Strong Intermolecular Association between Short Poly(ethacrylic acid

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J. Phys. Chem. B 2009, 113, 2300–2309

Strong Intermolecular Association between Short Poly(ethacrylic acid) Chains in Aqueous Solutions Sebastijan Peljhan,† Ema Zˇagar,‡ Janez Cerkovnik,† and Ksenija Kogej*,† Department of Chemistry and Biochemistry, Faculty of Chemistry and Chemical Technology, UniVersity of Ljubljana, AsˇkercˇeVa 5, P.O. Box 537, SI-1001 Ljubljana, SloVenia, and National Institute of Chemistry SloVenia, HajdrihoVa 19, SI-1001 Ljubljana, SloVenia ReceiVed: July 17, 2008; ReVised Manuscript ReceiVed: January 5, 2009

The behavior of poly(R-ethylacrylic acid), PEA, was studied in aqueous solutions at 25 °C and at a polymer concentration 0.01 mol carboxyl groups/L by conductometric, potentiometric, calorimetric, and fluorescence measurements. PEA chains were characterized for molar mass, eventual crystallinity, and tacticity. The complete thermodynamic characterization of the transition of PEA chains from a contracted to an expanded form is reported. The results show that short PEA chains are strongly associated in water. Intermolecular association is effective in the whole range of degrees of ionization of carboxyl groups and was ascribed to the formation of hydrogen bonds between un-ionized groups with a favorable contribution of the hydrophobic ethyl side groups. Molecular modeling was performed on short PEA chains, either purely isotactic or syndiotactic ones. The optimized models resulted in a “bent” or “curved” conformation for both stereoisomers and confirmed the presence of intermolecular hydrogen bonds between predominately isotactic chains. 1. Introduction The behavior of vinyl-based poly(carboxylic acids), PCAs, in aqueous solutions depends on the nature of substituent R on the R-C atom (Scheme 1). By changing R, the affinity of PCAs for water is varied. This brings around several interesting properties that form the basis for applications of these compounds as pH-responsive materials, e.g., in drug delivery systems.1 Thus, the simplest analogue, poly(acrylic acid), PAA (R ) H), is considered as a hydrophilic PCA characterized by a continuous expansion of the chain upon ionization of carboxyl groups. On the other hand, poly(methacrylic acid), PMA (R ) CH3), already shows markedly different properties in aqueous solutions from those of PAA, which can be explained by taking into account the hydrophobic character of the methyl group.2 The most significant of these properties is the occurrence of a conformational transition in the PMA case that takes place when the chain is gradually charged by increasing the solution pH and concurrently the ionization of carboxyl groups. The conformation of the PMA chain changes from a more contracted form at low pH to a more extended one at high pH in a cooperative manner. This process depends strongly on chain microstructure, i.e., on its tacticity. The relatively few studies3-7 of solution behavior of the isotactic form of PMA, i-PMA, indicate that this stereoisomer is not soluble in water at low degrees of ionization, R, typically below R ≈ 0.2.3,6,7 This is in contrast with its atactic form, a-PMA, which is soluble in the entire R region. i-PMA also exhibits an irreversible change in conformation that is most evidently displayed by a hysteresis loop in titration curves.4 The next PCA in line is poly(ethacrylic acid), PEA (R ) C2H5), which is also believed to experience an analogous conformational change in water as PMA. This conclusion was * Corresponding author. Tel.: +(386-1)-2419-412. Fax: +(386-1)-2419425. E-mail: [email protected]. † University of Ljubljana. ‡ National Institute of Chemistry Slovenia.

SCHEME 1: Monomer Unit of Poly(carboxylic acids): R ) H (Poly(acrylic acid), PAA), R ) CH3 (Poly(methacrylic acid), PMA), and R ) C2H5 (Poly(ethacrylic acid), PEA)

likewise reached on the basis of titration behavior of PEA.8-10 However, it was shown in a recent small-angle X-ray scattering (SAXS) study11 that the structure of the contracted forms and the extended coils of PEA and a-PMA are different. (Note that the atactic form of PMA is the most often studied one and practically always serves as the basis for comparison with other PCAs, although a more appropriate comparison would be with the PMA form that, similarly to PEA, does not dissolve in water at R ) 0, i.e., with i-PMA.) These differences were attributed to a greater size and larger hydrophobicity of the ethyl side group in comparison with the methyl one. The PEA form at low R was approximated with a swollen gel network, whereas that at high R by a wormlike chain.11 This is an indication that PEA chains may be subjected to significant intermolecular association, as it was argued6 and also experimentally demonstrated for i-PMA.7 All these studies indicate that the precise nature of the contracted forms and the mechanism of the conformational transition are not fully understood, in particular for PCAs like PEA and i-PMA that do not dissolve in water at R ) 0. The rigidity of polymer chains, which is strongly influenced by chain microstructure7,12,13 and by the nature of substituents on the polymer backbone, plays an important role here. Thus, the term “compact form”1,2,14 that is often used to describe the state of hydrophobic PCAs in water at low R is herein replaced by a more universal one, “contracted form”.

10.1021/jp806312u CCC: $40.75  2009 American Chemical Society Published on Web 02/04/2009

