Osmotic and Volume Properties of Stereoregular Poly(methacrylic

Mar 8, 2007 - The αN dependence of the ΦV data pointed out that all PMA isomers bind an appreciable amount of water in the elementary dissociation p...
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J. Phys. Chem. B 2007, 111, 8435-8443

8435

Osmotic and Volume Properties of Stereoregular Poly(methacrylic acids) in Aqueous Solution: Role of Intermolecular Association† Bosˇtjan Jerman,‡ Matija Breznik,‡ Ksenija Kogej,*,‡ and Sergio Paoletti§ Department of Chemistry and Biochemistry, Faculty of Chemistry and Chemical Technology, UniVersity of Ljubljana, Asˇkercˇ eVa 5, P. O. Box 537, SI-1000 Ljubljana, SloVenia, and Department of Biochemistry, Biophysics, and Macromolecular Chemistry, UniVersity of Trieste, I-34127 Trieste, Italy ReceiVed: NoVember 16, 2006; In Final Form: January 18, 2007

Osmotic coefficients, φ, and apparent molar volumes, ΦV, of aqueous solutions of isotactic, syndiotactic, and atactic poly(methacrylic acid), i-PMA, s-PMA, and a-PMA, respectively, were measured at 298 K in dependence on polymer concentration and on degree of neutralization, RN, of carboxyl groups. The solutions of i-PMA have lower φ values than those of a-PMA and s-PMA in the whole region of RN. Molecular dynamics simulation studies of the isotactic and the syndiotactic PMA 101-mer have shown that lower φ is a consequence of a shorter distance between charges, which leads to a greater charge density of the isotactic polymer and thus to stronger binding of counterions. The experimental φ data were analyzed using a cylindrical cell model. Good agreement between theory and experiment was achieved when charges on the polyion were distributed periodically along the z-axis of the polyion in accordance with the simulation results. The RN dependence of the ΦV data pointed out that all PMA isomers bind an appreciable amount of water in the elementary dissociation process (electrostriction). For a- and s-PMA, the ΦV values decrease linearly with increasing RN, whereas they show a marked nonlinear dependence in the case of i-PMA for RN < 0.6. The latter finding was ascribed to a very high intermolecular association tendency of the isotactic polymer. This association tendency of PMA chains was confirmed by light scattering measurements. It is present in both i- and a-PMA solutions but is much more pronounced in the i-PMA case.

1. Introduction Poly(methacrylic acid) (PMA) can be prepared in various isomer forms: as an atactic or heterotactic poly(methacrylic acid), a-PMA, and also as a highly regular syndiotactic or isotactic polyacid, s- or i-PMA, respectively. Solution properties of PMA are strongly influenced by chain microstructure.1-10 i-PMA is, in contrast to a- or s-PMA, insoluble in water below a certain critical degree of neutralization of carboxyl groups, Rcrit,3,4,8,10 and it behaves as a weaker acid over the whole range of degrees of neutralization, RN.2,6,9,10 On the other hand, aand s-PMA display similar solution behavior.2,6 The latter becomes obvious if one takes into account that the so-called conventional PMA (or a-PMA) is usually predominantly syndiotactic.7 All three forms undergo a pH induced transition between two mean conformations or states, a less extended one at low RN and a more extended one at high RN.2,6,9,10 The former conformation is very prone to give a massive interchain association due to, e.g., hydrogen bonding, van der Waals and/ or hydrophobic interactions, producing very compact aggregates.2,6,9,10 The associative process is strongly kinetically controlled, giving rise to long-lasting aggregates,7 which are particularly stable in the case of i-PMA.4,5,10 Obviously, the conformational change is one important aspect of the solution behavior of PMA isomers. Previous interpretation † Part of the special issue “International Symposium on Polyelectrolytes (2006)”. * Corresponding author: Ksenija Kogej. Telephone: +(386-1)-2419412. Fax: +(386-1)-2419-425. E-mail: [email protected]. ‡ Department of Chemistry and Biochemistry. § Department of Biochemistry, Biophysics, and Macromolecular Chemistry.

of this phenomenon is almost entirely based on a presumption that this conformational change in dilute aqueous solution is an intramolecular event. However, a recent extensive light scattering study of a-PMA at low pH revealed7 that the picture of an intramolecularly bonded compact coil in water is not supported by any direct experimental evidence. As pointed out in this research,7 the compact structure of a-PMA at RN ) 0 is a subject to significant intermolecular association even in very dilute solutions. This intermolecular association was related to shear induced aggregation (negative thixotropy) in a-PMA solutions.7,11-13 Still stronger intermolecular association may be expected for i-PMA mainly on the basis of its limited solubility in water. As a matter of fact, it was reported recently4 that i-PMA forms gels in concentrated aqueous solutions in a narrow window of RN just above the solubility limit (RN g Rcrit). The mechanism of this gelation is believed to consist of a coilto-helix conformational transition, followed by an intermolecular association, which was ascribed to cooperative hydrogen bonding.4 Clearly, intermolecular association is the second important aspect of solution behavior of PMA, irrespective of its tacticity. This phenomenon was largely unrecognized in the past, in particular in the interpretation of various thermodynamic properties of PMA. Ion binding is an important property of a polyelectrolyte solution and has been studied extensively for a wide variety of polyions. However, the influence of the type and the amount of chain stereoregularity on the binding of counterions by PMA is a subject of only a limited number of reports.14-17 Nevertheless, all these reports point to marked differences in binding phenomena for various PMA isomers. Simple counterions, like monovalent14 (Na+) or divalent ones15 (Cu2+, Mg2+), display

10.1021/jp0676080 CCC: $37.00 © 2007 American Chemical Society Published on Web 03/08/2007

