Brownian Dynamics simulation of reversible polymeric networks

In this paper we describe the construction of a Brownian Dynamics simulation of reversibly cross-linked networks. The simulation differs from existing analytical approaches and computer simulations of networks in the sense that we also take the topology of the network into account. The motion of the junction points between different molecules is not prescribed but is calculated from a force balance. This makes it possible to measure the effect of network reorganisations on the stress relaxation. The response of networks to shear flow is measured and analysed in terms of transient network theory and within the framework of linear viscoelasticity. It is shown that the average motion of the junction is affine but that there is a long time diffusive process around the affine path. It was found that, even in systems with Gaussian chains and fixed association and disociation rates, a shear thickening of the viscosity and primary normal stress coefficient can occur. The reason was found to be that dangling segments are recaptured by the network before they had the opportunity to fully relax to the equilibrium state where the probability of reattachment to the network increases linearly with the length of a segment. Due to this mechanism the fraction of long segments present in the network is increased. This explanation of shear thickening seems to be consistent with experimental findings.