J. Phys. Chem. B 2000, 104, 8471-8476
8471
Phase Transitions in Adsorption Layers at the Water/Hexane Interface V. B. Fainerman† and Reinhard Miller*,‡ International Medical Physicochemical Centre, Donetsk Medical UniVersity, Prospekt Ilischa 16, 340003 Donetsk, Ukraine, and Max-Planck-Institut fu¨ r Kolloid- und Grenzfla¨ chenforschung, Max-Planck-Campus, D-14476 Golm, Germany ReceiVed: February 10, 2000; In Final Form: June 9, 2000
Data from literature, interpreted in terms of phase transitions in the adsorption layer, are analyzed with a recently developed thermodynamic model that considers the formation of small aggregates or larger clusters at the interface. The interfacial tension isotherms for perfluorinated (FC12OH and FC10OH) and aliphatic (C20OH and C18OH) alcohols at the water/hexane interface can be satisfactorily explained by this thermodynamic model. It is also shown that an interfacial phase transition would require a change in the interfacial tension isotherm opposite to that observed experimentally.
Introduction Critical phenomena taking place, for example, in a threedimensional nonideal gas or in a two-dimensional insoluble monolayer at the interface between two liquid bulk phases can be explained qualitatively using an equation of the van der Waals type. For a monolayer, the two-dimensional analogue reads1
Π)
a* RT A - ω A2
(1)
where Π is the surface pressure, R is the gas law constant, T is the temperature, a* is the constant of intermolecular interactions, ω and A are the partial molar area and the area per mole of the insoluble component in the monolayer, respectively. If the value of a* is large enough, then at constant temperature, eq 1 has three real roots; three different values of the area per mole (or molecule) A correspond to the same surface pressure Π. As the monolayer should be mechanically stable, dΠ/dA e 0, so that the system undergoes a jump through the instability region, from a value of A determined by the largest root of eq 1 to that corresponding to the smallest root. This jump is known as twodimensional condensation of the monolayer. Similar considerations can be applied to the condensation in an adsorption layer, which can be described by the Frumkin equation of state for a surfactant solution2
Π)-
RT [ln(1 - θ) + aθ2] ω
(2)
where θ ) Γω is the surface layer coverage, Γ is the adsorption, and a is the intermolecular interaction constant. The dependence of the relative pressure Π* ) Πω/RT on the surface coverage θ, calculated for various values of the intermolecular interaction constant a, is shown in Figure 1. It is seen that three different roots of eq 2 exist for a > 2. The region enclosed by the dashed lines (shown in Figure 1 for a ) 2.5) corresponds to unstable states of the system. The surface pressure that corresponds to the coexistence of the condensed * To whom correspondence should be addressed. † International Medical Physicochemical Centre. ‡ Max-Planck-Institut fu ¨ r Kolloid-und Grenzfla¨chenforschung.
Figure 1. Dependence of relative surface pressure calculated for the Frumkin equation of state (2) for: a ) 0.5 (1); a ) 1 (2); a ) 1.5 (3); a ) 2.0 (4); a ) 2.5 (5); and a ) 3.0 (6); for details, see text.
