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Self-consistent field theory simulations of wormlike chains on cylindrical surface. (English) Zbl 1408.35186

Summary: 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.

MSC:

35Q82 PDEs in connection with statistical mechanics
82D60 Statistical mechanics of polymers
82B80 Numerical methods in equilibrium statistical mechanics (MSC2010)
81V70 Many-body theory; quantum Hall effect
81T10 Model quantum field theories
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