4416
Langmuir 2001, 17, 4416-4421
A Look at the Thermodynamics of the Association of Amphiphilic Polyelectrolytes in Aqueous Solutions: Strengths and Limitations of Isothermal Titration Calorimetry B. Bangar Raju,† Franc¸ oise M. Winnik,*,† and Yotaro Morishima‡ Department of Chemistry and Faculty of Pharmacy, Universite´ de Montre´ al, C. P. 6128 succursale Centre-ville, Montre´ al, QC H3C 3J7 Canada, and Department of Macromolecular Science, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043 Japan Received November 7, 2000. In Final Form: April 11, 2001 The dissolution in water of the sodium salts of poly(2-acrylamido)-2-methylpropanesulfonic acid (PAMPS), N,N-di-n-octadecyl-endcapped-poly(2-acrylamido)-2-methylpropanesulfonic acid [(C18)2-PAMPS], cholesteryl-endcapped-poly(2-acrylamido)-2-methylpropanesulfonic acid (Chol-PAMPS), and a random copolymer of AMPS and N-dodecylmethacrylamide (PAMPS-Dod20) was studied by isothermal titration calorimetry (ITC). The endcapped polymers form multimolecular aggregates in aqueous solutions. The concentration range for aggregation and the enthalpy of micellization were determined as functions of the electrolyte concentration (0.01 M < [NaCl] < 0.3 M) and temperature (288 K < T < 308 K) for solutions of (C18)2PAMPS. At 298 K and 0.2 M NaCl, aggregation of this amphiphilic polyelectrolyte occurs in solutions with concentrations ranging from about 1 to 14 mmol of AMPS L-1 (0.5-2.7 g L-1) with an enthalpy of micellization of ∼100 J (mol of AMPS)-1. The effect of the experimental conditions, such as the method of preparation of the polymer stock solution and its concentration, on the ITC results is described in the case of CholPAMPS. Titrations performed with poly(sodium-2-acrylamido-2-methylpropane sulfonate) (PAMPS) confirmed that PAMPS does not aggregate in aqueous NaCl, whereas PAMPS-Dod20 forms predominantly unimolecular micelles. The advantages and limitations of ITC for studying the micellization thermodynamics of amphiphilic polyelectrolytes are discussed.
Introduction The application of calorimetry to the study of micellization is quite old.1,2 Most such investigations have been concerned with the aggregation of surfactants, a cooperative process that occurs over a narrow surfactant concentration range and is characterized by rather large enthalpies of micellization (between -2 and -25 kJ/mol).3,4 Hydrophobically modified water-soluble polymers (HMpolymers) also aggregate in water.5-7 Not many direct data are available on the thermodynamic parameters of this association process. It would seem that isothermal titration calorimetry (ITC) is the ideal technique to measure, in the absence of any probe, the heat of micellization and the critical aggregation concentration. Engberts and co-workers used the technique, together with fluorescence spectroscopy, to study the pH-dependent aggregation of mono-endcapped hydrophobically modified poly(acrylic acids),8 and preliminary ITC data were also presented to corroborate the results of an extensive study * Corresponding author. E-mail:
[email protected]. Phone: (514) 343 6123. Fax: (514) 343 2362. † Universite ´ de Montre´al. ‡ Osaka University. (1) Paredes, S.; Tribout, M.; Ferreira, J.; Leonis, J. Colloid Polym. Sci. 1976, 254, 637. (2) Birdi, K. S. Colloid Polym. Sci. 1983, 261, 45. (3) Paula, S.; Su¨s, W.; Tuchtenhagen, J.; Blume, A. J. Phys. Chem. 1995, 99, 11742. (4) Majhi, P. R.; Moulik, S. P. Langmuir 1998, 14, 3986. (5) Zang, Y. X.; Da, A. H.; Hogen-Esch, T. E.; Butler, G. B. In Water Soluble Polymers: Synthesis, Solution Properties and Applications; Shalaby, S. W., McCormick, C. L.; Butler, G. B., Eds.; ACS Symposium Series 467; American Chemical Society: Washington, D.C., 1991; p 159. (6) Laschewsky, A. Adv. Polym. Sci. 1995, 124, 1. (7) Morishima, Y. In Solvents as Self-organization of Polymers; Webber, S. E., Tuzar, D., Munk, P., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1996; p 331.
