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A method for Monte Carlo studies of phase equilibrium in confined systems is presented using an example of vapor-liquid equilibrium (capillary condensation and evaporation) in cylindrical pores. The method, named the gauge cell method, allows one to construct the full phase diagram of a confined fluid in the form of a van der Waals loop, which includes stable, metastable, and unstable equilibrium states. The phase coexistence is then determined by thermodynamic integration along the metastable and unstable regions of the phase diagram employing Maxwell's rule of equal areas. The simulation results agree with experimental data on the capillary condensation of nitrogen at its boiling temperature on mesoporous molecular sieves. The method can be applied to other phase transitions in confined systems such as fluid-fluid separation, layering, and freezing.

The statistical geometry of cavities in a confined Lennard-Jones (LJ) fluid is investigated with the focus on metastable states in the vicinity of the stability limit of the liquidlike state. For a given configuration of molecules, a cavity is defined as a connected region where there is sufficient space to accommodate an additional molecule. By means of grand canonical Monte Carlo simulations, we generated a series of equilibrium stable and metastable states along the adsorption-desorption isotherm of the LJ fluid in a slit-shaped pore of ten molecular diameters in width. The geometrical parameters of the cavity distributions were studied by Voronoi-Delaunay tessellation. We show that the cavity size distribution in liquidlike states, characterized by different densities, can be approximated by a universal log-normal distribution function. The mean void volume increases as the chemical potentialmgr; and, correspondingly, the density decreases. The surface-to-volume relation for individual cavities fulfills the three-dimensional scaling S(cav)=gV(2/3)(cav) with the cavity shape factor g=8.32-9.55. The self-similarity of cavities is observed over six orders of magnitude of the cavity volumes. In the very vicinity of the stability limit,mgr;--mgr;(sl), large cavities are formed. These large cavities are ramified with a fractal-like surface-to-volume relation, S(cav) approximately V(cav). Better statistics are needed to check if these ramified cavities are similar to fragments of a spanning percolation cluster. At the limit of stability, the cavity volume fluctuations are found to diverge as (V(2)(cav)-V(cav)(2)) approximately [(mgr;-mgr;(sl))/kT](-gamma(c)) with the exponent gamma(c) approximately 0.93. This exponent can be referred to as the cavity pseudocritical exponent, in analogy with the other pseudocritical exponents characterizing the divergence of thermodynamic quantities at the spinodal point.

Methods for characterization of self-affine surfaces and measurements of their roughness exponents H are developed. It is shown that for smoothed surfaces, which underwent particular coarse graining or averaging of the small-scale fluctuations, the excess surface area ${\mathit{S}}_{\mathrm{ex}}$ and the mean square root radius of curvature ${\mathit{a}}_{\mathit{c}}$ are related by two distinct asymptotic power laws if ${\mathit{a}}_{\mathit{c}}$ is well below or well above a certain crossover scale ${\mathit{a}}_{\mathrm{cr}}$. In the local regime of self-affinity, when ${\mathit{a}}_{\mathit{c}}$\ensuremath{\ll}${\mathit{a}}_{\mathrm{cr}}$, ${\mathit{S}}_{\mathrm{ex}}$\ensuremath{\propto}(${\mathit{a}}_{\mathit{c}}$/${\mathit{a}}_{\mathrm{cr}}$${)}^{\mathrm{\ensuremath{-}}(1\mathrm{\ensuremath{-}}\mathit{H})}$. In the global regime of self-affinity, when ${\mathit{a}}_{\mathit{c}}$\ensuremath{\gg}${\mathit{a}}_{\mathrm{cr}}$, ${\mathit{S}}_{\mathrm{ex}}$\ensuremath{\propto}(${\mathit{a}}_{\mathit{c}}$/${\mathit{a}}_{\mathrm{cr}}$${)}^{\mathrm{\ensuremath{-}}2(1\mathrm{\ensuremath{-}}\mathit{H})/(2\mathrm{\ensuremath{-}}\mathit{H})}$. The former scaling relationship is consistent with the well known definition of local fractal dimensions ${\mathit{d}}_{\mathrm{loc}}$=${\mathit{d}}_{\mathrm{top}}$+1-H. The latter scaling relationship offers alternatives for characterization of self-affinity over large scales by means of excess dimensions defined as ${\mathit{d}}_{\mathrm{ex}}$=${\mathit{d}}_{\mathrm{top}}$+2(1-H)/(2-H) and can be used for determination of roughness exponents from the measurements provided in the global regime. The thermodynamic method of fractal analysis, proposed earlier for self-similar surfaces (A.V. Neimark, Pis'ma Zh. Eksp. Teor. Fiz. 51, 535 (1990) [JETP Lett. 51, 607 (1990)]; Physica A 191, 258 (1992)), is extended for self-affine surfaces for determination of fractal dimensions and roughness exponents from adsorption and capillary experimental data.

We describe a phenomenon of ribbon-to-fiber transformation observed in the process of spinning of single wall carbon nanotubes dispersed in polymer solutions. In the process of spinning, a gel-like ribbon comprised of nanotube bundles bound by polymer is withdrawn from a solvent bath. We show that upon crossing the liquid-air interface, the ribbon may either retain its flat shape or fold into a compact hairlike fiber. The ribbon-to-fiber transformation is caused by the capillary action of the liquid meniscus embracing the ribbon. Only sufficiently stiff ribbons can withhold the capillary compression. The critical conditions of folding, as well as the number of folds in the contractive ribbon, depend on the ribbon width, its flexural rigidity, and the solvent surface tension. We show that the ribbon rigidity can be efficiently modulated by varying the solvent composition, allowing us to control the pore structure of carbon-nanotube fibers.

We study the equilibrium and stability of metastable states and capillary condensation hysteresis of a Lennard-Jones fluid in cylindrical pores by means of the canonical ensemble density functional theory and gauge cell Monte Carlo simulations. We demonstrate a possibility for the existence of multiple laterally uniform internal states of equal density inside the hysteresis loop. The region of multiple states is bounded by the states of zero compressibility. The internal states can be stabilized in Monte Carlo simulations constraining the density fluctuations.

The nonlocal density functional theory (NLDFT) of confined fluids is tested against Monte Carlo simulations by using the example of Lennard-Jones (LJ) fluid sorption in slit-shaped and cylindrical nanopores ranging from 0.3 to 10 nm in width. The fluid-fluid and solid-fluid parameters of the LJ potentials were chosen to represent several experimentally important adsorption systems: nitrogen and carbon dioxide in activated carbons, zeolites, and mesoporous molecular sieves of the MCM-41 type. Freezing in nanopores is discussed using the example of methane sorption in carbon at 111 K. Comparison with reference experiments is given when available. Two versions of NLDFT, the smoothed density approximation and the fundamental measure theory, are considered. It is shown that NLDFT approaches with properly chosen parameters provide quantitative agreement with the results of Monte Carlo simulations and reference experiments. Appreciable deviations are found in extremely narrow pores of less than two molecular diameters in width. In wider pores, NLDFT models can be used for quantitative predictions of reversible and hysteretic adsorption isotherms and analyses of the specifics of phase transformations, including the equilibrium and spinodal phase transitions.