Association between Short Poly(ethacrylic acid) Chains Various forces have to be considered in the interpretation of solution behavior of hydrophobic PCAs, among them intra- and intermolecular hydrogen bonding, van der Waals interactions, and so-called “hydrophobic interactions”15-17 associated with the hydrophobic side groups. Hydrogen bonding is an important driving force for complex formation between macromolecules.18 It may display a high degree of cooperativity and thus lead to rather strong interaction. In addition, it has been shown19 that electron-withdrawing or electron-donating capacity of the substituent on aliphatic or aromatic carboxylic acids has a strong effect on the hydrogen-bond energy. The presence of an electron-donating group, such as methyl or ethyl, increases the hydrogen-bond energy and simultaneously contributes to a less acidic compound. This effect is dramatically weakened if the substituent is bound to a position that is farther from carboxyl group.19 It may be expected that compounds with multiple acidic sites and also multiple aliphatic electron-donating groups (this is the case with polymeric carboxylic acids such as PMA or PEA) display an even more pronounced effect on the energy of the hydrogen bond than the monomer analogues. In addition, solvent effects may also be rather complicated and specific. Hirose et al.20 have shown that the dissociation of carboxyl groups may be depressed because of the decrease of the dielectric constant in the vicinity of the main chain and that the dissociation behavior of polyelectrolytes is determined more strongly by the local carboxyl group distribution than by the overall charge density. Another unambiguous demonstration of a strong effect of local chain conformation on solution properties was given recently by Jerman et al.7 who studied ion-binding and volume properties of chemically identical polyelectrolytes, i.e., of i-PMA and a-PMA, that differed only in their stereoregular composition. With i-PMA, for example, stereoregularity is the basis for a helical chain conformation that brings around higher polyion charge densities and thus stronger counterion binding. We may conclude that hydrogen-bonding equilibria and hydrophobic interactions play an important role in solution behavior of hydrophobic PCAs and should be taken into account in interpretation of experimental findings. A few reports on PEA that can be found in the literature deal mainly with its potentiometric titration behavior.8-10 The already mentioned study of Muroga et al.11 presents a more thorough investigation of PEA chain conformations by SAXS. In addition to these, several studies of Tirrell et al.21-23 describe the use of PEA in tuning the response of the pH sensitive membranes. The same group reports also on the synthesis of PEA with a well-defined microstructure/tacticity.24 Otherwise, studies of solution behavior of PEA are scarce. The present paper is devoted to a thorough investigation of properties of PEA in aqueous solution and to the identification of the underlying reasons for the clearly expressed associative behavior between PEA chains. 2. Experimental Section 2.1. Materials. Poly(R-ethylacrylic acid), shortly poly(ethacrylic acid), PEA, was obtained from Polymer Source Inc. (sample no. P3488B-EtAA) and was prepared by free radical polymerization from R-ethylacrylic acid, which gave the desired polyacid directly. The polymer was purified by dialysis through dialysis membranes (Sigma, cutoff 2000 g/mol). NaOH and HCl were Titrisol solutions from Merck and their precise concentration was determined by usual standardization procedures. All other compounds (pyrene, Aldrich, optical grade; 1,4-dioxane, Merck; nitrobenzen-d5, Aldrich; D2O, Aldrich; CDCl3, Aldrich) were used as received.

J. Phys. Chem. B, Vol. 113, No. 8, 2009 2301 For the determination of tacticity, the purified PEA was transformed into the ester form, poly(methyl R-ethylacrylate), PMEA, with diazomethane by the procedure reported in the literature.25 The tacticity of the resulting PMEA was determined from the ester methyl signals in the 1H NMR spectrum of a PMEA solution in nitrobenzene-d5.24 2.2. Preparation of Solutions. The sample of PEA used in our study did not dissolve in water at degree of neutralization, RN, equal to 0. Note that RN differs from degree of ionization R; the difference is important at low RN value, but can be ignored at RN above around 0.2. The relation between R and RN will be reported in Results and Discussion. Upon addition of NaOH, the suspension of PEA with a concentration 0.01 mol COOH groups/L gradually started to clear up at pH above 6.5. The turbidity was checked by naked eye and also by a red laser beam. Above pH ≈ 7.5, the solution was almost clear as indicated by a very weak trace of the laser beam. Completely clear solutions were only obtained above pH ≈ 8.5-9 (no trace of the laser beam). This pH value almost corresponds to the equivalent point in the titration curve of PEA. Upon addition of HCl to the dissolved ionized PEA (i.e., the sodium salt form, poly(sodium ethacrylate), NaPEA), precipitation did not start until pH was below 5.2, which corresponds to RN around 0.1. Even below pH ) 5.2, there was no phase separation of insoluble polymer within a period of several days. Such solubility behavior of PEA is similar to the one reported in the literature.9 In ref 9 the authors argued that the lack of solubility is due to a presumably high molar mass of the studied sample (the precise value of the molar mass was not reported9). This is likely not the reason in our case (see the molar mass value reported below). In view of these solubility characteristics, stable PEA solutions were prepared in the direction of decreasing RN. A calculated amount of NaOH was added to the suspension of PEA to achieve RN above 0.6 (pH above 7.5). The solution was mixed overnight in order to ensure complete dissolution of the polymer and then used for further measurements, in which RN was decreased by the addition of HCl. Some experiments (e.g., conductometric titrations) were only performed in the direction of increasing RN, starting from a thoroughly suspended PEA in water at RN ) 0. The concentration of PEA is expressed in moles of all carboxyl groups on the polymer, which was calculated from the weighed amount of the dry sample. This concentration will be termed nominal, cnom p , as distinguished from the concentration of carboxyl groups, cp, that are accessible for reaction or interaction with other species. The necessity for the use of these two concentration units will be demonstrated in the Results and Discussion. All measurements with PEA were performed at cnom p ) 0.01 mol COOH/L unless otherwise specified. 2.3. Methods. Elemental Analysis. The purified PEA sample was characterized by elemental analysis. The calculated composition for the monomer unit of PEA (-CH2-C(C2H5)COOH) is C, 59.99%; H, 8.05% and the one found is C, 59.55%; H, 8.36%. Wide-angle X-ray diffraction (WAXD). WAXD measurements were performed on a PANalytical X’pert PRO MPD diffractometer with a Cu KR wavelength (1.54 Å). Measurements were performed in a reflection mode and diffraction was measured at an angle 2θ ranging between 2° and 65° in steps of 0.034°. The integration time was 100 s. Divergence and antiscatter slits were 10 mm, and the primary and the secondary Soller slits were 0.02 radians. The WAXD diffraction pattern of solid PEA is shown in Figure 1.

2302 J. Phys. Chem. B, Vol. 113, No. 8, 2009

Figure 1. Wide-angle X-ray diffraction pattern of solid PEA.

