Irreversibly grown nanostructures: The quasi -thermodynamics of slow deposition

Sequential quenching is an idealized model for a class of slow irreversible deposition in which particles are added one by one onto a substrate. Each new particle is allowed to diffuse and thus equilibrate within the disordered matrix formed by all previous particles before it is quenched in place. This situation occurs when there is a separation in the characteristic times such that diffusion is much faster than quenching, which itself is much faster than particle addition. Sequential quenching is considered here as an instance of quasi-thermodynamics because although the whole built-up structure is not strictly in equilibrium, each of its component particles was itself in equilibrium at one time. Thus, the problem is amenable to a treatment via the Replica Omstein-Zernike integral equations. For structural problems, we apply both a polydisperse treatment, where we regard each particle as a different species, and a binary-mixture approximation, where each particle is a component in a quenched-annealed mixture. The latter treatment is also used in the development of an integral-equation theory for connectedness. We apply the theory to a system of hard spheres, whose sequential quenching is equivalent to Random Sequential Adsorption (RSA). Simple short-range potentials such as the square-well and triangular-well models are introduced to study the effect of attractive forces. These forces lead to a clustering of the particles and raise the percolation thresholds and the jamming limits above those for RSA. Monte Carlo simulations are used to verify the theory and also to study systems at high densities and low temperatures, for which integral equations did not converge. We also study the sub-monolayer growth of a system of triangular-well particles and observe a crossover from nucleation to growth. The ultimate structures exhibit a continuously varying degree of ordering with varying temperature, ranging from a virtually perfect triangular crystal in the low temperature limit to a disordered network at the RSA limit. The deposition of ellipsoidal particles leads to interesting modes of clustering, which are strongly dependent on the ratio of side-by-side to end-to-end attractive energies. We proposed an intermolecular potential that allowed us to explore this effect systematically