J . Phys. Chem. 1990, 94, 4289-4295 TABLE 111: Effect of MV*+ on the Steady-State Photocurrent Generated in DHP Vesicles' [ MV2+], M i, nA pA/cm2 0.0 0.0 0.0 0.1 0.3 0.5 0.7 0.9
2.0 4.0 8.8 11.6 13.6
0.07 0.13 0.29 0.38 0.45
"2.0 mL, 2.0 X IO-' M vesicles coated by 2.0 X M ZnSe in the presence of 1.0 X lo-' M cysteine and 4.0 X IO4 M NaCI. pH = 8.5. A constant potential of -0.5 V (vs SCE) was applied during the experiments.
Negatively charged DHP vesicles attract, of course, the positively charged MV2+. This ensures the efficacy of reaction 4. Reduced methylviologen is more negative than MV2+. It is likely to be repelled from the potential field of the ZnSe-coated DHP vesicles. The escape of MV'+ from the potential field of MV2+-coated anionic micelles is well documented.)* Increasing pH values, at given methylviologen concentrations, increased the observed ZnSe-mediated photocurrent linearly above a certain value (Figure 7). The extrapolation of the linear portion of the curves to the base line gave a value of pHo = 9.2 f 0.5 for the onset of the photocurrent. Apparently, the potential of photoelectrons is more negative (Le., they have stronger reducing powers) in alkaline than in acidic solutions. Similar behavior was found in both sodium hexametaphosphate and D H P vesicle stabilized CdS parti~1es.I~ At pH values below pHo, the conduction (38) Gratzel, M. Energy Resources Through Photochemistry and Catalysis: Academic Press: New York, 1983.
4289
band of semiconductor particles are on the positive side of Eo(MV2+/MV'+) and the photocurrent corresponds, therefore, to that in the absence of an acceptor. Photoelectron Transfer. The results of steady-state irradiation of a deoxygenated solution of DODAB-vesicle-incorporated CdSe particles in the presence of methylviologen and cystein are shown in Figure 8. Irradiation is seen to result in the development of new absorption bands with maxima at 395 and 605 nm. These bands correspond to MV'+, formed in the transfer of the CdSe conduction band electrons to MVZ+governed by an equation analogous to (4)). Spectrophotometry and photocurrent measurements are entirely in accord with the proposed semiconductor-particle-mediated photoelectron transfer. The role of cystein is to regenerate the holes by electron transfer (a process which is governed by an equation analogous to ( 5 ) ) . In the system shown in Figure 7, bandgap irradiation leads to increasing photoreduction, up to a limiting concentration of 7.1 X 10" M MV" formed (taking cbO5 nm = 13700 M-l cm-l for MV"). This limiting concentration and the rate of MV" formation were found to be independent of the pH of the solution in the 6-10 range. No MV'+ was formed in the absence of the semiconductor particles. Conclusion
Viable methods have been developed for the in situ formation of ultrasmall selenide semiconductor particles in surfactant vesicles which mediate sacrificial photoelectron transfers.
Acknowledgment. Support of this work by a grant from the Department of Energy is gratefully acknowledged. W.F.P. thanks Utica College for a Summer Grant. Registry No. DHP, 2197-63-9; DODAB, 3700-67-2; MV, 1910-42-5; CdSe, 1306-24-7; PhSe, 12069-00-0; In2Se,, 12056-07-4; ZnSe, 131509-9; cysteine, 52-90-4; glucose, 50-99-7.
Phase Diagram of a System of Cationic Surfactant and Anionic Polyelectrolyte: Tetradecyltrlmethylammonium Bromide-Hyaluronan-Water Kyrre Thalberg,*,t Bjorn Lindman,t and Gunnar Karlstromf Physical Chemistry 1 and Theoretical Chemistry, Chemical Center, University of Lund, P.O. Box 124, 221 00 Lund, Sweden (Received: October 9, 1989)
The phase behavior of the system tetradecyltrimethylammonium bromide (TTAB)-sodium hyaluronate (NaHy)-water has been investigated. Samples giving phase separation have been equilibrated, and the compositions of the separate phases have been determined. The results are summed up in a ternary phase diagram, the major feature of which is a droplet-shaped two-phase region, hanging from the water corner of the diagram. The two-phase region is entirely enclosed by a one-phase region. Furthermore, its shape shows marked dissymmetry with respect to the bisector of the water corner. Thus, a solution concentrated in the polyelectrolytecan dissolve a quite large amount of surfactant while a concentrated surfactant solution almost immediately phase-separatesupon addition of polyelectrolyte. Phase diagrams have also been calculated theoretically, using the Flory-Huggins theory. If the surfactant is treated as a second polymer, phase diagrams of the same type as the experimental one may result. Adjusting the polymerization numbers and the interaction parameters of the theoretical system, a good agreement between experiment and theory is achieved. The presented model calculations indicate that the physical origin of the observed phase behavior is a fairly strong effective attraction between the polymer and the surfactant.
Introduction
Polymer-surfactant interaction in aqueous solution is a rapidly developing field of research. It has been reviewed first by Robb,' and more recently a detailed review was given by G&jard.2 Most work has been performed on systems containing either uncharged water-soluble polymers and charged surfactants or charged polymers (polyelectrolytes) and surfactants of opposite charge. 'Physical Chemistry I . Theoretical Chemistry.