by fluorescence of the solution properties of monoendcapped poly(sodium-2-acrylamido-2-methylpropane sulfonates).9 The main advantage of ITC over other techniques is that a single measurement yields not only the critical aggregation concentration (cac), but also the enthalpy of aggregation, from which it is possible to derive the free energy, entropy, and heat capacity of micellization. Nonetheless, there are difficulties associated with the study of polymer micellization by ITC. These difficulties stem from the facts that, unlike surfactant micellization, in most cases, HM-polymer association is only weakly cooperative and the enthalpy of micellization is often small, especially for the association of HM-polyelectrolytes. In this study, we use ITC to investigate the thermodynamics of association of hydrophobically modified poly(2-acrylamido)-2-methylpropanesulfonic acid (HM-PAMPS) in aqueous solution. From the bank of samples available, we selected three polymers that have been investigated previously by a variety of analytical tools (Figure 1). Two copolymers, (C18)2-PAMPS9 and Chol-PAMPS,10 carry hydrophobic groups at one chain end. They are known to form multipolymeric micelles. The third copolymer, PAMPS-Dod20,11,12 carries dodecyl groups grafted along the chain. It exhibits a marked preference for aggregation in the form of unimers which, under certain conditions, can associate to form multipolymeric micelles. Enthalpies of micellization were determined for all polymers. The (8) Klijn, J. E.; Kevelam, J.; Engberts, J. B. F. N. J. Colloid Interface Sci. 2000, 226, 76. (9) Mizusaki, M.; Morishima, Y.; Raju, B. B.; Winnik, F. M. Eur. Phys. J. E. 2001, 5, 105. (10) Yusa, S.-I.; Kamachi, M.; Morishima, Y. Macromolecules 2000, 33, 1224. (11) Yamamoto, H.; Hashidzume, A.; Morishima, Y. Polym. J. 2000, 32, 745. (12) Morishima, Y.; Nomura, S.; Ikeda, T.; Seki, M.; Kamachi, M. Macromolecules 1995, 28, 2874.
10.1021/la001554i CCC: $20.00 © 2001 American Chemical Society Published on Web 06/09/2001
Strengths and Limitations of ITC
Langmuir, Vol. 17, No. 14, 2001 4417
Figure 1. Structures of the polymers studied.
micellization of (C18)2-PAMPS was examined in detail, with particular attention on the effects of salt concentration and temperature on the thermodynamics of micellization. Materials and Methods Water was deionized with a Millipore deionizing system. The polymers, PAMPS,9 (C18)2-PAMPS,9 Chol-PAMPS,10 and PAMPSDod2011 were prepared and characterized as described earlier. Special care was taken in solution preparation because, in general, the dynamic structure of micelles depends on the method of preparation. When a solid polymer is dissolved in water directly, micellization equilibrium can be established reasonably rapidly. In some micellar systems, however, a system might reach only a local free energy minimum within experimentally reasonable time scales (a few hours). In this case, micellar solutions might be annealed by simple standing at room temperature over long periods of time (several days), or sometimes, the annealing process is promoted by some heat treatment. Solutions of (C18)2-PAMPS and PAMPS-Dod20 were prepared as follows. The desired amount of polymer was added in solid form to a NaCl solution of known concentration (0.01-0.3 M). Each solution was stirred for at least 24 h at room temperature prior to measurements. To prepare solutions of Chol-PAMPS (20 g L-1), we followed a previously described protocol:10 The solid polymer was added to an aqueous NaCl solution (0.1 M). The mixture was then heated to 90 °C for 15 min, cooled, and kept at room temperature for 24 h prior to analysis. Solutions of Chol-PAMPS (5.0 g L-1) were stirred at room temperature for 24 h and were not subjected to heat treatment. Isothermal Titration Calorimetry (ITC). Heats of dilution and demicellization were measured using a VP-ITC titration microcalorimeter (MicroCal, Northampton, MA). The sample cell had a volume of 1.43 mL. It was filled with water or aqueous NaCl prior to each experiment. Polymer solutions (20 g L-1, 0.087 mol L-1, unless otherwise stated) were placed in a 300-µL continuously stirred (300 rpm) syringe. Injected into the sample
