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 »
- Authors:
-
- Michigan State Univ., East Lansing, MI (United States)
- Publication Date:
- 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
Citation Formats
Morovati, Vahid, and Dargazany, Roozbeh. Improved approximations of non-Gaussian probability, force, and energy of a single polymer chain. United States: N. p., 2019.
Web. doi:10.1103/physreve.99.052502.
Morovati, Vahid, & Dargazany, Roozbeh. Improved approximations of non-Gaussian probability, force, and energy of a single polymer chain. United States. https://doi.org/10.1103/physreve.99.052502
Morovati, Vahid, and Dargazany, Roozbeh. Fri .
"Improved approximations of non-Gaussian probability, force, and energy of a single polymer chain". United States. https://doi.org/10.1103/physreve.99.052502. https://www.osti.gov/servlets/purl/1614104.
@article{osti_1614104,
title = {Improved approximations of non-Gaussian probability, force, and energy of a single polymer chain},
author = {Morovati, Vahid and Dargazany, Roozbeh},
abstractNote = {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 be used in micromechanical constitutive models.},
doi = {10.1103/physreve.99.052502},
journal = {Physical Review E},
number = 5,
volume = 99,
place = {United States},
year = {Fri May 10 00:00:00 EDT 2019},
month = {Fri May 10 00:00:00 EDT 2019}
}
Web of Science
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Works referencing / citing this record:
A generalized approach to generate optimized approximations of the inverse Langevin function
journal, November 2018
- Morovati, Vahid; Mohammadi, Hamid; Dargazany, Roozbeh
- Mathematics and Mechanics of Solids, Vol. 24, Issue 7