Critical phenomena in finite-size systems

The critical phenomena and peculiarities of phase transitions in the confined fluid systems are investigated. A system with the geometry of a planeparallel layer is chosen in order to discuss the influence of the space limitations on the critical characteristics of fluids. The main ideas of the Munster iteration procedure were used to find the pair and the direct correlation functions. Such an important characteristic of the system as the correlation length was found and correspondent results were analyzed in the terms of the scaling theory. Special attention is paid to the calculation of the shifts of the critical parameters (critical temperature and density). The three-moment approximation is used to investigate anisotropic liquids. The system of the Ornstein-Zernike (OZ) integral equations is involved to investigate the correlative properties of the binary fluid mixtures. It is shown for the fluids with the isomorphic character of the interaction that the approximation may be used that makes the system similar to the OZ onecomponent liquid model. The asymptotic formulae for the pair correlation functions are found and the validity of the Munster method for the binary mixtures is considered. The peculiarities of critical light opalescence for the systems with the special geometry are considered.

“…Taking the zeroth boundary conditions to satisfy the limiting transition to the infinite system one may find the direct and the pair correlation functions in the following form [8,9]:…”

Section: The Correlation Functionsmentioning

confidence: 99%

Critical Behaviour of Confined Systems

Chalyi¹,

Chernenko²,

Василев³

2000

“…On the other hand, our results in limiting cases, i.e. for simple and binary systems (spatially infinite and finite-size), give a well-known formulae that was previously received for these systems in numerous works (see for example [1,6,7,21]) and we can conclude that they are absolutely realistic.…”

Section: Discussionmentioning

confidence: 84%

Critical parameters and pair correlations in confined multicomponent liquids

Василев¹,

Chalyi²

2006

We investigate multicomponent finite-size liquid systems with geometry of plane-parallel layer and cylinder. We consider these systems are being affected by weak external field which causes their anisotropy. For these systems we find pair correlation functions and analyze the effect of space limitation and external field on correlative behaviour of multicomponent liquid. We compare our results with the data for simple and binary finite-size systems.

“…Basic conditions of the similar universal behaviour for infinite-size (bulk) systems of different nature are well-known [1-3, 9, 10]: (i) space dimensionality; (ii) the number of components of order parameters; (iii) the type (short-or long-range) of the intermolecular interaction; (iv) symmetry of Hamiltonian (fluctuation part of the thermodynamic potential). Similar universal behaviour for confined systems needs the following basic conditions in addition to four previous ones: (v) geometric factors (the number of monolayers) for system confinement; (vi) low crossover dimensionality defined by the shape of the restricted volume, (see below for a more detailed explanation); (vii) the type of boundary conditions; (viii) the physical properties under consideration [6][7][8][11][12][13]. These basic conditions of similar universal behavior of confined systems will be illustrated herein below.…”

Section: Universality Classes For Infinite (Bulk) and Finite-size Sysmentioning

confidence: 99%

“…It appears that the temperature variable τ * is characterized by the following formula in liquids with confined geometry [11,16,17]:…”

Section: Diffusion Processes In Mesoscale Liquid Systemsmentioning

confidence: 99%

“…Methods of the theory of phase transitions in the spatially limited systems are used here to study the diffusion coefficient of water molecules in cylindrical pores, as well as the effects of spatial dispersion and low crossover dimensionality (geometrical form) on the diffusion processes [6][7][8][11][12][13][14][15][16][17].…”

Section: Diffusion Processes In Mesoscale Liquid Systemsmentioning

confidence: 99%

See 1 more Smart Citation

Universality classes and critical phenomena in confined liquid systems

Chalyi¹,

Bulavin²,

Чехун³

et al. 2013

It is well known that the similar universal behavior of infinite-size (bulk) systems of different nature requires the same basic conditions: space dimensionality; number components of order parameter; the type (short-or longrange) of the intermolecular interaction; symmetry of the fluctuation part of thermodynamical potential. Basic conditions of similar universal behavior of confined systems needs the same supplementary conditions such as the number of monolayers for a system confinement; low crossover dimensionality, i.e., geometric form of restricted volume; boundary conditions on limiting surfaces; physical properties under consideration. This review paper is aimed at studying all these conditions of similar universal behavior for diffusion processes in confined liquid systems. Special attention was paid to the effects of spatial dispersion and low crossover dimensionality. This allowed us to receive receiving correct nonzero expressions for the diffusion coefficient at the critical point and to take into account the specific geometric form of the confined liquid volume. The problem of 3D⇔2D dimensional crossover was analyzed. To receive a smooth crossover for critical exponents, the Kawasaki-like approach from the theory of mode coupling in critical dynamics was proposed. This ensured a good agreement between data of computer experiment and theoretical calculations of the size dependence of the critical temperature T c (H) of water in slitlike pores. The width of the quasi-elastic scattering peak of slow neutrons near the structural phase transition in the aquatic suspensions of plasmatic membranes (mesostructures with the typical thickness up to 10 nm) was studied. It was shown that the width of quasi-elastic peak of neutron scattering decreases due to the process of cell proliferation, i.e., with an increase of the membrane size (including the membrane thickness). Thus, neutron studies could serve as an additional diagnostic test for the process of tumor formation.