arXiv subjects

V. M. Zaskulnikov

Publications and source records attributed to V. M. Zaskulnikov.

5 recordsLinked to original sources

arXiv2011

Statistical mechanics of fluids at a permeable wall

The problem of surface effects at a fluid boundary created by the force field of finite value is investigated. A classical simple fluid with a locally introduced field imitating a permeable solid is considered. The cases of micro- and macroscopically smooth boundary are examined and the analysis of static membranes is performed. Henry constant of adsorption and its connection with Henry constant of absorption, specific surface grand potential (gamma) and the surface number density are determined. High-temperature expansions and low-temperature limit for basic values are obtained. "The surface tension coefficient" decomposes into a value proportional to Henry constant of adsorption depending on the position of the separating surface, and a universal nonlinear surface coefficient. Two approaches to this problem are analyzed: through the surface cluster expansion and through the pressure tensor. Within the first approach, the series in powers of activity is obtained for gamma. This expression is similar to the cluster expansion for pressure but in contrast to this case the integrals of Ursell factors contain the multipliers depending on the potential of particles interaction with the external field. Within the second approach, Kirkwood-Buff formula for gamma is extended for the case of the field of finite value. A complete identity of the approaches of "cluster expansion" and "pressure tensor" is demonstrated, and the near-surface virial expansion which determines the exact equation of state of the "two-dimensional" gas of the near-surface region is constructed. Coincidence of pressure acting on a transverse wall and the tangential component of pressure tensor, both averages over the transition layer as well as the symmetry of the solution with respect to the permutation of sorbent - fluid are demonstrated.

cond-mat.stat-mech↗

arXiv2011

Statistical mechanics of fluids at an impermeable wall

The problem of surface effects at a fluid/force field boundary is investigated. A classical simple fluid with a locally introduced field simulating a solid is considered. For the case of a hard-core field, rigid, exponential, realistic, and macroscopically smooth boundaries are examined. Two approaches to this problem are analyzed. With some degree of arbitrariness, they can be referred to as "adsorption" vs "surface tension" or "cluster expansion" vs "pressure tensor". The "adsorption" approach is used to obtain a series in powers of the activity for gamma. For Mayer-type expansion the integrals of the Ursell functions contain factors which depend on the particle/wall interaction potential. In the case of a hard wall, the coefficients of the series reduce to the first moments of the Ursell functions taken over certain regions. The "surface tension" approach is used to expand the Kirkwood-Buff formula for gamma to the arbitrary localization of the dividing surface. "The surface tension coefficient" breaks up into the term proportional to the Henry constant, depending on the dividing surface position, and universal nonlinear surface coefficient. It is shown that the derivative of the tangential component of the pressure tensor with respect to the chemical potential coincides with the near-surface number density on average over the transition region, that has two consequences. Firstly, it proves complete identity between "tension" and "adsorption" approaches in the domain of their existence. Secondly, it gives the near-surface virial expansion, which determines the exact equation of state of near boundary "two-dimensional" fluid. The tangential component of the pressure tensor averaged over the transition region plays the role of pressure, and the average number density - the role of number density.

cond-mat.stat-mech↗

arXiv2011

Open statistical ensemble: new properties (scale invariance, application to small systems, meaning of surface particles, etc.)

A new statistical ensemble is examined using the example of classical one-component simple fluid. It's logical to call it an open ensemble, because its peculiarity is the inclusion in the consideration some surrounding area. Calculations point to the necessity of taking into account the restricting surface, exactly when the system is not separated by anything from the bath, and the whole medium is uniform. The "surface tension coefficient", included in the partition function corresponds to the interface of the fluid and hard solid, due to the strict compliance of probability and potential limitations. The number of surface particles corresponds exactly to near surface number density distortions (oscillations) arising in the neighborhood of fluctuation cavities. In contrast to grand canonical ensemble, an open statistical ensemble satisfies the scale invariance requirement: general term of the included subsystem distribution corresponds to that of the original system. It is this ensemble which should be used where consideration of a truly open system is required, since it properly integrates the surface terms. Furthermore, this ensemble may be employed in studies of small systems, since it has no lower limits for the volume of the system. Finally, it is useful in the investigation of fluctuations. For example, it demonstrates that the variance (the mean square deviation) of the number of particles is divided into the bulk and surface terms.

cond-mat.stat-mech↗

arXiv2010

Surface in statistical ensembles

The present contribution deals with surface terms appearing immediately in distributions and partition functions of statistical ensembles. It is shown that all ensembles under study, including ordinary canonical and grand canonical ensembles, involve surface terms. For a canonical ensemble both surface and volume terms correspond to a closed system. For a grand canonical ensemble the volume term corresponds to an open system, while the surface one - to a closed one. Finally, for the recently introduced open statistical ensemble the specific feature of which is the consideration of some surrounding region both volume and surface terms correspond to an open system. In conclusion, surface particles at solid/fluid boundary are interpreted as particles corresponding to number density oscillations near the surface; this completely agrees with the earlier introduced concept of surface tension at such a boundary.

cond-mat.stat-mech↗

arXiv2009

Open statistical ensemble and surface phenomena

In the present work we investigate a new statistical ensemble, which seems logical to be entitled the open one, for the case of a one-component system of ordinary particles. Its peculiarity is in complementing the consideration of a system with the inclusion of a certain surrounding area. The calculations indicate the necessity of taking into account the surface that delimits a given system even in the case when the latter is a part of a uniform medium and is not singled out one way or another. The surface tension coefficient behaves unlike two-phase systems in equilibrium and depends on two variables - pressure as well as temperature - and belongs to the boundary separating a hard solid from a fluid. As for the mathematical mechanism ensuring the fulfillment of thermodynamic relations, the emphasis is shifted from operating with series, like in the grand canonical ensemble, towards employing the recurrence relations of a new class of functions that incorporate Boltzmann and Ursell factors as their extreme cases and towards utilizing generating functions. The second topic of discussion that the present article deals with is the consideration of the surface tension and adsorption observed at the boundary of a solid body and a liquid or gas carried out on the basis of the analysis of the classical system found in a field of force of general type. The surface terms are calculated with the aid of field functions and the correlation functions of an unperturbed volume phase and behave somewhat vaguely; particularly, as a function of activity, they may start with a linear or quadratic term.

cond-mat.stat-mech↗