Configurational Entropy of Disordered Polymer Melts

Abstract

The configurational entropy of a dense polymer melt governs its structural relaxation near the glass transition, yet
direct estimation remains difficult because the relevant microstates are neither easily enumerated nor cleanly
separated from vibrational contributions. We report molecular dynamics simulations of coarse-grained polymer
melts, chain lengths N = 20 to 200 beads, at 36 state points spanning reduced temperatures T* = 0.38 to 1.20 and a
fixed monomer density of 1.02 sigma^-3, and estimate configurational entropy per monomer using the two-phase
thermodynamic method combined with inherent-structure sampling over 4,800 independent quenches per state
point. Configurational entropy per monomer, s_c, decreased from 1.84 k_B at T* = 1.20 to 0.31 k_B at T* = 0.42,
tracking an Adam-Gibbs relation with fitted Kauzmann temperature T*_K = 0.36 +/- 0.02 across all chain lengths
tested, and the relaxation time extracted from the self-intermediate scattering function followed tau = tau_0 exp(A /
(T s_c)) with A = 0.29 +/- 0.03 and R^2 = 0.987 over four decades of relaxation time. Chain length affected s_c
systematically: for N >= 50 the entropy per monomer collapsed onto a single master curve within 4%, while shorter
chains (N = 20) showed 12-18% higher configurational entropy at fixed T* due to larger chain-end free-volume
contributions, an effect that diminished progressively with increasing N and was essentially absent by N = 100. The
fragility parameter D in the Vogel-Fulcher-Tammann form, extracted independently from the relaxation data,
correlated with the Adam-Gibbs entropy slope A across chain lengths with Pearson r = 0.91 (p < 0.001, n = 5 chain
lengths), supporting a common thermodynamic origin for both the entropy collapse and the fragility trend. A
sensitivity analysis varying the inherent-structure quench protocol (steepest descent versus conjugate gradient, and
quench rates spanning two orders of magnitude) changed absolute s_c estimates by less than 6% and left the fitted
Kauzmann temperature unchanged within uncertainty, indicating that the reported entropy-relaxation coupling is
robust to methodological choices in inherent-structure sampling. These results provide a chain-length-resolved,
quantitatively validated link between configurational entropy and dynamical arrest in polymer melts, with direct
implications for coarse-grained models used to predict processing behavior near the glass transition in industrial
polymer formulations.