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Associative interactions and surface tension in ionic surfactant solutions at concentrations much lower than the cmc
Associative Interactions and Surface Tension in Ionic Surfactant Solutions at Concentrations Much Lower than the CMC A. NIKOLOV, G. MARTYNOV, 1 AND D. EXEROWA Institute of Physical Chemistry, Bulgarian Academy of Sciences, Sofia 1040, Bulgaria Received August 15, 1979; accepted August 25, 1980 The surface pressure isotherms Acr(C~) of the ionic surfactants sodium dodecyl sulfate (NaDoS) and sodium octyl sulfate (NaOS) were measured using at different electrolyte concentration an accurate and sensitive sphere tensiometer. At 10-1 mole/liter NaC1, two particular points on the isotherms were noticed for surfactant concentrations below 10-4 mole/liter. The first, at Atr ~ 0.5 dyn/cm, corresponds to the formation of fiat premicelles in the solution, whereas the second corresponds to a phase transition in the adsorbed layer and this is probably associated with the disintegration of the premicelles on the surface but not in the bulk of the solution. The supplementary measurements of the surface potential and the time dependence of the surface tension show evidence of this hypothesis. INTRODUCTION
It has been generally accepted that micelles start to form only at the critical micelle concentration (CMC) and that in the case of concentrations lower than the CMC the solutions are molecular. The idea of bulk surfactant association prior to the CMC has been discussed by many authors. A review of the literature on this problem has been given by Zimmels et al. (1) and further work on this topic has been published by Farinato et al. (2). It seems to us worth following further the idea of surfactant association at concentrations lower than the CMC using more accurate methods. The most sensitive method for determining the CMC is that of surface tension (o-). Hitherto this method has been insufficiently sensitive for very dilute solutions. However, the sphere tensiometric method recently developed by Scheludko and Nikolov (3) is sensitive enough and in this work we 1 Present address: Institute of Physical Chemistry, Academy- of Sciences of the USSR, Moscow, USSR.
0021-9797/81/050116-09502.00/0 Copyright© 1981by AcademicPress,Inc. All rightsof reproductionin any formreserved.
use it to study the formation of premiceUes at concentration two orders of magnitude lower than the CMC. In comparing o- measured by two different authors, the results showed considerable differences (4, 5). These differences become quite significant in those cases when as a result of evaporation, or in the presence of impurities, etc., no equilibrium in the system can be immediately established. As methods which are insufficiently based theoretically are usually used, the obtained meaning of o- cannot be considered reliable. Thus, for example, in the cases of the drop volume method (6, 7) the correction made after Harkins and Brown, treating the drop deformation under the effect of gravitation is still insufficient to regard as reliable any meanings obtained by this method. The same is also true of the method of DuNouy as far as the corrections made in (8) are not considered. Considerable error can also arise as a result of the assumption that the three-phase contact angle is equal to zero, which has not been proved by direct measurements.
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SURFACE TENSION IN SURFACTANT SOLUTIONS
All these considerations made us go back to measuring the ionic surfactant surface tensions in the presence of electrolyte but this time with the help of an accurate and sensitive method (3) tested both theoretically and practically. METHODS AND MATERIALS
Certain progress in measurement techniques for surface tension was achieved as a result of the use of electronic feedback scales. The maximum weight of a ring, a sphere, or a cone, drawn from the solution interface, is measured (9-11). In the case of the sphere it is possible to describe theoretically the weighing technique of surface tension measurement which has been impossible so far on the basis of the method of Wilhelmy and DuNouy. Another advantage is the good reproducibility of the maximum weight and the wetting angle which is homogeneous and regular for small angles as a result of the small wetting perimeter (e.g., in case of alkyl sulfate aqueous solutions it ranges from 4 to 6 °, at 2' accuracy of ho- measurement corresponding to _+1.10 -3 dyn/cm (at radius of the s p h e r e - - R = 0.0563 cm (12, 13)). N a D o S is a typical representative of the ionic surfactants and has been a subject of numerous investigations (4-7, 14-24). The physicochemical properties of adsorbed films of N a D o S in the presence of electrolyte are usually interpreted on the basis of the A~(Cs) isotherms, where Ao- = O-o - o" is the surface tension drop with respect to o0, corresponding to the pure solvent, and Cs is the surfactant concentration. NaDoS, made by Henkel Company, had no maximum in the Ao-(Cs) isotherm which is observed using Wilhelmy's method for concentration before CMC, in the presence of D o O H (dodecyl alcohol) (24). The NaC1 - - a pure sample from Merck was roasted at 500°C to eliminate any trace surface active impurities. The solutions were made with distilled water with specific electric conductivity of 10-6 1)-1 cm -1 at 22°C.
1 17
Because the spherotensiometric method has sensitivity of 1 x 10.3 dyn/cm, the problem of what to accept as an equilibrium value of o- arises. We accepted a value for o-, which remained constant for 2 hr within the range sensibility of the method. A special device (sintered glass filter G-5) with an inbuilt heater was designed to guarantee constant pressure of the saturated vapors above the solution preventing any evaporation, which has a great effect on the value of Ao-. Due to the measures taken the changes of Cs and CNacb as a result of evaporation, were quite insignificant. Thus, for example, in the case of a solution containing 10.5 mole/liter N a D o S and 10-1 mole/liter NaC1 the concentration change after 24 hr, as a result of evaporation was 10-7 and 10-3 mole/liter, respectively. As we already said, changes occur over the long period of time necessary to establish complete equilibrium in the system. In addition, a constant temperature of 22°C is maintained continuously, for which two thermostats are used. One is designed for rough temperature control with an accuracy of -+ I°C with the help of an air thermostat, and the other, supplied with a special thermistor, is for fine temperature control with an accuracy of +0.02°C. A copper constant thermocouple measuring the water/air temperature permitting continuous recording with an accuracy of -+0.01°C was used as an indicator. The volume of the solution whose surface was measured was 30 cm 3 and its free surface was 30 cm 2. For this reason even in low volume concentration in the order of 10-5 mole/liter and high degree of molecule saturation in the order of F = 2 x 10TM moles/cm 2, the change of the volume concentration, as a result of adsorption, does not exceed the error of the solution preparation (e.g., in Cs = 10-5 mole/liter the magnitude of the error ~Cs is equal to 3 x 10-7 mole/liter). Regardless of the fact that N a D o S contains no D o O H (please see above), before every measurement the solution surface in Journal o f Colloid and Interface Science, Vol. 81, No. 1, May 1981
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NIKOLOV, MARTYNOV, AND EXEROWA
the measurement container was sucked by means of a special device 30 min after pouring.