and gaseous states can be determined by using the so-called Maxwell’s construction.1 That is, the areas enclosed by the dashed lines corresponding to this coexistence pressure and the two portions of the loop should be equal to each other on the Π* vs A dependence. For the case of a ) 2.5, this pressure is shown in Figure 1 as the bold line. Despite the obvious capability of the models described by eq 1 or (2) to provide explanation of the phenomena of condensation due to strong intermolecular interaction, there is evidence that this model is incompatible with the actual physical processes governing the two-dimensional condensation of surfactants in either spread or adsorbed interfacial layers. At first, there is only poor agreement with experimental data obtained for gases (pressure vs volume isotherms) and the ordinary van der Waals equation. The two-dimensional analogue of this equation, eq 2, leads to a still worse agreement with respective experimental data. With very few exceptions, the experimental surface pressure vs area per molecule (Π vs A) isotherms are not parallel to the abscissa in the coexistence region (between condensed and gaseous phases or between aggregates and monomers). On the contrary, there is always a slight increase of surface pressure with decreasing A,3-12 and the slope of this part of the isotherm increases with temperature. In both regions, precritical and transcritical, the eqs 1 and 2
10.1021/jp0004563 CCC: $19.00 © 2000 American Chemical Society Published on Web 08/16/2000
8472 J. Phys. Chem. B, Vol. 104, No. 35, 2000
Fainerman and Miller
involve the same surface layer entities, namely the monomers. In these equations, no distinction is made between free monomers and molecules involved into aggregates. It is known from experiments that in the transcritical region of spread monolayers or adsorption layers, the formation of aggregates starts, and the relative fraction of the surface occupied by monomers decreases with increasing surfactant surface concentration.3-15 Clearly, the intermolecular interaction between the molecules within the aggregates could not affect the surface pressure in the same manner as the interaction between nonaggregated monomers does. Moreover, the degree of freedom characteristic to aggregated monomers is insufficient to produce an appreciable effect on the surface pressure even in an ideal monolayer. More rigorous theoretical models, developed recently,11,12,16-20 take into account different effects of monomers and aggregates on the surface pressure, therefore leading to better agreement with experiments. The curve shown in Figure 1 for a ) 2.5 exhibits a steplike variation of the monolayer coverage, from 0.1 to 0.85, that is, the adsorptions of monomers and aggregates become several times greater. Note that for this case, the Frumkin adsorption isotherm equation [2]
bc )
θ exp(-2aθ) (1 - θ)
(3)
which follows from eq 2, and the Gibbs equation for one dissolved component, predicts a relatively small jump of the surfactant bulk concentration, namely 20 to 30% (b is the adsorption equilibrium constant). Therefore, in the framework of the van der Waals approach, the two-dimensional condensation in the adsorption layer should be accompanied by a sharp increase in the adsorption at constant pressure, while at the same time involving no significant increase in the surfactant concentration in the solution. This concept was widely used in the analysis of surface tension vs concentration (γ vs c) isotherms for solutions of various surfactants adsorbed at liquid/gas and liquid/liquid interfaces.21-32 Sharp inflection in γ vs c isotherms accompanied by an increase of the isotherm slope was ascribed to a surfactant condensation at the interface. This explanation, although in agreement with the van der Waals model, contradicts with both the physical essence of the condensation phenomenon and the Gibbs equation, which accounts for all of the components in the interfacial layer. In the following, we will discuss this contradiction in detail. For the interpretation of these results, most authors use the Gibbs equation in the following form21-32
Γ)-
1 dγ RT d ln c
(4)
where Γ is the adsorption, γ is the surface tension, and c is the bulk concentration or the activity of the surfactant. In some cases, the parameters characterizing the dissociation of ions and other influences are incorporated into eq 4. Applying eq 4 to the data given in refs 21-32, the surface pressure Π ) γ0 - γ vs molar area A isotherms were obtained (here, γ0 is the surface tension of the solvent). The Π(A) curves obtained in this way exhibit horizontal sections. (As Γ ) 1/A, the form of these curves corresponds to a mirror reflection of the curves shown in Figure 1 with respect to the ordinate). This interpretation of the experimental data is erroneous, because the γ(c) and Π(A) isotherms are incompatible from a thermodynamic point of view. Indeed, the two-dimensional aggregation in an adsorption layer or a spread insoluble
