Dimo Kashchiev

Solution of the non-steady state problem in nucleation kinetics

Abstract An approximate solution of the Zeldovich-Frenkel equation is obtained. Expressions are derived for the transient nucleation rate and for the time-lag. The analysis shows that the phenomena in the critical region play the decisive role during the establishment of the steady state. Finally, the possibility is indicated of comparing the theoretical results with experimental data.

On the relation between nucleation work, nucleus size, and nucleation rate

A general thermodynamic relation is proved to exist between the nucleation work and the nucleus size regardless of the model for the excess free energy of the nucleus. When this energy is supersaturation independent, the relation reads as follows: the number of atoms (or molecules) in the nucleus equals the derivative with minus sign of the nucleation work with respect to the supersaturation Δμ. It is shown that, experimentally, a reliable determination of the nucleus size is possible when data for the stationary nucleation rate J are plotted in coordinates kT ln J vs. Δμ (k is the Boltzmann constant and T is the absolute temperature). The slope of such an experimental curve gives information about the nucleus size independently of the kind of nucleation: classical or atomistic, homogeneous or heterogeneous, three dimensional or two dimensional, etc.

A general relation between the nucleation work and the size of the nucleus in multicomponent nucleation

We prove a general theorem that relates the variation of the work of formation of the critical nucleus with chemical potential and the size and composition of the critical nucleus. Applications are made to multicomponent nucleation and to both isothermal and nonisothermal phase transformations. We show that the excess number of molecules and the excess entropy of the critical nucleus are thus accessible to experimental determination with the help of data for the dependence of the nucleation rate on supersaturation. The results derived do not rely on classical nucleation approximations and thus apply down to the smallest nuclei of a few molecules only.

Induction time in crystallization of gas hydrates

Abstract The kinetics of the initial stage of crystallization of one-component gas hydrates in aqueous solutions are analyzed. The temporal evolution of the volume of hydrate crystallized and the moles of gas consumed are determined. Expressions are derived for the supersaturation dependence of the hydrate crystallite growth rate and the induction time in hydrate crystallization. These expressions are used for revealing how additives in the solution that act as kinetic inhibitors of hydrate crystallization can affect the induction time of the process. The results obtained are applied to crystallization of methane, ethane and cyclopropane hydrates.

Nucleation of gas hydrates

The kinetics of nucleation of one-component gas hydrates in aqueous solutions are analyzed. The size of the hydrate nucleus and the work for nucleus formation are determined as functions of the supersaturation Δμ. Expressions for the stationary rate J of hydrate nucleation are derived. These expressions describe the J(Δμ) dependence for homogeneous nucleation and for heterogeneous nucleation at the solution/gas interface or on solid substrates and nucleation-active microparticles in the solution. The results are applied to nucleation of methane hydrate in solutions containing additives that may act as kinetic inhibitors of the process.

Driving force for crystallization of gas hydrates

A general expression is derived for the supersaturation for crystallization of one-component gas hydrates in aqueous solutions. The supersaturation is the driving force of the process, since it represents the difference between the chemical potentials of a hydrate building unit in the solution and in the hydrate crystal. Expressions for the supersaturation are obtained for solutions supersaturated in isothermal or isobaric regime. The results obtained are applied to the crystallization of hydrates of methane, ethane and other one-component gases.

Induction time and metastability limit in new phase formation

An analysis is made of the induction time ti in new phase formation, i.e. of the time elapsing before the onset of the process. A general formula for ti is proposed which is valid for any number of nuclei appearing and growing in the parent phase and which unites the known expressions for ti only applicable when either one or a large number of nuclei are involved in the process. This formula for ti is used for determination of the metastability limit in new phase formation, i.e. of the critical (or maximum) supersaturation below which the parent phase can stay long enough in metastable equilibrium.

Stability and permeability of amphiphile bilayers

In this review the rupture and permeability of bilayers are considered on the basis of a mechanism of the formation of microscopic holes as fluctuations in the bilayers. The hole formation is treated as a nucleation process of a new phase in a two-dimensional system with short-range intermolecular forces. Free rupture and deliberate rupture (by alpha-particles) of foam bilayers (Newtonian black films) are discussed. A comparison is made between the rupture of foam and emulsion bilayers. Experimental methods for obtaining foam and emulsion bilayers from thin liquid films are considered. Methods for investigating the stability and permeability of foam bilayers, which are based on a microscopic model allowing the use of amphiphile solutions with very low concentrations, are described. Experimental dependences of the lifetime of bilayers, the probability of observing the foam bilayer in a foam film, the gas permeability of bilayers, etc. on the concentration of amphiphile molecules in the solution are reported. The influence of temperature and external impact (e.g. alpha-particle irradiation) have also been experimentally studied. A good agreement between theory and experiment is established, allowing determination of several characteristics of foam and emulsion bilayers obtained from ionics or non-ionics: the specific edge energy of bilayer holes, equilibrium surfactant concentration below which the bilayer is thermodynamically metastable, work for the formation of a nucleus hole, number of vacancies in the nucleus hole, coefficient of gas diffusion through the bilayer, etc. On the basis of the effect of temperature on the rupture of foam bilayers the binding energy of a surfactant molecule in the bilayer is determined. The adsorption isotherm of surfactant vacancies in the foam bilayer is obtained which shows a first-order phase transition. Some applications to scientific, technological and medical problems are considered. The foam bilayer is used as a model for investigating short-range forces in biological structures, the interaction between membranes and cell fusion. It is also shown that the foam bilayer is a suitable model for studying the alveolar surface and stability. On that basis a clinical diagnostic method is developed for assessment of the human foetal lung maturity.

Determination of nucleation and growth rates from induction times in seeded and unseeded precipitation of calcium carbonate

Abstract Theoretical expressions for the supersaturation dependence of the induction time in seeded and unseeded precipitation are derived for different mechanisms of crystallite growth. On the basis of the theory a combined analysis of the induction time in both seeded and unseeded precipitation is presented, which allows separate determination of the nucleation and growth rates. Induction times in both seeded and unseeded precipitation of calcium carbonate in the absence and presence of additives are measured and interpreted in the light of the proposed theory. The analysis provides full information about the growth and nucleation rates in the investigated systems.

Bilayer lipid membrane permeation and rupture due to hole formation

A theory is developed for the permeation and rupture of bilayer lipid membranes due to fluctuation formation of holes (or pores) in them. The two monolayers of the bilayer lipid membrane are considered as mutually adsorbed on each other and the bilayer lipid membrane equilibrium is described by an adsorption isotherm in mean field approximation. The theory of nucleation is used for determination of the work for hole formation and the hole equilibrium size distribution as functions of the concentration C of monomer lipid in the solution. The bilayer lipid membrane permeation and rupture are analyzed from a unified point of view and expressions are derived for the dependence of the bilayer lipid membrane diffusion permeability coefficient and lifetime on C. The effect of foreign bodies (e.g., proteins) on the bilayer lipid membrane permeation and rupture is considered and a possible experimental application of the theory is discussed. The results obtained are directly applicable to dense monolayer films on liquid surfaces.