Some aspects of adsorption processes occurring on titanium dioxide particles

Some aspects of adsorption processes occurring on titanium dioxide particles

141 Progress in Organic Coatings, 7 (1979) 141-166 @ Elsevier Sequoia S.A., Lausanne - Printed in Switzerland SOME ASPECTS OF ADSORPTION TITANIUM DI...

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141

Progress in Organic Coatings, 7 (1979) 141-166 @ Elsevier Sequoia S.A., Lausanne - Printed in Switzerland

SOME ASPECTS OF ADSORPTION TITANIUM DIOXIDE PARTICLES P. M. HEERTJES,

PROCESSES OCCURRING ON

C. I. SMITS* and P. M. M. VERVOORN

Laboratory of Chemical Engineering,

University of Technology,

Delft (The Netherlands)

Contents 1 Introduction.

141

.............................................

2 Results of the adsorption experiments ............................. 2.1 The adsorption of an alkyd resin. ............................. 2.1.1 Alkyd resin adsorption from dilute solutions ................. 2.1.2 Alkyd resin adsorption from concentrated solutions. ............ 2.1.3 Alkyd resin adsorption on precoated titanium dioxide pigments. .... 2.1.4 The adsorption of steric acid and linoleic acid in the presence of the alkydresin ........................................ 2.2 The adsorption of water on Tiofine R-30 ........................ 2.3 The adsorption of saturated fatty acids .........................

143 143 144 148 149

3 The hehaviour of some systems built up of 3.1 The rheologicai behaviour of titanium 3.2 The influence of adsorption of water strength of titanium dioxide granules.

titanium dioxide .............. dioxide dispersions ............. and fatty acids on the formation and

161 161

..........................

163

References.

................................................

150 153 157

165

1. Introduction Stabilization of pigment dispersions in apolar media is mainly caused by the mechanism of steric hindrance. This mechanism occurs if the dispersed particles are covered by an adsorbed layer which prevents the particles approaching each other closely enough for irreversible flocculation to result. Theoretical investigations [l - 31 have shown that the degree of stability is strongly dependent on the composition and the thickness of the adsorbed layer. Due to the important role of the adsorbed layer in the stabilization of pigment dispersion many investigations have been carried out on the adsorption of binders on pigments [4 - 141, in particular of alkyd resin on titanium dioxide pigments. The alkyd resin adsorption occurs mainly by the forma tion of hydrogen bonds between the polar groups of the alkyd resin and those present on the pigment surface. Also, interactions via the n-electrons of the aromatic nuclei and the double bonds in the alkyd resin molecules will contribute to the adsorption process. *Present address: Sigma Coatings B.V., Uithoorn, The Netherlands.

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Investigations carried out in the early sixties [4, 51 have shown that the alkyd resin adsorption from dilute solutions can be very well described by means of a Langmuir isotherm. An adsorption saturation value is found which indicates that the alkyd resin molecules are adsorbed in the form of a monomolecular layer. The location of the isotherm depends on the physical properties of pigment, resin and solvent, and according to Doorgest [ 51, on the amount of water present in the system. This last aspect is rather important because none of the pigments used in practice is completely free of water. The investigations of Schiitte and RehaEek [8 - 111 and of Goldsbrough and Peacock [ 131 have shown that the adsorption isotherm starts to decline at increasing relatively high equilibrium concentration, which is caused by the entrapment of solvent molecules in the adsorbed layer. One aspect of the alkyd resin adsorption has received scant attention so far, that is the size of the alkyd resin molecules preferentially adsorbed. Based on the fact that the acid number and the hydroxyl number of the adsorbed alkyd resin are larger than those of the initial resin [ 51, it is generally assumed that the polar, low molecular alkyd resin fractions are preferentially adsorbed. This assumption can be verified by comparing the molecular size distributions (MSD) of the initial resin and the residual resin. This method has hardly been applied until now, probably due to the lack of rapid and reliable techniques to determine the MSD of alkyd resins. With the introduction of gel permeation chromatography it has become possible to carry out such an investigation in a rather easy way, as has been shown by Felter and Ray [ 151. Using this technique these authors have shown that high molecular weight polyvinylchloride polymer was preferentially removed from chlorobenzene solutions by adsorption on the surface of calcium carbonate. With the same technique Crow1 [16] showed that both the low and the high molecular fractions of a soya pentaerythritol long oil alkyd are adsorbed on a titanium dioxide surface. Crow1 reports that the MSD of the residual resin in the adsorption process still varies even after contact times of several weeks. From this he concludes that the adsorption equilibrium will only very slowly be reached. Using the same method, adsorption of an alkyd resin on titanium dioxide has also been studied by two of the present authors. The results have already been published in part [ 141. The adsorption behaviour of alkyd resins is of great complexity and the use of many additives by paint manufacturers makes the practical situation even more complicated. To increase the rate of the dispersion process, for instance, dispersing agents are added to the millbase. The dispersing agents used are generally non-polymeric surfactants with a strong affinity for the pigment surface. It seems therefore likely that in systems in which an alkyd resin as well as a dispersing agent is present, part of the adsorption sites will be occupied by molecules of the dispersing agent, thereby affecting the alkyd resin adsorption. Consequently the influence of the dispersing agents is not restricted to the dispersion process but is also of importance with respect to the

143

stability of the resulting pigment dispersion. To understand the influence of non-polymeric surfactants on the paint properties, it is therefore necessary to know the adsorption behaviour of these surfactants in the absence of as well as in the presence of alkyd resins. Such information, however, is lacking in the literature [14] . To fill this gap, the present authors have investigated the simultaneous adsorption of alkyd resin with stearic acid and with linoleic acid. Stearic acid and linoleic acid have been chosen as substitutes for the commonly used non-polymeric surfactants because a substantial amount of information about the adsorption behaviour of these compounds is already available. Also, the molecular structures of stearic acid and linoleic acid resemble rather closely the molecular structure of many dispersing agents used in practice. The adsorption of stearic acid on titanium dioxide has been investigated by Doorgeest [ 51, Witvoet [ 171 and Vervoorn [ 181. An interesting aspect found by Doorgeest was the influence of water on the adsorption behaviour of stearic acid. Witvoet [ 171, who studied the adsorption of a number of fatty acids to explain the rheological behaviour of titanium dioxide dispersions in solutions of these acids in n-heptane, confirms the influence of small amounts of water on the adsorption process. From the investigations of Witvoet it can be deduced that during the fatty acid adsorption a partition equilibrium exists between the water molecules on the pigment surface and those in solution. Vervoom [ 181 has presented quantitative information about this partition equilibrium. Both Witvoet and Vervoom have shown that if the water concentration is relatively high, the fatty acid adsorption does not occur on the titanium dioxide surface itself, but on the adsorbed water layer. It was shown that the affinity of the fatty acids for such a “wet” surface is weaker than for a completely dry surface. Moreover, it was found that the orientation of the adsorbed fatty acid molecules on the solid surface is affected by the length of the acid molecules and the amount of water present on the pigment surface. Information about the adsorption behaviour of linoleic acid can be obtained from the publication of Ottewill and Tiffany [19]. They demonstrated that the n-electrons of unsaturated fatty acids may show interaction with the titanium dioxide surface. As a result of this the orientation of unsaturated fatty acids differs from the orientation of saturated fatty acids. The results of our investigations on the adsorption behaviour of an alkyd resin, of water and of fatty acids are presented in the following section. The influence of adsorbed layers on the physical properties of some systems composed of titanium dioxide (particles) is demonstrated in a subsequent section. Explanations for the observed influence are based on the results of our adsorption measurements. 2. Results of the adsorption

