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J. Phys. Chem. 1996, 100, 4612-4617
Dissociation Behavior of Poly(2-methyleneglutaric acid) by Potentiometric Titration and Intrinsic Viscosity. Criterion of Two-Step Dissociation Yuji Hirose, Yoshifumi Sakamoto, Hideki Tajima, Seigou Kawaguchi,* and Koichi Ito* Department of Materials Science, Toyohashi UniVersity of Technology, Tempaku-cho, Toyohashi 441, Japan ReceiVed: NoVember 6, 1995X
The potentiometric titration, intrinsic viscosity, and 13C NMR have been measured under various conditions to investigate the dissociation behavior of poly(2-methyleneglutaric acid) (PMGA), which has a charge density twice that of poly(acrylic acid) (PAA). The titration curves show that PMGA exhibits an apparent one-step dissociation similar to PAA, remarkably different from those of poly(maleic acid), poly(fumaric acid), and poly(itaconic acid), all having the same average charge density. The electrostatic interaction of PMGA does not level off at degrees of dissociation (R > 0.5), and the negative logarithm of the intrinsic dissociation constant (pK0) of PMGA is 4.20 ( 0.05, similar to that of PAA. The intrinsic viscosity of a PMGA solution containing 0.05 N NaCl increases linearly with R. It has been shown from 13C NMR measurements that the carboxyl groups on the side chain of PMGA dissociate preferentially in the region of R < 0.4. The electrostatic work required to remove H+ from the rod surface calculated from a smeared charge model is in good agreement with the experimental data of PMGA, only for R e 0.5. The dissociation of carboxyl groups of PMGA in R > 0.5 is strongly depressed because of the decrease of the dielectric constant of water.
Introduction Aqueous polyelectrolyte solutions contain polyions and small counterions and may contain excess simple electrolytes. The most remarkable feature of polyelectrolytes is their ability to condense small ions on the polyion. This has been a central subject of both experimental and theoretical studies of the polyelectrolyte solutions. The theories include the counterion condensation theory,1 analysis of the cylindrical PoissonBoltzmann equation,2 hypernetted chain theory,3 and Monte Carlo simulation.4 Most of these theoretical approaches have reached qualitatively similar conclusions, and often in reasonable agreement with experiments.5 The titration behavior of polyelectrolytes is one of the phenomena reflecting counterion condensation.6-11 Despite quite a number of experimental and theoretical studies on the dissociation, many questions remain. Historically, the smeared charge models have been applied, in which the polyelectrolyte chain is modeled as a rod or a line with smeared charges on the surface. Some experimental titration curves were quantitatively interpreted.12 However, the radius of the rod for fitting the experimental data sometimes must assume a physically unreasonable value.13-15 Over the past decade, we have been interested in the dissociation properties of the polyelectrolytes, from the viewpoint of local carboxyl group density and distribution on a polyelectrolyte chain.16-18 We observed a very characteristic dissociation behavior in polyelectrolytes with a charge density twice that of the conventional vinylic polyelectrolyte, poly(acrylic acid) (PAA). The unusual dissociation behavior always occurs when the local carboxyl group separation on a polyelectrolyte chain becomes shorter than that of PAA, ca. 0.25 nm. That is, poly(maleic acid) (PMA) and its stereoisomer, poly(fumaric acid) (PFA),16 and poly(itaconic acid) (PIA)18 exhibit an apparent two-step dissociation at the degree of dissociation R ) 0.5. The smeared charge model for an infinite rod could not express the behavior over the whole range of R. The
experimental titration curve can be explained in terms of the discrete charge model including short-range interaction. Marcus first introduced the Ising model to account for the two-step dissociation of the polyelectrolytes.19 We proposed an improved method which is useful for the interpretation of the titration curves, where the dielectric constant much smaller than in bulk water was assumed.17,18,20 In these high-charge-density polyelectrolytes, the short-range electrostatic interaction plays a dominant role in the dissociation behavior, and one has to consider individually the electrostatic contributions from each charge,21,22 instead of the approximation for smearing of the charges. In these polyelectrolyte solutions intramolecular hydrogen bonds are found to be formed only between ionized and nearest neighbor un-ionized carboxyl groups.23,24 This is an inherent behavior of the polyelectrolytes with R,β-dicarboxylic acid units. The dissociation behavior can be also expressed well in terms of Ising model considering the contribution of the hydrogen bonding.17,24 Therefore, the characteristic dissociation behavior of the polyelectrolytes with a higher charge density than PAA can be interpreted by electrostatics and/or by hydrogen bonding. This, however, does not necessarily imply that the smeared charge model is inapplicable to the dissociation behavior of the polyelectrolytes with high charge density. Polyelectrolytes with R,β-dicarboxylic acid units are a special case in which a specific short-range interaction such as hydrogen bonding may enhance the electrostatic interaction. Here we study the dissociation behavior of another model polyelectrolyte which has the same average charge density as PMA, PFA, and PIA, but where hydrogen bonding is impossible. Poly(2-methyleneglutaric acid) (PMGA) is a model polyelectrolyte, whose molecular structure is
* To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, February 15, 1996.
