4324
J. Phys. Chem. B 2001, 105, 4324-4330
Dynamics and Phase Transition in Adsorbed Monolayers of Sodium Dodecyl Sulfate/ Dodecanol Mixtures V. B. Fainerman,‡ D. Vollhardt,*,† and G. Emrich† Max-Planck-Institut fu¨ r Kolloid- und Grenzfla¨ chenforschung, D-14424 Potsdam/Golm, Germany, and Medical Physicochemical Center, Donetsk Medical UniVersity, 16 Ilych AVenue, Donetsk 340003, Ukraine ReceiVed: NoVember 22, 2000
The coadsorption of sodium dodecyl sulfate (SDS)/n-dodecanol mixtures from aqueous solution is theoretically and experimentally studied and compared with the adsorption of the single components. The results of the surface pressure adsorption kinetics are combined with imaging of the surface by Brewster angle microscopy (BAM). First-order phase transition with subsequent formation of condensed phase domains can occur in the adsorbed monolayers of the mixtures over a large range of usual measuring conditions. A simple theoretical model is developed for the description of the adsorption of the surfactant mixtures. The approach is based on the calculation of the surface pressure isotherm of the mixture from the corresponding dependencies of the single components, also including condensation (aggregation) of one component in the adsorbed monolayer. The approach can be used to calculate the dynamic surface pressure for the diffusion adsorption mechanism. The results obtained by the application of the theoretical model are in qualitative agreement with the experimental data. The theoretical results reproduce not only the experimental findings that the condensed phase consists only of dodecanol but also the shift of the phase transition point to essentially shorter adsorption times.
Introduction The permanent interest in the characterization of the SDSdodecanol system is due to the large effect of the dodecanol traces on the properties of the main component SDS.1,2 Caused by the synthesis, n-dodecanol is the most frequent contaminant of SDS and hardest to remove. This fact is of general importance as SDS represents the mostly used model surfactant in the colloid and interface research. The use of well-defined and pure SDS samples is therefore a precondition for the interpretation of model experiments.3-5 Even though procedures and criteria for surfactant purification have been developed, there are controversial arguments in the evaluation of the purity of the SDS samples.6-8 The dominant effect of n-dodecanol, even in trace amounts, on the coadsorption of SDS/dodecanol mixtures from aqueous solutions has been corroborated by recent papers.9-12 Our results are based on comparative studies of the pure and mixed surfactants by equilibrium surface pressure measurements, surface pressure transients, and BAM.12 Fundamental differences in the adsorption properties and phase behavior of the main surfactant SDS and the trace component n-dodecanol have been obvious. The adsorbed monolayers of surface-chemical pure SDS do not show a phase transition, even at bulk concentrations above the cmc and low temperatures, so that condensed phase domains cannot be formed. On the other hand, the adsorbed dodecanol monolayers can have a first-order phase transition and subsequent growth of condensed phase domains. Recently, it has been evidenced by tailored amphiphiles that first-order phase transition can occur in adsorbed monolayers.13,14 In * To whom correspondence should be addressed. † Max-Planck-Institut fu ¨ r Kolloid- und Grenzfla¨chenforschung. ‡ Medical Physicochemical Center, Donetsk Medical University.