8436 J. Phys. Chem. B, Vol. 111, No. 29, 2007 to some extent opposite behavior. The activity coefficients of sodium ions14 show that the fraction of sodium ions bound by i-PMA is higher than that bound by a-PMA over the entire range of RN. Similarly, it has been shown that i-PMA is approximately three times more efficient in binding Cu2+ ions, but on the other hand binds Mg2+ ions somewhat less efficiently than the syndiotactic species.15 This finding was explained by a different nature of Cu2+ and Mg2+ chelate structures with the two PMA isomers and points to the presence of specific effects in ion binding by PMA. Studies of binding of more complex surfactant ions by two PMA isomers (a- and i-PMA) pointed to an even more intricate behavior.17 An opposite binding affinity for aand i-PMA was demonstrated in this case at the onset of cooperative binding and toward its end. The association at the onset of binding, where electrostatic effects dominate in cooperative interactions between polyelectrolytes and oppositely charged surfactants, is stronger with the isotactic form. In contrast, more surfactant is bound by a-PMA in the region where polyion becomes saturated with surfactant ions and chain flexibility controls interactions between surfactant micelles and the polyion. Whether intermolecular association plays a role in all these findings or not cannot be deduced from the above studies14,15,17 because the employed experimental methods are “blind” to eventual aggregation/association. Such evidence can be obtained only in combination with some specific macromolecular techniques like the scattering ones. The main purpose of this study is (1) to report results of osmotic coefficient measurements and of volume properties for various PMA isomers with well-defined stereoregular composition in dependence on polymer concentration and on degree of neutralization of its functional groups and (2) to give an account of the observed trends in view of potential intermolecular association. In order to achieve the second objective, light scattering measurements were performed by using a spectrofluorimeter. The experimental results of osmotic coefficients were analyzed using a cylindrical cell model. In the first part of the theoretical treatment, the charge was uniformly distributed (smeared) along the z-axis of the polyion’s cylinder and the model was examined by solving an appropriate PoissonBoltzmann equation. In the second model, discrete charges were assumed to be fixed along the z-axis. The distribution of these charges and the average separation between them were obtained by the help of molecular dynamics. Purely iso- and syndiotactic polymer chains were modeled for this purpose. 2. Experimental Methods 2.1. Materials. Iso- and syndiotactic poly(methacrylic acid) were prepared by the hydrolysis of the corresponding poly(methylmethacrylates), i-PMMA (Aldrich) and s-PMMA (Polymer Source Inc.), following the procedure reported previously.3,4,7,18 A different sample of i-PMA was used for light scattering (LS) measurements: the starting i-PMMA was a gift from Professor Hugo Berghmans from the University of Leuven. The tacticity of the starting ester forms and the degree of hydrolysis of the ester groups for the hydrolyzed products were determined from the 1H NMR spectrum in a CDCl3 and in a D2O solution, respectively.4,7 The results are reported in Table 1 together with the data on the average degree of polymerization (DP) of various samples. The degree of hydrolysis for the final acid forms was in all cases greater than 98%. For final purification of i- and s-PMA, dialysis was used as described previously.17 The isotactic polymer was obtained as a solid precipitate17 and stored in a desiccator, whereas the syndiotactic one was kept as a concentrated stock solution in the refrigerator.

Jerman et al. TABLE 1: Degree of Polymerization (DP) and the Stereochemical Composition of PMA Isomers stereochemical composition (% of triads) sample

DP 1523a

isotactic 12d

syndiotactic heterotactic

a-PMA 49d s-PMA 380b ∼0 80.8 (80.6e) i-PMA 6900b 91.6 (91.8e) ∼4 4 i-PMA (for LS) >=1000c 94

39d 19.2 ∼4 2

a From Mw of the Na salt of a-PMA determined by light scattering.7 Data for the starting ester forms as provided from the supplier. c From the GPC data for the ester form and comparison with refs 4 and 8. d The stereochemical composition of a-PMA was determined from the ester form that was obtained by methylation of a-PMA. e Values in parenthesis provided by the supplier.

b

The atactic form of PMA was obtained by polymerization of methacrylic acid using a standard procedure and was characterized previously by light scattering measurements.7 In order to determine its tacticity, a-PMA was methylated with diazomethane and analyzed in deuterated chloroform by NMR.7 The tacticity and the DP of a-PMA are reported in Table 1. a-PMA was purified by dialysis and stored as a concentrated stock solution in the refrigerator. a- and s-PMA are soluble in water at RN ) 0. Stock solutions with RN ) 1 were prepared by adding 1 M NaOH solution to the stock solution of the polymer with RN ) 0 until the pH of the solution was around 9. This pH value corresponds to the equivalent point in the titration curve of PMA with NaOH and was determined for both polyacids in a separate experiment. Other RN values were obtained by mixing solutions with RN ) 0 and 1 in proper proportions. Solutions with lower polymer concentrations were prepared by diluting the stock solutions with a defined RN with pure water. The concentration of the polymer was expressed in moles of monomer units per volume of solution and designated as monomol/L. In contrast to a- and s-, i-PMA is not soluble in water below Rcrit,3,4,8,17 which depends on the tacticity and also on the concentration of the polymer.4 For dilute solutions (polymer concentrations below 0.1 monomol/L) of i-PMA samples used in this study, the solubility limit was at Rcrit ≈ 0.2 for the sample with DP ) 690017 and at Rcrit ≈ 0.3 for the sample with DP >= 1000. Solutions with RN > 0.2 (or 0.3) were prepared in the following way. A weighed amount of solid i-PMA was suspended in water. A calculated amount of 1 M NaOH solution (for the particular RN value), in small volume increments, was slowly and gradually added to this suspension under continuous stirring and blowing through with nitrogen to ensure complete dissolution of the polymer. At RN values close to the solubility limit, this took up to 1 day. A solution of i-PMA with RN ) 0.1 was prepared in the reverse direction.17 At first, 1 M NaOH was added to the suspension of solid i-PMA so that RN was 0.4. After the polymer had dissolved, the solution was slowly re-titrated with a standard 1 M HCl solution in order to adjust RN to 0.1. Because chain association, which would eventually take place in solutions with RN < Rcrit, is likely to be kinetically controlled, precipitation of i-PMA was in this way delayed for some time. At sufficiently low polymer concentrations, this was up to several days. This time was then sufficient to perform the measurements.17 Because chain association is strongly dependent on polymer concentration, only experiments in the low range of cp were performed for RN ) 0.1. For osmotic coefficient and density measurements, the salt (NaCl) that resulted from such a procedure had to be removed. This was achieved by dialysis of this solution against distilled water. The absence of Na+ ions was checked by flame reaction. Because

