Statistical mechanics of a quenched van der Waals fluid

The equilibrium properties of a quenched one-dimensional fluid with a high density phase transition are calculated using the formalism of Mazo in which the free energy is first calculated as a function of a certain quenched parameter and the quenched free energy is evaluated by averaging over the probability that the constraint is realized in the quenching process. The model system studied here is one in which the particles interact through a pair potential with a shoulder in the repulsive wall. The quenched parameter is taken to be the width of the shoulder, corresponding to the introduction of disorder or free volume into the quenched phase. Assuming a Gaussian distribution of shoulder widths it is possible to calculate the quenched free energy exactly and compare the thermodynamic properties of the quenched fluid to those of the equilibrium fluid. The quenched disorder softens the first-order freezing transition into a second-order-like glass transition which qualitatively reproduces the quasiequilibrium properties of real glasses