Controlling the shape of small clusters with and without macroscopic fields

Abstract

Despite major advances in the understanding of the formation and dynamics of nano-clusters in the past decades, theoretical bases for the control of their shape are still lacking. We investigate strategies for driving fluctuating few-particle clusters to an arbitrary target shape in minimum time with or without an external field. This question is recast into a first passage problem, solved numerically, and discussed within a high temperature expansion. Without field, large-enough low-energy target shapes exhibit an optimal temperature at which they are reached in minimum time. We then compute the optimal way to set an external field to minimize the time to reach the target, leading to a gain of time that grows when increasing cluster size or decreasing temperature. This gain can shift the optimal temperature or even create one. Our results could apply to clusters of atoms at equilibrium, and colloidal or nanoparticle clusters under thermo-or electrophoresis.

Equilibrium return times of small fluctuating clusters and vacancies

“…[32]. The expected return time from a configuration to itself exhibits similar properties as first passage times [32] and is an easier starting point for numerical and analytical approaches. * olivier.pierre-louis@univ-lyon1.fr…”

“…In the following, we focus on a different kinetic property of small fluctuating clusters: their time of return to a given configuration. This focus is motivated by our recent attempt to describe first passage times from one arbitrary configuration to another [32]. These first passage times were evaluated numerically using iterative evaluation techniques in Ref.…”

“…These first passage times were evaluated numerically using iterative evaluation techniques in Ref. [32]. The expected return time from a configuration to itself exhibits similar properties as first passage times [32] and is an easier starting point for numerical and analytical approaches.…”

“…In the present paper, we therefore report on the evaluation of the equilibrium expected return time to a given configuration. We work with an extended class of models that allows us to discuss not only case of clusters with edge diffusion [32], but also the case of particle diffusion inside vacancies with slow attachment-detachment kinetics. The expressions derived here lead to simpler and faster estimates of the expected return times as compared to the numerical evaluation based on iterative evaluation [32].…”

“…We work with an extended class of models that allows us to discuss not only case of clusters with edge diffusion [32], but also the case of particle diffusion inside vacancies with slow attachment-detachment kinetics. The expressions derived here lead to simpler and faster estimates of the expected return times as compared to the numerical evaluation based on iterative evaluation [32]. They also lead to an easier and generalized analysis of the high temperature expansion discussed in Ref.…”