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Anomalous Dynamic Surface Tension of Mixtures of Nonionic Surfactants with Different Partial Molar Areas at the Water-Air Interface V. B. Fainerman†,‡ and R. Miller*,‡ Institute of Technical Ecology, Blvd. Shevchenko 25, 340017 Donetsk, Ukraine, and MPI fu¨ r Kolloid- und Grenzfla¨ chenforschung, Rudower Chaussee 5, D-12489 Berlin, Germany Received July 23, 1996. In Final Form: October 28, 1996X On the basis of a thermodynamic model, the adsorption isotherm and a surface tension equation are derived for mixtures of nonionic surfactants with different partial molar surface area. The ratio of these partial molar areas of the two surfactants ω1/ω2 has significant influence on the form of the dynamic surface tension curve. For ω2 > ω1 a maximum in the γ(t) dependence can be expected, even under the assumption of a pure diffusion-controlled adsorption and desorption of both mixture components. The anomalous behavior can be observed when a significant desorption of the more concentrated surfactant sets in due to a starting competitive adsorption of the less concentrated but more surface active component of the mixture. Experiments are performed with different surfactant mixtures chosen such that all three cases could be studied: ω2 > ω1, ω2 ≈ ω1, or ω2 < ω1. The surfactants used are Triton X-405 (large molecular area), alkyl dimethyl phosphine oxides (medium molecular area), and n-alkanols (small molecular area). Anomalous effects are experimentally observed for ω2 > ω1.
Introduction In practice surfactants are often used in mixtures. Even if only one surfactant is present in a system, its content in highly surface active compounds makes it necessary to treat it as a surfactant mixture. Many interfacial properties can be controlled only by such mixtures. The adsorption equilibrium and adsorption kinetics of single-component systems are studied experimentally and theoretically very extensively, and most of the phenomena can be described today quantitatively. The situation with surfactant mixtures is different, as only very few experimental studies exist and many features are still not understood. Calculations based on diffusion-controlled adsorption kinetics for surfactant mixtures1 show that a plateau region in the γ(t) plot appears if the concentrations and surface activities of the main surfactant and the second component differ by several orders of magnitude. These model calculations were performed on the basis of a generalized Langmuir isotherm assuming the same surface area for both surfactants. Experimental evidence for the existence of a plateau region in the γ(t) curves exists for mixtures of sodium dodecyl sulfate (SDS) with dodecanol2,3 and with Tritons of different EO content.4 Under certain experimental conditions even maxima were observed in the course of γ(t),3 although the difference in surface activity of the two surfactants was less than three orders of magnitude. The findings were explained in ref 4 by an energy barrier for the main component in the moment when the second component starts to adsorb so that the main component must desorb. * Corresponding author. † Institute of Technical Ecology. ‡ MPI fu ¨ r Kolloid- und Grenzfla¨chenforschung. X Abstract published in Advance ACS Abstracts, January 15, 1997. (1) Miller, R.; Lunkenheimer, K.; Kretzschmar, G. Colloid Polym. Sci. 1979, 257, 1118. (2) Fainerman, V. B.; Makievski, A. V.; Miller, R. Colloids Surf., A 1994, 87, 61. (3) Mac Leod, C. A.; Radke, C. J. J. Colloid Interface Sci. 1993, 160, 509. (4) Fainerman, V. B.; Miller, R. Colloids Surf., A 1995, 97, 65.
Figure 1. Dynamic surface tension as a function of effective adsorption time of blood serum samples of three persons with oncological deceases; two of the samples exhibit a plateau or a maximum in the curves.