Size Exclusion Chromatography (SEC). Molar mass averages and molar mass distribution were determined by SEC coupled to a multiangle light scattering photometer (SEC-MALS). Details of the SEC-MALS measurements are provided in Supporting Information. Weight average molar mass (Mw) and polydispersity (PI) of un-ionized PEA (RN ) 0) were determined at two different PEA concentrations (cpnom ) 0.01 and 0.001 mol COOH/L) using 0.1 M solution of LiBr in N,Ndimethylacetamide (DMAc) as the solvent and as the eluent under the following conditions: (a) after 1 and 4 days of dissolution time at room temperature and (b) after heating the sample solution to 60 °C and cooling it down. Furthermore, Mw and PI of PEA with RN ) 1 (pH ≈ 9) were determined also in pure H2O and in 0.1 M NaCl/H2O. The calculation of Mw from MALS requires a sample-specific refractive index increment, dn/dc, which was determined from the refractive index response assuming a sample mass recovery from the column of 100%. The dn/dc value for PEA was dn/dc ) 0.089 mL/g (in 0.1 M LiBr/DMAc) and 0.170 mL/g (in 0.1 M NaCl/H2O, pH ) 9). NMR Spectroscopy. 1H and 13C NMR spectra were recorded on NMR spectrometers Bruker Advance DPX 300 MHz and Varian Unity Inova-600. Tetramethylsilane was used as the internal standard. The following solvents and temperatures were employed: (a) for PEA: D2O, 30 °C, RN > 0.5 (a small amount of solid NaOH was added in order to dissolve the polymer; (b) for PMEA: CDCl3, 30 °C, and nitrobenzene-d5, temperatures in the range from 120 to 170 °C.24 Spectra in nitrobenzene-d5 at elevated temperatures were recorded in a 600 MHz NMR spectrometer. The NMR results for PEA in D2O (see 13C NMR spectra in Figure S1a and Figure S1b and APT spectrum in Figure S1c, Supporting Information) have excluded the presence of ester or anhydride groups in the sample. This result, which is in accordance with the one obtained from elemental analysis, shows that we are dealing with a purely acid form of the polymer. From the 1H NMR spectrum of methylated PEA (i.e., PMEA) in CDCl3 (see Figure S1d, Supporting Information) the ratio of integrals of peaks at 3.563 ppm (protons in the ester group) and at 0.861 ppm (the CH3 protons in the ethyl side group) was evaluated. It is equal to 0.8:1 instead of 1:1 as would be expected from the stoichiometric formula of a completely methylated PEA sample. This indicates that only approximately 80% of COOH groups were transformed into COOCH3 ones in the reaction with diazomethane. The same result was obtained by repeating the methylation procedure and will be discussed in Results and Discussion. Conductometric Titrations. Measurements of specific conductance, κ, were performed with a Metrohm 712 conductivity meter using a Metrohm cell with a cell constant 0.091 cm-1 in PEA solutions in water at 25 and at 60 °C and in water-dioxane mixtures at 25 °C. The dioxane content was 50, 75, and 100 vol %. For comparison, titrations in water were performed also with PAA (K & K Laboratories, Inc., Plainview, NY), a-PMA,

Peljhan et al. and i-PMA. The a-PMA and i-PMA samples were those characterized earlier.7,25 i-PMA was chosen because it is, similarly to PEA, not soluble in water at RN ) 0.3,6,7 The nominal concentration of polymer solutions for conductometric titrations was in all cases cpnom ) 0.01 mol COOH/L and the starting volume was 12 mL. In the case of PAA and a-PMA, stock solution with RN ) 0 and known concentration was diluted with water in order to obtain this concentration, whereas in the case of i-PMA and PEA, solid samples were weighed and an appropriate amount of solvent was added to the titration vessel so that the final nominal concentration of COOH groups was 0.01 mol/L. The suspensions of i-PMA and PEA were mixed with a magnetic stirrer overnight. Potentiometric Titrations. Potentiometric titrations were performed at 25 °C with a pH meter Iskra MA 5740 by using a combined electrode from Mettler-Toledo (InLab 406). The electrode was calibrated with two aqueous buffer solutions having pH values 6.865 and 9.18 at 25 °C. Solid PEA was weighed and an appropriate amount of degassed water (the starting volume of solution was the same as for conductometric titrations) was added to the titration vessel so that cpnom ) 0.01 mol COOH/L. The suspension was mixed overnight. Titrations were carried out under an atmosphere of nitrogen. During titration of PEA and i-PMA solutions, the nitrogen blanket was maintained over the sample to avoid foaming, which was taking place when RN approached 0. Standardized aqueous solutions of NaOH (in the forward titration path; increasing RN) and HCl (in the backward titration path; decreasing RN) with concentrations 0.1 mol/L were added with a microsyringe buret. Fluorescence Spectroscopy. Pyrene was used as the external fluorescence probe to monitor eventual conformational or other changes in polarity of microenvironment in PEA solutions. The fluorescence emission spectra of pyrene were recorded on a Perkin-Elmer model LS-50 luminescence spectrometer at 25 °C. All measurements were performed both in the direction of increasing (starting from a suspension of solid PEA in water) and decreasing RN (starting from a completely dissolved PEA). Each solution was prepared separately in a volumetric flask by weighing solid PEA and adding a calculated volume of water and standardized NaOH (or HCl) solution to get a desired cp and RN values. Suspensions were mixed overnight before the spectra were recorded. Isothermal Titration Calorimetry (ITC). Calorimetric measurements were made at 25 °C by using a TAM 2277 calorimeter (Thermometric AB, Sweden). Because of the insolubility of PEA at RN ) 0, the ionization enthalpies of PEA were determined as protonation enthalpies. Aqueous solution of PEA with cpnom ) 0.01 mol COOH/L and initial degree of neutralization RN,in > 0.5 was prepared with degassed water by adding a calculated amount of standardized NaOH solution and titrated in the calorimeter with a standardized aqueous HCl solution. The negative value of the measured heat effects, corrected for the enthalpies of dilution of both PEA and HCl, are equal to the ionization enthalpy, ∆Hi. The heats of dilution of HCl and PEA were measured in a separate experiment and were found to be negligible in comparison with heats of protonation. Molecular Modeling. Low energy conformations accessible to the oligomer chains of PEA were investigated by using quantum mechanical semiempirical molecular orbital (MO) calculations. All details on molecular modeling are described in ref 13. The calculations were performed in vacuo and in an implicit solvent with a dielectric constant 78.4 for one chain

Association between Short Poly(ethacrylic acid) Chains

J. Phys. Chem. B, Vol. 113, No. 8, 2009 2303

Figure 2. 600 MHz 1H NMR spectrum of PMEA in nitrobenzene-d5 at 170 °C in the region of the ester methyl signals.