Figure 2. Determination of the enthalpy of demicellization, the aggregation concentration, and the concentrations ST and ET from experimental enthalpograms (a) fitted to a sigmoidal function or (b) following the method described in ref 8. The enthalpograms were obtained for titrations of b-(C18)2-PAMPS in 0.2 M NaCl at (a) 25 and (b) 20 °C. cell were 28 aliquots (10 µL) in intervals of 400 s. Each titration was performed three times to ensure reproducibility of the results. Data analysis was carried out using Microcal ORIGIN software. The principles and basic thermodynamic conventions of ITC are discussed in a recent publication.13 Analysis of the Enthalpograms. Method 1. Sigmoidal curves were analyzed by the nonlinear sigmoidal function provided in Origin 5.0 (Microcal) to obtain the value of cac. To determine ∆Hdemic, linear fits of the data sets in the lower and upper concentration domains were performed. Then, the ordinates of the last (highest) value in the fitted raw data of the lower concentration range and of the first (lowest) value in the fitted raw data of the higher concentration range were determined (see Figure 2a). The difference between the two ordinates gives the enthalpy of demicellization. Method 2. Curves that did not present clear sigmoidal features were analyzed by a data treatment analogous to that suggested by Klijn et al.8 Linear fits of the data sets in the lower and upper concentration domains were performed. The abscissa of the last (highest) value in the fitted raw data of the lower concentration range, ST, and of the first (lowest) value in the fitted data of the (13) Biocalorimetry, Applications of Calorimetry in the Biological Sciences; Ladbury, J. E., Chowdhry, B. Z., Eds.; John Wiley & Sons: Chichester, U.K., 1998.
4418
Langmuir, Vol. 17, No. 14, 2001
Raju et al.
higher concentration domain, ET, were taken as the polymer concentrations corresponding to the start and end of micellization, respectively (see Figure 2b). The intercepts of the two straight lines were determined. The difference between the two intercepts yields the enthalpy of demicellization. Determination of the Thermodynamic Parameters. The standard Gibbs free energy of transfer of a surfactant monomer from a micelle into water, ∆Gdemic, is expressed as14
∆Gdemic ) µow - µomic ) -RT ln cmc - RT ln fw + (RT/m) ln(cmc/m) (1) where µow and µomic are the standard chemical potentials of the surfactant monomer in water and in the micelle, respectively; fw is the activity coefficient of the surfactant monomers in water; m is the micelle aggregation number; and R and T have their usual meanings. Assuming a sufficiently high value for m and ideal behavior of the monomers in water, the second and third terms become very small and can be neglected. Then, ∆Gdemic can be approximated by
∆Gdemic ) µow - µomic ) -RT ln cmc
(2)
This approximation, of course, is not strictly applicable for systems of hydrophobically modified polymers in water, as the micellization is only weakly cooperative. The change in entropy ∆Sdemic can easily be obtained using the Gibbs-Helmoltz equation
∆Sdemic ) (∆Hdemic - ∆Gdemic)/T
(3)
The change in heat capacity, ∆Cp(demic) ) -∆Cp(mic) was determined graphically from a plot of ∆Hdemic (obtained by either method 1 or method 2) as a function of temperature.