equilibrium finally, the surface can be completely covered by the condensed phase. More comprehensive experimental studies of the dynamic and equilibrium behavior of the adsorbed dodecanol monolayers provided the basis for a theoretical description by the diffusion kinetics of surfactant adsorption from solutions, which assumes the formation of small and large aggregates in the adsorbed monolayer.15 Because of the dominant influence of the dodecanol adsorption, coadsorption of SDS/dodecanol mixtures from aqueous solution is mainly investigated for trace amounts of n-dodecanol. Two limiting cases are of interest for such mixture ratios, namely where a phase transition occurs or cannot occur. In the case that a phase transition does not take place and consequently the state of the adsorbed monolayer is fluid, both components (SDS and n-dodecanol) exist in comparable amounts in the adsorbed monolayer. The corresponding adsorptions (surface concentrations) have been calculated by an orthogonal collocation solution for a two-component system.12 The present work focuses on the SDS/dodecanol coadsorption also under the condition that the mixture contains only trace amounts of dodecanol at a constant ratio. The effect of the concentration of the dissolved surfactants and of the temperature on the two-dimensional phase behavior during the adsorption kinetics are studied. Corresponding BAM investigations are performed to evaluate the features of the condensed phase. A new simple theoretical model is proposed for the surfactant mixture, which is based on the calculation of the surface pressure isotherm of the mixture from the corresponding dependencies for the single components. The approach includes also the case that the adsorbed monolayer of one surfactant is able to aggregate (condense). The solution procedure is most straightforward for the present mixture where the concentration of one component is much higher than that of the other one.
10.1021/jp004273s CCC: $20.00 © 2001 American Chemical Society Published on Web 04/11/2001
Sodium Dodecyl Sulfate/Dodecanol Mixtures
J. Phys. Chem. B, Vol. 105, No. 19, 2001 4325
Theory For the case when the aggregation of a surfactant in the adsorption layer takes place, the equation of state for the surface layer and the adsorption isotherm equation were derived in refs 16 and 17, where Butler’s equation for chemical potentials, Lucassen-Reinders’ dividing surface convention, which assigns equal values to the molar surface areas of solvent and surfactant, and mass action law were used. In the limiting case of large aggregates, these equations expressed via the molar area of monomers ω1, and the critical adsorption (surface concentration) of aggregation Γ1c can be written in the following form 16
RTΓ1c Π1 ) ln[1 - ω1Γ1] ω1Γ1 b1c1 )
Γ1ω1 [1 - ω1Γ1]Γc/Γ1
(1)
(2)
where Π is the surface pressure (the difference between surface tension of the solvent and that of the solution), R is the gas constant, and T is the temperature. In these equations, the adsorption Γ1 is expressed via the observable total adsorption of monomers Γ11 and aggregates Γn1 recalculated as monomers
Γ1 ) Γ11 + nΓ1n
(3)
where n is the aggregation number, n.1. In eqs 1-3 when applied to the solution of a single surfactant, all above subscript “1” could be omitted; these subscripts were introduced to ensure the consistency of the notation for surfactant mixtures. Equations 1 and 2 assume ideal behavior of the monolayer in the transcritical adsorption range. This is almost certainly correct when the contribution to the surface pressure from the clustercluster and cluster-monomer interaction is considered, because for n . 1, the adsorption of clusters as kinetic entities Γ1n is negligibly small. This is incorrect for the monomer-monomer interactions (except for the case when Γ1c , 1/ω1). However, as for n . 