On the hysteresis loop and equilibrium transition in slit-shaped ink-bottle pores

Bin grand canonical Monte Carlo simulations have been carried out to study adsorption–desorption of argon at 87.3 K in a model ink-bottle mesoporous solid in order to investigate the interplay between the pore blocking process, controlled by the evaporation through the pore mouth via the meniscus separating the adsorbate and the bulk gas surroundings, and the cavitation process, governed by the instability of the stretched fluid (with a decrease in pressure) in the cavity. The evaporation mechanism switches from pore blocking to cavitation when the size of the pore neck is decreased, and is relatively insensitive to the neck length under conditions where cavitation is the controlling mechanism. We have applied the recently-developed Mid-Density scheme to determine the equilibrium branch of the hysteresis loop, and have found that, unlike ideal simple pores of constant size and infinite length, where the equilibrium transition is vertical, the equilibrium branch of an ink-bottle pore has three distinct sub-branches within the hysteresis loop. The first sub-branch is steep but continuous and is close to the desorption branch (which is typical for a pore with two open ends); this is associated with the equilibrium state in the neck. The third sub-branch is much steeper and is close to the adsorption branch (which is typical for either a pore with one end closed or a closed pore), and is associated with the equilibrium state in the cavity. The second sub-branch, connecting the other two sub-branches, has a more gradual slope. The domains of these three sub-branches depend on the relative sizes of the cavity and the neck, and their respective lengths. Our investigation of the effects of changing neck length clearly demonstrates that cavitation depends, not only on fluid properties, as frequently stated, but also on pore geometry.     

Nucleation in hydrophobic cylindrical pores: a lattice model

We consider the nucleation process associated with capillary condensation of a vapor in a hydrophobic cylindrical pore (capillary evaporation). The liquid-vapor transition is described within the framework of a simple lattice model. The phase properties are characterized both at the mean-field level and with Monte Carlo simulations. The nucleation process for the liquid to vapor transition is then specifically considered. Using umbrella sampling techniques, we show that nucleation occurs through the condensation of an asymmetric vapor bubble at the pore surface. Even for highly confined systems, good agreement is found with macroscopic considerations based on classical nucleation theory. The results are discussed in the context of recent experimental work on the extrusion of water in hydrophobic pores.     

Influence of surface chemical heterogeneities on adsorption/desorption hysteresis and coexistence diagram of metastable states within cylindrical pores

Grand canonical Monte Carlo simulations are performed to determine the adsorption/desorption isotherms at different temperatures of a Lennard-Jones fluid confined within a simple model of cylindrical pores presenting chemical heterogeneities. A complex hysteresis loop is observed, showing hysteresis subloops (scanning curves). This is shown to be consistent with the existence of several metastable states (local minima in the system free energy). A recent extension to the Gibbs ensemble technique is then used to calculate the complete coexistence diagram of these local minima.     

Entropic selectivity of binary mixtures in cylindrical pores

We show that a simple model consisting of a binary hard-sphere mixture in a narrow cylindrical pore can lead to strong size selectivity by considering a situation where each species of the mixture sees a different radius of the cylinder. Two mechanisms are proposed to explain the observed results depending on the radius of the cylinder: for large radii the selectivity is driven by an enhancement of the depletion forces at the cylinder walls whereas for the narrowest cylinders excluded-volume effects lead to a shift of the effective chemical potential of the particles in the pore.     

Calculations of the distribution of trace impurities in cylindrical pores

The equilibrium distribution of a trace impurity and the self-diffusion coefficients of molecules of the base component and the trace impurity in narrow cylindrical pores were calculated using the lattice-gas model. Two types of lattice structures with six and eight closest neighbors were considered. The sizes of the base component and impurity molecules were taken to be identical. Lateral interactions were taken into account in the quasi-chemical approximation. The equilibrium distributions of the trace impurity across a pore section in the gas and liquid phases of the base component and at the interface for the case of capillary condensation were considered. The probability of existence of isolated dimeric clusters was estimated and the self-diffusion coefficients of the base component and trace impurity for a single-phase distribution of the base component were calculated. The effects of the energy of interaction of impurities with the pore walls and the concentration of the base component on the diffusion mobility of the impurities were analyzed. The concentration dependences of the partition coefficient for the trace impurity between the pore center and the pore wall and the concentration dependences of the self-diffusion coefficients for the trace impurity molecules become nonmonotonic with an increase in the base component concentration. These effects are due to the displacement of the impurity from the near-surface area to the bulk of a pore following an increase in the pore coverage by the base component and to higher mobility of the impurity in the free bulk of the pore. Further filling of the pore bulk reduces the mobility of all molecules. The energetics of intermolecular interactions also plays a certain role. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 605–615, April, 2000.     

