Poly(N‐vinylimidazole) hydrogels immersed in aqueous acid solutions produce an increment in the pH of the bath because of proton uptake by basic imidazole moieties, leading to hydrogel protonation. Both kinetic and equilibrium measurements of the pH of the bath have been performed under a variety of conditions and with different hydrogel samples. The kinetics of the xerogel protonation process (which includes solvent and titrant diffusion, the true protonation reaction or ion–dipole association, and the polymer relaxation to a new conformation) are mostly driven by the size of the hydrogel sample, whereas other magnitudes, such as the initial pH, the effective polymer concentration, and the network structure, governed by the crosslinker ratio and total comonomer concentration in the feeding, have a minor influence. pKa changes with the degree of protonation (α), delimitating two different regions: (1) a broad α range in which pKa decreases with increasing α but less pronouncedly with increasing ionic strength and (2) an α range close to α = 1 in which pKa decreases abruptly, more markedly with sulfate than with chloride counteranions and with larger ionic strengths. In the first region, pKa is determined by repulsive electrostatic interactions and so is larger for titration with H2SO4 than with HCl and increases as the effective polymer concentration and ionic strength increase. Two steps (i.e., two protonation sites) can be observed in the titration curves, the second one corresponding to abrupt changes in the basicity of the second pKa‐versus‐α region. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2294–2307, 2004

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The number of variables controlling the behavior of ionic gels is large and very often some of them are unknown. The aim of this work is to interpret quantitatively the swelling behavior of pH sensitive gels, with the minimum number of simplifying assumptions. With this purpose, the equilibrium degree of swelling (S) and protonation (alpha) of chemically cross-linked poly(N-vinylimidazole) (PVI) immersed in aqueous salt solutions were measured as a function of the ionic strength (mu), in the whole range of pH. In acid solutions with pH in the range 0 to 4, imidazole moieties become protonated, and PVI behaves as a polyelectrolyte gel: S decreases upon increasing mu both for NaCl and for CaCl(2), with HCl as protonating acid. In aqueous solutions with larger pH, between 4 and 12, the hydrogel is practically neutral, and S increases as mu rises, showing a salting-in effect. From the quantitative analysis of these results, the following facts emerged. Protonation induces chain stiffness (as measured by the non-Gaussian factor) and worsening of the solvent quality of the aqueous media (as measured by the polymer-solvent interaction parameter). For alpha below 33%, swelling seems to be governed by the excess of mobile counterions inside the gel with respect to the bath, with a minor but still significantly negative contribution of the osmotic swelling pressure due to polymer-solvent mixing. Above 33% protonation, it is necessary to consider Manning counterion condensation to get parameters with physical meaning. The crossover between polyelectrolyte and salting-in effects corresponds to alpha and mu values with the same ionic and mixing contributions to the osmotic swelling pressure. The formation of ionic nonpermanent cross-links, with H(2)SO(4) as the protonating acid, was discarded.

This article reports the scaling laws relating the synthesis conditions with the crosslinking density (νe) and swelling degree (S) of poly(N‐vinylimidazole) hydrogels (PVI) prepared by radical crosslinking copolymerization in aqueous solution, with N,N′‐methylene bisacrylamide (BA) as crosslinker. Multiple linear regression of νe versus BA concentration ([BA]) and total comonomers concentration (CT) in double log scale render the scaling law νe ∼ C italicT0.81 × [BA]1.04 as comparable to that predicted by the model of polymer network with pendant vinyl groups (νe ∼ CT × [BA]), and showing inverse dependence on CT to that expected, following from stoichiometry, for an ideal network (νe ∼ 2[BA]/CT). S scales with νe through a solvent‐dependent exponent ranging from −0.46 to −0.54, only slightly over the value predicted by the Flory–Rehner theory (−0.6) or the blob's model by de Gennes (−0.5 to −0.8). Finally, the scaling law of S with the composition of the reacting mixture is also solvent‐dependent and it seems to result not only from the dependence of νe on CT and [BA] but also from that of v2r, the polymer volume fraction in the reference state, and χ, the polymer–solvent interaction parameter. Models used seem to overestimate the contribution of entanglements to the effective crosslinking density of PVI. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 263–269, 2007

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The pH inside a dissolved polyelectrolyte coil or a swollen ionic polymer network is not accessible to direct measurement. It is here calculated through a simple model, based on Donnan equilibrium, counterion condensation (for charge density exceeding the critical value), and balance of mobile ions, without any assumption on the pKa of the ionizable groups. The data needed for the calculation with this model are polymer concentration, pH value in the initial solution, and pH value in the bath at equilibrium. All three can be determined experimentally by a batch method where the polymer is immersed in a different pot for each starting pH. The model is applied to a sample system, namely, chemically cross-linked poly(N-vinylimidazole) immersed in acidic baths of different pH values. The imidazole units are basic and become protonated by the acid, thus changing the pH of the initial bath. The model shows how the pH developed inside the swollen gel is several units higher than the pH of the bath at equilibrium, both with or without the correction for counterion condensation. Consequently, when the pKa of the polyelectrolyte is determined in the usual way (with the pH measured in the external bath), it gives an apparent value that is several units below the pKa determined from the actual pH inside the swollen gel at equilibrium. The inclusion of the counterion condensation decreases very slightly the polymer basicity. Surface effects and intramolecular association between protonated and unprotonated imidazole rings are discussed to explain the pKa behavior in the limit of low degree of ionization.

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The pH inside a swollen polyelectrolyte network is calculated through a simple model, based on Donnan equilibrium and balance of mobile ions, extended to include the presence of a supporting electrolyte (salt) in the solution that swells the particle. This pH inside the gel, although needed to characterize the ionization properties of the polyelectrolyte, is generally not accessible to direct measurement. The main advantage of our model is that it is free from any simplification concerning the pK a of the ionizable groups. A common univalent anion is assumed for the acid and salt. The model was applied to chemically cross-linked poly(N-vinylimidazole) (PVI) immersed in acidic aqueous baths containing variable concentrations of HCl and NaCl as supporting electrolyte. The imidazole units are basic and become protonated by the acid, thus changing the pH of the initial bath. The data needed for the calculation of the proton concentration inside the gel, the degree of ionization, and the pK a of the polyelectrolyte are: polymer concentration, pH and salt concentration in the initial solution, and pH in the bath at equilibrium. All of them can be determined experimentally by a batch method, where the polymer is immersed in a different pot for each starting pH and salt concentration. It was thus found that in salt free solutions the pH inside the gel is several units higher than the pH in the external bath at equilibrium, but this difference between internal and external pH faints with added salt. The intrinsic pK a of PVI, determined from the pH in the gel, is slightly higher than the pK a of the model molecule, for salt free solutions, but it is lower with added salt (possibly due to the formation of a hydrogen bond between two imidazole units and its disruption by chloride). It was concluded that the pH inside the polymer must be employed instead of the pH outside, in order to calculate pK a , not only for a swollen polymer network, but also for a dissolved coil.