monolayer should be regarded as the formation of another type of adsorbed particles, namely two-dimensional aggregates or n-mers (cf.11-20,33,34). It is important to note that the surface concentration of the monomers for A < Ac, i.e., the molar area of states below the critical value Ac remains virtually unchanged with an decreasing average area per molecule A. At the same time, however, the number and size of aggregates in the surface layer increases.11-20 Therefore, eq 4 is valid only in the region that corresponds to concentrations lower than the critical concentration, whereas for concentrations higher than the critical one, the Gibbs equation should correctly read
ΓΣ ) Γ1 + Γn ) -
1 dγ RT d ln c
(5)
For monolayers in a condensed state, the value of n is very high (103 or more, cf.33,34), so that in eq 5, the adsorption of aggregates Γn can be neglected, as compared with the adsorption of monomers Γ1 (Γn , Γ1). Note, however, that the value of n‚Γn is not small and can be of the same order of magnitude as Γ1. Therefore, the adsorption corresponding to states below the critical concentration c should be approximately the same as the adsorption of monomers immediately above the critical concentration. When we assume that a phase transition takes place in the adsorption layer and remember that the value of Γ as calculated from eq 4 should be approximately equal to ΓΣ as calculated from eq 5, we can conclude that the values of dγ/d ln c corresponding to states below the presumed phase transition point should be roughly the same as those that correspond to states immediately above this point. It then follows that the phase transition could not be identified from an inflection point in the γ(c) isotherm because (at least, in the first approximation) in the phase transition point the condition dγ/d ln c ) const holds. A more rigorous theory describing the aggregation in adsorption layers33,34 and accounting for the molar areas of aggregates and monomers indeed predicts the existence of an inflection point in the γ(c) isotherm. However, according to this theory, the slope of the curve dγ/d ln c for the states above this point becomes lower than that for the states below this point. Thus, it is not a sharp increase of the slope but a decrease that indicates a first-order phase transition in the adsorption layer. It should be noted that no experimental evidence in favor of the existence of aggregates in the monolayer was presented in refs 21-32. However, in ref 35, the Brewster angle microscopy was employed to demonstrate that aggregates are formed in monolayers of FC12OH (1,1,2,2-tetrahydroperfluorododecanol) and C18OH (1-octadecanol) at the water/hexane interface. The existence of a condensation in the adsorption monolayer of these compounds and also of FC10OH (1,1,2,2-tetrahydroperfluorodecanol) and C20OH (1-icosanol) at the water/hexane interface was proved by the analysis of γ vs c isotherms, based on the Gibbs eq 4.26-32 However, this analysis is not completely correct, as contradiction exists between the experimental results and their theoretical interpretation. Below, we want to analyze the results presented in refs 26-32 in the framework of a recent theoretical model that accounts for the aggregation of molecules in adsorption layers.33,34 It will be shown that this model predicts critical surfactant concentrations for aggregation lower than those calculated in refs 26-32 from the Gibbs eq 4, whereas the observed pronounced inflection in γ(c) isotherms does not correspond to any aggregation but rather to the saturation of the monolayer by aggregates and monomers.
Phase Transitions at the Water/Hexane Interface
Figure 2. Dependence of surface pressure on concentration for FC12OH in hexane at the water/hexane interface at 15 °C; experimental points are data from [27]; solid curves are calculated for the Frumkin model for ω ) 1.56‚105 m2/mol and a ) 2.0 ( ) 7.4%); dashed curve are calculated for the aggregation model with ω1 ) 1.7 × 105 m2/mol, n ) 9 and Γc ) 5.5 × 10-8 mol/m2 ( ) 0.9%).
J. Phys. Chem. B, Vol. 104, No. 35, 2000 8473
Figure 4. The same as in Figure 2 at 35 °C; solid curve is calculated for the Frumkin model for ω ) 1.56 × 105 m2/mol and a ) 2.0 ( ) 4.0%), dashed curves are calculated for the aggregation model with: ω1 ) 1.38 × 105 m2/mol, n ) 8 and Γc ) 2.4 × 10-7 mol/m2 (curve 1, ) 4.3%); ω1 ) 1.72 × 105 m2/mol, n ) 100 and Γc ) 2.6 × 10-7 mol/m2 (curve 2, ) 6.3%).