1 in the transcritical adsorption range, the relation Γ11 ) const ) Γ1c is valid, the contribution resulting from the non-ideality of the monomers (≈Γ1c2) does not depend on Γ1 and can be approximately accounted for by appropriate correction of the Γ1c value. For an ideal (both in the bulk and at the surface) mixture of two surfactants (“1” and “2”), of which only the first one (surfactant “1”) is capable of the formation of large two-dimensional aggregates in the adsorption layer, one can apply the theory described in refs 16-18 to derive the equations
Π)-
RT ln[1 - ω1(Γ11 + nΓ1n) - ω2Γ2] ω
b1c1 ) b2c2 )
ω1(Γ11 + nΓ1n) [1 - ω1(Γ11 + nΓ1n) - ω2Γ2]ω1/ω ω2Γ2 [1 - ω1(Γ11 + nΓ1n) - ω2Γ2]ω2/ω
ω)
ω1(Γ11 + nΓ1n) + ω2Γ2 Γ1c + Γ2
(4)
component 1, Γ2 is the adsorption of component 2, and ω1 and ω2 are the partial molar areas of the monomers for components 1 and 2, respectively. In the precritical adsorption region of the component 1, the relations n‚Γ1n ) 0 and Γ1c ) Γ11 ) Γ1 are valid; therefore, one can reduce eqs 4-7 to the expressions that were obtained previously for the mixture of two surfactants incapable of aggregation.17,19 Assuming that the partial molar areas of the two surfactant monomers are equal to each other, ω1 ) ω2, one can reduce eqs 4-6 to the most simple form
Π)-
RT(θc + θ2) ln(1 - θ1 - θ2) ω1(θ1 + θ2)
b 1c 1 ) b 2c 2 )
θ1 (1 - θ1 - θ2)(θc+θ2)/(θ1+θ2) θ2 (1 - θ1 - θ2)(θc+θ2)/(θ1+θ2)
(8) (9)
(10)
where θ1 ) ω1Γ1 ) ω1(Γ11 + nΓ1n), θ2 ) ω1Γ2 and θc ) ω1Γ1c are the degrees of monolayer coverage by component 1 (aggregates and monomers), component 2, and the critical value of the monolayer coverage which corresponds to the aggregation onset of component 1, respectively. It appears that the simplifications used to derive eqs 8-10 are too rough to provide any satisfactory agreement between the experimental data and the theoretical predictions. This concerns not only the assumption of ideal behavior of the monolayer and the equality ω1 ) ω2 but also in what regards the influence of the second component on the critical adsorption value (aggregation onset) for the component 1, the possible variation of the ωi values in mixed monolayer etc. In the present work, another procedure has been applied to calculate the theoretical dependence of surface pressure on concentration, which we believe to be less dependent on the deficiencies of the model. If the dependencies of the surface pressure for the single solutions of species 1 and 2 on the concentration c of these surfactants are known, then the equations presented above enable one to calculate the corresponding dependency for the mixture of these surfactants at any concentration of the components from the experimental dependencies of Γ on c for single solutions. Thus, it is assumed that specific interaction of the mixed components does not occur in the monolayer. To derive this procedure, one transforms eqs 8-10 first to the form
exp(Π/R) ) b1c1(1 - θ1 - θ2)R-1 + b2c2(1 - θ1 - θ2)R-1 + 1 (11)
(5)
(6)
(7)
where Γ11 and nΓ1n are the surface concentrations of the component 1 in the monomeric and aggregated (recalculated in the terms of monomers) form, respectively, Γ1c is the critical adsorption, which corresponds to the aggregation onset for the
where Π ) Πω1/RT is a dimensionless surface pressure, and R ) (θc + θ2)/(θ1 + θ2) is the fraction of monomers in the total adsorption of the two surfactants. In this equation, the bici values can be expressed via the corresponding monolayer pressures for single solutions, using eqs 1 and 2 for aggregating surfactant and the Langmuir equation for the solution of surfactant 2
Π2 )
RT ln(b2c2 +1) ω2
This procedure leads to the expression
(12)
4326 J. Phys. Chem. B, Vol. 105, No. 19, 2001
exp(Π/R) ) exp(Π1/β)
(1 - θ1 - θ2)R-1 (1 - θ/1)β-1
Fainerman et al.
