Improved approximations of non-Gaussian probability, force, and energy of a single polymer chain
- Michigan State Univ., East Lansing, MI (United States)
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.
- Research Organization:
- Michigan State Univ., East Lansing, MI (United States)
- Sponsoring Organization:
- USDOE Office of Energy Efficiency and Renewable Energy (EERE)
- Grant/Contract Number:
- EE0008455
- OSTI ID:
- 1614104
- Alternate ID(s):
- OSTI ID: 1511894
- Journal Information:
- Physical Review E, Vol. 99, Issue 5; ISSN 2470-0045
- Publisher:
- American Physical Society (APS)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
A generalized approach to generate optimized approximations of the inverse Langevin function
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journal | November 2018 |
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