Π)-
( ( ) )]
[
Γ1 RT ln 1 - Γ1ωΣ 1 + ωΣ Γc
n-1
(6)
the adsorption isotherm for monomers
bc )
Γ1ωΣ [1 - Γ1ωΣ(1 + (Γ1/Γc)n-1)]ω1/ωΣ
(7)
Here, the mean molar area of monomers and aggregates is defined by
1 + n(Γ1/Γc)n-1
ω Σ ) ω1
Figure 3. The same as in Figure 2 at 25 °C; solid curve is calculated for the Frumkin model for ω ) 1.58‚105 m2/mol and a ) 2.0 ( ) 5.0%); dashed curves are calculated for the aggregation model with: ω1 ) 1.7 × 105 m2/mol, n ) 7 and Γc ) 3.7 × 10-8 mol/m2 (curve 1, ) 3.2%); ω1 ) 1.6 × 105 m2/mol, n ) 100 and Γc ) 2.6 × 10-7 mol/m2 (curve 2, ) 3.5%).
Results and Discussion The experimental Π(c) isotherms from27 for FC12OH at the water/hexane interface for temperatures 15, 25, and 35 °C, respectively, are reproduced in Figures 2-4. These results indicate inflection points in the isotherms at concentrations of 0.2 mmol/kg (Figure 2), 0.5 mmol/kg (Figure 3), and 1.2 mmol/ kg (Figure 4). On the other hand, the existence of large (BAMvisible) clusters in the FC12OH adsorption layer at the water/ hexane interface, at a concentration of 0.73 mmol/kg and 25 °C was reported in ref 35. Note, an insufficient purity of the FC12OH used was mentioned. However, for the purpose of our discussion, only the fact of clusters formation is essential (note, that the aggregation number of BAM-visible clusters is 106 or more). For the theoretical calculation of Π(c) isotherms of FC12OH, the following two models were used: the Frumkin model described by the equation of state (2) and adsorption isotherm (3), and the aggregation model developed in refs 33, 34. The main equations of the aggregation model are the equation of state for the adsorption layer of aggregating surfactant
1 + (Γ1/Γc)n-1
(8)
Here, Γ1 and ω1 are the adsorption and partial molar area of the monomers, Γc is the critical adsorption value, related to the adsorption equilibrium constant; for n . 1, the value of Γc is equal to the adsorption of monomers at the aggregation onset and in the mixed interfacial layer. All of the equations above involve the adsorption of aggregates, defined as Γn ) Γ1(Γ1/ Γc)n-1. To determine the values of the parameters, a fitting procedure was used in following way.36 For each particular set of values for ω1, n, and Γc, the respective values of bi in each of the m experimental points Πi ) Πi(ci), i ) 1, 2, and so forth, m were calculated and averaged in the following way m
b)
bi ∑ i)1 Π
∆Πi n
- Π1
(9)
∆Πi ) (Πi+1 - Πi-1/2 is the Π range corresponding to the ith point. The values of the parameters ω1, n and Γc were varied stepwise within corresponding intervals between certain limits of the parameters. The set of parameters was considered to be optimum when the “target function” was at a minimum m
)
∆ci
∑ i-1 c
ex,i
∆Πi Πm - Π 1
) min
(10)
with ∆ci ) |cex,i - ∆ccal, i|. The subscripts “ex” and “cal” refer to the experimental and calculated (for the same Πi) surfactant concentrations, respectively; is the weighted (over Π) average of the relative deviations between the experimental and calcu-
8474 J. Phys. Chem. B, Vol. 104, No. 35, 2000 lated ci values. For the Frumkin model, the parameters ω and a were varied. The results of calculations performed in the framework of the two models are illustrated in Figs. 2 to 4. Here, for the aggregation model, two sets of curves are presented in Figures 3 and 4. The first is calculated for the optimum value of the aggregation number, whereas the second corresponds to the formation of clusters, i.e., n was kept constant (n ) 100). The other parameters were optimized. It should be noted here that for n > 50, any variation in the aggregation number does not affect the shape of the theoretical isotherm remarkably. In Figure 