Model of diffusion-drift charge carrier transport in layers with a fractal structure

A new theoretical (semiempirical) model of diffusion-drift charge carrier transport in layers with a fractal structure based on a partial differential equation with a fractional time derivative has been proposed. It has been shown by numerical calculations that a decrease in the order of the fractional derivative in the presence of the external electric field leads to broadening and asymmetry of the spatial distributions of charge carriers, which physically corresponds to intensification of scattering processes.     

Application of fractional integro-differentiation to the calculation of the thermodynamic properties of surfaces

The thermodynamic properties of an atomically rough surface with a fractal structure are analyzed. Expressions for the Gibbs energy and the Gibbs adsorption are derived using the mathematical apparatus of fractional integro-differentiation. A relation between the exponent of the fractional derivative and the fractal dimension of the surface is determined within the proposed model. The results of the calculations are compared with the theoretical and experimental data available in the literature.     

Some Questions Concerning a Small Sessile Bubble

Colloid Journal - Equations have been derived for the size dependence of the interfacial tension and contact angle of a small spherical sessile bubble under isothermal conditions. It has been shown...     

New Method for Describing Damped Vibrations of a Beam with a Built-in End

Technical Physics - We propose a method for describing damped vibrations of a beam with a built-in end considering the dynamic hysteresis that determines mechanical energy dissipation due to...     

Influence of the size-dependent surface tension of a liquid film on a capillary force in an atomic force microscope

An adsorbed water film always exists between the sample and the probing tip of an atomic force microscope operating at atmospheric conditions. A new expression for the capillary force that acts between the tip and the thin liquid film has been obtained taking into account the size dependence of the surface tension of the liquid described by an exact solution of the Gibbs-Tolman-Koenig-Buff equation. The calculation agrees fairly well with the experimental results.     

On the size dependence of the surface tension

The general form of a differential equation that deduces a size dependence of the surface tension is derived. The well-known Gibbs-Tolman-Koenig-Buff equation for the spherical surface is a particular case of the newly derived one. Analytical solutions to this equation for the spherical, cylindrical, parabolic, and conical surfaces are found.     

Non-steady-state electrical conduction of polymers in the model with fractional integro-differentiation

A simple dynamic model with a fractional time derivative is considered for conducting polymers. The elementary theory of electrical conduction is developed using the fractional equation of motion. In the framework of the model under consideration, the relaxation of the velocity of charge carriers is described by the Mittag-Leffler function. A kinetic equation with the fractional derivative is derived. The electrical conductivity is calculated to a first approximation with the use of the derived kinetic equation. It is demonstrated that the spectral characteristic of non-steady-state current fluctuations in a polymer should be proportional to 1/f.     

Formation of nanoparticles in liquid phase processes

The thermodynamic and kinetic regularities of the formation of inorganic nanoparticles in solutions containing additives of highly adsorbable organic compounds were examined. The dependences of the surface tension on the nanoparticle size and surface coverage and of the size dependences of the rate constants of all reactions were taken into account. A kinetic equation describing the formation of nanoparticles was derived, important limiting cases considered, and simplified analytical solutions obtained. It was demonstrated that, at the initial stage, the nanoparticle grows linearly with time, whereas at later stages (large nanoparticle radii) and high intensity of organic compound adsorption, it grows in the formation regime. The properties of size distribution function of nanoparticles under steady-state conditions are analyzed. It was shown that the presence of a highly adsorbable organic compound in the solution substantially diminishes the variation of nanoparticles in size and makes them smaller.     

A dislocation mechanism of friction between a nanoprobe and solid surface

A dislocation mechanism of friction between an atomic-force microscope (AFM) probe and an atomically smooth solid surface is put forward. In this mechanism, the contact region is represented by an edge dislocation. The triboacoustic emission measured with an AFM shows the dislocation nature of friction. The friction force is calculated for a parabolic tip.     

On the radiation of a dielectric fractal cluster

A semiphenomenological model of radiation from a dielectric fractal cluster illuminated by a laser beam has been studied. The fractality is taken into account for the evaluation of the cluster volume, and the photon absorption cross section has been calculated using the Havriliak-Negami dielectric function, which is used for dielectric materials with a fractal structure (in particular, for polymers). Some well-known facts have been explained in terms of the proposed model.