3
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2
I
.'=. 30 RESULTS
AND
DISCUSSION
b 25
The AS(Cs) isotherms for NaDoS obtained from the spherotensiometric method are shown in Fig. (1); curves 1, 2, and 3 correspond to concentrations CNac~ = 10-1, 3.5 x 10-1, and 5 x 10-1 mole/liter, respectively. All three curves have a discontinuity in slope in the region 8 - 1 0 dyn/cm and have been drawn through the points using a square spline regression analysis (25). On all three salt solutions the high Ao- end of the data can be described by a linear sector, the onset of which has been calculated by differentiation of the polynomial spline functions and indicated by an arrow in each case. Previously, linear Ao- versus log C~ plots have been obtained by other authors (14-18) for data in the same concentration range as that in Fig. (1), which contrast with the discontinuities in the Ao- (log C~) plots derived from the data displayed here. Another unusual feature is shown by the Ao- results on very dilute surfactant solutions (10 - 6 - 1 0 -5 mole/liter) which for clarity are displayed on an expanded Cs scale in Fig. 2 for one salt concentration only, namely, 10-1 mole/liter. The initial region is linear from the origin up to 5o- ~ 0.5 dyn/ cm after which the derivative d A o - / d C ~ ~ 0 over a small range of Cs. Figure 3 illustrates the relation Ao-(Cs) for sodium octyl sulfate (NaOS) on 10-1 mole/liter NaC1. The measurement of Aofor NaOS was made by both the Wilhelmy plate (black dots) and the sphere tensiometric method (open circles). Evidently the two methods give satisfactorily close results but with different scatter. An exception is in the zone of concentration close to the bend in the curve Ao-(log Cs), the sphere tensiometric method gives a jump in the derivative at Ao- = 1.8 dyn/cm, whereas Journal of Colloid and Interface Science, Vol. 81, No. 1, M a y 1981
20
15
o!
%, -6
c~,
-5
-4
. -3 io~ [Cs(mol/ll]
FIG. 1. Dependence of surface tension on the NaDoS concentration. Curve 1 - - C N a c l = 10 1 mole/ liter; curve 2--CNacl = 3.5.10-* mole/liter; curve 3-CNaCl= 5.10 1 mole/liter at 22°C,
Wilhelmy's method gives 1.7 dyn/cm. The discontinuity is less pronounced here than in Fig. 1 for NaDoS. A comparison of the data on Fig. 3 with curve 1 on Fig. 1 indicates that here is a qualitative congruence and this is supported by the plots of Figs. 2 and 4. In the latter two figures initially there is a linear portion, probably where F = K C s (where F is the surface excess and K is adsorption constant), followed by a horizontal part where F ~ const. Finally there comes a curve of parabolic shape. This curve ends by a bend (Figs. 3 and 5) after which the dependence Ao- vs log Cs becomes linear. Similar curves obtained for two surfactants (NaDoS and NaOS) at several different electrolyte concentrations suggest that something of the same kind should be also observed in other ionic surfactants (and may be quite possible also for nonionic surfactants as indeed observed by E x e r o w a and Scheludko (26)). The unusual behavior of the Ao-(Cs) curves should be examined in more detail. From now on, for greater clarity we shall restrict ourselves to the case N a D o S and CNaCl = 10-1 mole/liter.
119
S U R F A C E T E N S I O N IN S U R F A C T A N T S O L U T I O N S
To
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c,, 106 [mot/t] FIG. 2. D e p e n d e n c e of surface tension on the N a D o S concentration w h e n CNaCl = 10 -x mole/liter at 22°C.
The initial linear portion of the curve Ao= K'C~ (Fig. 2) evidently corresponds to Henry's adsorption isotherm F = KC~ which
T
Z 10
41" log c s Imol/ll
FIG. 3. D e p e n d e n c e of surface tension and surface potential (AV) o f solution/air interface of the concentration o f N a O S w h e n C~acl = 10-1 mole/liter and t = 22°C for Ao-(log Cs) and for AV(log Cs) at 20°C. T h e values for Act after Wilhelmy are given in black dots and t h o s e of the spherotensiometric m e t h o d by circles; the values of AV obtained from Volhardt and Wtisteek are given in arrows.
conforms to a low degree of surface saturation and the absence of interaction between the adsorbed molecules. It seems that the strict linearity of the isotherm is preserved until Cs = 2.5 x 10-6 mole/liter, where the slope of the straight line suddenly drops to zero. Such a jump can be explained either by processes occurring in the adsorbed film or processes occurring in the bulk. Let us first discuss the first alternative. The simplest thing which we can admit is to assume that at Cs = 2 . 5 - 3 x 10-6 mole/ liter, some phase transition occurs in the surface. A more thorough analysis of the experimental data would make us give up this hypothesis. The strict preservation of H e n r y ' s coefficient K up to Cs = 2.5 × 10-6 mole/liter would indicate a complete lack of interaction between the adsorbed molecules before the turning p o i n t - - a n d a phase transition is impossible without such an interaction. Secondly, from Gibbs' isotherm F = dAo-/dlxs, where/z~ is the chemical potential of the surfactant, it follows that when Cs < 2.5 × 10-6 mole/liter the adsorption F has a definite value (F = KCs), Journal o f Colloid and Interface Science, Vol. 81, No. 1, M a y 1981
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NIKOLOV, MARTYNOV, AND EXEROWA
t~
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C$, 10s [mol/I] FIG. 4. Dependence of surface tension on the NaOS concentration when CNac~= 10-a mol/1 and t = 22°C. in the interval 2.5 x 10-6 mole/liter <-Cs 3 x 10 -6 mole/liter it is equal to zero, and atC~ = 3 x 10-6 mole/literit again j u m p s to the same value (or even higher) of F at C~ = 2.5 x 10.6 mole/liter. H o w e v e r , if the adsorbed molecules n u m b e r is equal to zero (F = 0) the question of what causes the phase transition arises. It is more natural to assume that the phase transition occurs not in the adsorbed m o n o l a y e r but in the bulk. As is generally k n o w n the chemical potential ~ remains unchanged and a/xs = 0 in the zone of two-phase existence. As a result of this in this concentration zone Gibbs' isotherm F = dAo-/dlx~ is reduced to F = 0/0, this according to the L ' H o s p i t a l rule can be equal to a r a n d o m finite value (including the F value at C~ = 2.5 x 10.6 mole/liter). In this way there is no longer any need for the unreliable assumption F = 0, and it becomes clear why in the beginning and at the end of the horizontal sector the value of F is approximately the same. I f in the concentration interval C~ = 2 . 5 - 3 x 10 .6 mole/liter at CNacl = 10 -1 mole/liter a phase transition occurs in the bulk of the solution, this has to affect not only the type o f the isotherm Ao-(C~), but also the other properties of the system. It is k n o w n that the lower the degree of supersaturation, the slower the new Journal of Colloid and Interface Science, Vol. 81, No. 1, May 1981
phase grows. F o r this reason we should expect that at Cs < 2.5 x 10-6 mole/liter when the system is m o n o p h a s e , the time for establishing the equilibrium should be relatively short, 2 at Cs = 2.5 x 10 -6 mole/liter when the new p h a s e appears, but the degree of supersaturation is very small, the time for establishing the equilibrium should rapidly increase and then decrease with the increase of the concentration (i.e., of the supersaturation). It is convenient during the establishing of equilibrium of the s y s t e m to w a t c h the change of Air with time (Fig. 6). Our measurements showed relaxation time t ~ 25 hr, at Cs = 2 x 10 -6 mole/liter, at Cs = 3 x 10 -5 mole/liter it increases to several hundred hours (200), and at Cs = 2.5 x 10 -4 mole/liter it is only a few hours. So there is full agreement with these assumptions. As was already shown (27), the process of surface tension establishment is controlled by the surfactant diffusion to the surface. For this reason the value of (Ao-) -1, plotted in coordinate ( 0 -1/2, p r o v e d to be a straight line ( t - - t i m e ) . The same thing h a p p e n e d in our case at Cs < 2.5 x 10 -6 mole/liter (Fig. It should be borne in mind that the solutions are very dilute--C, = 10-6 mole/liter and therefore the time for establishing equilibrium through diffusion to surface and adsorption, etc., is rather long.
