(232b) Evaluation of Energetic and Entropic Contributions to the Free Energy of Oriented Polymer Melts

Evaluation of
Energetic and Entropic Contributions to the Free Energy of Oriented Polymer
Melts

Introduction

Writing
constitutive equations for polymeric flows has been one of the major engineering
challenges for the past half century. In the mid 1970's, under the premise that
the total free energy of the fluid is determined entirely by the conformational
entropy of the material, the Theory of Purely Entropic Elasticity (PEE)
emerged [1-3]. Under this premise, the internal energy density of any fluid
particle, ε, was taken as a function of temperature only. In other words,
the internal energy of a melt does not change when the melt is subjected to
deformation, and the change in free energy due to orientation is entirely due
to the change in entropy. The aim of this work is to test the validity of the PEE
through a series of atomistic simulations of long chain alkane systems.

Approach

We
investigated polydisperse systems of n-alkanes, with average chain
lengths ranging from C₂₄ up to C₇₈. The simulations were
carried out using the End-Bridging Monte Carlo scheme (EBMC) of Pant and Theodorou
[4], as implemented by Mavrantzas et al [5-7]. The melts were oriented using
the uniaxial orienting field of Mavrantzas and Öttinger [7]. The chains were
modeled using the united atom approach of Siepmann et al. [8]. The free energy
of the melts was evaluated using two different approaches: via direct
thermodynamic integration [7, 9] and from the FENE-P and the UCM visco-elastic models
[10].

Results

Our
results indicate that the free energy of the systems under investigation has
contributions from both energetic and entropic origins. Moreover, we show that
the relative magnitude of the energetic and entropic contributions has a strong
dependence on temperature, orienting field strength and molecular weight. For
example, the relative effect of the energetic to the entropic contributions
tends to diminish with increasing molecular weight. All of these effects will
be presented and discussed in detail, as well as their implications to the Theory
of Purely Entropic Elasticity.

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