Biomedical subjects
Publications and source records attributed to A Maciołek.
An exact derivation of the surface magnetizations of the two phases m(1)I and m(1)II coexisting below the bulk critical temperature for the semi-infinite two-dimensional Ising ferromagnet subject to a surface field is given. The surface critical behavior of the difference m(1)I - m(1)II is that of the ordinary transition only in a limit of a weak surface field below the wetting temperature.
An exact statistical mechanical derivation of corner filling in the two-dimensional Ising ferromagnet is given. The surface fields on the edges that meet at the corner are not required to be the same in the solution. Both thermodynamic results and microscopic structure are obtained.
A lattice model of 3He-4He mixtures which takes into account the continuous rotational symmetry O(2) of the superfluid degrees of freedom of 4He is studied in the molecular-field approximation and by Monte Carlo simulations in three dimensions. In contrast to its two-dimensional version, for reasonable values of the interaction parameters the resulting phase diagram resembles that observed experimentally for 3He-4He mixtures, for which phase separation occurs as a consequence of the superfluid transition. The corresponding continuum Ginzburg-Landau model with two order parameters describing 3He-4He mixtures near tricriticality is derived from the considered lattice model. All coupling constants appearing in the continuum model are explicitly expressed in terms of the mean concentration of 4He, the temperature, and the microscopic interaction parameters characterizing the lattice system.
The solvation force of a simple fluid confined between identical planar walls is studied in two model systems with short ranged fluid-fluid interactions and long-ranged wall-fluid potentials decaying as -Az(-p),z--> infinity, for various values of p. Results for the Ising spins system are obtained in two dimensions at vanishing bulk magnetic field h=0 by means of the density-matrix renormalization-group method; results for the truncated Lennard-Jones (LJ) fluid are obtained within the nonlocal density functional theory. At low temperatures the solvation force f(solv) for the Ising film is repulsive and decays for large wall separations L in the same fashion as the boundary field f(solv) approximately L(-p), whereas for temperatures larger than the bulk critical temperature f(solv) is attractive and the asymptotic decay is f(solv) approximately L(-(p+1)). For the LJ fluid system f(solv) is always repulsive away from the critical region and decays for large L with the the same power law as the wall-fluid potential. We discuss the influence of the critical Casimir effect and of capillary condensation on the behavior of the solvation force.
We obtain the exact solution for a two-dimensional rectangular Ising ferromagnet forming a corner with a surface field applied to the spins on edges. We establish the existence of the filling transition and give the condition for the filling temperature. We discuss the basic properties of the transition.
Two-dimensional Ising strips subject to identical surface fields h(1)=h(2) > or =0 are studied for temperatures above and below the bulk critical temperature T(c) and a range of bulk fields h by means of the density-matrix renormalization-group method. In the case of nonvanishing surface fields, the near-critical behavior of the solvation force f(solv), total adsorption Gamma, inverse longitudinal correlation length xi(parallel)( -1) and specific heat C(H) is strongly influenced by the (pseudo) capillary condensation that occurs below T(c). We obtain scaling functions of f(solv), Gamma, and xi(parallel)(-1). C(H) exhibits a weakly rounded singularity on crossing the pseudocoexistence line. We contrast these results with those for the case of free boundaries where, for temperatures slightly below T(c), f(solv) and C(H) exhibit a sharp extremum away from h=0. Our results have direct repercussions for the properties of near-critical Ising films in three dimensions and we argue that the long-ranged solvation (Casimir) force in confined fluids should be more attractive in the neighborhood of the capillary critical point than exactly at the bulk critical point.
We argue that in a fluid, or magnet, confined by adsorbing walls which favor liquid, or the (+) phase, the solvation (Casimir) force in the vicinity of the critical point is strongly influenced by capillary condensation which occurs below the bulk critical temperature T(c). At T slightly below and above T(c), a small bulk field h<0, which favors gas, or the (-) phase, leads to residual condensation and a solvation force which is much more attractive (at the same large wall separation) than that found exactly at the critical point. Our predictions are supported by results obtained from density-matrix renormalization-group calculations in a two-dimensional Ising strip subject to identical surface fields.
We investigate two dimensional critical Ising films of width L with surface fields H(1)=H(L) in the crossover between ordinary (H(1)=0) and normal (H(1)=infinity) transitions. Using exact transfer-matrix diagonalization and density matrix renormalization-group (DMRG) methods, we calculate magnetization profiles m(z), the excess magnetization Gamma, and the analog of the solvation force f(solv) as functions of H1 for several L. Scaling functions of the above quantities deviate substantially from their asymptotic forms at fixed points for a broad region of the scaling variable LH21 approximately L/l(1), where l(1) is the length induced by the surface field H1. The scaling function for /f(solv)/ has a deep minimum near LH(2)(1)=1, which is about one order of magnitude smaller than its value at both fixed points (the "Casimir" amplitude). For weak H1 (l(1)>L) the magnetization profile has a maximum at the center of the film, and f(solv) decays much faster than L-2. For stronger H1 (1 >l(1) the solvation force decays according to the universal power law f(solv) approximately L(-2). The results of the approximate DMRG method show remarkable agreement with the exact ones.
The adsorption of a near-critical fluid confined in a slit pore is investigated by means of density functional theory and by Monte Carlo simulation for a Lennard-Jones fluid. Our work was stimulated by recent experiments for SF6 adsorbed in a mesoporous glass, which showed the striking phenomenon of critical depletion, i.e., the adsorption excess Gamma first increases but then decreases very rapidly to negative values as the bulk critical temperature T(c) is approached from above along near-critical isochores. By contrast, our density functional and simulation results, for a range of strongly attractive wall-fluid potentials, show Gamma monotonically increasing and eventually saturating as the temperature is lowered toward T(c) along both the critical (rho=rho(c)) and subcritical isochores (rho T(+)(c). For rho<rho(c) we find that in the fluid the effective bulk field, which is negative and which favors desorption, is insufficient to dominate the effects of the surface fields which favor adsorption. We compare this situation with earlier results for the lattice gas model with a constant (negative) bulk field where critical depletion was found. A qualitatively different behavior of the density profiles and adsorption is found in simulations for intermediate and weakly attractive wall-fluid potentials, but in no case do we observe the critical depletion found in experiments. We conclude that the latter cannot be accounted for by a single pore model.