Capillary condensation hysteresis in overlapping spherical pores: a monte carlo simulation study

The mechanisms of hysteretic phase transformations in fluids confined to porous bodies depend on the size and shape of pores, as well as their connectivity. We present a Monte Carlo simulation study of capillary condensation and evaporation cycles in the course of Lennard-Jones fluid adsorption in the system of overlapping spherical pores. This model system mimics pore shape and connectivity in some mesoporous materials obtained by templating cubic surfactant mesophases or colloidal crystals. We show different mechanisms of capillary hysteresis depending on the size of the window between the pores. For the system with a small window, the hysteresis cycle is similar to that in a single spherical pore: capillary condensation takes place upon achieving the limit of stability of adsorption film and evaporation is triggered by cavitation. When the window is large enough, the capillary condensation shifts to a pressure higher than that of the isolated pore, and the possibility for the equilibrium mechanism of desorption is revealed. These finding may have important implications for practical problems of assessment of the pore size distributions in mesoporous materials with cagelike pore networks.     

Freezing of hard spheres confined in narrow cylindrical pores

Monte Carlo simulations for the equation of state and phase behavior of hard spheres confined inside very narrow hard tubes are presented. For pores whose radii are greater than 1.1 hard sphere diameters, a sudden change in the density and the microscopic structure of the fluid is neatly observed, indicating the onset of freezing. In the high-density structure the particles rearrange in such a way that groups of three particles fit in sections across the pore.     

Critical temperature of capillary condensation in narrow cylindrical pores

The dependence of the critical temperature of capillary condensation of an adsorbate in cylindrical pores on the diameter of pores is investigated. The calculation is carried out in the quasi-chemical approximation with a calibration function providing the agreement of results for small pores with exact values obtained by the fragment method. The contribution of the size effect to the calibration function as a function of the diameter of pores is considered in terms of the concept of quasi-one-dimensional behavior of the adsorbate in narrow pores. Various adsorbate-adsorbate potentials are considered.     

Nature of adsorption and desorption branches in cylindrical pores

To examine the nature of the adsorption and desorption branches in hysteretic adsorption isotherms of gases on mesoporous materials, we measured the temperature dependence of the adsorption and desorption isotherms of argon, oxygen, and carbon dioxide onto MCM-41 with a pore diameter of 4.4 nm. The results clearly show that in the open-ended cylindrical pores of MCM-41, capillary condensation rather than evaporation takes place near a thermodynamical equilibrium transition, as opposed to the general statement that capillary evaporation can occur via a meniscus formed at the pore mouth, and, thus, takes place at equilibrium.     

Structure of liquid and glassy methanol confined in cylindrical pores

We present a neutron scattering analysis of the density and the static structure factor of confined methanol at various temperatures. Confinement is performed in the cylindrical pores of MCM-41 silicates with pore diameters D=24 and 35 A. A change of the thermal expansivity of confined methanol at low temperature is the signature of a glass transition, which occurs at higher temperature for the smallest pore. This is evidence of a surface induced slowing down of the dynamics of the fluid. The structure factor presents a systematic evolution with the pore diameter, which has been analyzed in terms of excluded volume effects and fluid-matrix cross correlation. Conversely to the case of Van der Waals fluids, it shows that stronger fluid-matrix correlations must be invoked most probably in relation with the H-bonding character of both methanol and silicate surface.     