+
exp(Π2/R)(1 - θ1 - θ2)R-1 - 1 (13) where θ/1 ) ω1Γ/1 is the degree of monolayer coverage by component 1 in the single solution at any given Π1 ) Π1ω1/ RT; here β ) Γ/1c/Γ* and Π2 ) Π2ω2/RT is the dimensionless surface pressure for the single solution of component 2. Note that the values of dimensionless pressures of single solutions in eq 13 correspond to the same concentrations of the components 1 and 2 as in the mixture. In the precritical adsorption region of the component 1, the relation R ) β ) 1 is valid, and eq 13 becomes
expΠ ) expΠ1 + expΠ2 - 1
(15)
where k1 ) exp(1/β - 1/R)((1 - θ1 - θ2)R-1/(1 - θ/1)β-1), k2 ) exp(-1/R)(1 - θ1 - θ2)R-1, and k3 ) exp(-1/R). As R > β, and also R < 1 and β < 1, then k1 > 1, k2 < 1 and k3 < 1. It is seen that the influence of ki on the first and second terms in the right-hand side of eq 15 have opposite signs. As approximation, it can be therefore assumed that k1 ) k2 ) 1, whereas the value of k3 can vary from k3 ) 1 at the onset of component 1 phase transition to k3 = 0 in the extremely saturated monolayer for relatively low Γ1c and Γ2 values. It follows then that the equation
expΠ ) expΠ1 + expΠ2 - k3
xDπ[c xt - ∫
Γ1 ) 2
(16)
in the range k3 ) 1 - 0 can be used to calculate approximate values of surface pressure for mixed solutions of two surfactants in the transcritical adsorption region. It should be noted that the account for nonideality effects which take place both in the bulk and in the surface layer of single solutions leads to rather insignificant changes in the form of eq 16 because these effects are almost entirely incorporated into the Π1 and Π2 values. Equation 16 is approximately valid for the case of the generalized Frumkin’s equation for the mixture of two surfactants,17 provided that a12 ) (a1 + a2)/2, where a1 and a2 are the Frumkin’s constants for the single species. This condition is often satisfied for the mixtures of non-ionic surfactants and for mixtures of a non-ionic surfactant with an ionic surfactant.20 If the diffusion mechanism of the surfactant adsorption takes place (for this case, it is known that the relation between the dynamic adsorption and the subsurface concentration of a surfactant is given by the adsorption isotherm), then all the mathematics applied to the above equation of state eq 8 remains valid for the dynamic surface pressure of mixed solution. The main problem of a mixed solution is the calculation of the adsorption time which corresponds to the dynamic surface pressure calculated from eq 16. The situation becomes most simple when the mixture of two surfactants is considered, of which one (say, component 1) possesses significantly higher activity than the other component, but the bulk concentration of this component 1 is much lower than that of component 2. This results in a situation that the adsorption of component 2 takes first place. Therefore, the
1
xt
0
c1(0,t - λ)dxλ]
(17)
where D is the diffusion coefficient, t is time, and λ is a dummy integration variable. Comparing the dynamic adsorption of component 1 in the single solution Γ/1 with the dynamic adsorption in the mixed solution (Γ1), from eq 17 one obtains the approximate expression for the adsorption time in the mixed solution
t ) t*(Γ1/Γ/1)2
(14)
To analyze eq 13 in the transcritical region of the adsorption of component 1, one transforms it into the form
expΠ ) k1 expΠ1 + k2 expΠ2 - k3
dynamic surface pressure of component 2 in eq 16 is just the equilibrium surface pressure of this component. The adsorption kinetics of the component 1 either in the single or in mixed solution obeys the Ward & Tordai equation21
(18)
where t* is the adsorption time of component 1 in the single solution. Using eqs 1, 2, 8, and 9 one can transform eq 18 into the form
(
)
2ω1(Π - Π1) RT
t ) t* exp -
(19)