experiments

and discussion

2.1 The adsorption of an alkyd resin The investigations on the adsorption behaviour of the alkyd resin were carried out with titanium dioxide pigments conditioned at a temperature of

144

25 “C and a relative humidity of 56%. In all experiments the pigment volume concentration was kept constant at 10 vol.%. The alkyd resin studied was a long oil pentaerythritol esterified alkyd resin, modified with linseed oil. Toluene, carefully dried on a molecular sieve, was chosen as the solvent. These experimental conditions given, only part of the water present on the pigment surface can dissolve in the resin solution during the alkyd resin adsorption process. As a result of this the alkyd resin adsorption does not take place on the TiOs surface itself, but on a water layer. The average thickness of the water layer was shown to be 1.5 moles. 2.1.1 Alkyd resin adsorption from dilute solutions The alkyd resin adsorption on Tiofine R-30, an untreated TiOs pigment from dilute solutions in toluene, is presented in Fig. 1. As observed earlier [4, 51 the adsorption isotherm shows the characteristics of a Langmuir isotherm. In order to determine which alkyd fractions had been preferentially adsorbed, a comparison was made between the MSDs of the initial resin and the residual resin remaining in solution after adsorption. Because it was not sure whether the composition of the adsorbed layer would remain constant along the isotherm, this comparison was made at four equilibrium concentrations: 5 and 10 g/l (in the bend of the isotherm) and 20 and 50 g/l (on the plateau of the isotherm). The results of the analyses are shown in Fig. 2. In this graph, curve 1 represents the MSD of the original alkyd resin. It follows from this curve that the alkyd resin used is composed of molecules with equivalent chain lengths varying from 80,000 A to 27 A. The low molecular material consists of phthalic acid, phthalic acid anhydride, free fatty acids and esters of glycerol and pentaerythritol. The MSD of the resin remaining in solution after adsorption is represented by the curves 2, 3,4 or 5, decreasing in equilibrium concentration in that order. These distribution curves result from experiments in which the pigment has been in contact with the alkyd resin solution ,for 24 h. On prolonged dispersion, up to 48 h, no variations have been observed in the MSD of the residual resin. Also, after storage of the dispersions for one month, the residual resin showed the same distribution curve.

20 -t

-cj

E

. . .

. --

lcT-+l l

c”

10-o

1’

0

0

-

10

20

30

40

50

c,$ (g/l)

Fig. 1. Adsorption isotherm of an alkyd resin on titanium dioxide in dilute solutions.

145

1048,

103A

1028.

I

I

I

,-

I-

I-

I0 -

-/

“60

100 ml.

120

140

160

T.H.F.

Fig. 2. Molecular size distribution of the initial alkyd resin (1) and of the residual resin at different equilibrium concentrations: (2) C, = 50.0 g/l, (3) C, = 20.4 g/l, (4) C, = 10.5 g/l, (5) c, = 5.1 g/l.

These results show that adsorption equilibrium was attained within 24 h. It is difficult to indicate the cause of the diverging results obtained by Crow1 [16] who observed, as mentioned above, that the MSD of the residual soya pentaerythritol alkyd resin varied even after several weeks of contact between pigment and resin solution. The distribution curves presented in Fig. 2 show some interesting features. Probably most striking is the fact that at all equilibrium concentrations the residual resin contains a relatively larger amount of low molecular weight material, indicating that the high molecular fractions have been removed from the solution by adsorption on the pigment surface. It is evident that the observed change in the MSD is most pronounced if a larger fraction of the original resin has been adsorbed. Therefore the highest relative deviation from the MSD of the original alkyd resin is found at the smallest equilibrium concentration (curve 5).

146

0 0 -

00

100

ml

120

140

160

T.H.F.

Fig. 3. Molecular size distribution of the adsorbed alkyd resin for: (1) C, = 5.1 g/l, (2) c, = 10.5 g/l, (3) c, = 20.4 g/l, (4) C, = 50.0 g/l.

The fact that at small equilibrium concentrations the residual resin hardly contains any high molecular material is an indication of a strong affinity of this fraction for the pigment surface. More detailed information about the adsorption behaviour can be obtained from the distribution curves of the adsorbed resin as shown in Fig. 3. These curves were obtained from the differences present in the MSD of the original alkyd resin and the residual resin after adsorption. From the almost identical course of the differential distribution curves it follows that the composition of the adsorbed layer is reasonably constant in the concentration range studied. Occasional differences mainly occurring in the low molecular size region are possibly caused by the inaccuracy of the indirect method of analysis. It can also be concluded that all fractions are adsorbed with a pronounced maximum at an equivalent chain length of - 2,800 A. In this context it is interesting to note that Crow1 found that fractions of a soya pentaerythritol alkyd with chain lengths from 2,000 - 3,000 A are rapidly adsorbed on titanium dioxide. The adsorption of low molecular weight material is represented by the peak in the elution volume range of 145 - 165 ml THF, corresponding with equivalent chain lengths of 75 - 25 A. The fraction in this region consists of free fatty acids, mono- and diglycerides and probably also of phthalic acid, phthalic acid anhydride and phthalic acid half-esters. Strong affinity of the half-esters has been found [20] . It seems‘likely that, especially due to the presence of these compounds,

