J . Phys. Chem. 1992, 96, 1468-1475
1468
Study of the Interaction between Dodecyltrimethyiammonium Bromlde and Poiy(maieic acid-co-aikyi vinyl ether) in Aqueous Soiution by Potentiometry and Fluorescence Probing M. Benrraou, R. Zana,* R. Varoqui, and E.Pefferkorn Institut Charles Sadron (CRM-EAHP), CNRS-ULP Strasbourg, 6, rue Boussingault, 67083 Strasbourg, CZdex, France (Received: May 31, 1991; In Final Form: September 6, 1991)
The binding of dodecyltrimethylammonium bromide (DTAB) to poly(ma1eic acid-co-alkyl vinyl ether) has been investigated by means of potentiometry and fluorescence probing, using pyrene as a probe, as a function of the length of the copolymer alkyl chain (methyl, ethyl, butyl, hexyl, decyl, and hexadecyl; these copolymers being referred to as PS1, PS2, PS4, PS6, PS10, and PS16, respectively) and for PSI, PS2,and PS4 as a function of the copolymer neutralization degree, a,concentration, and the ionic strength. The binding has been found to be cooperative for PS1 and PS2 in the whole range of a. It is still cooperative with PS4 at a b 0.75 but becomes anticooperative at a Q 0.5. It is anticooperative for PS6, PS10, and PS16 even at a = 1.00. For PS1 and PS4 the cooperativity parameter, u, and the binding constant, K,are independent of the copolymer concentration, within the experimental error. Upon increasing ionic strength, u increases for PS1 but appears to decrease for the more hydrophobic PS4. These results are compared to those reported in the literature. The change in the nature of the binding with the copolymer alkyl chain length is discussed in terms of the difference in free energies for the binding of an oncoming surfactant ion to a copolymer site where it interacts with another bound surfactant and for a binding site where it interacts with copolymer alkyl chains. This difference decreases and changes sign as the length of the alkyl chain increases. The existence of hydrophobic microdomains in the solutions of copolymers with long alkyl chains is taken into account.
around a value aT which increases with X.33-36For X b 10, the Introduction copolymers appear to retain a fairly compact conformation in the Recently, easy to construct and reliable cationic surfactantsensitive electrodes have become available based on plasticized poly(viny1 chloride) containing or not containing a surfactant (1) Tanaka, T.; Hiiro, K.; Kawahara, A. Anal. Lett. 1974, 7, 173. complex.’” This has resulted in a large number of studies of (2) Cutler, S.; Meares, P.; Hall, D. G. J. Electroanal. Chem. 1977,85, 145. the thermodynamics of micellization of cationic ~urfactants,’,~ of (3) Davidson, C.; Meares, P.; Hall, D. G . J. Membr. Sci. 1988, 36, 511. mixed micellization involving cationic surfactants,+13 and of the (4) Zana, R. In Surfactant Solutions. New Methods of Investigation; binding of cationic surfactants to neutral polymers,’”” colloidal Zana, R., Ed.; Dekker: New York, 1987; Chapter 9 and references therein. (5) Campbell, W. C.; Dowie, C. J. Brit. UK Pat. Appl. 1989,2207,250A. partic1es,l8J9 and polyanions.2*28 The last studies aimed at (6) Maeda, T.; Ikeda, M.; Shibahara, M.; Haruta, T.; Satake, I. Bull. understanding the nature of the interaction between cationic Chem. Soc. Jpn. 1981.54, 94. surfactants and polyanions and the mode of binding of cationic (7) Maeda, T.; Satake, I. Bull. Chem. Soc. Jpn. 1984,57,2396; 1988,61, surfactants to polyanions. For this purpose, rather extensive studies 1933. (8) Palepu, R.;Hall, D. G.; Wyn-Jones, E. J. Chem. Sm., Faraday Trans. of the effect of the surfactant nature and alkyl chain le11gth,2~-~~ 1990,86, 1535. concentration of added sa1t,22,23,26 and of the nature of the polymer (9) Sepulveda, L.; Cabrera, W. J. Colloid Interface Sci. 1989, 131, 8. have been p e r f ~ r m e d . ~ For ~ * ~a ~large J ~ number of polyanions, (10) Abuin, E.; Lissi, E.; Nunez, R.;Olea, A. Lungmuir 1989, 5, 753. it has been found that the interaction is cooperative and that its (1 1) Shirahama, K.; Nishiyama, Y.; Takisawa, N. J. Phys. Chem. 1987, 91, 5928. strength (expressed by a binding equilibrium constant K ) increases (12) Takasaki, M.; Takisawa, N.; Shirahama, K. Bull. Chem. Soc. Jpn. much with the surfactant chain length and hydrophobicity of the 1987,60, 3849. polyanion.22-26,28This cooperativity indicates that the polymer (13) Kresheck, G.; Kale, K.; Erman, J. In Solution Behauior of Surfacbinds the surfactant under the form of aggregates similar to tants; Mittal, K. L., Fendler, E. J., Eds.;Plenum Press: New York, 1982; Vol. 1, p 677. micelles. However, there have been no systematic study of the (14) Painter, D.; Bloor, D.; Takisawa, N.; Hall, D. G.; Wyn-Jones, E. J . effect of the polymer hydrophobicity because series of polyanions Chem. Soc., Faraday Trans. 1 1988,84, 2087. of increasing hydrophobicity are not easily available. The electrical (15) Shirahama, K.; Ohishi, M.; Takisawa, N. Colloids Surf. 1989, 40, charge density of the polyanion is another parameter whose effect 261. (16) Hoffmann, H.; Huber, G. Colloids Surf, 1989, 40, 181. on surfactant binding has been little investigated.26 (1 7) Carlsson, A.; Lindman, B.; Watanabe, T.; Shirahama, K. Lungmuir For our part, we have been recently interested in the behavior 1989, 5, 1250. of the alternated copolymers poly(ma1eic acid-co-alkyl vinyl ether) (18) Hayakawa, K.; Ayub, A. L.; Kwak, J. C. T. Colloids Surf. 1982.4, referred to below as PSX (X = number of carbon atoms of the 389. (19) Ayub, A. L.; AI Taweel, A. M.; Kwak, J. C. T. Coal Prep. (Gordon alkyl chain) in aqueous s o l ~ t i o n . ~ ~These - ~ ~ polymers are & Breach) 1985, 1 , 117. transformed into anionic polyelectrolytes by partial or total (20) Shirahama, K.; Takashima, K.; Takisawa, N. Bull. Chem. Soc. Jpn. neutralization of the carboxylic groups of the maleic acid moieties. 