Homogeneous nucleation process: Analytical approach

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.

Section: ͔mentioning

confidence: 99%

Cluster birth–death processes in a vapor at equilibrium

Soto¹,

Cordero²

1999

“…Since this coefficient is quite difficult to estimate from a microscopic model, several phenomenological models have been put forward. 18,26 Also, some models that incorporate the internal degrees of freedom have been advanced. 27,28 To be able to evaluate the collision rate between clusters and monomers it is necessary to have the equilibrium velocity distribution function for every species k. HNT assumes that every species k has a Maxwell distribution f k (0) with the same temperature T as the system, and kinetic theory is used straightforwardly to derive the collision rates.…”

Section: Introductionmentioning

confidence: 99%

“…There are many articles predicting the equilibrium concentration of clusters, most of them assuming that the cluster gas mixture can be modeled as an ideal gas mixture, in which case the equilibrium concentration can be expressed in terms of the free energy of formation of a cluster. [11][12][13][14][15][16][17][18][19][20] The free energy can be calculated by means of thermodynamic models or directly from microscopic models. There have also been some works where excluded volume effects are taken into account 21-23 and detailed calculations were made in the Percus-Yevick approximation.…”

Section: Introductionmentioning

confidence: 99%

Cluster velocity distributions in a vapor at equilibrium

Soto

Cordero

1998

We present the microscopic description of the vapor using the concept of cluster. Taking into consideration nonideal contributions, the distribution functions of every cluster species are obtained. From these distribution functions it is possible to derive kinetic “temperatures” associated with each cluster species and it is shown that the internal kinetic temperature and the kinetic temperature associated with the center of mass of the clusters are different from the thermodynamic temperature of the system as a whole. Molecular dynamic simulations show that the internal temperatures are smaller than the thermodynamic one, which is smaller than the kinetic temperatures for all cluster sizes. For the case of monomers more precise predictions can be made and they are in excellent agreement with our simulations.

“…Much more detailed discussion of the transient stage of nucleation can be found elsewhere. [15][16][17][18][19] In the case when the stationary-on-average distribution of subcritical solute clusters has been achieved the fluctuations of solute concentration in a metastable state lead to either attachment or detachment of separate solute molecules to the already existing subcritical solute clusters. However, the average size-distribution of subcritical solute clusters remains unchanged ͑stationary͒, since the processes of random attachments and detachments are balanced in the stationary limit.…”

Section: Introductionmentioning

confidence: 99%

Diffusion in supersaturated solutions: Application to the case of supersaturated protein solutions

Izmailov¹,

Myerson²

2000

The derivation of solute diffusion coefficient from the quasiequilibrium probability density function of the underlying stochastic quantity-characteristic size of subcritical solute clusters, was carried out within the classical formalism of metastable state relaxation ͑nucleation͒. It has been demonstrated that ͑a͒ the solute diffusion coefficient is necessarily concentration dependent; ͑b͒ the concentration dependent solute diffusivity is the function of only two parameters, solute diffusivity at saturation and total surface energy of a solute molecule. This energy, in principle, can be also a function of solute concentration for supersaturated solutions such as protein supersaturated solutions. In addition to that it has been demonstrated for supersaturated solutions of the proteins such as lysozyme and Bovine Pancreatic Trypsin Inhibitor ͑BPTI͒ solutions that ͑a͒ the total surface energy of lysozyme and BPTI molecules in the metastable state is concentration dependent. ͑b͒ The solute diffusivity as a function of solute concentration, observed in supersaturated protein solutions such as lysozyme and BPTI, can be accurately reproduced ͑with error less than 1.2%͒ on the base of classical theory of the metastable state relaxation, given that the surface energy of the protein molecules is concentration dependent.