Elastic constants of colloidal glass

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Abstract
The theory of elastic constants of crystalline solids, which relates the elastic constants to the derivatives of the interatomic potential is generalized for a noncrystalline structure. The nearest-neighbour (NN) distance is assumed to have a distribution about its mean. Analytic expressions for the elastic constants C11, C12 and C44 are obtained when only NN interactions are taken into account. The current theory predicts the isotropy (i.e. C11-C12=2C4) of a glassy system. The theory is applied to a two-component colloidal glass where the average interaction potential is obtained by a mean-field approach. For a number of simple probability distributions, closed-form expressions are derived for bulk and shear moduli. The calculated shear moduli agree well with the reported values for colloidal glasses.

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