0022-3654/96/20100-4612$12.00/0
© 1996 American Chemical Society
Dissociation of Poly(2-methyleneglutaric acid)
J. Phys. Chem., Vol. 100, No. 11, 1996 4613
Figure 2. Potentiometric titration curves of PMGA at different Cs at 25 °C. The pH values are plotted against R in NaCl solutions at 0.010, 0.050, and 0.10 N, from top to bottom, respectively. Cp ) 15.7 mN.
Figure 1. The 270-MHz 1H NMR spectra of (a) 2-methyleneglutaric acid and (b) PMGA in D2O. The peak of water (4.78 ppm) was used as the reference peak.
One finds that PMGA has the same average charge density as PMA, PFA, and PIA but does not include R,β-dicarboxylic acid units in the polyelectrolyte chain. The nearest-neighboring carboxyls are separated by the three carbon atoms, as in PAA. The distance in the molecular structure between 1- and 5-carboxyl groups in the same monomer units is the same as between the 1-carboxyl groups in the neighboring monomer units. Thus, PMGA cannot form intramolecular hydrogen bonding as observed in R,β-dicarboxylic acid polyelectrolytes. Another interesting point to be noted in the molecular structure is the difference in the number of nearest-neighbor carboxyl groups between 1- and 5-carboxyl groups: a 1-carboxyl group on the main chain is surrounded by three carboxyl groups (one 5-carboxyl group on the same unit and two 1-carboxyls on the neighbors), and a 5-carboxyl group on the side chain has only one carboxyl group (1-carboxyl on the same unit). This may influence how the carboxyl groups of PMGA dissociate. We apply 13C NMR spectroscopy to establish the relative rates at which the two different carboxyls ionize during the titration of PMGA. We report in the present paper the dissociation behavior of PMGA and compare it with that of other polyelectrolytes and the smeared charge model for an infinite rod. We also present the results of 13C NMR studies in the course of neutralization. Experimental Section Materials. 2-Methyleneglutaric acid, supplied from the Iwata Chemical Co. Ltd., was used without further purification. The monomer (5.0 g) was polymerized in 50.0 mL of water with 0.169 g of K2S2O8 as an initiator at 60 °C for 1 day. The reaction mixture was repeatedly dialyzed against water, passed through a mixed bed of ionic exchange resins, and finally freezedried. The polymer was obtained in 48% yield. The chemical structure of PMGA was confirmed with 1H NMR, as shown in Figure 1. One can see that the peaks of 2-methylene in the monomer disappeared completely in the spectrum of PMGA. A part of the polymer was converted to the methyl ester by
reacting with diazomethane in benzene for characterization by gel permeation chromatography (GPC) and 1H NMR. The weight-average molecular weight (Mw) is 1.53 × 104, and the polydispersity index (Mw/Mn) 1.81 from the GPC measurement of the methyl ester of PMGA, where Mn is a number-average molecular weight. Propanoic acid (PRA) was used as received. The sample of PAA is the same as in the previous papar.16 Water purified by a Millipore Milli Q purification system was used in all experiments. Measurements. GPC measurements were carried out with an HPLC (Jasco, PU-980), equipped with a refractive index detector (Shodex SE-61) and GPC columns (Shodex A-803 and A-804). THF was used as the eluent at a flow rate of 1 mL/ min at 40 °C. The molecular weights were calibrated with a series of standard poly(styrene) samples from Tosoh Co. Ltd. 270-MHz 1H NMR spectra were run at room temperature on an FT NMR spectrometer of JEOL type GX-270. The solutions of PMGA for the measurements were prepared by passing them again through a mixed bed of ion exchange resins and adding a required amount of NaCl just before measurements. The potentiometric titration was carried out with an Orion Research EA-920 ion analyzer with a Ross pH complex glass electrode Model 8102, under argon atmosphere at 25 °C. The details of experimental procedures of the potentiometric