Results Critical Aggregation Concentration (cac) and Enthalpy of Demicellization (∆Hdemic). Discussed first are the results obtained for the end-modified sample (C18)2PAMPS, a polymer forming multipolymeric micelles.9 In a typical experiment, aliquots of a concentrated aqueous polymer solution (20 g L-1) are titrated at constant temperature into an aqueous NaCl solution of same electrolyte concentration. The heat evolved with each injection is measured. The area under each peak is plotted against polymer concentration in the calorimeter sample cell. The enthalpogram obtained from dilution of a solution of (C18)2-PAMPS in 0.2 M NaCl into 0.2 M NaCl at 298 K (Figure 2a) can be subdivided into three polymer concentration parts: the middle concentration range (3.7 mmol L-1 < [AMPS] < 10 mmol L-1) in which the reaction enthalpy decreases sharply, and the low and high concentration domains where the changes in reaction enthalpy are much less pronounced. This enthalpogram reflects the following events. After the first few injections, the final concentration in the sample is lower than the aggregation concentration, and the large enthalpic effects result from three phenomena: the dilution of the polymeric micelles, the demicellization, and the dissolution of individual polymer chains. The significant decrease in reaction enthalpy for [AMPS] > 3.7 mmol L-1 indicates that the concentration corresponding to aggregation has been reached; therefore, the contribution of the enthalpy of demicellization to the total dilution heat becomes progressively smaller above this concentration. As micellar polymer solution is added beyond the aggregation concentration, the micelles no longer dissociate, and the heat measured is due only to the dilution of the micelles. The range of polymer concentrations over which micellization (14) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes, 2nd ed.; Wiley: New York, 1980.
takes place was characterized by three values, ST, ET, and cac (see Materials and Methods), which correspond, respectively, to the start of aggregation, the end of aggregation, and the midpoint of the transition. When an equilibrated, concentrated polymer micelle solution is added to water or aqueous NaCl, a new equilibrium might be established sufficiently rapidly on the time scale of the experiment. However, there are situations in which micellar systems stay in a nonequilibrium state because the kinetics of any equilibration process is frozen at the time scale of the experiment. In general, it is extremely difficult to distinguish equilibrium micelles from kinetically frozen micelles; our results indicate that ITC, in fact, can be used as a diagnostic tool. The sigmoidal curve, which presents a clear break corresponding to the cac (Figure 2a), suggests that the micelles are in equilibrium and that both the demicellization upon dilution and the reequilibration processes of (C18)2-PAMPS micelles are sufficiently fast compared to the time scale of the ITC measurements (several minutes). In this case, it is possible to determine the thermodynamic parameters of the process nearly as precisely as in the case of surfactants. Microcalorimetry experiments were also performed with solutions of PAMPS to determine the enthalpy associated with the dilution of the polymer in the absence of hydrophobic interactions leading to association. A straight line was obtained for ∆H as a function of polymer concentration, corresponding to a heat of dilution of -10 J (mol of AMPS)-1 for the addition of a PAMPS solution (20 g L-1, 0.2 M NaCl) to a 0.2 M NaCl solution at 25 °C. As noted also for the dilution of poly(sodium acrylate),8 the magnitude of the heat evolved depends on the concentration of the stock solution. The dilution becomes more exothermic with increasing concentration of the polymer stock solution, an effect attributed to the closer packing of polymeric units in the more concentrated stock solution and the resulting stronger interactions between solutes. Effect of Ionic Strength on the Association of (C18)2-PAMPS. Enthalpograms recorded for the dilution of solutions of (C18)2-PAMPS (20 g L-1) of various ionic strengths (0.01 0.3 M NaCl) are shown in Figure 3. Comparing the four parts of Figure 3, one notices clearly that the overall heat of reaction (Q) becomes increasingly less negative (the reaction becomes less exothermic) with increasing ionic strength. This decrease in the amplitude of Q with increasing salt concentration reflects, on the one hand, the fact that the demicellization becomes increasingly less exothermic, and, on the other hand, a decrease in the enthalpies of dilution of both the polymeric micelles and the individual polymer chains. The dilution of PAMPS, measured in a separate set of experiments, also was shown to become less exothermic with increasing electrolyte concentration (Table 1), in agreement with earlier studies on the thermodynamics of mixing of polyelectrolytes with simple salts.15 We note that the curves corresponding to the solutions of higher ionic strengths present a sigmoidal shape. The curves recorded for solutions of lower ionic strengths, however, cannot be fitted easily by a sigmoidal function. Nonetheless, they present clear breaks, which were used to estimate the enthalpies of demicellization listed in Table 1. The loss of resolution of the curves reflects the fact that, with decreasing ionic strength, the heat of dilution becomes increasingly larger compared to the heat effect of demicellization. (15) Boyd, G. E.; Wilson, D. P.; Manning, G. S. J. Phys. Chem. 1976, 80, 808.