147

the acid number and the hydroxyl number of the adsorbed layer are larger than those of the original resin, as found by Doorgeest [ 51. Finally it can be concluded that the fraction with an equivalent chain length of -100 W is adsorbed on the pigment either not at all or in only very small amounts. This might be caused by the fact that this fraction consists of triglycerides and pentaerythritol tetraesters which are relatively apolar compounds. More information about the adsorption process can be obtained by studying the adsorption of alkyd resin fractions of different molecular weight. These fractions have been obtained by a precipitation process with water using dilute solutions of the resin in acetone (5%). In this manner five fractions have been isolated from the alkyd resin A. These have been characterized by their MSDs. - An alkyd resin fraction (H), for the greater part consisting of high molecular material, has been obtained by precipitation from a water-acetone mixture containing 3.7% of water. From the remaining solution an alkyd resin fraction with a reduced content of high molecular material has been obtained (A-H). - An alkyd resin fraction with a reduced content of low molecular material (A-L) has been obtained by precipitation from a water-acetone mixture containing 8.1% of water. From the remaining solution an alkyd resin fraction mainly consisting of low molecular material (L) has been obtained. - Via a two-step fractionation an alkyd resin fraction has been obtained from which the high as well as the low molecular weight material had been removed (A-H-L). The adsorption behaviour of these fractions is shown in Fig. 4. Because the initial slope of the adsorption isotherms is a measure of the affinity of the different fractions for the pigment surface, it follows from these isotherms that fraction H exhibits the strongest affinity. The affinity of the fractions decreases with increasing content of low molecular weight material. Ordering the fractions according to decreasing affinity, the following arrangement is obtained: H, A-L, A-H-L, A-H, L. The strong affinity of the high molecular fraction H can probably be attributed to the fact that

t

A-H

-

0 e

10

20 ce

30

40

L

50

(Q/l)

Fig. 4. Adsorption isotherms of alkyd resin fractions on titanium dioxide.

148

with increasing molecular size the molecules are attached to the pigment via an increasing number of polar groups and double bonds. In this respect it is of interest to note that the number of functional end-groups (carboxylic acid groups and hydroxyl groups) is increasing with an increasing content of the polyfunctional alcohol in the molecules. It further follows from the given data that the adsorption saturation value increases with decreasing content of low molecular material in the fraction. This can be explained by assuming that with increasing molecular size the adsorbed molecules will protrude further from the pigment surface into the surrounding solution. As a result of this the adsorbed layer will become thicker and consequently a larger amount of material can be adsorbed per unit of surface area. The adsorption behaviour of the individual alkyd resin fractions is in agreement with the results obtained from the gel permeation chromatograms, showing that adsorption of fractions of all molecular sizes can take place. From these results it follows that during the dispersion process alkyd resin molecules will compete for adsorption sites. Therefore the composition of the adsorbed layer will not only be determined by the affinity of the different fractions for the pigment surface but by their concentration in the total alkyd resin as well. Also, molecular interactions in solution as well as at the pigment-medium interface may be of importance in the adsorption process. 2.1.2 Alkyd resin adsorption from concentrated solutions The result of the alkyd resin adsorption experiments on Tiofine R-30 from relatively concentrated solutions in toluene is presented in Fig. 5. Above an equilibrium concentration of about 50 g/l a decline of the adsorption isotherm occurs. Because the adsorbed amount is calculated from the concentrations of the initial and the final solution, this indicates that, with the exception of alkyd resin, adsorption of solvent also takes place. Therefore the value found is not that of the actual alkyd adsorption but represents an apparent adsorption. In dilute solutions the difference between the real adsorption and the apparent adsorption is negligible. The fact that a relatively large amount of the apolar solvent can be adsorbed together with the

-.

1lj+---y_ I

0 -

I

50

Ce

I

I

I

100

150

200

I

250

(g/l)

Fig. 5. Adsorption isotherm of an alkyd resin on titanium dioxide in concentrated solution.

149 TABLE 1 Specifications of the precoated titanium dioxide pigments

Kronos Kronos Kronos Kronos Kronos Kronos

RN-56 RN-57 RN-45 RN-59 RN-61 RN-57P

Precoated with

TiOg content (wt.%)

Carbon content (wt.%)

Specific surface (m2/g)

A1203.SiOg AlgOa.SiOg Al203 + org. Al203 + org. A1203.Si02 + org. A120a.Si02 + org.

95 90 95 91 93.5 89

_ _ 0.07 0.18 0.18 0.20

7.4 10.6 11.8 13.5 10.5 11.6

polaric alkyd resin molecules can be explained by assuming that the solvent molecules are trapped in the extending loops and tails of the adsorbed alkyd resin molecules. The amount of solvent trapped in the adsorbed alkyd resin layer will be determined mainly by the adsorption behaviour of the alkyd resin. Especially the presence of high molecular alkyd resin fractions in the adsorbed layer enables the entrapment of a considerable amount of toluene. 2.1.2 Alkyd resin adsorption on precoated titanium dioxide pigments In the paint industry it is common practice to apply precoated titanium dioxide pigments. The effect of these precoats on the adsorption behaviour of the alkyd resin will be discussed in this section. It has to be pointed out beforehand that particularly with pigments with an organic coating, part of the organic layer may be dislodged from the pigment surface by alkyd resin molecules, thus disturbing the gravimetric determination of the equilibrium concentration. As a result of this, a false value for the amount adsorbed will be obtained. Experiments with titanium dioxide precoated with stearic acid have confirmed that this possibility is real. It is evident that this problem would not occur if the organic compound was attached to the pigment surface by means of a chemical bond. The specifications of the precoated titanium dioxide pigments used are summarized in Table 1. The results of the adsorption measurements obtained with these pigments are shown in Fig. 6 and in Fig. 7. Because the specific area of the different pigments was not the same, for comparison it was necessary to express the alkyd resin adsorption per m2 of pigment surface and not, as before, per g of pigment. It has been assumed that the total surface area as determined by nitrogen adsorption would be available for the attachment of alkyd resin molecules. From the presented adsorption isotherms it follows that the affinity of the alkyd resin for the precoated titanium dioxide pigments is somewhat smaller than the affinity for the untreated pigment, and also that at a.llconcentrations the amount of alkyd resin adsorbed is reduced by precoating. With the exception of Kronos RN-61, the smallest alkyd resin adsorption was found with the organically coated pigments.

