Volume 16, Issue 2
Self-Consistent Field Theory Simulations of Wormlike Chains on Cylindrical Surface

Qin Liang, Lu Chen, Hui ZhangDongliang Zhang

Int. J. Numer. Anal. Mod., 16 (2019), pp. 357-374.

Published online: 2018-10

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  • Abstract

Experimental investigation has shown that semiflexible polymers can wrap orderly around a cylinder. Recent Monte Carlo simulations also show that semiflexible polymers can develop linear or helical or random phase structures, depending on the rigidity or length of the polymer. Here, we use wormlike chain model and self-consistent field theory with Onsager interaction to study the micro-phase structure of polymers with local rigidity. We first give the modified diffusion equation for a wormlike chain on cylindrical surface, and then solve the equilibrium equations of the self-consistent field. A time splitting scheme is developed to solve the modified diffusion equation. However, only two kinds of nematic structures (N1 and N2) are detected in our simulation. In N1, the polymers are mainly oriented perpendicular to the axis of the cylinder; while in N2, the polymers are mainly oriented parallel to the axis of the cylinder. N1 is a metastable structure with free energy higher than N2.

  • Keywords

wormlike chain model modified diffusion equation self-consistent field theory cylindrical surface micro-phase structure.

  • AMS Subject Headings

35Q48 03C99.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

nanbululu@mail.bnu.edu.cn (Lu Chen)

alpha59@163.com (Hui Zhang)

zhangdongliang@hotmail.com (Dongliang Zhang)

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@Article{IJNAM-16-357, author = {Liang , Qin and Chen , Lu and Zhang , Hui and Zhang , Dongliang}, title = {Self-Consistent Field Theory Simulations of Wormlike Chains on Cylindrical Surface}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {16}, number = {2}, pages = {357--374}, abstract = {

Experimental investigation has shown that semiflexible polymers can wrap orderly around a cylinder. Recent Monte Carlo simulations also show that semiflexible polymers can develop linear or helical or random phase structures, depending on the rigidity or length of the polymer. Here, we use wormlike chain model and self-consistent field theory with Onsager interaction to study the micro-phase structure of polymers with local rigidity. We first give the modified diffusion equation for a wormlike chain on cylindrical surface, and then solve the equilibrium equations of the self-consistent field. A time splitting scheme is developed to solve the modified diffusion equation. However, only two kinds of nematic structures (N1 and N2) are detected in our simulation. In N1, the polymers are mainly oriented perpendicular to the axis of the cylinder; while in N2, the polymers are mainly oriented parallel to the axis of the cylinder. N1 is a metastable structure with free energy higher than N2.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12808.html} }
TY - JOUR T1 - Self-Consistent Field Theory Simulations of Wormlike Chains on Cylindrical Surface AU - Liang , Qin AU - Chen , Lu AU - Zhang , Hui AU - Zhang , Dongliang JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 357 EP - 374 PY - 2018 DA - 2018/10 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/12808.html KW - wormlike chain model KW - modified diffusion equation KW - self-consistent field theory KW - cylindrical surface KW - micro-phase structure. AB -

Experimental investigation has shown that semiflexible polymers can wrap orderly around a cylinder. Recent Monte Carlo simulations also show that semiflexible polymers can develop linear or helical or random phase structures, depending on the rigidity or length of the polymer. Here, we use wormlike chain model and self-consistent field theory with Onsager interaction to study the micro-phase structure of polymers with local rigidity. We first give the modified diffusion equation for a wormlike chain on cylindrical surface, and then solve the equilibrium equations of the self-consistent field. A time splitting scheme is developed to solve the modified diffusion equation. However, only two kinds of nematic structures (N1 and N2) are detected in our simulation. In N1, the polymers are mainly oriented perpendicular to the axis of the cylinder; while in N2, the polymers are mainly oriented parallel to the axis of the cylinder. N1 is a metastable structure with free energy higher than N2.

Qin Liang, Lu Chen, Hui Zhang & Dongliang Zhang. (2020). Self-Consistent Field Theory Simulations of Wormlike Chains on Cylindrical Surface. International Journal of Numerical Analysis and Modeling. 16 (2). 357-374. doi:
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