Properties Of Critical Clusters Research Articles

Specific heats of alkali metal halides and universal estimates of the surface tension of their melts based on the thermal properties of critical clusters

A dimensionless parameter is determined that relates the thermophysical and capillary characteristics of alkali metal halides. It is shown that the high-temperature surface tension of alkali metal halides can be determined from the results of the high-temperature measurements of specific heat in the temperature range up to their boiling points.

Ion‐mediated nucleation in the atmosphere: Key controlling parameters, implications, and look‐up table

Nucleation is an important source of atmospheric particles and ubiquitous ions in the atmosphere have long been known to promote nucleation. An ion‐mediated nucleation (IMN) mechanism based on a kinetic model is supported by recent measurements of the excess charge on freshly nucleated particles and ion cluster evolution during nucleation events. Here we investigate the dependence of steady state IMN rate (JIMN) on key controlling parameters. We find that sulfuric acid vapor concentration, temperature, relative humidity, ionization rate, and surface area of preexisting particles have profound and nonlinear impacts on JIMN. The sensitivities of JIMN to the changes in these key parameters may imply important physical feedback mechanisms involving climate and emission changes, solar variations, nucleation, aerosol number abundance, and aerosol indirect radiative forcing. We also describe a five‐dimensional JIMN look‐up table derived from the most recent version of the IMN model, with the key parameters covering a wide range of atmospheric conditions. With the look‐up table and a multiple‐variable interpolation subroutine, JIMN and the properties of critical clusters can be determined efficiently and accurately under given atmospheric conditions. The look‐up table reduces the computational costs of the IMN rate calculations significantly (by a factor of around 8000) and can be readily incorporated into multidimensional models to study the secondary particle formation via IMN and associated climatic and health effects.

Updated H2SO4‐H2O binary homogeneous nucleation look‐up tables

The calculated rates of H2SO4‐H2O binary homogeneous nucleation (BHN), which is the only nucleation mechanism currently widely used in global aerosol models, are well known to have large uncertainties. Recently, we have reduced the uncertainties in the BHN rates on the basis of a kinetic quasi‐unary nucleation (KQUN) model, by taking into account the measured bonding energetics of H2SO4 monomers with hydrated sulfuric acid dimers and trimers. The uncertainties were further reduced by using two independent measurements to constrain the equilibrium constants for monomer hydration. In this paper, we present updated BHN rate look‐up tables derived from the improved KQUN model which can be used by anyone to obtain the BHN rates under given conditions. The look‐up tables cover a wide range of key parameters that can be found in the atmosphere and laboratory studies, and their usage significantly reduces the computational costs of the BHN rate calculations, which is critical for multidimensional modeling. The look‐up tables can also be used by those involved in experiments and field measurements to quickly assess the likeliness of BHN. For quick application, one can obtain the BHN rates and properties of critical clusters by browsing through the tables. A comparison of results based on the look‐up tables with those from widely used classical BHN model indicates that, in addition to several orders of magnitude difference in nucleation rates, there also exists substantial difference in the predicted numbers of sulfuric acid molecules in the critical clusters and their dependence on key parameters.

Unorthodox properties of critical clusters

We look at the properties of clusters of order parameter Φ at critical points in thermal systems and consider their significance to statistical–mechanical ground rules. These properties have been previously obtained through the saddle-point approximation in a coarse-grained partition function. We examine both static and dynamical aspects of a single large cluster and indicate that these properties fall outside the canonical Boltzmann–Gibbs (BG) scheme. Specifically, (1) the faster than exponential growth with cluster size of the space-integrated Φ suggests non-extensivity of the BG entropy but extensivity of a q-entropy expression. (2) The finding that the time evolution of Φ is described by the dynamics of an intermittent nonlinear map implies an atypical sensitivity to initial conditions compatible with q-statistics and displays an ‘aging’ scaling property. (3) Both the approach to criticality and the infinite-size cluster limit at criticality manifest through a crossover from canonical to q-statistics and we discuss the non-uniform convergence associated with these features.

Dynamics of first-order phase transitions in multicomponent systems: a new theoretical approach

In the theoretical description of nucleation–growth processes, currently Gibbs's classical thermodynamic theory of heterogeneous systems is predominantly employed for the description of the properties of the clusters. However, Gibbs's approach does not make it possible to describe, in general, the properties of critical clusters (determining the rate of nucleation) in a sufficiently correct way. Moreover, Gibbs's approach is restricted by its applicability to thermodynamic equilibrium states exclusively. For this reason, it does not give a theoretically founded prescription for a determination of the possible states of clusters of sub- and supercritical sizes in dependence on supersaturation and size of the clusters. In order to overcome these shortcomings, in recent years a generalization of Gibbs's classical approach has been developed and employed for the description of nucleation processes. This generalization of Gibbs' classical method leads, for a variety of different applications, to dependencies of the work of critical cluster formation on supersaturation, which are qualitatively and widely even quantitatively in agreement with density-functional computations. The theoretical methods and results are summarized in the first part of the present paper. They are then extended for the first time to a description of processes of growth of single clusters and ensembles of clusters. In order to fulfill this task, a new method for determination of the parameters of sub- and supercritical clusters is developed. It turns out as the result of the analysis that a variety of thermodynamic and kinetic parameters, determining cluster growth, become dependent on cluster size as well. The results are illustrated for a model system (segregation in regular solutions) and applied to the interpretation of experimental results on segregation processes in solutions and crystallization processes in glass-forming melts. It is shown that the newly developed approach resolves a variety of problems in the interpretation of experimental data on the kinetics of phase formation processes which could not be given a satisfactory explanation so far.

Generalized percolation models for frustrated spin systems

A brief review on how to study frustrated spin models by mapping them into generalized percolation models is given. The percolation models associated to a number of deterministic frustrated models are discussed with particular attention on the properties of critical clusters.