150

“E Pi

E 2

I

/

-

Ce

(g/l)

-

I

I

I

I

20

40

60

80

Ce

(g/1)

Fig. 6. Adsorption isotherms of an alkyd resin on Tiofine R-30 (o), Kronos RN-56 (a), Kronos RN-57 (0). Fig. 7. Adsorption isotherms of an alkyd resin on Kronos RN-61 (o), Kronos RN-45 (o), Kronos RN-59 (a), Kronos RN-57P (X ).

This might have been caused by the detachment of the organic layer by alkyd resin molecules. The MSD of the adsorbed layer on the precoated titanium dioxide pigments showed that again the residual resin after adsorption contains a relatively larger amount of low molecular weight material than the initial resin, indicating that the high molecular alkyd resin fractions are preferentially adsorbed. The MSD of the adsorbed layer on Kronos RN-56 and Kronos RN-57 appeared to be the same as that found for the noncoated Tiofine R-30 (see Fig. 3). Apparently treatment with aluminasilica does not affect this aspect of the alkyd resin adsorption. From the MSD of the alkyd resin fractions adsorbed on the organictreated pigments, it appeared that the residual resin contained a larger amount of low molecular weight material than had been introduced into the system via the alkyd resin. This was most pronounced for the pigments Kronos RN-59 and Kronos RN-57P. The cause is most probably the dislodgment of the organic layer from the pigment surface by alkyd resin molecules. As a result of this it is impossible to present information about the MSD of the alkyd resin fractions adsorbed on the organically treated titanium dioxide pigments. Attention has to be drawn to the fact that the adsorption isotherms for the precoated titanium dioxide pigments start to decline at a smaller equilibrium concentration than for the untreated Tiofine R-30. This result indicates that the degree of solvation of the adsorbed layer depends on the pretreatment of the pigment. Apparently the space configuration of the adsorbed alkyd resin molecules is affected by the surface properties of the pigment used. 2.1.4 The adsorption of stearic acid and linoleic acid in the presence of the alkyd resin For the adsorption of an alkyd resin in the presence of stearic acid and linoleic acid on Tiofine R-30 it follows from Fig. 8 that in this complex

151

50

0 __t

t,mc

(hours)

Fig. 8. The adsorption of stearic acid as a function of the time of contact in simultaneous adsorption with the alkyd resin. Initial resin concentration Cl = 40.4 g/l, stearic acid concentration Ci = 38.3 x low3 mol/l.

0

-

10

20 Ce (mol

30

40

50

10m3/l)

Fig. 9. Adsorption isotherms of stearic acid on Tiofine R-30 in simultaneous adsorption with an alkyd resin. Alkyd resin concentration Ci: (A) = 0 g/l, (0) = 3.2 g/l, (X) = 10.8 g/l, (0) = 40.4 g/l, (=) = 107 g/l, (“) = 230 g/l.

P

2

4

t

0 .

L

0

E

. b

z

I

0

10

20

30

40

50

Ce (mol.10-3/l)

Fig. 10. Adsorption isotherms of linoleic acid on Tiofine R-30 in simultaneous adsorption with an alkyd resin. Alkyd resin concentration Cl: (a) = 0 g/l, (a) = 3.4 g/l, (0) = 11.4 g/l, (x) = 27.7 g/l,(e) = 230 g/l.

mixture, once again a contact time of 24 h between pigment and solution is sufficient to reach equilibrium. In Fig. 9 and Fig. 10 the stearic acid adsorption and the linoleic acid adsorption in toluene, determined by a radiochemical tracer technique, is presented as a function of the equilibrium concentration with the alkyd’resin concentration as a parameter. The isotherm representing the stearic acid adsorption in the absence of the alkyd resin

152

increases gradually with the equilibrium concentration and unlike with stearic acid adsorption from heptane solutions, no plateau region was observed in the same concentration range studied. This should be ascribed to the interaction of the aromatic solvent with the pigment and also to the presence of water in the systems under observation. In addition, the adsorption isotherms of stearic acid and linoleic acid in toluene can very well be described by Langmuir’s equation (see Section 2.3). With the aid of this equation it was found by extrapolation that complete surface coverage would occur at a stearic acid adsorption of 4.9 X lop5 mol/g. This result is in fair agreement with the adsorption saturation value found when stearic acid adsorption was studied from n-heptane solutions (4.8 X 10m5 mol/g). For linoleic acid it was calculated that complete surface coverage would occur at an adsorption of 1.4 X 10e5 mol/g, the result of which is in good agreement with the adsorption saturation value experimentally determined. From these results and the known specific area of the pigment it follows that at monolayer coverage an adsorbed stearic acid molecule occupies a surface area of 21.5 A2, suggesting that the adsorbed molecules are vertically oriented and attached to the pigment surface by the carboxylic acid group. For linoleic acid it was found that one molecule occupies a surface area of 77 A2. With the aid of molecular models it was shown that such an area is occupied if the linoleic acid molecules are adsorbed in flat orientation. Consequently linoleic acid adsorption occurs not only by interaction of the carboxylic acid group, but also by interaction of the 7r-electrons of the double bonds with the pigment surface. Due to this three point attachment the affinity of linoleic acid for the pigment surface is larger than the affinity of stearic acid, which is clearly indicated by the initial slope of the isotherms. Further, it follows from the course of the linoleic acid isotherm that the orientation of the adsorbed molecules does not alter in the concentration range studied. This result is not in accordance with the results of Ottewill and Tiffany [ 191 who studied fatty acid adsorption on titanium dioxide from solutions in n-heptane. The isotherms representing the adsorption of the unsaturated fatty acids appeared to have a stepwise character. From this Ottewill and Tiffany concluded that at very small equilibrium concentrations the unsaturated fatty acids are adsorbed in flat orientation, whilst with increasing equilibrium concentration the orientation of the adsorbed molecules changes from flat to perpendicular. At very large concentrations even multi-layer adsorption was observed. These differences might be caused by the presence of water in our systems, while Ottewill and Tiffany carried out their investigations under water-free conditions. Ottewill and Tiffany have, in fact, pointed out that the orientation of the adsorbed molecules can be affected by the presence of small amounts of water, which follows from the work of Sokola et al. [ 211. They found that in the adsorption behaviour of linoleic acid from toluene solutions a stepwise isotherm is obtained under water-free conditions while in the presence of small amounts of water the isotherm showed the characteristics of a Langmuir isotherm.

