On the contact conditions for the charge profile in the theory of the electrical double layer for nonsymmetrical electrolytes

The contact value of the charge profile for nonsymmetrical electrolytes is presented as the sum of three contributions. One of them is the normal component of the Maxwell electrostatic stress tensor. The second one is the surface electrostatic property defined as the integral of the product of the gradient of the electrical potential and the density distribution function of coions. The third term is the bulk contribution defined by the sum for anions and for cations of the product of their charge and their partial pressure. For noncharged surfaces only the last two are present and have the same sign in the case of size asymmetry. In the case of charge asymmetry the contact value of the charge profile is the result of the competitions of bulk and surface terms in which the bulk term is dominant. Using both the contact theorems for the density and the charge profiles, the exact expressions for the contact values of the profiles of coions and counterions are obtained and some related properties are discussed.Comment: 5 page

Isotropic-nematic transition in a mixture of hard spheres and hard spherocylinders: scaled particle theory description

The scaled particle theory is developed for the description of thermodynamical properties of a mixture of hard spheres and hard spherocylinders. Analytical expressions for free energy, pressure and chemical potentials are derived. From the minimization of free energy, a nonlinear integral equation for the orientational singlet distribution function is formulated. An isotropic-nematic phase transition in this mixture is investigated from the bifurcation analysis of this equation. It is shown that with an increase of concentration of hard spheres, the total packing fraction of a mixture on phase boundaries slightly increases. The obtained results are compared with computer simulations data.Comment: 11 pages, 4 figure

Cluster expansion for the description of condensed state: crystalline cell approach

A well-known cluster expansion, which leads to virial expansion for the free energy of low density systems, is modified in such a way that it becomes applicable to the description of condensed state of matter. To this end, the averaging of individual clusters over the states of an ideal gas is replaced by the averaging over the states of a non-correlated crystal using single-particle cell potentials. As a result, we arrive at the expansion of the partition function in correlations on the basis of single-particle functions corresponding to the multiplicative approximation. The cell potentials defining these functions are found from the condition of the minimum of the remainder in the constructed decomposition.Comment: 16 page

Scaled particle theory for a hard spherocylinder fluid in a disordered porous medium: Carnahan-Starling and Parsons-Lee corrections

The scaled particle theory (SPT) approximation is applied for the study of the influence of a porous medium on the isotropic-nematic transition in a hard spherocylinder fluid. Two new approaches are developed in order to improve the description in the case of small lengths of spherocylinders. In one of them, the so-called SPT-CS-PL approach, the Carnahan-Starling (CS) correction is introduced to improve the description of thermodynamic properties of the fluid, while the Parsons-Lee (PL) correction is introduced to improve the orientational ordering. The second approach, the so-called SPT-PL approach, is connected with generalization of the PL theory to anisotropic fluids in disordered porous media. The phase diagram is obtained from the bifurcation analysis of a nonlinear integral equation for the singlet distribution function and from the thermodynamic equilibrium conditions. The results obtained are compared with computer simulation data. Both ways and both approaches considerably improve the description in the case of spherocylinder fluids with smaller spherocylinder lengths. We did not find any significant differences between the results of the two developed approaches. We found that the bifurcation analysis slightly overestimates and the thermodynamical analysis underestimates the predictions of the computer simulation data. A porous medium shifts the phase diagram to smaller densities of the fluid and does not change the type of the transition.Comment: 13 pages, 5 figure

Modern trends in liquid state theory: a Festschrift for Yurij Kalyuzhnyi

On July 20, 2011 Yurij Kalyuzhnyi celebrated his 60th birthday. On this occasion the Editorial Board of "Condensed Matter Physics" decided to honour him with a collection of scientific papers. Numerous researchers, colleagues and co-workers of Yura have gladly contributed their articles. On behalf of the "Condensed Matter Physics" Editorial Board, I want to express sincere gratitude to all of them. Highly skilled contributions reflect the modern development of liquid state theory in different areas which are close to Yu. Kalyuzhnyi's interests during many years of his scientific activity

Spontaneous polarisation of the neutral interface for valence asymmetric coulombic systems

In this paper, we discuss the phenomenon of a spontaneous polarisation of a neutral hard planar interface for valence asymmetric coulombic systems. Within a field theoretical description, we account for the existence of non trivial charge density and electric potential profiles. The analysis of the phenomenon shows that the effect is related to combinatorics in relation with the existence of the two independent species cations and anions. This simple and basic feature is related to the quantum mechanical properties of the system. The theoretical results are compared with numerical simulations data and are shown to be in very good agreement, which a fortiori justifies our physical interpretation.Comment: 12 pages, 11 figure