SURFACE TENSION IN SURFACTANT SOLUTIONS
121
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FIo. 5. Dependence on the surface tension (Ao-)and surface potential (AV) on solution/air interface of NaDoSconcentrationwhenCNacl = 10-1mole/literand t = 22°C. The values of Ao- are given in circles and values for AV are given in arrows.
7, c u r v e 1). A t Cs > 2.5 x 10 -6 m o l e / l i t e r t h e e x p e r i m e n t g a v e b r o k e n s t r a i g h t lines ( c u r v e 2 on Fig. 7). F r o m t h e p o i n t o f v i e w o f t h e i d e a p u t f o r w a r d h e r e , this
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FIG. 6. Time relation of surface tension or(t). Curve 2 × 10-6 mole/liter; c u r v e 2 - - C N a o o S = 3 × 10-3 mole/liter; curve 3--CNaDos = 2.5 × 10-4 mole/liter at CNac~= 5 × 10-1 mole/liter and t = 22°C. 1--CNaDoS =
10
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-3
log Cs E r n o l / I ]
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ii i t
i
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FIG. 7. Relation of the depression of surface tension on time in plots 1/Acr(1/tl/Z)--on the top of the abscissa (t) is given in minutes, below in hours. Curve 1--CNaDoS= 1.5 x 10-6 mole/liter; curve 2 - CNaDoS= 4 X 10-6 mole/liter at CNaci = 10-1 mole/liter at 22°C.
result can be explained quite simply. In the initial m o m e n t , w h e n the n e w p h a s e h a s n o t b e e n f o r m e d y e t , t h e s y s t e m b e h a v e s as a monophase one. At t ~ 5 hr the number of particles of the new phase becomes already sufficiently high a n d t h e f u r t h e r c o u r s e o f t h e p r o c e s s is d e t e r m i n e d b y t h e d i f f u s i o n s p e e d to t h e i n t e r f a c e o f t h e s e p a r t i c u l a r "new" particles. From the diffusion equations it is w e l l k n o w n t h a t t h e i r s o l u t i o n d e p e n d s n o t s i m p l y on 1/t 1/2 b u t on t h e c o m b i n a t i o n ( 1 / D ) I 1/2, w h e r e D is t h e d i f f u s i o n c o e f f i c i e n t . F o r this r e a s o n t h e b r e a k o f t h e s t r a i g h t line in c u r v e 2 (Fig. 7) i l l u s t r a t e s the difference of the diffusion coefficients of the particles of the "old" and the "new" p h a s e . B u t as D ~ 1/R, w h e r e R is t h e e q u i v a l e n t r a d i u s o f t h e p a r t i c l e , t h e d a t a in Fig. 7 m e a n t h a t t h e p a r t i c l e r a d i i o f t h e n e w p h a s e a r e a p p r o x i m a t e l y t w i c e a s big as t h a t o f t h e o l d o n e , f o r m e d b y t h e i n d i v i d ual m o l e c u l e s . E v i d e n t l y this is o n l y p o s s i b l e in t h e c a s e Journal o f Colloid and Interface Science, Vol. 81, No. 1, M a y 1981
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NIKOLOV, MARTYNOV, AND EXEROWA
when the " n e w " phase of micelles consists of a fairly small number of N a D o S molecules. Insofar the Cs = 2.5 x 10-6 mole/ liter concentration is approximately two orders lower than the critical concentration of micelle formation (CMC) where the spherical micelles of MacBain form, we should assume that here a formation of simple fiat micelles is possible. H e n c e f o r t h we shall call them premicelles and the surfactant concentration at which their formation begins shall be called critical premicelles formation concentration (CPC). Unlike the peculiarity arising in the curve h~r(log Cs) at C+ = CPC, the jump of the derivative dAo-/d log C+ at Ao--~ 10 dyn/ cm and Cs = 10-~ mole/liter (Figs. 1 and 5) can be explained only by a phase transition in the adsorbed layer. Actually the data on the dependence of the surface potential indicate that at C+ ~ 10-~ mole/liter for NaDoS and at C+ ~ 10-3 mole/liter for NaOS there is a clearly expressed minimum (Figs. 3 and 5). At the same time no peculiarities are adsorbed in the curves for the relaxation time relation t(Cs) characterizing the volume properties of the solution at C~ = 10-5 mole/liter. The clear correlation of two surface properties is a clear evidence of the "surface" character of the phase transition. The nature of the "surface" phase transition can be understood if we assume that at Cs > CPC, an adsorption not if individual surfactant molecules but of whole premicelles occurs. When lying on the surface the flat disks of the premicelles cannot secure sufficiently complete surface saturation. For this reason, at Cs ~ 10-~ mole/ liter, disintegration of the premicelles at the surface takes place, followed by adsorption of individual molecules. Furthermore, while in Henry's zone these molecules are situated "lying" at the surface, now they occupy an " e r e c t " position, because in this case the adsorption of individual molecules can guarantee a larger capacity of the adsorbed layer. The disintegration of the premicelles at the surface can be accomJournal of Colloid and Interface Science, Vol. 81, No. 1, May 1981
panied of the mental curves
by a certain reduction in the size adsorption (the latter is an experifact, as it can be seen in Fig. 1, 1, 2, 3, the slope of the curves dA~r/d log C + - F on the left side of the phase transition is larger than that of the right side and the point of the phase transition, therefore, diminishes in F). To understand the reason for such a decrease we should remember that any premicelle should be neutral as a whole? The electrostatic forces of repulsion between the adsorbed individual premicelles should, therefore, be either very small or completely absent (the electrolyte concentration in the solution is equal to CNacl = 10-1 mole/liter, or even higher, which is an indication of strong suppression of the Debye atmospheres). When the premicelles are destroyed, the electric neutrality in the adsorption plane (coinciding with the water-air interface) is violated, great forces of repulsion appear between the individual D o S - ions and the absolute number of the adsorbed NaDoS molecules is reduced. During the further increase of the surfactant volume concentration the number of the adsorbed ions shall increase. In the same way the change in the charge of the double layer and the jump of the potential AV, which it determines, are also experimentally observed (see Figs. 3 and 5). The relation AV(log Cs) for NaDoS solutions in the presence of 10-1 mole/liter of NaC1 was measured by the method of the radioactive probe (22, 23). The results obtained are given in Fig. 5 (by double arrows). They are in good agreement with those measured by other authors (20, 22). The surfactant concentration at which the destruction of the premicelles adsorbed at the interface should naturally be called As a whole it is, of course, preserved, but only at the expense of their attraction by Na+ in the solution, now situated under the DoS- adsorption layer, i.e., at the expense of the double electric layer formed.
