Toward a molecular theory for homogeneous bubble nucleation

Korosh Torabi, Purdue University

Abstract

Homogeneous bubble nucleation refers to the process by which a first-order phase transition occurs within a bulk metastable liquid phase in the absence of external impurities or perturbations. Due to the random movements of the particles comprising the liquid, regions of lower density spontaneously form at random locations within the bulk metastable liquid. Since a metastable phase is not the lowest free energy state at the conditions of the system, occasionally some of these spontaneously formed low density regions grow into the macroscopic vapor phase. The local density fluctuations within the metastable phase that have a considerable probability of instigating a phase transition are called the transitional (or critical) nucleation sites. In the present thesis, we develop a theoretical framework and the relevant molecular simulation techniques to indentify the transitional nucleation sites and to calculate their number density within the bulk metastable liquid. In addition, we present a procedure to calculate the forward rate coefficient of the critical nuclei. As a result, we have developed a methodology to calculate the rate of homogeneous bubble nucleation in terms of number of bubbles form per unit time per unit volume of the bulk metastable liquid phase. In order to study the numerous possible density fluctuations (i.e., configurations of the liquid particles at a given location), we introduce an embryo definition based on the two order parameters n and v, where n is the number of vapor-like particles that can be contained in a spherical boundary of volume v within the bulk metastable liquid. Similar order parameters have been employed in the previous work by Uline and Corti [Phys. Rev. Lett. 99, 076102 (2007)]. Yet, in our new embryo definition, we distinguish between the vapor-like and liquid-like particles within a configuration of the system. Also, the volume of the spherical boundary of the embryo is set based on a shell particle which is defined to be the closest liquid-like particle to the center of the embryo. These modifications guarantee the unique mapping of the various liquid-state configurations onto the (n,v) order parameter space. We also develop simulation techniques to generate the free energy surface in the (n,v) order parameter space. We determine the transitional (critical) region of the order parameter space based on a committor probability analysis in a way that the dynamical trajectories initiated from the transitional region have the same probability of falling back to the basin of attraction of the metastable phase or to continue forward with a phase transition. With this analysis we demonstrate that transitional nucleation sites are concentrated and locally confined regions of vapor-like density as opposed to what has been suggested by models that make use of global order parameters. In addition, we calculate the average number of the transitional nucleation sites per unit volume of the metastable liquid phase based on the information provided by the (n,v) free energy surface. We show how the probability of finding an (n,v) embryo at a fixed point in space is equal to the average volume fraction available within the liquid phase for insertion of a sphere of volume v that happens to contain only n vapor-like particles. We develop a Monte Carlo simulation procedure to calculate the volume quanta that maps the probability of the critical embryos into the number density of the critical embryos within the bulk metastable liquid. Finally we present a framework to calculate the forward rate coefficient of the transitional nucleation sites based on the data provided by a large number of trajectories generated via molecular dynamics simulation. Overall, we develop a molecular level theory for homogenous bubble nucleation within a model metastable liquid by not only shedding light onto the necessary details of a proper equilibrium embryo definition suitable for bubble nucleation but also by considering the kinetic aspects of the inherently dynamical process of nucleation.

Degree

Ph.D.

Advisors

Corti, Purdue University.

Subject Area

Physical chemistry|Chemical engineering|Theoretical physics

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