0022-3654/90/2094-4289$02.50/0
Due to the favorable electrostatic interaction between polyelectrolyte and surfactant, the interactions are much stronger in systems of the latter kind. In these systems, Phase separation in general OCCUrS at Certain pOlyeleCtrOlyte/SUrfaCtant ratios, while this is not commonb " I n t e r e d in systems of uncharged ( I ) Robb, I. D. In Anionic Surfactants-Physical Chemistry of Surfnctant Action; Lucassen-Reynders, E., Ed.; Marcel Dekker: New York, 1981; Surfactant Sci. Ser., Vol. 11, Chapter 3. (2) Goddard, E. D. Colloids Surf. 1986, 19, 2 5 5 .
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water-soluble polymers and surfactants. Still, uncharged polymers and polyelectrolytes display large similarities in their interaction with surfactants. In both cases, highly cooperative binding of the surfactant to the polymer chain is observed, resulting in the formation of micelle-like clusters of surfactant molecules adsorbed to the polymer chain. In this context, it should be mentioned that nonionic surfactants give no or very weak interaction with polymers (both charged and uncharged).* Most work in the field of polyelectrolytesurfactant interactions has been performed at very low polyelectrolyte concentrations. Surfactant is then added to the system, and the concentration of free surfactant monomers required for binding of surfactant to the polyelectrolyte to start, denoted c1 or TI,has been determined. Sometimes the entire binding isotherm, Le., the equilibrium relation between the concentration of polymer-bound and free surfactant molecules, has been obtained. Thanks to the extensive work of Hayakawa, Kwak, and co-~orkers,~-* the dependence of the interaction upon polyelectrolyte charge density, surfactant chain length, temperature, and addition of salt is now known in dilute solution, and a review article IS soon to appear.9 Few articles, however, deal with the phase behavior and to our knowledge, the only systematic studies are those carried out by Goddard and co-workers.1w12 In our previous study,I3 we investigated the interaction between a weakly charged linear polysaccharide, hyaluronan (abbreviated Hy), and cationic surfactants of the alkyltrimethylammonium bromide type. Hyaluronan, which plays an important role in the extracellular matrix in the human b ~ d y , ' ~consists * ' ~ of alternating units of N-acetyl-P-D-glucosamine and @-D-ghCUrOniCacid, and at neutral pH it bears one negative charge on every second residue. The distance between charges has been estimated to be about 1.2 In particular, we reported that binding of cationic surfactant to Hy starts at a well-defined concentration, denoted c I , below the critical micelle concentration (cmc) of the surfactant and results in the formation of surfactant micelles adsorbed to the polyelectrolyte chain. It was concluded that Hy behaves a5 an ordinary polyelectrolyte with respect to surfactant binding in dilute solution, taking into account its low linear charge density. Upon further addition of surfactant above the c, concentration, the solutions turn turbid due to phase separation. These dispersions then phase-separate macroscopically, and the precipitate transforms into a transparent, highly viscous phase, which we call the gel phase. The supernatant phase, which is also clear, has a viscosity close to that of pure water. The dispersions can be redissolved by addition of simple electrolyte (NaBr) or by adding a large excess of surfactant to the system. The mechanisms behind these "redissolution" phenomena were discussed. In the present work, we continue our investigation of the Hycationic surfactant systems with focus on the phase behavior. A systematic study of the two-phase region is presented, with tetradecyltrimethylammonium bromide (TTAB) as surfactant. The quantities and compositions of the separated phases were determined, and on the basis of these data a phase diagram is presented. This experimental phase diagram is then compared with theoretically calculated three-component phase diagrams using the Flory-Huggins theory. Treating the TTAB micelles as a second (3) Hayakawa, K.; Kwak, J. J . Phys. Chem. 1982, 86, 3866. (4) Hayakawa, K.; Kwak, J . J . Phys. Chem. 1983, 87, 506. (5) Hayakawa, K.; Santerre, J. P.; Kwak, J. Macromolecules 1983, 16,
1642. (6) Santerre, J. P.; Hayakawa, K.; Kwak, J. Colloids Surf. 1985, 13, 35. (7) Malovikova. A , ; Hayakawa, K.; Kwak, J. J . Phys. Chem. 1984, 88. 1930. (8) Shimizu, T.; Seki, M.; Kwak, J. Colloids Surf. 1986, 20, 289. (9) Hayakawa, K.; Kwak, J. In Cationic Surfactants: Physical Chemistry;
Rubingh, D., Holland, P. M., Eds., in press. (IO) Goddard, E. D.; Hannan, R. B. J . Am. Oil Chem. Soc. 1977,54, 561. ( 1 I ) Leung, P. S.; Goddard, E. D. Colloids Sur/. 1985, 13, 47. (12) Ananthapadmanabhan, K. P.; Leung, P. S.;Goddard, E. D. Colloids Surf, 1985, 13. 63. (13) Thalberg, K.; Lindman, B. J . Phys. Chem. 1989, 93, 1478. (14) Comper, W. D.; Laurent, T. C. Physiol. Reu. 1978, 58 ( I ) , 255. (15) Laurent, T. C . Acta Oto-Laryngol., Suppl. 1987, 442, 7. (16) Preston, B. N.; Snowden, J. McK.; Houghton, K. T. Biopolymers 1972. 1 1 . 1645.