with 12 or 24 monomer units and for two chains each with 12 monomer units. 3. Results and Discussion 3.1. Basic Characterization of PEA. Elemental analysis has resulted in a correct composition of the polymer and has, in accordance with NMR, excluded the presence of ester or anhydride type of bonds in the sample. The WAXD pattern of PEA (Figure 1) is characterized by a single broad maximum at around 2θ ) 12.5°. By comparing this result with the one in the case of unstructuralized i-PMA6 (in this case the broad peak was found at 2θ ) 15.1°) it was concluded that solid PEA is predominately amorphous. The difference in 2θ for PEA and i-PMA can be attributed to a larger size of ethyl side groups in comparison with the methyl ones. SEC-MALS measurements indicated that PEA chains are rather short with Mw ) 3600 g/mol (weight-average degree of polymerization around 36) and a reasonably low polydispersity, PI ) 1.5. In solvents with added salts, the radius of gyration (Rg) values were on the limit of the instrument sensitivity, which is around 10 nm; only a rough estimate of Rg could be made and this was Rg ≈ 7 nm. For comparison, the length of a fully stretched vinyl chain with 36 units is around 9 nm. Molar mass averages were independent of solution concentration, dissolution time, the kind of solvent used, and previous heating of the sample solution. These results indicate that PEA was dissolved in solvents with added simple salts on a molecular level. On the contrary, the molar mass average and size of the ionized PEA (RN ≈ 1) determined in pure water were considerably larger and molar mass distribution broader (Mw in the range of 105 g mol-1, Rg ≈ 80 nm), indicating that ionized PEA in salt-free aqueous solutions is intermolecularly associated to a high extent. The tacticity of the polymer was determined from the 1H NMR spectrum of PMEA in nitrobenzene-d5 (Figure 2) from the peaks in the range 3.8-4.0 ppm that correspond to the ester methyl signals in different triads.24,26 The peak at the highest field (∼3.7 ppm) is assigned to syndiotactic and the one at the lowest field (3.75-3.77 ppm) to isotactic triads. The triad tacticities are usually determined by integration of these peaks.24 Since the peaks are not well resolved (neither at 120 °C nor at 170 °C, which is the temperature reported in Figure 2) only an approximate triad composition could be calculated from their heights. It is to be noted that the distance between peaks slightly decreases with increasing temperature, whereas the height ratio

Figure 3. Conductometric titration curves of aqueous PEA at 25 and 60 °C, and of aqueous PAA, a-PMA, and i-PMA at 25 °C. The nominal concentration of carboxyl groups is in all cases cnom ) 0.01 p mol COOH/L.

between them remains approximately the same. The PEA chain contains around 35% of syndiotactic, 38% of atactic, and 27% of isotactic triads. This composition applies to the 80% of COOH groups that were esterified (see NMR results reported in Experimental Section and in Supporting Information) and is typical for atactic polymers. The remaining 20% have an unknown stereoregular composition. 3.2. Conductometric Titrations. Conductometric titration curves of PEA (cpnom ) 0.01 mol COOH/L) in water at 25 and 60 °C and in various water-dioxane mixtures at 25 °C are shown in Figures 3 and 4, respectively. In Figure 3, titration curves that were recorded for PAA, a-PMA, and i-PMA solutions with the same nominal concentration of carboxyl ) 0.01 mol COOH/L) in water at 25 °C are plotted groups (cnom p for comparison. The titration end points were in all cases determined by extrapolating two linear portions of the κ vs VNaOH curves as indicated in the figures. The end points in the case of PAA, a-PMA, and i-PMA are found at the correct (calculated) value of VNaOH (which is 1.22 mL for the particular concentration of NaOH solution used in titrations; see the vertical dashed line), whereas in the case of PEA, the end points appear at a considerably lower VNaOH value: VNaOH ) 0.95 and 0.87 mL (resulting in cp ) 7.787 and 7.13 × 10-3 mol COOH/L) at 25 and at 60 °C, respectively. Clearly, the result for the concentration of COOH groups on the PEA chain is too low in and heating does not present any improvecomparison with cnom p ment. It even has a negative effect, i.e., VNaOH (or cp) is

2304 J. Phys. Chem. B, Vol. 113, No. 8, 2009

Figure 4. Conductometric titration curves of PEA in water, in dioxane-water mixtures with 50 and 75 vol % of dioxane, and in 100% dioxane, all at 25 °C. The nominal concentration of carboxyl groups is in all cases cnom ) 0.01 mol COOH/L. p

significantly lower at 60 °C than it is at 25 °C. The difference is beyond experimental uncertainty. The above results indicate that all COOH groups on the PEA chain are not available for the neutralization reaction with NaOH, whereas in the case of PAA and PMA they are. An explanation may be that PEA chains are very strongly associated, by which carboxyl groups on the polymer are effectively blocked. This could take place through hydrogen bonding between un-ionized carboxyl groups of different chains, leaving the hydrophobic ethyl groups exposed to the aqueous environment. Consequently, we have considered adding dioxane to water because dioxane is known to have a strong tendency for the formation of H-bonds both with itself and with other compounds, and may thus be able to destroy intermolecular H-bonds between PEA chains. It was for example demonstrated that a 1:1 mixture of water and dioxane dissolves the hydrophobic form of i-PMA at RN ) 0,27 which is believed to be associated via hydrogen bonds.6 Indeed, all water-dioxane mixtures (similarly as pure dioxane) proved to be good solvents also for our PEA sample. PEA remained dissolved in waterdioxane mixtures up to RN > 1, except in pure dioxane where it gradually started to form a turbid solution at RN ≈ 0.55 due to the increasingly ionic character of the polymer. Yet, it can be seen from titration curves in water-dioxane mixtures (Figure 4) that dioxane has practically no effect on the titration end points: VNaOH is around 0.95 mL both in 50 and in 75% dioxane (the same as in water at 25 °C; Figure 3). Although dioxane promotes dissolution of PEA at RN ) 0, it is evidently not able to disintegrate intermolecular aggregates. This is a sound argument in favor of strong intermolecular H-bonds proposed above. The equivalent volume of NaOH in 100% dioxane is higher than 1.22 mL. However, titration in 100% dioxane may be open to discussion because of a high complexity of the system, which includes the formation of a 3-1 complex between solvent molecules (note that water is being gradually introduced into dioxane in the course of titration with aqueous NaOH) and possible preferential solvation of different functional groups on PEA by dioxane or by this complex. Such preferential solvation was observed in the case of PMA.28 It can be concluded that results of conductometric titrations in water-dioxane mixtures agree with the presumption on very strong intermolecular association of PEA chains through hydrogen bonding, which makes a part of carboxyl groups unavailable for neutralization reaction with hydroxyl ions. Extensive intermolecular association (possibly network formation11) could be deduced already from Mw value determined in

