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Influence of Ionic Strength on Surface Tension of Cetyltrimethylammonium Bromide Z. Adamczyk,* G. Para, and P. Warszyn´ski Institute of Catalysis and Surface Chemistry Polish Academy of Sciences, ul. Niezapominajek 1, 30-239 Krako´ w, Poland Received March 2, 1999. In Final Form: June 7, 1999 The effect of KCl addition on the surface tension of aqueous solutions of cetyltrimethylammonium bromide (CTAB) was measured by the drop-weight method. A significant reduction in the solution surface tension was observed with increasing electrolyte concentration in accordance with previous literature data obtained for the CTAB/NaBr system. However, in contrast to these results, no indication of cloud point appearance or CTAB dimerization was observed for KCl concentration reaching 1 M. The relative surface excess of CTAB at cmc was determined from the Gibbs equation. This quantity was found to decrease from 6.9 × 10-10 to 5.3 × 10-10 mol/cm2 when the KCl bulk concentration was varied between 0 and 1 M. The experimental surface tension data were quantitatively interpreted in terms of the theoretical model based on the assumption that the surfactant and counterions undergo nonequivalent adsorption within the Stern layer which consequently acquires a net charge. The distribution of electric potential in this layer was calculated according to the modified Stern model, whereas the diffuse part of the double layer was described using the Gouy-Chapman model.
Introduction The interfacial tension of the liquid-liquid or liquidgas interfaces exerts a significant influence on the kinetics of many important technological processes such as emulsification, emulsion coalescence and break-up, oil recovery, extraction, detergency, froth flotation, investment casting, etc. Interface dynamics also plays an important role in enzymatic catalysis in reverse micelles in biological and physiological phenomena, e.g., breathing. Since the interfacial tension is strongly reduced by the presence of surface active substances (surfactants) numerous experimental works have been performed to quantify this effect, especially for nonionic surfactants. Although the significance of salt addition in promoting ionic surfactant adsorption was demonstrated long ago,1-3 our understanding of this process still remains fairly incomplete. One can find in the literature only a few systematic works dealing with the effect of the ionic strength on interface tension of ionic surfactants. The existing results concern mostly sodium dodecyl sulfate (SDS) adsorption. Matuura et al.4 were probably the first who measured the adsorption of SDS in different salt solutions, especially NaCl. These results seem valuable since the direct radiotracer method was used (with 35S as a label) for evaluating the quantity of SDS adsorbed. The resulting surface tension changes of the surfactant-air interface were simultaneously measured using the Wilhelmy plate method. Although the accuracy of the measurements for dilute electrolyte seems limited, a significant increase of the amount of SDS adsorbed upon salt addition was unequivocally demonstrated. Similar measurements were carried out by Tajima et al.5 and Tajima6 who also used the radiochemical methods for studying adsorption of tritum labeled SDS. According * To whom correspondence should be addressed. (1) Davis, J. T. Trans. Faraday. Soc. 1952, 48, 1052. (2) Pethica, B. A. Trans. Faraday. Soc. 1954, 50, 412. (3) Nilsson, G. J. Phys. Chem. 1957, 61, 1135. (4) Matuura, R.; Kimizuka, H.; Yatsunami, K. Bull. Chem. Soc. Jpn. 1959, 32, 546. (5) Tajima, K.; Muramatsu, M.; Sasaki, T. Bull. Chem. Soc. Jpn. 1970, 43, 1991. (6) Tajima, K. Bull. Chem. Soc. Jpn. 1970, 43, 3063; 1971, 44, 1767.