Thalberg et ai. polymer, theoretical phase diagrams quite similar to the experimental one can be obtained, thus revealing the driving force behind the phase separation in our system. In particular, the influence of the Flory interaction parameters and the polymerization numbers of the two polymers on the extension and shape of the two-phase region is studied. Experimental Section Materials. Hyaluronan, sodium salt (i.e., sodium hyaluronate), was from Pharmacia AB, Uppsala, Sweden. The molecular weight of the polymer was reduced by acid hydrolysis with HCI, pH 1, at 70 "C for 30 min under gentle stirring. The sample was then immediately neutralized with NaOH and cooled and then dialyzed against pure water for several days to eliminate the excess salt. After freeze-drying, the polymer was kept in a desiccator containing P20s until used for sample preparations. Two batches of Hy thus prepared had weight-average molecular weights, M,, of 300000 and 240000 as determined by low angle laser light scattering (LALLS) and viscometry. The Hy concentration is expressed in weight percent or as the concentration of the repeating dissacharide unit. The molecular weight of the repeating unit is close to 400 g/mol including Na' as counterion; Le., a 1.0% solution of NaHy corresponds to a concentration of 25.0 m M of the monovalently charged repeating unit and 25.0 mM of Na+ counterions. Tetradecyltrimethylammonium bromide (TTAB, >98% pure) was purchased from Tokyo Kasei Inc., Japan, and was used without further purification. Orange OT, i.e., (0-tolylazo)-@naphthol, was from the same company. Sample Preparation. Samples were prepared by mixing aqueous solutions of NaHy and TTAB. The samples were mixed by turning end over end for several days and were then left to phase-separate. In order to enhance the rate of this process, centrifugation at a rather low speed (3700 rpm, corresponding to approximately 1OOOg) was carried out. After centrifugation the samples were again left to equilibrate for at least 1 week. Sample preparation, equilibration, and all analyses were performed at room temperature (22-25 "C). After this treatment, all phase-separated samples show two neatly separated, clear and isotropic phases. The supernatant phases have viscosities close to that of pure water, while the bottom phases are highly viscous and gellike. We hereafter refer to this phase as the "gel" phase. The two phases were separated and their weights were assessed. As the density of the gel phase is quite similar to that of the supernatant phase, it was assumed that these densities were equal when weight fractions were converted into volume fractions. This assumption facilitates the evaluation of the composition of the phases. In this context it could be noted that if heavy water is used instead of ordinary water, then the gel phase is the upper phase indicating that the difference in density is of the order of only 2%. However, this assumption makes the composition of polymer-rich gel phases somewhat uncertain. Methods. The concentration of hyaluronan (Hy) was determined by optical activity measurements at 436 nm using a Jasco DIP 360 polarimeter from Jasco Inc., Japan. Hy concentrations were calculated from the specific optical activity, being -1 60.7' at 25 "C a t this wavelength." Addition of TTAB did not influence the optical activity of Hy. Bromide concentrations were determined by titration with mercury(I1) nitrate which precipitates Br-.'* The end point was detected with diphenylcarbazone, which forms a blue-violet complex with mercury(1I) ions. A sodium specific electrode from Orion Inc., Cambridge, MA, was used in combination with a standard KCI calomel electrode for sodium determinations. Unfortunately, the accuracy in these determinations was poor, as the presence of surfactant and polyelectrolyte perturbed the performance of the electrode. ( 17) Per MQnsson, Pharmacia AB, personal communication. (18) Vogel. A. 1. Quantitatice Inorganic Analysis, 3rd ed.; Longmans: hew York, 1962: p 2 7 5 .
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Phase Diagram of TTAB-Hyaluronan-Water
I
100 I
-
EE
ta
75
D
0.0
b*
0
-
'
100
"
200
300
400
0 25 50 75 100 Total TTAB concentration (mM)
500
125
Total l T A B concentration (mM)
500
Figure 1. Volume fraction of gel (+) and supernatant (D) for samples containing 0.9% NaHy, TTAB, and water.
The concentration of the surfactant cation, TTA', was analyzed in three different ways. First, as a qualitative test for the presence of micelles, the solubilization of the uncharged hydrophobic dye Orange O T was studied in samples of low TTA+ concentration. The method is described in our previous paperI3 and has also been applied to other polymer-surfactant systems.ll,I9 For samples of higher TTA+ concentration, self-diffusion measurements were carried out by the ' H FT-PGSE method. This technique has been described by StilbsZoand has recently been applied to polymersurfactant system^.^^^^^ In order to transform the obtained self-diffusion coefficients into TTA+ concentrations, the results were compared with the self-diffusion coefficients of reference samples containing known amounts of TTAB in 25 mM NaBr (Le., a salt concentration similar to that in the samples). Finally, the TTA+ concentration was determined from elemental analyses of the carbon, nitrogen, and hydrogen content of freeze-dried samples, using a Carlo Erba 1106 elemental analyzer. As the Hy content of these samples often was negligible, conversion into TTA+ content could easily be made. The agreement between this method and the self-diffusion measurements was taken as a proof of satisfactory TTA+ analysis in the sample. Another test of the validity of the analyses was to check for charge neutrality in the examined solutions. Analyses were performed mainly on the supernatant phase, and from the results, the concentrations of the analyzed species in the corresponding gel phase were easily derived by means of the known total concentrations and volume fractions.