153

From Fig. 9 and Fig. 10 it follows that the fatty acid adsorption is reduced with increasing alkyd resin concentration, showing that the alkyd resin molecules successfully compete with the fatty acid molecules for adsorption sites. In the most concentrated alkyd resin solution hardly any fatty acid adsorption was observed, indicating that in these systems the pigment surface is almost completely covered by alkyd resin molecules. Because the alkyd resin adsorption from dilute solutions, as well as the fatty acid adsorption, could be described by Langmuir’s equations, it was verified whether the competitive adsorption of these components could also be described in this way. Using Langmuir’s equations describing the adsorption of two adsorbates [ 221 in combination with mass balances, the stearic acid adsorption and the linoleic acid adsorption have been calculated as a function of the equilibrium concentration with the initial alkyd resin concentration as a parameter [23] . In all cases the calculated stearic acid adsorption and linoleic acid adsorption appeared to be larger than the values determined experimentally. For stearic acid the deviation was 5 - 20%; for linoleic acid deviations of 25 - 50% have been found. These results show that the competitive adsorption of alkyd resin and fatty acids is of too complex a nature to be described by this rather simple concept. A number of factors seems to be of importance. In a previous section it has been shown that the affinity of the different alkyd resin fractions for the pigment surface is different. It seems obvious that especially the alkyd resin fraction with the strongest affinity for the pigment surface will most strongly reduce the fatty acid adsorption; so calculations which are based on data valid as an average value for the “total” resin will predict too high a fatty acid adsorption. Another possible source of error might be that the orientation of the adsorbed molecules is affected by the presence of molecules of a different kind on the pigment surface. Except for these interactions in the adsorbed layer, interactions in the solution may also play an important role in the simultaneous adsorption of polymeric and non-polymeric substances, as has been shown by Thies [24, 251. A combination of the factors mentioned above will have caused the observed deviations between the calculated values of the fatty acid adsorption and the values experimentally determined. Although it is not possible to give a quantitative description of the simultaneous adsorption of the alkyd resin and the fatty acids, it follows from the investigations that the adsorption of fatty acids is strongly reduced by the presence of an alkyd resin. 2.2. The adsorption of water on Tiofine R-30 The adsorption of water on Tiofine R-30 was studied in the absence, as well as in the presence, of a constant quantity of saturated fatty acid in the equilibrium solution. Different solvents were used with an increasing solubility for water, viz. heptane, benzene and acetone. The acids used in this investigation were propionic acid, lauric acid and stearic acid. From previous work [ 171 it is known that a plateau region in the acid adsorption

0

4

0

c,

__IL

12

16

(mol.

10-3/l)

20

24

26

32

Fig. 11. The adsorption isotherm of lauric acid on Tiofine R-30 and the amount of adsorbed water as a function of the acid concentration of the equilibrium solution (from benzene with 50 mg water/l). 4

-

0

E

f-

cm

-3

3

c” 0 ’ 0

-4

( 2-

-2

ot E”

-1

’ 0 Yc?, 0

4

0 w

c,

12

16

(rnOl

lo-3/l

20

24

I

I

28

32

-

0

I” OC _

I

Fig. 12. The adsorption isotherm of lauric acid on Tiofine R-30 and the amount of adsorbed water as a function of the acid concentration of the equilibrium solution (from benzene with 550 mg water/l).

isotherm also exists in the presence of water. The value of this plateau depends on the amount of water pre-adsorbed on the pigment surface. The fact that a plateau is formed indicates that there is also an equilibrium situation for the water adsorption. This assumption is supported by the results as presented in Figs. 11 and 12, in which the amount of water adsorbed on the pigment surface is given as a function of the acid concentration of the equilibrium solution. Both figures hold for the adsorption of lauric acid from benzene on a titanium dioxide surface which contained initially 0.5 mg water/g. On the left axis in these figures the amount of adsorbed acid/g pigment is given and on the right axis the water adsorption at the pigment surface at the corresponding acid concentration. In Fig. 11 the adsorption from benzene with a water content of 50 mg/l is shown; in this case there is a small desorption of water from the pigment surface when acid is present. The results given in Fig. 12 were obtained in benzene saturated with water (550 mg/l); in this case adsorption of water from the solution at the surface occurs. In both cases an equilibrium situation for the adsorption

155 was

reached in less than 20 hours. As can be seen from the figures, the presence of acid causes a decrease in the amount of adsorbed water, but when an acid surface coverage of about 70% is obtained, an increase in the acid equilibrium concentration does not give a measurable change in the amount of water adsorbed on the pigment surface. This point has been attained in ah cases at an equilibrium concentration of the acid of 25 mmol/l. At that moment the saturated fatty acid solution acts as one component with a much stronger affinity for the pigment surface than the pure solvent. The measured water adsorption isotherms for titanium dioxide will be presented as the amount adsorbed (mg water/g titanium dioxide) as a function of the equilibrium activity (a), which is independent of the solvent. The amount of water dissolved in a solution, in equilibrium with air, has by definition an activity equal to the relative water vapour pressure of the air (p/p,,) at the relevant temperature. The equilibrium curves of water dissolved in a solution at different activities were obtained by bubbling a stream of air with a known and constant water vapour pressure, through a solution which was kept at a constant temperature of 20 “C. After reaching equilibrium the concentration of water in the solution was determined. Due to the presence of acid in the solutions there is an increase in the solubility for water in the solvents. Therefore it was decided to carry out the measurements for the water adsorption in the presence of acid at a constant equilibrium concentration of -25 mmol/l. The amount of water dissolved in heptane as a function of the activity is given in Fig. 13. The same is given in Fig. 14 for benzene. Both graphs show the results for the pure solvent as well as for the case where -25 mmol acid/l are present. The

=SOO

-a

-a

Fig. 13. The relation between the activity and the amount of water dissolved in heptane (e), in heptane with -25 x 10q3 mol acid/l (X ). Fig. 14. The relation between the activity and the amount of water dissolved in benzene (*), in benzene with -25 x lop3 mol acid/l (x).

