Numerical simulation of the swelling and deswelling process of gel

                                
==Abstract==

It is well known that the entropy elasticity of rubberlike materials and Brownian motion are described by formally analogous equations as both originated from thermal fluctuations. In rubberlike materials, the shear modulus is conventionally considered to be proportional to the absolute temperature and the proportionality factor is the number density of polymer chains for an affine polymer chains’ network model. On the other hand, the self-diffusion coefficient of Brownian motion is described as the product of the mobility and the absolute temperature. However, for the polymer chains’ network in a solvent, the interaction between the polymer chains and the solvent molecules occurs and the collective diffusion coefficient of the solvent molecules should be different to the self-diffusion coefficient of Brownian motion. Moreover, the shear modulus of the resultant polymer gel should be dependent on the swelling ratio due to the nonaffine movement of polymer chains. Therefore, to verify the analogy of the equations for the shear modulus of the nonaffine polymer chains’ network model and the collective diffusion coefficient of the solvent molecules, in this study, the swelling and deswelling process of the polymer gel is investigated by the numerical simulations.