What is liquid in random porous media: the Barker-Henderson perturbation theory

We apply the Barker-Henderson (BH) perturbation theory to the study of a Lennard-Jones fluid confined in a random porous matrix formed by hard sphere particles. In order to describe the reference system needed in this perturbation scheme, the extension of the scaled particle theory (SPT) is used. The recent progress in the development of SPT approach for a hard sphere fluid in a hard sphere matrix allows us to obtain very accurate results for thermodynamic properties in such a system. Hence, we combine the BH perturbation theory with the SPT approach to derive expressions for the chemical potential and the pressure of a confined fluid. Using the obtained expressions, the liquid-vapour phase diagrams of a LJ fluid in HS matrix are built from the phase equilibrium conditions. Therefore, the effect of matrix porosity and a size of matrix particles is considered. It is shown that a decrease of matrix porosity lowers both the critical temperature and the critical density, while the phase diagram becomes narrower. An increase of a size of matrix particles leads to an increase of the critical temperature. From the comparison it is observed that the results obtained from the theory are in agreement with computer simulations. The approach proposed in the present study can be extended to the case of anisotropic fluid particles in HS matrices.Comment: 17 pages, 9 figure

ДЕРЖАВНИЙ КРЕДИТ НА ТЕРЕНАХ УКРАЇНИ НАПРИКІНЦІ ХVIII — НА ПОЧАТКУ ХХ СТОЛІТЬ: ІСТОРИКО-ПРАВОВА ХАРАКТЕРИСТИКА

The article deals with the historical and legal analysis of the formation and development of the state credit system in the Ukrainian lands. The article outlines the conditions and circumstances under which the organizational and legal foundations of the credit activity of banking and other state institutions were formed. During the incorporation of Ukraine into the Russian Empire, the elimination of Ukrainian statehood, and the encroachment upon the very cultural and national identity of the Ukrainians, the system of state credit actually did not exist. The attempts to create banking institutions were unsuccessful because there was niether any market formed nor money and securities in the feudal serfdom empire. The changes only took place in the course of capitalist modernization in the second half of the nineteenth century. The abolition of serfdom made available a large number of workers and the legislator faced the urgent task of creating legal foundations for the development of the credit market. The main reform was the creation of the State Bank in 1860, which, in addition to regulating money market, emission activities, made long-term loans. It was guided by the statutory statute, other regulatory legal acts. In order to promote the credit in the sphere of agriculture, in particular mortgage, the Peasant Land Bank and the State Noble Land Bank were established, which got advantages together with privately owned entities. The offices, branches and agencies of the State Bank and the branches of State Land Banks were directly active in Ukrainian provinces Their activity (and, accordingly, its legal regulation) was under the influenc of the specific features of Ukraine’s financial and economic development, namely, a much more higher pace of industrial and agricultural development than in other regions of the Russian empire. But the insufficient development of long-term crediing in Ukraine had the negative impact on that development.Здійснено історико-правовий аналіз становлення і розвитку системи державного кредиту на українських землях. Окреслено умови і обставини, за яких формувалися організаційно-правові засади кредитної діяльності банківських та інших установ держави. У період інкорпорації України Російською імперією, ліквідації української державності та наступу на саму культурно-національну ідентичність українців системи державного кредиту фактично не існувало. Спроби створити банківські установи були невдалими, оскільки у феодально-кріпосницькій імперії не існувало скільки-небудь сформованого ринку, у тому числі грошей та цінних паперів. Зміни настали лише у ході капіталістичної модернізації у другій половині ХІХ століття. Скасування кріпосного права вивільнило велику кількість робочих рук і перед законодавцем постало нагальне завдання створити правові основи розвитку кредитного ринку. Основною реформою стало створення 1860 року Державного банку, який поряд із регулюванням грошового ринку, емісійною діяльністю надавав довготермінові кредити. Він керувався законодавчо затвердженим статутом, іншими нормативно-правовими актами. Для активізації кредиту у сфері сільського господарства, зокрема іпотечного, були започатковані Селянський поземельний банк і Державний дворянський земельний банк, що отримали переваги поряд із суб’єктами приватної форми власності. Безпосередня діяльність в українських губерніях здійснювалася конторами, відділеннями і агентствами Державного банку та відділеннями державних земельних банків. На їхню діяльність (і відповідно її правове регулювання) особливий вплив мала специфіка фінансового та економічного розвитку України, а саме — значно вищі порівняно з іншими регіонами Російської імперії темпи розвитку промисловості й сільського господарства. Негативно відображався на цьому розвитку недостатній розвиток довготермінового кредиту на українських землях