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M. Napiorkowski

Publications and source records attributed to M. Napiorkowski.

14 recordsLinked to original sources
arXiv2019

Non-universal Casimir forces at Bose-Einstein condensation of an ideal gas: effect of Dirichlet boundary conditions

We analyze the Casimir forces for an ideal Bose gas enclosed between two infinite parallel walls separated by the distance D. The walls are characterized by the Dirichlet boundary conditions. We show that if the thermodynamic state with Bose-Einstein condensate present is correctly approached along the path pertinent to the Dirichlet b.c. then the leading term describing the large-distance decay of thermal Casimir force between the walls is 1/D^2 with a non-universal amplitude. The next order correction is lnD/D^3. These observations remain in contrast with the decay law for both the periodic and Neumann boundary conditions for which the leading term is 1/D^3 with a universal amplitude. We associate this discrepancy with the non-zero D-dependent positive value of the one-particle ground state energy in the case of Dirichlet boundary conditions.

cond-mat.stat-mech↗
arXiv2013

The imperfect Bose gas in d dimensions: critical behavior and Casimir forces

We consider the d-dimensional imperfect (mean-field) Bose gas confined in a slit-like geometry and subject to periodic boundary conditions. Within an exact analytical treatment we first extract the bulk critical properties of the system at Bose-Einstein condensation and identify the bulk universality class to be the one of the classical d-dimensional spherical model. Subsequently we consider finite slit width D and analyze the excess surface free energy and the related Casimir force acting between the slit boundaries. Above the bulk condensation temperature (T>T_c) the Casimir force decays exponentially as a function of D with the bulk correlation length determining the relevant length scale. For T=T_c and for T 4 and T\leq T_c.

cond-mat.stat-mech↗
arXiv2009

Effective Hamiltonian for a liquid-gas interface fluctuating around a corrugated cylindrical substrate in the presence of van der Waals interactions

We investigate liquid layers adsorbed at spherical and corrugated cylindrical substrates. The effective Hamiltonians for the liquid-gas interfaces fluctuating in the presence of such curved substrates are derived via the mean-field density functional theory. Their structure is compared with the Helfrich Hamiltonian which is parametrized by the bending and Gaussian rigidity coefficients. For long-ranged interparticle interactions of van der Waals type these coefficients turn out to be non-universal functions of interfacial curvatures; their form varies from one interface to another. We discuss implications of the structure of these functions on the effective Hamiltonian.

cond-mat.soft↗
arXiv2008

Effective Hamiltonian for fluid membranes in the presence of long-ranged forces

If the constituent particles of fluid phases interact via long-ranged van der Waals forces, the effective Hamiltonian for \emph{interfaces} between such fluid phases contains - in lateral Fourier space - non-analytic terms $ \sim q^4 \ln q$. Similar non-analytic terms characterize the effective Hamiltonian for two interacting interfaces which can emerge between the three possible coexisting fluid phases in binary liquid mixtures. This is in contrast with the structure of the phenomenological Helfrich Hamiltonian for membranes which does not contain such non-analytic terms. We show that under favorable conditions for the bulk densities characterizing a binary liquid mixture and for the long-ranged interparticle interactions the corresponding effective Hamiltonian for a model fluid \emph{membrane} does not exhibit such non-analytic contributions. We discuss the properties of the resulting effective Hamiltonian, with a particular emphasis on the influence of the long range of the interactions on the coefficient of the bending rigidity.

cond-mat.soft↗
arXiv2007

Conceptual aspects of line tensions

We analyze two representative systems containing a three-phase-contact line: a liquid lens at a fluid--fluid interface and a liquid drop in contact with a gas phase residing on a solid substrate. We discuss to which extent the decomposition of the grand canonical free energy of such systems into volume, surface, and line contributions is unique in spite of the freedom one has in positioning the Gibbs dividing interfaces. In the case of a lens it is found that the line tension is independent of arbitrary choices of the Gibbs dividing interfaces. In the case of a drop, however, one arrives at two different possible definitions of the line tension. One of them corresponds seamlessly to that applicable to the lens. The line tension defined this way turns out to be independent of choices of the Gibbs dividing interfaces. In the case of the second definition,however, the line tension does depend on the choice of the Gibbs dividing interfaces. We provide equations for the equilibrium contact angles which are form-invariant with respect to notional shifts of dividing interfaces which only change the description of the system. Conceptual consistency requires to introduce additional stiffness constants attributed to the line. We show how these constants transform as a function of the relative displacements of the dividing interfaces. The dependences of the contact angles on lens or drop volumes do not render the line tension alone but a combination of the line tension, the Tolman length, and the stiffness constants of the line.

cond-mat.soft↗
arXiv2006

Interfacial morphology and correlations in adsorption at a chemically structured substrate - exact results in d=2