Osmotic and Volume Properties of Stereoregular PMAs dialysis leads to dilution, the dialyzed solution was carefully concentrated to around cp ≈ 0.07 monomol/L (the precise concentration of this solution was determined by potentiometric titration) by vacuum distillation of the solvent at room temperature. Osmotic coefficient and density measurements for RN ) 0.1 were performed in a limited concentration region at rather low concentrations immediately after the preparation of solutions. In the preparation of solutions for light scattering measurements, the dialysis was not necessary because PMA solutions were prepared in 0.05 M NaCl. 2.2. Osmotic Coefficients. The osmotic coefficient measurements were performed at 25 °C with a Knauer vapor pressure osmometer (Model K-7000). The instrument was calibrated with standard KCl solutions. Accurate measurement could only be obtained at polymer concentrations above approximately 0.004 monomol/L. The i-PMA sample with DP ) 6900 was used for these measurements. A few values were obtained also with the other i-PMA sample (DP >= 1000) at RN ) 0.92 in order to check the dependence on DP. The accuracy in the measured osmotic coefficient values was estimated to range from (1 to ( 3% for RN g 0.25 for all stereoisomers in the whole concentration region. Larger uncertainties (up to (7%) were found only in solutions with RN ) 0.2 and 0.1 for cp below 0.03 monomol/L. 2.3. Density Measurements. Densities of solutions were measured with a Paar digital density meter DMA 60 with external measuring cell DMA 602. An ultrathermostat attached to the instrument controlled the temperature to 25 ( 0.002 °C. The accuracy of density measurements was within ( 4.5 × 10-6 g/cm3. 2.4. Light Scattering Measurements. Light scattering measurements were carried out using a spectrofluorimeter (Perkin-Elmer model LS-50 spectrometer) in the 90° configuration and a method described elsewhere.19 The excitation wavelength was 410 nm and the emission spectra were scanned through a wavelength region 400-420 nm. Excitation and emission slits were 2.5 nm, and a 1 cm path quartz cuvette for fluorimetry was used. The cuvette was placed into a thermostated sample holder at 25 °C, and the intensity of scattered light was measured after 10 min of thermal equilibration. Each spectrum was recorded five times, and then, the average was calculated. Scattering intensity of the pure solvent was also measured and subtracted from the one of the solutions. The concentration of PMA for these measurements was 0.002 (and in the case of i-PMA also 0.005) monomol/L, and 0.05 M aqueous NaCl was used as the solvent. A different sample of i-PMA was used for light scattering measurements. The degree of polymerization of this sample was comparable with the one of a-PMA, which resulted in a comparable light scattering intensities for i- and a-PMA. Stock solutions and the solvent were filtered prior to dilution and subsequent light scattering measurements through 0.45 µm cellulose filters (Minisart, Sartorius). The uncertainty in the measured intensity values was around (20%. 2.5. Molecular Dynamics. For the determination of the counterion-polyion contact distance, acalc, and the distance between charges on the polyion, bcalc, a molecular dynamics (MD) study of i- and s-PMA was performed. Two fully ionized polyions of 101 monomer units each were built (note that this is a completely arbitrary choice for the length of a polyion chain; the same results were obtained for example with 64 monomer units and also by a different computational procedure for 15 monomer units in ref 17) with sodium ions as counterions. The first one consisted only of isotactic and the second one only of

J. Phys. Chem. B, Vol. 111, No. 29, 2007 8437 syndiotactic triads. The Amber* (Assisted Model Building with Energy Refinement20a,b) force field with GB/SA (Generalized Born Solvatation Area20c) for water was used for all our calculations. For the energy minimization of the initial structures, the PRCG (Polak-Ribiere Conjugate Gradient20d) algorithm using Schro¨dinger Macromodel20e was employed. Molecular dynamics simulations were performed within the NVT ensemble, i.e., with fixed number of particles, at constant volume and at constant temperature of 300 K. The Verlet-Stro¨mer algorithm with a 1.0 fs time step was used. After 100 ps of equilibration time, we have started to collect the coordinates. This was done every 10 ps during a period of 10 ns. A Python script using a radial distribution function was written to determine the distances between the selected types of atoms on the polyelectrolyte chain and from this function; the most probable values of parameters acalc and bcalc were obtained. 3. Theoretical Analysis of Osmotic Coefficients. 3.1. Poisson-Boltzmann Cell Model.21 The polyelectrolyte solution is divided into equally sized parallel cylindrical cells of radius R and length h ) Nb, equal to the length of polyions. The polyions contain N monomer units (N . 1): the length of the projection of each monomer unit onto the chain axis is b. The cell radius is determined by the concentration of monomer units, cm, by the expression

cm ) 1/(πR2bNA)

(1)

where NA is Avogadro’s number. Parameter b enters the model through the linear charge density parameter ξ, which is defined as

ξ)

RNe20 4π0rkBTb

(2)

in the case of a weak polyelectrolyte with a degree of neutralization RN. As usual, e0 is the elementary charge, kB is the Boltzmann constant, and T is the absolute temperature, 0r is the permittivity of the medium, and b is the length of the monomer unit. In the case of PMA, the structural value of b (bstr) for the all-trans configuration is 0.252 nm, irrespective of its stereoregular composition. In the Poisson-Boltzmann (PB) approach, the fixed charge is assumed to be smeared uniformly along the polyion axis. All other details of PB calculations can be found in ref 22a. The osmotic coefficient within the cell model can be expressed as the ratio of the ion concentration at the cell boundary, c-(R), and the average concentration of counterions c- in the cell, as given by

φ)

c-(R) c-

(3)

The analytical solution for φ within the PB model has the form21

φ)

1 - β2 (1 - e-2γ) 2ξ

(4)

where γ ) ln(R/a) and β are the integration constants following from the solution of the PB equation. 3.2. Discrete Charge Model. Again, the solution is divided into cylindrical cells as described above. The main difference to the previous model is that we assume that the charges on the polyion are located discretely on the surface of the polyion.

