Do Transport Properties of Entangled Linear Polymers Scale with Excess Entropy?

Abstract

We analyze the range of validity of the empirical excess entropy scalings proposed independently by Rosenfeld and Dzugutov for the viscosity and the diffusion coefficient of monodisperse Lennard-Jones chains. They are long enough to be considered as entangled. Thus, the influence of entanglements on entropy scalings can be quantified. We make use of thermodynamic integration to determine the exact excess entropy. Different ways of approximating the excess entropy either based on conformational information or by employing the self-associating fluid theory (SAFT) are explored. The correlations between the various excess entropy estimates are investigated in detail. The conformational route appears to be the most suitable way for the studied Lennard-Jones systems. Its prediction is in qualitative agreement with those obtained by thermodynamic integration, which is computationally more demanding. The SAFT results are not always consistent with the simulation data. The main qualitative feature of both the Rosenfeld and Dzugutov scaling is the coexistence of two linear regimes in the correlation of different entropy expressions. The sharpness of the transition regime depends on the way the excess entropy is approximated. The Dzugutov scaling for the viscosity seems to have certain advantages in comparison to the Rosenfeld one. The influence of the chain length on the parameters appearing in the excess entropy scaling relationships is examined. Despite the pronounced chain length dependence of the scaling parameters, a master curve relating the diffusion coefficient to the excess entropy is derived when performing a suitable renormalization. The relation between the scaling parameters of the viscosity and the diffusion coefficient are—with one exception—in line with the predictions of the Stokes–Einstein law.