TRANSIENT NETWORK THEORY FOR SHEAR-THICKENING FLUIDS AND PHYSICALLY CROSS-LINKED SYSTEMS

A model is introduced to treat the dynamics of coexistence between a physically cross-linked network with temporary junctions and unbound chains. Focusing on unentangled networks in which the molecular weight between neighboring cross-links is smaller than the entanglement molecular weight, we introduce three types of chains in a network-forming system: the elastically effective chains in the network that undergo affine deformation, dangling chains with one end sticking to junctions that experience deformation only through viscous interactions, and unbound free chains. Kinetic exchange between these chains is described by deriving three rate equations. The condition of incompressibility allows us to solve these coupled equations for arbitrary macrodeformation. Under deformations that are invariant in time, we obtain explicit expressions for the steady-state number density of each type of chain, exchange rates between different chains, steady-state shear viscosity, and normal stress differences. This study, besides representing an important extension of previous transient network models, provides a theoretical basis for explaining shear-thickening phenomena in certain gellike systems.