156

0

0.2

0.4

0.6

0.0

1 .o

-a

Fig. 15. The adsorption isotherms of water in different media on Tiofine R-30: ( l ) air, (X ) heptane, (A) benzene, (m) heptane with -25 x low3 mol acid/l, (0) benzene with -25 x 10m3 mol acid/l.

results are not influenced by the chain length of the saturated fatty acids used. The use of propionic acid and stearic acid gives the same results. The adsorption isotherms of water on titanium dioxide from the different solutions and from air are shown in Fig. 15. The water adsorption equilibria in the solutions were in many cases obtained by adsorption of water from the solution as well as by desorption of water from the pigment surface. No differences could be detected. The amount of acid contained in a monolayer differs for the acids used [ 171, however, no influence of the chain length of the acid molecule on the water adsorption isotherm could be observed. By comparing the water adsorption isotherms it appears that the amount of water adsorbed depends on the medium and decreases in the sequence air, heptane, benzene. This indicates that liquid heptane has a stronger affinity for the pigment surface than air and that in turn, liquid benzene has a larger affinity than heptane. With the method of analysis used it is not possible to determine the adsorption isotherm for water from acetone. Due to the large amount of water in the acetone-water mixture, even at small activities, the error in the determination is in the order of magnitude of the amount of adsorbed water on the pigment surface. For that reason, and also due to the fact that in practice it is more interesting to know the interaction between water and the pigment surface in the presence of small quantities of water in acetone, the relationship between the amount of water in acetone and the activity was not determined. Therefore the adsorption behaviour of a titanium dioxide pigment surface covered with 0.4 mg water/g was studied by bringing the pigment in acetone with different water concentrations up to 3.5 g water/l and measuring the resulting equilibrium concentration of water. From these data the amount of water exchanged from the pigment surface

157

can be calculated. It appears that in all cases no adsorption of water from the solution occurs; in most cases some water was desorbed from the surface. These facts indicate the very strong competitive influence of acetone with respect to water for the pigment surface. This is confirmed by experiments in which a pigment with a water content of 3.6 mg/g was brought into contact with acetone with a water concentration of 35 mg/l. Under these circumstances all the adsorbed water (accuracy 0.1 mg water/g pigment) was desorbed from the pigment surface. Also in the presence of acid, under the same conditions, all the water was desorbed from the pigment surface. The water adsorption from air up to a relative humidity of 40% can be described with sufficient accuracy with the B.E.T. equation. With the aid of this equation and the known specific surface area of the pigment, it is calculated that 1.65 mg water per gram titanium dioxide is necessary for the formation of a monolayer. From solvents, however, it is not possible to describe the water adsorption with this equation although it can be concluded that the amount of water adsorbed on a pigment surface is determined both by the activity of water in the solvent and by the affinity of the solvent for the pigment surface. 2.3 The adsorption of saturated fatty acids The co-adsorption of saturated fatty acids and water by titanium dioxide was studied in the same solvents as used before. The adsorption of saturated fatty acids from heptane on titanium dioxide has already been published by Witvoet [ 171: From his work it is known that the adsorption saturation value of saturated fatty acids varies with the length of the apolar chain and with the amount of water on the pigment surface. This is shown in Fig. 16 in which the adsorption saturation value is given as a function of the chain length of the acid for two initial water contents of the pigment. This adsorption behaviour could be explained by assuming that the orientation of the adsorbed acid molecules on the pigment surface depends on the

fz:[ h, 2 x-,_

;/qF

3_

X-X-

JX

z”

I

o 2l0 -

111111111

2

4

6 6 10 12 number of C -atoms

14

16

18

Fig. 16. The adsorption saturation value (N,) as a function of the number of carbon atoms of the fatty acid. Initial water content of the pigment: (0) = 0.4 mg/g, (x) = 2.5 mg/g.

158

2 G

E

4

3

a E ul

3

b -

2

z” -lh 0 -

1

2

3

adsorbed

watel’

0

I

I

I

I

4

6

12

16

_

(m919)

Ce

I

I

I

I

20

24

26

32

(mol.10-3/l)

Fig. 17. The adsorption saturation value (N,) for lauric acid in heptane on Tiofine R-30 as a function of the adsorbed amount of water on the pigment surface. Fig. 18. Adsorption isotherms of lauric acid in benzene for different amounts of water on the Tiofine R-30 surface: (0) = 0.4 mg/g, (x) = 1.15 mg/g, (0) = 1.25 mg/g, (v) = 2.65 mg/g.

length of the chain of the acid molecules and on the amount of adsorbed water on the pigment surface. From this work it was, however, not possible to obtain information about the relationship between the amount of adsorbed acid and the water content of the pigment after adsorption of the acid. Therefore the influence of the amount of adsorbed water on the adsorption saturation value of the lauric acid adsorption from heptane on Tiofine R-30 was determined. The results are shown in Fig. 17, from which it follows that the smallest amount of acid is adsorbed on a surface which is completely covered with water. In Fig. 18 the adsorption isotherms of lauric acid from benzene onto surfaces with different quantities of adsorbed water are presented. The adsorption saturation value in benzene corresponds with the value as obtained in heptane (compare Fig. 17 and Fig. 18). The same has been found for the adsorption saturation value of stearic acid and propionic acid. Adsorption isotherms of lauric acid and stearic acid from dried acetone on two samples of titanium dioxide with different water content are given in Figs. 19 and 20. The pigments contained initially 0.4 and 3.6 mg water/g respectively. After adsorption of the acid all the water was completely desorbed from the pigment surface. As already mentioned in Section 2.1.4, the adsorption isotherms of saturated fatty acids on titanium dioxide can be described using the Langmuir equation. Writing the Langmuir relation in the form: 1 c,/n, = KklNs

+ celnr,

(1)

159

0

4

0

-Ce

12

16

I

I

I

I

20

24

26

32

(mot.10-3/I)

Fig. 19. The adsorption isotherms of lauric acid in dried acetone on Tiofine R-30. Initial water content of the pigment: (o) = 0.4 mg/g, (x) = 3.6 mg/g.

0 -pcC

4

0

12

16

(mol

10-3/l)

20

24

20

32

Fig. 20. The adsorption isotherms of stearic acid in dried acetone on Tiofine R-30. Initial water content of the pigment: (0) = 0.4 mg/g, (x) = 3.6 mg/g.

it follows that a linear relation between the quotient of the equilibrium concentration and amount adsorbed (c&z,) with the equilibrium concentration (c,) exists [ 191. The amount adsorbed at complete surface coverage (N,) and the adsorption equilibrium constant (K) can be calculated from this relation. The equilibrium constant (K) is a measure of the affinity of the acid for the pigment surface. This constant gives no information about the amount of adsorbed acid in a monolayer. The given equation is in fact only valid for the case that adsorption takes place in a solvent with no affinity for the pigment surface and in the absence of water. However, for relatively small acid equilibrium concentrations, generally used in these adsorption systems, this equation remains valid. In that case the adsorption equilibrium constant gives the affinity of an acid for the pigment surface in the solvent used.

