1946
Langmuir 1997, 13, 1946-1951
Thermodynamics in Micellar Solutions: Confirmation of Complex Formation between Sodium Dodecyl Sulfate and Polyethylene Glycol K. Ballerat-Busserolles, G. Roux-Desgranges,* and A. H. Roux Laboratoire Thermodynamique et Ge´ nie Chimique, URA CNRS 434, Universite´ Blaise Pascal, 63177 Aubiere Cedex, France Received April 23, 1996. In Final Form: December 13, 1996X The interactions between sodium dodecyl sulfate (SDS) and polyethylene glycol (PEG 10000) were investigated through density and heat capacity measurements at 298.15 K. From experimental data, apparent and transfer properties of solutes were deduced. The changes of these properties with the concentration of each solute are characteristic of the existence of preponderant hydrophobic interactions between SDS and PEG which lead to the formation of a rather stable complex corresponding to a ratio [EO]/[SDS] of about 2.3, [EO] being the concentration in repeat units of the polymer. When saturation of the polymer is attained, the properties of small adsorbed micelles are no more affected by the polymer in excess. While SDS is in excess, beyond polymer saturation, free normal micelles are identified in solution. This latter consideration is also verified when SDS concentrations are exceeding 0.2 mol‚kg-1 while the structure of micelles is changed in water-surfactant solutions. Our results show that until its complete saturation the polymer inhibits this transition, whereas at larger SDS concentrations, the free micelles in excess are able to undergo the postmicellar transition as observed in the absence of polymer.
Introduction Interactions between ionic surfactants and nonionic water soluble polymers have been extensively studied during the last decades, but the subject is not clearly understood. These systems are interesting from a fundamental as well as from a practical point of view. These complex mixtures have important properties for a wide range of industrial application fields such as floatation processes, foaming controls, detergency, and enhanced oil recovery. They are also of interest in formulation and conditioning for cosmetics, biological, pharmaceutical, or fine chemistry applications. On the fundamental level, the nature of the surfactant-polymer interactions leading to the formation of a complex, and likewise the physical structure and stability of this complex, is still a subject of controversy. Numerous works have been devoted to such studies, as can be found in the literature and in review articles.1-3 The particular systems formed with sodium dodecyl sulfate (SDS) and polyethylene glycols (PEG) have received much attention using different techniques.4-15 The com* Corresponding author. X Abstract published in Advance ACS Abstracts, March 1, 1997. (1) Robb, I. D. Anionic Surfactants-Physical Chemistry of Surfactant Action; Lucassen-Reynders, E. H., Ed.; Surfactant Sci. Ser. No. 11; Dekker: New York, 1981. (2) Goddard, E. D. Colloids Surf. 1986, 19, 255. (3) Hayakawa, K.; Kwak, J. C. T. Cationic Surfactants: Physical Chemistry; Rubingh, D. N., Holland, P. M., Eds.; Surfactant Sci. Ser. No. 37; Dekker: New York, 1991; p 189. (4) Franc¸ ois, J.; Dayantis, J.; Sabbadin, J. Eur. Polym. J. 1985, 46, 165. (5) Schwuger, M. J. J. Colloid Interface Sci. 1973, 43, 491. (6) Sasaki, T.; Kushima, K.; Matsuda, K.; Susuki, H. Bull. Chem. Soc. Jpn. 1980, 53, 1864. (7) Shirahama, K. Colloid Polym. Sci. 1974, 252, 978. (8) Cabane, B. J. Phys. Chem.1977, 81, 1639. (9) Cabane, J.; Duplessix, R. J. Phys. (Paris) 1982, 43,1529. (10) Cabane, J.; Duplessix, R. Colloids Surf. 1985, 13, 19. (11) Witte, F. M.; Engberts, J. B. F. N. J. Org. Chem. 1987, 52, 4767. (12) Zana, R.; Lang, J.; Lianos, P. Microdomains in Polymer Solutions; Dubin, P., Ed.; Plenum: New York, 1985; p 357. (13) Tondre, C. J. Phys. Chem. 1985, 89, 5101. (14) Chari, K.; Antalek, B.; Lin, M. Y.; Sinha, S. K. J. Chem. Phys. 1994, 100, 5294. (15) Olofsson, G.; Wang, G. Pure Appl. Chem. 1994, 66, 527.
