In the theoretical interpretation of the kinetics of first-order phase transitions, thermodynamic concepts developed long ago by Gibbs are widely employed giving some basic qualitative insights into these processes. However, from a quantitative point of view, the results of such analysis, based on the classical Gibbs approach and involving in addition the capillarity approximation, are often not satisfactory. Some progress can be reached here by the van der Waals and more advanced density functional methods of description of thermodynamically heterogeneous systems having, however, its limitations in application to the interpretation of experimental data as well. Moreover, both mentioned theories--Gibbs' and density functional approaches--lead to partly contradicting each other's results. As shown in preceding papers, by generalizing Gibbs' approach, existing deficiencies and internal contradictions of these two well-established theories can be removed and a new generally applicable tool for the interpretation of phase formation processes can be developed. In the present analysis, a comparative analysis of the basic assumptions and predictions of the classical and the generalized Gibbs approaches is given. It is shown, in particular, that--interpreted in terms of the generalized Gibbs approach--the critical cluster as determined via the classical Gibbs approach corresponds not to a saddle but to a ridge point of the appropriate thermodynamic potential hypersurface. By this reason, the classical Gibbs approach (involving the classical capillarity approximation) overestimates as a rule the work of critical cluster formation in nucleation theory and, in general, considerably.

Computer experiments on simulation of thermodynamic properties and structural characteristics of a Lennard-Jones fluid in one- and two-phase models have been performed for the purpose of checking the base concepts of the van der Waals theory. Calculations have been performed by the method of molecular dynamics at cutoff radii of the intermolecular potential r(c,1)=2.6sigma and r(c,2)=6.78sigma. The phase equilibrium parameters, surface tension, and density distribution have been determined in a two-phase model with a flat liquid-vapor interface. The strong dependence of these properties on the value of r(c) is shown. The p,rho,T properties and correlation functions have been calculated in a homogeneous model for a stable and a metastable fluid. An equation of state for a Lennard-Jones fluid describing stable, metastable, and labile regions has been built. It is shown that at T > or =1.1 the properties of a flat interface within the computer experimental error can be described by the van der Waals square-gradient theory with an influence parameter kappa independent of the density. Taking into account the density dependence of kappa through the second moment of the direct correlation function will deteriorate the agreement of the theory with data of computer simulation. The contribution of terms of a higher order than (nablarho)(2) to the Helmholtz free energy of an inhomogeneous system has been considered. It is shown that taking into account terms proportional to (nablarho)(4) leaves no way of obtaining agreement between the theory and simulation data, while taking into consideration of terms proportional to (nablarho)(6) makes it possible to describe with adequate accuracy all the properties of a flat interface in the temperature range from the triple to the critical point.

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A comparative analysis of the results of determination of the work of critical cluster formation in nucleation theory for three different methods of evaluation—Gibbs’ method (employing the capillarity approximation), the van der Waals–Cahn and Hilliard and a newly developed modified Gibbs’ approach—is given in application to phase formation in multicomponent systems. As an example, processes of boiling in binary liquid–gas solutions, in particular, in nitrogen–helium mixtures are investigated. In addition to the work of critical cluster formation, the bulk properties of the critical bubbles, their characteristic sizes and the values of the surface tension are determined in dependence on the initial supersaturation in the system or, equivalently, on the size of the critical clusters. It is shown that latter two mentioned methods (the van der Waals–Cahn and Hilliard and the modified Gibbs’ approach) lead, in the determination of the work of critical cluster formation, to qualitatively and widely even quantitatively equivalent results. As one of the more general consequences from the present analysis, it has been proven that the modified Gibbs’ approach represents a highly effective tool for the determination of the work of formation of clusters or bubbles of critical sizes not only for one-component and quasibinary systems, discussed earlier, but for phase formation in multicomponent systems of, in general, arbitrary numbers of components as well. It is shown that the modified Gibbs’ approach is preferable as compared with Gibbs’ original treatment not only due to its advantages with respect to an appropriate determination of the properties of clusters of critical sizes, but also from general theoretical considerations. In the limit of large sizes of the critical clusters, both approaches—Gibbs’ original treatment and the modified or generalized Gibbs’ approach—lead to equivalent results.

The first experiments on the observation of short pulsed superradiant (SR) emission with the excitation of a surface wave by a relativistic electron bunch moving in an oversized corrugated waveguide were performed. Subterahertz SR pulses with a central frequency of 0.14 THz, an ultrashort duration of 150 ps, and an extremely high peak power of 50-70 MW were generated. The experiments were based on a theoretical consideration including the quasioptical approach and direct particle-in-cell simulations.