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Encyclopedia of Complexity and Systems Science pp 6545–6565Cite as

Percolation and Polymer Morphology and Rheology

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Definition of the Subject

Elastic percolation networks described in the article by Duxbury (see also below), random resistor networks described in the articles by Hughes andBalberg, and a few continuum models [58] of heterogeneous materials providea comprehensive understanding of their transport properties. The purpose of this chapter is to describe and discuss applications of such percolationmodels to predicting the structure and rheolgy of an important class of disordered materials, namely, polymers and gel networks, and test their validityby comparing their predictions with the relevant experimental data.

The formation of the polymeric materials that we consider in this chapter is characterized by the existence of a percolation‐typetransition point; see below. The rigidity and linear elastic properties of disordered materials, including polymers, that are far from their percolationthreshold are well‐described and predicted by mean-field theories, such as the effective‐medium...

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Abbreviations

Branched polymers :

Large polymers below the gel point with radii larger than the correlation length

Chemical gels :

Gel networks in which the monomers are co‐valently bonded.

Critical gels:

The gel networks at the gel point

Elastic networks:

Networks in which each bond is an elastic element, such as a Hookean spring.

Gel point :

The point at which the critical gel network is formed for the first time.

Lattice animals :

Large percolation clusters below the percolation threshold with radii larger than the correlation length

Physical gels :

Gel networks in which the monomers or particles are connected through weak association.

Relaxation time spectrum :

The distribution of relaxation times that describes the linear viscoelastic behavior of liquids and solids.

Resistor networks :

Networks in which each bond is a resistor with a given conductivity.

Rigidity percolation :

Percolation networks in which each uncut bond is a Hookean spring, and there are no angle‐changing forces.

Sol:

The solvent + finite polymer clusters below the gel point

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Author information

Authors and Affiliations

  1. Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, USA

    Muhammad Sahimi

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  1. Muhammad Sahimi
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Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Sahimi, M. (2009). Percolation and Polymer Morphology and Rheology. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_388

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