In this expression, the Π value is calculated from eq 16, whereas the Π1 and t* values can be taken from the experiment for the single component 1. As Π > Π1, it follows from eq 19 that t < t*, that is, the time necessary to achieve equilibrium in the mixed solution is lower than that in the single solution. Similar behavior was shown to exist also for penetration of the soluble surfactant into a Langmuir monolayer.22,23 In this case, for a fixed concentration of the soluble surfactant the difference between the pressure of the mixed monolayer and that of the pure Langmuir monolayer ∆Π is equal to the surface pressure of the single solution of this surfactant. However, in the presence of the insoluble component, the monolayer coverage by the soluble component is proportional to the fraction of the surface free of the insoluble component, that is, a decrease of this fraction takes place. Thus, in the presence of an insoluble amphiphile the adsorption equilibrium is faster achieved. Moreover, it can be concluded from eq 19 that in the mixed monolayer the aggregation of the component 1, that is, the firstorder phase transition begins at lower times and therefore (cf. eq 18), at lower adsorption values than in the single solution. This fact is in good agreement with a phenomenon observed earlier, namely, that the phase transition point of the insoluble component is shifted to lower values of monolayer coverage by the penetration of dissolved surfactants into the insoluble monolayer.23-25 It is seen from the above that the only additional information required is the ω1 value for the reconstruction of the dynamic surface pressure (tension) dependence for mixed solution from the corresponding curves calculated for single solutions. Experimental Section Sodium dodecyl sulfate (SDS) was prepared and chemically purified as described previously.26 Possible surface-active impurities of SDS were below the detection limit of BAM and of the adsorption kinetics data. The purity of n-dodecanol (Fluka, puriss) distilled twice, was g99.5%, as analyzed by GLC. The water used was made ultrapure by a Millipore desktop (Millipore, Germany). To measure the dynamic surface tension of single and mixed solutions of SDS and n-dodecanol in the lifetime range of 1 ms
Sodium Dodecyl Sulfate/Dodecanol Mixtures
Figure 1. Time dependence of the dynamic surface pressure for the single 3 mM SDS solution (1), single 15 µM dodecanol solution (2), and the mixed 3 mM SDS/15 `ıM dodecanol solution (3) at 15 °C. Measured with the Wilhelmy method: solid lines; measured with the maximum bubble pressure method: × - (1); o, ∆ - (3).
to 50 s, the MPT2 tensiometer (Lauda, Germany) was used, which implements the maximum bubble pressure method.27-29 The Π(t) adsorption kinetics of the mixed SDS/dodecanol solutions in the range above 1 min were performed with a computer-interfaced film balance. This allows not only the direct monitoring of the surface during the adsorption process but also a good time resolution of the surface pressure changes during the adsorption process. At a selected temperature after a special calibration procedure with pure water, it was replaced by the mixed SDS/dodecanol solution. Immediately before starting the measurements, the adsorbed molecules were removed by sweeping off the surface with a barrier. For this reason, a pure water surface was obtained to be the initial condition (t ) 0) for recording the Π(t) transients. Details of the procedure have been described elsewhere.30 The continuous recording of the surface pressure with time was coupled with BAM monitoring. The Brewster angle microscope BAM 2 (NFT Go¨ttingen, Germany) provides images real in scale and angle, at a resolution of approximately 4 µm. Results and Discussion Figure 1 shows the dynamic surface pressures for the single solutions of SDS (concentration 3 mM) and n-dodecanol (concentration 15 µM), and the mixed solution of these components with the same concentrations at 15 °C. The measurements were performed by the maximum bubble pressure method and by the Wilhelmy plate method so that the range of the lifetimes studied extends over 7 decimal orders from 10-3 to 104 s. The data obtained by the two methods are seen to be consistent with each other in the time interval from 50 to 100 s. Already at time values of approximately 100 s, the surface pressure of the single SDS solution becomes constant being equal to 19 mN/m at 15 °C. The results for the single 15 µM dodecanol solution obtained by the maximum bubble pressure are not shown because in the range of 1 ms to 50 s the surface pressure of the solution is almost zero. Comparing the behavior of the mixed solution with the behavior of the single dodecanol solution, one can see that for the mixture the effect of the dodecanol adsorption on the surface pressure becomes evident at a more early stage of the adsorption process (at ∼10 s) than