Peljhan et al. salt free aqueous solution at RN ) 1. By taking into account only the results obtained from conductometric titrations in water at 25 °C, it was concluded that approximately 22% of COOH groups on the PEA chain do not participate in the neutralization reaction with NaOH, i.e., cp ) 0.78cpnom, where cp denotes the actual concentration of active/accessible COOH groups. This result is in surprising agreement with the one derived from NMR spectroscopy where it was indicated that only 80% of COOH groups were chemically modified by diazomethane. It should be stressed that while hydrogen bonds usually begin to dissociate at higher temperatures, hydrophobic interactions increase in strength with increasing temperature. Therefore, the result for accessible COOH groups at 60 °C suggests that the effect of hydrophobic interactions significantly reinforces upon heating and this even leads to a somewhat lower free carboxyl concentration at higher temperature. Because a similar demonstration of strong intermolecular association in the ionized state is absent in the PAA or PMA case, one of the conclusions may be that the presence of hydrophobic ethyl groups enhances intermolecular association through H-bond formation. An analogous effect of increased hydrophobicity of substituent R (Scheme 1) on the energy of H-bonds was recently found for monomeric carboxylic acids.19 Furthermore, suitable microstructure (tacticity) of the polymer chain could be another reason for such effective intermolecular association. Highly isotactic PMA, for example, is believed to be strongly associated through H-bonding.6,7 The stereoregular composition of our PEA sample (see above) applies only to the esterified (i.e., accessible) carboxyl groups. If we tentatively propose that all the unesterified groups are in an isotactic arrangement, the stereoregular composition of PEA would be 30% syndiotactic, 28% of atactic, and 42% of isotactic triads. In the case that the isotactic segments are sufficiently long, the assumption on effective H-bond formation becomes plausible. Since PEA chains are as well rather rigid due to the presence of bulky ethyl groups (the rigidity may be inferred from the Rg value, which is close to the length of a fully stretched PEA chain) and with low polydispersity, a very effective packing/association of chains through a “zipper-like” formation of H-bonds between COOH groups in the isotactic arrangement can be visualized. These assumptions were verified by molecular modeling. In the following, we report on calorimetric measurements of the enthalpy of ionization, ∆Hi, of PEA and on potentiometric measurements that aimed at the determination of the standard free energy, ∆Gtr°, and enthalpy, ∆Htr, change associated with the so-called conformational transition of the chain. These are the most relevant thermodynamic data for the process associated with the charging of the PEA chain. It has been shown that the enthalpy of ionization and the pKa of the simplest polycarboxylic acid PAA vary smoothly with increasing R,29,30 whereas in the case of PMA the course of the ∆Hi and the pKa vs R curves display a conformational transition of the chain.2,3,5,29-33 Analogously, some authors suggest a similar conformational transition in the case of PEA on the basis of potentiometric titration curves.8-10 3.3. Thermodynamic Characterization. 3.3.1. Potentiometric Titrations. An example of forward and backward titration curves (pH vs RNnom, where RNnom ) cNaOH/cpnom) for PEA in water is plotted in Figure 5a. The first titration curve with NaOH (solid circles) corresponds to the titration started from solid PEA suspended in water (see Experimental Section), followed by a back-titration with HCl (solid triangles; these two curves represent the first titration cycle). The large difference between forward and backward titration curves in the first titration cycle

Association between Short Poly(ethacrylic acid) Chains

J. Phys. Chem. B, Vol. 113, No. 8, 2009 2305 Titration curves of the type in Figure 5a resemble those for PMA and other polyelectrolytes with a conformational transition2,3,5,29-33 and were used to calculate the standard free energy change of the transition, ∆Gtr°, of the chain from an uncharged contracted form (state “a”) to an uncharged random coil (state “b”).33-36 The curves were treated in terms of the negative logarithm of the apparent dissociation constant, pKa, defined as

pKa ≡ pH + log

Figure 5. (a) Forward (circles) and backward (triangles) titration curves of PEA (cnom ) 0.01 mol COOH/L) in water; solid symbols (b, 2): p (1) titration cycle started from solid PEA; open symbols (O, 4): (2) titration cycle started from an already dissolved PEA; (b) an example of extrapolation of a titration curve (presented as pKa vs R for R < 0.6; see text) from the region of R values larger than 0.3 to R ) 0.

is attributed to the dissolution of PEA upon charging. The second titration cycle (open symbols) was started from an already dissolved polymer at pH ≈ 10 (achieved by adding NaOH), by first titrating it with HCl toward R ) 0 (open triangles) and then titrating it with NaOH (open circles). Clearly, the back and the forward titration curves in this second titration cycle practically coincide. A small difference arises from the fact that salt (NaCl) was gradually formed during the backward titration (the final NaCl concentration, cNaCl, after the second cycle was below 0.02 M). The dependence of titration curves on cNaCl was checked in a separate experiment by performing potentiometric titrations in 0.01, 0.05, and 0.1 M NaCl (see Figure S2 in Supporting Information). It can be seen in Figure S2 that the presence of salt decreases the solution pH. However, the effect of NaCl on the shape of titration curves in the pH region below 6, from which the ∆Gtr° is evaluated (see below), is small. In agreement with this, Dubin and Strauss found out that free enthalpy change of the conformational transition for the maleic acid, MA, copolymers is independent of ionic strength.33a Evidently, the titration end points in these curves do not appear at RNnom equal to 1, as they should; this is in agreement with previous results of conductometric titrations. Actually, an even lower value of RNnom is obtained (VNaOH ≈ 0.73 mL or RNnom ≈ 0.60; compare with RNnom ) 0.78 obtained from conductometric titration curves). Surprisingly, a very similar result can be deduced from the literature. Thomas et al.22 reported a titration curve for PEA with an inflection point at R around 0.6 and a rather broad transitional region. No comment about this finding has been made by the authors.