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Jerman et al.

The centers of the counterions are not allowed to penetrate within the cylinder of radius acalc, here chosen to be 0.41 nm. This is essentially the distance of the closest approach of a sodium ion to the polymethacrylate anion and was obtained from MD. The polyion was constructed in such a manner that it represented stereoregular conformations of either i- or s-PMA. The distances between charges on the polyion and the z-axis of the polyion were set at 0.21 nm, a value obtained from MD. Our MD study showed that the distribution of negative charges on the isotactic polyion is locally helical, whereas their position alternates (in a trans-trans or zigzag conformation) in the case of a syndiotactic chain.23,24 These results are in agreement with our previous quantum mechanical semiempirical molecular orbital calculations of considerably shorter (15 monomer units) and uncharged PMA chains17 and with investigations of local chain conformations of stereoregular poly(sodium methacrylates) by small-angle-X-ray scattering.24 Such charge distributions lead to a greater separation between neighboring charges (the distance bcalc) on the syndiotactic chain in comparison with the isotactic one and consequently to a lower charge density. At the same time, the trans-trans (zigzag) distribution of charges on the syndiotactic chain results in a more uniform charge density on the polyion cylinder, closer to the picture of a uniformly smeared charge. On the other hand, the charges on the isotactic chain are accumulated on a strip-like helically propagating portion of the polyion surface. The average distances between charges (bcalc values), as determined by MD, were 0.25 and 0.28 nm for the fully ionized iso- and syndiotactic PMA, respectively, and were used for the calculation of the interaction potential between the charged groups. For the calculation of osmotic coefficients, the canonical Monte Carlo method was used according to the procedure described before.22,25 The uncertainty in the calculated osmotic coefficient values is estimated to be around (2%. 4. Results and Discussion 4.1. Osmotic Coefficients. It is well-known that polyelectrolyte solutions display markedly nonideal behavior due to strong electrostatic interactions between the highly charged polyions and small counterions in solution. A convenient measure of this nonideality is the osmotic pressure,26-31 which is always found to be less than predicted by assuming that all counterions contribute to it. This discrepancy can be resolved by dividing counterions into “bound” and “free” with only the free ones contributing to the osmotic pressure. Low osmotic pressure values are usually expressed in the form of the osmotic coefficient, defined as the ratio of the experimental osmotic pressure to the ideal osmotic pressure of all counterions. The results of osmotic coefficient, φ, measurements are presented in Figure 1a-c for all PMA isomers. The investigated concentration region was in most cases between 0.004 and 0.8 monomol/L, and RN was varied between 0.1 and 1. For the majority of data in Figure 1, the size of the error bars for the measured φ values is equal to or smaller than the size of the data points. We can see that the measured values are rather insensitive to the polyelectrolyte concentration for all isomers, but depend substantially on RN. The low φ values (all experimental values in Figure 1 are lower than 0.7) indicate that PMA solutions exhibit the expected large deviations from the ideal behavior. The data for the iso- and syndiotactic forms are herein reported for the first time. On the other hand, the osmotic coefficient values for a-PMA in different concentration regions (corresponding to the one in this study29 or considerably higher than this30) are available in the literature.29,30 In these reports,

Figure 1. Experimental values of osmotic coefficients, φ, of (a) a-PMA, (b) s-PMA, and (c) i-PMA as a function of polymer concentration for various RN values.

the tacticity of the samples was not determined, and moreover, the results differ appreciably. To overcome those inconsistencies, and to verify to what extent the different experimental conditions might affect the results, it was decided to repeat the measurements for a-PMA. Moreover, it was thought important to experimentally verify the expected similarity between the osmotic properties of the different stereoisomers of PMA. Care was taken that measurements for a-PMA were performed under identical conditions as in the case of the other two isomers in order to have a reliable basis for comparison. The necessity of this repetition will become evident below when comparing our φ data in a-PMA solutions with the literature values.29,30 The comparison of osmotic coefficients for various isomers of PMA is presented in Figure 2, where φ is plotted as a function of RN for cp ) 0.1 monomol/L (the uncertainty in these values is around (2%, resulting in error bars equal to or smaller than the size of data points). The vertical dotted line in this figure at RN ) 0.2 marks the solubility limit of i-PMA (RN ) Rcrit). In agreement with expectations, the φ values for all stereoregular forms decrease with increasing RN. The slope of this dependence is considerably higher for RN < 0.5 than it is for RN > 0.5. Above RN ) 0.5, the change in φ is practically linear, which is the most evident in the i-PMA case (see the dash-dot lines that were obtained as linear fits of the data points for RN g 0.5). Knowing that the PMA chain undergoes a conformational

Osmotic and Volume Properties of Stereoregular PMAs

J. Phys. Chem. B, Vol. 111, No. 29, 2007 8439

Figure 2. Dependence of osmotic coefficients of a- (b), s- (9), and i-PMA (2, DP ) 6900; 4, DP >= 1000) on degree of neutralization, RN, at cp ) 0.1 monomol/L. For comparison, the data for osmotic coefficients of a-PMA from refs 29 (0) and 30 (O: the data from ref 30 are interpolated to cp ) 0.1 monomol/L) are included. The vertical dotted line indicates the solubility limit for i-PMA.

