Theory of volume phase transition of slide-ring gels

Volume phase transition is a phenomenon in which gels drastically swell or shrink with an infinitesimal change in the external environment. This behavior is well explained by the Flory-Rehner-Tanaka theory. However, some assumption in the theory breaks down in a slide-ring gel composed of grand canonical chains in which the segment number between cross-linking junctions can change. The stress-strain behavior of the slide-ring gel is in a qualitative agreement with the free junction model, in which the segment number changes to maximize the entropy under the condition that the total sum of the segment number is constant. However, the model cannot work well to isotropic swelling of the slide-ring gel. To describe the volume phase transition of the slide-ring gel, we propose a new theory based on the free junction model with the effects of dangling strands, uncross-linked cyclic molecules (free rings), and high elongation. As a result, it turns out that the exchange of segments between effective and dangling strands leads to the suppression of the volume phase transition in the highly cross-linked gel and the promotion in the loosely cross-linked one. The suppression and promotion of the volume phase transition became more obvious as free rings decreased.