Self-similar chain conformations in polymer gels

TL;DR

This study uses molecular dynamics simulations to investigate the swelling behavior and internal structure of polymer gels, revealing new scaling laws that challenge classical theories and proposing a self-similar model for network strands.

Contribution

It introduces a novel exponent for the internal structure of swollen polymer networks and a simple Flory argument supporting a self-similar interpenetrating strand model.

Findings

Equilibrium swelling saturates at Q_eq = N_e^(3/5).

Internal structure characterized by exponent nu=0.72, contradicting classical predictions.

Proposes a self-similar interpenetrating strand model with nu=7/10.

Abstract

We use molecular dynamics simulations to study the swelling of randomly end-cross-linked polymer networks in good solvent conditions. We find that the equilibrium degree of swelling saturates at Q_eq = N_e**(3/5) for mean strand lengths N_s exceeding the melt entanglement length N_e. The internal structure of the network strands in the swollen state is characterized by a new exponent nu=0.72. Our findings are in contradiction to de Gennes' c*-theorem, which predicts Q_eq proportional N_s**(4/5) and nu=0.588. We present a simple Flory argument for a self-similar structure of mutually interpenetrating network strands, which yields nu=7/10 and otherwise recovers the classical Flory-Rehner theory. In particular, Q_eq = N_e**(3/5), if N_e is used as effective strand length.