transition in aqueous solutions in the region 0.2 < RN < 0.4, which depends to some extent on the stereoregularity,5,6,10 this change in slope may be attributed to a different mode of sodium ion binding by the two extreme conformations of PMA. The experimental activity coefficients of Na+ in solutions of a- and i-PMA provided similar evidence.14 The fact that i-PMA is not soluble in water for RN values below 0.2 is not reflected in the φ dependence on RN. The φ value for i-PMA at RN ) 0.1, although slightly higher, agrees with those for a- and s-PMA within the limits of experimental error. The literature data25,26 on osmotic coefficients of a-PMA at cp ) 0.1 monomol/L are also included in Figure 2. They show deviations both in the negative29 and in the positive direction30 from the ones determined in our study. The data of Torrence et al.,30 which are between 0 and 12% higher than ours, were also obtained by the vapor pressure method, whereas Alexandrowicz29 has used the so-called “concentration osmometer” to determine φ. The latter technique29 relies on adjusting the concentration of a standard polyethylene glycol solution in such a way that it is in osmotic equilibrium with the investigated solution. The author29 reports on experimental difficulties associated with the leaking of the solute through the membrane, which could give rise to lower φ values. Indeed, φ values in ref 29 are between 27% (at RN ) 0.1) and 40% (at RN ) 0.8) lower than ours. By our opinion, this relatively large difference in φ may also come from the fundamental difficulty of using membranes for measuring osmotic pressure in the case of PMA (we tried to use also that method, but the results were not reproducible and are therefore not reported here). In view of this comparison with the literature data, reasons for repeating the measurements for a-PMA become clear. One can see from Figure 2 that φ values of i-PMA for RN g 0.2 (above the solubility limit) are systematically lower than those of a- and s-PMA. The difference is significant for RN g 0.5; i.e., it is almost 18% at RN ) 1 and drops to around 11% at RN ) 0.5. Below RN ) 0.5, it is within the limits of the experimental error (3-6%). The φ value for the i-PMA sample with DP >= 1000 (RN ) 0.92) demonstrates that the higher DP of i-PMA can be excluded as the reason for lower φ (see also the relevant φ data for this sample in Figure 1c). The osmotic coefficients for a- and s-PMA, on the other hand, are in excellent mutual agreement. The latter finding is not surprising because our a-PMA sample is actually rich in syndiotactic sequences.7 The result on lower osmotic coefficient

Figure 3. Comparison of experimental (points) and calculated values of osmotic coefficients for (a) s-PMA (O) and a-PMA (b) at RN ) 1 and for (b) i-PMA at RN ) 0.92: Poisson-Boltzmann (dotted line) and Monte Carlo results (solid line).

values in the i-PMA case suggests that sodium ions bind more strongly to i-PMA than they do to a- and s-PMA. In agreement with this conclusion, fluorescence intensity measurements with trivalent terbium metal ion demonstrated a six to one preference for the binding with i- over s-PMA.32 Similarly, the interaction of monovalent surfactant counterions in the initial stage of cooperative binding is considerably stronger with the isotactic form of the polymer.17 The latter finding was attributed to a greater charge density along with a greater hydrophobicity of i-PMA.17 Hydrophobicity has an important influence in surfactant-polyelectrolyte interactions, whereas in the case of simple counterions like Na+ charge density is far more important. Experimental results on osmotic coefficients reported herein likewise indicate that the charge density on the isotactic chain is higher than that on the atactic one. This result was further examined by model calculations. Structural parameters for the purely iso- and syndiotactic chains needed for these calculations were derived from MD simulations. The comparison between calculated and experimental osmotic coefficients is shown in Figure 3 for a- and s-PMA solutions with RN ) 1 (Figure 3a) and for i-PMA solutions with RN ) 0.92 (Figure 3b). The results suggest that the more realistic discrete-charge model predicts stronger binding (smaller osmotic coefficients) than the Poisson-Boltzmann equation and weaker concentration dependence of φ and thus gives a much better agreement with the experimental values. Up to polymer concentrations around 0.2 monomol/L, the theoretical and experimental values in the case of a-PMA (or s-PMA) agree well within the experimental error. Our main interest was the dependence of φ on the polyion charge density, the latter being proportional to RN. Experimental and calculated osmotic coefficients are presented as a function of RN in Figure 4 for polymer concentration cp ) 0.01 monomol/ L. The value of cp ) 0.01 monomol/L was chosen for

8440 J. Phys. Chem. B, Vol. 111, No. 29, 2007

Jerman et al. where F0 is the density of pure solvent (water), m is the molality of the solution (in monomol/kg solvent), and M2 is the average molar mass of the monomer unit of PMA, which depends on the degree of neutralization in the following way:

M2 ) Mm + (1 - RN)MH + RNMNa

Figure 4. Dependence of osmotic coefficients of a-, s-, and i-PMA on degree of neutralization, RN, at cp ) 0.01 monomol/L (same symbols as in Figure 2): Poisson-Boltzmann model (dotted line); Monte Carlo results for s-PMA (solid line connecting open diamonds) and for i-PMA (dash-dot line connecting open triangles). For details on model calculations, see text.