S0743-7463(96)00396-4 CCC: $14.00
plexes which are formed are rather stable, and consequently these systems have been widely studied to be chosen as model systems. Generally, most of the studies were focused only on the influence of the polymer close to the micellization of surfactant involving the adsorption of surfactant micelles on the polymer chains.4-8,15 The size and shape of free micelles or bound aggregates as well as the conformational changes of polymer chains in the presence of surfactants were some investigated aspects.9,14-18 In the presence of polymer, micellization of surfactant arises at a lower concentration than the usual critical micelle concentration (cmc) and appears independent of the polymer concentration.4 The micelles thus formed have a smaller aggregation number and are regularly adsorbed on different sites of the polymer chain until saturation of the polymer is attained.4,10-12 When surfactant becomes in excess, free micelles can then readily exist having the aggregation number usually estimated for (polymer free) micellar solutions.10,12 The nature of the interactions leading to the formation of complexes where micelles are bound on the polymer chains has not been yet clearly elucidated. Generally it is emphasized that hydrophobic interactions are in a major part responsible since adsorption depends on the hydrophobic character of both components.19-22 The methylene groups of PEG can interact with the surfactant aliphatic chains near the polar head groups surrounding micelles from where some water molecules are removed.8,12,19,20 However, this interpretation seems insufficient on the grounds that such adsorption of PEG is not observed with cationic surfactants.3,23 As a consequence, polar attractive interactions in the aqueous micellar layers between the oxygens of ether groups of PEG chains, being proton (16) Wang, G.; Olofsson, G. J. Phys. Chem. 1995, 99, 5588. (17) Maltesh, C.; Somasundaran, P. Langmuir 1992, 8, 1926. (18) Benkhira, A.; Franta, E.; Francois, J. J. Colloid Interface Sci. 1994, 164, 428. (19) Nagarajan, R.; Kalpakci, B. Microdomains in Polymer Solutions; Dubin, P., Ed.; Plenum: New York, 1985; p 369. (20) Nagarajan, R. Colloids Surf. 1985, 13, 1. (21) Ruckenstein, E.; Huber, G.; Hoffmann, H. Langmuir 1987, 3, 387. (22) Gilanyi, T.; Wolfram, E. Microdomains in Polymer Solutions; Dubin, P., Ed.; Plenum: New York, 1985; p 383. (23) Brackman, J. C.; Engberts, J. B. F. N. Langmuir 1991, 7, 2097.