1987, 60, 43. For X d 2, these polymers behave like normal hydrophilic po(21) Shirahama, K.; Tashiro, M. Bull. Chem. SOC.Jpn. 1984, 57, 377. (22) Hayakawa, K.; Kwak, J. C. T. J. Phys. Chem. 1982,86,3866; 1983, lyelectrolytesand undergo a progressive conformational expansion 87, 506. when the neutralization degree a of the carboxylic groups is (23) Hayakawa, K.; Santerre, J.; Kwak, J. C. T. Macromolecules 1983, i n c r e a ~ e d . ~For ~ -X ~ ~b 4, however, the increase of a results in 16, 1642. a conformational transition whereby the copolymer coil goes from (24) Hayakawa, K.; Santerre, J.; Kwak, J. C. T. Biophys. Chem. 1983,17, 175. a compact globular conformation stabilized by hydrophobic in(25) Malovikova, A.; Hayakawa, K.; Kwak, J. C. T. In Structure/Perteractions between the alkyl side chains at low a to the normal formance Relationships in Surfactants; Rosen, M. J., Ed.; ACS Symposium extended conformation of polyelectrolytes at higher a.33-35 The Series 253; American Chemical Society: Washington,DC,1984. Malovikova, transition takes place within a fairly narrow range of a,centered A.; Hayakawa, K.; Kwak, J. C. T. J. Phys. Chem. 1984,88, 1930. *To whom correspondence should be addressed.
(26) Shimizu, T.; Mitsutaka, S.; Kwak, J. C. T. Colloids Surf. 1986, 20, 289.
0022-3654/92/2096-1468%03.00/00 1992 American Chemical Society
Interaction between DTAB and a Copolymer whole range of a.31*32 Fluorescence p r ~ b i n g and ~ ~ chemical .~~ rea~tivity)~ studies showed the presence of hydrophobic microdomains. The present study was undertaken because we felt that the PSX series would permit the study of the effect of the polyanion hydrophobicity and density of electrical charge in a more systematic manner than it has been done thus far on the binding of cationic surfactants. Moreover, we and others have been involved in determining the values of the average number of alkyl chains per hydrophobic microdomain in aqueous solutions of PSX3°.37 and related copolymer^.^^ We intend to investigate the size and composition of the mixed micelles formed upon binding of cationic surfactants by PSX.29 The determination of the number of surfactant chains per mixed micelle requires the knowledge of the amount of bound surfactant at any surfactant and polymer concentrations. This quantity is most easily determined using surfactant-specific electrodes. We report below measurements of binding of dodecyltrimethylammonium bromide to two typical short chain copolymers: PS1, which behaves like a weak polyelectrolyte, and PS4, which shows a conformational transition at uT Y 0.2534(value at midtransition), as a function of the copolymer concentration and degree of neutralization and of the ionic strength (added KBr). For the sake of comparison, some measurements were also performed with PS2, which behaves similarly to PS1, PS6, which shows a conformational transition at aT 0.45,34 PS10, and PS16. The potentiometric measurements were complemented by fluorescence probing studies, using pyrene as a probe, in order to get a better insight into the nature of the surfactant aggregates formed on the copolymer^.^^ The results clearly show that, as the hydrophobicity of the copolymer is increased by increasingX or decreasing a,the binding becomes less cooperative but at the same time stronger (larger binding constant).
Experimental Section Materials. The surfactant, dodecyltrimethylammonium bromide (DTAB), was obtained and purified as described.40 The copolymer poly(ma1eic anhydride-co-methyl vinyl ether) was purchased from Monomer-Polymer Labs (Borden Inc., Philadelphia), transformed into PS1, purified, and titrated in aqueous solution as previously described.29 The copolymers poly(ma1eic anhydridecealkyl vinyl ether) with X = 2 and 4 were synthesized and purified by repeated p r e c i p i t a t i ~ n . ~The ~,~~ poly(ma1eic anhydridecehexyl vinyl ether) was a gift from Prof. U. P. Strauss. The poly(ma1eic anhydridecedecyl and hexadecyl vinyl ethers) were the same as in previous in~estigations?~.'~ All these copolymers were transformed into PSX,with X = 2,4,6, 10, and 16.29J0 The PS16 used in the studies below was in the form of a disodium salt, as it is insoluble in water at a! C 0.70.
(27) 35. (28) (29) (30) (31)
Santerre, J.; Hayakawa, K.; Kwak, J. C. T. Colloids Surf.1985.13,
Shimizu, T.; Seh, M.Rep. Prog. Polym. Phys. Jpn. 1985, 28, 21. Binana-Limbclt, W.; Zana, R. Macromolecules 1987, 20, 1331. Binana-Limbclt, W.; Zana, R. Macromolecules 1990, 23, 2731. Varoqui, R.; Pefferkorn, E. Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 1982, 23,9 and references therein. Varoqui, R.; Pefferkorn, E. Microdomains in Polymer Solution. Dubin, P., Ed.;Polym. Sci. Technol. (Plenum) 1985,30. 225. (32) Pefferkorn, E.; Schmitt, A.; Varoqui, R. C. R . Seances Acad. Sci., Ser. C 1968.268. 349. (33) Stra.uss, U. P.; Varoqui, R. J. Phys. Chem. 1968, 72, 2657. (34) Dubin, P.; Strauss, U. P. J. Phys. Chem. 1967, 71, 2757; 1970, 74, 2482; 1973, 77, 1427. (35) Strauss, U. P.; Vcsnaver. G. J. Phys. Chem. 1975, 79, 1558. (36) De Groot, A. J.; Jager, J.; Engbcrts; J. B. F. N. Eur. Polym. J. 1988, 24, 45. (37) Hsu, J.-L.; Strauas, U. P. J. Phys. Chem. 1987, 91,6238. (38) (a) Chu,D.-Y.; Thomas, J. K. Macromolecules 1987,20,2133. (b) Chu, D.-Y.; Thomas, J. K. J. Am. Chem. Soc. 1986,108,6270. (39) Zana, R. In Surfactant Solutions. New Methods of Investigation; Zana, R., Ed.;Dekker: New York, 1987; Chapter 5. (40)Zana, R. J. Colloid Interface Sci. 1980, 78, 330.
The Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1469 The molecular weights of the PSX were not known but are believed to be above 50000 in view of the molecular weights of the corresponding poly(ma1eic anhydride-co-alkyl vinyl ether) which were all above 100OOO. The copolymer concentration , C is expressed in mole of repeat unit per liter. The neutralization degree a equals 1.00 when the maleic acid moieties are fully neutralized. The sample of pyrene was the same as in the previous investigation~.~~.~~ Potentiometry. The cationic surfactant-specific electrode was prepared as described by Shirahama et al." Its sensitive element was a 0.2 mm thick, 1 cm diameter membrane of poly(viny1 chloride) (PVC) plasticized by bis(2-ethylhexyl) phthalate (2080 w/w), containing no surfactant complex. The membrane was glued at one end of a 1 cm diameter, 10 cm length PVC tubing and included in the following concentration cell.
I
I
calomel electrode 3M NH&1 reference solution in saturated KC1 agar bridge So
I
I
I
membrane
I
investigated solution 3M N h C 1 calomel electrodein (with or without PSX) agar bridge saturated KCl The reference solution So filling the PVC tubing was at a concentration of the investigated surfactant and of KBr. The concentration was 2-3 times smaller than the cmc of the as rmmmended.4' surfactant in aqueous KBr at concentration The electrode response to an ionic surfactant is given by E = Eo + p log a (1)
e, es
e,
e,,
where a is the surfactant activity and Eoa constant which depends on the setup. Most of our experiments were performed at surfactant concentrations, Cs, below 1 mM and in the presence of 5 mM KBr. Thus, activities were set equal to concentrations. At 25 OC, the slope p should be 59.2 mV for a change of Csby a factor of 10 for the uni-univalent surfactant used in the present study, for Nernstian electrodes. In the absence of polymer, the emf E should be equal to zero This fact when Csbecomes equal to the inner concentration and the value of the slope p were used to test the performance of the surfactant electrode. A typical experiment involved three stages. First, a calibration plot E vs log Cswas determined for the investigated surfactant in the absence of PSX,in a wide range of concentrations ( 5 X 10" M up to nearly the cmc). This experiment was repeated in the presence of copolymer. Finally the calibration run was repeated and compared to the first one as a check. The copolymer concentration C, was maintained in the 10-3-104 M range because the electrode response was affected at higher . , C More specifically, at very low Csin systems where no surfactant binding takes place, the E vs log Cs plot at a , C above 3 X M was found to run parallel to the calibration plot rather than being coincident with this plot. Note that the previously reported studies also used such low polymer contents.2*28 An ionometer Orion Model 701A was used for the emf measurements. The emf reached a constant value to within b0.2 mV after about 5 min at very low Cs M). This time was reduced to about 1 min or less at higher Cs (=lo-' M). The measurements were performed by successive additions of known amounts of a concentrated surfactant solution to a known volume of aqueous KBr or polymer solution in aqueous KBr. In the second case, the added surfactant solution also contained the copolymer at the same concentration as the initial copolymer solution in aqueous KBr. Fluorescence Probing. The fluorescence emission spectra of pyrene solubilized in the investigated system were recorded using a Hitachi F-4010 spectrofluorimeter in the range 350-500 nm, at an excitation wavelength of 335 nm. The pyrene concentration was always close to 1W M, which ensured the absence of excimers. The ratio 11/13 of the intensities of the first and third vibronic peaks was used to monitor the formation of hydrophobic micro-
eS.
(41) Kresheck, G.; Constantinidis, I. Anal. Chem. 1984, 56, 152.
Benrraou et al.
1470 The Journal of Physical Chemistry, Vol. 96, No. 3, 1992
GIM)
I
Figure 1. Electrode response to the DTAB concentration Cs in 2 X lo4 M PS1 solutions at a = 1.00 in the presence of KBr: ( 0 )lW3; (0) lo-*; (*) 4 X low2M. The calibration plot (in the absence of PSI) is the dotted M KBr at C, > line. Precipitation occurred in the presence of 4 X 10-3M.
p
0.6
0.4
-
0.2
-
O'I
.
I
Figure 4. Binding isotherms of DTAB to PSI at C, = 5 X M, (Y = 1.00, and C, = lo4 (X), 2 X lo4 (O), and 4 X lo-' M (0). A single curve has been drawn through the three sets of experimental results.
Figure 2. Binding isotherms of DTAB by PS1,obtained from the results in Figure 1 (see text), at KBr concentrations: ( 0 ) (0) (*) 4 X M.
(+) 5 X
d o m a i n ~ . ~This ~ + ~ratio ~ J ~decreases when the average microenvironment of pyrene becomes less polar.39*42The measurements used two equimolar solutions of copolymer with equal contents of pyrene and KBr, at a given a and widely differing Cs. These solutions were mixed in variable proportions and the emission spectra of the mixtures recorded and analyzed. All measurements were performed at 25 OC.
