Size and Scaling in Ideal Polymer Networks. Exact Results
Abstract
The scattering function and radius of gyration of an ideal polymer network are calculated depending on the strength of the bonds that form the crosslinks. Our calculations are based on an exact theorem for the characteristic function of a polydisperse phantom network that allows for treating the crosslinks between pairs of randomly selected monomers as quenched variables without resorting to replica methods. From this new approach it is found that the scattering function of an ideal network obeys a master curve which depends on one single parameter x=(ak)^2 N/M, where ak is the product of the persistence length times the scattering wavevector, N the total number of monomers and M the crosslinks in the system. By varying the crosslinking potential from infinity (hard δconstraints) to zero (free chain), we have also studied the crossover of the radius of gyration from the collapsed regime where R_gsimeq mathcal{O}(1) to the extended regime R_gsimeq mathcal{O}(sqrt{N}). In the crossover regime the network size R_g is found to be proportional to (N/M)^{1/4}. The latter result can be understood in terms of a simple Flory argument.
 Publication:

Journal de Physique I
 Pub Date:
 November 1996
 DOI:
 10.1051/jp1:1996157
 arXiv:
 arXiv:condmat/9608001
 Bibcode:
 1996JPhy1...6.1451S
 Keywords:

 Condensed Matter
 EPrint:
 latex, figures available on request, to be published: J. Phys I France