Due to the large importance of the phenomenon, in practice a more detailed understanding of the adsorption of mixtures is needed. Just as an example, the dynamic surface tensions of three blood samples shown in Figure 1 exhibit plateau regions. We assume that the peculiarities observed in the moment of the start of desorption of one of the components due to increasing adsorption of the second one are controlled not only by the difference in surface activity but also by the difference in the surface partial molar area ωi or the maximum relative adsorption Γ∞i ) 1/ωi. In the present paper we give a theoretical estimate of the effect of ωi of the individual compounds of a surfactant mixture on the course of γ(t). Moreover, experimental examples for mixtures of nonionic surfactants are presented which support qualitatively the effect of different ωi values for the main and secondary surfactant on γ(t) curves. In a forthcoming paper theoretical and experimental studies on surfactant mixtures will be presented where the concentrations of the two components are comparable.
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Theory
i)0
There are several works known dealing with the thermodynamic and kinetic description of the adsorption of mixed surfactant systems; some of them assume different molecular interfacial areas for the individual surface active species.5-13 To derive conditions under which a plateau in the γ(t) curves or even a maximum may exist, a thermodynamic model for the mixed adsorption layer is needed. Such a model can be derived for example on the basis of the Butler equation and using the principle of Braun-Le Chatelier for the adsorption of a surfactant mixture. Using these relationships, the conditions for a possible extremum in the γ(t) curves can be derived. The chemical potentials µi of the components i in the bulk (subscript b) and at the surface (subscript s) can be described by5,6
∑Γ ) 1/ω i
According to Lucassen-Reynders7,8 the selection of the dividing surface neglects the adsorption layer thickness from eq 3 and the mole fractions xsi are given by xsi ) ΓiωΣ. Equation 3 is invariant with respect to the choice of ω0. After the thickness of the adsorption layer as a parameter has been excluded, the parameters xsi can be calculated from the molar volumes of all components in the system, as it was demonstrated for example in ref 11. The most interesting case is a system containing two surfactants. For this case from eq 3 one obtains
Π)µsi
)
µsi0
+ RT ln
fsi
xsi
- γωi
µni ) µbi0 + RT ln fbi xbi , i ) 0, 1, 2, ... b µi0
(1)
bici )
(3)
(xsi /xbi )xif0 b
where K0 ) 1 and Ki ) are the distribution coefficients, Π ) γ0 - γ is the surface pressure, and γ0 is the surface tension of the pure solvent. In order to derive an equation of state (or an adsorption isotherm, or a surface tension isotherm) the parameter ω0 must be defined and the mole fractions in the surface xsi must be replaced by the adsorption values Γi. From the 3 assuming only one surfactant and setting Kixbi ) b1c1, one obtains
(
(
)
Πω0 RT
xs1 ) b1c1 exp -
Γ i ωΣ
(4)
)
Πω1 RT
(5)
Here, the parameter b1 is the equilibrium adsorption constant and c1 is the surfactant bulk concentration. If ω0 ) ω1, from eqs 4 and 5 the von Szyszkowski equation is obtained. The condition for the validity of this relationship is the selection of the dividing surface in such a way that the total adsorption of components 1 and 2 is constant and given by Γ∞ ) 1/ω1.7,8 For surfactant mixtures with different values of ωi the value of ω0 has to be defined as the average of all partial molar areas ωΣ, which is equivalent to (5) Butler, J. A. V. Proc. R. Soc. London, Ser. A 1952, 138, 348. (6) Lucassen-Reynders, E. H. Colloids Surf., A 1994, 91, 79. (7) Lucassen-Reynders, E. H. J. Phys. Chem. 1966, 70, 1771. (8) Lucassen-Reynders, E. H. Colloid Interface Sci. 1972, 41, 156; 1982, 85, 178. (9) Damaskin, B. B. Elektrokhimiya 1969, 5, 249. (10) Damaskin, B. B.; Frumkin, A. N.; Borovaja, N. A. Elektrokhimiya 1972, 8, 807. (11) Doullard, R.; Daoud, M.; Lefebvre, J.; Miner, Ch.; Lecanny, G.; Coutret, J. Colloid Interface Sci. 1994, 163, 277. (12) Joos, P. Bull. Soc. Chim. Belg. 1967, 76, 591. (13) Joos, P.; Serrien, G. Colloid Interface Sci. 1991, 145, 291.