1-R 0.434 dGel ) pK0 + R RT dR

(1)

In this equation, R is the degree of ionization of the active COOH groups, calculated from the measured pH by using the expression R ) RN + ([H+] - [OH-])/cp (with cp ) 0.78cpnom, RN ) cNaOH/cp, [H+] ) 10-pH, and [OH -] ) 10-(14-pH)), K0 is the intrinsic ionization constant obtained by extrapolating the left-hand side of eq 1 to R ) 0 and dGel is the incremental change in electrostatic Gibbs free energy accompanying an incremental change in R. This term represents the additional amount of work needed to remove a dissociated H+ ion against the strong electrostatic field of the polyion. A plot of pKa in dependence on R is shown in Figure 5b. The region of negative slopes in pKa vs R curve is attributed to the conformational transition coupled with intermolecular association of chains at low R and resembles for example curves of i-PMA27 in water and in water-dioxane mixtures or of MA copolymers in 5 M urea solutions.33b An estimate of ∆Gtr° was obtained from the following integral9,10,32-37

∆Gtr° ) 2.303RT

∫0R [pKa(a) - pKa(b)] dR

(2)

which is proportional to the area bounded by experimental titration curve a, pKa(a), and a hypothetical titration curve b, pKa(b), which is obtained by extrapolating the portion of the titration curve after the conformational transition to R ) 0. The details and justification of this method of determining ∆Gtr° have been given previously by several authors for various weak polyacids.32-36 The same approach was followed in this paper. An average value of ∆Gtr° obtained from two backward titrations at cpnom ) 0.01 mol COOH/L is ∆Gtr° ) 0.81 ( 0.12 kJ/mol. One titration was performed in PEA solution with cpnom ) 0.02 mol COOH/L and the resulting ∆Gtr° value was ∆Gtr° ) 0.82 kJ/mol. Within experimental error, these two values do not allow making any conclusions on the dependence of ∆Gtr° on polymer concentration. Clearly, a considerably larger ∆Gtr° would be obtained from the titration curve that started from solid PEA. In comparison with the literature data, the above ∆Gtr° values are somewhat low and point to a rather uncooperative change in PEA chain conformation. For comparison, Joyce and Kuruscev9 obtained ∆Gtr° ) 1.6 kJ/mol for a backward titration in water for a PEA sample that also exhibited limited solubility. Sugai et al.10 report ∆Gtr° ) 2.5 J/mol (for cp ) 1.47 × 10-2 mol COOH/L and a solution with ionic strength I ) 0.01) and Fichtner and Scho¨nert8 a much larger value ∆Gtr° ) 4.2 J/mol (for cp ) 6.25 × 10-3 mol COOH/L in water). The latter two reports8,10 give no indication about limited solubility of the particular PEA samples employed; these large ∆Gtr° values could thus be attributed also to the dissolution process in the forward titration path. The low ∆Gtr° for our PEA sample can be explained by taking into account that PEA chains are rather

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Figure 6. Enthalpy of ionization, ∆Hi, of PEA in water at 25 °C as a function of degree of ionization, R. Results of two titration experiments that were started from a different initial R value are shown. The enlargement of the region 0 e R < 0.8 is shown in the inset.

Figure 7. Intensity ratio I1/I3 of the fluorescence of pyrene as a function of degree of ionization, R: (full symbols) forward titration (with NaOH); (open symbols) backward titration (with HCl).

short and most probably considerably stiff. It is reasonable to assume that stiff chains cannot form a very compact (globularlike) conformation. Moreover, the manifested strong intermolecular association may also prevent a larger change in the overall chain dimensions and thus lead to a lower ∆Gtr°. 3.3.2. Calorimetric Titrations. The ∆Hi values that refer to ionization of PEA are plotted in dependence on R in Figure 6 for two titration experiments. In each case, titration was started from a different initial R value in the direction of decreasing R (see Experimental Section). In a few cases an excess of NaOH was added, which is reflected in the calculated R value that is larger than 1 (see open symbols in Figure 6). Concentration of NaCl that has formed in the backward titration was never larger than 0.012 M at the end of titration. The heat effects associated with ionization (or dissociation) of H+ from the PEA chain are all endothermic. The ∆Hi values at R > 0.8 show a pronounced increase toward the value 55.8 kJ/mol, which is the ionization enthalpy of H2O at 25 °C (∆Hi,H2O). For R > 1 (this value denotes an excess of NaOH), the principal reaction is the neutralization of OH- with H+ making ∆Hi,H2O the main contribution to the measured heat effect. The well-defined maximum in ∆Hi curves in the region R < 0.8 clearly shows that the ionization behavior of PEA is not usual. In the PAA case30 where the expansion of the polymer chain induced by ionization of carboxyl groups is continuous, i.e., without a cooperative conformational change, the ∆Hi values decrease monotonically with R. On the contrary, for polyelectrolytes like a-PMA, s-PMA,30 or poly(L-glutamic acid), PGA,38 which are typical examples of polymers displaying a conformational transition, ∆Hi shows a pronounced maximum in the R region where the change in chain conformation occurs. This finding is usually interpreted by proposing that additional endothermic effects are superimposed on the enthalpy of ionization curves that are ascribed to the conformational transition. The immediate conclusion therefore is that PEA chains undergo a similar conformational change as PMA or PGA. However, taking into account the results on pronounced intermolecular association indicated by other techniques and on comparatively low ∆Gtr° value, it was concluded that a significant contribution to these heat effects comes from intermolecular association (or deassociation). The transitional enthalpy, ∆Htr, was evaluated from the area under the peak30,31,38 (see the dashed baseline) and it is ∆Htr ) 1.54 ( 0.05 kJ/mol at 25 °C (cpnom ) 0.01 mol COOH/L). This value is an average of four determinations. Literature data on direct calorimetric determination of ∆Htr for other PCAs are rather scarce. For a-PMA and s-PMA,

Crescenzi et al.30 report ∆Htr ≈ 0.99 and 1.03 kJ/mol, respectively. For PGA, Godec et al.38 have determined values for two polyelectrolyte concentrations: ∆Htr ) 2.0 and 1.7 kJ/mol for 0.002 and 0.01 monomolar solution, respectively (the monomolar concentration corresponds to the concentration of COOH groups in our case). When comparing the ∆Hi vs R curves, several differences are noticed between PEA on the one hand and a-PMA and s-PMA (or PGA) on the other. For PEA, the baseline is close to 0 in the whole region of R (see inset in Figure 6), whereas it noticeably depends on R in the PMA (or PGA) case. The endothermic heat effects due to the conformational change of the PMA (PGA) chain (see, for example, ref 30 or 38) are clearly superimposed on an exothermic effect of the electrostatic contribution to the enthalpy of ionization. In the PEA case, the transition is spread over a wide R range (from around 0 up to almost 0.8), again in sharp contrast with a- or s-PMA where the conformational change is completed at R ≈ 0.4. Similar calorimetric results as for PEA were obtained in our laboratory for i-PMA that likewise displays a large tendency toward intermolecular association. From ∆Gtr° and ∆Htr, the transitional entropy, ∆Str, can be estimated. It must be realized that ∆Htr determined by calorimetry is not a standard value. However, it has been demonstrated by Crescenzi et al.30 that dilution does not lead to an appreciable change in ∆Htr in the case of PMA. Assuming that the same holds for PEA, we have estimated the following standard ∆Str value at 25 °C: ∆Str° ) +(2.4 ( 0.4) J (K mol)-1. This value is larger in comparison with the one obtained for the conformational transition in the a-PMA or s-PMA case30 (∆Str° ) +0.84 and +0.71 J (K mol)-1 at 25 °C for a-PMA and s-PMA, respectively) and signifies that additional contribution (besides the change of conformation also, e.g., deassociation) to ∆S may be involved in the PEA case. On the basis of the observation that the change in conformation seems to be rather unexpressed, we believe that the most important contribution to ∆Str° comes from deassociation of intermolecular aggregates between PEA chains. On the other hand, the main contribution to thermodynamic functions for a-PMA and s-PMA30 is without doubt the conformational transition. 3.4. Fluorescence Measurements. The sensitivity of the vibronic peaks in the fluorescence spectra of pyrene to the polarity of microenvironment was used to probe the formation of hydrophobic microdomains in PEA solutions. The ratio of intensities of the first and the third vibronic peak, I1/I3, is plotted in Figure 7 as a function of R for the forward and the backward titration path. Similarly to potentiometric titrations, these two