to these authors this allowed for an increase in the precision of the surface coverage determination. However, the range of NaCl concentration was rather limited, i.e., 10-3-10-2 M. In the above cited works, the experimental results were interpreted in terms of the Gibbs adsorption equation with no attempt to quantitatively characterize the electrical double layer formed as a result of the surfactant and counterion adsorption. More recently Fainerman7,8 measured the effect of NaCl (for concentrations reaching 1 M) on adsorption of SDS using the maximum bubble pressure method. The results obtained were interpreted in terms of the Davis and Rideal9 and Borwankar and Wasan10 theory exploiting the simple Gouy-Chapman model of the electrical double layer. Kalinin and Radke11 reinterpreted these (and other) results in terms of the ion binding model postulating the counterion adsorption on top of the adsorbed surfactant layer. On the other hand, Warszyn´ski et al.12 interpreted their own results and those of Matuura et al.4 concerning SDS adsorption in the presence of NaCl using a new theoretical model based on the assumption of counterion adsorption within the Stern layer. It seems that, in view of the inherent difficulty in obtaining pure SDS with no admission of the hydrolysis product,13-16 this surfactant is not particularly suitable for precise measurements. Significantly more accurate results can be derived for the cationic type surfactants, especially the quaternary (7) Fainerman, V. B. Colloid J. USSR 1978, 40, 769. (8) Fainerman, V. B. Colloids Surf. 1991, 57, 249. (9) Davis, J. T.; Rideal, E. K. Interfacial Phenomena; Academic Press: New York, 1963. (10) Borwankar, R. P.; Wasan, D. T. Chem. Eng. Sci. 1988, 43, 1323. (11) Kalinin, V. V.; Radke, C. J. Colloids Surf. 1996, 114, 337. (12) Warszyn´ski, P.; Barzyk, W.; Lunkenheimer, K.; Fruhner, H. J. Phys. Chem. B 1998, 102, 10 948. (13) Elworthy, P. H.; Mysels, K. J. J. Colloid Interface Sci. 1966, 21, 331. (14) Mysels, K. J.; Florence A. T. J. Colloid Interface Sci. 1973, 43, 577. (15) Vollhardt, D.; Czichocki, G. Langmuir 1990, 6, 317. (16) Fang, J. P.; Joos, P. Colloids Surf. 1992, 65, 113.
10.1021/la990241o CCC: $18.00 © 1999 American Chemical Society Published on Web 09/18/1999
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ammonium salts. Thus, in the case of CTAB the effect of KBr addition (i.e., the common anion) was studied by using the Wilhelmy plate method17 and the drop weight method.18 Because of the high Krafft point of CTAB, the maximum electrolyte concentration was limited, however, to 5 × 10-2 M.18 Analogous surface tension measurements in electrolytes with the common anion were carried out by Ozeki and Ikeda19 in the case of dodecyldimethylammonium chloride (DDAC) and by Okuda et al.20 for dodecyldimethylammonium bromide (DDAB). It seems that determining the influence of other electrolytes on the surface tension of CTAB would shed more light on the underlying mechanism of counterion (anion) adsorption. In particular one can get information to which extent various anions are adsorbed specifically. This was the goal of this paper dealing with KCl. The advantage of this electrolyte is that it can be used for concentrations up to 1 M without causing cloud point appearance. Experimental Section Materials. In our experimental studies CTAB of > 99% purity (Fluka) was used. KCl was further cleaned by manifold recrystallization from six times distilled water obtained according to the procedure described earlier,21 and then roasted for 8 h at a temperature of 500 °C. The purity of KCl stock solution was further checked by the tensammetric measurements performed according to the method described elsewhere.22 No capacitance change of the hanging mercury electrode was observed for 1 h experiments. Experimental Procedure. The surface tension measurements were carried out using the drop weight method23-26 which can be treated as the quasi-static limit of the widely used growing volume method.27 This simple and reliable technique also enables nonstationary (dynamic) surface tension measurements characterized by transition times on the order of a minute and longer. As mentioned,17 for cationic surfactants, the drop weight method seems superior to the Wilhelmy plate method because the interface dewetting problems are avoided. The experimental setup used for determining surface tension by the drop weight method was of the standard type.28 The main part of the apparatus was the quartz capillary of outer diameter of d ) 0.3125 cm placed in a thermostated chamber of regulated humidity to prevent drop evaporation during the measurement. The liquid drop was squeezed out from the capillary tip by a precise syringe driven by an electric motor. The surface tension determination was based on the Tate’s law with the correction factor being a function of the ratio of capillary radius to the cube root of the volume of the drop.25 To increase the accuracy of the method, special precautions were undertaken to eliminate vibrations and to form the drop in a reproducible way. All the surface tension measurements were carried out at 295 K. The averaged surface tension of the distilled water at this temperature was determined to be 72.4 mN/m (at pH 6).