© 1997 American Chemical Society
Thermodynamics in Micellar Solutions
acceptors, and the negative polar heads of SDS must be considered. More precisely, Dubin et al.24 invoked the role of intermediate played by the cation Na+, which can be bound directly onto the oxygen atoms along the ethoxylated PEG chains, favoring strong electrostatic interactions between PEG and SDS and therefore by this co-operative effect facilitating micellization and micellar adsorption along polymer chains. Thermodynamic properties are often a useful tool to characterize interactions in solutions and to investigate structural changes occurring in the medium.25,26 Although few studies have been devoted to the thermodynamics of these mixed systems,27,28 at relatively high surfactant concentration a quantitative estimation of thermodynamic properties upon structural changes can be expected from our study. The evolution of the micellar shape in aqueous SDS solutions has been reported previously along with the increase of surfactant concentration.29 More particularly in our previous works,30-32 we have shown a transition arising close to m2* ) 0.2 mol‚kg-1. This transition is most likely favored by an increase of β, the association ratio of counterions bound to the micelles, as suggested by Quirion et al.26 The modification of shape is accompanied by an important increase of the solubility of various solutes,28 and within this concentration domain unexpected behavior of some thermodynamic properties is observed. In the present work, we are interested in the effect of water soluble polymers in the semidilute range of SDS concentrations in order to evidence the formation of complexes, as observed close to the cmc, which can act in promoting or inhibiting the formation of ellipsoid or cylindrical micelles. For this purpose, we have particularly selected the system SDS-PEG 10000 for which reliable data exist for comparison. The aim of the present work is to examine how volumic and heat capacity properties may reflect the nature of the interactions between SDS and PEG 10000 through complex formation and be affected by the evolution of micellar structures depending on polymer concentration. Experimental Section Sodium dodecyl sulfate (SDS) was a pure (>99%) grade reagent from Merck and used without further purification. Polyethylene glycol (PEG 10000), with a polydispersity of 1.54, was provided from Aldrich. All solutions were prepared by weight with deionized and degassed water prior use. The densities of the solutions, F, were measured at a low flow rate with a vibrating tube densimeter (Sodev 03D), calibrated using water and vacuum. The heat capacities by volume unit, σ, were determined with a Picker flow microcalorimeter (Setaram) based on the thermal balance principle, operating at a flow rate of 0.01 cm3‚s-1. For these two apparatuses the temperature was maintained constant at 298 K within 0.005 K. The procedures (24) Dubin, P. L.; Gruber, J. H.; Xia, J.; Zhang, H. J. Colloid Interface Sci. 1992, 148, 92. (25) Desnoyers, J. E.; De Lisi, R.; Ostiguy, C.; Perron, G. Solution Chemistry of Surfactants; Mittal, K. L., Ed.; Plenum: New York, 1979; p 221. (26) Quirion, F.; Desnoyers, J. E. J. Colloid Interface Sci. 1986, 112, 565. (27) Perron, G.; Francoeur, J.; Desnoyers, J. E.; Kwak, J. C. T. Can. J. Chem. 1987, 65, 990. (28) Aucouturier, C.; Roux-Desgranges, G.; Roux, A. H. J. Therm. Anal. 1994, 41, 1295. (29) Reiss-Husson, F.; Luzzati, V. J. Colloid Interface Sci. 1966, 21, 534. (30) Roux-Desgranges, G.; Roux, A. H.; Grolier, J.-P. E.; Viallard, A. J. Solution Chem. 1982, 11, 357. (31) Roux-Desgranges, G.; Roux, A. H.; Viallard, A. J. Chim. Phys. 1985, 82, 441. (32) Roux-Desgranges, G.; Bordere, S.; Roux, A. H. J. Colloid Interface Sci. 1994, 162, 284.
Langmuir, Vol. 13, No. 7, 1997 1947 are well documented in the literature.33,34 In the present experimental conditions the sensitivities were 3 × 10-6 g‚cm-3 and 10-4 J‚K-1‚cm-3 for densities and heat capacities, respectively. The specific heat capacities, cp, were obtained from the differential measurement of heat capacities by volume unit through the relation:
(
cp ) cp,r 1 +
)
σ - σr Fr σr F
(1)
where subscript r refers to the property of the reference solvent. The apparent molar volumes and heat capacities of solute i were calculated from densities and specific heat capacities using the usual relations:
Vφ,i )
Mi 1000(F - F0) F miFF0
Cφ,i ) Micp +
1000(cp - cp0) mi
(2)
(3)
where Mi and mi are respectively the molar mass and the molality of solute i. In binary systems, water (1) + SDS (2) or water (1) + PEG (3), water is always the reference solvent35 with F0 ) 0.997 047 g‚cm-3 and cp,0 ) 4.1793 J‚K-1‚g-1 at 298.15 K. In ternary systems, water (1) + SDS (2) + PEG 10000 (3), the reference solvent is the binary system associated to the ternary; thus water + SDS is the “solvent” when PEG is considered as the solute and reciprocally. In ternary systems the molar properties of the solute i are generally discussed in terms of their transfer from water to binary aqueous solutions. If the concentrations of transferred solutes are kept constant and as much as possible just between the binary and the ternary system, the following relation can be used directly:
∆Yi(water f water + SDS) ) Yφ,i(water + SDS) - Yφ,i(water) (4) For this purpose, densities and heat capacities of the ternary solutions were measured along dilution lines by the solute, from binary solutions at fixed compositions. Ternary solutions are obtained from stock binary solutions by weighed additions of solute into different aliquots of the binary. Along these dilution lines, the apparent properties of the solute were then determined. Conversely, the apparent properties relative to the cosolute were also determined using the same relations, taking into account in their case the change of concentration imposed by the change of reference solvent; i.e., solute molalities have to be recalculated relative to the appropriate mixed solvent.32
Results and Discussion Volumes and heat capacities are generally considered as sensitive properties to the evolution of the structure of solutions since they are reflecting packing density and energy fluctuations. Specifically, the profiles of the apparent or transfer molar quantities of the solutes along their concentrations exhibit particular variations in the domain where structural transitions occur. These variations are related to the shift of the different equilibria, i.e., surfactant association and distribution of the solute, with addition of a solute or with temperature. In the case of cmc, thermodynamic models, like the mass action law and partition model developed by Roux et al.36,37 are able to well predict the observed behavior. The lowering of (33) Picker, P.; Tremblay, E.; Jolicoeur, C. J. Solution Chem. 1974, 3, 377. (34) Picker, P.; Leduc, P. A.; Philip, P. R.; Desnoyers, J. E. J. Chem. Thermodyn. 1971, 3, 631. (35) (a) Kell, G. S. J. Chem. Eng. Data 1977, 12, 66. (b) Stimson, H. F. Am. J. Phys. 1955, 23, 614. (36) Roux, A. H.; Hetu, D.; Perron, G.; Desnoyers, J. E. J. Solution Chem. 1984, 13, 1.
1948 Langmuir, Vol. 13, No. 7, 1997
Ballerat-Busserolles et al.
Figure 1. Apparent molar volumes of PEG 10000, Vφ,3, versus its molality (m3) at different concentrations of SDS (m2): 4, 0.01; f, 0.05; O, 0.1; b, 0.2; 9, 0.4; dotted line, pure water.
Figure 2. Apparent molar heat capacities of PEG 10000, Cφ,3, versus its molality (m3) at different concentrations of SDS (m2): 4, 0.01; f, 0.05; O, 0.1; b, 0.2; 9, 0.4; dotted line, pure water.
the cmc and solubilization of the solute are accompanied by an increase of the micellar phase, which is reflected by an increase of apparent or transfer volumes of the solutes and a decrease of heat capacities, followed by an extremum in the case of the more hydrophobic solutes. With heat capacities, the shape of the curve may be somewhat more complex since a maximum could appear preceding the minimum, related to the double shift of the quoted equilibria with temperature. In more concentrated micellar solutions, when transitions are occurring, a similar thermodynamic treatment might be applied, although it is somewhat more complicated. However, the shape of the experimental curves can be qualitatively analyzed along previous considerations used when characterizing postmicellar transitions. In this way, the analysis of the variations of the properties can provide valuable information on the nature of the interactions between SDS and PEG 10000 as well as quantitative estimation on the composition of the obtained complex. Thermodynamic Properties of Solutes in SDS Solutions. Apparent Molar Properties of PEG 10000 in SDS Solutions. These properties were determined along dilution lines by PEG 10000 of binary solutions of SDS at fixed compositions. The SDS concentrations were chosen in order to cover the domain including the transitions previously defined30 at cmc ) 0.008 and m2* ) 0.2 mol‚kg-1. The variations of the apparent molar volumes of PEG 10000, Vφ,3, and heat capacities, Cφ,3, have been reported in Figures 1 and 2, respectively, as a function of the PEG molality. Vφ,3 values are always higher and Cφ,3 values lower than their respective values in pure water (dotted curves), but the shapes of curves depend on the SDS concentration. Close to the cmc, Vφ,3 reaches larger values and then decreases rapidly toward the value of PEG in pure water at higher PEG concentrations. When SDS concentration is increased, the profiles are more the same and, following the initial decrease, a broad maximum is observed before reaching the value in pure water. In parallel, both the observed minima and maxima are shifted toward higher molalities of PEG. The variations of the apparent heat capacities are opposite. Cφ,3 takes a very low value near infinite dilution of PEG and increases rapidly toward the value in water when SDS concentration
Figure 3. Transfer molar volumes of SDS, ∆V2, versus PEG molality (m3) at different transferred SDS concentrations (m2): 4, 0.01; f, 0.05; O, 0.1; b, 0.2; 9, 0.4.