J. Phys. Chem. B, Vol. 105, No. 19, 2001 4327 for the pure dodecanol solution (at ∼50 s). The Π(t) curves for pure dodecanol (curve 2) and also for the mixture show a noticeable break point, which indicates a main phase transition of first order in the adsorption layer. Up to the break point, the adsorbed material should be homogeneously distributed in a fluid state in the interval before the break point. In the time interval after the break point, the formation of condensed phase domains surrounded by a fluid phase is expected. The firstorder phase transition and, thus, the two-dimensional condensation (aggregation) commences for the mixed monolayer at much lower time (140 s) as compared with a pure dodecanol solution (930 s). BAM measurements can provide direct evidence for a first order phase transition. A sequence of representative BAM images was obtained at different times during the adsorption of 3 mM SDS/12 µM dodecanol solutions at 5 °C (Figure 2). As expected, condensed phase domains can be observed only after the break point in the dynamic surface pressure curves so that indeed the break point corresponds the main phase transition of first-order. It can be clearly seen that after the phase transition point condensed phase patterns, surrounded by a homogeneous fluid phase, are formed and grow rather rapidly in an approximately shape-preserving way. The fingered domains are irregularly shaped. In the following stages, they become more compact, coalesce, and approach, near the equilibrium, an approximately homogeneous condensed phase. The morphological behavior resembles to that observed for pure dodecanol monolayers15 but the growth kinetics are more rapid. This similarity indicates that the condensed phase is formed only by dodecanol. For the SDS solution, a ω1 value of 1.2 × 105 m2/mol was calculated per 1 mol of SDS when using a factor of 2 in the Gibbs’ adsorption equation written for the surface active DSions.12 A similar value of the molar area ω1 ) 1.3 × 105 m2/ mol was reported for adsorbed dodecanol.15 This fact, and also the fast adsorption of SDS, substantiates the application of the approximate eqs 16 and 19 for the description of the system considered. Note that the Frumkin equation provides a more accurate description of the SDS surface tension isotherm than the Langmuir equation, cf. refs 12 and 31, whereas for the dodecanol solution, the aggregation isotherm was shown to be quite satisfactory.15 Figures 3-5 illustrate the dynamic surface pressures for single dodecanol solutions at a concentration of 12 µM and temperatures of 15°C, 10°C, and 5°C, respectively, and those for mixed dodecanol/SDS solutions with a SDS concentration 3 mM for the same dodecanol concentration and temperatures. Again, it can be seen that the dynamic surface pressure curves of all mixed solutions have a break point characteristic for a first-order phase transition, the position of which is located at significantly lower time values. Figure 5 also shows the theoretical curves for the solution of pure dodecanol reproduced from ref 15. The curves were calculated using eqs 1-3, assuming equilibrium between the average dimers and large aggregates in the dodecanol monolayer. For the 3 mM SDS solution, the Π2 value at 5-15°C is bounded within the limits of 21 to 19 mN/m so that in the calculations with eqs 16 and 19 this value was taken to be 20 mN/m for all temperature values. The results of the calculations for k3 ) 1 and for k3 varying within the range of 0.5 (for low times) to 0 (at large time limit) are shown in Figures 3-5 as curves 1 and 2, respectively. It can be seen that in the time range below 10 min, the experimental dependencies are located between these theoretical curves, that is, the approximate theoretical model agrees well with the experiment. Moreover,
4328 J. Phys. Chem. B, Vol. 105, No. 19, 2001
Fainerman et al.
Figure 2. BAM images obtained after the break point in the Π(t) curve of an aqueous 3 mM SDS/12µM dodecanol solution at different times and at 5 °C.