Results and Discussion As suggested in previous works16 the sensitivity of surface tension to the drop time is a precise criterion for estimating the surfactant purity. Therefore, all our (17) Rijnbout, J. B. J. Colloid Interface Sci. 1977, 62, 81. (18) Okuda, H.; Imae, T.; Ikeda, S. Colloids Surf. 1987, 27, 187. (19) Ozeki, S.; Ikeda, S. Bull. Chem. Soc. Jpn. 1980, 53, 1832. (20) Okuda, H.; Ozeki, S.; Ikeda, S. Bull. Chem. Soc. Jpn. 1984, 57, 1321. (21) Adamczyk, Z.; Para, G. Bull. Pol. Ac. Sci. 1993, 41, 121. (22) Adamczyk, Z.; Para, G. J. Colloid Interface Sci. 1996, 178, 274. (23) Harkins, W. D.; Brown, F. E. J. Am. Chem. Soc. 1925, 41, 499. (24) Wilkinson, M. C. J. Colloid Interface Sci. 1972, 40, 14. (25) Pierson, F. W.; Whitaker, S. J. Colloid Interface Sci. 1976, 54, 203, ibid 219, ibid 231. (26) Miller, R.; Schanko, K. H. Colloid Polym. Sci. 1986, 264, 277. (27) MacLeod C. A.; Radke, C. J. J. Colloid Interface Sci. 1993, 160, 435, ibid 1994, 166, 73. (28) Adamczyk, Z.; Para, G.; Karwin´ski, A. Tenside. Surf. Det. 1998, 35, 261.
Adamczyk et al.
Figure 1. Dependence of the dynamic surface tension γ of CTAB solutions on the drop time t (determined by the drop weight method) at various bulk surfactant concentrations: (1) c ) 0 (six times distilled water); (2) c ) 10-5 M; (3) c ) 1 × 10 -4 M; (4) c ) 3 × 10 -4 M; (5) c ) 5 × 10-4 M.
Figure 2. Dependence of the dynamic surface tension γ of CTAB solutions in 0.1 M KCl on the drop time t (determined by the drop weight method) at various bulk surfactant concentrations: (1) c ) 0 (10-1M KCl); (2) c ) 5 × 10-6 M; (3) c ) 10-5 M; (4) c ) 3 × 10-5 M; (5) c ) 10 -4 M.
measurements were performed in such a way that surface tension variations under transient conditions (i.e., the surface tension γ vs the drop time t dependencies) were first determined for each run. Then, using these data a true equilibrium surface tension was determined for a fixed value of surfactant and KCl concentration. Typical results of the transient measurements for CTAB at various concentrations with no KCl addition are shown in Figure 1. Analogous results for 0.1 M KCl solution are presented in Figure 2. For comparison, the reference measurements of distilled water are shown as well. One can notice that within 40 min the changes in the surface tension of water were limited to 0.2 mN/m which suggests that the water quality was sufficient for further measurements. It can also be observed in Figures 1-2, both for pure and KCl containing CTAB solutions, that the steady-state surface tension values were established after 30 min even at surfactant concentrations as low as 5 × 10 -6 M. This agrees with the relaxation times estimated previously,29-30 i.e., τ ) Γ∞2/c2D (where Γ∞ is the monolayer concentration, c is the surfactant bulk concentration, and D is the surfactant diffusion coefficient). By contrast, the estimates (29) Adamczyk, Z.; Petlicki, J. J. Colloid Interface Sci. 1987, 118, 20. (30) Adamczyk, Z.; Para, G.; Warszyn´ski, P. Bull. Pol. Ac. Sci. 1997, 45, 341.
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and KCl; µ and µs are the CTAB and KCl chemical potentials; S is the excess entropy of the surface phase; and T is the absolute temperature. Note that in formulating eq 1 the adsorption of OH-, H+, and HCO- ions has been neglected. From eq 1 one can determine Γ as the partial derivative of γ on CTAB concentration at constant temperature and KCl concentration, i.e.,
Γ)-
Figure 3. Dependence of the equilibrium surface tension of CTAB solutions on log c determined experimentally for fixed concentrations of KCl in the bulk equal: (1) 1 M; (2) 0.1 M; (3) 0.01 M; (4) 0 M. The straight lines denote the slops of the -∂γ/∂ ln c ) Γ dependence evaluated at the cmc. Table 1. Critical Micelle Concentration Co, Apparent Surface Excess Γa Obtained from the Slope of Experimental Adsorption Isotherms and from the WBLF Model, Minimum Surface Tension γo for Solutions of CTAB in KCl, T ) 295 K, pH ) 6 Cs [mol/dm3]
Co [mol/dm3]
0
8.4 × 10-4 (9.82 × 10-4a) 3 × 10-4 6 × 10-5 2 × 10-5
10-2 10-1 1 a
Γa × 1010 ΓaWBLF × 1010 γo [mol/cm2] [mol/cm2] [mN/m] 6.9 (6.17a) 3.5 4.5 5.3
6.9 3.9 4.7 5.4
37 36 37 35 28.5
Literature data of Okuda et al.16 T ) 298 K.