(37) Hetu, D.; Roux, A. H.; Desnoyers, J. E. J. Solution Chem. 1987, 16, 529.
is close to the cmc. On the other curves, Cφ,3 presents a minimum corresponding closely to the maxima observed on Vφ,3 curves. For the particular SDS concentration m2*, the curve is shifted to highest heat capacity values being even higher than the value of PEG in water, then with the increase of PEG molality this overage is reduced and all the curves are superimposing. Transfer Properties of SDS from Water to Water + PEG 10000 Solutions. Concerning SDS, the transfer molar volumes (∆V2) and heat capacities (∆C2) were calculated as indicated in the Experimental Section for different SDS concentrations and are represented as a function of the molality of PEG 10000 in Figures 3 and 4, respectively. The transfer volumes are always positive, the initial increase marked by an inflection point is more important when the SDS concentration is smaller and a slight maximum is even observed for the most dilute solutions. Then, the different ∆V2 curves level off toward a nearly constant plateau for higher PEG content. The transfer heat capacities are less regular and are depending on the SDS concentration. In the domain of spherical micelles (below m2*) initially a pronounced minimum is observed
Thermodynamics in Micellar Solutions
Langmuir, Vol. 13, No. 7, 1997 1949
Figure 4. Transfer molar heat capacities of SDS, ∆C2, versus PEG molality (m3) at different transferred SDS concentrations (m2): 4, 0.01; f, 0.05; O, 0.1; b, 0.2; 9, 0.4.
Figure 5. Transfer heat capacities of SDS versus the ratio [EO]/[SDS] at different transferred SDS concentrations (m2): 4, 0.01; f, 0.05; O, 0.1; b, 0.2; 9, 0.4.
Table 1. Ratio [EO]/[SDS] As Determined from Polymer Concentrations Associated Respectively to the Maximum on VO,3 (m3) and to the Minimum on ∆C2 (m3) Curves at Different SDS Compositions
invariant position of the minimum ∆C2[EO]/[SDS] for the different surfactant compositions leading to a stoichiometry for the complex close to a value of 2.3. Our average value is a little smaller than those generally deduced with other properties and more specifically from enthalpies where a ratio of 2.8 was given by Olofsson et al.15 Particularly with heat capacities, the effects related to the equilibrium shifts close to a transition being relatively important, the quantitative information on adsorption of the micelles on polymer might be slightly affected. Nevertheless, depending on the techniques and the method of determination, the value of this ratio is different and therefore cannot be always accurately defined. For example, Tondre,13 from relaxation kinetics measurements on the system SDS-PEG 10000, proposed that a stoichiometric complex entity would involve between 0.5 and 1 chain of PEG 10000 per micelle, that is to say a ratio varying from 2.8 to 5.6. Likewise, supported by NMR paramagnetic relaxation study of PEG’s of different molar masses in SDS solutions (0.24 mol‚kg-1), Kwak and colleagues38 suggested a [EO]/[SDS] ratio equal to 1.9 with PEG in excess. For comparison, Figure 6 shows the variations of PEG concentrations relative to those of SDS corresponding to the complex as obtained from different techniques. The different results are sufficiently scattered to consider that our present results are in fairly good agreement with other data. The large variations occurring close to the cmc are expressing the most important changes happening within the