Association between Short Poly(ethacrylic acid) Chains curves indicate pronounced irreversibility in the first titration cycle. The I1/I3 keeps rather constant at around 1.3 for R < 0.4 and then gradually increases toward 1.8. The value 1.3 reflects environmental polarity comparable to that of methanol, whereas the value 1.8 is typical for pyrene solubilized in a very polar surroundings of water.39,40 Thus, the change in I1/I3 reflects a pronounced change of micropolarity in PEA solutions upon ionization of carboxyl groups. This change occurs not earlier than above R ) 0.4, again in marked contrast with polyelectrolyte chains that are known to undergo a typical conformational transition. For example, the I1/I3 in a-PMA solutions shows an abrupt increase from a considerably lower value (I1/I3 ≈ 0.9) to over 1.8 in a very narrow region of RN (0.05 e RN e 0.2), indicating a highly cooperative unfolding of the chain and a very low polarity of the un-ionized a-PMA coil.13 A possible scenario to account for large differences between PEA and a-PMA would be that the conformational change in PEA solutions is postponed (or maybe even largely prevented) to higher charge densities on the chain due to strong intermolecular association between PEA chains. This picture is corroborated with results of Muroga et al.11 On the basis of SAXS data, these authors have concluded that the compact form of PEA at R ) 0.2 and 0.3 is best mimicked by a swollen gel having a network structure. As indicated by our fluorescence data, such gel network persists for our PEA sample up to R ≈ 0.4. The micropolarity of the network corresponds to that of methanol supporting the assumption that interchain contacts are established through H-bonding between carboxyl groups. Such H-bonded structure is apparently the solubilization site for pyrene. When the charge on the chain becomes sufficiently large, the gel network melts and pyrene is exposed to polar aqueous surroundings. 3.5. Molecular Modeling. Molecular modeling was first carried out for one oligomer chain of PEA with 12 or 24 monomer units, which was made up of either only isotactic (i-PEA) or only syndiotactic triads (s-PEA). These chain lengths were chosen as a compromise between physically relevant system (i.e., on the basis of Mw data) and consumption of computer time for calculations. The calculated low-energy conformations of i-PEA and s-PEA are shown in Figure 8a,b (for 24-mers) and in Figure S2a and S2b (for the corresponding 12-mers, see Supporting Information). The comparison of formation energies, Ef, of these oligomers calculated in vacuo and in water environment (Table 1) shows that an appreciable stabilization of the oligomers occurs in solvent as compared to the vacuum conditions. This stabilization (given as ∆Esolv ) Ef,water - Ef,vacuum) is larger for s-PEA than for i-PEA, indicating that syndiotactic segments are generally more hydrophilic, which is in agreement with similar calculations for i-PMA and s-PMA.13 Both stereoisomers of 24-mer PEA have a locally “bent” or “curved” conformation similar to s-PMA. However, the chains are more curVed in the PEA case and besides, no helical conformation was found for PEA (neither isotactic nor syndiotactic) in contrast with for example i-PMA where a 10/1 helix was established.13,41 These differences are attributed to the presence of ethyl groups on the PEA chain that are considerably more bulky than the methyl ones on PMA. Bulky ethyl groups prevent the formation of a helix by steric hindrance and force the chain to be more curved and rigid. From the calculations that were performed for two oligomers with 12 monomer units in the chain, the interaction energy, Eint, between the molecules could be estimated from the simple additivity relation Ef ) Ef,mol A + Ef,mol B + Eint. The various energies are reported in Table 2. We have used these results

J. Phys. Chem. B, Vol. 113, No. 8, 2009 2307

Figure 8. Low-energy conformations of single oligomer chains of i-PEA (a) and s-PEA (b) with 24 monomer units and of two i-PEA (c) or s-PMA (d) chains with 12 monomer units each after geometry optimization in implicit solvent. Parts e and f show parallel (e) and antiparallel (f) setting of two 12-mer PEA chains with the same stereoregular composition (see text).

and the optimized models (Figure 8c-f) to deduce on the presence of H-bonds. The following criteria were used for H-bonds: the distance between the proton donor (X-H) and the proton acceptor (Y) should be below 3.1 Å, the bond angle X-H · · · Y should not exceed 146°, and the energy of intermolecular H-bonds should fall in the range 2-167 kJ/mol.42 The system with two isotactic chains in vacuum points to strong favorable intermolecular interaction: the interaction energy is around -221 kJ/mol and the number of H-bonds between these chains is 18. Thus, the energy per one mole of H-bonds is -12.3 kJ/mol. When explicit water was added to the system, both the energy and the number of H-bonds decreased and the resulting energy per one mole of H-bonds was -4.7 kJ/mol. Extensive formation of H-bonds can be easily deduced from the model in

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TABLE 1: Calculated Energies of Formation, Ef (in kJ mol-1), for i-PMA and s-PMA Chains with 12 (12-mer) and 24 (24-mer) Monomer Units in Vacuum and in Implicit Water Solventa i-PEA Ef,vacuum Ef,water ∆Esolv

s-PEA

12-mer

24-mer

12-mer

24-mer

-4939 -5165 -226

-9804 -10221 -417

-5051 -5304 -252

-9997 -10466 -469

a ∆Esolv corresponds to the energy difference between the oligomer chains optimized in vacuo and in implicit solvent.