Adsorption at a 1-dimensional planar substrate equipped with a localized chemical inhomogeneity is studied within the framework of a continuum interfacial model from the point of view of interfacial morphology and correlation function properties. Exact expressions for the one-point and two-point probability distribution functions $P_\Gamma (l_\Gamma)$ and $P_{\Gamma_1, \Gamma_2}(l_{\Gamma_1},l_{\Gamma_2})$, $l_\Gamma$ being the interface position above a fixed point $\Gamma$ of the substrate, are derived for temperature corresponding to the inhomogeneity's wetting transition. It is demonstrated that in the limit of macroscopic inhomogeneity's size the net effect of the remaining homogeneous parts of the substrate on the interfacial morphology above the inhomogeneity is exactly equivalent to appropriate pinning of the interface at its boundaries. The structure of the average interfacial morphology and correlation function in this limit are discussed and compared to earlier results obtained for systems with homogeneous substrate.

cond-mat.stat-mech↗
arXiv2006

Point tension in adsorption at a chemically inhomogeneous substrate in two dimensions

We study adsorption of liquid at a one-dimensional substrate composed of a single chemical inhomogeneity of width $2L$ placed on an otherwise homogeneous, planar, solid surface. The excess point free energy $η(L,T)$ associated with the adsorbed layer's inhomogeneity induced by the substrate's chemical structure is calculated within exact continuum transfer-matrix approach. It is shown that the way $η(L,T)$ varies with $L$ depends sensitively on the temperature regime. It exhibits logarithmic divergence as a function of $L$ in the limit $L\to\infty$ for temperatures such that the chemical inhomogeneity is completely wetted by the liquid. In the opposite case $η(L,T)$ converges for large $L$ to $2η_0$, where $η_0$ is the corresponding point tension, and the dominant $L$-dependent correction to $2η_0$ decays exponentially. The interaction between the liquid layer inhomogeneities at $-L$ and $L$ for the two temperature regimes is discussed and compared to earlier mean-field theory predictions.

cond-mat.stat-mech↗
arXiv2003

Phase Transitions in Multicomponent String Model

We propose a one-dimensional model of a string decorated with adhesion molecules (stickers) to mimic multicomponent membranes in restricted geometries. The string is bounded by two parallel walls and it interacts with one of them by short range attractive forces while the stickers are attracted by the other wall. The exact solution of the model in the case of infinite wall separation predicts both continuous and discontinuous transitions between phases characterised by low and high concentration of stickers on the string. Our model exhibits also coexistence of these two phases, similarly to models of multicomponent membranes.

cond-mat.soft↗
arXiv2000

Liquid drop in a cone - line tension effects

The shape of a liquid drop placed in a cone is analyzed macroscopically. Depending on the values of the cone opening angle, the Young angle and the line tension four different interfacial configurations may be realized. The phase diagram in these variables is constructed and discussed; it contains both the first- and the second-order transition lines. In particular, the tricritical point is found and the value of the critical exponent characterizing the behaviour of the system along the line of the first-order transitions in the neighbourhood of this point is determined.

cond-mat.stat-mech↗
arXiv2000

Interfacial fluctuations near the critical filling transition

We propose a method to describe the short-distance behavior of an interface fluctuating in the presence of the wedge-shaped substrate near the critical filling transition. Two different length scales determined by the average height of the interface at the wedge center can be identified. On one length scale the one-dimensional approximation of Parry et al. \cite{Parry} which allows to find the interfacial critical exponents is extracted from the full description. On the other scale the short-distance fluctuations are analyzed by the mean-field theory.

cond-mat.stat-mech↗
arXiv2000

Adsorption on a periodically corrugated substrate

Mean field analysis of the effective interfacial Hamiltonian shows that with increasing temperature the adsorption on a periodically corrugated substrate can proceed in two steps: first, there is the filling transition in which the depressions of the substrate become partially or completely filled; then there is the wetting transition at which the substrate as a whole becomes covered with a macroscopically thick wetting layer. The actual order and location of both transitions are related to the wetting properties of the corresponding planar substrate and to the form of corrugation. Certain morphological properties of the liquid-vapor interface in the case of a saw-like corrugated substrate are discussed analytically

cond-mat.stat-mech↗
arXiv1998

Filling transition for a wedge

We study the formation and the shape of a liquid meniscus in a wedge with opening angle $2ϕ$ which is exposed to a vapor phase. By applying a suitable effective interface model, at liquid-vapor coexistence and at a temperature $T_ϕ$ we find a filling transition at which the height of the meniscus becomes macroscopically large while the planar walls of the wedge far away from its center remain nonwet up to the wetting transition occurring at $T_w>T_ϕ$. Depending on the fluid and the substrate potential the filling transition can be either continuous or discontinuous. In the latter case it is accompanied by a prefilling line extending into the vapor phase of the bulk phase diagram and describing a transition from a small to a large, but finite, meniscus height. The filling and the prefilling transitions correspond to nonanalyticities in the surface and line contributions to the free energy of the fluid, respectively.

cond-mat.soft↗