Results and Discussion The results concem the changes in the amount of bound DTAB and in Zl/Z3 with Cs for different copolymers PSX at various a and C, and various ionic strengths (added KBr at a concentration
CI). We shall successively examine the results for PS1 and PS2, which are the most hydrophilic copolymers investigated, then for PS4, which is sufficiently hydrophobic to show a globule to extended coil transition upon increasing a,and finally PS6, PS10, and PS16. PS1 and PS2. Figure 1 shows typical electrode responses to the DTAB concentration in solutions of PS1 at increasing KBr concentrations. At very low Cs, the E vs log Cs plots nearly coincide with the calibration plot obtained in the absence of PS1. However, above a critical concentration C+s, the two plots separate, indicating that binding is taking place. Clsis seen to increase with CI.At any C,,corresponding to an emf value E, the concentration of free surfactant, 6,, is obtained from the calibration curve, at the same E value. This permits one to prepare the binding isotherms @ = (C, - ds)/2Cps vs log ds>*zE where @ is the fraction of occupied sites, shown in Figure 2. With this definition, @ = 1 corresponds to one bound surfactant per carboxylic group. At high C,, the error on @ can be large because (42) Kalyanasundaram, K.; Thomas, J. K. J. Am. Chem. SOC.1977, 99, 2039.
'I
1.4
Figure 5. Variations of 1,/13with Cs for the same systems as in Figure 4. (X), (O), and ( 0 )as in Figure 4; (+) C, = lo-) M. For this last system, the solutions at high Cs were slightly turbid.
the calibration plot and the E vs log C . plot in the presence of PSX are fairly close. A small systematic shift in the calibration plot by, for example, 1 mV can give rise to a systematic trend, i.e., an increase or a decrease of @ upon increasing Cs, at high Cs. For this reason, the results at high Cs are not discussed. The binding isotherms in Figure 2 show a steep rise in @ above cCs, indicating that the binding of DTAB by PS1 is cooperative. This result is similar to that found in other studies of binding of cationic surfactants by polyanions such as sodium dextran sulfate, sodium polystyrenesulfonate (NaPS), sodium polyacrylate (NaPA), sodium alginate, Na-DNA, In Figure 2, the cooperativity appears to be restricted to the early stage of binding since all binding isotherms show a pronounced decrease of slope above j3 = 0.3-0.4. A similar result was reported for NaPS,22NaPA,23 and Na-DNA.24 Note that PSis much lower than the cmc of DTAB in the absence of PS1. For instance, at C, = lW3 M KBr, the values of cmc and cCs are 1.5 X and 5.5 X lo4 M, respectively. Figure 3 shows the fluorescence probing results for the systems in Figure 2. At low Cs,the high Il/Z3value indicates that pyrene resides in an aqueous environment and is not bound by PS1. Above a value of Cs which is close to cCs,Z,/Z3 shows a sigmoidal decrease upon increasing C,. At high Cs, Zl/13 levels out with a value equal to that in pure DTAB micelles (see the Z,/Z3 vs Csplot in the absence of PS1 in Figure 3). The decrease of Z1/Z3 becomes steeper as CI increases.
The Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1471
Interaction between DTAB and a Copolymer I
0.6
I
I
,
I
p
2.0
I
I1/I3
Figure 9. Variations of 11/13with Cs for the same systems as in Figure 8. The same symbols are used. Figure 6. Binding isotherms of DTAB to PS1 at C, = 2 X lo-" M, C, =5 X M and at a = 0 (0)and 1.00 (X). The binding isotherm at a = 0.50 is coincident with that at a = 1.00, within the experimental error.
I
2
3
5
Cs(M) 2
a 10-3
3
Figure 7. Variations of 1,/13with Cs for the same PS1-DTAB systems as in Figure 6, with a = 0 (0),0.50 (+), and 1.00 (X).
Figure 8. Binding isotherms of DTAB to PS2 at C, = 2 = 5 X lo-) M and a = 0 (0),0.5 (+), and 1.00 (X).
X
lo4 M, C,
Figures 4 and 5 show that the effect of the PS1 concentration, at a = 1.0,on the binding isotherms and on the changes of ZI/Z3 with Csis small. In particular, Csdoes not depend on C,, within the experimental error, for the C, range investigated. A similar mult has been found in studies of ionic surfactant-neutral polymer interaction^,^^.^^^^ and C swas considered as the cmc of the surfactant in the presence of the polymer. This is further discussed below. Finally, Figures 6 and 7 show the effect of the neutralization degree of PS1 on the binding isotherms and the changes of Z1/Z3 with Cs. As a is increased from 0 to 1.00,C svaries little but the binding isotherms become steeper. The results for PS2 concem only the effect of CY on the changes of B and Zl/13 with Cs (Figures 8 and 9). The increase of a shifts the 11/13vs CSplots and the binding isotherms to slightly higher CSvalues for PS2 but to slightly lower values for PS1 (Figures (43) Shirahama, K. Colloid Polym. Sei. 1974, 252, 918. (44) Shirahama, K.; Himuro, A.; Takisawa, N. Colloid Polym. Sci. 1987, 265, 96. (45) Binana-Limbel€, W.; Zana, R. Colloids Surf. 1986, 21, 483. (46) a na,R.; Lang, J.; Liana. P. In Mfcrodomains in Polymer Solutions; Dubin, P., Ed.; Plenum Press: New York, 1985; p 357.