2, the calculations for n ) 100 gave almost the same results as for n ) 9 (the corresponding values of were 2.0% and 0.9%, respectively). Therefore, only one curve is shown. The optimized values of model parameters and mean deviations of are given in the legends to the figures. For the Frumkin model, the value of the intermolecular interaction constant was assumed to be constant a ) 2. This value corresponds to the critical state of the monolayer; the curve for this value exhibits the inflection point at dΠ*/dΘ ) 0, cf., Figure 1. For a < 2 the agreement between the experimental data and the theory was worse. It is quite possible that for some experimental isotherms shown in Figs. 2-4, the value of a could exceed 2. However, in such cases a problem arises related to the solution of eqs 2 and 3 in the phase coexistence region, which should be performed according to Maxwell’s construction, see above. In the present work, such an attempt was not made because the case of a > 2 is physically meaningless. However, the Maxwell construction was recently done37,38 for the Frumkin model to explain nonideal adsorption behavior of 7-tetradecyl-6, 9-diol at the water/air interface. It is seen that theoretical curves for the aggregation model agree well with the experimental results, and the values of for the curves presented in Figures 2 and 3 are much lower than those calculated for the Frumkin model. Note that the curves calculated with n ) 100 indicate the existence of a sharp inflection (for concentrations of 0.5-0.6 mmol/kg in Figure 3 and concentrations of 1.0-1.2 mmol/kg in Figure 4). We will discuss this point in more detail below. To improve the agreement between the aggregation model and the experimental data presented in Figure 4, we can assume that in dilute FC12OH surface layers, small aggregates are formed, whereas for concentrated solutions, larger clusters appear. The decrease in the slope of the experimental curve shown in Figure 4 in the concentration range of 0.7 to 1.2 mmol/ kg, as compared with the data for lower FC12OH concentrations, suggests this cluster formation. The corresponding theoretical curve obtained for dimers and clusters is shown in Figure 5. This curve agrees with experimental data in every detail. The existence of a sharp inflection in isotherms for n ) 100 as shown in Figures 3, 4, and 5 can be explained from the analysis of the concentration dependence of the adsorption of monomers Γ1 and total adsorption of monomers and aggregates recalculated to a total number of monomers Γ ) Γ1 + nΓn. These theoretical dependencies at 25 °C for n ) 7 (minimum in Figure 3) and n ) 100 are shown in Figure 6. It is seen that for n ) 100, the adsorption of monomers attains a maximum at 0.025 mmol/kg and remains unchanged with further increasing concentration. However, the total adsorption increases due to the adsorption of aggregates. This total adsorption attains a plateau at the FC12OH concentration of 0.6 mmol/kg. It is due to the almost complete surface coverage that a sharp increase of the surface pressure appears at this concentration, cf., Figure 3. As aggregation takes place, the value of ωΣ is high [cf., eq
Fainerman and Miller
Figure 5. Same as in Figure 4, the curves were calculated from the aggregation model: in the region c < 0.7 mmol/kg for the parameters ω1 ) 1.47 × 105 m2/mol, n ) 2 and Γc ) 4.0 × 10-7 mol/m2 ( ) 2.8%); in the region c > 0.7 mmol/kg for ω1 ) 1.47 × 105 m2/mol, n ) 100 and Γc ) 4.0 × 10-7 mol/m2 ( ) 3.1%).
Figure 6. Dependence of monomer adsorption Γ1 and total adsorption of monomers and aggregates Γ on the FC12OH concentration in hexane at 25 °C calculated for n ) 7 (solid lines) and n ) 100 (dashed lines).