(8)
(1 - ωΣ(Γ1 + Γ2))ωi/ωΣ
and the surface tension isotherm has the form
(
b1c1 exp -
)
(
)
(
)
Πω1 Πω2 ΠωΣ + b2c2 exp ) 1 - exp RT RT RT
(9)
The average partial molar area can be calculated from the molar areas of the components and their concentration in the surface, according to Lucassen-Reynders,8
ωΣ )
Πωi ln )b RT K i xi
(7)
The adsorption isotherms for the two components read
where and are the standard chemical potentials in the bulk and at the interface, respectively, ωi are the partial molar areas, fi are the activity coefficients, xi are the mole fractions of components i, γ is the surface tension, R is the gas law constant, and T is the absolute temperature. Equation 1 is known as the Butler equation. In the following only the ideal behavior of the surface and the bulk will be considered, i.e., fbi ) fsi ) 1. If one takes the pure liquid as the standard state for the solvent (i ) 0), xb0 ) 1, and the condition of infinite dilution, xbi f 0, for the solutes (i g 1), from the set of eqs 1 and 2 we obtain
xs0 ) exp -
RT ln[1 - ωΣ(Γ1 + Γ2)] ωΣ
(2)
s µi0
xsi
(6)
Σ
n
ω1Γ1 + ω2Γ2 Γ1 + Γ2
(10)
Equation 9 is equivalent to the surface tension isotherm derived by Joos.12 The only difference to the latter is that here ω0 ) ωΣ is used while Joos set ω0 ) ωH2O. As will be shown later, this difference is significant. Thus, the set of eqs 7-10 represents a model which uses a dividing surface according to LucassenReynders’ definition, assuming that the solvent molecule has a molecular area equal to the average molecular area of all adsorbing components. The kinetics of adsorption of a surfactant mixture will be analyzed now only for the situation when the first and major component has reached its equilibrium state of adsorption and has to desorb due to the significant increase in adsorption of the second component. Note that of course the adsorption process is of dynamic character and at any time there is an adsorption flux to and a desorption flux from the surface, which is balanced in the equilibrium state. A desorption process set in this situation refers to a process where we have a net desorption, i.e. a desorption flux stronger than the adsorption flux. After component 1 has reached the maximum, the amount adsorbed is more or less directly controlled by the competitive adsorption of component 2 so that one can assume a constant concentration of component 1 in the subsurface c1 (x ) 0, t > tmax) equal to the bulk concentration c10.4 For the initial moment of the net desorption of component 1 and under the conditions c1 . c2 and b1c1 = b2c2 > 1 one can assume ωΣ ) ω1 and obtains from eq 8
∂Γ1 b1c1 ω2 )∂Γ2 1 + b1c1 ω1
(11)
Under the condition b1c1 . 1 eq 11 yields
ω2 ∂Γ1 )∂Γ2 ω1
(12)
In the special case ω1 ) ω2 one gets ∂Γ1/∂Γ2 ) -1, which finally leads to results discussed earlier.4 The rate of surface pressure change due to a desorption of component 1 and an adsorption of component 2 can be given by
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dΠ ∂Π ∂Γ1 ∂Π ∂Γ2 ) + dt ∂Γ1 ∂t ∂Γ2 ∂t
(13)
From eqs 7, 10, and 12 the partial derivatives can be determined, and finally eq 13 transfers into
(
)
ω2 ∂Γ2 ln(1 - B) dΠ ) RT (ω1 - ω2) Γ2 - Γ1 2 dt ω1 ∂t B
(14)
