Numerical Analysis of PRISM-PY Calculations for Hard- and Soft-Core Generic Polymer Models

Qiang Wang

doi:10.1007/s10118-023-3055-7

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Numerical Analysis of PRISM-PY Calculations for Hard- and Soft-Core Generic Polymer Models

RESEARCH ARTICLE | Updated：2024-03-14

- Numerical Analysis of PRISM-PY Calculations for Hard- and Soft-Core Generic Polymer Models
- Numerical Analysis of PRISM-PY Calculations for Hard- and Soft-Core Generic Polymer Models
- 高分子科学（英文版） 2024年42卷第4期页码：532-543
- Affiliations：
  
  Department of Chemical and Biological Engineering, Colorado State University, 1370 Campus Delivery, Fort Collins, CO 80523-1370, USA
- Author bio：
  
  q.wang@colostate.edu
- Funds：
  
  Q. W. thanks the two anonymous reviewers for their suggestions of adding Flowchart 1 and Table 1. Acknowledgement is made to the donors of The American Chemical Society Petroleum Research Fund for partial support of this research.
- DOI：10.1007/s10118-023-3055-7
  中图分类号：
- 收稿：2023-08-17，
  
  修回：2023-9-17，
  
  录用：2023-9-20，
  
  网络首发：2023-11-11，
  
  纸质出版：2024-04-01
- Accepted：
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Wang, Q. Numerical analysis of PRISM-PY calculations for hard- and soft-core generic polymer models. Chinese J. Polym. Sci. 2024, 42, 532–543

Qiang Wang. Numerical Analysis of PRISM-PY Calculations for Hard- and Soft-Core Generic Polymer Models[J]. Chinese Journal of Polymer Science, 2024, 42(4): 532-543.
Wang, Q. Numerical analysis of PRISM-PY calculations for hard- and soft-core generic polymer models. Chinese J. Polym. Sci. 2024, 42, 532–543 DOI： 10.1007/s10118-023-3055-7.

Qiang Wang. Numerical Analysis of PRISM-PY Calculations for Hard- and Soft-Core Generic Polymer Models[J]. Chinese Journal of Polymer Science, 2024, 42(4): 532-543. DOI： 10.1007/s10118-023-3055-7.

摘要

In PRISM-PY calculations of homopolymer melts

the local extrema of the interchain indirect pair correlation function (PCF)

$${\hat \gamma _{\rm{e}}} $$

http://notExist.jpg

decay much faster with wavenumber

than those of the interchain direct PCF

$${\hat c_{\rm{e}}} $$

http://notExist.jpg

for both the tangent hard-sphere chain (left) and the dissipative particle dynamic chain (right) models at various chain lengths

Abstract

Generic polymer models capturing the chain connectivity and excluded-volume interactions between polymer segments can be classified

according to whether or not the 3D integral of the latter diverges

into hard- and soft-core models. Taking homogeneous systems of compressible homopolymer melts (or equivalently homopolymer solutions in an implicit

good solvent) in the continuum as an example

we recently compared the correlation effects on the structural and thermodynamic properties of the hard- and soft-core models given by the polymer reference interaction site model (PRISM) theory with the Percus-Yevick (PY) closure (

Polymers

2023

1180). Here we analyzed in detail the numerical errors and behavior of the interchain pair correlation functions (PCFs) given by the PRISM-PY calculations of these models using an efficient numerical approach that we proposed. Our numerical approach has the least number of independent variables to be iteratively solved

analytically treats the discontinuities caused by the non-bonded pair potential (such as that of the hard spheres) and takes only the inverse Fourier transform of the interchain indirect PCF between polymer segments (which is continuous and decays towards 0 with increasing wavenumber much faster than both the interchain direct and total PCFs)

and is essential for us to accurately solve the PRISM-PY theory for chain length

as large as 10

. To capture the correlation-hole effect

the real-space cut-off in the PRISM calculations should be proportional to the square root of

关键词

Keywords

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