of Pierson and Whitaker,25 who suggest that τ ) 100 Γ∞2/ c2D seem too large since for c ) 10-5 M the relaxation time of 500 min is predicted (for Γ∞ ) 4 × 10-10 mol/cm2). It can also be noted by comparing Figures 1-2 that the purity of CTAB seems satisfactory because the variations in γ for c ) 10-4 M are negligible within the time interval 5-40 min. The equilibrium surface tension data obtained from the above transient measurements in the limit of long times are presented in Figure 3 in the form of the γ vs log c dependencies. These experimental results exhibit qualitatively the same features as previously observed for SDS/ NaCl,4-6 DDAC/Cl19 and DDAB/Br20 systems, i.e., a significant increase in the surface tension depression with increasing KCl concentration. For every salt concentration studied, i.e., 0, 0.01, 0.1, and 1 M, a critical CTAB concentration was observed above which γ assumed a minimum value, independent of further increase in concentration c. Since no appearance of a cloud point was detected for the entire CTAB and salt concentration range studied, this effect was attributed to micelle formation. The experimental data shown in Figure 3 can also be used not only for determining the minimum surface tension and the critical micelle concentration (cmc) but also the surface excess of CTAB. This can be achieved by using the Gibbs equation written as
-dγ ) Γdµ + Γsdµs + SdT
(1)
where Γ and Γs are the relative surface excesses of CTAB
1 ∂γ kT ∂ ln a
(
)
T,cs
) ΓCTA+ + ΓBr-
(2)
where a is the CTAB activity, k is Boltzmann’s constant, ΓCTA+ is the surface excess of the CTA+ and ΓBr- is the surface excess of Br-. Since the CTAB concentration was in all cases smaller than 0.001 M, the activity in eq 2 can be replaced with bulk concentration. The Γ values calculated in this way at cmc for various salt concentration are collected in Table 1 together with the cmc and the minimum surface tension γo. As can be seen, for zero salt concentration Γ ) 6.9 × 10-10 mol/cm2 which agrees reasonably well with the results of Okuda et al.,16 i.e., 6.17 × 10 -10 mol/cm2 who performed, however, their measurements at slightly higher temperature, i.e., 298 K. Analogous results for DDAC19 and DDAB20 are 7.66 × 10-10 mol/cm2 and 8.96 × 10-10 mol/cm2, respectively. Assuming the electroneutrality postulate as has been done widely before,4-6,17,19-20 one can expect that the overall adsorption excess of CTA+ equals that of Br-, hence ΓCTA+ ) ΓBr- ) Γ/2 ) 3.45 × 10 -10 mol/cm2. However, it is not possible to determine the distributions of CTA+ and Br- in space and describe the electrical double layer without accepting a nonthermodynamic hypothesis. As far as CTA+ ions are concerned, one may expect that due to strong specific adsorption, their concentration peak should be located close to the interface, at distances of the order of Ångstro¨ms. Accepting this hypothesis one can estimate using the above value of ΓCTA+ that the specific area per CTA+ ion equals 49 Å2. This is comparable with the value of 44 Å2 estimated from low-angle X-ray scattering in the lamellar phase31 or from direct radiotracer studies.32 Consequently, one can estimate that the surface charge produced by the amount of CTA+ ions adsorbed σo equals eΓ ) 9.7 × 104 esu (where e is the elementary charge). On the other hand, it is more difficult to predict the distribution of Br- ions because their specific adsorption is expected to be much weaker,33 so a considerable part of the ions remains in the diffuse double layer. Assuming no specific adsorption of Br- one can estimate the surface potential produced by CTA+ ion adsorption from the Gouy-Chapman equation.34
x
j o + σ2o + 4 kT σ ln ψ )2 e 2 o
(3)
where σo is the dimensionless surface charge defined as (31) Husson, F.; Mustacchi, H.; Luzatti, V. Acta Crystallogr. 1960, 13, 668. (32) Jones, M. N.; Ibbotson, G. Trans. Faraday Soc. 1970, 66, 2394. (33) Habib, M. A.; Bockris, J. O’M. Specific Adsorption of Ions. In Comprehensive Treatise of Electrochemistry. The Double Layer, Bockris, J. O’M.; Conway, B. E.; Yeager, E., Eds.; Plenum Press: New York 1980, Vol. 1, p 141. (34) Adamczyk, Z.; Warszyn´ski, P. Adv. Colloid Interface Sci. 1996, 63, 41.