Results Phase Composition. The volume fractions of supernatant and gel in samples with initially 22.5 mM (0.9%) of NaHy are shown in Figure 1 as a function of the total TTAB concentration in the samples. As can be seen, samples with a low total TTAB concentration give a very small gel fraction, less than or about 10% of the total sample volume. Only at higher TTAB concentrations does the volume fraction of the gel phase increase significantly, and in fact, it may eventually exceed the volume fraction of the supernatant. At high enough TTAB concentration phase separation no longer occurs (above 500 mM TTAB at 0.9% Hy). We will refer to this as "redissolution" and discuss it further on in this work. In Figure 2a,b, the concentrations of Hy, TTA+, and Br- in the supernatant phase are shown as a function of the total TTAB concentration in the samples. First consider the Hy concentration. From an initial concentration of 22.5 mM (0.9%), the Hy concentration in the supernatant phase decreases with increased total TTAB concentration, and after an addition of 2 times as much TTAB (50 mM), practically no Hy remains (Figure 2a). The Hy content of the supernatant phase then remains close to zero throughout the entire region studied. Only at the very highest TTAB concentrations within the two-phase region could a slight (19) Lange, H. Kolloid Z . Z. Polym. 1971, 243, 101. (20) Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosr. 1987, 19, 1. (21) Carlsson, A,; Karlstrom, G.; Lindman, B. J . Phys. Chem. 1989, 93, 3673.
b
0
100
200
300
400
500
Total TTAB concentration (mM)
Figure 2. Concentrations of Hy ( O ) , TTA' (m), and Br- (A) in the supernatant phase for samples with 0.9% NaHy, TTAB, and water. 800 I
I
0 100 200 300 400 Total TTAB concentration (mM)
Figure 3. Concentrations of Hy (O),TTAt
(W),
500
and Br- (A)in the gel
phase. increase be detected; Le., at a total TTAB concentration of 450 mM, the supernatant contains about 1 mM Hy. The TTA+ concentration in the supernatant phase behaves quite differently. For samples with a total TTAB concentration less than 75 mM, no TTAB micelles could be detected in the supernatant (cmc is about 4 mM in the absence of salt). It may be expected that the TTA' concentration in the supernatant phase increases from the cl concentration (about 0.5 mM13) to a value close to the cmc value in this region. At a total concentration of about 75 mM TTAB, free micelles start to appear in the supernatant, and from this point the TTA+ concentration of the supernatant increases linearly with added TTAB with a slope close to 1. The binding of surfactant to Hy in the gel phase thus seems to reach saturation at a ratio of about three 'ITA' molecules for every Hy carboxylate group, and further added TTAB to the system above this point distributes evenly between the two phases. The bromide concentration in the supernatant follows a pattern similar to that of =A+, only shifted some 25 mM toward higher concentrations. The Na+ concentration in the supernatants was largely unaffected by the gel formation and remained close to the initial overall concentration of 22.5 mM. At the lowest TTAB concentrations, however, a decrease was observed, which because of the very small gel volume fraction implies a rather high Na+ concentration in the corresponding gels. The concentrations of Hy, TTA+, and Br- in the gel phase are shown in Figure 3. A maximum in Hy concentration is seen at
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%NaHy
-
Figure 4. Experimental three-component phase diagram for the system NaHy-TTAB-H,O. The compositions of some samples are indicated. Open circles refer to initial sample compositions, and filled circles connected by tie lines refer to the compositions of the two phases in equilibrium. The dashed part of the phase boundary indicates larger uncertainty i n this region.