8], resulting in a very small value of the prelogarithmic factor in eq 6, which in turn leads to a low surface pressure throughout the region of medium monolayer coverage. Also the increase of the surface pressure is very slow. This situation holds until the term under the logarithm becomes almost zero (due to the increase of the total surface layer coverage). Then a sharp pressure increase is observed almost independent of ωΣ. If the aggregation number is not too high (see adsorption curves for n ) 7 in Figure 6), then the monolayer is saturated more slowly with monomers and aggregates. In this case ωΣ is not too small (cf. eq 8) and, therefore, the slope of the corresponding Π(c) isotherm varies slowly, as one can see in Figure 3. The experimental and theoretic curves for FC10OH at 15, 25, and 35 °C, reproduced from ref 30, are shown in Figure 7. In ref 30, it was argued that for each temperature, two singular points exist in these experimental isotherms: for 15 °C these points were located at 0.5 and 1.5 mmol/kg, for 25 °C at 1.25 and 4.0 mmol/kg, and for 35 °C at 3.0 and 9.0 mmol/kg. With the exception of 4.0 mmol/kg for 25 °C, all of the singular points perfectly correspond to the theoretical curves calculated for values of the model parameters given in Table 1. It is noteworthy that both models provide good agreement with the experiment. For the Frumkin model, the values of a do not exceed 2 and, from physical considerations, quite expectedly become lower with increasing temperature. However, the aggregation model leads to smaller mean deviations . The aggregation number n is not high and becomes lower with increasing temperature.
Phase Transitions at the Water/Hexane Interface
J. Phys. Chem. B, Vol. 104, No. 35, 2000 8475
Figure 7. Dependence of Π(c) for FC10OH in hexane at the water/ hexane interface at 15, 25, and 35 °C experimental points from [30]. Solid curves are calculated for the Frumkin model; dashed curves are calculated for the aggregation model; values of the model parameters are listed in Table 1.
TABLE 1. Optimum Values for Model Parameters for FC10OH in Hexane at the water/hexane interfac aggregation mode temp (°C) 15 25 35
Figure 8. Dependence of surface pressure on concentration for C20OH in hexane at the water/hexane interface at 25 °C; experimental points from [31]; solid curves are calculated for the Frumkin model with ω ) 1.0 × 105 m2/mol and a ) 2.0 ( ) 10.8%); dashed curve is calculated for the aggregation model: in the region c < 5 mmol/kg for ω1 ) 1.0 × 105 m2/mol, n ) 3.5 and Γc ) 1.4 × 10-6 mol/m2 ( ) 0.9%); in the region c > 5 mmol/kg for ω1 ) 1.0 × 105 m2/mol, n ) 100 and Γc ) 1.4 × 10-6 mol/m2 ( ) 2.0%).
Frumkin model
ω1 (m2/mol)
Γc (mol/m2)
n
(%)
ω (m2/mol)
a
(%)
1.74 × 105 1.84 × 105 1.23 × 105
1.0 × 10-6 1.15 × 10-6 5.5 × 10-6
8 6 3
1.3 2.3 2.1
1.6 × 105 1.5 × 105 1.0 × 105
1.1 0.8 0.0
3.0 3.1 2.2
Unfortunately, the BAM method cannot be applied to confirm or refute these results, as the aggregates are too small. At the same time, measurements of the dynamic interface tension are extremely sensitive with respect to the formation of aggregates,39 and it could, therefore, be expected that an inflection will occur in the dynamic curves for FC10OH adsorption close to the critical surface coverage (ca. 10-6 mol/m2). For the temperature 35 °C, the value a of the Frumkin model was zero, thus, the Langmuir model provides good description of experimental data. Hence, the application of the