with Β ) Γ1ω1 + Γ2ω2. This expression will be analyzed now in order to specify the conditions for a plateau or even a temporary maximum in the surface tension time dependence. In essence, eqs 7 and 10 allow already a discussion of possible maxima in γ(t) curves; however, an analysis based on eq 14 is more general. As 0 < B < 1 one has ln(1 - B) < 0. The function ∂Γ2/∂t > 0. As long as Γ2 , Γ1, one also has (Γ2(ω2/ω1) - Γ1) < 0 and the sign of dΠ/dt is given only by (ω1 - ω2). For the case ω1 ) ω2 one gets dΠ/dt ) 0, which is in agreement with the results given earlier.1 If ω1 > ω2, the common change of surface tension with time results, while, for ω1 < ω2, eq 14 suggests an anomalous course of γ(t) with a possible temporary maximum. The complete conditions for such anomalous behavior are ω1 < ω2, c1 . c2, and cibi . 1. The discussion of eq 14 shows that also for a diffusion-controlled adsorption of a surfactant mixture an anomalous surface tension behavior can result if the molecular area of the second component is considerably larger than that of the main component. In contrast in a recent paper4 the role of a desorption barrier for the desorption of the main component was used to explain an irregular surface tension behavior. In that case the area per molecule of the main surfactant SDS was much larger than that of the second component dodecanol (ω1 > ω2), so that the explanation is reasonable. The nature of this unexpected course of γ(t) is interesting, as it seems to be in contradiction with thermodynamics, i.e. with the fact that any processes in an isolated system are directed to a state of minimum free energy. From eq 3 a relationship for the ratio of the adsorption of the two components results
[
]
Γ1 b1c1 Π(ω1 - ω2) ) exp Γ2 b2c2 RT
(15)
This equation is the formulation of the principle of Braun-Le Chatelier for adsorption: an increase of the surface pressure Π is caused by an increase in the adsorption of the component with the smaller molecular area demand at the interface. For ω1 < ω2 a decrease in Π is accompanied by an increase in the ratio Γ2/Γ1, which is the case for the observed plateaus or maxima in the γ(t) curves. While the free energy of the entire system decreases, the surface energy may temporarily increase due to the different chemical potentials of the two competing surfactants.
Materials and Methods The measurements of dynamic surface tension were performed using the automatic tensiometers MPT1 (maximum bubble pressure method) and TVT1 (drop volume method), both produced by LAUDA, Germany. The measuring procedures and instruments were described in detail elsewhere.14,15 The measurements with the MPT1 in the surface lifetime range t > 2 s were performed in the stopped-flow regime,4 while in the time range of milliseconds and sub-milliseconds a special measuring cell was used.16 The correction in the drop volume with respect to hydrodynamic effects was based on the relationship (14) Fainerman, V. B.; Miller, R.; Joos, P. Colloid Polym. Sci. 1994, 272, 731. (15) Miller, R.; Hofmann, A.; Hartmann, R.; Schano, K.-H.; Halbig, A. Adv. Mater. 1992, 4, 370. (16) Fainerman, V. B.; Miller, R. J. Colloid Interface Sci. 1995, 175, 118.