160

w

C,

(mol.10-3/l)

Fig. 21. Langmuir relations for the lauric acid adsorption on Tiofine R-30. ( v) in acetone, (x) in benzene, (0) in heptane.

As described earlier, no change in the water concentration on the surface is observed even at small equilibrium concentrations. Therefore the presence of water does not hinder the use of the Langmuir relation either. For lauric acid adsorption in the different solvents the c&z, values are plotted against c, in Fig. 21. In all three cases the adsorption took place on a pigment conditioned in air dried over phosphorus pentoxide in dried solutions. From the given curves the equilibrium constants for the acids can be found. The lauric acid adsorption in heptane shows the largest value for the equilibrium constant, indicating that the affinity of heptane for the pigment surface is the smallest of the three solvents. Increasing affinity follows for the solvents benzene and acetone. From this figure it also follows, via the slope of the curves, that the amount of acid adsorbed in a monolayer is almost the same for adsorption from heptane and benzene. For acetone, however, a much smaller value is found. This contradictory result cannot be explained by the stronger affinity of the solvent acetone for the pigment surface, because a strong affinity of the solvent for the pigment surface only results in the fact that the plateau value for the acid adsorption will be reached at a higher equilibrium concentration of the acid. A possible explanation may be a changing orientation of the adsorbed acid molecule due to the presence of the solvent acetone. This is to be expected because of the changing orientation due to a varying chain length of the acid molecule and the amount of water on the surface. From the investigations described in this section it can be concluded that the adsorption of saturated fatty acids not only occurs on the titanium dioxide surface itself, but also on the layers of adsorbed water. On the adsorbed water layer the orientation of the adsorbed acid molecules changes, thereby reducing the amount of saturated fatty acids adsorbed. This orientation is probably also affected by the solvent acetone.

161

3. The behaviour

of some systems built up of titanium

dioxide

3.1 The rheological behaviour of titanium dioxide dispersions The interaction energy between dispersed particles is mainly determined by the composition and the thickness of the adsorbed layer. The result that the alkyd resin and stearic acid, and the alkyd resin and linoleic acid occupy the adsorption sites in mutual competition, offers the possibility of studying in which way a gradual change in the composition of the adsorbed layer will manifest itself in the physical properties of the dispersion. In this section the influence of fatty acids on the rheological behaviour of TiO, dispersions in alkyd resin solutions will be discussed. The rheological behaviour of TiOa dispersions in alkyd resin solutions is Newtonian [ 231, which indicates that the attractive forces between the dispersed particles are rather weak. On the other hand the rheological behaviour of TiO, dispersions in fatty acid solutions shows Bingham characteristics [17], indicating that the attractive forces between the dispersed particles are so strong that a network structure is formed. The effect of stearic acid on the rheological behaviour of titanium dioxide dispersions in alkyd resin solutions in toluene is shown in Fig. 22. Here the Bingham yield values are presented as a function of the stearic acid concentration in the initial solution with the alkyd resin concentration as a running parameter. From the curves it appears that the Bingham yield value of these dispersions increases, indicating progressive flocculation induced by stearic acid. This is in accordance with the adsorption phenomena occurring in these systems; part of the adsorption sites on the titanium dioxide surface are gradually occupied by stearic acid molecules. During stearic acid adsorption the area available for alkyd resin attachment is reduced. Although it is still uncertain which alkyd resin fractions are preferentially excluded from the pigment surface by stearic acid adsorption, it is very likely that the adsorption of all resin fractions is affected, as is the case in the adsorption of the high molecular weight resin fraction, which gives the largest contribution to the stabilizing action of the adsorbed layer. Consequently, the ability of the adsorbed layer to protect the dispersed particles against flocculation is gradually reduced with increasing stearic acid concentrations, which is manifested in the rheological behaviour. Because of the competitive nature of the adsorption process, more stearic acid is required to modify the adsorbed layer to the same extent with increasing alkyd resin concentrations, which explains the shift of the transition from Newtonian to Bingham behaviour for higher stearic acid concentrations with increasing alkyd resin content of the solution. In Fig. 23, the Bingham yield values are presented as a function of the surface coverage fraction 0 of stearic acid molecules. It follows that a direct relationship exists between the rheological behaviour of the dispersions and the composition of the adsorbed layer. In sharp contrast to the observation with stearic acid, the rheological properties of the titanium dioxide dispersions in alkyd resin solutions are not

162

200

c

0

-

Ci

(moles

10

-3/

I)

0.5

1.0

-e

Fig. 22. The Bingham yield values as a function of the stearic acid concentration in the initial solution dependent on the alkyd resin concentration of the initial solution. (0) = 3.2 g/l, (A) = 10.8 g/l, (0) = 24.5 g/l,(m) = 40.4 g/l. Fig. 23. The Bingham yield values as a function of the stearic acid surface coverage 0.

modified by the presence of linoleic acid in the same acid concentration range as used for stearic acid. The rheological behaviour remains Newtonian with increasing linoleic acid concentration. An increase in the relative viscosity was not observed either. This result was unexpected because it was demonstrated in Section 2.1.4 that linoleic acid, as much as stearic acid, adsorbs in the presence of alkyd resin. The fact that linoleic acid has no influence on the rheological behaviour of the pigment dispersions is probably caused by the manner in which the linoleic acid molecules are adsorbed on the pigment surface. For stearic acid it is known that these molecules adsorb in perpendicular orientation on the pigment surface, whilst the linoleic acid molecules are adsorbed in flat orientation on the titanium dioxide surface. To verify whether the influence of fatty acids is determined by the length of the apolaric chain protruding from the pigment surface into the solution after adsorption, some investigations were carried out on the influence of a number of saturated fatty acids with different chain lengths on the rheological behaviour of titanium dioxide dispersions in alkyd resin solutions. The following saturated fatty acids were used: stearic acid, myristic acid, lauric acid, capric acid and caproic acid. It is known that these fatty acids adsorb in more or less perpendicular orientation on the titanium dioxide surface [ 171. In the experiments with these acids the alkyd resin concentration of the solutions was kept at a constant value (26 g/l). The

163

----lcconcentration

of

acid

(mol.