aggregation model cannot improve the agreement between theory and experiment. Here, it should be noted that overly large Γc values for certain temperatures indicate that the aggregation process at this temperature is rather improbable. Very interesting results can be drawn from the comparison of the aggregation theory with experimental data reported in ref 31 for the C20OH solution in hexane at the water/hexane interface. It should be noted that the results presented in ref 35 unambiguously indicate the formation of C18OH aggregates at this interface. Therefore, this process should be far more probable for the system containing C20OH. In Figure 8, the experimental results from31 are compared with calculations for the Frumkin and aggregation models. It was argued in ref 31 that the inflection point observed at the concentration of 11 mmol/kg is caused by an aggregation process, whereas according to the aggregation model the “retarded” shape of the curve at the concentration of about 5 mmol/kg should be ascribed to the onset of the formation of large clusters. We supposed, therefore, that for concentrations below 5 mmol/kg, small aggregates are formed, whereas for higher concentrations, larger clusters with n > 50 appear. The theoretical curves calculated for this case are in perfect agreement with the experimental data. The calculations predict that saturation of the C20OH adsorption layer is reached at a concentration of about 12 mmol/kg. For C18OH adsorption layers at the water/hexane interface similar results follow from the aggregation model. Experimental γ(c)
isotherms for this alcohol (however, in less detail than for C20OH) were presented in ref 26. Recently, the formation of clusters was reported for adsorption layers and spread monolayers of 1-dodecanol at the water/air interface.39 In analogy to the systems discussed above, good agreement between the experimental results and the theoretical calculations for 1-dodecanol was achieved when small aggregates (dimers-trimers) in the precritical region, and larger clusters in the trans-critical region were assumed. Hence, certain general properties in the behavior of normal alcohols at the two interfaces compared are evident. Conclusions The results of interface tension measurements for perfluorinated (FC12OH and FC10OH) and aliphatic (C20OH and C18OH) alcohols at the water/hexane interface can be satisfactorily explained in the framework of the thermodynamic model, which assumes the formation of aggregates in the adsorption layer. It is essential that the inflection points existing in γ(c) isotherms with a sharp increase of the slope can be explained by the saturation of the surface layer by monomers and aggregates. If this were true, aggregates would have to be formed at lower concentrations, and the indication of this process was not an increase, but on the contrary, a decrease in the slope of the γ(c) isotherms. This explanation is in contrast to the assumption accepted in the literature that it is caused by the onset of a twodimensional aggregation process in the surface layer, as treated in the framework of the van der Waals-Frumkin model. Studies of the dynamic interfacial tension of such systems are suitable to further support the obtained results of an interfacial aggregation, as this property is highly sensitive to molecular aggregations. Such investigations are under way for the surfactants discussed here by using a very accurate and reliable video drop shape method. Acknowledgment. This work was financially supported by the Fonds der Chemischen Industrie (R.M. 400429) and research grants from the Max Planck society. References and Notes (1) De Boer, J. H. The Dynamical Character of Adsorption, Oxford University Press: London, 1945.
