The applications of the wormlike chain model on polymer physics

Abstract

The continuum version of the wormlike chain model (WLC), which was initially developed by Saito, Takahashi and Yunoki in 1967, is particularly suitable for description of polymer conformational properties affected by the chain rigidity. The WLC model is capable of covering an extensive range of chain rigidity, from the flexible chains to the rigid chains, by tuning the persistence length directly. It is widely accepted as a coarse-grained model that can be used to capture the physical properties, such as conformation and structures, of a larger class of real polymers than the Gaussian chain (GSC). Recently, the WLC model attracts increasing interests because of its advantages in studying a variety of polymeric systems, including liquid crystalline polymers and conjugated polymers. This review article focuses on applications of the WLC model, incorporated in the framework of self-consistent field theory, which is an effective method in theoretical exploration of phase separation in polymer systems. The article also pays particular attention to the developments of the numerical schemes to solve the modified diffusion equation governing the probability distribution of polymers. In addition, we summarize recent applications of the self-consistent field theories based on WLC model in the following three areas: phase transitions in liquid-crystalline polymers; the influence of surface curvature on polymeric systems involving the chain orientation effects; self-assembly of wormlike block copolymers. These studies are beyond the scope of self-consistent field theories based on a GSC model, which have been utilized in a large number of theoretical studies in recent years. Finally, we propose the perspectives of theoretical developments in field-theory simulations based on the WLC model for future work. In the polymer literature, it is generally appreciated that chain-rigidity is an important factor that influences the properties of structural stabilities on the meso-scale. The theoretical studies indentify the key physical mechanisms that play crucial roles in many experimental systems with attractively promising applications in practice, for systems such as liquid crystalline polymers and organic solar cell based on the conjugated polymers.