Strengths and Limitations of ITC
Langmuir, Vol. 17, No. 14, 2001 4419
Table 1. Thermodynamic Data for Demicellization of (C18)2-PAMPS and Dilution of PAMPS in Solutions of Various Ionic Strengths (T ) 298 K) (C18)2-PAMPS
PAMPS
[NaCl] (mol L-1)
STa (mmol of AMPS L-1)
ETa (mmol of AMPS L-1)
cacb (mmol of AMPS L-1)
∆Hdemic [J (mol of AMPS)-1]
∆Gdemic [kJ (mol of AMPS)-1]
∆Sdemic [eu (mol of AMPS)-1]
∆Hdilc (J mol-1)
0.01 0.1 0.2 0.3
8.8 ( 1.0a 7.9 ( 1.0a -
11.3 ( 1.0a 14.4 ( 1.0a -
7.1 ( 2.0b 7.2 ( 2.0b
-185.4 ( 5.0a -131.8 ( 5.0a -103.0 ( 5.0b -82.4 ( 5.0b
12.3 ( 0.1b 12.2 ( 0.1b
-41.6 ( 0.5b -41.3 ( 0.5b
-41.2 ( 4 -20.6 ( 4 -10.3 ( 8 -6.2 ( 8
a ST and ET values calculated by method 2, which does not yield cac values (see Materials and Methods). b Midpoint of the transition (sigmoidal fit of the enthalpogram); this data treatment (method 1, experimental) does not yield ST and ET values. c Average value for 0 < [AMPS] < 18 mmol L-1 (entire enthalpogram).
Figure 3. Dilution enthalpograms for solutions of (C18)2PAMPS (20 g L-1, 25 °C) in solutions of different ionic strengths. The x axis (common for all plots) is the concentration of polymer (AMPS units) in the sample cell.
Effect of Temperature on the Association of (C18)2PAMPS in 0.2 M NaCl. Titrations of (C18)2-PAMPS were performed in 0.2 M NaCl at four different temperatures from 288 to 308 K (Figure 4). Curves recorded at 293 and 298 K retain a sigmoidal feature, but titrations performed at 288 and 308 K generated enthalpograms that could not be fitted accurately by a sigmoidal curve. These data were analyzed by the second method described in Materials and Methods. Overall, as the temperature increases, the demicellization becomes progressively less exothermic (Table 2). The dilution of PAMPS also decreases in exothermicity with increasing temperature (Table 2). The heat capacity of the micellization process, ∆Cp(mic), can be estimated from the slope of a plot of ∆Hmic (-∆Hdemic) as a function of temperature [-216 J K-1 (mol of polymer)-1].16 In the case of surfactants, ∆Cp(mic) has been found to be a linear function of the hydrophobic surface area of amphiphiles that become excluded from water through micellization.17,18 For an unbranched saturated hydrocarbon chain, such as an octadecyl chain, this (16) The heat capacity per mole of polymer was calculated assuming that each polymer chain contains, on average, 90 AMPS units. This degree of polymerization was determined by end-group analysis based on 1H NMR data.