microenvironment of each solute. The interactions of PEG and SDS molecules lead to a loss of hydrophobic hydration for both solutes which favors the formation of micelles. The substitution of water molecules in the hydration layer of PEG by a more hydrophobic surrounding is expressed by a sharp increase of the apparent volume and inversely a large diminution of heat capacity of PEG, the more important the smaller the PEG concentration is. Moreover, the unexpectedly large transfer properties noticed for SDS confirm the induced enhancement of the micellar volume and, because a larger number of surfactant monomers is involved in micelles, volumes ∆V2 (m3) increase while heat capacities ∆C2 (m3) decrease. These variations are magnified near the cmc where the presence of polymer forces a largest relative number of surfactant molecules to participate in micelles (cmc being low). Furthermore, the existence of a shallow maximum on transfer volumes ∆V2 (Figure 3) can be justified, through
mSDS, mol‚kg-1
mEO (Vφ,3), mol‚kg-1
[EO]/[SDS]
mEO (∆C2), mol‚kg-1
[EO]/[SDS]
0.05 0.1 0.2 0.4
0.11 0.23 0.42 0.79
2.2 2.3 2.1 2.0
0.11 0.22 0.46 0.87
2.3 2.2 2.3 2.2
before the plateau is attained. Close to the postmicellar transition (m2*) firstly a positive maximum is present preceding the minimum. In the last domain, beyond m2*, ∆C2 is monotonously decreasing to a more negative but constant value. The different variations of volumes and heat capacities of SDS and PEG 10000 along with PEG concentration are characteristic of the extent of the interactions between surfactant and polymer. Firstly, the typical variations (positive volumes and negative heat capacities) are reflecting the predominant hydrophobic interactions between surfactant and polymer. Secondly, the composition of the complex formed between SDS and PEG can be evaluated from characteristic points, such as extrema or inflection, shown by the different curves. When the polymer chain is long enough, for molar masses of PEG larger than 4000, the concentration of monomer repeat units in the molecule is a significant parameter to estimate the influence of the polymer.12,38,39 For most authors, the saturation of the polymer is corresponding to about a ratio of one molecule of SDS interacting with three repeat EO units,9,15,39,40 and a favorable situation is encountered with PEG 10000 where the polymeric chain is long enough to wrap around about one micelle of SDS.13,39 Considering the above mentioned characteristic points with volumes and heat capacities, the calculated ratios of [EO]/[SDS] are given in Table 1. A nearly constant ratio [EO]/[SDS] is obtained, indicating the formation of a stable complex having a well-defined composition. As for example, in Figure 5, the profiles of the transfer heat capacities ∆C2 are reported as a function of the ratio [EO]/[SDS]. Remarkably they show an (38) Gao, Z.; Wasylishen, R. E.; Kwak, J. C. T. J. Phys. Chem. 1991, 95, 462. (39) Lissi, E. A.; Abuin, E. J. Colloid Interface Sci. 1985, 105, 1. (40) Veggeland, K.; Austad,T. Colloids Surf. 1993, 76, 73.
1950 Langmuir, Vol. 13, No. 7, 1997
Figure 6. SDS concentrations associated to polymer saturation as function of the molality of PEG 10000 depending on different techniques used: 4, 2, temperature jump (ref 13); *, calorimetric titration (ref 15); 0, translational diffusion (ref 8); 9, surface tension (ref 8); b, transfer heat capacities of SDS; O, apparent molar volumes of PEG 10000.
