Nucleation Theory

This monograph covers the major available routes of theoretical research of nucleation phenomena––phenomenological models, semi-phenomenological theories, density functional theories and microscopic approaches––with emphasis on the formation of liquid dro

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Extended Modified Liquid Drop Model and Dynamic Nucleation Theory

In the classical theory and its modifications an arbitrary cluster is characterized by one parameter—the number of molecules in it. In a series of papers [1–3] Reiss and co-workers discussed an alternative form of cluster characterization. It was suggested that a cluster should be characterized not only by the particle number, i, but also by its volume v. As a result dynamics of such an i, v-cluster becomes two-dimensional (as opposed to the CNT, where it is one-dimensional) resembling nucleation in binary systems. Using these arguments Weakliem and Reiss [4] put forward the modified liquid drop model and performed extensive Monte Carlo simulations to calculate free energy of the i, v-clusters. Based on these ideas Reguera et al. [5] put forward the “extended modified liquid drop” model (EMLD), taking into account the effect of fluctuations which are important for the formation of tiny droplets in a small N V T system. More recently Reguera and Reiss [6] combined EMLD with the Dynamic Nucleation Theory (DNT) of Shenter et al. [7, 8]. The new model, called “Extended Modified Liquid Drop Model-Dynamical Nucleation Theory” (EMLD-DNT), is discussed in the next sections.

6.1 Modified Liquid Drop Model The CNT studies formation of droplets in an open system. The main feature of the modified liquid drop model of Ref. [4] is that it considers the closed system containing N molecules confined within a small spherical volume V at a temperature T . This small N V T system is called an EMLD-cluster. Within the volume V various sharp n-clusters can form, n = 1, . . . , N . The important difference between the closed an open system is that in the system with the fixed total amount of molecules N the formation and growth of droplets is accompanied by the depletion of the vapor—the effect neglected in CNT, which assumes the existence of an infinite source of vapor molecules. The depletion of the vapor molecules in EMLD results in the decrease of supersaturation so that the droplet can not become arbitrarily large. Following

V. I. Kalikmanov, Nucleation Theory, Lecture Notes in Physics 860, DOI: 10.1007/978-90-481-3643-8_6, © Springer Science+Business Media Dordrecht 2013

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6 Extended Modified Liquid Drop Model and Dynamic Nucleation Theory

Fig. 6.1 A schematic representation of the EMLDcluster: a closed system of N molecules confined inside the volume V of the radius R. n out of N molecules form a liquid drop of the radius r , while the rest N −n molecules remain in the vapor phase

V, T

N-n R

n

r

Ref. [6] we analyze the properties of the EMLD-cluster using purely thermodynamic considerations. The spherical volume V of the radius R is assumed to have impermeable hard walls. Under certain conditions a liquid drop with n molecules, n ≤ N − 1, can be formed inside V . The rest N − n molecules remain in the vapor phase, occupying the volume V − n vl , where vl is the volume per molecule in the bulk liquid phase (see Fig. 6.1). This vapor has the pressure

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