Figure 4. Dilution enthalpograms for solutions of (C18)2PAMPS (20 g L-1, 0.2 M NaCl) in solutions for titrations carried out at different temperatures. The x axis (common for all plots) is the concentration of polymer (AMPS units) in the sample cell.
hydrophobic surface can be expressed by the empirical relationship ∆Cp(mic) ) -33nH (J mol-1 K-1), where nH is the number of hydrogen atoms that are part of this surface.3 The contribution to ∆Cp(mic) from changes in the hydration of the PAMPS chains upon micellization is difficult to assess on the basis of models derived for the micellization of surfactants, even though only the AMPS units in close proximity to the end-group are expected to experience significant changes in hydration. The large negative value of ∆Cp(mic) implies that ∆Hmic decreases rapidly with increasing temperature and becomes zero and then negative above a certain temperature. This temperature, extrapolated from the plot of ∆Hmic with temperature, is estimated to have a value of ∼343 K. A similar decrease in the absolute value of the enthalpy of micellization was also observed for endcapped poly(acrylates) (∆Hmic ) 0 at 45 °C, Mn ) 3000).8 The Case of Chol-PAMPS. This polymer was prepared by free-radical polymerization using a cholesterylsubstituted initiator,10 rather than the di(n-octadecyl)containing initiator used to prepare (C18)2-PAMPS.9 Unlike (17) Gill, S. J.; Wads, I. Proc. Natl. Acad. Sci. U.S.A. 1976, 73, 2955. (18) Jolicoeur, C.; Philip, P. R. Can. J. Chem. 1974, 52, 1834.
4420
Langmuir, Vol. 17, No. 14, 2001
Raju et al.
Table 2. Thermodynamic Data for the Demicellization of (C18)2-PAMPS and for the Dilution of PAMPS as a Function of Temperature ([NaCl] ) 0.2 M) (C18)2-PAMPS
PAMPS
temp (K)
STa (mmol of AMPS L-1)
ETa (mmol of AMPS L-1)
cacb (mmol of AMPS L-1)
∆Hdemic [J (mol of AMPS)-1]
∆Gdemic [kJ (mol of AMPS)-1]
∆Sdemic [eu (mol of AMPS)-1]
∆Hdilc (J mol-1)
288 293 298 308
5.0 ( 1.0a 9.6 ( 0.1a
10.3 ( 1.0a 12.4 ( 1.0a
5.6 ( 0.2a 7.1 ( 0.2a -
-123.4 ( 5.0a -92.7 ( 5.0b -103.0 ( 5.0b -74.2 ( 5.0a
12.6 ( 0.1 12.3 ( 0.1 -
-43.5 ( 0.5 -41.6 ( 0.5 -
-20.6 ( 4 -24.7 ( 4 -10.3 ( 8 -8.2 ( 8
a Calculated by method 2 (see Materials and Methods). b Midpoint of the transition determined from the sigmoidal fit of the enthalpogram (method 1, Materials and Methods). c Average value for 0 < [AMPS] < 18 mmol L-1 (entire enthalpogram).
Figure 5. Titration of Chol-PAMPS (25 °C, 0.1 M NaCl): (a) polymer concentration ) 5 g L-1; (b) polymer concentration ) 20 g L-1. The top portion of each section represents the calorimetric traces (heat flow vs time). The bottom part of each section depicts the corresponding enthalpograms [reaction enthalpy vs concentration of polymer (AMPS units) in the sample cell].
