Cluster birth–death processes in a vapor at equilibrium

Abstract

A method is presented to analyze and observe, in molecular dynamic simulations, the statistical properties of instantaneous cluster transitions, mainly fusions and fissions for a homogeneous vapor at equilibrium. The method yields the way to obtain mean lives, branching ratios and, to some extent, transition rates as well. To the best of our knowledge branching rations in cluster decays have not been measured before (simulationally or experimentally). An application of this method to a model system provides a critical reassessment of the standard Homogeneous Nucleation Theory (HNT). Our own simulations show that transitions different from absorbing or evaporating a monomer are quite important, representing in some cases 50% of all decay events. Our method also shows unequivocally that the decay processes involving clusters classified by size alone are not Markovian.

A dynamical definition of quasibound molecular clusters

“…Soto and Cordero [19] have developed Hill's criterion, and Barrett [16] has performed Monte Carlo modelling of molecular configurations, excluding those which decay in molecular dynamics within a suitable period. The idea of introducing a residence time has also been discussed by both Bahadur and McClurg [20] and Pugnaloni and Vericat [21].…”

Molecular cluster decay viewed as escape from a potential of mean force

“…assuming the integration limits do not depend on r 1 . Fortunately, the second term on the right hand side of equation (19) can be simplified. We represent the derivative of the delta function as the limit of…”

“…Implicit in any microscopic theory of nucleation, however, is the need for a clear definition of what is meant by a cluster. This is a subtle matter, and one which has received considerable attention 6,7,[15][16][17][18][19][20][21][22][23][24][25][26] . Intuitively, a cluster should comprise a set of molecules located close to one another.…”

“…We have recently developed a definition of a cluster involving energy rather than position 24 . It is widely recognised that an energetic rather than a positional criterion is an indicator of a quasi-bound structure 19,23,27 . We have added the essential feature that in order to escape from a cluster, a molecule needs not only to acquire positive energy, through thermal fluctuations, but must also be able to move away from the cluster, avoiding recapture.…”

Theoretical approaches to nucleation in the gas phase. With a glimpse at experiments and dust formation in astrophysics

“…This point of view is fundamental for classical nucleation theory, but has also been adopted in early computational investigations [8], followed by many others [9][10][11][12], for its relevance in many areas and primarily in atmospheric science. At equilibrium, the homogeneous nucleation equilibrium can be summarized by the reactions…”