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σ j o ) (4πeLe/kT)σ
Adamczyk et al.
(4)
The Debye’s screening length is Le ) κ-1 ) ( kT/8 π e2 I)1/2, is the dielectric constant of water, and I is the ionic strength of the surfactant solution at cmc. Substituting the above estimated value of δo one obtains from Eqs 3-4 ψo ) +260 mV. Because this value is very large, one can expect that even in absence of specific adsorption a considerable amount of Br- ions should accumulate due to electrostatic attraction within the layer where the surfactant headgroups are located. The amount of Br- accumulated can be estimated from the formula derived assuming a Boltzman distribution of Br- ions in this layer, i.e., o
a ψ e/kT ΓBr - ) δce
Figure 4. Schematic representation of the WBLF model.17
(5)
where δ is the thickness of the adsorbed layer. Substituting δ ) 2 Å one can calculate from eq 5 that ΓBr- ) 4 × 10-10 mol/cm2 for surfactant concentration approaching the cmc. As can be seen, this is close to the amount of CTA+ ion adsorption. This means that a considerable amount of interface charge is compensated at distances comparable with 2 Å. It should not be expected, however, that the interface layer becomes totally electroneutral. For lower electrolyte concentration the compensation of surface charge is expected to decrease. As a result, the interface potential increases which reduces CTA+ adsorption in comparison with neutral surfactants. The theoretical predictions above seem to be qualitatively confirmed by the experimental results shown in Figure 3 since surface tension in the presence of electrolyte is lower than for pure surfactant solution and the slope of the γ vs log c dependence is larger for low surfactant concentration solutions. A different situation arises, however, for surfactant concentration approaching the cmc values. As one can see in Figure 3 (the relevant data are specified in Table 1) the value of Γ ) - ∂γ/(kT ∂ ln c) for 0.01 M KCl is reduced to 3.5 × 10-10 mol/cm2 (at cmc) in comparison with pure surfactant. Since Γ always reflects the sum of CTA+ and Br - adsorption (the Cl- adsorption is not reflected by this derivative) the decrease in Γ can only be interpreted as the reduction in Br- presence in the adsorbed layer due to the appearance of Cl- ions. This supports the hypothesis that Br- accumulation in the adsorbed layer is mostly due to electrostatic attraction so these ions can easily be replaced by Cl- ions when KCl is added to the surfactant solution. Assuming that in the adsorption layer Br- ions are entirely replaced by Cl- ions, Γ ) ΓCTA+ - ) 3.5 × 10-10 mol/cm2 and one obtains 47 Å2 for surface area per CTA+ ion which is about 7% larger than the above value reported by Jones et al.32 For a KCl concentration equal to 0.1 M, Γ at cmc was found to equal 4.5 × 10 -10 mol/cm2, and for 1 M KCl, Γ ) 5.3 × 10-10 mol/cm2. Interpreting as previously, Γ as due solely to CTA + ion adsorption one obtains surface area of 37 and 32 Å2, respectively. The increase in Γ (decrease in surface specific area) with increasing KCl concentration can be interpreted in terms of decreased electrostatic repulsion among the surfactant headgroups. It should be mentioned that an analogous trend was observed19,20 in the case of DDAC and DDAB adsorption. In contrast, in another work Okuda et al.18 determined that for 0.01 M KBr (common counterion case), the value of Γ increased to 6.6 × 10-10 mol/cm2 A quantitative interpretation of our experimental data was carried out in terms of the recently formulated
Figure 5. (a) Comparison of different models for fitting the experimental γ vs log c dependencies for CTAB obtained for bulk KCl concentrations equal to 1 aThe continuous lines denote the WBLF model.12 bThe dashed lines represent the Kalinin and Radke model.11 - 1 M; 2. 0.1 M; 3. 0.01 M; 4. 0 M. Electric potential of the Stern layer (surfactant headgroup adsorption plane) ψs (dashed lines) and the diffuse double layer ψφ (continuous lines) predicted theoretically from the WBLF model for KCl concentrations equal to 1, 1′, 1 M; 2, 2′, 0.1 M; 3, 3′, 0.01 M’ 4, 4′, 0 M.
