Odd-Even Effect of Junction Functionality on the Topology and Elasticity of Polymer Networks

The junction functionality of polymer networks is a key design variable to tune the material properties through changing the network connectivity. Here, we perform a Monte Carlo simulation to study the topology and elasticity of end linked polymer networks constructed by junctions with different functionalities. The effect of junction functionality on the topological structure of the network displays both universal features and odd even effects. For all junction functionalities, the primary loop fraction shows a linear dependence on the dimensionless product of concentration with single chain pervaded volume. The slopes of the lines exhibit strong odd even alternation: primary loops are formed more frequently for junctions with an odd number of functional groups. The secondary loop fraction has a maximum when plotted against the normalized primary loop fraction, where the value of the maximum also shows odd even alternation. The topological information obtained through Monte Carlo simulation is then incorporated into the modified affine network theory and modified phantom network theory (real elastic network theory). For affine networks, the odd even alternation in the cyclic topology leads to nonmonotonic dependence of elastic modulus on the junction functionality. For phantom networks, the effect of decreasing junction fluctuations due to a larger number of interjunction connections dominates over the changes in loop concentration as junction functionality increases, leading to monotonically increasing elastic modulus with junction functionality.