Theory of mechanochemical systems

An electrolytic theory is developed for the swelling and deswelling mechanism of mechanochemical systems by methods established by the authors, who are concerned with the problem of polyelectrolyte solutions. The model employed in the theory is a macroscopic cylindrical fiber of rubberlike material with many dissociative radicals. It is assumed, for the sake of simplicity, that the average charge density of the ionized radicals is spread uniformly inside the fiber. The result of the theory shows that almost all the gegenions are bound by the fiber, and that the contributions of the electrostatic energy and entropy to the electrostatic free energy are two‐ and three‐dimensional, respectively, when the density of the ionized radicals remains constant. In combination with theoretical results of rubberlike elasticity and of nonelectrolytic swelling, it is concluded that the osmotic pressure of the gegenions bound by the system makes the system swell against the restoring force due to the rubberlike elasticity of the system. The free swelling of systems is, for instance, expressed by the following relation: where α is the relative elongation, N the number of the dissociative radicals per chain ξ the degree of neutralization, and B the factor due to the full stretching effect of each chain. This relation is in good agreement with experimental results.