the association and partition model,37 by the additional contribution of the cmc shift by the solute. With heat capacities, the model is predicting a more complex shape of the curve ∆C2 (Figure 4) as resulting from a double shift of equilibria as explained previously, a small maximum preceding a deep minimum. When the SDS concentration is increased, the variations of apparent and transfer properties are more regular since the relative effects due to the equilibrium shifts are attenuated as expected. Referring to Figure 6, when concentrations of solutes are comprise in the left domain defined by the characteristic line of the complex, for ratios [EO]/[SDS] lower than 2.3, the increase of Vφ,3 and the decrease of Cφ,3 (Figures 1 and 2) are indications of the progressive adsorption of micelles on the polymer chains until saturation, in agreement with the loss of hydrophobic hydration resulting of surfactant-polymer interactions. On Vφ,3 curves the initial minimum preceding the maximum is probably a consequence of two superimposed effects, a marked decrease related to the equilibrium shifts counterbalanced by the increase of Vφ,3 owing to the progressive complexation of PEG chains. Similarly, the increase of ∆V2 (Figure 2) is correlated with the increase of Vφ,3 and the inflection point is related to the maximum on Vφ,3 curves. The more complex shapes of transfer heat capacities ∆C2 (m3) seen in Figure 4 are due to the nature of this property, as second derivative of Gibbs energy with temperature. The initial decrease due to the cmc depression followed by the minimum corresponding to the polymer saturation is more marked when the surfactant concentration is lower. When surfactant concentration is chosen close to m2*, an initial positive maximum of ∆C2 appears as a characteristic of the equilibrium shifts near this transition. When PEG is in excess, the ratio [EO]/[SDS] being greater than 2.3, the apparent properties of PEG (Figures 1 and 2) are leveling off with PEG concentration to tend to their respective values in pure water. The surfactantfree polymer chains surrounded only by water molecules are becoming relatively preponderant compared to the complexed micelles-polymer chains. All the micelles are thus adsorbed on polymers and the concentration of surfactant monomers in equilibrium with micelles in the aqueous phase is nearly constant at a value slightly lower
Ballerat-Busserolles et al.
Figure 7. Apparent molar volumes of SDS, Vφ,2, versus its molality (m2) in mixed solvent water + PEG 10000: 4, 0 (ref 28); O, 0.002 mol‚kg-1; b, 0.005 mol‚kg-1.
than the cmc. Thus with respect to SDS the structure of the medium does not change and consequently the transfer values of SDS remain almost constant. The plateau values are reflecting the difference of SDS properties between micelles in aqueous solution and adsorbed micelles in a mixed solvent containing polymer. They reveal the neat contribution of the hydrophobic SDS-PEG interactions on the concerned thermodynamic quantities. The approximate values 1 cm3‚mol-1 for volume and respectively -15 or -50 J‚K-1‚mol-1 for heat capacity depending on whether the transferred SDS molality is lower or higher than m2*, are characterizing this interaction. The adsorbed micelles cannot undergo the postmicellar transition, transition which manifests itself in aqueous solutions by an increase of about 35 J‚K-1‚mol-1 of the apparent heat capacity, as shown in Figure 8. Thermodynamic Properties of SDS in Mixed Polymer Aqueous Solutions. The variations of the apparent molar volumes (Vφ,2) and heat capacities (Cφ,2) of SDS in water and in aqueous solutions of PEG 10000 at 2 × 10-3 and 5 × 10-3 mol‚kg-1 are reported in Figures 7 and 8, respectively. The general evolution of Vφ,2 looks relatively similar in aqueous or in polymer solutions. However, with the increasing of the polymer content, the initial rising due to micellization is occurring at lower SDS molality and is more marked. Similarly, constant values at the plateau are reached more rapidly being even higher to the corresponding value in water. Likewise, in the presence of hydrophobic solutes, such behavior is typical of the lowering of cmc accompanying the formation of more stable micelles. With heat capacities, similar remarks can be drawn concerning the initial decrease of Cφ,2. Nevertheless, heat capacities are more appropriate to evidence the transition in water near m2*, which manifests itself at higher concentrations by an increase of the apparent heat capacity of SDS. In this domain, the rise is still observed when the PEG concentration is 2 × 10-3 mol‚kg-1 while it has disappeared at 5 × 10-3 mol‚kg-1, and therefore Cφ,2 is continuously decreasing in the investigated domain. The role of polymer on the micellar structure is also clearly shown through the use of the pseudophase model41 with which the variation of the apparent property should be linear with the inverse of molality in a domain of stable structure; thus when a (41) Douhe´ret, G.; Viallard, A. J. Chim. Phys. 1981, 78, 85.
