Title: Improved approximations of non-Gaussian probability, force, and energy of a single polymer chain

Abstract

The mechanical behavior of polymers such as their probability density function (PDF), strain energy, and entropic force, has long been described by the non-Gaussian statistical model. Non-Gaussian models are often approximated by the Kuhn-Grün (KG) distribution function, which is derived from the first-order approximation of the complex Rayleigh's exact Fourier integral distribution. Furthermore, the KG function is widely accepted in polymer physics, where the non-Gaussian theory is often used to describe energy of the chains with various flexibility ratios. However, the KG function is shown to be relevant only for long chains and becomes extremely inaccurate for chains with fewer than 40 segments. In comparison to the KG model, other approximations of the non-Gaussian statistical model are often less accurate, and those with higher accuracy are usually too complex to be implemented in large-scale simulations. Here a new accurate approximation of the non-Gaussian PDF, entropic force, and strain energy of a single chain subsequently is developed to describe the mechanics of a polymer chain. With a similar level of complexity, the presented approximations of non-Gaussian PDF, strain energy, and entropic force are at least 10 times more accurate than KG approximations and thus are an excellent alternative option to bemore » used in micromechanical constitutive models.« less

Authors:

Morovati, Vahid ^[1]; Dargazany, Roozbeh ^[1]

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1. Michigan State Univ., East Lansing, MI (United States)

Publication Date:

Fri May 10 00:00:00 EDT 2019

Research Org.:

Michigan State Univ., East Lansing, MI (United States)

Sponsoring Org.:

USDOE Office of Energy Efficiency and Renewable Energy (EERE)

OSTI Identifier:

1614104

Alternate Identifier(s):

OSTI ID: 1511894

Grant/Contract Number:  

EE0008455

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review E

Additional Journal Information:

Journal Volume: 99; Journal Issue: 5; Journal ID: ISSN 2470-0045

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

42 ENGINEERING; Physics; Classical statistical mechanics; Random walks