a total TTAB concentration of about 25 mM, Le., at equimolar total amounts of Hy and TTAB. At lower TTAB concentrations than this, part of the polyelectrolyte remains in the supernatant. At higher TTAB concentrations, the decrease in Hy concentration reflects the swelling of the gel phase, since effectively all of the polymer is located in this phase. The TTA+ concentration in the gels increases rapidly with the amount of TTAB added to the system. A very high level of TTA' in the gel phase is already reached at a TTAB concentration of 50 mM. Hereafter, the TTA' concentration remains fairly constant up to the very highest total TTAB concentrations, where a slight decrease is seen. As for the Br- concentration in the gel phase, again it parallels that of TTA', this time shifted somewhat toward lower concentrations. Phase Diagram. For a proper discussion of phase separation phenomena in general, the results should be summed up in a phase diagram. This system consists of five different species, namely, the Hy polyelectrolyte, N a f , TTA', Br-, and water. The requirement for charge neutrality reduces the number of independent components by one; therefore, a four-component phase diagram would be needed for a proper description of the system. Such a diagram is usually drawn as a trigonal bipyramid with corners in our case corresponding to pure H 2 0 , NaHy, TTABr, NaBr, and TTAHy. The inherent complexity of such a diagram and the difficulty to represent it prompt a search for possible simplifications. Often one tries in such cases to introduce a pseudocomponent, which is a combination of two components. In the present case we have found it most illustrative to present the system in terms of a three-component phase diagram with the components TTAB, NaHy, and water. Such a three-component diagram is shown in Figure 4. The TTAB content has been calculated from the concentration of TTA' in the phase and the NaHy content, analogously, from the Hy concentration. The compositions of some samples are indicated in the diagram. Open circles refer to the initial total composition of the samples, and filled circles joined by tie lines indicate the composition of the two phases in equilibrium. However, it must be indicated that compositions of separated samples do not in general fall in the plane illustrated; for the purpose of the present discussion it may, however, be a reasonable approximation. As seen in Figure 4, the phase-separated samples together trace out a closed loop, which represents the boundaries of the two-phase region. This region is anchored in the water-rich corner of the diagram and extends in the direction of the TTAB-NaHy side. The supernatant phase is located to the left side of the loop, close to the water corner and the water-TTAB side of the diagram, while the gel phase is found at the opposite side. Apparently, there is no distinct boundary between these two phases; in fact, both supernatant and gel belong to the same large isotropic phase which
Thalberg et
ill.
encloses the entire two-phase region and also includes pure water as well as aqueous NaHy solutions. It should be noted that the boundary at the bottom of the two-phase region is always well above the water-Hq base line of the diagram, as a certain minimum concentration of free surfactant, c I , is needed for surfactant binding to the polyelectrol~te to take place.13 Also, the left boundary of the two-phase region must differ from the water-TTAB axis, as some Hy chains have to be located also in the supernatant. However, the two-phase region is very close to the water-TTAB axis and the Hy content in most of the samples was below the detection limit of our method (0.2 mM). As is seen, the slopes of the tie lines change in a region ranging from equimolar amounts of TTAB and Hy up to a TTAB-to-Hy ratio of about 3. For samples with a global TTAB-to-Hy ratio above this, the tie lines largely parallel each other. The uncertainty in the gel composition for samples containing little total TTAB is rather large, due to the very small volume of the gel phase in such samples. Therefore, the phase boundary in this part of the diagram is only approximative (dashed line). Some additional samples were prepared in order to investigate the generality and reproducibility of the phase separation process. Samples prepared with initially twice as much NaHy (1 3%)were seen to follow the same pattern, both regarding the composition of the separated phases and the slopes of the tie lines. Furthermore, samples where H 2 0 was replaced by D20largely reproduced the phase diagram in Figure 4 (after correction for differences in molar mass). We therefore believe that the phase diagram presented indeed refers to true equilibrium conditions and that samples located anywhere in the two-phase region will separate into two phases according to the tie lines drawn.
Theoretical Phase Diagrams Description of the Model. The Flory-Huggins theory, derived independently by Flory and Huggins in 1942, is a lattice theory describing the behavior of (concentrated and semidilute) polymer solutions.22 A cell in the lattice can be occupied by either a solvent molecule (index 1) or a segment from a polymer chain (index 2 ) . The requirement that the segments of the polymer chains be connected gives the entropy of mixing as S,,, = -RMoI~,In 41 + ( 4 d U In 421
(1)
while the interaction energy of the system is given by
u = MOWI24142
(2)
Mo is the total number of cells in the lattice, L2 is the polymerization number of the polymer, and 4, and 42 are the volume fractions of solvent and polymer, respectively. The interaction parameter w I 2is related to the normal Flory-Huggins interaction parameter through
The theory is easily expanded from two to three or more components, and Scott has calculated phase diagrams for different types of three-component systems, including systems of two different polymers and solvent.23 Also, systems of this type with water as solvent can be treated successfully by the theory despite the difference in molecular size between the polymer segments and a water molecule.24 Systems containing charged species are in principle beyond the limitations of the Flory-Huggins theory. The interaction energy term of the model is based on nearest-neighbor interactions, while electrostatic interactions typically are long-range in nature. Attempts have been made to single out the electrostatic interactions of the system and account for them by a separate term.25 (22) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, 1953. (23) Scott, R. L. J. Chem. Phys. 1948, 17, 268, 279. (24) Gustafsson, A,; Wennersttom, H.; Tjerneld, F. Polymer 1986. 27, 1768.
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Phase Diagram of TTAB-Hyaluronan-Water a
Polymer B
Polymer B
/
% Polymer A
b
I
-
‘Polymer A % Polymer A
.-Polymer A
-
Figure 6. Theoretically calculated phase diagram for a ternary system of two different polymers in a common solvent. w,, = -900 J/mol and w I 3 = +lo0 J/mol; other parameters are as in Figure 5a.
Polyyer B
Polymer B I
% Polymer A
-
Figure 5. Theoretically calculated phase diagrams for a ternary system of two different polymers in a common solvent. Index 1 stands for the solvent (water), index 2 for polymer A, and index 3 for polymer €3 (representing the surfactant). In both diagrams, w12= w13 = -400 J/mol and L, = L3 = 200. The interaction parameter between the two polymers, is -8000 J/mol in (a) and -7500 J/mol in (b).