given in ref 17. A general introduction into interfacial tensiometry is given in ref 18. The normal alcohols pentanol, hexanol, heptanol, and octanol (Fluka) and Triton X-405 (Serva) were used without further purification. Alkyldimethylphosphine oxides (ADMPO) with different alkyl chain lengths (8 C atoms, C8DMPO; 10 C atoms, C10DMPO; C atoms, C12DMPO; 13 C atoms, C13DMPO) were purchased from Gamma-Service Dr. Schano, Berlin, Germany, and were of special purity to be used directly for surface-chemical studies. Surfactant solutions were prepared using doublydistilled and deionized water. All measurements were performed at 25 °C. Results and Discussion The dynamic and equilibrium adsorption behavior of the individual surfactants Triton X-405, pentanol, and hexanol has been studied earlier.4,19 Equilibrium surface tension data of heptanol, octanol, and the different ADMPO solutions were determined through extrapolations via γ ) γ(1/xt) curves at t f ∞ (1/xt f 0). For C12DMPO and C13DMPO the equilibrium surface tensions were also measured by using the ring method (TE1, LAUDA, Germany, cf. ref 18). The results obtained from various methods were consistent with each other and also with literature data given for example in ref 20 with an accuracy better than (1 mN/m. A linear dependence was obtained for γ ) γ(1/xt) for all surfactants at 1/xt f 0. The slopes of these linear dependencies correspond to those calculated from the diffusion model.2,21 This shows that surface impurities can be assumed to be absent in the surfactant samples studied or at least do not significantly disturb in the time interval of the present experiments. For the solutions of Triton X-405 the adsorption kinetics at short t obey the diffusion model only if the reorientation of the polyoxyethylene part of the surfactant molecule is taken into consideration, as it was discussed in ref 22. This reorientation results in a faster decrease of surface tension for the same adsorption value. For solutions of pentanol and hexanol at t < 0.01 s the dynamic surface tension values are 1-8 mN/m larger than those calculated from the diffusion model. In ref 19 it was shown that these results are also consistent with the diffusion model, if one considers a nonequilibrium surface layer. The reason for the existence of such a nonequilibrium adsorption layer state is that both the bulk concentration of the alcohol and the concentration gradient in the diffusion layer are high and influence the dynamic surface tension. The existence of nondiffusional kinetics, so-called barrier- or kinetic-controlled kinetics, would be most probable at short adsorption time.2,23 Thus, the results obtained for the individual solutions allow us to conclude that all surfactants used in this study follow the diffusioncontrolled adsorption mechanism. (17) Miller, R.; Schano, K.-H.; Hofmann, A. Colloids Surf., A 1994, 92, 189. (18) Rusanov, A. I.; Prokhorov, V. A. Interfacial Tensiometry. In Studies of Interface Science; Mo¨bius, D., Miller, R., Eds.; Elsevier: Amsterdam, 1996; Vol. 3. (19) Fainerman, V. B.; Miller, R. Colloid Interface Sci. 1996, 178, 168. (20) Lunkenheimer, K.; Haage, K.; Miller, R. Colloids Surf. 1987, 22, 215. (21) Miller, R.; Joos, P.; Fainerman, V. B. Adv. Colloid Polymer Sci. 1994, 49, 249. (22) Fainerman, V. B.; Miller, R.; Makievski, A. V. Langmuir 1995, 11, 3054. (23) Dukhin, S. S.; Kretzschmar, G.; Miller, R. Dynamics of Adsorption at Liquid Interfaces: Theory, Experiment, Application. In Studies of Interface Science; Mo¨bius, D., Miller, R., Eds.; Elsevier: Amsterdam, 1995; Vol. 1. (24) Fainerman, V. B.; Lylyk, S. V. Kolloidn. Zh. 1982, 44, 598. (25) Joos, P.; Serrien, G. Colloid Interface Sci. 1989, 127, 97.
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Table 1. Equilibrium Adsorption Parameters of the Studied Surfactants ω1 surfactant
(105 (nm2/ m2/mol) molecule)
b1a (m3/mol)
Triton X-405 715 ( 80 pentanol 0.067 ( 0.003 hexanol 0.21 ( 0.02 heptanol 0.65 ( 0.05 octanol 2.3 ( 0.2 2 ( 0.4 C8DMPO 22 ( 4.0 C10DMPO 210 ( 30 C12DMPO 650 ( 80 C13DMPO
7.1 1.7 1.7 1.7 1.7 2.7 2.7 2.5 2.5
1.2 0.28 0.28 0.28 0.28 0.45 0.45 0.42 0.42
ref 4 19, 24, 25 19, 24, 25 this work, 24, 25 this work, 24, 25 this work, 20 this work, 20 this work, 20 this work, 20
a The given values are average values calculated for the entire concentration range. The comparatively strong deviations suggest that the isotherm in eq 5 does not perfectly describe the experimental data.