TABLE 2: Calculated Energies of Formation, Ef (in kJ mol-1), for Two i-PMA or s-PMA Chains with 12 Monomer Units, the Corresponding Energy Difference ∆Esolv, Number of Hydrogen Bonds, nH, and the Interaction Energies between Chains, Eint (in kJ mol-1), in Vacuum and in Implicit Water Solvent Ef,vacuum Ef,water ∆Esolv nH-bond,vakuum nH-bond,H2O Eint,vacuum Eint,water

i-PEA

s-PEA

-10044 -10305 -261 18 6 -221 (-12.3/H-bond) -28 (-4.7/H-bond)

-10161 -10569 -408 1 1 -81

Figure 8c. Both isotactic oligomers are oriented toward each other via COOH groups, forming a sort of “prosthesis-like” adduct. A very different result is obtained for two syndiotactic chains (Figure 8d). Two s-PEA chains in vacuum form only a very small contact area. The interaction energy is around -80 kJ/mol and only one H-bond was detected, which clearly results in an unrealistically high energy per H-bond. The interaction energy in water is positive and small (around +0.8 kJ/mol; not reported in Table 2) and suggests that there is no association between two s-PEA chains when they are immersed in water. The last calculation was performed for two identical chains where monomer groups in one-half of the chain (6 monomer units) were arranged in isotactic and in the other half in syndiotactic triads in order to more realistically mimic the stereoregular composition of our PEA sample. Two optimized models of the adduct of such chains are shown in Figure 8e (the parallel setting of chains, where the isotactic part of one chain faces the isotactic part in the other chain) and Figure 8f (antiparallel setting of chains, where the isotactic part of one chain faces the syndiotactic part in the other chain). The model with parallel setting of chains shows that the interaction between the isotactic segments of two chains is favorable, whereas the syndiotactic parts do not interact. In the antiparallel setting, the isotactic segment always faces the syndiotactic one and this orientation leads to a favorable interaction along the whole length of chains. We conclude that these molecular models confirm a strong tendency of PEA chains to associate and that this attractive interaction could be provided by H-bonding between chains. 4. Conclusions The behavior of short poly(ethacrylic acid), PEA, chains was studied in aqueous solutions. Various methods have shown that PEA chains are intermolecularly associated in water to a high extent. This association is effective in the entire range of degrees of ionization of carboxyl groups and was attributed to strong intermolecular hydrogen bonding between un-ionized carboxyl

groups. The basis for this may be short and considerably stiff polymer chains with a favorable stereoregular composition and the presence of the electron-donating ethyl groups on the R C-atom. The pronounced hydrophobic character of ethyl groups leads to enhancement of associative H-bonding at increased temperatures. Due to intermolecular association, the conformational change of PEA chains is postponed (or maybe even largely prevented) to higher charge densities on the chain. This is reflected in a rather low value for the standard free energy change of the transition on one hand, but in higher values of the associated enthalpy and entropy changes on the other. The latter two thermodynamic functions most likely contain contributions of cooperative change in conformation and of intermolecular association/deassociation. The large tendency of PEA chains toward H-bonding was confirmed by molecular modeling performed on chains with comparable length and tacticity as in case of our sample. Optimized models of two largely isotactic oligomer PEA chains with 12 monomer units resulted in an H-bonded adduct in aqueous medium and thus agree with experimental results. Acknowledgment. This work was supported by the Slovenian Research Agency through Physical Chemistry Research Program 0103-0201. The authors are grateful to Prof. J. Plavec and the staff of the Slovenian NMR center for the helpful support in recording the NMR spectra on Varian Unity Inova-600 spectrometer, and to Prof. A. Meden from the University of Ljubljana for performing the WAXD measurements. Supporting Information Available: Details on SEC-MALS measurements, additional NMR spectra, potentiometric titration curves, and molecular modeling results. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Yessine, M.-A.; Leroux, J.-C. AdV. Drug DeliVery ReV. 2004, 56, 999–1021. (2) Crescenzi, V. AdV. Polym. Sci. 1968, 5, 358–386, references cited herein. . (3) Loebl, E. M.; O’Neill, J. J. J. Polym. Sci. 1960, 45, 538–540. (4) Leyte, J. C.; Arbouw-van der Veen, H. M.R.; Zuiderweg, L. H. J. Phys. Chem. 1972, 76, 2559–2561. (5) Nagasawa, M.; Murase, T.; Kondo, K. J. Phys. Chem. 1965, 69, 4005–4012. (6) van den Bosch, E.; Keil, Q.; Filipcsei, G.; Berghmans, H.; Reynaers, H. Macromolecules 2004, 37, 9673–9675. (7) Jerman, B.; Breznik, M.; Kogej, K.; Paoletti, S. J. Phys. Chem. B 2007, 111, 8435–8443. (8) Fichtner, F.; Scho¨nert, H. Colloid Polym. Sci. 1977, 255, 230– 232. (9) Joyce, D. E.; Kurucsev, T. Polymer 1981, 22, 415–417. (10) Sugai, S.; Nitta, K.; Ohno, N.; Nakano, H. Colloid Polym. Sci. 1983, 261, 159–165. (11) Muroga, Y.; Iida, S.; Shimizu, S.; Ikake, H.; Kurita, K. Biophys. Chem. 2004, 110, 49–58. (12) Hatada, K. J. Polym. Sci. Part A: Polym. Chem. 1999, 37, 245– 260. (13) Vlachy, N.; Dolenc, J.; Jerman, B.; Kogej, K. J. Phys. Chem. B 2006, 110, 9061–9071. (14) Anufrieva, E. V.; Birshtein, T. M.; Nekrasova, T. N.; Ptitsyn, O. B.; Shevelea, T. V. J. Polym. Sci.Part C 1968, N16, 3519–3531. (15) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes, 2nd ed.; Wiley-Interscience: New York, 1980. (16) Southall, N. T.; Dill, K. A.; Haymet, A. D. J. J. Phys. Chem. B 2002, 106, 521–533. (17) Chandler, D. Nature 2005, 437, 640–647. (18) Khutoryanskiy, V. V. Int. J. Pharm. 2007, 334, 15–26. (19) Tao, L.; Han, J.; Tao, F.-M. J. Phys. Chem. A 2008, 112, 775– 782. (20) Hirose, Y.; Sakamoto, Y.; Tajima, H.; Kawaguchi, S.; Ito, K. J. Phys. Chem. 1996, 100, 4612–4617.

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