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In previous work we discussed the integral-equation formalism for the computation of the structure of systems built through sequential addition, equilibration and irreversible quenching in place of individual particles. This sequential quenching model, appropriate for slow irreversible deposition, can be investigated by the techniques of equilibrium liquid theory. In the case of hard particles the problem is identical to that of random sequential addition. Our earlier calculations showed that the integral equation results for hard disks are in good agreement with simulation. In this paper we explore the structures arising from sequential quenching of square-well disks, which are found to be very different from those for the corresponding equilibrium case. The most interesting result is the much higher degree of clustering observed when particles are quenched one by one, as opposed to what is observed from the instantaneous quenching of an entire equilibrium system.

We present an integral-equation solution of the structure of systems built through the sequential quenching of particles. The theory is based on the Replica Ornstein–Zernike equations that describe the structure of equilibrium fluids within random porous matrices. The quenched particles are treated as a polydisperse system, each of them labeled by the total density at the time of its arrival. The diagrammatic expansions of the correlation functions lead to the development of the liquid-theory closures appropriate for the present case. Numerical solutions for the deposition of hard disks show excellent agreement with simulation. We also discuss a binary-mixture treatment, which is shown to provide a very good approximation to the polydisperse approach.

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