Structure and elasticity of model gel networks

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Abstract
A random central force network model of a gel is constructed by relaxation of a bond diluted simple cubic lattice of Hooke's law springs under tension. The bond dilution procedure, which defines the model, involves the random removal of bonds connecting nodes at least one of which has a value greater than a prescribed maximum value. The structure and elastic properties of networks with either fourfold or threefold maximum node connectivity are calculated as a function of the model parameters. The elastic properties of the two types of network show similar trends in behaviour, but the characteristic structural features of the two are quite distinct. The effects of polydispersity are considered by introducing a natural length mismatch to the springs of the network. Randomly assigning the natural lengths of the network springs from a uniform range of values, to mimic the effects of a broad molecular weight distribution, is seen to give a good correlation between the structures from the model with a maximum fourfold node connectivity and experiments on microemulsion based organogels. Introducing a force constant mismatch to the network by randomly assigning a much greater spring strength to a fraction of the bonds leads to behaviour reminiscent of a percolative elastic-superelastic transition.

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