On the existence of a hysteresis loop in open and closed end pores

Critical effects and scaling at meniscus osculation transitions

We propose a simple scaling theory describing critical effects at rounded meniscus osculation transitions which occur when the Laplace radius of a condensed macroscopic drop of liquid coincides with the local radius of curvature R_{w} in a confining parabolic geometry. We argue that the exponent β_{osc} characterizing the scale of the interfacial height ℓ_{0}∝R_{w}^{β_{osc}} at osculation, for large R_{w}, falls into two regimes representing fluctuation-dominated and mean-field-like behavior, respectively. These two regimes are separated by an upper critical dimension, which is determined here explicitly and depends on the range of the intermolecular forces. In the fluctuation-dominated regime, representing the universality class of systems with short-range forces, the exponent is related to the value of the interfacial wandering exponent ζ by β_{osc}=3ζ/(4-ζ). In contrast, in the mean-field regime, which was not previously identified and which occurs for systems with longer-range forces (and higher dimensions), the exponent β_{osc} takes the same value as the exponent β_{s}^{co} for complete wetting, which is determined directly by the intermolecular forces. The prediction β_{osc}=3/7 in d=2 for systems with short-range forces (corresponding to ζ=1/2) is confirmed using an interfacial Hamiltonian model which determines the exact scaling form for the decay of the interfacial height probability distribution function. A numerical study in d=3, based on a microscopic model density-functional theory, determines that β_{osc}≈β_{s}^{co}≈0.326 close to the predicted value of 1/3 appropriate to the mean-field regime for dispersion forces.

Synthesis of magnetic tungsten disulfide/carbon nanotubes nanocomposite (WS2/Fe3O4/CNTs-NC) for highly efficient ultrasound-assisted rapid removal of amaranth and brilliant blue FCF hazardous dyes

In this research, the potentiality of magnetic tungsten disulfide/carbon nanotubes nanocomposite (WS₂/Fe₃O₄/CNTs-NC) as an adsorbent for the ultrasound-assisted removal of amaranth (AM) and brilliant blue FCF (BB FCF) dyes was investigated. The experiments were conducted using a central composite design (CCD) with the inputs of solution pH (X₁: 2.0-10), adsorbent mass (X₄: 4-20 mg), AM concentration (X₂: 10-50 mg L^-1), BB FCF concentration (X₃: 10-50 mg L^-1), and sonication time (X₅: 2-12 min). At the optimum conditions, the removal percentages of 99.30% and 98.50% were obtained for AM and BB FCF, respectively. The adsorption of the dyes was described by Langmuir isotherm and pseudo-second-order (PSO) kinetic models. The maximum adsorption capacities of AM and BB FCF were 174.8 mg g^-1 and 166.7 mg g^-1, respectively. The adsorption thermodynamic study showed that the adsorption of the dyes occurred endothermically and spontaneously. The removal percentages of AM and BB FCF from the real samples were in the range of 94.52-99.65% for the binary solutions. The removal percentage for each dye after five cycles of adsorption/desorption was > 90%. This work provides a useful insight to the potential application of CNTs-based magnetic nanocomposite for the treatment of wastewaters contaminated with dyes.

Filling, depinning, unbinding: Three adsorption regimes for nanocorrugated substrates

We study adsorption at periodically corrugated substrates formed by scoring rectangular grooves into a planar solid wall which interacts with the fluid via long-range (dispersion) forces. The grooves are assumed to be macroscopically long but their depth, width, and separations can all be molecularly small. We show that the entire adsorption process can be divided into three parts consisting of (i) filling the grooves by a capillary liquid; (ii) depinning of the liquid-gas interface from the wall edges; and (iii) unbinding of the interface from the top of the wall, which is accompanied by a rapid but continuous flattening of its shape. Using a nonlocal density functional theory and mesoscopic interfacial models all the regimes are discussed in some detail to reveal the complexity of the entire process and subtle aspects that affect its behavior. In particular, it is shown that the nature of the depinning phenomenon is governed by the width of the wall pillars (separating grooves), while the width of the grooves only controls the location of the depinning first-order transition, if present.