SURFACE TENSION IN SURFACTANT SOLUTIONS
critical concentration of the premicelle disintegration (CCPD). Premicelle formation for nonionic surfactants is also possible and so is their destruction in the adsorbed layer when the latter is saturated. But the destruction of premicelles in the nonionic surfactants can be accompanied by increasing of F and not by its decreasing because there are no electrostatic repulsion forces noting in them. If the jump of F is small, the CCPD point on the curve A~(Cs) may not be noticed. The above assumption of a phase transition in the bulk is connected with two circumstances: (a) constancy of monomer concentration after CPC, and (b) a marked change in the physicochemical properties of the system (density, refraction coefficient, viscosity, etc.) at CPC. The problem of association in the bulk can be treated from the standpoint of the mass action low as well (29). Such a consideration is worthwhile. The two approaches are equivalent for the case of CMC, when the number of molecules in the aggregates is high. CONCLUSION
All the data we have obtained concerning surface tension Ao-(Cs) and surface potential AV(Cs) may be explained by the formation of premicelles in the solution's bulk. The formation of premicelles needs, of course, a direct proof based on the alteration of some volume property of the surfactant solution. We have obtained such changes in very low bulk concentrations of the surfactant. We have used measurements of the specific conductivity in solutions of n-alkanols/ water (30). Referring to the literature, it is well known that in the case of nonaqueous solutions [CzHsOH/c-C6H12, ROH/CC14] there is a process of aggregation (31).
123
The above-mentioned considerations do not provide a strict proof for hypothesis. In the future we hope to make corresponding measurements in the bulk but as we are well aware there will be a lot of difficulties. The change of the specific conductivity, for example, is extremely small. The optic methods cannot be easily applied in the case because the medium is practically isotropic. REFERENCES 1. Zimmels, Y., Lin, I., and Friend, J., Colloid Polym. Sci. 253, 404 (1975). 2. Farinato, R. S., and Rowell, K. L., J. Colloid Interface Sci. 66, 483 (1978). 3. Scheludko, A., and Nikolov, A., Colloid Polym. Sci. 253, 396 (1975). 4. Pethica, B., Trans. Faraday Soc. 50, 413 (1954), 5. Vijayan, S., Woods, D. R., and Vaya, H., Canad. J. Chem. Eng. 55, 718 (1977). 6. Matijevic, E., and Pethica, B., Trans. Faraday Soc. 54, 1982 (1958). 7. Tajima, K., Bull. Chem. Soc. Japan 43, 3063 (1970). 8. Huh, C., and Mason, S. G., Colloid and Polym. Sci. 253, 566 (1975). 9. Burri, J., and Hartland, S., Tenside Deterg. 1, 13 (1976). 10. Huh, C., and Mason, S. G., Canad. J. Chem. 54, 969 (1976). 11. Cini, R., Loglie, G., and Ficabli, A., J. Colloid Sci., 41,287 (1972). 12. Nikolov, A., Jeliaskova, L., and Jeliaskov, J., God. Sofii Univ., Chim. Fac. 70, 401 (19751976). 13. Nikolov, A., Colloid Polym. Sci., in press. 14. Matijevic, E., and Pethica, B., Trans. Faraday Soc. 54, 1390 (1958). 15. Matijevic, E., and Pethica, B., Trans. Faraday Soc. 54, 1400 (1958). 16. Tajima, K., Bull. Chem. Soe. Japan 44, 1767 (1971). 17. Brady, A. P., J. Colloid Sci., 4, 417 (1949). 18. Tajima, K., Muramatsu, M., and Sasaki, T., Bull. Chem. Soc. Japan 43, 1991 (1970). 19. Sasaki, J., Tajima, K., and Sasaki, T., Bull. Chem. Soc. Japan 45, 348 (1972). 20. Pethica, B., and Few, A., Discussions Faraday Soc., 18, 258 (1954). 21. Zwierzykowski, W., CIP "Chemistry Physics and Journal of Colloid and Interface Science, Vol. 81, No. 1, May 1981
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22. 23. 24. 25.
26.
NIKOLOV, MARTYNOV, AND EXEROWA Application of Surface Active Substances" (Brusselles) II, 801 (1964). Vollhardt, D., and Wiistek, R., Kolloid J. M. 36, 1121 (1974). Betts, I., and Pethica, B., Trans. Faraday Soc. 56, 1515 (1960). Harrold, S. P., J. Colloid Sci., 15, 280 (1960). Krug, G. K., and Kaishev, V. K., Thesis of the Reports of the Vth Russian Conference on design and automation of experiments in scientific investigation, p. 14, Moscow, 1976. Exerowa, D., and Scheludko, A., Proc. IV Intern. Congr. Surface Activity, Brussels, II, 1097 (1964).
1ournal of Colloid and Interface Science, Vol. 81, No. 1, May 1981
27. Baret, J. P., and Roux, R. A., Kolloid Z. 225, 139 (1968). 28. Frayer, D., K6hler, P., and Ohlanbusch, H. D., Kolloidchem. Z. 196, 153 (1963). 29. Gorkill, J. M., Goodman, J. F., and Tate, J. B., in "Hydrogen-Bonded Solvent Systems" (A. K. Covington and R. Jones, Eds.), p. 181. Barnes & Noble, New York, 1968. 30. Nikolov, A., Kashchiev, D., Exerowa, D., God. Sofii Univ. Chim. Fac. 73, in press. 31. Prigogine, I., Defay, R., "Chemical Thermodynamics", p. 385. Longmans, London, 1954.
