Critical adsorption and finite-geometry effects

Interplay Between Adsorption and Hydrodynamics in Nanochannels: Towards Tunable Membranes

We study how the adsorption of a near-critical binary mixture in a nanopore is modified by flow inside the pore. We identify three types of steady states upon variation of the pore Péclet number (Pe_{p}), which can be reversibly accessed by the application of an external pressure. Interestingly, for small Pe_{p} the pore acts as a weakly selective membrane which separates the mixture. For intermediate Pe_{p}, the flow effectively shifts the adsorption in the pore, thereby opening possibilities for enhanced and tunable solute transport through the pore. For large Pe_{p}, the adsorption is progressively reduced inside the pore, accompanied by a long-ranged dispersion of the mixture far from the pore.

Critical adsorption and critical Casimir forces in the canonical ensemble

Critical properties of a liquid film between two planar walls are investigated in the canonical ensemble, within which the total number of fluid particles, rather than their chemical potential, is kept constant. The effect of this constraint is analyzed within mean-field theory (MFT) based on a Ginzburg-Landau free-energy functional as well as via Monte Carlo simulations of the three-dimensional Ising model with fixed total magnetization. Within MFT and for finite adsorption strengths at the walls, the thermodynamic properties of the film in the canonical ensemble can be mapped exactly onto a grand canonical ensemble in which the corresponding chemical potential plays the role of the Lagrange multiplier associated with the constraint. However, due to a nonintegrable divergence of the mean-field order parameter profile near a wall, the limit of infinitely strong adsorption turns out to be not well-defined within MFT, because it would necessarily violate the constraint. The critical Casimir force (CCF) acting on the two planar walls of the film is generally found to behave differently in the canonical and grand canonical ensembles. For instance, the canonical CCF in the presence of equal preferential adsorption at the two walls is found to have the opposite sign and a slower decay behavior as a function of the film thickness compared to its grand canonical counterpart. We derive the stress tensor in the canonical ensemble and find that it has the same expression as in the grand canonical case, but with the chemical potential playing the role of the Lagrange multiplier associated with the constraint. The different behavior of the CCF in the two ensembles is rationalized within MFT by showing that, for a prescribed value of the thermodynamic control parameter of the film, i.e., density or chemical potential, the film pressures are identical in the two ensembles, while the corresponding bulk pressures are not.

Nonmonotonic crossover from adsorption to desorption in supercritical fluid near a weakly attractive surface

The density profiles of a supercritical Lennard-Jones fluid near a weakly attractive surface are used to study the excess adsorption Gamma of supercritical fluid in a wide density range. We report the observation of two extrema of Gamma along the isotherm as a function of density. The attractive fluid-wall interaction potential tends to make Gamma positive, whereas the missing neighbor effect tends to make Gamma negative. The latter effect enhances with increasing fluid density due to the growth of the fluid-fluid attraction that results in the crossover from adsorption to depletion (Gamma=0) at some particular fluid density. With approaching the critical point, Gamma decreases as the bulk correlation length and passes through a minimum when the average density of confined fluid is close to the bulk critical density. Variation of Gamma with temperature and density is determined by the monotonic trend from adsorption to desorption upon increasing fluid density and by the increase of the absolute value of Gamma when approaching the critical point. Interplay of these trends results in two extrema of Gamma in the temperature-density plane. This effect may be responsible for the crossover from adsorption to desorption with approaching the critical temperature observed experimentally along the isotherms and along the critical isochore. The density profiles of a supercritical fluid are found to be exponential and the power law behavior predicted theoretically was not detected even when the bulk correlation length xi achieves 11 molecular diameters.

Adsorption at the liquid-vapor surface of a binary liquid mixture

In a binary liquid mixture, the component possessing the lowest surface tension preferentially adsorbs at the liquid-vapor surface. In the past this adsorption behavior has been extensively investigated for critical binary liquid mixtures near the mixture's critical temperature T(c). In this fluctuation-dominated regime the adsorption is described by a universal function of the dimensionless depth zxi where xi is the bulk correlation length. Fewer studies have quantitatively examined adsorption for off-critical mixtures because, in this case, one must carefully account for both the bulk and surface crossover from the fluctuation-dominated regime (close to T(c)) to the mean-field dominated regime (far from T(c)). In this paper we compare extensive liquid-vapor ellipsometric adsorption measurements for the mixture aniline+cyclohexane at a variety of critical and noncritical compositions with the crossover theory of Kiselev and co-workers [J. Chem. Phys. 112, 3370 (2000)].