titration and viscometry were the same as in previous work.16 13C NMR spectra of PRA, PAA, and PMGA in deuterated aqueous solution were measured at 25 °C with a Varian Unity Plus 400 MHz NMR spectrometer. Recording conditions were 6.8 µs pulse width, (2-10) × 103 scans, and 2 s relaxation delay. The chemical shifts were determined with DSS (sodium 3-(trimethylsilyl)propanesulfonate) as an internal standard. The polymer concentration Cp ) 0.985-1.36 N and the salt concentration Cs ) 0.10 N NaCl. Results and Discussion In Figure 2, the potentiometric titration curves of PMGA at different Cs are plotted against R ()([H+] - [OH-] + [COOH])/ Cp, where brackets designate the concentration. This figure shows that PMGA dissociates in one step, i.e., the pH increases smoothly with increasing R. The shape of the titration curves of PMGA is very similar to that of PAA, but remarkably different from that of PMA, PFA, and PIA, which all exhibit an apparent two-step dissociation at R ) 0.5. One can say from this figure that the dissociation behavior of the polyelectrolytes
4614 J. Phys. Chem., Vol. 100, No. 11, 1996
Hirose et al.
Figure 3. Plots of pKa vs R at different Cs. The symbols are the same as in Figure 2. The solid lines are calculated curves for PMGA, using the smeared charge model with the parameters given in the text.
Figure 4. Dependence of [η] of PMGA solution on R at Cs ) 0.050 N NaCl at 25 °C.
is determined more strongly by the local carboxyl group distribution than by the overall charge density. We may conclude that only polyelectrolytes with R,β-dicarboxylic acid units exhibit two-step dissociation, and that PMGA with R,γdicarboxylic acid units dissociates in one step, despite the same average carboxyl density. In the former, the strong short-range interaction between R and β-carboxyl groups is a key factor. The potentiometric titration of the polyelectrolyte solutions is usually treated in terms of the negative logarithm of the apparent dissociation constant (pKa), defined by11
1-R R
pKa ≡ pH + log
(1)
The pKa is the sum of two terms:
dGel pKa ) pK0 + 0.4343 RT dR
(2)
where K0 is the intrinsic dissociation constant independent of R, R the gas constant, T the absolute temperature, and Gel the electrostatic Gibbs free energy of dissociation of 1 mol of protons. If Gel is the free energy only from the electrostatic interaction, it is related to the electrostatic potential (ψ) on the surface of the polyelectrolyte chain by
dGel/dR ) NAeψ
(3)
where NA is Avogadro’s constant and e is the elementary electric charge. The electrostatic potential ψ was calculated from the solution of Poisson-Boltzmann equation, where the polyelectrolyte chain is treated as an infinite rod.12 In Figure 3, apparent dissociation constants (pKa) at different Cs are plotted against R. The pKa value of PMGA increases with R up to R ) 0.5, levels off, and then increases again with R. The slope of pKa against R increases with R for R > 0.5. The titration curves of PMGA show a reverse S shape. This increase of pKa of R > 0.5 will be discussed later. The solid lines in this figure represent the theoretical values determined by direct solution of the Poisson-Boltzmann equation by use of a computer.12,16 In this calculation, we assumed that the apparent diameter of a rod is 0.55 nm, the dielectric constant of water is 78, the temperature is 298.15 K, and intercharge distance at R ) 1 is 0.125 nm. One sees that the theoretical curves are in good agreement with the experimental titration data of PMGA in the limited region of R < 0.5. Figure 4 shows a plot of intrinsic viscosity ([η]) versus R at Cs ) 0.05 N NaCl. As one can see, [η] of PMGA increases
Figure 5. Plot of pKa vs charge density parameter (ξ) at Cs ) 0.10 N. (O) PMGA and (0) PAA reproduced from ref 16. The solid line are calculated curves by using Dθ and Dr reported by Takashima,29 which are the dielectric constants in tangential and radial directions.