It has been generally accepted that micelles start to form only at the critical micelle concentration (CMC) and that in the case of concentrations lower than the CMC the solutions are molecular. The idea of bulk surfactant association prior to the CMC has been discussed by many authors. A review of the literature on this problem has been given by Zimmels et al. (1) and further work on this topic has been published by Farinato et al. (2). It seems to us worth following further the idea of surfactant association at concentrations lower than the CMC using more accurate methods. The most sensitive method for determining the CMC is that of surface tension (o-). Hitherto this method has been insufficiently sensitive for very dilute solutions. However, the sphere tensiometric method recently developed by Scheludko and Nikolov (3) is sensitive enough and in this work we 1 Present address: Institute of Physical Chemistry, Academy- of Sciences of the USSR, Moscow, USSR.
0021-9797/81/050116-09502.00/0 Copyright© 1981by AcademicPress,Inc. All rightsof reproductionin any formreserved.
use it to study the formation of premiceUes at concentration two orders of magnitude lower than the CMC. In comparing o- measured by two different authors, the results showed considerable differences (4, 5). These differences become quite significant in those cases when as a result of evaporation, or in the presence of impurities, etc., no equilibrium in the system can be immediately established. As methods which are insufficiently based theoretically are usually used, the obtained meaning of o- cannot be considered reliable. Thus, for example, in the cases of the drop volume method (6, 7) the correction made after Harkins and Brown, treating the drop deformation under the effect of gravitation is still insufficient to regard as reliable any meanings obtained by this method. The same is also true of the method of DuNouy as far as the corrections made in (8) are not considered. Considerable error can also arise as a result of the assumption that the three-phase contact angle is equal to zero, which has not been proved by direct measurements.
116
Journal of Colloldand Interface Science, Vol.81, No. 1, May 1981
SURFACE TENSION IN SURFACTANT SOLUTIONS
All these considerations made us go back to measuring the ionic surfactant surface tensions in the presence of electrolyte but this time with the help of an accurate and sensitive method (3) tested both theoretically and practically. METHODS AND MATERIALS
Certain progress in measurement techniques for surface tension was achieved as a result of the use of electronic feedback scales. The maximum weight of a ring, a sphere, or a cone, drawn from the solution interface, is measured (9-11). In the case of the sphere it is possible to describe theoretically the weighing technique of surface tension measurement which has been impossible so far on the basis of the method of Wilhelmy and DuNouy. Another advantage is the good reproducibility of the maximum weight and the wetting angle which is homogeneous and regular for small angles as a result of the small wetting perimeter (e.g., in case of alkyl sulfate aqueous solutions it ranges from 4 to 6 °, at 2' accuracy of ho- measurement corresponding to _+1.10 -3 dyn/cm (at radius of the s p h e r e - - R = 0.0563 cm (12, 13)). N a D o S is a typical representative of the ionic surfactants and has been a subject of numerous investigations (4-7, 14-24). The physicochemical properties of adsorbed films of N a D o S in the presence of electrolyte are usually interpreted on the basis of the A~(Cs) isotherms, where Ao- = O-o - o" is the surface tension drop with respect to o0, corresponding to the pure solvent, and Cs is the surfactant concentration. NaDoS, made by Henkel Company, had no maximum in the Ao-(Cs) isotherm which is observed using Wilhelmy's method for concentration before CMC, in the presence of D o O H (dodecyl alcohol) (24). The NaC1 - - a pure sample from Merck was roasted at 500°C to eliminate any trace surface active impurities. The solutions were made with distilled water with specific electric conductivity of 10-6 1)-1 cm -1 at 22°C.
1 17
Because the spherotensiometric method has sensitivity of 1 x 10.3 dyn/cm, the problem of what to accept as an equilibrium value of o- arises. We accepted a value for o-, which remained constant for 2 hr within the range sensibility of the method. A special device (sintered glass filter G-5) with an inbuilt heater was designed to guarantee constant pressure of the saturated vapors above the solution preventing any evaporation, which has a great effect on the value of Ao-. Due to the measures taken the changes of Cs and CNacb as a result of evaporation, were quite insignificant. Thus, for example, in the case of a solution containing 10.5 mole/liter N a D o S and 10-1 mole/liter NaC1 the concentration change after 24 hr, as a result of evaporation was 10-7 and 10-3 mole/liter, respectively. As we already said, changes occur over the long period of time necessary to establish complete equilibrium in the system. In addition, a constant temperature of 22°C is maintained continuously, for which two thermostats are used. One is designed for rough temperature control with an accuracy of -+ I°C with the help of an air thermostat, and the other, supplied with a special thermistor, is for fine temperature control with an accuracy of +0.02°C. A copper constant thermocouple measuring the water/air temperature permitting continuous recording with an accuracy of -+0.01°C was used as an indicator. The volume of the solution whose surface was measured was 30 cm 3 and its free surface was 30 cm 2. For this reason even in low volume concentration in the order of 10-5 mole/liter and high degree of molecule saturation in the order of F = 2 x 10TM moles/cm 2, the change of the volume concentration, as a result of adsorption, does not exceed the error of the solution preparation (e.g., in Cs = 10-5 mole/liter the magnitude of the error ~Cs is equal to 3 x 10-7 mole/liter). Regardless of the fact that N a D o S contains no D o O H (please see above), before every measurement the solution surface in Journal o f Colloid and Interface Science, Vol. 81, No. 1, May 1981
118
NIKOLOV, MARTYNOV, AND EXEROWA
the measurement container was sucked by means of a special device 30 min after pouring.
3
r--i 3,5 E
2
I
.'=. 30 RESULTS
AND
DISCUSSION
b 25
The AS(Cs) isotherms for NaDoS obtained from the spherotensiometric method are shown in Fig. (1); curves 1, 2, and 3 correspond to concentrations CNac~ = 10-1, 3.5 x 10-1, and 5 x 10-1 mole/liter, respectively. All three curves have a discontinuity in slope in the region 8 - 1 0 dyn/cm and have been drawn through the points using a square spline regression analysis (25). On all three salt solutions the high Ao- end of the data can be described by a linear sector, the onset of which has been calculated by differentiation of the polynomial spline functions and indicated by an arrow in each case. Previously, linear Ao- versus log C~ plots have been obtained by other authors (14-18) for data in the same concentration range as that in Fig. (1), which contrast with the discontinuities in the Ao- (log C~) plots derived from the data displayed here. Another unusual feature is shown by the Ao- results on very dilute surfactant solutions (10 - 6 - 1 0 -5 mole/liter) which for clarity are displayed on an expanded Cs scale in Fig. 2 for one salt concentration only, namely, 10-1 mole/liter. The initial region is linear from the origin up to 5o- ~ 0.5 dyn/ cm after which the derivative d A o - / d C ~ ~ 0 over a small range of Cs. Figure 3 illustrates the relation Ao-(Cs) for sodium octyl sulfate (NaOS) on 10-1 mole/liter NaC1. The measurement of Aofor NaOS was made by both the Wilhelmy plate (black dots) and the sphere tensiometric method (open circles). Evidently the two methods give satisfactorily close results but with different scatter. An exception is in the zone of concentration close to the bend in the curve Ao-(log Cs), the sphere tensiometric method gives a jump in the derivative at Ao- = 1.8 dyn/cm, whereas Journal of Colloid and Interface Science, Vol. 81, No. 1, M a y 1981
20
15
o!
