The Influence of Crosslinking and Deformation on Polymer Crystallization and Melting: A Molecular Dynamics Study

TL;DR

This work tackles how crosslinking and external deformation influence crystallization and melting in a highly entangled polymer melt. It employs large-scale coarse-grained MD of poly(vinyl alcohol) (CG-PVA) with controlled crosslinking, uniaxial pre-stretch, and cooling/heating cycles under both constant-strain and constant-stress conditions. Key findings show that uniaxial deformation shifts crystallization and melting temperatures to higher values, that crosslinks elevate nucleation barriers during deformation but can suppress final crystallinity, and that constant-stress conditions induce spontaneous elongation and stronger crystalline orientation, revealing shape-memory-like hysteresis. These results advance understanding of thermo-mechanical history effects in semi-crystalline elastomers and offer design principles for shape-memory polymers.

Abstract

We investigate the crystallization of crosslinked and entangled polymers under external deformation using a coarse-grained poly(vinyl alcohol) (CG-PVA) model and molecular dynamics simulations. Following uniaxial deformation, the systems are cooled at a constant rate to form semi-crystalline states and subsequently heated at a constant rate to induce melting. For unstretched systems, network junctions do not significantly affect the nucleation temperature but increase the amorphous fraction and reduce the melting temperature. Uniaxial deformation accelerates nucleation and markedly increases the crystallization temperature, with more strongly crosslinked polymers exhibiting larger shifts that correlate with an enhanced orientation order parameter. We further compare cooling and heating cycles under constant-strain and constant-stress conditions. Under constant stress, crystallization induces additional elongation beyond the initial pre-stretch and leads to pronounced mechanical hysteresis upon heating, a behavior characteristic of reversible shape-memory materials.

Figures (10)

• Figure 1: (a) A summary flowchart of the steps involved in the protocol. Step $0$ includes the melt preparation and relaxation. The simulation results of each of these steps can be found in the following figures. Please refer Figure \ref{['fig:protocol_cl']} for step $2$, Figure \ref{['fig:protocol_deform']} for step $3$, SI Figure \ref{['fig:nvt']} for step $4$, SI Figure \ref{['fig:npt']} for step $5$ and SI Figures \ref{['fig:pressure']} and \ref{['fig:box_len']} for steps $6$ and $7$, respectively. (b) An illustration (not to scale) of two crosslinks (left) and the deformation of two entangled polymer chains along the x-axis (middle). A combination of the crosslinking and deformation processes is drawn on the right.
• Figure 2: Illustrations of the crosslinking and deformation steps involved in the protocol. (a) Starting with a relaxed melt state, we introduce crosslinks in the system. The dashed line marks the evolution of crosslinks, whereas the colored upright triangles denote the characteristic configurations of average bonds per chain chosen to apply the deformation in the next step. (b) Following the process of crosslinking, the system is uniaxially deformed along the x-axis, $\lambda$. The system with $\lambda=1.0$ is the undeformed system, refer to Equation \ref{['eq:lambda']}. Deformation steps continue until $\lambda$ reaches $3.0$.
• Figure 3: (a) True stress ($\sigma_{true}$) and (b) the Mooney-Rivlin plot at high temperature $T=0.9$ as a function of $\lambda$ and $1/\lambda$, respectively. We see the contribution of pure entanglements and deformation in the uncrosslinked system ($0bpc$), and the additional contribution of the network part in the cases of $1bpc$ and $2bpc$. The values of Mooney constants are: $C_1 = [0.031,~ 0.040, ~0.008]$ and $C_2= [0.656,~0.851,~1.115]$ for $0bpc$, $1bpc$, and $2bpc$, respectively.
• Figure 4: (a) The gel fraction shown as the development in the largest network size ($n_{max}$) of the system with an increasing average number of crosslinks per chain. (b) Histogram of elastic network strands, i.e. part of the polymer chain between two crosslinking ends for $1bpc$ and $2bpc$. (c) Lengths of dangling strands, i.e. part of the chains with at least one free end. The straight lines correspond to the binomial distribution (Equation \ref{['eq:binomial']}) of the dangling strands. Since the network fills most of the sample as we reach the density of $2bpc$, we do not consider the case of $3bpc$ for further figures in the panel.
• Figure 5: Definition of characteristic temperatures as used in this work. The graph presents the first derivative of the total volume with respect to temperature (thermal expansion coefficient) during cooling (continuous line) and heating (dotted line) cycles for the undeformed sample $0bpc$.