Elastic properties of swollen polyelectrolyte gels in aqueous salt solutions

The elastic relaxation responding to a uniaxially stretched poly(acrylic acid) rodlike gel in the aqueous NaCl solution was investigated. The relaxation elucidated the shear (mu) and bulk (K) moduli and the frictional coefficients (sigma) of the fully ionized gel at pH above 9 as functions of the degree of swelling, which was controlled by the NaCl concentration (C(S)) of the solution. Two gels, cross-linked chains of which consist of 500 (GelA500) and 50 (GelA50) monomeric units, were examined to investigate the effect of the chain length on the elastic behavior. The moduli of GelA500 increased with swelling at C(S) below 100 mM and decreased at C(S) above it. The mu values of both gels can be characterized by the power function of gel diameter, d as mu proportional, variantd(beta). The beta values being -1 at C(S) above 100 mM transitionally changed to 1.2 at C(S) about 100 mM. That is, the dimensionality of space for the chains to distribute, n(dim) [= (beta+5)/(beta+2) according to the conventional theory [Sasaki et al., J. Chem. Phys. 102, 5694 (1995)]], changed from 4 (n(dim) of ideal chain) to 1.9 at C(S) = 100 mM. This indicates that the electrostatic repulsion between gel chains reduces the n(dim) at C(S) below 100 mM but not at C(S) above it. It was found that the K values of GelA500 were well described by the conventional theory but those of GelA50 not. The sigma(zr)/sigma(rr) (sigma(zr) is an off-diagonal element of the friction coefficient tensor and sigma(rr) is a diagonal element of the friction coefficient tensor) was found to be 2.7 x 10(-2), which was the same as the previously reported value for the swollen poly(acrylamide) gel [Sasaki, J. Chem. Phys. 120, 5789 (2004)]. The sigma(rr) of unit volume of the GelA500 is well explained by the free draining model while the sigma(rr) of GelA50 is less than that of the free draining model, suggesting the slip between water and ionized chain.