Nucleation theory transition

When a phase transition occurs from a pure single state and in the absence of wettable surfaces the embryogenesis of the new phase is referred to as homogeneous nucleation. What is commonly referred to as classical nucleation theory is based on the following physical picture. Density fluctuations in the pre-transitional state result in local domains with characteristics of the new phases. If these fluctuations produce an embryo which exceeds a critical size then this embryo will not be dissipated but will grow to macroscopic size in an open system. The concept is applied to very diverse phenomena ... 

Nucleation rate based on the classical nucleation theory The nucleation rate is the steady-state production of critical clusters, which equals the rate at which critical clusters are produced (actually the production rate of clusters with critical number of molecules plus 1). The growth rate of a cluster can be obtained from the transition state theory, in which the growth rate is proportional to the concentration of the activated complex that can attach to the cluster. This process requires activation energy. Using this approach, Becker and Coring (1935) obtained the following equation for the nucleation rate ... 

All approaches are based either on the thermodynamical description of the gas-solid phase transition by classical nucleation theory or on a detailed discussion of the relevant chemical reactions leading finally to critical clusters (e.g. review by Gail, Sedlmayr, 1987d). We will refrain from a presentation of these various approaches but only list the basic molecules from which the primary condensates are likely to be formed ... 

It is well known that water dispersions of amphiphile molecules may undergo different phase transitions when the temperature or composition are varied [e.g. 430,431]. These phase transitions have been studied systematically for some of the systems [e.g. 432,433]. Occurrence of phase transitions in monolayers of amphiphile molecules at the air/water interface [434] and in bilayer lipid membranes [435] has also been reported. The chainmelting phase transition [430,431,434,436] found both for water dispersions and insoluble monolayers of amphiphile molecules is of special interest for biology and medicine. It was shown that foam bilayers (NBF) consist of two mutually adsorbed densely packed monolayers of amphiphile molecules which are in contact with a gas phase. Balmbra et. al. [437J and Sidorova et. al. [438] were among the first to notice the structural correspondence between foam bilayers and lamellar mesomorphic phases. In this respect it is of interest to establsih the thermal transition in amphiphile bilayers. Exerowa et. al. [384] have been the first to report such transitions in foam bilayers from phospholipids and studied them in various aspects [386,387,439-442]. This was made possible by combining the microscopic foam film with the hole-nucleation theory of stability of bilayer of Kashchiev-Exerowa [300,402,403]. Thus, the most suitable dependence for phase transitions in bilayers were established. 

This equation states that the change in the free energy of the critical germ with the chemical potential per molecule of species / in the original phase (i.e., the mother liquor) equals the negative of the excess number An of molecules of type i in the nucleus over that present in the same volume of original space. The nucleation theorem is independent of the model and of the transition it holds true for classical nucleation theory, density functional theory, or cluster kinetic analysis and for gas-to-liquid or liquid-to-solid conversions. 

On closer scrutiny the crystal growth data for PEO fractions deviated somewhat from those expected from secondary nucleation theory there were departures from linearity of Gvs AT near the Tcm transition temperatures,185 188 and the value of a derived from the kinetics was unrealistically low.187... 

This type of equation is also encountered in other areas, such as nonlinear waves, nucleation theory, and phase field models of phase transitions, where it is known as the damped nonlinear Klein-Gordon equation, see for example [165, 355, 366]. In the (singular) limit r 0, (2.15) goes to the reaction-diffusion equation (2.3). Front propagation in HRDEs has been studied analytically and numerically in [149, 150, 152, 151, 374]. The use of HRDEs in applications is problematic. Such equations are obtained indeed very much in an ad hoc manner for reacting and dispersing particle systems, and they can be derived neither from phenomenological thermodynamic equations nor from more microscopic equations, see below. 

Major topics include rate equations, reactor theory, transition state theory, surface reactivity, advective and diffusive transport, aggregation kinetics, nucleation kinetics, and solid-solid transformation rates. The theoretical basis and mathematical derivation of each model is presented in detail and illustrated with worked examples from real-world applications to geochemical problems. The book is also supported by online resources self-study problems put students new learning into practice and spreadsheets provide the full data used in figures and examples, enabling students to manipulate the data for themselves. 

Oxtoby, D.W., and Evans, R. (1988) Nonclassical nucleation theory for the gas-liquid transition, J. Chem. Phys. 99,151. ... 

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