6 and 7). The values of Csfor a given a are lower for PS2 than for PS1 at a = 0 and 0.5 but nearly equal at a = 1.00. The high values of Z1/13at low Cs,irrespective of the value of a,C, and C,, reveal that pyrene is not bound to PS1 or PS2. This result may look surprising, particularly at a = 0, as one would expect the unneutralized copolymer to be somewhat hydrophobic. However, one of the two C02H groups of maleic acid has a pK, of 3.5.34 It is thus largely ionized at C, < M, as used in this work. This may make the copolymer hydrophilic enough to prevent pyrene binding even at a = 0. The comparison of the results in Figures 1-9 reveals that in the binding isotherms the surfactant concentration CSs at which the binding becomes less cooperative closely corresponds to the concentration where the E vs log C, plots show an increase of slope and where the Zl/Z3 vs log Cs plots tend to level out. Thus the range of c',values where /3 increases rapidly (cooperative binding) corresponds to the range between C sand CSs where most of the decrease of ZI/Z3 occurs. This conclusion also holds for PS4 at a = 1.00 (see below) and suggests that the pyrene added to the PSX-DTAB system does not affect much the formation of mixed aggregates. In previous s t ~ d i e s , we 4 ~ had ~ ~ taken C sas the cmc of the surfactant in the presence of copolymer. However the Z,/Z3 plots suggest that should be used for this purpose. Indeed in Figure 3, the Z1/Z3 plot for DTAB in the absence of PS1 shows M) corresponds to and a similar that the cmc (1.5 X result has been obtained for several nonionic and ionic surfactar1ts.4~ Thus,11/13starts decreasing before the cinc and reaches a constant low value at the cmc. In all studies similar to the present 0ne,1e17*mz8948 the binding isotherms were successfully analyzed using the theoretical treatment for cooperative binding with nearest-neighbor intera c t i o n ~ . This ~ ~ ~treatment, ~~ which is also used in the present study, considers only the two equilibria
+ S K (OE) (OE) + S & (00) (EE)
(2) (3)
where E represents an empty polymer binding site, 0 an occupied binding site, and S the free surfactant. K and Ku are the equilibrium constants, and u is the cooperativity parameter. Reaction 3 represents the binding of a surfactant to a site adjacent to an occupied site. It is seen that u = [EE] [00]/[EEI2, where the bracketed quantities stand for concentrations. [OE] is the concentration of isolated bound surfactants, and u is really the equilibrium constant for the aggregation process of bound surf a c t a n t ~ .It~ reflects ~ the extra free energy of hydrophobic nature favoring the binding of an oncoming surfactant ion to a site adjacent to an occupied site where the alkyl chain of the oncoming surfactant can interact with that of the surfactant bound to the occupied site. (47) (48) 1044. (49) (50)
Zana, R. Unpublished results. Hayakawa, K.; Murata, H.; Satake, I. Colloid Polym. Sci. 1990,268, Satake, I.; Yang, J. T. Biopolymers 1976, 15, 2263. Schwarz, G. Eur. J . Biochem. 1970, 12, 442.
1472 The Journal of Physical Chemistry, Vol. 96, No. 3, 1992
The relevant equations are22,49*so j3 = ( 1
+ (s - l)/[(l
- S)Z
+ 4s/u]'/2)/2
s = KUds
(Qdo.5
= 1/Ku
(da/d log 6 s ) , s = ~ ' / ~ / 4
(4) (5)
(6) (7)
(C& is the concentration of free surfactant corresponding to 0 = 0.5. Hayakawa et al.z3 noted that the nearest-neighbor interaction model is an oversimplification in view of the complexity of the effects considered. Nevertheless it provides a useful basis for a semiquantitative comparison of the effect of various parameters on the binding process, as is the purpose of the present work. The values of Ku, u, and K have been obtained from the values of dsat p = 0.5 (eq 6) and from the maximum slope of the 0 vs Osplot (eq 7). This procedure involves an extrapolation of the 0 vs dsplot to 0 = O S , which yields Ku with a reasonable accuracy (f50%), but, as in previous s t ~ d i e s , the ~ ~ errors - ~ ~ on K and u can be rather large. The procedure adopted yields lower bound values of Ku and u and upper bound values of K because the range of cooperative binding is restricted to 0 < 0.3-0.4 (Figures 2, 4, 6, and 8 and below). Table I lists the values of Ku, u, and K obtained from the binding isotherms. The values of u increase with a for both PSI and PS2, do not depend on C, in the range investigated, increase in going from PS2 to PS1, at given C, a,and CI values, and increase with CI (a similar result has been reported for other polyanion~~*q~~). The results in Table I also show that the variations of K with a,C, CI,and the nature of the copolymer are generally opposite to those of u. Thus,the stronger the binding process (taking place at low Cs, characterized by a large K value) the lower the cooperativity (small u). This conclusion appears to hold for all of the systems investigated. Similar results have been reported for other Finally Figure 10 shows that the variation of log Ku with log CI is linear with a slope of -0.55. A similar result was found for the interaction of alkyltrimethylammoniumhalides with various p o l y a n i o n ~with , ~ ~ ~values ~ ~ of the slope ranging between 4 - 5 8 and 4 . 7 5 . It has been notedU that these values are close to those characterizing the change of the cmc of conventional surfactants with added salt. PS4. The effect of CI, a,and C, on the electrode response to the DTAB concentration in solutions of PS4, on the binding isotherms of DTAB to PS4, and on the changes of 11/13 with Cs are shown in Figures 11-17. The binding isotherms and the 11/13 vs Cs plots are seen to be nearly independent of C, and the added KBr shifts the binding isotherms and the 11/13 plots to higher Cs, as for PS1. There are however three important differences with respect to the binding of DTAB to PS1. First, under comparable experimental conditions, DTAB binding takes place at much lower Cs values than in PS1 solutions, typically at Cs below 10" M, compared to above 10-4 M (Figures 11, 13, 14, and 16). Second, the binding is cooperative only at a > 0.5. This is clearly seen in Figure 13 where at a = 0 and 0.5 and low Cs the electrode response is well below the calibration plot. This corresponds to a nearly quantitative binding of DTAB at low Cs (ds/Cs N 0), and the value of , ! Iincreases slowly and monotonously with ds, at higher Cs (Figure 14). The binding is now anticooperative as the u values at ar = 0,0.25, and 0.5 are smaller than 1. Even at a > 0.5, the cooperativity for DTAB binding to PS4 is lower than that to PS1 and PS2. This lower cooperativity shows in the changes of IJZ3 with Cs in Figure 15, which are less steep than for PS1 or PS2. Third, at ar = 0 the values of ZI/Z3 are well below those for water, indicating that pyrene is at least partly bound by PS4 (Figure 15). Recall that PS4 retains a compact conformation up to a neutralization degree aT * 0.25 at C, = 5 X lW3 M.34 In the present work, CF is in the l@-lW3 M range and the self-ionization of the first a & c group of maleic acid ( p P ,
Benrraou et al. TABLE I: Values for Ku,K,and u for the Bindiag of DTAB to pS1 and pS2 under Various Experimental Conditions 1 o~c,, 10-3~~, polymer M a C,, M M-l u K. M-' PSI 2" 1.00 5 X 4.2 26 1.6 X lo2 2 0.50 5 X 4.2 26 1.6 X lo2 2 0.00 5 X 1.5 2.5 6.5 X lo2 PS1 2 1.00 10-3 8.7 8 1.1 X lo3 2" 1.00 5 X lo-' 4.1 23 1.8 X lo2 2 1.00 10-2 2.5 26 1.0 X lo2 PS1 1 1.00 5 x 10-3 3.9 36 1.1 x io2 2" 1.00 5 X lo-' 4.1 60 70 4 1.00 5 X 3.5 40 90 PS2 2 1.00 5 X lo-' 5.4 23 2.4 X lo2 2 0.50 5 X lo-' 5.2 6.5 8.0 X lo2 2 0.00 5 x 10-3 2.2 2 1.1 x 103
" These three results correspond to three different determinations. They show that the error on Ku is small but that the errors on K and u can be quite large.
