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# Chemical Potential of a Flexible Polymer Liquid in a Coarse-Grained Representation

journal contribution

posted on 2023-12-18, 17:07 authored by M. Dinpajooh, J. Millis, J. P. Donley, M. G. GuenzaWhile the excess chemical potential
is the key quantity in determining
phase diagrams, its direct computation for high-density liquids of
long polymer chains has posed a significant challenge. Computationally,
the excess chemical potential is calculated using the Widom insertion
method, which involves monitoring the change in internal energy as
one incrementally introduces individual molecules into the liquid.
However, when dealing with dense polymer liquids, inserting long chains
requires generating trial configurations with a bias that favors those
at low energy on a unit-by-unit basis: a procedure that becomes more
challenging as the number of units increases. Thus, calculating the
excess chemical potential of dense polymer liquids using this method
becomes computationally intractable as the chain length exceeds

*N*≥ 30. Here, we adopt a coarse-grained model derived from the integral equation theory for which inserting long polymer chains becomes feasible. The integral equation theory of coarse graining (IECG) represents a polymer as a sphere or a collection of blobs interacting through a soft potential. We employ the IECG approach to compute the excess chemical potential using Widom’s method for polymer chains of increasing lengths, extending up to*N*= 720 monomers, and at densities reaching up to ρ = 0.767 g/cm^{3}. From a fundamental perspective, we demonstrate that the excess chemical potentials remain nearly constant across various levels of coarse graining, offering valuable insights into the consistency of this type of procedure. Ultimately, we argue that current Monte Carlo algorithms, originally designed for atomistic simulations, such as configurational bias Monte Carlo (CBMC) methods, can significantly benefit from the integration of the IECG approach, thereby enhancing their performance in the study of phase diagrams of polymer liquids.## History

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## Keywords

offering valuable insightsintegral equation theorychain length exceedsgrained model derivedwidom insertion methoddetermining phase diagramslong polymer chainsexcess chemical potentialdense polymer liquidsflexible polymer liquidphase diagramspolymer chainschemical potentialpolymer liquidsgrained representationsoft potentialdensity liquids≥ 30units increasesthereby enhancingsignificantly benefitsignificant challengeoriginally designedn low energykey quantityinvolves monitoringinternal energyincreasing lengthsfundamental perspectivedirect computationdensities reachingcalculated usingblobs interactingatomistic simulations767 g720 monomers

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