On the canonical isotherms for bulk fluid, surface adsorption and adsorption in pores: A common thread

Kinetic Monte Carlo simulated isotherms calculated in the canonical ensemble, at temperatures below the critical temperature, for bulk fluid, surface adsorption and adsorption in a confined space, show a van der Waals (vdW) loop with a vertical phase transition between the rarefied and dense spinodal points at the co-existence chemical potential, µ_co. Microscopic examination of the state points on this loop reveals features that are common to these systems. At state points with chemical potentials greater than μ_co the microscopic configurations show clusters, which coalesce to form two co-existing phases along the vertical section of the loop (the coexistence line). As more molecules are added, the dense region expands at the expense of the rarefied region, to the point where the rarefied region becomes spherical (cylindrical for 2D-systems) with a curvature greater than that of the coexisting phases. This results in a decrease of chemical potential from µ_co to the liquid spinodal point where the rarefied region disappears. With a further increase in loading, the chemical potential and the density increase. The existence of a vdW loop is the microscopic reason for the hysteresis observed in the grand canonical isotherm, where the adsorption and desorption boundaries of the hysteresis loop are first-order transitions, enclosing the vertical section of the vdW loop of the canonical isotherm. However, a first-order transition is rarely observed in experiments where transitions are usually steep, but not vertical. From our extensive simulations, we provide two possible reasons: (1) the finite extent of the system and (2) the existence of high energy sites that localize the clusters. In the first case, the desorption branch, and in the second case the adsorption branch, either comes close to, or collapses onto the coexistence line. When both occur, the hysteresis loop disappears and the isotherm is reversible, as often observed experimentally.

Continuous condensation in nanogrooves

We consider condensation in a capillary groove of width L and depth D, formed by walls that are completely wet (contact angle θ=0), which is in a contact with a gas reservoir of the chemical potential μ. On a mesoscopic level, the condensation process can be described in terms of the midpoint height ℓ of a meniscus formed at the liquid-gas interface. For macroscopically deep grooves (D→∞), and in the presence of long-range (dispersion) forces, the condensation corresponds to a second-order phase transition, such that ℓ∼(μ_{cc}-μ)^{-1/4} as μ→μ_{cc}^{-} where μ_{cc} is the chemical potential pertinent to capillary condensation in a slit pore of width L. For finite values of D, the transition becomes rounded and the groove becomes filled with liquid at a chemical potential higher than μ_{cc} with a difference of the order of D^{-3}. For sufficiently deep grooves, the meniscus growth initially follows the power law ℓ∼(μ_{cc}-μ)^{-1/4}, but this behavior eventually crosses over to ℓ∼D-(μ-μ_{cc})^{-1/3} above μ_{cc}, with a gap between the two regimes shown to be δ[over ¯]μ∼D^{-3}. Right at μ=μ_{cc}, when the groove is only partially filled with liquid, the height of the meniscus scales as ℓ^{*}∼(D^{3}L)^{1/4}. Moreover, the chemical potential (or pressure) at which the groove is half-filled with liquid exhibits a nonmonotonic dependence on D with a maximum at D≈3L/2 and coincides with μ_{cc} when L≈D. Finally, we show that condensation in finite grooves can be mapped on the condensation in capillary slits formed by two asymmetric (competing) walls a distance D apart with potential strengths depending on L. All these predictions, based on mesoscopic arguments, are confirmed by fully microscopic Rosenfeld's density functional theory with a reasonable agreement down to surprisingly small values of both L and D.

Adsorption in alumina pores open at one and at both ends

We have studied adsorption in regular, self-ordered alumina pores open at both ends or only at one end. The straight, non-connected pores have diameters ranging from 22 to 83 nm, with a relative dispersion below 1% in the pore size. Adsorption isotherms measured in open pores with a torsional microbalance show pronounced hysteresis loops characterized by nearly vertical and parallel adsorption and desorption branches. Blocking one end of the pores with glue has a strong influence on adsorption, as expected from classical macroscopic arguments. However, the experimental measurements show an unexpectedly rich phenomenology dependent on the pore size. For large pores (Dp ≥ 67 nm), the isotherms for closed end pores present much narrower hysteresis loops whose adsorption and desorption boundaries envelop the desorption branches of the isotherms for the corresponding open pores of the same size. The loop for small closed end pores (Dp = 22 nm) is slightly wider than that for open pores while the adsorption branches coincide. For large pores, in contrast, the desorption branches of pores with the same Dp overlap regardless of the pore opening. These observations are in agreement with our grand canonical Monte Carlo (GCMC) simulations for a cylindrical pore model with constrictions, suggesting that the alumina pores could be modeled using a constricted pore model whose adsorption isotherm depends on the ratio of the constriction size to the pore size (Dc/Dp).