%, -6
c~,
-5
-4
. -3 io~ [Cs(mol/ll]
FIG. 1. Dependence of surface tension on the NaDoS concentration. Curve 1 - - C N a c l = 10 1 mole/ liter; curve 2--CNacl = 3.5.10-* mole/liter; curve 3-CNaCl= 5.10 1 mole/liter at 22°C,
Wilhelmy's method gives 1.7 dyn/cm. The discontinuity is less pronounced here than in Fig. 1 for NaDoS. A comparison of the data on Fig. 3 with curve 1 on Fig. 1 indicates that here is a qualitative congruence and this is supported by the plots of Figs. 2 and 4. In the latter two figures initially there is a linear portion, probably where F = K C s (where F is the surface excess and K is adsorption constant), followed by a horizontal part where F ~ const. Finally there comes a curve of parabolic shape. This curve ends by a bend (Figs. 3 and 5) after which the dependence Ao- vs log Cs becomes linear. Similar curves obtained for two surfactants (NaDoS and NaOS) at several different electrolyte concentrations suggest that something of the same kind should be also observed in other ionic surfactants (and may be quite possible also for nonionic surfactants as indeed observed by E x e r o w a and Scheludko (26)). The unusual behavior of the Ao-(Cs) curves should be examined in more detail. From now on, for greater clarity we shall restrict ourselves to the case N a D o S and CNaCl = 10-1 mole/liter.
119
S U R F A C E T E N S I O N IN S U R F A C T A N T S O L U T I O N S
To
/.
1.9
3
2
1
o
1
2
I
I
I
I
l
I
I
I
3
/.
5
6
7
8
9
10
c,, 106 [mot/t] FIG. 2. D e p e n d e n c e of surface tension on the N a D o S concentration w h e n CNaCl = 10 -x mole/liter at 22°C.
The initial linear portion of the curve Ao= K'C~ (Fig. 2) evidently corresponds to Henry's adsorption isotherm F = KC~ which
T
Z 10
41" log c s Imol/ll
FIG. 3. D e p e n d e n c e of surface tension and surface potential (AV) o f solution/air interface of the concentration o f N a O S w h e n C~acl = 10-1 mole/liter and t = 22°C for Ao-(log Cs) and for AV(log Cs) at 20°C. T h e values for Act after Wilhelmy are given in black dots and t h o s e of the spherotensiometric m e t h o d by circles; the values of AV obtained from Volhardt and Wtisteek are given in arrows.
conforms to a low degree of surface saturation and the absence of interaction between the adsorbed molecules. It seems that the strict linearity of the isotherm is preserved until Cs = 2.5 x 10-6 mole/liter, where the slope of the straight line suddenly drops to zero. Such a jump can be explained either by processes occurring in the adsorbed film or processes occurring in the bulk. Let us first discuss the first alternative. The simplest thing which we can admit is to assume that at Cs = 2 . 5 - 3 x 10-6 mole/ liter, some phase transition occurs in the surface. A more thorough analysis of the experimental data would make us give up this hypothesis. The strict preservation of H e n r y ' s coefficient K up to Cs = 2.5 × 10-6 mole/liter would indicate a complete lack of interaction between the adsorbed molecules before the turning p o i n t - - a n d a phase transition is impossible without such an interaction. Secondly, from Gibbs' isotherm F = dAo-/dlxs, where/z~ is the chemical potential of the surfactant, it follows that when Cs < 2.5 × 10-6 mole/liter the adsorption F has a definite value (F = KCs), Journal o f Colloid and Interface Science, Vol. 81, No. 1, M a y 1981
120
NIKOLOV, MARTYNOV, AND EXEROWA
t~
2.0
113
I
I
t
I
i0
20
30
40
C$, 10s [mol/I] FIG. 4. Dependence of surface tension on the NaOS concentration when CNac~= 10-a mol/1 and t = 22°C. in the interval 2.5 x 10-6 mole/liter <-Cs 3 x 10 -6 mole/liter it is equal to zero, and atC~ = 3 x 10-6 mole/literit again j u m p s to the same value (or even higher) of F at C~ = 2.5 x 10.6 mole/liter. H o w e v e r , if the adsorbed molecules n u m b e r is equal to zero (F = 0) the question of what causes the phase transition arises. It is more natural to assume that the phase transition occurs not in the adsorbed m o n o l a y e r but in the bulk. As is generally k n o w n the chemical potential ~ remains unchanged and a/xs = 0 in the zone of two-phase existence. As a result of this in this concentration zone Gibbs' isotherm F = dAo-/dlx~ is reduced to F = 0/0, this according to the L ' H o s p i t a l rule can be equal to a r a n d o m finite value (including the F value at C~ = 2.5 x 10.6 mole/liter). In this way there is no longer any need for the unreliable assumption F = 0, and it becomes clear why in the beginning and at the end of the horizontal sector the value of F is approximately the same. I f in the concentration interval C~ = 2 . 5 - 3 x 10 .6 mole/liter at CNacl = 10 -1 mole/liter a phase transition occurs in the bulk of the solution, this has to affect not only the type o f the isotherm Ao-(C~), but also the other properties of the system. It is k n o w n that the lower the degree of supersaturation, the slower the new Journal of Colloid and Interface Science, Vol. 81, No. 1, May 1981
phase grows. F o r this reason we should expect that at Cs < 2.5 x 10-6 mole/liter when the system is m o n o p h a s e , the time for establishing the equilibrium should be relatively short, 2 at Cs = 2.5 x 10 -6 mole/liter when the new p h a s e appears, but the degree of supersaturation is very small, the time for establishing the equilibrium should rapidly increase and then decrease with the increase of the concentration (i.e., of the supersaturation). It is convenient during the establishing of equilibrium of the s y s t e m to w a t c h the change of Air with time (Fig. 6). Our measurements showed relaxation time t ~ 25 hr, at Cs = 2 x 10 -6 mole/liter, at Cs = 3 x 10 -5 mole/liter it increases to several hundred hours (200), and at Cs = 2.5 x 10 -4 mole/liter it is only a few hours. So there is full agreement with these assumptions. As was already shown (27), the process of surface tension establishment is controlled by the surfactant diffusion to the surface. For this reason the value of (Ao-) -1, plotted in coordinate ( 0 -1/2, p r o v e d to be a straight line ( t - - t i m e ) . The same thing h a p p e n e d in our case at Cs < 2.5 x 10 -6 mole/liter (Fig. It should be borne in mind that the solutions are very dilute--C, = 10-6 mole/liter and therefore the time for establishing equilibrium through diffusion to surface and adsorption, etc., is rather long.
