Abstract
The application of single chain mean-field theory (SCMFT) on semiflexible chain brushes is reviewed. The worm-like chain (WLC) model is the best mode of semiflexible chain that can continuously recover to the rigid rod model and Gaussian chain (GC) model in rigid and flexible limits, respectively. Compared with the commonly used GC model, SCMFT is more applicable to the WLC model because the algorithmic complexity of the WLC model is much higher than that of the GC model in self-consistent field theory (SCFT). On the contrary, the algorithmic complexity of both models in SCMFT are comparable. In SCMFT, the ensemble average of quantities is obtained by sampling the conformations of a single chain or multi-chains in the external auxiliary field instead of solving the modified diffuse equation (MDE) in SCFT. The precision of this calculation is controlled by the number of bonds used to discretize the chain contour length L and the number of conformations M used in the ensemble average. The latter factor can be well controlled by metropolis Monte Carlo simulation. This approach can be easily generalized to solve problems with complex boundary conditions or in high-dimensional systems, which were once nightmares when solving MDEs in SCFT. Moreover, the calculations in SCMFT mainly relate to the assemble averages of chain conformations, for which a portion of conformations can be performed parallel on different computing cores using a message-passing interface (MPI).
Highlights
Advances in studies of natural and artificial polymer systems in both bioscience and material science continually raise new challenges for theories in polymer physics
worm-like chain (WLC)-single chain mean-field theory (SCMFT) is useful for the study of polymer brushes
We reviewed SCMFT for the WLC model, which is based on the path integral description of the ensemble average
Summary
Advances in studies of natural and artificial polymer systems in both bioscience and material science continually raise new challenges for theories in polymer physics. The theoretical methods of semiflexible polymers developed rapidly in recent years, only low-dimensional ordered structures with higher symmetry were studied to avoid the difficulty with multi-degrees of freedom [18]. It is hard for the existing theoretical methods to solve the confinement effects on semiflexible polymers, especially in the vicinity of curved surfaces.
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