Mesoscopic clusters

S. Constas and R. Kapral,/. Chem.Phys., 104,4581 (1996).Dynamics of Proton Transfer in Mesoscopic Clusters. 

S. Consta and R. Kapral. Dynamics of proton transfer in mesoscopic clusters. J. Chem. Phys., 104(12) 4581-4590, 1996. 

The macroscopic properties of liquid suspensions of fumed powders of silica, alumina etc. are not only affected by the size and structure of primary particles and aggregates, which are determined by the particle synthesis, but as well by the size and structure of agglomerates or mesoscopic clusters, which are determined by the particle-particle interactions, hence by a variety of product- and process-specific factors like the suspending medium, solutes, the solid concentration, or the employed mechanical stress. However, it is still unclear how these secondary and tertiary particle structures can be adequately characterized, and we are a long way from calculating product properties from them [1,2]. 

The underlying physical model, reflecting the transformation from an individual mesoscopic cluster or particle, through the interacting particle regime to the thin film, has been investigated. 

Dissipative particle dynamics (DPD) is a meshless, coarse-grained, particle-based method used to simulate systems at mesoscopic length and timescales (Coveney and Espafiol 1997 Espafiol and Warren 1995). In simple terms, DPD can be interpreted as coarse-grained MD. Atoms, molecules, or monomers are grouped together into mesoscopic clusters, or beads, that are acted on by conservative, dissipative, and random forces. The interaction forces are pairwise additive in nature and act between bead centers. Connections between DPD and the macroscopic (hydrodynamic, Navier-Stokes) level of description (Espanol 1995 Groot and Warren 1997), as well as microscopic (atomistic MD) have been well established (Marsh and Coveney 1998). DPD has been used to model a wide variety of systems such as lipid bilayer membranes (Groot and Rabone 2001), vesicles (Yamamoto et al. 2002), polymersomes (Ortiz et al. 2005), binary immiscible fluids (Coveney and Novik 1996), colloidal suspensions (Boek et al. 1997), and nanotube polymer composites (Maiti etal.2005). 

The term nanosized cluster or nanocluster or simply cluster is used presently to denote a particle of any kind of matter, the size of which is greater than that of a typical molecule, but is too small to exhibit characteristic bulk properties. Such particles enter the size regime of mesoscopic materials. 

Fig. 6 compares the nuclearity effect on the redox potentials [19,31,63] of hydrated Ag+ clusters E°(Ag /Ag )aq together with the effect on ionization potentials IPg (Ag ) of bare silver clusters in the gas phase [67,68]. The asymptotic value of the redox potential is reached at the nuclearity around n = 500 (diameter == 2 nm), which thus represents, for the system, the transition between the mesoscopic and the macroscopic phase of the bulk metal. The density of values available so far is not sufficient to prove the existence of odd-even oscillations as for IPg. However, it is obvious from this figure that the variation of E° and IPg do exhibit opposite trends vs. n, for the solution (Table 5) and the gas phase, respectively. The difference between ionization potentials of bare and solvated clusters decreases with increasing n as which corresponds fairly well to the solvation free energy of the cation deduced from the Born solvation model [45] (for the single atom, the difference of 5 eV represents the solvation energy of the silver cation) [31]. 

This is not the only possible way of adding terms to the master equation that give rise to the macroscopic terms (4.1). The molecules might be injected, e.g., in clusters. Such a different choice for the mesoscopic description would affect the fluctuations in n. In general, whenever a system is subject to an external force or agency, one cannot compute the fluctuations if that force is merely known macroscopically, one must also know its stochastic properties. ... 

Of special interest in the recent years was the kinetics of defect radiation-induced aggregation in a form of colloids-, in alkali halides MeX irradiated at high temperatures and high doses bubbles filled with X2 gas and metal particles with several nanometers in size were observed [58] more than once. Several theoretical formalisms were developed for describing this phenomenon, which could be classified as three general categories (i) macroscopic theory [59-62], which is based on the rate equations for macroscopic defect concentrations (ii) mesoscopic theory [63-65] operating with space-dependent local concentrations of point defects, and lastly (iii) discussed in Section 7.1 microscopic theory based on the hierarchy of equations for many-particle densities (in principle, it is infinite and contains complete information about all kinds of spatial correlation within different clusters of defects). 

A many-atom system may contain hundreds of atoms, as in clusters, or macroscopic amounts of matter, as in the cases of condensed matter solutions or solid surface phenomena. Mesoscopic systems and nanostructures fall in between those two extremes. These objects may be embedded in a medium in thermodynamical equilibrium, which imposes constrains of temperature, pressure, or chemical potentials. The medium may alternatively be excited and near equilibrium, or even far from it, in which cases it may strongly affect the time evolution of the object of interest. A unified treatment of these situations can be done with the density operator and its L-vN equation of motion. 

Ray Kapral came to Toronto from the United States in 1969. His research interests center on theories of rate processes both in systems close to equilibrium, where the goal is the development of a microscopic theory of condensed phase reaction rates,89 and in systems far from chemical equilibrium, where descriptions of the complex spatial and temporal reactive dynamics that these systems exhibit have been developed.90 He and his collaborators have carried out research on the dynamics of phase transitions and critical phenomena, the dynamics of colloidal suspensions, the kinetic theory of chemical reactions in liquids, nonequilibrium statistical mechanics of liquids and mode coupling theory, mechanisms for the onset of chaos in nonlinear dynamical systems, the stochastic theory of chemical rate processes, studies of pattern formation in chemically reacting systems, and the development of molecular dynamics simulation methods for activated chemical rate processes. His recent research activities center on the theory of quantum and classical rate processes in the condensed phase91 and in clusters, and studies of chemical waves and patterns in reacting systems at both the macroscopic and mesoscopic levels. 

The hydrodynamics of a circulating fluidized bed can be analyzed from both the macroscopic and mesoscopic points of view. The nonuniformity of the solids concentration in the radial and axial directions represents macroscopic behavior. The existence of solid clusters characterizes mesoscopic behavior (see 10.5). The hydrodynamic behavior in a macroscale is discussed in the following. 

Abstract. Clean metal surfaces often display an atomic arrangement at the surface that differs from the one in the bulk. Some of these surface reconstructions show mesoscopic order and are very adequate to act as a template for the ordered growth of arrays of atoms, molecules or clusters. The electronic states at some surfaces can be prototypes of highly dense 2D electron gases where a number of fundamental properties can be addressed in detail. Localized surface states, on the other hand, are relevant in chemical processes at surfaces. The recent developments in experimental and theoretical techniques allow the exploration of these issues with unprecedented precision. 

---