Exact Results for a Semiflexible Polymer Chain in an Aligning Field

• Published in: Macromolecules Vol. 37; no. 15; pp. 5814 - 5823
• Main Authors: Spakowitz, Andrew J, Wang, Zhen-Gang
• Format: Journal Article
• Language: English
• Published: Washington, DC American Chemical Society 27.07.2004
• Subjects: Applied sciences; Exact sciences and technology; Organic polymers; Physicochemistry of polymers; Properties and characterization; Structure, morphology and analysis; Semiflexible chain; Strain energy; Chain elongation; Theoretical study; Two dimensional model; Nematic crystals; Modeling; Quadrupole field; Structure factor; Three dimensional model; Partition function; SCF method; Liquid crystal polymers; Dipole field; Liquid nematic transformation
• ISSN: 0024-9297; 1520-5835
• DOI: 10.1021/ma049958v

We provide exact results for the Laplace-transformed partition function of a wormlike chain subject to a tensile force and in a nematic field, in both two and three dimensions. The results are in the form of infinite continued fractions, which are obtained by exploiting the hierarchical structure of a moment-based expansion of the partition function. The case of an imaginary force corresponds to the end-to-end distance distribution in Laplace−Fourier space. We illustrate the utility of these exact results by examining the structure factor of a wormlike chain, the deformation free energy of a chain in a nematic field, and the self-consistent-field solution for the isotropic−nematic transition of wormlike chains.