SURFACE TENSION IN SURFACTANT SOLUTIONS
121
k~
7 30
2.0
y
b
<~
l
1,5 °
20
1,0 _.,-.------0--2 -50
0.5 I/VT(iO 3 ) -6
-5
-4
I
FIo. 5. Dependence on the surface tension (Ao-)and surface potential (AV) on solution/air interface of NaDoSconcentrationwhenCNacl = 10-1mole/literand t = 22°C. The values of Ao- are given in circles and values for AV are given in arrows.
7, c u r v e 1). A t Cs > 2.5 x 10 -6 m o l e / l i t e r t h e e x p e r i m e n t g a v e b r o k e n s t r a i g h t lines ( c u r v e 2 on Fig. 7). F r o m t h e p o i n t o f v i e w o f t h e i d e a p u t f o r w a r d h e r e , this
73.2
=., .-o, 7 2 . 7 b
72.2 170h
61.0
o
60.9
a-
2
38.2
37,7
37.2
~
n
i
5
i
I0
o
i
15
~
3
u-
2
0
215
,[hi
FIG. 6. Time relation of surface tension or(t). Curve 2 × 10-6 mole/liter; c u r v e 2 - - C N a o o S = 3 × 10-3 mole/liter; curve 3--CNaDos = 2.5 × 10-4 mole/liter at CNac~= 5 × 10-1 mole/liter and t = 22°C. 1--CNaDoS =
10
5
-3
log Cs E r n o l / I ]
15
ii i t
i
i I
i
8
~.
3
2
I
i i
h
FIG. 7. Relation of the depression of surface tension on time in plots 1/Acr(1/tl/Z)--on the top of the abscissa (t) is given in minutes, below in hours. Curve 1--CNaDoS= 1.5 x 10-6 mole/liter; curve 2 - CNaDoS= 4 X 10-6 mole/liter at CNaci = 10-1 mole/liter at 22°C.
result can be explained quite simply. In the initial m o m e n t , w h e n the n e w p h a s e h a s n o t b e e n f o r m e d y e t , t h e s y s t e m b e h a v e s as a monophase one. At t ~ 5 hr the number of particles of the new phase becomes already sufficiently high a n d t h e f u r t h e r c o u r s e o f t h e p r o c e s s is d e t e r m i n e d b y t h e d i f f u s i o n s p e e d to t h e i n t e r f a c e o f t h e s e p a r t i c u l a r "new" particles. From the diffusion equations it is w e l l k n o w n t h a t t h e i r s o l u t i o n d e p e n d s n o t s i m p l y on 1/t 1/2 b u t on t h e c o m b i n a t i o n ( 1 / D ) I 1/2, w h e r e D is t h e d i f f u s i o n c o e f f i c i e n t . F o r this r e a s o n t h e b r e a k o f t h e s t r a i g h t line in c u r v e 2 (Fig. 7) i l l u s t r a t e s the difference of the diffusion coefficients of the particles of the "old" and the "new" p h a s e . B u t as D ~ 1/R, w h e r e R is t h e e q u i v a l e n t r a d i u s o f t h e p a r t i c l e , t h e d a t a in Fig. 7 m e a n t h a t t h e p a r t i c l e r a d i i o f t h e n e w p h a s e a r e a p p r o x i m a t e l y t w i c e a s big as t h a t o f t h e o l d o n e , f o r m e d b y t h e i n d i v i d ual m o l e c u l e s . E v i d e n t l y this is o n l y p o s s i b l e in t h e c a s e Journal o f Colloid and Interface Science, Vol. 81, No. 1, M a y 1981
122
NIKOLOV, MARTYNOV, AND EXEROWA
when the " n e w " phase of micelles consists of a fairly small number of N a D o S molecules. Insofar the Cs = 2.5 x 10-6 mole/ liter concentration is approximately two orders lower than the critical concentration of micelle formation (CMC) where the spherical micelles of MacBain form, we should assume that here a formation of simple fiat micelles is possible. H e n c e f o r t h we shall call them premicelles and the surfactant concentration at which their formation begins shall be called critical premicelles formation concentration (CPC). Unlike the peculiarity arising in the curve h~r(log Cs) at C+ = CPC, the jump of the derivative dAo-/d log C+ at Ao--~ 10 dyn/ cm and Cs = 10-~ mole/liter (Figs. 1 and 5) can be explained only by a phase transition in the adsorbed layer. Actually the data on the dependence of the surface potential indicate that at C+ ~ 10-~ mole/liter for NaDoS and at C+ ~ 10-3 mole/liter for NaOS there is a clearly expressed minimum (Figs. 3 and 5). At the same time no peculiarities are adsorbed in the curves for the relaxation time relation t(Cs) characterizing the volume properties of the solution at C~ = 10-5 mole/liter. The clear correlation of two surface properties is a clear evidence of the "surface" character of the phase transition. The nature of the "surface" phase transition can be understood if we assume that at Cs > CPC, an adsorption not if individual surfactant molecules but of whole premicelles occurs. When lying on the surface the flat disks of the premicelles cannot secure sufficiently complete surface saturation. For this reason, at Cs ~ 10-~ mole/ liter, disintegration of the premicelles at the surface takes place, followed by adsorption of individual molecules. Furthermore, while in Henry's zone these molecules are situated "lying" at the surface, now they occupy an " e r e c t " position, because in this case the adsorption of individual molecules can guarantee a larger capacity of the adsorbed layer. The disintegration of the premicelles at the surface can be accomJournal of Colloid and Interface Science, Vol. 81, No. 1, May 1981
panied of the mental curves
by a certain reduction in the size adsorption (the latter is an experifact, as it can be seen in Fig. 1, 1, 2, 3, the slope of the curves dA~r/d log C + - F on the left side of the phase transition is larger than that of the right side and the point of the phase transition, therefore, diminishes in F). To understand the reason for such a decrease we should remember that any premicelle should be neutral as a whole? The electrostatic forces of repulsion between the adsorbed individual premicelles should, therefore, be either very small or completely absent (the electrolyte concentration in the solution is equal to CNacl = 10-1 mole/liter, or even higher, which is an indication of strong suppression of the Debye atmospheres). When the premicelles are destroyed, the electric neutrality in the adsorption plane (coinciding with the water-air interface) is violated, great forces of repulsion appear between the individual D o S - ions and the absolute number of the adsorbed NaDoS molecules is reduced. During the further increase of the surfactant volume concentration the number of the adsorbed ions shall increase. In the same way the change in the charge of the double layer and the jump of the potential AV, which it determines, are also experimentally observed (see Figs. 3 and 5). The relation AV(log Cs) for NaDoS solutions in the presence of 10-1 mole/liter of NaC1 was measured by the method of the radioactive probe (22, 23). The results obtained are given in Fig. 5 (by double arrows). They are in good agreement with those measured by other authors (20, 22). The surfactant concentration at which the destruction of the premicelles adsorbed at the interface should naturally be called As a whole it is, of course, preserved, but only at the expense of their attraction by Na+ in the solution, now situated under the DoS- adsorption layer, i.e., at the expense of the double electric layer formed.