the samples of (C18)2-PAMPS examined here, the cholesteryl end-substituted PAMPS samples contained a small amount of polymers carrying hydrophobic groups at both chain ends.10 Dynamic light scattering measurements carried out with solutions of Chol-PAMPS of increasing concentration indicated that the polymer forms distinct multipolymeric micelles in solutions ranging in concentration from 0.5 to 20 g L-1 (0. 1 M NaCl). The aggregates range in average diameter from 50 nm (1-5 g L-1) to ∼105 nm (20 g L-1). Presumably, at low polymer concentrations, the disubstituted macromolecules are incorporated in single micelles formed by the mono-endcapped polymers, whereas at higher concentrations, they serve as links between polymeric micelles, creating a network. Aware of these complications, we carried out initial titrations of a Chol-PAMPS solution of 5 g L-1, a concentration regime in which no intermicellar network can be detected by dynamic light scattering. Under these conditions, a nonsigmoidal enthalpogram featuring breaks at ST ≈ 1.0 mmol of AMPS L-1 and ET ≈ 1.9 mmol of AMPS L-1 was obtained and ascribed to the processes of
dilution and demicellization of multipolymeric micelles [∆Hdemic ≈ -50 J (mol of AMPS)-1] (Figure 5a). However, dilution of a 20 g L-1 Chol-PAMPS solution generated a complex enthalpolgram (Figure 5b). This result is consistent with the presence of a network of interpolymeric micelles. It is unrealistic to draw any further conclusions from the titration curve, presented here to highlight the limitations of ITC and to point out that, given its inherent sensitivity, ITC might, in fact, be an excellent diagnostic tool for detecting inhomogeneities in polymer samples. The Case of PAMS-Dod20. Finally, we performed titrations of a random copolymer of AMPS and n-dodecylmethacrylamide, PAMPS-Dod20, which contains approximately 20 mol % of hydrophobic groups. The characterization and solution properties of this polymer have been described in detail elsewhere.11 In aqueous NaCl solution, this copolymer adopts a collapsed conformation as a result of the intrapolymeric association of the hydrophobic groups. These unimers, in turn, can form dimers or trimers via interpolymeric hydrophobic association. Interpolymeric association is
Strengths and Limitations of ITC
Langmuir, Vol. 17, No. 14, 2001 4421
to the dilution of a concentrated solution of PAMPS-Dod20 (20 g L-1 in NaCl) presented a sigmoidal trend (Figure 6), with an aggregation concentration of ∼7.8 mmol of AMPS L-1 and an enthalpy of demicellization of approximately -70 J (mol of AMPS)-1. The demicellization process spans a polymer concentration range (2.3-18 mmol of AMPS) that is wider than the range over which the demicellization of (C18)2-PAMPS takes place (Tables 1 and 2). In conclusion, we note that, if one were to titrate a solution of kinetically frozen polymeric micelles, the enthalpogram would represent only the heat of dilution of the micelles, which is expected to be independent of the polymer concentration in the sample cell. There might be cases, however, in which micellar systems that appear to be in equilibrium on the basis of the experimental enthalpogram actually consist of locally kinetically frozen systems. In such cases, the enthalpogram reflects only the equilibrium part of the process. Amphiphilic polyelectrolytes randomly grafted with hydrophobic groups can form micelle-like aggregates via intra- and interpolymeric hydrophobic associations. PAMPS-Dod20 represents a case in point. For this polyelectrolyte, therefore, ITC will not detect the dissociation of unimers; rather, it will report only on the dilution of the intrapolymeric micelles and on the dissociation of interpolymeric aggregates, assuming that the latter is an equilibrium process and that reequilibration occurs within the time frame of the measurement. Figure 6. Titration of a solution of PAMPS-Dod20 (20 g L-1, 25 °C, 0.2 M NaCl). The top portion represents the calorimetric trace (heat flow vs time). The bottom part depicts the corresponding enthalpogram [reaction enthalpy vs concentration of polymer (AMPS units) in the sample cell].
more favorable in highly concentrated solutions, whereas in the low concentration domain, only intrapolymeric association takes place. The enthalpogram corresponding
Acknowledgment. This work was supported by a grant from the Natural Sciences and Engineering Research Council of Canada to F.M.W. The polymers were prepared by Dr. M. Mizusaki (Osaka University), Dr. S. Yusa (Osaka University), and Mr. H. Yamamoto (Osaka University), who are gratefully acknowledged. LA001554I