2
5
3
8 10-2
CI(MI 2
3
4
Figure 10. Variations of Ku with the concentration of added KBr, C,, for PSI (+) and PS4 (0)at C, = 2 X lo4 M and a = 1.00. 0.8'
'
'
1
I
P
Figure 11. Binding isotherms of DTAB by PS4 at a = 1.00 and C, = 2 X 10-4 M in the presence of KBr: (0) (+) 5 X (0) (X) 4 X M.
2.0
p
Cs(M) 10'
4
8,i-S
2
3
5
8 10-L '
2
Figure 12. Variations of 1,/13with C, for the same systems as in Figure 11. The same symbols are used.
= 3.5 f O.l)Mreduces aT.Nwertheless, a potentiometric titration performed in the absence of KBr at C, = 2.1 X 10-4 M, as part
Interaction between DTAB and a Copolymer
The Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1473 TABLE II: Values of Ku, K , and u for the Binding of under Various Experimental Conditions 104cm, M a c,, M KU, M-1 u 5x a a 2 0 a a 2 0.25 5 X 2.4 X lo4 0.4 2 0.50 5 X 2 0.75 5 x 10-3 5.5 x 104 3.7 2 1.00 5 x 10-3 4.3 x 104 4.1 1.7 X lo5 8.4 2 1.00 10-3 2.7 x 104 3.9 2 1.00 10-2 8.3 X lo3 2.7 2 1.00 4 X 1 1.00 5 x 10-3 3.7 x 104 3.5 4 1.00 5 x 10-3 3.3 x 104 3.8
DTAB to PS4
K. M-) ~
a a 6
X
lo4
1.5 x 104 1 x 104
2.0 x 104 7 x 103 3.1 x 103 104 8.6 X lo3
Noncooperative.
Figure 13. Electrode response to the DTAB concentration in 2 X IO-" M KBr and increasing degree of M PS4 solution at Cl = 5 X neutralization: (0)0; (e) 0.5; (X) 1.00. The corresponding plots for a = 0.25 and 0.75 are very close to those for a = 0 and 1.00 and are not shown for the sake of clarity. The calibration curve is shown as the dotted line.
between 1.33 and 1.36 at high Cs,irrespective of the values of a and CI (Figures 12, 15, and 17). The higher value of Z,/Z3 at , C = IO4 M and high Cs reflects the fact that the mixed PS4-DTAB aggregates solubilizing pyrene are essentially made of DTAB with a few PS4 repeat units because of the low CB value used. As C, increases, the aggregates become richer in repeat units (as in the mixed micellization of two conventional surfact a n t ~ and ) ~ ~pyrene senses a less polar environment. On this basis, one would expect Zl/Z3 to increase from the value 1.33-1.36 to 1.43 (pure DTAB micelles) by further increasing Cs,at constant C, larger than lo4 M. This expectation is borne out by the results in Figure 18. At high Cs, with C, = 2 X 10" M, Z , / 4 is seen to increase with Cs and to tend toward the value in pure DTAB micelles, reflecting the progressive enrichment of the mixed aggregates in DTAB. In all the plots in Figures 12, 15, and 17, Zl/Z3 decreases when Csincreases from lobsto lo4 M owing to the partition of pyrene between mixed aggregates and bulk phase. A partition with a single partition constant K p obeys the equation
RE = RE + (Rw - R ~ s/)(1 + &cs)
(8)
where RE,R,, and Rw are the values of ZJZ3 in the system, in pure water (1.88) and in the mixed aggregates at Cs = 2 X 10" Figure 14. Binding isotherms of DTAB by FS4 for the same systems as M (where Z1/Z3 is a minimum of about 1.33). However, eq 8 did in Figure 13 with C, = 2 X lo4 M, C, = 5 X M KBr and a = 0 not fit to the Zl/Z3 vs Csdata in the range 10-6-2 X 1 p M. Indeed (O), 0.25 (V), 0.5 (e), 0.75 (A), and 1.00 (X). it is likely that the size of the aggregates increases with Cs, as for the binding of ionic surfactants to neutral polymers,46and that of this work, showed a plateau in the pH + log [a/(l - a)]vs they become richer in DTAB, as in mixed micellizati~n.~~ The a plot, up to a! = 0.15-0.2. This result reveals a globule to partition constant of pyrene will thus increase with Cs,since pyrene extended coil transition and the presence of microdomains. It does not bind to PS4 at a = 1.00 but is strongly bound to DTAB explains why the Z1/Z3 value for PS4 at a = 0 and low Cs is micelles resulting in a steeper decrease of Z1/Z3 than predicted by significantly lower than at higher a. Nevertheless the Zl/Z3 vs eq 8 (for a partition equilibrium, the decrease of 11/13 would stretch Cs plots and the binding isotherms show no features which can over two decades of Csvalues, whereas the decreases stretch over be readily related to a conformational transition of PS4 induced about one decade in Figures 12, 15, and 17). by the binding of the surfactant. This point is further discussed The last point to be discussed concerns the large effect of CY below. on u in the binding of DTAB to PS4. Cooperativity in PS1 and The values of Ku,u, and K for PS4 listed in Table I1 show that PS2 binding of DTAB arises because a surfactant tends to bind within the experimental error u is independent of C,, as for PS 1, at a site adjacent to a site which has