We have chosen to adopt a quite different approach and instead include the electrostatic interactions into the interaction parameters wij. These may then be considered as effective interaction parameters, including all kinds of interactions, enthalpies as well as possible interaction entropies (orientation effects), between the two species i and j in the system. In our attempts to reproduce the experimental phase diagram in Figure 4, we found it reasonable to treat the surfactant as a second polymer (index 3). This approach has been found successful in systems of uncharged polymer, ionic surfactant, and water.26 The “polymerization number” L3 ascribed to the surfactant should then not be regarded as representing the aggregation number of the surfactant micelles in the system, but rather as a fitting parameter chosen to give good agreement with experiment. Obviously, there exists a relation between the aggregation number of the micelle and the parameter L3 in the model; Le., larger aggregation number corresponds to larger L3values. Our system is then analogous to a solventI-polymerA-polymerBsystem and is governed by the following equations: Smix
= - R M o ( ~InI 41 + (42/L2) In 42 + (43/L3) In
u = M0(w,2d)1d’2+ w13d’1d’3
-k w23d’2d’31
431 (4) (5)
In these equations index 1 stands for water, 2 for polymer A, and 3 for polymer B. Since we have a three-component system, in principle three phases may coexist and the total free energy of the system may be written Atot = Atot(n]1,n21,n31,n12,n22,n32) (6) where n/ specifies the number of moles of component i in phase j . The composition of the third phase follows directly since the
(25) Michaeli, I.; Overbeek, J. Th. G.; Voorn, M. J. J . Polym. Sci. 1957, 23, 443. (26) Karlstrom. G.;Carlsson, A.; Lindman, B. J . Phys. Chem., in press.
H20
10 20 % Polymer A
30
-Polymer A 40
Figure 7. Theoretically calculated phase diagram for a ternary system of two different polymers in a common solvent. Interaction parameters w,, are as in Figure 5a; L2 = 400 and L3 = 100.
total composition nPt is given. The problem of calculating the phase diagram is reduced to minimizing A,,, with respect to the indicated parameters with the conditions x j n / = nPt where all $ 1 0. In the model, there are five independent parameters which will control the phase behavior, namely, the three interaction parameters wi, and the two “polymerization numbers”, L2 and L3. As in our present system the size of a repeating unit of hyaluronan is different from the size of a surfactant molecule, and these two are indeed very much different from the size of a water molecule; the choice of polymerization numbers is somewhat arbitrary. For the reasons given above, the same is valid for the choice of interaction parameters, wiJ. However, there is a subtle balance among all five of these different parameters as will be shown in the following phase diagrams. In the first two theoretical phase diagrams (Figure 5a,b), the interaction parameters w12and w13have been set equal, as well as the polymerization numbers L2and L3. The result is a twophase region in the water-rich part of the diagram, symmetric with respect to the bisector of the H 2 0 corner. The strength of the interaction between polymer A and polymer B (the surfactant) given by w23determines the size of the two-phase region. The influence of wlz and ~ 1 on3 the phase diagram is shown in Figure 6. Decreasing wlz, Le., making polymer A more hydrophilic, and increasing wlj, Le., making polymer B less hydrophilic, both result in a displacement of the two-phase region toward the water-polymer B axis accompanied by a steepening of the tie lines. Increasing the polymerization number of polymer A relative to that of polymer B will give a similar effect (Figure 7 ) . (If both polymerization numbers are increased by the same amount, the result is a larger two-phase region, but with the same orientation as before.) A combination of both these effects may produce a phase diagram not too different from the experimentally observed one (Figure 8).
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The Journal of Physical Chemistry, Vol. 94, No. 10, 1990 Polymer B f
io
20
30
.Polymer A 40
% Polymer A Figure 8. Theoretically calculated phase diagram for a ternary system of two different polymers in a common solvent. w I 2= -200 J/mol, w,, = +lo00 J/mol, w2, = -5200 J/mol, L2 = 300, and L, = 25.