Universality of the thermodynamic Casimir effect

Recently a nonuniversal character of the leading spatial behavior of the thermodynamic Casimir force has been reported [X. S. Chen and V. Dohm, Phys. Rev. E 66, 016102 (2002)]. We reconsider the arguments leading to this observation and show that there is no such leading nonuniversal term in the systems with short-ranged interactions if one treats properly the effects generated by a sharp momentum cutoff in the Fourier transform of the interaction potential. We also conclude that lattice and continuum models then produce results in mutual agreement independent of the cutoff scheme, contrary to the aforementioned report. All results are consistent with the universal character of the Casimir force in the systems with short-ranged interactions. The effects due to dispersion forces are discussed for the systems with periodic or realistic boundary conditions. In contrast to the systems with short-ranged interactions, for L/xi>>1, one observes leading finite-size contributions governed by power laws in L due to the subleading long-ranged character of the interaction, where L is the finite system size and xi is the correlation length.

Adsorption from alkane+perfluoroalkane mixtures at fluorophobic and fluorophilic surfaces. II. Crossover from critical adsorption to complete wetting

Using neutron reflectometry, adsorption from an equimolar mixture of hexane + perfluorohexane to a fluorophobic, octadecyl-coated, silicon substrate has been investigated as a function of temperature in the one-phase region upon approach to liquid-liquid coexistence. The composition of the investigated mixture, x(F) = 0.50, is well removed from the critical composition of x(F) = 0.36, where x(F) is the perfluorohexane mole fraction. To aid the modeling, mixtures with three different neutron refractive index contrasts have been used: namely, mixtures of C(6)H(14) + C(6)F(14) (H-F), C(6)D(14) + C(6)F(14) (D-F), and a mixture of C(6)H(14) + C(6)D(14) + C(6)F(14) which has been adjusted to have the same refractive index as silicon (CMSi). For all three contrasts, the principal features of the composition profile normal to the interface follow similar trends as the temperature T is reduced towards T(0), the coexistence temperature. These features consist of: (i) a hexane-rich primary adsorption layer appended to the octadecyl coupled layer. This primary layer is 22 +/- 5 A thick and becomes increasingly enriched in hexane as T(0) is approached. (ii) A tail that decays exponentially towards the bulk composition with a characteristic decay length zeta. As T(0) is approached, zeta increases. The scattering length density profiles have been converted to volume fraction profiles and the surface excess of hexane Gamma has been determined as a function of temperature for all three contrasts. As T(0) is approached Gamma increases, and its behavior can be represented using the scaling law Gamma approximately |T - T(0)|(-m). The resulting values of m are 0.71 +/- 0.09, 0.68 +/- 0.04, and 0.68 +/- 0.06 for the D-F, H-F, and CMSi contrasts, respectively. The behavior of Gamma with temperature does not adhere to the Gamma approximately |T - T(0)|(-1/3) law expected for complete wetting in systems with van der Waals interactions nor does it correspond to Gamma approximately |T - T(c)|(-0.305) expected for critical adsorption. The magnitude of the exponent m indicates that the adsorption resides in the crossover region between critical adsorption and complete wetting.

Simplified crossover droplet model for adsorption of pure fluids in slit pores

We present a generalized crossover (GC) model for the excess adsorption of pure fluids at a flat solid-liquid interface, which reproduces scaling behavior of the excess adsorption in the critical region and is reduced to the classical, van der Waals-type analytical model far away from the bulk critical point. In developing this model, we used the density-functional theory (DFT) approach for the order parameter profile calculations with a generalized corresponding states model for the local free-energy density. The GC DFT model well represents the available experimental adsorption data for Kr/graphite, C2H4/graphite, C3H8/graphite, CO2/silica, and SF6/graphite systems in the entire density range 0 < rho < or = 3rhoc and temperatures up to 1.7Tc. In the critical region 0.5 rhoc < r < or = 1.5rhoc and T < or = 1.15Tc, the GC DFT model is consistent with the predictions of the asymptotic renormalization-group crossover model for the critical adsorption in a semi-infinite system developed earlier. For the excess adsorption on the critical isochore, both theories predict a scaling-law behavior Gamma proportional tau(-nu+beta), but fail to reproduce a "critical depletion" of the excess adsorption along the critical isochore of the SF6/graphite system near Tc. We show that an anomalous decrease of adsorption observed in this system at tau = T/Tc - 1 < 10(-2) can be explained by finite-size effect and develop a simplified crossover droplet (SCD) model for the excess adsorption in a slit pore. With the effective size of the pore of L = 50 nm, the SCD model reproduces all available experimental data for SF6/graphite, including the critical isochore data where tau-->0, within experimental accuracy. At L >> xib (where xib is a bulk correlation length) the SCD model is transformed into the GC DFT model for semi-infinite systems. Application of the SCD model to the excess adsorption of carbon dioxide on the silica gel is also discussed.

Solvation force for long-ranged wall–fluid potentials

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.

Effects of confinement on critical adsorption: absence of critical depletion for fluids in slit pores

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<rho(c)). Such behavior results from the increasingly slow decay of the density profile away from the walls, into the middle of the slit, as T-->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.