Figure 3. Dependence of the dynamic surface pressure for the single 12 µM dodecanol solution (lower thin curve 1) and for the mixed 3 mM SDS/15 µM dodecanol solution (upper solid curve 2) at 15 °C measured using the Wilhelmy method. The theoretical curves were calculated from eqs 16 and 19: o for ω1 ) 1.2 × 105 m2/mol, k3 ) 1; ∆ for k3 ) 0.5 ÷ 0; 0 for ω1 ) 1 × 105 m2/mol, k3 ) 1.
the critical time of the dodecanol aggregation onset, which corresponds to the break point of the theoretical curve, is in
perfect agreement with the experimental data. However, at time values exceeding 10 min, the theoretical values of the dynamic surface pressure calculated with k3 ) 0 are by 6 to 8 mN/m lower than the experimental ones. To explain this discrepancy between the experimental data and calculated values, one must consider the effect of the limiting adsorption value increase (the decrease of the area per one molecule) which takes place in the mixed monolayer. Figures 3 - 5 also illustrate the calculations performed using eqs 14 and 19 with ω1 ) 105 m2/mol for the mixed monolayer and with ω1 ) 1.2‚105 m2/mol for the single monolayers. At high time values (g30 min), the calculated surface pressure values are in excellent agreement with the experimental data. It seems that in the intermediate time range one can also achieve correspondence between the theory and experimental data, if the ω1 value is considered to be a variable amount in the range of (1.0-1.2)‚105 m2/mol. The time for the onset of the dodecanol aggregation in the mixed solution is 4-6 times lower as compared to that for the single dodecanol solutions, see Figures 3-5. According to eq 18, this fact indicates the 2-2.5 times decrease of the critical adsorption value characteristic of the onset of aggregation in the mixed solution. Similar results were also obtained for insoluble monolayers, where the penetration of a soluble surfactant into the monolayer results in the fact that the insoluble surfactant
Sodium Dodecyl Sulfate/Dodecanol Mixtures
Figure 4. Dependence of the dynamic surface pressure for the single 12 µM dodecanol solution (lower thin curve 1) and for the mixed 3 mM SDS/15 µM dodecanol solution (upper solid curve 2) at 10 °C measured using the Wilhelmy method. The theoretical curves were calculated from eqs 16 and 19: o for ω1 ) 1.2 × 105 m2/mol, k3 ) 1; ∆ for k3 ) 0.5 ÷ 0; 0 for ω1 ) 1 × 105 m2/mol, k3 ) 1.
J. Phys. Chem. B, Vol. 105, No. 19, 2001 4329
Figure 6. Dynamic surface pressure for 10 µM dodecanol solution (lower thin line 1) and mixed 3 mM SDS/10 µM dodecanol solution (upper solid line 2) at 15 °C, measured by the Wilhelmy method.
surfactant concentration in the mixture corresponds to lower equilibrium adsorption value. This is the reason why SDS, which does not form any aggregates without salt,32,33 affects the aggregate formation of dodecanol in the monolayer almost in the same way as found for pure dodecanol. Conclusions
Figure 5. Dependence of the dynamic surface pressure for the single 12 µM dodecanol solution (lower thin curve 1) and for the mixed 3 mM SDS/15 µM dodecanol solution (upper solid curve 2) at 5 °C measured using the Wilhelmy method. The theoretical curves were calculated from eqs 16 and 19: o for ω1 ) 1.2 × 105 m2/mol, k3 ) 1; ∆ for k3 ) 0.5 ÷ 0; 0 for ω1 ) 1 × 105 m2/mol, k3 ) 1. ×, ( for the theoretical curves of single dodecanol solution, data presented in ref 15.