Figure 3. Dynamic surface tension of aqueous mixtures of C8DMPO (c1) and C13DMPO (c2) at different compositions: c1 ) 0 mol/m3/c2 ) 0.1 mol/m3 (9); c1 ) 0/c2 ) 0.2 mol/m3 (0); c1 ) 10 mol/m3/c2 ) 0 mol/m3 (0); c1 ) 10 mol/m3/c2 ) 0.1 mol/m3 (0); c1 ) 10 mol/m3/c2 ) 0.2 mol/m3 (2).
Figure 2. Dynamic surface tension of aqueous mixtures of Triton X-405 (c1) and C12DMPO (c2) at different compositions: c1 ) 0 mol/m3/c2 ) 0.1 mol/m3 (9); c1 ) 0/c2 ) 0.2 mol/m3 (0); c1 ) 1 mol/m3/c2 ) 0 mol/m3 ([); c1 ) 1 mol/m3/c2 ) 0.1 mol/m3 (]); c1 ) 1 mol/m3/c2 ) 0.2 mol/m3 (2). Table 2. Composition of Studied Nonionic Mixtures no. of mixture
main component (1)
second component (2)
ω1/ω2 3 3 1.6
0.05-0.1 0.02-0.1 0.01-0.1
c2/c1
1 2 3
Triton X-405 Triton X-405 C8DMPO
ω1 > ω2 C12DMPO C13DMPO octanol
4 5
C8DMPO C10DMPO
ω 1 ) ω2 C13DMPO C13DMPO
1 1
0.001-0.01 0.02-0.1
C8DMPO pentanol pentanol pentanol pentanol hexanol heptanol
ω 1 < ω2 Triton X-405 C8DMPO C10DMPO C12DMPO C13DMPO C13DMPO C13DMPO
0.38 0.62 0.62 0.67 0.67 0.67 0.67
0.05-0.2 0.1-0.2 0.02-0.1 0.002-0.015 0.001-0.005 0.005-0.1 0.05-0.1
6 7 8 9 10 11 12
The equilibrium adsorption characteristics of the studied surfactants are summarized in Table 1. As one can see, the nonionic surfactants chosen here can be used to compose mixtures with different ratios of minimum adsorption area ω1/ω2 and surface activities. The compositions of the mixtures studied here are given in Table 2. In mixtures 1-5 the surface areas are chosen such that ω1 g ω2, while for mixtures 6-12 the reversed relation holds, ω2 > ω1. The individual concentrations in all cases are chosen such that bici > 1.
Figure 4. Dynamic surface tension of aqueous mixtures of pentanol (c1) and C13DMPO (c2) at different compositions: c1 ) 0 mol/m3/c2 ) 0.2 mol/m3 (9); c1 ) 40 mol/m3/c2 ) 0 mol/m3 (0); c1 ) 40 mol/m3/c2 ) 0.2 mol/m3 ([).
For mixtures 1-5 with ω1 g ω2 no anomalies were found. For example, the results for mixtures 1 and 4 are given in Figures 2 and 3, respectively, together with the curves for the individual surfactant. For mixtures of ADMPO homologues (Figure 3) the concentrations were chosen such that bici > 10 and c2/c1 ≈ 0.01. However, no plateau and maximum were found in the curves. This fact agrees well with the calculations performed in ref 1. For the existence of a plateau, the inequality c2/c1 g 10-4 has to be fulfilled at b1c1 ≈ b2c2. As follows from Figure 3, a significant decrease of γ for the mixture occurs when the adsorption of the admixture begins, i.e., at t g 1 s. Much more complicated is the behavior of the mixtures with ω1 < ω2. Figure 4 shows the results for mixture 10 (40 mmol/m3 of pentanol + 0.2 mmol/m3 of C13DMPO). One can see that, for approximately the same ratio c2/c1 used for the ADMPO homologues (Figure 2), the character of the γ ) γ(t) dependence is rather different. In the region t ≈ 0.1 s a plateau is present followed by a sharp decrease
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Figure 5. Dynamic surface tension of aqueous mixtures of pentanol (c1) and C13DMPO (c2) at different compositions: c1 ) 40 mol/m3/c2 ) 0.2 mol/m3 (9, 0, [); c1 ) 50 mol/m3/c2 ) 0.1 mol/m3 (2).
