화학공학소재연구정보센터
Journal of Catalysis, Vol.211, No.1, 19-32, 2002
A new Monte Carlo model for supported-catalyst sintering
We present a new 2D Monte Carlo model of supported-catalyst sintering that is capable of generating all known catalyst sintering behaviors, including atom emission and recapture (Ostwald ripening), particle migration and coalescence, and vapor-phase transport. This model differs from previously reported phenomenological models in that no mechanism is presupposed; rather sintering is allowed to arise naturally from atomic-scale interactions among metal atoms and the support. The model uses a classical Metropolis algorithm to determine movement of metal atoms on a support. The metal-support system is represented by a two-dimensional rectangular mesh oriented perpendicular to the support surface. The top and bottom rows of the mesh represent the support, so that the total mesh represents a long, narrow pore. The simulations are initialized by placing metal atoms into the mesh to obtain a desired initial state. The Metropolis algorithm randomly selects a metal atom and a neighboring site and, if the neighboring site is empty, moves the metal atom to the neighboring site with a probability proportional to exp(-DeltaE/kT), where DeltaE is the change in energy associated with the move. Energies of the initial and final states are calculated from pairwise interactions between the sites involved and their nearest neighbors. The simulation is run for 10(6)-10(7) Monte Carlo time steps (MCS), where a single MCS corresponds to a number of attempted moves equal to the number of metal atoms in the simulation. Our model bears certain resemblances to previously published Monte Carlo models but introduces several improvements. First, our model properly calculates probabilities of metal atom migration by using the change in energy associated with the move, rather than simply using the energy of the initial state. Second, our model includes sites in the center of the pore and can therefore model gas-phase transport of meta atoms. Earlier models used a two-dimensional mesh oriented parallel to the support surface and, therefore, did not include sites corresponding to the gas phase. Third, our choice of two-dimensional plane allows modeling of contact angles between metal particles and the support. Countering this advantage is our inability to model the shape of the contact surface between the metal particles and the support. Finally, because our two-dimensional model includes gas-phase sites, generalization to three dimensions is conceptually simple, requiring only the extension of the mesh in the third dimension. Extension of the earlier models to three dimensions would require inclusion of new concepts since the gas phase is not present in the two-dimensional plane chosen.