  The Non-equilibrium Self-consistent Generalized Langevin Equation theory of
irreversible relax- ation [Phys. Rev. E (2010) 82, 061503; ibid. 061504] is
applied to the description of the non- equilibrium processes involved in the
spinodal decomposition of suddenly and deeply quenched simple liquids. For
model liquids with hard-sphere plus attractive (Yukawa or square well) pair
potential, the theory predicts that the spinodal curve, besides being the
threshold of the thermo- dynamic stability of homogeneous states, is also the
borderline between the regions of ergodic and non-ergodic homogeneous states.
It also predicts that the high-density liquid-glass transition line, whose
high-temperature limit corresponds to the well-known hard-sphere glass
transition, at lower temperature intersects the spinodal curve and continues
inside the spinodal region as a glass-glass transition line. Within the region
bounded from below by this low-temperature glass-glass tran- sition and from
above by the spinodal dynamic arrest line we can recognize two distinct domains
with qualitatively different temperature dependence of various physical
properties. We interpret these two domains as corresponding to full gas-liquid
phase separation conditions and to the for- mation of physical gels by arrested
spinodal decomposition. The resulting theoretical scenario is consistent with
the corresponding experimental observations in a specific colloidal model
system.