already bound a surfactant. and increases with a,as for PSI and PS2. However, u decreases Indeed the hydrophobic interaction between the alkyl chains of as the ionic strength (C,)is increased, contrary to PS1. Recall the two bound surfactants provides a free energy gain with respect that u was reported to be independent of CI within the (large) to the binding to an isolated site. In the case of PS4, microdomains experimental error, in the case of polystyrenesulfonate,22another exist up to a a = 0.15-0.2 (mid-transition, see above) and smaller hydrophobic polyelectrolyte. Also the comparison of the results microdomains are likely to exist at higher a,probably up to a in Tables I and I1 shows that the increase of hydrophobicity in = 0.5. The binding of a surfactant to a microdomain, even a small going from PS1 to PS4 results in a decrease of u. The last two one, includes a hydrophobic contribution, and the binding constant results are at variance with those reported for others polymers can be much larger than that to PS1. However binding to miof increasing hydrophobicity,poly-L-lysine and poly-L-ornithine.48 crodomains will be anticooperative, as entropy will tend to favor As suggested by 0thers,2~-~~ these differences in behavior probably the binding of an oncoming surfactant to an empty microdomain reflect the importance of the chemical structure of the polymer in the binding process. Indeed, the reported r e s ~ l t s ~were ~ v ~ ~ rather than to one containing a surfactant. Of course, as a is increased the microdomains disappear completely and some coconcerned with hydrophobic polymers with charged groups located operativity is recovered, as observed at a = 0.75 and 1.00. Other at the end of the hydrophobic side chains, fairly far from the factors, such as the flexibility of the copolymer backbone, may polymer backbone. In the PSX copolymers, the charged groups also contribute to the change of u with a,but their effect is more are located close to the polymer backbone and are well separated difficult to assess. Nevertheless, one would expect the binding from the hydrophobic groups. Figure 17 shows that the value of Zl/Z3 at C, = lo4 M and high C .is the same as for DTAB micelles in the absence of PS4 (51) Malliaris, A.; Binana-Limbel€,W.; Zana, R. J. Colloid Interface Sci. (1.43). However, as C, increases, Zl/Z3 decreases to values 1986, 110, 114.
1474 The Journal of Physical Chemistry, Vol. 96, No. 3, 1992 I
Benrraou et al.
I
I
2.0
-
1.2
-
-
-
-
Ii/%
Cs ( M I 1
I
Figure 15. Variations of Zl/Z3 with Cs for the same systems as in Figure 14. The same symbols are used.
,
0.6
,
,
.,
I
,
,,a
2.01
0.L
0.2 CsIMl I
0
,b6
Figure 16. Binding isotherms of DTAB by PS4 at a = 1.00and C, = 5 X lo-’ M,at increasing concentration of PS4: (0)lo4; (X) 2 X lo4; (+) 4 X lo4 M.
2 3
5
alo5
,
,
.
2
3
5
,
a1,-4
I
,
,
2
3
,
,
la
1.6-
O6
I
1
t
t
1.2
of DTAB to be anticooperative,even at a = 1-00with copolymers having a side chain longer than the butyl chain. The results below confirm this expectation. PS6, PS10,and PS16. The E vs Cs plots in the presence of PS6, PS10,and PS16 at CY = 1.00are very similar to those for PS4 at CY < 0.5. Figure 19 shows that the binding isotherms are anticooperative,as expected from the above discussion. Thus the increase of the copolymer alkyl side chain from butyl to hexyl changes the nature of the binding from cooperative to anticooperative at a = 1.00. The same change was achieved at a = 0 by going from PS2 to PS4 (see above). Figure 18 shows the variations of 11/13 with Cs for the same copolymers. We have also represented the corresponding plots for DTAB in the absence of copolymers and in the presence of PS1,PS2, and PS4. Although some trends are apparent, the changes of Z1/Z3 with C, are complex and their interpretation involves three effects. The first one (effect I) is the partition of
2
Figure 18. Variations of ZJZ3 with C, in water (e) and in PSX solutions at C, = 2 X lo4 M,a = 1.00,and Cl = 5 X lo-’ M KBr for PSI (X), PS2 (0), PS4 (+), PS6 (A),PSlO (0)and , PS16 ( 0 ) . For PS6,PSlO, and PS16,we have showed as A, 0 , and 0 at the left side of the figure the respective values of Z,/Z3 in the absence of DTAB. These values indicate that Zl/Z3 gocs through a maximum for PSlO,decreases for PS6, and increases for PS16 as Cs increases, at very low C,.
-
Figure 17. Variations of ZI/Z, for the same systems as in Figure 16 with the same symbols except for 0 which refers to C, = lo-’ M and A which refers to DTAB in water (upper concentration scale).
