Stress evolution in a phase-separating polymeric gel

A polymer network can swell tremendously to form a gel which is typically transparent at room temperature. Upon temperature quenching, however, the gel can undergo phase separation and become opaque. We revisit and formulate the dynamics of phase separation of gels through co-evolution of polymer volume fraction and left Cauchy-Green tensor; both are physical and measurable quantities. A hybrid Fourier spectral method and an isotropic finite difference method is proposed to solve the evolution equations, and the scheme is verified to be efficient for either an isotropically or anisotropically swollen gel. For the isotropic swelling gel, a percolating network structure, where the shrunken phase encloses the solvent-rich phase, is formed during phase separation. With the formation of network structure, an inhomogeneous stress field builds up within the network and evolves simultaneously with concentration modulation. The effective stress levels in the common vertices of several shrunken phases are relatively low while the network segments between two vertices constitute the high stress region. A plausible stress-supporting mechanism is proposed to explain the formation of network structure and the phase-inversion phenomenon.