presentation instead of cp ) 0.1 monomol/L (which is used in Figure 2) in this case, because agreement between theory and experiment is better at lower concentrations. Experimental φ values at these two concentrations differ insignificantly. Clearly, the Poisson-Boltzmann model cannot predict any differences in osmotic coefficients for various PMA isomers because the structural value for the length of the monomer unit (bstr) is the same for all of them (bstr ) 0.252 nm). Consequently, only one curve is obtained in this case. The discrete-charge model, however, takes into account that the distribution of charges on the polyion cylinder differs for i- and s-PMA and thus results in different curves for each of them. The calculated dependence of φ on RN using the discrete-charge model correctly predicts that φ values are lower for the isotactic form, which is a consequence of its greater charge density (lower bcalc value). However, the absolute difference in φ values increases with decreasing RN, contrary to experimental observations: it is around 0.025 at RN ) 1 and larger than that (around 0.03) at RN ) 0.25. Theories examined here overestimate the osmotic coefficient. This is a common observation when only Coulomb interactions between the polyion and its counterions are considered.24 The discrepancy between measured and calculated φ values becomes rather high for RN < 0.5. The conclusion is that the Coulomb interactions are not the only source of nonideal behavior in solutions of PMA. This is most clearly demonstrated if we tentatively extrapolate the measured data to RN ) 0. The osmotic coefficient obviously does not approach unity when the charge of the polymer is decreased toward zero. A value somewhere between 0.75 and 0.8 is obtained for φ of a hypothetical discharged PMA. We believe that the hydrophobic character of PMA (i.e., the interaction of the macromolecule with water) plays a very important role here. An additional drawback of theoretical values is that they do not reflect the possible conformational transition of the PMA chain or eventual intermolecular association. 4.2. Apparent Molar Volumes. Density measurements at constant RN showed that the density, F, of PMA solutions varies linearly with concentration. The apparent molar volume, ΦV, was calculated from the measured F values by using the usual relationship:

ΦV )

[

( )]

1 1 F - F0 M2 F m F0

(5)

(6)

In this equation, MH and MNa are the molar masses of hydrogen and sodium atoms, respectively, and Mm (85 g/mol) is the molar mass of the monomer unit of PMA without the counterion (-CH2C(CH3)COO-). The calculated apparent molar volumes are presented in Figure 5 as a function of cp for all PMA forms. For concentrations greater than 0.01 monomol/L, ΦV is practically independent of cp. This is usually observed for polyelectrolyte solutions.31,33 Thus, values at cp ) 0.1 monomol/L that are plotted in Figure 6 as a function of RN may be considered as being similar to those obtained by extrapolation of these constant ΦV values to infinite dilution. Clearly, ΦV in Figure 6 decreases with increasing RN for all PMA isomers. A simple treatment of the data in Figure 6 can be done according to

+ (1 - RN)ΦNa ΦV(RN) ) RNΦHPMA V V +

-

+PMA-

(7)

PMA where ΦHPMA and ΦNa stand for the molar volume of the V V undissociated (HPMA) and of the dissociated (the sodium salt Na+PMA-) forms of PMA, respectively. It can be seen from Figure 6 that a perfect linear dependence of ΦV on RN is obtained for the a- and s-PMA. The resulting apparent molar volume of the undissociated a- or s-PMA is 58.3 cm3/monomol. This agrees satisfactorily with the literature value 59.3 cm3/ monomol.33,34 Neutralization leads to a decrease of ΦV to reach the value of 35.6 cm3/monomol at RN ) 1 (for Na+PMA-). The slope of the straight line corresponds to the molar volume change accompanying dissociation (R-COOH f R-COO- + H+) and is equal to -22.7 cm3/mol H+. The values reported in the literature for a-PMA are -26.634 and -19.735 cm3/mol H+. The negative volume change of dissociation is a universal observation for poly(carboxylates), both natural (e.g., pectic acid36) and synthetic (e.g., poly(acrylic acid), PAA,35,37 or maleic-acid, MA, copolymers38). The accepted explanation is that the poly(carboxylate) chain binds a substantial amount of water (electrostriction) during the dissociation process. This leads to a decrease in the apparent molar volume upon neutralization as observed also in the case of PMA isomers. The comparison with different polycarboxylates can be of help. The reported values for PAA in water are -19.734 and from -12.5 to -16 cm3/mol H+.37 As for MA copolymers, Yamashita and Kwak34 report -16.1 and -22.2 cm3/mol H+ for the copolymer with ethene (MAE) and styrene (MASt) in water, respectively, whereas from the paper by Crescenzi et al.38 one estimates the average value of -18.2, -19.8, and -20.2 cm3/ mol H+ for the MA copolymers with ethene, propene, and isobutene in aqueous 0.05 M (CH3)4NClO4, respectively. An estimation of the number of water molecules getting electrostricted in an elementary dissociation process can be obtained by taking into account ultrasonic absorption experiments39 and refractivity measurements.35 These experiments indicated that the density of electrostricted water around both, counterions and polycarboxylates, is about 1.1 g/cm3.35,39,40 The explanation for the negative volume change upon neutralization of PMA can then be explained by an increase in the density of 0 electrostr 3 water from Ffree ) 1.1 g/cm3. The w ) Fw ) 1.0 g/cm to Fw concomitant volume change associated with the binding of water

Osmotic and Volume Properties of Stereoregular PMAs

J. Phys. Chem. B, Vol. 111, No. 29, 2007 8441

Figure 5. Concentration dependence of the apparent molar volumes, ΦV, of a-PMA and s-PMA (Figure 5a) and of i-PMA (Figure 5b) in water at 25 °C for various RN values.