Discussion
Experimental Phase Diagram. In this work, a phase diagram is presented for a system of a polyanion and a cationic surfactant in aqueous solution. There exists close to the H 2 0 corner a two-phase region, which is surrounded by a continuous isotropic one-phase region. The two-phase region shows marked dissymmetry with respect to the H20-TTAB and HzO-NaHy axes, with a clear bias toward the TTAB side. This implies that a micellar solution of TTAB will phase-separate when only little Hy is added, while for a concentrated solution of Hy, a large amount of TTAB is required for phase separation to occur. For samples located in the two-phase region, phase separation will result in the formation of a highly viscous gellike phase, concentrated in both polyelectrolyte and oppositely charged surfactant, in chemical equilibrium with a supernatant phase very dilute with respect to at least one of these species. How can we understand this phase behavior? In the first place, binding of an oppositely charged surfactant to a polyelectrolyte will lead to a reduced charge of the resulting complex, thereby lowering its hydrophilicity and the interpolymer repulsion, and with increasing binding precipitation would be expected. Indeed, precipitation has been reported for many systems of polyelectrolyte and oppositely charged s ~ r f a c t a n t . ~ ~One ~ ~may ~ ~ also ~ ~ -take *~ the approach that the solubility of water in the polyelectrolytesurfactant complex decreases when the charge density is reduced. Most polyelectrolytes investigated have been reported to bind considerable amounts of oppositely charged surfactant without being precipitated (especially in the work of Hayakawa, Kwak, and co-workers where binding degrees of 0.6-0.8 frequently are reported in one-phase solution). When precipitation finally occurs, a dense solid precipitate results, which thereafter remains practically ~nchanged.,~Hyaluronan seems to differ from this pattern. In the first place, a very low degree of surfactant binding, about or below 0.20, often induces phase ~ e p a r a t i 0 n . l ~In fact, for DoTAB (dodecyltrimethylammonium bromide) no Hy-micelle complexes at all could be detected in solution, so binding seems here to entail phase separation immediately. Secondly, the phase-separated Hy-surfactant complexes always transform into a transparent and isotropic gel, of relatively high water content. The presence of this gel phase, containing about 70% water, in our opinion reflects the large hydrophilicity of the resulting complexes in this system and probably facilitates the establishment of equilibrium in the system. To our knowledge, no such gel formation has been reported earlier in polyelectrolyte-surfactant systems, and neither has a phase diagram. Interestingly, however, a rather similar phase diagram is reported in a system of anionic silica spheres and cationic polymer in aqueous solution.M Though (27) Chu, D.; Thomas, J . K. J . Am. Chem. SOC.1989, 108, 6270. (28) Shirahama, K.; Tashiro, M. Bull. Chem. SOC.Jpn. 1984, 57, 377. (29) Unpublished results concerning the polyelectrolytes polyacrylate (PA), polyvinylsulfonate (PVS), and polymer JR.
this is a quite different type of system, it may be governed by similar mechanisms. Comparison with Calculated Phase Diagrams. In order to obtain theoretical three-component phase diagrams similar to the observed one, one has to treat the surfactant as a second polymer, thereby introducing a “surfactant polymerization number”. The main effect this will have is to significantly reduce the entropy of mixing for the surfactant molecules, thereby increasing the phase-separating tendency of the system. As T A B tends to form it is natural micellelike clusters adsorbed to Hy in dilute s~lution,’~ to assume that this structure may also exist in the gel phase. In fact, many features of our data support this picture: first of all, the relatively high surfactant concentration in the gel phase, always well above the cmc. The high solubility of the uncharged water-insoluble dye Orange O T in the gel phase clearly indicates hydrophobic domains due to surfactant clusters. Furthermore, the gel phase remains isotropic, which excludes hexagonal or lamellar arrangement of the surfactant. (The hexagonal liquid crystalline phase appears at about 40 wt % surfactant in the TTAB-H,O system.) It seems therefore relatively clear that we have a structure of micellar clusters of surfactant molecules also in the gel phase, and the theoretical phase diagrams indeed further strengthen this picture. The second condition that must be fulfilled in order to obtain the observed type of phase diagram is that ~ 2 is3 more negative ; the polymer and the surfactant prefer than both wI2 and ~ 1 3 Le., to interact with each other rather than with the water. Because of the gain in interaction energy given by ~ 2 3 & / #a~phase 3 , concentrated in polymer and surfactant will then be favored relative to a dilute one in spite of the entropy cost for redistributing the molecules. In other words, the system wants to phase-separate because more contacts between polymer and surfactant can be formed in the concentrated phase. The marked dissymmetry in the observed phase diagram with respect to the bisector of the H 2 0 corner can be accounted for in two ways. The first is to introduce a larger polymerization number for the Hy polymer than for the TTAB micelles. The weight-average molecular weight for the main Hy preparation used in this study was about 240000, corresponding to approximately 600 repeating disaccharide units. The number average may, however, be considerably smaller due to the large polydispersity of the polymer sample, and as it is the number average that is relevant in the entropy calculations, a polymerization number of 300 for Hy may be a reasonable assumption. (It is clear that the slight difference in M , between the two Hy preparations used in this study can be disregarded.) Concerning TTAB, the aggregation number for micelles in 0.1 M solution is about 80.3’ We have at present no information about the aggregation number of the Hy-bound micelles. However, altering the surfactant polymerization number within reasonable limits will not give as much displacement of the two-phase region as is observed in the experimental system. The second way of influencing the orientation of the two-phase region may now be taken into account. A better fit between observed and calculated phase diagrams is obtained if the surfactant is made less hydrophilic than the Hy polymer, Le. w13 > w I 2 . This is reasonable, as the surfactant tends to phase-separate and form liquid crystalline phases at higher concentrations while Hy is soluble in water at in principle all concentrations. The calculated phase diagram in Figure 8 gives a reasonably good fit to the experimental one, considering the simplicity of the model. Redissolution by Excess Surfactant. Redissolution of precipitates has also been reported in other polyelectrolyte-surfactant systems, and different mechanisms have been suggested.’w13The redissolution phenomenon is not trivial. Indeed, different systems may show redissolution by totally different mechanisms. The most often encountered model is that redissolution occurs This due to excess surfactant binding by the (30) Cabane, B.; Wong, K.; Duplessix, R. In Polymer Association Structures; El-Nokaly, M. A,, Ed.; ACS Symposium Series No. 384; American Chemical Society: Washington, DC, 1989. (31) Berr, S. S. J . Phys. Chem. 1987, PI, 4760