Thermodynamics in Micellar Solutions
Langmuir, Vol. 13, No. 7, 1997 1951
nearly normal size is supported by our observation that micelles can normally undergo the shape transition close to m2*. Taking into account the saturation concentration evaluated previously, with 2 × 10-3 mol‚kg-1 PEG, the saturation limit would be reached below m2*; thus for this latter concentration surfactant is in excess and free normal micelles undergo the transition, leading to the usual rise of heat capacity. At the opposite, when PEG concentration is 5 × 10-3 mol‚kg-1, all SDS molecules are adsorbed and no free micelle exists in solution. Accounting only for one kind of micelles, the pseudophase model calculations give the variation of Cφ,2 represented by the dotted line in Figure 8. It fits quite well the experimental data obtained with 5 × 10-3 mol‚kg-1 PEG considering the crude approximations used with the model; thus, the existence of only adsorbed micelles until polymer saturation is most probably the case. Conclusion Figure 8. Apparent molar heat capacities of SDS, Cφ,2, versus its molality (m2) in mixed solvent water + PEG 10000: 4, 0 (ref 28); O, 0.002 mol‚kg-1; b, 0.005 mol‚kg-1; - - -, pseudophase model.
structural change occurs, the slope of the linear variation is modified. In the insert of Figure 8 the transition is observed in water as well as in 2 × 10-3 mol‚kg-1 PEG solutions, whereas for PEG at 5 × 10-3 mol‚kg-1 an almost straight line is observed meaning that the transition is not occurring. It was suggested that the postmicellar transition revealed with heat capacities could be related to an evolution of the micellar shape from spherical to cylindrical going along with an increase of the degree of counterion binding which results in an increase of the apparent property.26 In the presence of polymer, it is well-known that small micelles are adsorbed onto the polymer. However, there is some controversy about the aggregation number N. Some authors have asserted that N remained constant (about 35-40) from cmc until the concentration of saturation by the polymer,4,39 then SDS in excess aggregates into normal size micelles (N ∼ 60). Other authors suggested that micelles formed at the cmc being very small (N ∼ 15) grow in a regular manner until the normal size (60), when the polymer is saturated.12,42 With SDS in excess, the existence of normal free micelles simultaneously with bound micelles having reached a (42) Van Stam, J.; Almgren, M.; Lindblad, C. Prog. Colloid Polym. Sci. 1991, 84, 13.
The analysis of volumes and heat capacities of aqueous mixtures, containing PEG 10000 in SDS micellar solutions over a wide concentration range, supports strongly the formation of stoichiometric complexes between surfactant micelles and polymer like previously revealed by different methods. However, estimated at around 2.3 in this work, the ratio between the repeat unit [EO] of polymer and the dodecyl sulfate molecule [SDS] in these complexes is not accurately defined if one considers that the value is depending on the investigated property although each technique gives an internally consistent value of the constant ratio. Moreover, the study of apparent heat capacities of SDS in mixed aqueous PEG solutions has allowed a clear demonstration of the role of these complexes onto the sphere-to-rod micellar transition. When the polymer concentration remains sufficiently low, normal free micelles, which coexist with bound micelles on polymer chains, are able to undergo the shape transition. Contrarily when polymer concentration is large enough to bind all surfactant molecules, the spherecylinder transition is completely inhibited. Of course the existence of such complexes is very sensitive to the chemical nature of polymeric entities as well as to the electrostatic charge of polar head groups of surfactants (work in progress). In this work, the thermodynamic investigation of mixed surfactant-polymer solutions is shown to be an efficient means to enhance the knowledge of these interesting but complicated systems in terms of possible properties to consider. LA960396L