linearly with increasing R. This is also quite different from the behavior of PMA, PFA, and PIA, which showed a maximum point in [η] at R ) 0.5. Also, PMGA does not show any conformational transition from a compact to an extended coil in the low-R region. Sugai et al.25 reported that poly(ethacrylic acid) which has ethyl groups on R-carbon atoms of the main chain shows a clear conformational transition with neutralization due to balance between hydrophilic and hydrophobic interactions. The substitution of a carboxylethyl group should weaken the hydrophobic interaction. It is an interesting to compare the present result with that of PAA. To do this, the titration curves are normalized by introducing the charge-density parameter (ξ),11 defined by
ξ)
e2 DkTb
(4)
where D is the dielectric constant of water, k is the Boltzmann constant, and b is intercharge distance (0.125 nm for PMGA and 0.25 nm for PAA). In Figure 5, the pKa values of PMGA at Cs ) 0.10 N are replotted against ξ, together with those of PAA. The pKa values of PMGA are almost the same as those of PAA over the region of 0 e ξ e 2. The agreement in pKa between the two polyelectrolytes is very interesting, because the carboxyl distribution along a polymer chain is very different. Above ξ ) 2, the pKa values of PAA are bigger than those of PMGA. In PAA, all carboxyl groups are bonded to the main chain. PMGA has two kinds of carboxyl groups, one bonded to the
Dissociation of Poly(2-methyleneglutaric acid) main chain and the other to the side chain. This difference may lead to the dissociation of 1-COOH first in very low R region. The 1-carboxyl group is surrounded by three carboxyl groups, resulting in the decrease of pK0, when compared to the 5-carboxyl group in the side chain. The 5-carboxyl groups in the side chain, however, will begin to dissociate preferentially, as the neutralization proceeds, since the effect of the electric potential of the polyion is weaker than for 1-COOH. Also, the decrease in the dielectric constant of the surrounding medium resulting in an enhancement of the electrostatic interaction is less effective for 5-COOH because its average position is located outside of the main chain. Therefore, the pKa values of PMGA are smaller than those of PAA above ξ ) 2. The extrapolation of the pKa to R ) 0 gives 4.20 ( 0.05 for the pK0 of PMGA and PAA, within the experimental error. The value of pK0 is mainly influenced by the inductive effect or the electron-withdrawing effect of the substituents, the dielectric constant of the solvent, and the chain conformation of polyelectrolyte. The agreement of pK0 of PMGA with that of PAA may be discussed in terms of the inductive effect. We reported in a previous paper14 that the inductive effect of a β-carboxyl group is about 2.6 kJ mol-1. In PAA, an 1-carboxyl group is surrounded by two 1-carboxyl groups on the neighbors. On the other hand, in PMGA, a 1-carboxyl group is surrounded by three carboxyl groups. There should be a difference in pK0 between PMGA and PAA. However, the addition of neighboring carboxyls does not result in a decrease of pK0, because the effect through the chain decreases steeply with increasing distance. The smeared charge model can explain both the dissociation behavior of PAA and PMGA in the region of 0 < ξ < 2. We conclude that the smeared charge model is appropriate for describing the dissociation of the polyelectrolytes without strong short-range interaction. However, theoretical curve begins to deviate from the experimental data of both PMGA and PAA above ξ > 2. Whereas the theoretical potential levels off with increasing charge density, the experimental pKa of PAA and PMGA increases further. Such disagreement was also observed in syndiotacticity-rich PAA26 and poly(crotonic acid) solutions.27 In