theoretical model.12 The basic assumption of this model, hereafter referred to as the WBLF approach, is that the counterions can penetrate the adsorption layer where the surfactant headgroups are located (Stern layer), see in Figure 4. Hence, in this respect, our approach differs significantly from the Borwankar-Wasan 10 and Kalinin-
Influence of Ionic Strength on Surface Tension of CTAB
Radke11 models, which neglect counterion penetration of the Stern layer. Moreover, as a result of electrostatic repulsion the accumulation of the co-ions in this layer is assumed negligible. Therefore, in the WBLF model the Stern layer is regarded as a two-dimensional electrolyte characterized by the lack of electroneutrality because, in general, the surfactant ion and counterion adsorption in that layer is different. The electric potential changes are assumed to be linear within the Stern layer whereas the potential distribution in the diffuse part is reflected by the Gouy-Chapman theory. The surfactant and counterion binding isotherms are described by the Frumkin equation, allowing for the difference in size of surfactant headgroups and counterions. The surface coverage was determined numerically from the set of resulting nonlinear isotherm equations using the Newton-Raphson method and the surface tension lowering is calculated by using the Gibbs equation. The detailed mathematical formulation of the WBLF model and its application to SDS adsorption at the air-solution interface was given previously by Warszyn´ski et al.12 The interpretation of our experimental data concerning CTAB adsorption in terms of the above WBLF model is shown graphically in Figure 5. In the upper part the surface tension dependence on ln c is shown, whereas in the lower part the calculated Stern potential ψs and diffuse double layer potential ψd as a function of ln c is plotted for various KCl concentrations. The apparent surface excess for various KCl concentrations calculated from the WBLF model is given in Table 1. As can be observed in Figure 5 the WBLF model describes the experimental data satisfactorily for the entire range of surfactant and salt concentrations studied. The agreement with experimental data is certainly better than for the Kalinin-Radke model depicted by broken lines in Figure 5. This was quantitatively confirmed by evaluating the standard deviation between the experimental and theoretical data evaluated at a discrete set of points. The deviation of the KalininRadke model from experimental data is larger for high electrolyte concentrations which indeed seems to confirm the hypothesis of counterion adsorption within the Stern layer. This effect is also responsible for the reduction of the Stern and diffuse double layer potential (see Figure
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5b) equal 200 mV for pure CTAB solution at cmc in comparison with the above estimated value of 260 mV. It should also be noted that even at KCl concentration equal 1 M, the double layer potential remains as large as 60 mV which suggests a further reduction in surface tension of CTAB for more concentrate KCl solutions. However, an experimental proof of this hypothesis seems rather complicated in view of limited solubility of KCl and the possible appearance of a cloud point. Concluding Remarks It was found experimentally that the relaxation time needed to attain equilibrium surface tension of CTAB solutions, both in the absence and presence of electrolyte, was comparable with Γ2/c2D. The solutions with the addition of KCl exhibited in all cases lower surface tension than pure surfactant solutions at the same concentration. At zero salt concentration the surface excess of CTAB calculated according to the Gibbs equation was found equal to 6.9 × 10 -10 mol/cm2 (at cmc). On the other hand, at KCl ) 0.01 M we found Γ ) 3.5 × 10 -10 mol/cm2 which corresponds to a specific surface area of 47 Å2. These results unequivocally suggest that a considerable penetration of Br- ions into the Stern layer takes place due to nonspecific, electrostatic interactions. Upon addition of KCl, the Brions are replaced by the Cl- ion, also accumulating nonspecifically in the Stern layer. However, from the surface tension data alone the adsorption of separate ions in the CTAB/KCl system cannot be evaluated without accepting a nonthermodynamic hypothesis. These experimental data were quantitatively interpreted in terms of the WBLF model postulating counterion penetration into the Stern layer. This model gives better agreement with experimental data in comparison with previous approaches of Davis and Rideal,9 Borwankar and Wasan,10 and Kalinin and Radke.11 However, to unequivocally determine the range of validity of the WBLF model, simultaneous measurements of surface tension and surface potential will be needed to be carried out for other salts and for a broader concentration range. LA990241O