I
8,63
5
C L (MI
1
J . Phys. Chem. 1992,96, 1475-1478 repulsions between the charged carboxylic groups and results in the formation of mixed micro domain^.'^^ Effect I11 should bring about a decrease of 11/13but would occur only in PSX solutions with X 2 4. Obviously, for PS1 and PS2 the changes of 11/13are essentially due to effect I. The decreases of 11/13in the presence of PS1 or PS2 are only slightly less steep than in pure water. A partial recoiling of the copolymer (effect 111) would have no impact on as pyrene is not bound by PS1 or PS2 in the the change of 11/13, whole a range (see Figures 7 and 9 at very low Cs). On the contrary, PS16 appears to correspond to a situation where partition is unimportant. Indeed the value of 11/13in the absence of DTAB in Figure 18, at C, = 2 X lo4 M, is close to that found at C, = 10-* M.29 This indicates that pyrene is nearly completely solubilized in the microdomains and that effect I is negligible. The increase of 11/13with Csreflects the progressive enrichment of the microdomains in DTAB (effect 11). Recall that in PS16 most repeat units appear to be forming micro domain^.^^ Thus effect I11 discussed above is negligible. Note that the 11/13 vs C , plot for PS16 extends to a Csvalue slightly below that where a DTAB-PS16 complex precipitates out. PS4, PS6, and PSlO correspond to intermediate situations. A minimum is expected to result from the superimpositionof effects I and I1 in the variation of 11/13with Csat high Cs where effect I1 becomes predominant. This minimum is observed for the three copolymers. Evidence for the contribution of effect I11 can be found in the results for PS10. Microdomains are known to exist in PSlO solutions, but at a = 1.00 "sinformation involves only 15%repeat units.30 Nevertheless as for PS16 the Z1/I3 value at Cs = 0 indicates that pyrene is nearly completely solubilized within these domains. Thus effect I contributes only little to the change of 11/13at low Cs. This is borne out by the increase of 11/13with Cs at very low Cs. One would therefore expect a monotonous increase of I'll3 from the value of 1.10 in the absence of DTAB to 1.45 at very high Cs. The leveling off of 11/13and its subsequent decrease in Figure 18 reveal that a new effect sets in where additional repeat units become involved in microdomains, together with the added DTAB. These additional repeat units can only be those not involved in microdomains at low C,. Their
1475
involvement corresponds to a w i l i n g of PSlO (effect 111). When most of the free repeat units have been used up by this process, 11/13 is expected to increase again with Cs, as observed. A similar process is likely to occur in PS4 and PS6 solutions. M then In the latter, 11/13slowly decreases up to Cs = 3 X decreases faster up to 2 X lo4 M DTAB. These two concentrations probably determine the range where PS6 recoils.
Conclusions The above study of the binding of DTAB to a series of homologous but increasingly hydrophobic copolymers has clearly shown that the cooperativity in the binding is modulated by the hydrophobicity of the copolymer. As one goes from hydrophilic to hydrophobic copolymem, the binding constant increases (binding takes place at lower surfactant concentrations) and the binding goes from cooperative to anticooperative. This behavior has been explained in terms of the difference in free energies for the binding of an oncoming surfactant to a copolymer site where it interacts with another bound surfactant and for the binding to a site where it interacts with the copolymer alkyl side chains self-assembled in microdomains. This difference decreases and changes sign as the length of the side chain increases. For the copolymers used, the range of fraction of occupied sites where the binding is cooperative is restricted to about 0.4. In systems where the binding is cooperative, the comparison of the changes of 11/13with Cs to the binding isotherms reveals that 11/13begins to decrease at the concentration Cswhere binding starts and that 11/13becomes nearly constant at where binding is no longer cooperative. The concentration cC*s may be considered as the cmc of DTAB in the presence of PSX. Acknowledgment. This work has benefited from the financial support of Rhane-Poulenc (Mr. J. C. Vitat). The authors thank Prof. U. P. Strauss (Rutgers University) for the gift of the PS6 sample and Profs. J. C. Kwak (Dalhousie University, Canada), K. Shirahama (Saga University, Japan), G. Kresheck (Northern Illinois University) and K. Hayakawa (Kagoshima University, Japan) for stimulating discussions and many helpful suggestions in building and handling the surfactant-specific electrodes.
Mutual Diffusion Coefficients in the Water-Rich Region of WateVPhenoi Mixtures and Their Relation to Aggregate Formation Rolando Castillo,* Cristina Carza, and Jorge Orozco Instituto de Fisica, U.N.A.M.. P.O. Box 20-364, Mexico D.F. OlOOO, Mexico (Received: June 4, 1991)
Mutual diffusion coefficients in the one-phase water-rich region of the phase diagram of the phenollwater system (0-10 wt % phenol) were measured using the Taylor dispersion technique, at several temperatures and mole fractions. The values range from 0.71 to 1.88 X mz/s. In order to obtain evidence about the formation of aggregates of pseudomicelles in this system, as it is invoked in the interpretation of bulk and surface properties, correlation lengths of the concentration fluctuations have been calculated at 328 K using the diffusion data and measured viscosities. They agree with the assumption of aggregate formation in the bulk of the solution at a phenol weight fraction about 7-8 wt %.
Introduction Systematicstudies of aqueous solutions of amphiphilic molecules with a small aliphatic tail, hence with no clearly defined amphipathy to be considered as conventional surfactants, are quite interesting. A remarkable example is the 2-butoxyethanol(2BE) water (W) mi~ture.l-~Here, the concentration dependence
of its surface and bulk properties is very similar to those associated with micellization of normal surfactants. The analogous behavior of 2BE W with well-established micellar systems has suggested'+ that there is some form of organization or aggregation in the bulk of the solution. Hence, the 2BE can be classified as a borderline surfactant.
( 1 ) Castillo, R.; Dominguez, H.; Costas, M.J. Phys. Chem. 1990,94,8731. (2) Elizalde, F.; Gracia, J.; Costas, M. J . Phys. Chem. 1988, 92, 3565. (3) Rao, N. P.; Verral, R. Con. J . Chem. 1987, 65, 810.
(4) Kato, S.;Jok, D.; Rao, N. P.; Ho, C. H.; Verrall, R. E. J. Phys. Chem. 1986, 90, 4167. (5) Kato, T., J . Phys. Chem. 1985, 89, 5750.
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0022-36S4/92/2096-1475$03.00/0
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0 1992 American Chemical Society
