Molecular clusters, thermodynamic properties

It was also observed, in 1973, that the fast reduction of Cu ions by solvated electrons in liquid ammonia did not yield the metal and that, instead, molecular hydrogen was evolved [11]. These results were explained by assigning to the quasi-atomic state of the nascent metal, specific thermodynamical properties distinct from those of the bulk metal, which is stable under the same conditions. This concept implied that, as soon as formed, atoms and small clusters of a metal, even a noble metal, may exhibit much stronger reducing properties than the bulk metal, and may be spontaneously corroded by the solvent with simultaneous hydrogen evolution. It also implied that for a given metal the thermodynamics depended on the particle nuclearity (number of atoms reduced per particle), and it therefore provided a rationalized interpretation of other previous data [7,9,10]. Furthermore, experiments on the photoionization of silver atoms in solution demonstrated that their ionization potential was much lower than that of the bulk metal [12]. Moreover, it was shown that the redox potential of isolated silver atoms in water must... 

In the following, we first describe (Section 13.3.1) a statistical mechanical formulation of Mayer and co-workers that anticipated certain features of thermodynamic geometry. We then outline (Section 13.3.2) the standard quantum statistical thermodynamic treatment of chemical equilibrium in the Gibbs canonical ensemble in order to trace the statistical origins of metric geometry in Boltzmann s probabilistic assumptions. In the concluding two sections, we illustrate how modem ab initio molecular calculations can be enlisted to predict thermodynamic properties of chemical reaction (Sections 13.3.3) and cluster equilibrium mixtures (Section 13.3.4), thereby relating chemical and phase thermodynamics to a modem ab initio electronic stmcture picture of molecular and supramolecular interactions. 

The study of small, homonuclear clusters of atoms Is Important In understanding nucleatlon because such clusters are Intermediates In the formation of bulk condensed phases. The dynamic process of condensation from a gas must Initially Involve the formation of tiny aggregates of the new phase. This can be Illustrated by the reaction sequence A(g)—A2(g)— A3(g)— . . . — A(1). One of the major weak points In the present day understanding of such nucleatlon phenomena Is the unknown thermodynamic properties of clusters. Certainly, the common practice of treating a 2-200 atom cluster as a tiny piece of the bulk with a large surface Is Inexact. There Is a need for precise thermodynamic data on atomic and molecular clusters to better define nucleatlon kinetics. 

One of the more active and growing areas of research into the study of condensed matter is the investigation of the properties of atomic and molecular clusters. A detailed understanding of clusters is vital to the study of such diverse phenomena as condensation, the dispersion of supported catalysts, cloud formation, molecular generation on interstellar grains, - and the thermodynamic properties of powders. In addition, the study of clusters is of fundamental importance to the understanding of the transition from finite to bulk behavior. 

Size-dependent structure and properties of Earth materials impact the geological processes they participate in. This topic has not been fully explored to date. Chapters in this volume contain descriptions of the inorganic and biological processes by which nanoparticles form, information about the distribution of nanoparticles in the atmosphere, aqueous environments, and soils, discussion of the impact of size on nanoparticle structure, thermodynamics, and reaction kinetics, consideration of the nature of the smallest nanoparticles and molecular clusters, pathways for crystal growth and colloid formation, analysis of the size-dependence of phase stability and magnetic properties, and descriptions of methods for the study of nanoparticles. These questions are explored through both theoretical and experimental approaches. 

The discussions in the previous sections of this chapter have focused on the thermodynamics of single particles. However, there is an important class of problems involving the. statistical properties of interacting clouds of particles in the molecular cluster size range. The size distribution of these particles can be calculated using a simple spherical particle model as... 

As we described in Section III.G, perturbation theories can be extended in a systematic way using cluster expansion techniques. These techniques have recently been applied to the calculation of the thermodynamic properties and vapor-liquid equilibrium of 12-6 diatomics and seem to offer a clear improvement over the first-order perturbation theories. To illustrate this point. Table I shows values of the critical density and critical temperature predicted by the ISF-ORPA theory and the first-order perturbation theory together with results recently obtained from molecular dynamics... 

Molecular clusters are formed due to weakly attractive forces between molecules, the Van der Waals forces. Except under conditions of low temperature, it is difficult to observe and study in the laboratory clusters containing more than a few molecules, so that details about their properties are sparse. Our understanding of the nucleation process consequently relies mainly on theoretical concepts based largely on the principles of statistical mechanics. The theory of homogeneous nucleation developed by Volmer and Weber (1926), Flood (1934), Becker and Doering (1935), and Reiss (1950) assumes that certain thermodynamic properties, such as the molar volume or the surface tension, that can be determined for bulk material... 

Weakleim, C. L., and Reiss, H. (1993) Toward a molecular theory of vapor-phase nucleation. III. Thermodynamic properties of argon clusters from Monte Carlo simulations and a modified liquid drop theory, J. Chem. Phys. 99, 5374-5383. 

Giant clusters can serve as useful models for imderstanding the structure and chemical behavior of dispersed metals. Magnetic and thermodynamic measurements in the vicinity of absolute zero showed the Pdsei species to be the smallest particles which still have the properties of molecular clusters that distinguish them from bulk metal. 

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