Nonequilibrium theory of the linear viscoelasticity of glass and gel forming liquids

We propose a first-principles theoretical approach for the description of the aging of the linear viscoelastic properties of a colloidal liquid after a sudden quench into a dynamically arrested (glass or gel) state. Specifically, we couple a general expression for the time-evolving shear-stress relaxation function G(τ;t), written in terms of the non-equilibrium structure factor S(k;t) and intermediate scattering function F(k,τ;t), with the equations that determine S(k;t) and F(k,τ;t), provided by the non-equilibrium self-consistent generalized Langevin equation theory. In this manner, we obtain a closed theoretical scheme that directly connects interparticle forces with experimentally accessible rheological properties of nonequilibrium amorphous states of matter. The predictive capability of the resulting theoretical formalism is illustrated here with its concrete application to the Weeks–Chandler–Andersen model of a soft-sphere fluid.