SURFACE TENSION IN SURFACTANT SOLUTIONS
critical concentration of the premicelle disintegration (CCPD). Premicelle formation for nonionic surfactants is also possible and so is their destruction in the adsorbed layer when the latter is saturated. But the destruction of premicelles in the nonionic surfactants can be accompanied by increasing of F and not by its decreasing because there are no electrostatic repulsion forces noting in them. If the jump of F is small, the CCPD point on the curve A~(Cs) may not be noticed. The above assumption of a phase transition in the bulk is connected with two circumstances: (a) constancy of monomer concentration after CPC, and (b) a marked change in the physicochemical properties of the system (density, refraction coefficient, viscosity, etc.) at CPC. The problem of association in the bulk can be treated from the standpoint of the mass action low as well (29). Such a consideration is worthwhile. The two approaches are equivalent for the case of CMC, when the number of molecules in the aggregates is high. CONCLUSION
All the data we have obtained concerning surface tension Ao-(Cs) and surface potential AV(Cs) may be explained by the formation of premicelles in the solution's bulk. The formation of premicelles needs, of course, a direct proof based on the alteration of some volume property of the surfactant solution. We have obtained such changes in very low bulk concentrations of the surfactant. We have used measurements of the specific conductivity in solutions of n-alkanols/ water (30). Referring to the literature, it is well known that in the case of nonaqueous solutions [CzHsOH/c-C6H12, ROH/CC14] there is a process of aggregation (31).
123
The above-mentioned considerations do not provide a strict proof for hypothesis. In the future we hope to make corresponding measurements in the bulk but as we are well aware there will be a lot of difficulties. The change of the specific conductivity, for example, is extremely small. The optic methods cannot be easily applied in the case because the medium is practically isotropic. REFERENCES 1. Zimmels, Y., Lin, I., and Friend, J., Colloid Polym. Sci. 253, 404 (1975). 2. Farinato, R. S., and Rowell, K. L., J. Colloid Interface Sci. 66, 483 (1978). 3. Scheludko, A., and Nikolov, A., Colloid Polym. Sci. 253, 396 (1975). 4. Pethica, B., Trans. Faraday Soc. 50, 413 (1954), 5. Vijayan, S., Woods, D. R., and Vaya, H., Canad. J. Chem. Eng. 55, 718 (1977). 6. Matijevic, E., and Pethica, B., Trans. Faraday Soc. 54, 1982 (1958). 7. Tajima, K., Bull. Chem. Soc. Japan 43, 3063 (1970). 8. Huh, C., and Mason, S. G., Colloid and Polym. Sci. 253, 566 (1975). 9. Burri, J., and Hartland, S., Tenside Deterg. 1, 13 (1976). 10. Huh, C., and Mason, S. G., Canad. J. Chem. 54, 969 (1976). 11. Cini, R., Loglie, G., and Ficabli, A., J. Colloid Sci., 41,287 (1972). 12. Nikolov, A., Jeliaskova, L., and Jeliaskov, J., God. Sofii Univ., Chim. Fac. 70, 401 (19751976). 13. Nikolov, A., Colloid Polym. Sci., in press. 14. Matijevic, E., and Pethica, B., Trans. Faraday Soc. 54, 1390 (1958). 15. Matijevic, E., and Pethica, B., Trans. Faraday Soc. 54, 1400 (1958). 16. Tajima, K., Bull. Chem. Soe. Japan 44, 1767 (1971). 17. Brady, A. P., J. Colloid Sci., 4, 417 (1949). 18. Tajima, K., Muramatsu, M., and Sasaki, T., Bull. Chem. Soc. Japan 43, 1991 (1970). 19. Sasaki, J., Tajima, K., and Sasaki, T., Bull. Chem. Soc. Japan 45, 348 (1972). 20. Pethica, B., and Few, A., Discussions Faraday Soc., 18, 258 (1954). 21. Zwierzykowski, W., CIP "Chemistry Physics and Journal of Colloid and Interface Science, Vol. 81, No. 1, May 1981
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22. 23. 24. 25.
26.
NIKOLOV, MARTYNOV, AND EXEROWA Application of Surface Active Substances" (Brusselles) II, 801 (1964). Vollhardt, D., and Wiistek, R., Kolloid J. M. 36, 1121 (1974). Betts, I., and Pethica, B., Trans. Faraday Soc. 56, 1515 (1960). Harrold, S. P., J. Colloid Sci., 15, 280 (1960). Krug, G. K., and Kaishev, V. K., Thesis of the Reports of the Vth Russian Conference on design and automation of experiments in scientific investigation, p. 14, Moscow, 1976. Exerowa, D., and Scheludko, A., Proc. IV Intern. Congr. Surface Activity, Brussels, II, 1097 (1964).
1ournal of Colloid and Interface Science, Vol. 81, No. 1, May 1981
27. Baret, J. P., and Roux, R. A., Kolloid Z. 225, 139 (1968). 28. Frayer, D., K6hler, P., and Ohlanbusch, H. D., Kolloidchem. Z. 196, 153 (1963). 29. Gorkill, J. M., Goodman, J. F., and Tate, J. B., in "Hydrogen-Bonded Solvent Systems" (A. K. Covington and R. Jones, Eds.), p. 181. Barnes & Noble, New York, 1968. 30. Nikolov, A., Kashchiev, D., Exerowa, D., God. Sofii Univ. Chim. Fac. 73, in press. 31. Prigogine, I., Defay, R., "Chemical Thermodynamics", p. 385. Longmans, London, 1954.