Description of the mechanical properties of gelling polymer solutions far from gelation threshold: Generalized effective-medium calculations of the superconductor-conductor site percolation problem

C. Allain; L. Limat; L. Salomé

doi:10.1103/PhysRevA.43.5412

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Description of the mechanical properties of gelling polymer solutions far from gelation threshold: Generalized effective-medium calculations of the superconductor-conductor site percolation problem

C. Allain, L. Limat, L. Salomé

DOI 10.1103/PhysRevA.43.5412 · Physical Review A

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Abstract

We introduce effective-medium theory to describe the mechanical properties observed on sols and gels formed by addition of a cross-linker to semidilute polymer solutions. We experimentally observe that, in the entire range outside the critical domain, the variation of the viscosity (η) is well described by a linear decrease of 1/η as a function of the concentration in cross-link points. This behavior is to be related to a similar regime that we find for the resistivity of a superconductor-conductor site percolating lattice. The effective-medium calculations have been generalized to include nonsymmetrical properties of the links joining two sites of different nature, allowing us to describe the relative positions of the gelation threshold and the threshold extrapolated from the linear decrease of 1/η.