Langmuir, Vol. 13, No. 3, 1997 413
Figure 7. Dynamic surface tension of aqueous mixtures of pentanol (c1) and C13DMPO (c2) at different compositions: c1 ) 40 mol/m3/c2 ) 0.1 mol/m3 ([); c1 ) 80 mol/m3/c2 ) 0.1 mol/m3 (9); c1 ) 80 mol/m3/c2 ) 0.2 mol/m3 (0).
a sharp decrease in γ when the main component fills the adsorption layer to the maximum possible extent before the admixture starts to adsorb. The same condition, i.e. b1c1 . 1, was used for the derivation of eq 14. For mixture 10 the anomalous behavior becomes even more pronounced with increasing c1 (cf. Figure 7). In two of the dependencies, real maxima of the order of more than 0.5 mN/m can be observed. Similar results were obtained for mixture 11. Future work is focused on a quantitative solution of the derived theoretical model in order to fit experimental data. Moreover, further systematic experimental studies will be performed in order to find systems with even more pronounced maxima in the γ(t) curves. Conclusions
Figure 6. Dynamic surface tension of aqueous mixtures of pentanol (c1) and C12DMPO (c2) at different compositions: c1 ) 10 mol/m3/c2 ) 0.1 mol/m3 (9); c1 ) 10 mol/m3/c2 ) 0.2 mol/m3 (0); c1 ) 25 mol/m3/c2 ) 0.1 mol/m3 ([); c1 ) 40 mol/m3/c2 ) 0.2 mol/m3 (]); c1 ) 80 mol/m3/c2 ) 0.2 mol/m3 (2).
in γ. This part of the plot is shown for two mixtures in another scale in Figure 5. The experiments were repeated two or three times, giving essentially the same form of curves. Another remarkable difference between the mixtures with ω2 > ω1 and those with ω2 e ω1 is that the point at which γ of the mixture starts to decrease sharply is shifted significantly toward shorter time as compared with that for the individual admixture solution (Figure 4). From eq 14 this effect can be explained by an apparent increase in Γ2 for ω2/ω1 > 1. The concentration of the main component affects significantly the form of the γ(t) dependence for mixtures with ω2 > ω1. The results obtained for mixture 9 at different relative concentrations b1c1 ) 6.7, 26.8, and 53.6 in the range of c2/c1 values from 2 × 10-2 to 2.5 × 10-3 are shown in Figure 6. An extended plateau is followed by
Equations are derived which describe the equilibrium adsorption and equilibrium surface tension of mixtures of nonionic surfactants with different partial molar surface areas. The effect of the ratio of the partial molar area of the main surfactant ω1 to that of the admixture ω2 on the form of the time dependence of dynamic surface tension is studied theoretically and experimentally. For ω2 > ω1 an extended plateau or even a maximum in the γ(t) dependence can appear in the region where a net desorption of the main surfactant sets in due to the start of a significant adsorption of the admixture. This effect is observed even under the assumption of a pure diffusion mechanism for the adsorption and desorption of both components of the mixture. Acknowledgment. The work was financially supported by projects of the European Community (INCO 96-5069 and INTAS 93-2463) and by the Fonds der Chemischen Industrie (RM 400429). The authors also thank Dr. V. Popov from the Institute of Physico-Organic Chemistry in Donetsk and Dr. S. V. Lylyk from the Institute of Technical Ecology in Donetsk for their support in the preparation and measurements of the ADMPO. LA960727U