8476 J. Phys. Chem. B, Vol. 104, No. 35, 2000 (2) Frumkin, A. N. Z. Phys. Chem. (Leipzig) 1925, 116, 466. (3) Mo¨hwald, H. Annu. ReV. Phys. Chem. 1990, 41, 441. (4) Vollhardt, D. AdV. Colloid Interface Sci. 1996, 64, 143. (5) Miller, A.; Mo¨hwald, H. J. Chem. Phys. 1987, 86, 4258. (6) Mingotaud, A.-F.; Mingotaud, C.; Patterson, L. K., Handbook on Monolayers, Academic Press: New York, 1993. (7) Sankaram, M. B.; Marsh, D.; Thompson, T. E. Biophys. J. 1992, 63, 340. (8) Zhu, J.; Eisenberg, A.; Lennox, R. B. Macromolecules 1992, 25, 6547. (9) Vollhardt, D.; Gehlert, U.; Siegel, S. Colloids Surfaces A 1993, 76, 187. (10) Gehlert, U.; Weidemann, G.; Vollhardt, D. J. Colloid Interface Sci. 1995, 174, 392. (11) Fainerman, V. B.; Vollhardt, D.; Melzer, V. J. Phys. Chem. 1996, 100, 15 478. (12) Fainerman, V. B.; Vollhardt, D. J. Phys. Chem. B 1999, 103, 145. (13) Melzer, V.; Vollhardt, D. Physical ReView Lett. 1996, 76, 3770. (14) Vollhardt, D.; Melzer, V. J. Phys. Chem. B. 1997, 101, 3370. (15) Melzer, V.; Vollhardt, D.; Brezesinski, G.; Mo¨hwald, H. J. Phys. Chem. B 1998, 102, 591. (16) Ruckenstein, E.; Bhakta, A. Langmuir 1994, 10, 2694. (17) Israelachvili, J. N. Langmuir 1994, 10, 3774. (18) Ruckenstein, E.; Li, B. J. Phys. Chem. 1996, 100, 3108. (19) Ruckenstein, E.; Li, B. Langmuir 1996, 12, 2309. (20) Ruckenstein, E.; Li, B. J. Phys. Chem. B 1998, 102, 981. (21) Motomura, K.; Matubayasi, N.; Aratono, M.; Matuura, R. J. Colloid Interface Sci. 1978, 64, 356. (22) Lin, M.; Firpo, J.-L.; Mansoura, P.; Baret, J. F. J. Chem. Phys. 1979, 71, 2202. (23) Motomura, K.; Iwanaga, S.-I.; Hayami, Y.; Uryu, S.; Matuura, R. J. Colloid Interface Sci. 1981, 80, 32.
Fainerman and Miller (24) Hayami, Y.; Matuura, R. In Phenomena in Mixed Surfactant Systems; Scamehorn, J. P., Ed.; ACS Symposium Series 311, American Chemical Society: Washington, DC, 1986; p. 312. (25) Aratono, M.; Uryu, S.; Hayami, Y.; Motomura, K.; Matuura, R. J. Colloid Interface Sci. 1984, 98, 33. (26) Matubayasi, N.;, Motomura, K.;, Aratono, M.; and Matuura, R. Bull. Chem. Soc. Jpn. 1978, 51, 2800. (27) Hayami, Y.; Uemura, A.; Ikeda, N.; Aratono, M.; Motomura, K. J. Colloid Interface Sci. 1995, 172, 142. (28) Takiue, T.; Yanata, A.; Ikeda, N.; Motomura, K. Aratono, M. J. Phys. Chem. 1996, 100, 13 743. (29) Takiue, T.; Yanata, A.; Ikeda, N.; Hayama, Y.; Motomura, K.; Aratono, M. J. Phys. Chem. 1996, 100, 20 122. (30) Takiue, T.; Uemura, A.; Ikeda, N.; Motomura, K.; Aratono, M. J. Phys. Chem. B 1998, 102, 3724. (31) Takiue, T.; Matsuo, T.; Ikeda, N.; Motomura, K.; Aratono, M. J. Phys. Chem. B 1998, 102, 4906. (32) Takiue, T.; Toyomasu, T.; Ikeda, N.; Aratono, M. J. Phys. Chem. B 1999, 103, 6547. (33) Fainerman, V. B.; Lucassen-Reynders, E. H.; Miller, R. Colloids Surfaces A 1998, 143, 141. (34) Fainerman, V. B.; Miller, R. Langmuir 1996, 12, 6011. (35) Uredat, S.; Findenegg, G. H. Langmuir 1999, 15, 1108. (36) Fainerman, V. B.; Miller, R.; Wu¨stneck, R. J. Phys. Chem. B 1997, 101, 6479. (37) Ferry, J. K.; Stebe, K. J. Colloids Surfaces A 1999, 156, 567. (38) Ferry, J. K.; Stebe, K. J. J. Colloid Interface Sci. 1999, 208, 1. (39) Vollhardt, D.; Fainerman, V. B.; Emrich,G., submitted to J. Phys. Chem. B.
