Scaling of the dynamics of flexible Lennard-Jones chains

Abstract

The isomorph theory provides an explanation for the so-called power law density scaling which has been observed in many molecular and polymeric glass formers, both experimentally and in simulations. Power law density scaling (relaxation times and transport coefficients being functions of ρ γ S /T , where ρ is density, T is temperature, and γS is a material specific scaling exponent) is an approximation to a more general scaling predicted by the isomorph theory. Furthermore, the isomorph theory provides an explanation for Rosenfeld scaling (relaxation times and transport coefficients being functions of excess entropy) which has been observed in simulations of both molecular and polymeric systems. Doing molecular dynamics simulations of flexible Lennard-Jones chains (LJC) with rigid bonds, we here provide the first detailed test of the isomorph theory applied to flexible chain molecules. We confirm the existence of isomorphs, which are curves in the phase diagram along which the dynamics is invariant in the appropriate reduced units. This holds not only for the relaxation times but also for the full time dependence of the dynamics, including chain specific dynamics such as the end-to-end vector autocorrelation function and the relaxation of the Rouse modes. As predicted by the isomorph theory, jumps between different state points on the same isomorph happen instantaneously without any slow relaxation. Since the LJC is a simple coarse-grained model for alkanes and polymers, our results provide a possible explanation for why power-law density scaling is observed experimentally in alkanes and many polymeric systems. The theory provides an independent method of determining the scaling exponent, which is usually treated as a empirical scaling parameter.

Thermodynamic scaling of vibrational dynamics and relaxation

“…In the MD study the polymer chain is modelled with either rigid or semi-rigid bonds. The variant of the polymer model with semi-rigid bonds, differently from the one with rigid bonds [90], is not a strongly-correlating liquid, as previously noted [27] and recently reported [28] for a closely related model, owing to the competition between the bonding and the non-bonding interactions [25,26]. This means that there is no effective inverse-power law potential replacing the actual particle-particle interaction potential, thus precluding the usual TS interpretation.…”

Communication: Polymer entanglement dynamics: Role of attractive interactions

“…with either purely repulsive or attractive interactions as one approaches the glass transition. [12][13][14][15][16][17][18][19] Common to all computational studies, the nature of the interactions is at the core of their ability to adequately probe polymeric properties. Therefore accessing the basic assumption that polymer chains can be described solely by repulsive interactions is one critical aspect of probing polymers computationally.…”

Communication: Simple liquids’ high-density viscosity

“…This fact is not reliant on a particular form of the potential as long as the system has strong virial potential-energy correlations at the state points in question. 28 In particular, it is not restricted to inverse-power potentials or even to pair potentials, and several molecular systems have been shown to conform to the isomorph theory in computer simulations 32,33 and experiments. [34][35][36] Not all systems have isomorphs, though.…”

“…31,44 For such systems, the scaling property is rarely obvious from the mathematical expression for U(R) for which reason the term "hidden scale invariance" is sometimes used. 28,33,[45][46][47][48][49] The R-simple region of a given system is identified in computer simulations as the state points characterized by strong virial potential-energy correlations in constant-volume canonical-ensemble fluctuations. 28,50,51 For the LJ liquid, our simulations have shown that the Pearson correlation coefficient obeys R > 0.94 at all state points with density and temperature higher than those of the liquid at the triple point.…”