Abstract
The paper discusses the size of a randomly cross-linked polymer chain. The calculations are based on an exact theorem for the characteristic function of a polydisperse phantom network that allows for treating the cross-links between pairs of randomly selected monomers as quenched variables without resorting to replica methods. By variation of the cross-linking potential from infinity (hard constraints) to zero (free chain), we have studied the cross-over of the radius of gyration from the branched polymer regime where R g⋍O(1) to the extended regime R g⋍O(√N). In the cross-over regime the network size R g is found to be proportional to (N/M)1/4, where M is the total number of cross-links and N the number of monomers in the system. Our exact results can also be understood in terms of simple scaling arguments.
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© 1997 Springer-Verlag
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Vilgis, T.A., Solf, M.P. (1997). Cross-linked polymer chains: Scaling and exact results. In: Rubí, M., Pérez-Vicente, C. (eds) Complex Behaviour of Glassy Systems. Lecture Notes in Physics, vol 492. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0104843
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DOI: https://doi.org/10.1007/BFb0104843
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