(435i) Calculating the Entropy of an Entangled Linear Polyethylene Melt Under Shear and Elongational Flows Via Atomistic Simulation | AIChE

# (435i) Calculating the Entropy of an Entangled Linear Polyethylene Melt Under Shear and Elongational Flows Via Atomistic Simulation

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University of Tennessee at Knoxville
University of Tennessee
University of Tennessee
The theory of nonequilibrium thermodynamics as applied to polymeric liquids is limited by the inability to accurately identify and quantify the systemâ€™s overall entropy. From an experimental perspective, a technique to measure the entropy of a polymer solution or melt simply does not exist, and as far as is known, no one is seriously trying to develop one. On the other hand, one might expect that entropy, a purely statistical property of the polymeric liquid based on counting the occupancy of configurational microstates of the constituent macromolecules, could be readily calculated via atomistic simulation of nonequilibrium flow systems, similarly to the internal energy. This expectation is not justified in practice, however, for two major reasons: 1) a theory is necessary to relate atomic positions to configurational microstates and these microstates to entropy; and 2) immense computational resources are required to perform the intensive integrations involved in determining the 3-dimensional probability distribution functions that relate the configurational microstates to the entropy. In this paper, we resolve both of these issues for a linear, entangled polyethylene melt undergoing both shear and elongational flow. We calculate the entropy using Wallâ€™s expression in terms of 3-d probability distribution functions of the configurational microstate of the system over several length and time scales at multiple strain rates in both types of flow. We also compute the entropy using an expression developed by Booij for the Rouse Model, and demonstrate that a modified form of this equation reproduces the entropy calculation from Wallâ€™s expression unexpectedly well. This is tremendously helpful since the Booij expression requires only information about the second moments of the probability distributions, which are very inexpensive to calculate during an atomistic simulation and are statistically quite accurate.