The shear modulus of metastable amorphous solids with strong central and bond-bending interactions

TL;DR

This paper derives explicit expressions for the shear modulus of deeply-quenched amorphous solids with strong central and bond-bending interactions, applicable to covalent and colloidal glasses.

Contribution

It introduces a continuum-limit approach to calculate shear modulus from microscopic Hamiltonians for complex amorphous materials.

Findings

Derived shear modulus expressions for covalent and colloidal glasses.

Applicable to dense, strongly bonded amorphous solids.

Provides a theoretical framework for understanding mechanical properties.

Abstract

We derive expressions for the shear modulus of deeply-quenched, glassy solids, in terms of a Cauchy-Born free energy expansion around a rigid (quenched) reference state, following the approach due to Alexander [Alexander, Phys. Rep. 296, 1998]. Continuum-limit explicit expressions of the shear modulus are derived starting from the microscopic Hamiltonians of central and bond-bending interactions. The applicability of the expressions to dense covalent glasses as well as colloidal glasses with strongly attractive and adhesive bonds is discussed.