Covariant van Hove function in dilute polymer solutions

Abstract

A statistically covariant relation, based on a recent Brownian relativity that was able to provide a new macromolecular scaling picture, has been obtained in order to connect the statistical features of liquid and chain molecules forming a polymer solution. A generalized van Hove distribution function turns out to extend the Gaussian statistics to correlated media and, for dilute polymer solutions with large chain unit numbers, infers the form of a Vineyard-like convolution integral for density correlations. Depending on the imposed covariance, and the link to fundamental issues in fluid statistical mechanics, this picture encourages us to investigate conformational statistics of macromolecules in terms of the surrounding liquid correlations alone, and seeking further, which general scaling principles a Brownian-like statistic may generally undergo.

Acknowledgements

I thank V. Magnani (DM-SNS, Pisa) for stimulating discussions and F. Vittur for his kind hospitality.