Wormlike Chain Polymers Under External Fields with Applications to Nanotechnology

Abstract

Polymers are long molecular chains formed from smaller molecular units called monomers. Polymers display interesting macroscopic properties, are ubiquitous in everyday materials, and are also important biomolecules among much else. The field of polymer science has been widely recognized for its contribution to using and understanding polymers in a wide range of applications. Here, using the common wormlike chain (WLC) polymer model, two systems are investigated. The first is polymer stretching. Finite length polymers are modelled under an external stretching field, and the resulting extension is analysed. The calculations are done numerically, as well as analytically when possible. Representative measures of the polymer conformations are computed using a novel perturbation theory, and the results are compared to other theories. Interpolation formulas are presented to summarize the theoretical findings. The second system is a single walled carbon nanotube, wrapped by a semiflexible polymer in a helical configuration. This type of spontaneous helical wrapping is widely studied experimentally due to its beneficial effects on nanotube solvation, with minimal effects on the underlying electronic properties of the nanotube. The WLC model is used to calculate the expected helix pitch, which is then compared against experimental observations. It is found to reproduce the results, as well as outperform the predictions of another competing model. The findings in both cases are summarized, and possible future research directions are discussed.