I have found an analytical expression for the radius of gyration for a wormlike chain that ignores excluded volume effects in Zhao, Sun, and Zhang, "Statistics of wormlike chains. I. Properties of a single chain", J. Chem. Phys. 106, 2520 (1997). In this work, they demonstrated that the radius of gyration (squared) and the mean-squared end-to-end distance scale with the contour length of the polymer.
I also know that with excluded volume effects included in the model, the scaling exponent for the mean-squared end-to-end distance changes from 1 to 6/5 in the limit of 0 persistence length.
Would someone be able to provide a citation to an analytical expression for the radius of gyration of the worm-like chain with excluded volume effects? I suspect it will also scale like 6/5 with the contour length of the chain, but I may be wrong.
Thanks!
http://scitation.aip.org/content/aip/journal/jcp/106/6/10.1063/1.474096
I think a good starting point are the publications by the Frey group in Munich on the end to end distance distribution of worm-like chains.
A more practical approach would be to look for experimental determinations of hydrodynamic sizes obtained, e g by viscometry, dynamic light scattering or by diffusion.
I did find an analytical solution of the wormlike chain with excluded volume effects in chapter 5 of this book: R. Borsali and R. Pecora, "Soft-Matter Characterization," vol. 1, Springer, 2008. References are included in this chapter as well.
Thanks all!
http://www.springer.com/materials/book/978-1-4020-4464-9
I happened to get involved in the problem years ago. I wanted to see the effect of the excluded volume on the modulus in the framework of the theory of rubber elasticity. For that I considered statistical distributions of the end-to-end distance partially accounting for intramolecular excluded volume. Although my paper (attached is a scanned copy) was in Italian, the references can be of some help to you.
In Flory's Principles of Polymer Chemistry, appendix C of Chapter X ("Chain Configuration") contains a derivation of the relationship between root-mean-square end to end distance (r) and radius of gyration (s). It's 3 pages long and contains a number of additional references.
This book is the original "bible" of polymer chemistry that is well worth having as a primary reference for all things polymeric. Copyrighted in 1953, I use the 7th printing (1969) simply because that's when I began my employment in the polymer-related industry. While other text books on polymer science tend to be heavily descriptive of polymer organic chemistry, Flory's book is heavily slanted towards polymer physics. To me, that's what makes it both unique and highly useful.
I would recommend Pierre-Gilles de Gennes' "Scaling concepts in Polymer Physics" if you can lay your hands on a copy.A must. Very conceptual, it might escape you but it's well worth digging your teeth into it.
Otherwise you might find a trail in Doi and Edwards' "Theory of Polymer Dynamics".
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