Effects of Shear Modulus of Polymer Gels

Abstract

Gels exhibit mechanical properties characteristic of both solid and liquid-gas systems. From the compressibility (bulk modulus) point of view, a gel network system behaves like liquid-gas system. The value of the bulk modulus of a gel is small in the dilute (corresponding to the gas) phase and is large in the dense (corresponding to the liquid) phase. However, the shear modulus of a liquid-gas system is zero, but is finite for a gel (although much smaller than solids). Thus, the gel network behaves like a solid from the rigidity (shear modulus) point of view. These special properties make the gel system a unique material for theoretical study and practical applications. Compared with the liquid-gas, the free energy of a gel is $$ dF = - SdT - PdV - YdX. $$ (1) Where Y and X are the shear stress and the shear deformation. The bulk (K) and shear (µ) moduli are related with the second derivatives of F with respect to V and X, respectively [1]. The shear modulus given by Flory’s theory is µ = v eRT, with v e the effective number of chains per unit volume at 6 temperature [2]. In most of the experiments, the gel is free of macroscopic shear constraints and hence the last term in Eq.(l) can be neglected when the system is far from the critical point. For this reason the analogy between the phase transition of the gel system and liquid-gas system is often used in discussion of the gel phase transitions. Near the critical point, this term will suppress the density fluctuations of the system.