Understanding the role of cross-link density in the segmental dynamics and elastic properties of cross-linked thermosets

Abstract

Cross-linking is known to play a pivotal role in the relaxation dynamics and mechanical properties of thermoset polymers, which are commonly used in structural applications because of their light weight and inherently strong nature. Here, we employ a coarse-grained (CG) polymer model to systematically explore the effect of cross-link density on basic thermodynamic properties as well as corresponding changes in the segmental dynamics and elastic properties of these network materials upon approaching their glass transition temperatures ( Tg). Increasing the cross-link density unsurprisingly leads to a significant slowing down of the segmental dynamics, and the fragility K of glass formation shifts in lockstep with Tg, as often found in linear polymer melts when the polymer mass is varied. As a consequence, the segmental relaxation time τα becomes almost a universal function of reduced temperature, ( T − Tg)/ Tg, a phenomenon that underlies the applicability of the “universal” Williams–Landel–Ferry (WLF) relation to many polymer materials. We also test a mathematical model of the temperature dependence of the linear elastic moduli based on a simple rigidity percolation theory and quantify the fluctuations in the local stiffness of the network material. The moduli and distribution of the local stiffness likewise exhibit a universal scaling behavior for materials having different cross-link densities but fixed ( T − Tg)/ Tg. Evidently, Tg dominates both τα and the mechanical properties of our model cross-linked polymer materials. Our work provides physical insights into how the cross-link density affects glass formation, aiding in the design of cross-linked thermosets and other structurally complex glass-forming materials.

Competing Effects of Cohesive Energy and Cross-Link Density on the Segmental Dynamics and Mechanical Properties of Cross-Linked Polymers

“…The molecular structure used in this work is the same as that in our previous work. 47 The molecules are mixed in a large cubic…”

“…Here, we describe the simulation methods, which have also been described in our preceding study focusing on the same thermoset model where only the cross-link density was varied. 47 All the MD simulations are performed in Large Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software. 51 The initial mixture of linear chains and cross-linkers is relaxed in an NPT ensemble at a temperature T = 1.0 and a pressure P = 0 to ensure that linear chains and cross-linkers are homogeneously mixed.…”

“…A subsequent multiple cross-linking−relaxation algorithm developed by Varshney et al 52 is performed to connect the molecules into a three-dimensional network, which has been found to be well consistent with the experiments. 47,52,53 For every iteration, we bond the unreacted reactive bead pairs within the cutoff distance first, and then an energy minimization process and NPT relaxation process are performed to reduce the energy fluctuations caused by the introduction of new chemical bonds. The cross-linking− relaxation cycle stops when more than 98% reactive beads are reacted.…”

“…A comprehensive analysis about the effect of varying cross-link density alone on the thermodynamic properties can be found in our previous work. 47 3.2. Segmental Relaxation Dynamics.…”

“…In our preceding work, we explored the influence of varying the cross-link density on the segmental dynamics and basic mechanical properties of network polymers described by a simple CG model in which no changes in cohesive interaction strength were considered. 47 The principal goal of this earlier work was to understand the effect of crosslinking in isolation from other contributing factors on the thermoset dynamics. In the present work, we systematically investigate the segmental relaxation dynamics and mechanical properties of cross-linked thermosets over a wide range of cross-link densities and a large range of cohesive energy governing the strength of local short-range attractive interactions in the material.…”