addition, we also observe a reverse S-shape curve in the titration curve of PAA in Figure 5. This may be due to the decrease of the dielectric constant of water in the vicinity of charges28,29 or near the polymer backbone.30,31 First, we consider the former effect. The properties of water bound to a charge are well-known to be remarkably different from those in bulk. Hasted at al.28 and Takashima et al.29 calculated the dielectric constant of water bound to an ion as a function of the distance from a charge, using Onsager’s internal field in Debye’s equation. They found the steep decrease in dielectric constant at the distances ) 0.2 ( 0.05 nm. This distance corresponds to the average carboxyl group distance of the polyelectrolytes in ξ > 2. We thus combine the PoissonBolztmann equation with the local dielectric constant values. The calculation results are shown in Figure 5. The theoretical curves interestingly exhibit a reverse S shape and appear to explain well both the experimental titration curves of PAA and PMGA. Another effect to be considered is the decrease of dielectric constant in the vicinity of the main chain. According to Kirkwood and Westheimer’s idea,30,31 the low effective dielectric constant in the neighborhood of dicarboxylic acids is due to the fact that the electric lines of force pass partially through the organic medium. Their treatment was bolstered by the finding that substitution with alkyl groups of the chain between the carboxylic groups greatly increased the ratio of the first to the second dissociation constant (K1/K2). In the high ξ region, 1-carboxyl group near the main chain is going to
J. Phys. Chem., Vol. 100, No. 11, 1996 4615
Figure 6. 13C NMR spectra of propanoic acid solution at various R and plots of peak frequencies vs R. The chemical shifts were normalized with DSS as an internal standard. Cp ) 0.985 N and Cs ) 0.10 N NaCl. The neutralization was adjusted using NaOD solution.
dissociate as will be discussed below. This will be influenced by the dielectric constant in the vicinity of the main chain. However, one cannot estimate quantitatively how the dielectric constant decreases. All that can be concluded is that the dissociation of carboxyl groups of PMGA and PAA in the region of high R is depressed by the decrease of the dielectric constant. NMR measurements would be helpful to establish the relative rates at which the two different carboxyls ionize during the titration, because the chemical shift and spin coupling constant are sensitive to their ionization. Zetta,32 Nunes,33 and more recently Lit34 have used vicinal proton-proton NMR couplings to estimate the changes in conformational equilibria for succinic acid as a function of pH. Also, NMR technique has been used to determine the microscopic dissociation constants for amino acids and peptides which contain two or more acidic groups of comparable acidity.35-40 We use the 13C NMR technique to determine the relative rates for the different carboxyls in a polyelectrolyte chain, one is the carboxyl in the main chain and other is in the side chain, both of which have nearly the same pK0.41 First, we have measured 13C NMR spectrum for propanoic acid (PRA) solution as a function of R to know how one can obtain the information from it. In Figure 6, 13C NMR spectra of PRA at various R are shown, together with the figures in which each peak chemical shift is plotted against R. Only one peak is seen for each species at each R and shifts downfield
4616 J. Phys. Chem., Vol. 100, No. 11, 1996
Figure 7. 13C NMR spectra of poly(acrylic acid) solution at various R and plots of peak frequencies against R. Cp ) 1.32 N and Cs ) 0.10 N. The peak frequency due to mr triad for COOH and CH and to r diad for CH2 is plotted, where m and r mean meso and racemic diad.
