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Semiflexible polymer solutions. I. Phase behavior and single-chain statistics

Spakowitz, Andrew J. and Wang, Zhen-Gang (2003) Semiflexible polymer solutions. I. Phase behavior and single-chain statistics. Journal of Chemical Physics, 119 (24). pp. 13113-13128. ISSN 0021-9606. http://resolver.caltech.edu/CaltechAUTHORS:SPAjcp03

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Abstract

We study the thermodynamics and single-chain statistics of wormlike polymer solutions with Maier–Saupe-type interactions using self-consistent-field (SCF) theory. The SCF equations are derived using a systematic field-theoretical approach which yields the SCF equations as the lowest order approximation, but permits fluctuation corrections to be incorporated. We solve the SCF equations using the spheroidal functions, which provides a nonperturbative description of the thermodynamics and single-chain statistics in the nematic state for arbitrary degrees of nematic order. Several types of phase diagrams are predicted, with an emphasis on the limit of metastability (spinodal) associated with each phase. The shape and location of these spinodals suggest interesting scenarios for the phase transition kinetics. A large but finite persistence length is shown to significantly decrease the isotropic–nematic transition temperature relative to that for rigid rods. In the nematic state, the mean-square end-to-end distance in the parallel and perpendicular directions are governed by two separate correlation lengths. An exact relationship between these correlation lengths and the eigenvalues of the spheroidal functions is provided, which reproduces the analytical expressions predicted from earlier studies in the limit of large nematic strength. The dominant contribution to the single-chain thermodynamics is shown to arise from small amplitude undulations in the directions perpendicular to the nematic direction; the presence of hairpins, though crucial for determining the dimensions of the polymer, has insignificant consequences on the single-chain thermodynamics.


Item Type:Article
Additional Information:©2003 American Institute of Physics. Received 1 August 2003; accepted 30 September 2003. This work was supported in part by the National Science Foundation (DMR-9970589).
Subject Keywords:polymer solutions; liquid crystal polymers; thermodynamic properties; SCF calculations; macromolecules; intramolecular mechanics; phase diagrams; fluctuations; liquid crystal phase transformations; eigenvalues and eigenfunctions
Record Number:CaltechAUTHORS:SPAjcp03
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:SPAjcp03
Alternative URL:http://dx.doi.org/10.1063/1.1628669
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4170
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:07 Aug 2006
Last Modified:26 Dec 2012 08:58

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