10m3/l)

Fig. 24. The influence of saturated fatty acids on the rheological behaviour of titanium dioxide dispersions in alkyd resin solutions. Initial alkyd resin concentration: 26 g/l, (0) stearic acid, (0) myristic acid, (A) lauric acid, (x) capric acid, (w) caproic acid.

results of the rheological measurements are given in Fig. 24, in which the Bingham yield values of the dispersions are given as a function of the initial concentration of the saturated fatty acids in solution. From the curves it appears again that the rheological behaviour changes from Newtonian to Bingham at a certain acid concentration. These transitions occur at a higher acid concentration for the added saturated fatty acid with smaller chain length. Capric acid and caproic acid, in which the chain length is less than 10 carbon atoms, have hardly any influence on the rheological behaviour of the titanium dioxide dispersions in alkyd resin solutions. It can therefore be concluded that the influence of the saturated fatty acids on the rheological behaviour indeed depends on the length of the apolaric chain which protrudes in the surrounding solution - the smaller the chain the smaller the influence. 4 possible explanation could be that the small chains are incorporated in the coils of the alkyd resin molecules present on the pigment surface. 3.2 The influence of adsorption of water and fatty acids on the formation and strength of titanium dioxide granules The granulation of titanium dioxide powder was carried out by the socalled “spherical agglomeration process” [26, 271. With this method the powder is brought into contact with an apolar liquid and by rotating these compounds in a bottle, granules can be formed. In the presence of water as the sole adsorbant this is indeed the case. The porosity of the granules obtained decreases with increasing rotation time and after one week (100 rot./ min) the porosity of the granules becomes constant. This equilibrium porosity is a function of the amount of adsorbed water; the more water adsorbed on the pigment surface the lower the porosity of the granules, indicating that the adsorption of water decreases the attraction force between the particles in the granules. The influence of the amount of adsorbed water on the compression strength of granules in air is given by Fig. 25. In the case of adsorption of

164

IC

adsorbed

water

(m9l9)

Fig. 25. The compression strength of titanium dioxide amount of adsorbed water on the pigment surface.

granules as a function

of the

water from air with a low relative humidity, the strength of granules is determined by the London-van der WaaIs forces and the cohesion forces between the adsorbed layers. At high relative humidities of the air capillary condensation occurs in the granules; the cohesion forces then change into forces caused by liquid bridges. The increase in strength of the granules at very low water content is caused by cohesion forces. The subsequent decrease in the strength of the granules is due to the influence of adsorbed water layers on the London-van der Waals forces, according to the theory of Vold [ 1,181. The subsequent increase of the strength of the granules with higher water content is caused by the formation of liquid bridges. From Sections 2.1.4 and 2.3 it is known that saturated fatty acids adsorb in a more or less perpendicular orientation on a dry titanium dioxide surface. The presence of water affects this orientation but not in such a manner that the thickness of the adsorbed acid layer will change substantially. It may therefore be expected that a strong decrease in the attraction force between the particles, caused by the adsorption of the saturated fatty acid molecules [l] , will result and therefore no granules can be formed in the presence of a layer of adsorbed acid. However, for the granulation process in the presence of saturated fatty acids two cases are distinguishable. In the presence of small quantities of water no granules are in fact formed if there is a sufficient amount of saturated fatty acid available to form a monolayer. Surprisingly, in the case where there is at least one monolayer of water adsorbed on the pigment surface, granules are always formed in the presence of saturated fatty acids. This indicates that under these circumstances, at the contact points of the particles, the apolaric tail of the adsorbed molecules is

165

forced to lie more or less flatly on the surface of the particle, contrary to the adsorption behaviour on free particles. The adsorption of a monolayer of saturated fatty acid reduces the strength of the granules obtained in such a manner as compared to the strength of granules with only water adsorbed on the pigment surface. As follows from Table 2, the strength of the granules is not influenced by the chain length of the saturated fatty acid. This indicates that at the contact points the thickness of the adsorbed layer is in fact not determined by the chain length of the acid molecules. TABLE 2 The influence of adsorbed acid on the strength (D) of granules in the granulation liquid, in the presence of a monolayer of adsorbed water Medium

D (g/mm2)

Porosity

Pure heptane Heptane + caproic acid Heptane + laurie acid Heptane + stearic acid

1.9 2.0 2.3 2.3

0.56 0.53 0.55 0.54

References

1 M. J. Vold, J. Colloid Sci., 16 (1961) 1. 2 D. W. J. Osmond, B. Vincent and F. A. Waite, J. Colloid Interface Sci., 42 (1973) 262. 3 B. Vincent, J. Colloid Interface Sci., 42 (1973) 270. 4 E. C. Rothstein, Off. Dig., 36 (479) (1964) 1448. 5 T. Doorgeest, Thesis, Delft, 1965; J. Oil Colour Chem. Ass., 50 (1967) 841. 6 R. W&-wag and K. Hamann, Proc. VIIth FATIPEC Congr., Verlag, Vichy, 1964, p. 306. 7 E. Honak, Farbe + Lack, 70 (1964) 791. 8 H. Schiitte, Plaste Kautsch., 11 (1964) 248. 9 K. RehaEek and H. Schiitte, Plaste Kautsch., 16 (1969) 773. 10 P. Kijlling and H. Schiitte, Plaste Kautsch., 17 (1970) 286. 11 K. RehJek, Farbe + Lack, 76 (1970) 656. 12 R. Haug, Farbe + Lack, 76 (1970) 753. 13 K. Goldbrough and J. Peacock, J. Oil Colour Chem. Assoc., 54 (1971) 506. 14 P. M. Heertjes and C. I. Smits, Powder Technol., 17 (1977) 197. 15 R. E. Felter and L. N. Ray, J. Colloid Interface Sci., 32 (1970) 349. 16 V. T. Crowl, J. Oil Colour Chem. Assoc., 55 (1972) 388. 17 W. C. Witvoet, Thesis, Delft, 1971. 18 P. M. M. Vervoorn, Thesis, Delft, 1977. 19 R. H. Ottewill and J. M. Tiffany, J. Oil Colour Chem. Assoc., 50 (1967) 844. 20 A. F. Sherwood and S. M. Rybicka, J. Oil Colour Chem. Assoc., 49 (1966) 648. 21 K. Sokoll, B. Rotrekl, L. P&g&ova and J. Exner, Chem. Prum., 10 (1964) 597.

166 22 J. H. de Boer, The Dynamical Character of Adsorption, Oxford Univ. Press, London, 1968. 23 C. I. Smits, Thesis, Delft, 1978. 24 C. Thies, Macromolecules, 1 (1968) 335. 25 C. Thies, J. Collojd Interface Sci., 27 (1968) 734. 26 D. J. Stock, Nature, 170 (1952) 423. 27 H. M. Smith and I. E. Puddington, Can. J. Chem., 38 (1960) 1911.