aggregates at lower surface concentrations as compared with the phase transition point of the insoluble monolayer without penetration of dissolved components.23-25 This can explain the existence of 2D condensation in form of pure dodecanol in the mixed solution (3 mM SDS and 10 µM dodecanol) at 15 °C, see Figure 6. However, a single dodecanol solution does not aggregate at this concentration and temperature. It is interesting to note that according to the theory17 used to derive eq 16, the chemical potentials of surface active components in the bulk solution is nearly independent of the presence of other components therein, whereas the chemical potentials in the surface layer depend on the composition of the layer and surface pressure. Therefore, if equilibrium exists between the bulk solution (subsurface layer) and the surface, then the same
The dominant influence of dodecanol at the coadsorption from aqueous solutions of SDS and dodecanol in trace amounts has been experimentally and theoretically demonstrated. The adsorbed monolayers of the single components SDS and dodecanol show fundamental differences in the two-dimensional phase behavior. The experimental results are based on comparative studies of the single components with the mixed systems by combination of dynamic surface pressure measurements with BAM studies. The adsorbed monolayers of both pure dodecanol and SDS/mixtures show two-dimensional phase transition and subsequent formation of condensed dodecanol phase, though the conditions of their development are different. A high portion of SDS in the bulk phase accelerates the phase transition in the adsorbed monolayer of the mixture. A simple theoretical model has been introduced for the description of the coadsorption of surfactant mixtures, which enables one to calculate the surface pressure isotherm of the mixture from the corresponding dependencies of the single components, including also the case of aggregation of one surfactant in the adsorbed monolayer. The approach developed here is based on equilibrium between subsurface concentration and adsorption so that this method can also be used to estimate the dynamic surface pressure for the diffusion adsorption mechanism. The solution procedure is most straightforward for the case that the concentration of one component of the mixture is much higher than that of the second component. Various methods are employed to study the surface pressure of mixed SDS/dodecanol solutions. The proposed theoretical model is shown to be in qualitative agreement with the experimental data. The discrepancy between theory and experiment for the monolayer states close to equilibrium allows the conclusion that the influence of the monolayer components on the total adsorption is nonadditive. The theoretical results corroborate the fact that the formed condensed phase (large aggregates) in the mixed monolayer consists only of dodecanol. The presence of SDS in the adsorbed monolayer leads to a 2-2.5 times decrease in the critical
4330 J. Phys. Chem. B, Vol. 105, No. 19, 2001 adsorption value of dodecanol. This again results in a significant (several times) decrease in the time where the two-dimensional phase transition (aggregation) of dodecanol starts in the mixed monolayer at nonequilibrium. The theoretical model proposed adequately reproduces these experimental results. References and Notes (1) Vollhardt, D.; Czichocki, G. Colloids Surf. 1984, 11, 209. (2) Vollhardt, D.; Czichocki, G. Langmuir 1990, 6, 317. (3) Mysels, K. J.; Florence, A. T. J. Colloid Interface Sci. 1973, 43, 577. (4) Czichocki, G.; Vollhardt, D.; Seibt, H. Tenside Surf. Det. 1981, 18, 320. (5) Vollhardt, D.; Czichocki, G. Tenside Surf. Det. 1993, 30, 349. (6) Lunkenheimer, K. J. Colloid Interface Sci. 1993, 160, 509. (7) Hines, J. D. J. Colloid Interface Sci. 1996, 180, 488. (8) Lunkenheimer, K.; Fruhner, H.; Theil, F. Colloids Surf. A 1993, 76, 289. (9) Lu, J. R.; Purcell, I. P.; Lee, E. M.; Simister, E. A.; Thomas, R. K.; Rennie, A. R.; Penfold, J. J. Colloid Interface Sci. 1995, 174, 441. (10) Bain, C. D.; Davies, P. B.; Ward, R. N. Langmuir 1994, 10, 2060. (11) Ward, R. N.; Davies, P. B.; Bain, C. D. J. Phys. Chem. B 1997, 101, 1594. (12) Vollhardt, D.; Emrich, G. Colloids Surfaces A 2000, 161, 173. (13) Vollhardt, D.; Melzer, V. J. Phys. Chem. B 1997, 101, 3370. (14) Melzer, V.; Vollhardt, D.; Weidemann, G.; Brezesinski, G.; Wagner, R.; Mo¨hwald, H. Phys. ReV. E 2000, 57, 901. (15) Vollhardt, D.; Fainerman, V. B.; Emrich, G. J. Phys. Chem. B 2000, 104, 8536.
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