On the Deflection and Persistence Lengths of Mesogenic Worm-Like Rods

Abstract

Persistence length is a key quantity characterizing the conformation of chain-like particles. While it is clear to interpret qualitatively as the distance over which the direction of the chain persists, its quantitative definition is not unique. Very frequently, approximate formulae are used. However, as pointed out in a recent work [P. Cifra, Polymer 45, 5995 (2004)], their predictions are generally not correct when compared to what may be considered the exact estimate, and this especially happens for sufficiently stiff chains. The observed sensitivity of these formulae to the degree of internal flexibility of the chain has stimulated the present work, where, by employing Monte Carlo and Molecular Dynamics computer simulations, the outcomes of exact and approximate formulae are systematically studied for systems of short, semi-flexible rods which form liquid–crystalline phases. While the approximate expressions give consistent results for the isolated chain, their predictions differ in bulk ordered phases. Moreover, compared to the exact expression, the approximate formulae perform overall quite bad. Thus, if the usage of the approximate formulae is questionable in general, it is more so in the particular case of liquid–crystal phases. For mesogenic worm-like rods, another characteristic length was put forward, the deflection length. It was phenomenologically defined as the distance along the chain over which the chain behaves as isolated. It is illustrated how it can be readily evaluated from the exact definition of the persistence length.

Keywords:

• computer stimulation
• flexible particles
• lyotropic liquid crystals