Figure 6. The dependence of the apparent molar volume, ΦV, on degree of neutralization, RN, for a-PMA (b), s-PMA (O), and i-PMA (2) solutions at cp ) 0.1 monomol/L. The vertical dotted line indicates the solubility limit for i-PMA.

is easily obtained from these data in the following way:

∆Vw )

Mw electrostr Fw

-

Mw Ffree w

) -1.636 cm3(mol water)-1 (8)

The number of water molecules, w, getting electrostricted in the elementary dissociation process per mole of carboxyl groups in the a- and s-PMA case can then be estimated by taking into account the measured decrease in volume from the value at RN ) 0 to the value at RN ) 1 (-22.7 cm3/mol H+). The resulting value of w is 13.9, pointing to a substantial role played by hydration water molecules during the process of charging of the extended conformation of a- and s-PMA. This relatively large value of w may be related to the hydrophobic methyl groups of the PMA chain. Interestingly, the previously quoted data of MA copolymers indicate a slight but clear tendency to larger volume difference between the uncharged and the fully charged form upon increasing the hydrophobic nature of the comonomer. Given the accuracy of the data, one can state that a line with the same slope as that of a- and s-PMA reasonably fits the data points of i-PMA for RN > 0.6. It suggests that the water electrostriction accompanying the elementary process of dissociation is very similar (if not identical) for all the stereoisomers. However, this is not true for the molar volume of the HPMA form of the isotactic polymer. In fact, extrapolating the linear dependence of ΦV on RN for i-PMA in the region RN > 0.6 to RN ) 0, we can obtain a value of 50.4 cm3/monomol for the apparent molar volume of the unneutralized i-PMA. This

is a hypothetical value that is not a subject to direct experimental determination because i-PMA at RN ) 0 is not soluble in water. It refers to some hypothetical state of the isotactic polymer that would remain molecularly dispersed/dissolved in water when its charge is reduced to 0. A further comment concerns the difference in ΦV values for a- and i-PMA at RN ) 1, which is around 7 cm3/monomol and reflects differences in chain conformation for various isomer forms and in their overall hydration with water. It has been shown by quantum mechanical calculations that the isotactic polymer is more rigid and less extensively hydrated (i.e., it is more hydrophobic) in comparison with the atactic one.17 These characteristics of the i-PMA chain may lead to a different amount and arrangement of water molecules around it and thus to a lower ΦV. From ΦV values at RN ) 1, the size of the charged monomer group in the case of i- and a-PMA can be estimated. By approximating the monomer unit with a sphere of radius rs, one obtains rs ) 0.229 and 0.242 nm for i- and a-PMA, respectively. The result on smaller size of the monomer group in the case of i-PMA is in agreement with lower bcalc values for this stereoisomer obtained from MD calculations. For RN < 0.6, the experimental ΦV values for i-PMA deviate from the linear dependence. In a narrow region between RN ) 0.64 and 0.433 they increase by 13.7 cm3/monomol, that is, from 35.9 at RN ) 0.64 to 49.6 cm3/monomol at RN ) 0.433, but remain fairly constant (at around 50 cm3/monomol, note that this value is close to the hypothetical ΦV at RN ) 0) for RN < 0.4. Given the marked tendency to association of i-PMA in that region of RN,4 it seems reasonable to refrain from any quantitative estimate and, even more so, from any speculative interpretation. It suffices to say that intermolecular association is definitely reflected in the large value of ΦV at RN ) 0.1 (ΦV ≈ 70 cm3/monomol), which can be associated with the phase separation in i-PMA solutions in the region of RN below 0.2. Although no visible precipitation could be observed and the density of i-PMA solution at this RN value could be measured repeatedly, this ΦV reflects that i-PMA chains are subjected to considerable intermolecular association. 4.3. Light Scattering. Intermolecular association was monitored by static light scattering. The intensity, I, of light scattered by dilute i- and a-PMA solutions at 90° is shown in Figure 7 in dependence on RN. Albeit partial in nature, the 90° scattering experiments are likely able to give an overall view of the underlying molecular processes. In the a-PMA case, the intensity shows an increase at RN values above approximately 0.2-0.3. Incidentally, this RN region roughly agrees with the region of

8442 J. Phys. Chem. B, Vol. 111, No. 29, 2007

Figure 7. The intensity, I, of light scattered at 90° in i-PMA (2) and in a-PMA (b) solutions with cp ) 0.002 monomol/L in the presence of 0.05 M NaCl at 25 °C: dependence on RN.

the conformational transition of the a-PMA chain. Aggregation between a-PMA chains in the presence of various amounts of HCl (RN f 0) was unequivocally ascertained before by precise light scattering measurements.7 This could be reflected in the decrease of the intensity upon increasing RN from 0 to about 0.2. The small minimum at RN ) 0.2 could then very well reflect complex rearrangements of the aggregates present at low RN, accompanied by unpredictable variations of the local index of refraction, which eventually produce such an apparent anomaly. The increase of the intensity for RN > 0.3 roughly parallels the increase of (∂n/∂cp) with RN given for a-PMA by Franc¸ ois et al.41 The most relevant difference of the scattering profiles of i-PMA in the region with RN > 0.3 is that the intensity is smaller than the corresponding values of a-PMA. This is due to the smaller value of the molar mass of the isotactic form of the polyacid with respect to the atactic one (note that a sample of i-PMA with a lower molar mass than that of i-PMA used for φ and ΦV measurements was employed for light scattering experiments in order to bring the scattering intensity in the region RN > 0.2 close to the values measured in a-PMA solutions). Beyond RN ) 0.3, the intensity curves slowly increase to reach a maximum and then decrease to RN ) 1.0. The very rough nature of the present experiments does not allow drawing any conclusion on the underlying physical processes, with the same possible effects invoked for the a-PMA case. On the other hand, a very different behavior is found for i-PMA in the region 0.3 > RN > 0, where the intensity of scattered light increases sharply to values larger than 1000 (note that the upper detection limit of the fluorimeter is I ) 1000; therefore, the data points with I ) 1000 in Figure 7 actually correspond to I > 1000). This is more than a 10-fold increase in comparison with the scattering intensity at RN ) 0.3 and indicates that intermolecular association/aggregation is considerably stronger than the one found in a-PMA solutions. The above-reported scattering results for i-PMA (DP ) 6900) agree with the observed RN dependence of ΦV for i-PMA (DP >= 1000). In Figure 8, light scattering and volume measurements for these two samples are plotted simultaneously. The concentration region investigated in volume measurements was higher than the one in scattering experiments. Therefore, the scattering results at cp ) 0.005 monomol/L may be more relevant for comparison and are accordingly included in Figure 8. The very extensive intermolecular association, which in the I vs RN curve is indicated by an increase in I below RN ≈ 0.25 (cp ) 0.002 monomol/L) or below RN ≈ 0.45 (cp ) 0.005 monomol/L) for the sample with DP >= 1000, is indicated also

Jerman et al.

