

a, ml

H, %

a – the released amount of the disperse phase, ml H – the released amount of the dispersed phase as a percentage of its total volume (5 ml) is calculated by the formula: H

a  100% 5

(7.1)

Draw a graph H = f(τ). The point found by extrapolation of the initial rectilinear portion of the curve to the ordinate on the line H = 100% to the abscissa is the life time of emulsion A. According to the obtained data draw a graph A = f (Csurfactant) In the same way the emulsion is prepared with other solutions of surfactant (flasks 2-5), the life time of emulsion is determined and calculated. Determination of the type of emulsion. 1. A drop of emulsion and a drop of water are placed on the slide and tilt so that the droplets come in contact. If the drops merge, the dispersion medium is water (the emulsion is a direct-type), if do not merge – oil (the emulsion – reverse). 2. A drop of emulsion is applied to the filter paper. If the medium is water, the drop is immediately absorbed by the paper, on which a greasy stain remains. A drop of emulsion w/o is not absorbed. 7.2 Obtaining a reverse emulsion The order of implementation of work: Using the initial 0.01 M surfactant solution, an emulsion of vaseline oil (sunflower oil) is prepared in water (as instructed by the teacher) in accordance with method 1 and its life time is determined. 15 ml of 0.01 M surfactant solution is mixed with 15 ml of oil and emulsified in the installation. 10 ml of the obtained emulsion is transferred to a test tube with division and its life time is determined. The type of emulsion is determined. 118

The remaining part of the emulsion is mixed with 5 ml of electrolyte solution and emulsified in the installation or shaken for 5 minutes. 10 ml is transfered into a test tube and the life time of A is measured. The type of emulsion is determined. 7.3 Preparation of foams and study of their properties Foam – the dispersion of gas (more often air) in a liquid or solid dispersion medium – is a typical lyophobic system. There are diluted gas dispersions in a liquid – gas emulsions or spherical foams, in which the concentration of gas is small, and the thickness of liquid interlayers is comparable to the size of gas bubbles, and real foams with a gas phase content of more than 70% by volume. The structure of foams is determined by the ratio of the volumes of the gas and liquid phases, and depending on this ratio the foam cells can have a spherical or polyhedral (polyhedral) shape (Fig. 7.1). unit

membrane

a

b

duet

Fig. 7.1. A ball foam element of three bubbles (a) and a unit cell of polyhedral foam (b)

Cells of foam take a spherical shape when the volume of the gas phase exceeds the volume of the liquid by no more than 10-20 times. In such foams, the bubble films have a relatively large thickness. The smaller the ratio of the volumes of the gas and liquid phases, the thicker the film is. The cells of foams, in which this ratio is several tens or even 119

hundreds, are separated by very thin liquid films; their cells are polyhedra. In the process of construction, the spherical shape of the foam bubbles turns into a multifaceted one due to thinning of the films. Foam, like any disperse system, can be obtained in two ways: by combining very small (microscopic) gas bubbles into larger ones (condensation method) or by crushing large air bubbles into small ones (dispersion method). In the dispersed production process, the foam is formed as a result of intensive joint dispersion of the foaming solution and air. The condensation method of foaming can be performed by changing the parameters of the physical state of the system, for example, by lowering the pressure under the solution, by increasing the temperature of the solutions or by introducing into the solution substances that reduce the solubility of gases, as a result of chemical reactions. To evaluate foaming solutions and foams prepared from them, researchers use a variety of criteria: the volume or height of the foam column obtained under certain experimental conditions, the ratio of the height of the foam column to the time of its complete destruction, the change in the volume (height of the column) of the foam in time presented in the form of graphs, etc. The criterion more objective than the volume or height of the foam pillar is the multiplicity of the foam K – the ratio of the volume of foam to the volume of fluid contained in the foam: K =

Vg Vf (Vg  Vl ) ,  1 + Vlf Vl Vl

(7.2)

where Vf, Vl in foam are the volume of foam and the volume of liquid in the foam, Vl, Vg are the volumes of the liquid and gas phase. In construction and construction materials industry, foam is used with a multiplicity of 5-10, in laundries 10-20, in firefighting 70-90. Purpose of work: Acquaintance with the method for obtaining foams and determining the effect of concentration of surfactant solutions on stability of foams. Devices and reagents: Device for foam production, stopwatch, cylinder with divisions; various solutions of surfactants with concentrations of 10-2 M, 10-3 M, 10-4 M. Performance of work: Below is a diagram of the device for obtaining foam (Fig. 9.2). A solution of a foaming substance with a 120

volume of 10 ml is poured into a graduated cylinder of volume 600 ml. With the help of a micro-compressor to which a filter is attached, whose pore sizes range from 40 to 100 μm, a flow of air is supplied to the solution for 1 minute. The filter used must be clean. The experiments are carried out at room temperature.

Fig. 7.2. A foam device

The obtained data is added to Table 7.3: Table 7.3

Concentration, Сsurf, М

, s

Total volume V, ml

Volume of liquid, Vl, ml

Volume of foam Vf, ml

Volume of liquid in foam Vlf

Multiplicity of foam К

30 s 60 s 90 s

According to the obtained data, graphs of the dependence Vf = f () are constructed; Vg = f (); K = f () and determine the time during which the foam breaks down and compare with data obtained for other concentrations or other surfactants. Control questions 1. How are emulsions classified? 2. What substances are used as stabilizers for direct and inverse emulsions? 3. What are the features of stabilization of foams? 4. What parameters characterize the stability of foams? 5. Give examples of practical use of foams, and emulsions.

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REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.

