The effect of chain polydispersity on the elasticity of disordered polymer networks

Abstract

Due to their unique structural and mechanical properties, randomly-crosslinked polymer networks play an important role in many different fields, ranging from cellular biology to industrial processes. In order to elucidate how these properties are controlled by the physical details of the network (e.g. chain-length and end-to-end distributions), we generate disordered phantom networks with different crosslinker concentrations C 1

Onset of criticality in hyper-auxetic polymer networks

“…Indeed, theoretical works have addressed the occurrence of auxeticity in two-dimensional models of networks under tension [18,19].It is important to notice that these studies have flourished about twenty years ago, but the interest in hydrogel and microgel networks has increased again in the last few years, thanks to advances in chemical and in silico synthesis.In particular, it became recently possible to tune the amount of branching points (crosslinkers) to yield ultra-lowcrosslinked networks [20-23]. In parallel, numerical efforts have been able to realize fully-connected, disordered networks with arbitrary density and crosslinker concentrations [24,25].In this article, we numerically investigate the elastic properties of polymer networks under tension and demonstrate that auxeticity naturally emerges in the ultra-low-crosslinked limit. Combining stress-strain and equilibrium simulations, we show that low-density polymeric networks exhibit a non-monotonic behavior of K as well as ν, the latter becoming increasingly negative with reducing crosslinker concentration c. This phenomenology is found for both ordered diamond-like and disordered hydrogel realizations, indicating that there is no need of a specific topology to observe auxeticity in polymer networks.…”

“…In particular, it became recently possible to tune the amount of branching points (crosslinkers) to yield ultra-lowcrosslinked networks [20-23]. In parallel, numerical efforts have been able to realize fully-connected, disordered networks with arbitrary density and crosslinker concentrations [24,25].…”

“…Since the preparation procedure is based on the self-assembly of patchy particles [24,25], we cannot easily obtain disordered networks with smaller values of c, due to the nearby occurrence of phase separation. Thus, for lower degree of crosslinking, we focus only on diamond networks, having shown in Fig.…”

“…Since it is well-known that entropy plays a fundamental role for phase behaviour of polymer systems [30], we also quantify the effect of entropy by calculating the average single-chain entropy s l within a Langevin-approximation (see Methods and Ref. [25]).…”

“…This procedure is repeated for each configuration by deforming the network over all three directions independently, in order to improve the statistics of the results. The bond length l bond is calculated from the time averages of the particle separations, while the single chain entropy s l is obtained within the Langevin approximation [25]. We define an order parameter M as the zero average and unitary variance version of the order parameter M = ρ + se nb , where ρ is the density, s is a mixing parameter and e nb is the energy of non-bonded particles only.…”