Figure 8. Comparison of the intensity of scattered light, I, (2, 4 DP > = 1000) and of the apparent molar volumes, ΦV (b DP ) 6900), in i-PMA solutions (the concentration of i-PMA for LS measurements, cp ) 0.002 (2) and 0.005 monomol/L (4); the concentration of i-PMA for ΦV data, cp ) 0.1 monomol/L). The error bars are the same as in Figures 6 and 7.

in the ΦV vs RN curve (cp ) 0.1 monomol/L) for the sample with DP ) 6900: ΦV jumps from a rather constant value at around 50 cm3/monomol (in the region 0.25 < RN < 0.45) to around 70 cm3/monomol (below RN ) 0.2). On the basis of the data in Figure 8, it may be concluded that differences in DP of i-PMA samples may be excluded as the reason for different solubilization and aggregation behavior in comparison with a-PMA. Considerably higher DP of i-PMA used for φ and ΦV measurements is likewise not the reason for lower φ and ΦV values. However, only very extensive intermolecular aggregation, such as in the case of i-PMA, has an influence on volume properties but interestingly has no considerable effect on the osmotic coefficient. 5. Conclusions A comparative study of ion binding and of volume properties of three stereoisomer forms of PMA has been performed. PMA samples with precisely defined composition in triads were used. Although our main interest was in the comparison among the stereoisomers, we have focused on the behavior of the isotactic isomer. Actually, the literature data for the atactic form were scattered; we showed that only a simultaneous analysis of results obtained for all different isomers under the same experimental conditions leads to reliable conclusions. A general conclusion of the study is that differences in solution behavior of various PMA isomers can be explained by the conformation of the chain on the local level, which determines the charge density, the hydrophobicity, and the flexibility of the polymer as a whole. This was confirmed by the molecular dynamics study of the iso- and syndiotactic PMA chains. The marked hydrophobic character of PMA is responsible for its high intermolecular association tendency in aqueous solutions. This association tendency was ascertained by light scattering measurements. PMA association had undoubtedly been demonstrated for its atactic form:7 the present results show that it is much more clearly indicated in the i-PMA case. Ion binding was assessed by means of osmotic coefficient measurements. The data showed that ion binding is stronger for the isotactic form than for the a- and the syndiotactic ones. Molecular dynamics simulations of the i- and s-PMA chain showed that distances between charges on i-PMA are smaller than those on s-PMA. This gives rise to a locally higher charge density of the isotactic form and consequently to lower φ values.

Osmotic and Volume Properties of Stereoregular PMAs However, differences in ion binding as revealed by osmotic coefficient values are not larger than 18%. Although intermolecular association is undoubtedly very important in aqueous PMA solutions, in particular in the i-PMA case, this is not at all reflected in the φ values. Obviously, the osmotic coefficients alone may not be such a sensitive property as to reflect detailed differences of the electrostatic potential around the polyion related with intermolecular association. Dependence of the apparent molar volumes on degree of neutralization points to differences in the overall hydration of various PMAs. The isotactic form is the less extensively hydrated one. This is in agreement with the evidenced greater hydrophobicity of i-PMA. In agreement with this larger hydrophobic character, ΦV values in dependence on RN clearly indicate that intermolecular association and concomitant phase separation is taking place in i-PMA solutions. However, water electrostriction accompanying the process of dissociation is very similar for all three isomers. Acknowledgment. This work was supported by the Slovenian Research Agency through Physical Chemistry Research Program 0103-0201. The authors wish to thank Professor Hugo Berghmans for providing the isotactic polymer. References and Notes (1) Hatada, K. J. Polym. Sci., Part A: Polym. Chem. 1999, 37, 245260. (2) Crescenzi, V. AdV. Polym. Sci. 1968, 5, 358-386. (3) Loebl, E. M.; O’Neill, J. J. J. Polym. Sci. 1960, 45, 538-540. (4) van den Bosch, E.; Keil, Q.; Filipcsei, G.; Berghmans, H.; Reynaers, H.; Macromolecules 2004, 37, 9673-9675. (5) Leyte, J. C.; Arbouw-van der Veen, H. M. R.; Zuiderweg, L. H. J. Phys. Chem. 1972, 76, 2559-2561. (6) Nagasawa, M.; Murase, T.; Kondo, K. J. Phys. Chem. 1965, 69, 4005-4012. (7) Kogej, K.; Berghmans, H.; Reynaers, H.; Paoletti, S. J. Phys. Chem. 2004, 108, 18164-18173. (8) van den Bosch, E.; Berghmans, H. Polym. Bull. 2006, in press.. (9) Leyte, J. C.; Mandel, M. J. Polym. Sci., Part A 1964, 2, 18791891. (10) Jerman, B.; Kogej, K. Acta Chim. SloV. 2006, 53, 264-273. (11) Eliassaf, J.; Silberberg, XXXXX; Katchalsky, A. Nature 1955, 176, 1119. (12) Ohoya, S.; Matsuo, T. J. Colloid Interface Sci. 1979, 68, 593595. (13) Ohoya, S.; Hashiya, S.; Tsubakiyama, K.; Matsuo, T. Polym. J. 2000, 32, 133-139. (14) Costantino, L.; Crescenzi, V.; Quadrifoglio, F.; Vitagliano, V. J. Polym. Sci., Part A 1967, 5, 771-780. (15) O’Neill, J. J.; Loebl, E. M.; Kandanian, A. Y.; Morawetz, H. J. Polym. Sci., Part A 1965, 3, 4201-4294. (16) Kolawole, E. G.; Bello, M. A. Eur. Polym. J. 1980, 16, 325-332.

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