Amanzholova E.S. The method of sedimentation analysis of coarse systems. – Alma-Ata: KazSU, 1980. – 34 p. Amanzholova E.S., Musabekov K.B. Method for determining the specific surface of activated carbon during the adsorption of acetic acid from aqueous solutions. – Alma-Ata: KazGU, 1985. – 22 p. Laboratory work and tasks in colloid chemistry / Edited by Yu.G. Frolov and A.S. Grodsky. – Moscow: Chemistry, 1986. – 216 р. Friedrichsberg D.A. The course of colloid chemistry. – St. Pb.: Chemistry, 1995. – 368 p. Frolov Yu.G. The course of colloid chemistry. Surface phenomena and disperse systems. – M.: Chemistry, 1989. – 464 p. Schukin E.D., Pertsov A.V., Amelina E.A. Colloid chemistry. – M.: High School, 2006. – 444 p. Gelfman M.I., Kovalevich O.V., Yustratov V.P. Colloid chemistry. – St. Pb.: Lan, 2004. – 336 p. Calculations and problems of colloid chemistry / Edited by V.I. Baranova. – M.: High School, 1983. – 215 р.

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BIBLIOGRAPHY 1. 2. 3. 4. 5. 6. 7. 8.

Aмaнжоловa Е.С. Методикa проведения седиментaционного aнaлизa грубодисперсных систем. – Aлмa-Aтa: КaзГУ, 1980. – 34 с. Aмaнжоловa Е.С., Мусaбеков К.Б. Методикa определения удельной поверхности aктивировaнного угля по aдсорбции уксусной кислоты из водных рaстворов. – Aлмa-Aтa: КaзГУ, 1985. – 22 с. Лaборaторные рaботы и зaдaчи по коллоидной химии / под ред. Ю.Г. Фроловa и A.С. Гродского. – М.: Химия. 1986. – 216 с. Фридрихсберг Д.A. Курс коллоидной химии. – СПб.: Химия, 1995. – 368 с. Фролов Ю.Г. Курс коллоидной химии. Поверхностные явления и дисперсные системы. – М.: Химия, 1989. – 464 с. Щукин Е.Д., Перцов A.В., Aмелинa Е.A. Коллоиднaя химия. – М.: Высшaя школa, 2006. – 444 с. Гельфмaн М.И., Ковaлевич О.В., Юстрaтов В.П. Коллоиднaя химия. – СПб.: Лaнь, 2004. – 336 с. Рaсчеты и зaдaчи по коллоидной химии / под ред. В.И. Бaрaновой. – М.: Высшaя школa, 1983. – 215 с.

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CONTENT PREFACE ................................................................................................. 3 1. ADSORPTION FROM SOLUTIONS .................................................. 4 1.1 Determination of the specific surface area of solid adsorbent ............. 15 1.2 Investigation of adsorption on fabric ................................................... 21 1.3 Adsorption of acetic acid from aqueous solutions with activated carbon ................................................................................ 22 2. INFLUENCE OF SURFACE-ACTIVE SUBSTANCES ON WETTING AND ADHESION ........................................................... 40 2.1 Investigation of wetting of the solid surface and determination of adhesion work ......................................................... 43 2.2 Determination of unknown concentration of surfactant by the wetting isotherm ........................................................ 45 2.3 Determination of the wetting contact angle by measuring droplet parameters .............................................................. 46 3. DETERMINATION OF CRITICAL CONCENTRATION OF MICELLE FORMATION OF SURFACTANTS................................ 49 3.1 Determination of critical concentration of micelle formation by the method of solubilization ................................................................. 53 3.2 Determination of critical concentration of micelle formation by the surface tension ............................................................... 55 3.3 Determination of critical concentration of micelle formation by the conductometric method.................................................. 57 4. SEDIMENTATION ANALYSIS OF SUSPENSIONS ........................ 62 4.1 Sedimentation analysis by Figurovsky ................................................ 63 4.2 Sedimentation analysis of suspensions on torsion scales .................... 82 5. ELECTRO-KINETIC PHENOMENA .................................................. 85 5.1 Determination of the electro-kinetic potential of the sol by the macro-electrophoresis method .................................................. 88 6. STABILITY AND COAGULATION OF DISPERSE SYSTEMS ....................................................................... 93

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6.1 Determination of coagulation thresholds for sols of manganese dioxide and iron hydroxide................................................. 105 6.2 Synthesis of hydrosol of iron hydroxide, study of its coagulation and stabilization ............................................................ 108 7. FORMATION AND PROPERTIES OF LYOPHOBIC DISPERSE SYSTEMS ................................................ 115 7.1 Preparation of emulsions and study of their properties ....................... 115 7.2 Obtaining a reverse emulsion .............................................................. 118 7.3 Preparation of foams and study of their properties .............................. 119 REFERENCES.......................................................................................... 122

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Educational edition

Kuanyshbek Bituovich Musabekov Sagdat Mederbekovna Tazhibayeva Kainzhamal Iskanovna Omarova Azimbek Kokanbaevich Kokanbayev Saltanat Shoreevna Kumargaliyeva Akbota Orazbakeevna Adilbekova Zhanar Beysembaevna Ospanova Orynkul Arykbekovna Esimova Moldir Zhadraevna Kerimkulova

LABORATORY WORKS IN COLLOID CHEMISTRY Editor: L. Strautman Typesetting: U. Moldasheva Cover design: R. Skakov IB №13667

Signed for publishing 22.06.2020. Format 60x84 1/16. Offset paper. Digital printing. Volume 8 printer's sheet. 100 copies. Order №9561. Publishing house "Qazaq University" Al-Farabi Kazakh National University KazNU, 71 Al-Farabi, 050040, Almaty Printed in the printing office of the "Qazaq University" Publishing House.

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