with increasing R, since the exchange of the proton between protonated and ionized forms is rapid on the NMR time scale and the position of the peak is therefore linear in R. In Figure 7, 13C NMR spectra of PAA at various R are shown. The spectra are slightly complex, when compared with PRA, because of the tacticity. In the expanded spectra, one observes
Hirose et al. three lines for methine and carboxyl groups, which correspond to mm, mr, and rr triads, and two lines for methylene groups in meso and racemic diads. One finds that each peak of PAA shifts downfield linearly with R. In remarkable contrast to the 13C NMR spectra of PRA and PAA, one observes that the PMGA spectra and R dependence are quite complex, as shown in Figure 8. The most interesting point is that for R < 0.4, the averaged resonance pattern for the 5-COOH in the side chain shifts considerably downfield, while the averaged pattern for the 1-COOH shifts slightly. On the other hand, for R > 0.4, the NMR frequencies for the 1-COOH shift downfield, while the chemical shifts of 5-COOH remain relatively constant. This implies that the dissociation of the carboxyl group on the side chain occurs preferentially for R < 0.4. As discussed above, this is so since the electric potential for 5-carboxyl groups is weaker than for 1-carboxyl group. In this sense, we may conclude that PMGA shows apparently two-step dissociation, while the titration curve shows one-step. The difference seems to be characteristic of this polyelectrolyte. A detailed data analysis is now in progress. Finally, we rationalize the dissociation process of the polyelectrolytes, from the standpoints of local carboxyl distribution. What is a criterion for a one- and two-step dissociation of the polyelectrolytes? In PMA, PFA, and PIA, the titration curve shows a two-step dissociation. The two-step dissociation becomes less pronounced in the order PMA > PIA > PFA. The configurational difference between PMA and PFA plays a significant role in the dissociation through the specific shortrange interaction. The hydrogen bonding may be also affected by the decrease of the dielectric constant of water in the vicinity of ionized groups. In addition, the effective dielectric constant in the neighborhood of the ionizable group should be considered. It is clear that the dissociation behavior of the polyelectrolyte is determined mainly by the extent of the short-range interaction from first and second nearest neighbors. When the short-range interaction is weak, as in PAA and PMGA, the titration curve shows one-step dissociation and the electrostatic interaction between the charges on the polymer backbone can be treated as the electrostatic potential from the Poisson-Boltzmann equation. When the short-range electrostatic interaction is strong enough, one has to consider their interactions individually into a discrete model such as the Ising model. Two-step dissociation is observed in polyelectrolytes with R,β-carboxylic acid units.
Figure 8. Expanded 13C NMR spectra of carboxyl groups region of poly(2-methyleneglutaric acid) solution at various R.
Dissociation of Poly(2-methyleneglutaric acid) Conclusions We report the dissociation behavior of PMGA. PMGA is found to exhibit an apparent one-step dissociation similar to PAA but remarkably different from the polyelectrolytes having the same average charge density. The similarity in the titration behavior of PMGA and PAA may be interpreted as due either to the absence of hydrogen bonding or to the fact that the distance between nearest-neighbor carboxyl groups is similar in the two polymers. When the polyelectrolyte does not have strong short-range interaction, the smeared charge model for an infinite rod is a simple and appropriate model to describe the dissociation behavior, irrespective of the average charge density of the polyelectrolytes. When the charge density parameter, ξ, is greater than 2, the decrease of the dielectric constant of water in the vicinity of a charge or near the polymer backbone will affect significantly the dissociation. 13C NMR shows that the carboxyl groups on the side chain of PMGA dissociate preferentially for R < 0.4. Acknowledgment. The authors are greatly indebted to Mr. Yoshihito Yamauchi, Iwata Chemical Co., Ltd., Iwata, Shizuoka 438 for a donation of 2-methyleneglutaric acid. The authors express their appreciation to Prof. H. Morawetz for many valuable suggestions and comments on the manuscript. This work was supported in part by a Grant-in-Aid for the Encouragement of Young Scientists from the Ministry of Education, Science and Culture of Japan (04750735). References and Notes (1) Manning, G. S. J. Chem. Phys. 1969, 51, 924. (2) Hill, T. L. Arch. Biochem. Biophys. 1955, 57, 299. Dolar, D.; Peterlin, A. J. Chem. Phys. 1969, 50, 3011. Jayaram, B.; Beveridge, D. L. J. Phys. Chem. 1991, 94, 4666. (3) Bacquet, R.; Rossky, P. J. J. Phys. Chem. 1984, 88, 2660. (4) Le Bret, M.; Zimm, B. H. Biopolymers 1984, 23, 271. (5) Kowblansky, M.; Tomasula, M.; Ander, P. J. Phys. Chem. 1978, 82, 1491 and references therein. (6) Rice, S. A.; Nagasawa, M. Polyelectrolyte Solutions; Academic Press: New York, 1961. (7) Se´legny, E., Ed. Polyelectrolytes; Reidel: Amsterdam, 1972. (8) Mandel, M. Polyelectrolytes In: Encyclopedia of Polymer Science and Technology; John Wiley & Sons: New York, 1988; Vol. 11, and references therein. (9) Katchalsky, A. Pure Appl. Chem. 1971, 26, 327.
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