Phase Diagram of TTAB-Hyaluronan-Water leads to a charge reversal, and the inversely charged polyelectrolyte-surfactant complexes redissolve. This model, however, cannot account for the observed redissolution in this system, because we have free micelles present in the supernatant in equilibrium with the gel phase. Once having free micelles, the chemical potential of the surfactant no longer increases on addition of more surfactant to the system, and binding therefore will not increase. Further support for this conclusion is the observation that a higher surfactant concentration is needed in order to bring about redissolution in our systems, when the length of the hydrocarbon tail of the surfactant is increased.13 It is known that surfactant binding to a polymer or polyelectrolyte increases with increasing surfactant chain length.5*7J3Thus, a decrease in the surfactant concentration needed for redissolution with increasing hydrocarbon chain length would be expected if redissolution is governed by a charge reversal mechanism, which is contrary to observations. From the general shape of the calculated phase diagrams it is seen that one-phase solutions are always present at higher surfactant concentrations. Thus, “redissolution by excess surfactant” is in fact observed in all theoretically calculated phase diagrams with a reasonably strong attraction between polymer and surfactant. This indicates that there is no need for specific mechanisms in order to explain the redissolution in our system. The experimental phase diagram now provides the relation between Hy concentration and the concentration of surfactant required for redissolution to occur. From examining the phase diagrams, it is inferred that there also exists an analogous phenomenon, “redissolution by excess polyelectrolyte” in these kinds of systems, with the same explanation as above. Limitations of the Model. We have seen that the simple Flory-Huggins theory can account for the phase behavior observed in a polyelectrolyte-surfactant system. Adjusting the polymerization numbers for polymer and surfactant and the interaction parameters between the different species, a reasonably good fit between experimental and calculated phase diagrams can be obtained. However, the absolute strength of the interaction between the different components cannot be obtained, due to the limitations of the model. Some differences still remain between experimental and calculated phase diagrams. Let us first consider the extension of the two-phase region close to the water-Hy axis, Le., at low surfactant concentration. In the real system, the phase boundary is here largely determined by the c , concentration, Le., the concentration of free surfactant monomers required for surfactant binding to Hy to start. In the calculated system, however, surfactant monomers are disregarded and the model is therefore expected to be quite poor at low surfactant concentrations. In the region close to the water-TTAB axis, a difference between experimental and calculated phase diagrams emerges. The phase
The Journal of Physical Chemistry, Vol. 94, No. 10, 1990 4295 boundary in the experimental phase diagram takes off from the water-TTAB axis at lower TTAB concentrations than in the calculated ones. Possible reasons for this difference may be in the first place that the mean field approximation is not quite correct (see discussion below) and secondly, that the aggregation numbers for free and Hy-bound micelles are different, while the model only uses one common aggregation number for the surfactant. As for the tie lines, the theoretical phase diagrams, while giving good agreement as concerns the main orientation, fail to reproduce the fine structure observed in the experimental system. In the theory a mean field approximation is used; Le., an even distribution of solvent molecules and polymer segments is assumed in all phases. This is not the case in dilute polymer solutions, and the theory should therefore be restricted to semidilute and concentrated polymer solutions. Our system certainly is a structured one, as the surfactant molecules form micellar aggregates, both in water and upon binding to the polymer. It should, however, be remembered that the reference state for the surfactant molecules in our model is a micellar solution. Furthermore, it is likely that there are deviations from mean field behavior with respect to the distribution of the polymer segments around the micellar aggregates; Le., the concentration of polymer segments is expected to be increased close to the micellar surface relative to the mean concentration due to the favorable electrostatic interaction between surfactant and polymer segment. Despite these problems, we still believe that the theoretical modeling gives some insight into the physical origin of the phase behavior once it is known, but it is not capable to a priori predict these type of observations. A development of the understanding of these systems must be based on a correct treatment of the (long range) electrostatic interactions. The necessity of treating the polyion-ionic surfactant-water system as a polyanion-polycation-water system in the FloryHuggins calculations is stressed above. After completion of the present study the authors became aware of a study by Frugier3* on the latter problem. This author treated systems consisting of two oppositely charged polymers and a solvent with Flory-Huggins theory and an explicit term for the electrostatic energy derived from Debye-Huckel-like assumptions.
Acknowledgment. Dr. Bernard Cabane is gratefully acknowledged for fruitful discussions about the phase behavior, and Drs. Bengt Jonsson and Lennart Piculell are acknowledged for useful comments on the manuscript. We also thank Ingegerd Lind for skillful technical assistance and Ingela Hillang (Pharmacia AB) for molecular weight determinations with LALLS. This work was financially supported by Pharmacia AB. Registry No. TTAB, 11 19-97-7; sodium hyaluronate, 9067-32-7. (32) Frugier, D. Doctoral Thesis, Universite Pierre et Marie Curie, Paris, 1988.
