Search

We examine the validity of the Fokker-Planck equation with linear force coefficients as an approximation to the kinetic equation of nucleation in homogeneous isothermal multicomponent condensation. Starting with a discrete equation of balance governing the temporal evolution of the distribution function of an ensemble of multicomponent droplets and reducing it (by means of Taylor series expansions) to the differential form in the vicinity of the saddle point of the free energy surface, we have identified the parameters whereof the smallness is necessary for the resulting kinetic equation to have the form of the Fokker-Planck equation with linear (in droplet variables) force coefficients. The "non-smallness" of these parameters results either in the appearance of the third or higher order partial derivatives of the distribution function in the kinetic equation or in its force coefficients becoming non-linear functions of droplet variables, or both; this would render the conventional kinetic equation of multicomponent nucleation and its predictions inaccurate. As a numerical illustration, we carried out calculations for isothermal condensation in five binary systems of various non-ideality at T=293.15 K: 1-butanol--1-hexanol, water--methanol, water--ethanol, water--1-propanol, water--1-butanol. Our results suggest that under typical experimental conditions the kinetic equation of binary nucleation of classical nucleation theory may require a two-fold modification and, hence, the conventional expression for the steady-state binary nucleation rate may not be adequate for the consistent comparison of theoretical predictions with experimental data.

Using the formalism of the classical nucleation theory, we derive a novel kinetic equation for the size and composition distribution of an ensemble of aqueous organic aerosols, evolving via nucleation and concomitant chemical aging. This distribution can be drastically affected by the enthalpy of heterogeneous chemical reactions and the depletion of organic trace gases absorbed by aerosols. A partial differential equation of second order for the temporal evolution of this distribution is obtained from the discrete equation of balance via Taylor series expansions. Once reduced to the canonical form of the multidimensional Fokker-Planck equation, this kinetic equation can be solved via the method of complete separation of variables. The new kinetic equation opens a new direction in the development of the kinetic theory of first-order phase transitions, while its applications to the formation and evolution of atmospheric organic aerosols may drastically improve the accuracy of global climate models.

We propose an approximation for the total ice nucleation rate J=J(T,R) in supercooled water droplets as a function of both droplet radius R and temperature T, taking account of both volume-based and surface-stimulated nucleation modes. Its crucial idea is that, even in the surface-stimulated mode crystal nuclei initially emerge (as sub-critical clusters) homogeneously in the sub-surface layer, not "pseudo-heterogeneously" at the surface. This mode is negligible in large droplets, but becomes increasingly important with decreasing droplet size and is dominant in small droplets. The crossover droplet radius for the transition of homogeneous ice nucleation from the volume-based mode to the surface-stimulated mode nonmonotonically depends on T from 233 K to 239.5 K, ranging there from about 2 microns to about 100 microns. Using experimental data on ice nucleation rates in small droplets, we determine that the ice-air interfacial tension of basal facets of ice crystals monotonically increases from about 89 dyn/cm at T=234.8 K to about 91 dyn/cm at T=236.2 K., Comment: arXiv admin note: text overlap with arXiv:1702.02500

Using the formalism of the classical nucleation theory, we derive an expression for the reversible work $W_*$ of formation of a binary crystal nucleus in a liquid binary solution of non-stoichiometric composition (incongruent crystallization). Applied to the crystallization of aqueous nitric acid (NA) droplets, the new expression more adequately takes account of the effect of nitric acid vapor compared to the conventional expression of MacKenzie, Kulmala, Laaksonen, and Vesala (MKLV) [J.Geophys.Res. 102, 19729 (1997)]. The predictions of both MKLV and modified expressions for the average liquid-solid interfacial tension $\sigma^{ls}$ of nitric acid dihydrate (NAD) crystals are compared by using existing experimental data on the incongruent crystallization of aqueous NA droplets of composition relevant to polar stratospheric clouds (PSCs). The predictions based on the MKLV expression are higher by about 5% compared to predictions based on our modified expression. This results in similar differences between the predictions of both expressions for the solid-vapor interfacial tension $\sigma^{sv}$ of NAD crystal nuclei. The latter can be obtained by analyzing of experimental data on crystal nucleation rates in aqueous NA droplets and exploiting the dominance of the surface-stimulated mode of crystal nucleation in small droplets and its negligibility in large ones. Applying that method, our expression for $W_*$ provides an estimate for $\sigma^{sv}$ of NAD in the range from 92 dyn/cm to 100 dyn/cm, while the MKLV expression predicts it in the range from 95 dyn/cm to 105 dyn/cm. The predictions of both expressions for $W_*$ become identical in the case of congruent crystallization; this was also demonstrated by applying our method to the nucleation of nitric acid trihydrate (NAT) crystals in PSC droplets of stoichiometric composition.

The thermodynamics of hydration changes gradually from entropic for small solutes to enthalpic for large ones. The small-to-large crossover lengthscale of hydrophobic hydration depends on the thermodynamic conditions of the solvent such as temperature, pressure, presence of additives, etc... We attempt to shed some light on the temperature dependence of the crossover lengthscale by using a probabilistic approach to water hydrogen bonding that allows one to obtain an analytic expression for the number of bonds per water molecule as a function of both its distance to a solute and solute radius. Incorporating that approach into the density functional theory, one can examine the solute size effects on its hydration over the entire small-to-large lengthscale range at different temperatures. Knowing the dependence of the hydration free energy on temperature and solute size, one can obtain its enthalpic and entropic contributions as functions of temperature and solute size. These function can provide interesting insight into the temperature dependence of the crossover lengthscale of hydrophobic hydration. The model was applied to the hydration of spherical particles of various radii in water in the temperature range from T=293.15 K to T=333.15 K. The model predictions for the temperature dependence of the hydration free energy of small hydrophobes are consistent with the experimental and simulational data. Three alternative definitions for the small-to-large crossover length-scale of hydrophobic hydration are proposed, and their temperature dependence is obtained. Depending on the definition and temperature, the small-to-large crossover in the hydration mechanism is predicted to occur for hydrophobes of radii from one to several nanometers. Independent of its definition, the crossover length-scale is predicted to decrease with increasing temperature., Comment: arXiv admin note: substantial text overlap with arXiv:1303.4429

We present a probabilistic approach to water-water hydrogen bonding that allows one to obtain an analytic expression for the number of bonds per water molecule as a function of both its distance to a hydrophobic particle and hydrophobe radius. This approach can be used in the density functional theory (DFT) and computer simulations to examine particle size effects on the hydration of particles and on their solvent-mediated interaction. For example, it allows one to explicitly identify a water hydrogen bond contribution to the external potential whereto a water molecule is subjected near a hydrophobe. The DFT implementation of the model predicts the hydration free energy per unit area of a spherical hydrophobe to be sharply sensitive to the hydropobe radius for small radii and weakly sensitive thereto for large ones; this corroborates the vision of the hydration of small and large length-scale particles as occurring via different mechanisms. On the other hand, the model predicts that the hydration of even apolar particles of small enough radii may become thermodynamically favorable owing to the interplay of the energies of pairwise (dispersion) water-water and water-hydrophobe interactions. This sheds light on previous counterintuitive observations (both theoretical and simulational) that two inert gas molecules would prefer to form a solvent-separated pair rather than a contact one.