On the possibility of obtaining crystalline materials containing extended cylindrical pores

Using the example of studying the behavior of heated crystals of copper sulfate CuSO₄ · 5H₂O that are derived from an aqueous solution and contain three-dimensional inclusions of the mother environment, we show that the heating of these crystals in an inactive medium leads to the discharging of inclusions due to the emersion of their content on the surface. The routes for discharging mother-solution inclusions are determined using optical and electron microscopy and X-ray topography. According to the proposed model, the inclusions are discharged because they expand on being heated and press the crystal matrix. As a result, the solubility of copper sulfate in the mother environment increases, and, along the linear dislocation that passes close to the inclusions and emerges on the crystal surface, a cylindrical pore appears via which the mother solution goes from the bulk of the crystal to its surface. Finally, we obtain a porous material that can reversibly absorb appreciable amounts of an inert fluid (e.g., alcohol) from the ambient environment.     

Polymer brushes in cylindrical pores: simulation versus scaling theory

The structure of flexible polymers endgrafted in cylindrical pores of diameter D is studied as a function of chain length N and grafting density sigma, assuming good solvent conditions. A phenomenological scaling theory, describing the variation of the linear dimensions of the chains with sigma, is developed and tested by molecular dynamics simulations of a bead-spring model. Different regimes are identified, depending on the ratio of D to the size of a free polymer N(3/5). For D>N(3/5) a crossover occurs for sigma=sigma*=N(-6/5) from the "mushroom" behavior (R(gx)=R(gy)=R(gz)=N(35)) to the behavior of a flat brush (R(gz)=sigma(1/3)N,R(gx)=R(gy)=sigma(-1/12)N(1/2)), until at sigma**=(D/N)3 a crossover to a compressed state of the brush, [R(gz)=D,R(gx)=R(gy)=(N(3)D/4sigma)(1/8)相似文献   

Adsorption hysteresis for a slit-like pore model

The Frenkel-Halsey-Hill equation is used to describe the adsorption branch of a hysteresis loop upon polylayer adsorption with an H3 loop according to IUPAC nomenclature. The equation for the desorption branch of a hysteresis loop is derived from a combined solution to the equation for the Gibbs potential change, given the adsorbent swelling and pore connectivity function, and the Laplace equation taken for the conditions of infinitely elongated meniscus. This equation is shown to connect the adsorbate relative pressure in a bulk phase for the desorption branch of a hysteresis loop with the key parameters of the adsorption system. The equation obtained was verified by a water adsorption isotherm on natural mineral schungite.     

Close-packed structures and phase diagram of soft spheres in cylindrical pores

It is shown for a model system consisting of spherical particles confined in cylindrical pores that the first ten close-packed phases are in one-to-one correspondence with the first ten ways of folding a triangular lattice, each being characterized by a roll-up vector like the single-walled carbon nanotube. Phase diagrams in pressure-diameter and temperature-diameter planes are obtained by inherent-structure calculation and molecular dynamics simulation. The phase boundaries dividing two adjacent phases are infinitely sharp in the low-temperature limit but are blurred as temperature is increased. Existence of such phase boundaries explains rich, diameter-sensitive phase behavior unique for cylindrically confined systems.     

Thermal hysteresis loop of the spin-state in nanoparticles of transition metal complexes: Monte Carlo simulations on an Ising-like model

Theoretical investigation with Monte Carlo simulations predicts that thermal spin-switching hysteresis of transition-metal complexes appears even in nanoparticles, but the hysteresis width does not depend only on the interaction strength between molecules but also strongly on the shape and size of the particles.     

Ergodicity breaking and conformational hysteresis in the dynamics of a polymer tethered at a surface stagnation point

We study the dynamics of long chain polymer molecules tethered to a plane wall and subjected to a stagnation point flow. Using a combination of theory and numerical techniques, including Brownian dynamics (BD), we demonstrate that a chain conformation hysteresis exists even for freely draining (FD) chains. Hydrodynamic interactions (HI) between the polymer and the wall are included in the BD simulations. We find qualitative agreement between the FD and HI simulations, with both exhibiting simultaneous coiled and stretched states for a wide range of fixed flow strengths. The range of state coexistence is understood by considering an equivalent projected equilibrium problem of a two state reaction. Using this formalism, we construct Kramers rate theory (from the inverse mean first passage time for a Markov process) for the hopping transition from coil to stretch and stretch to coil. The activation energy for this rate is found to scale proportionally to chain length or Kuhn step number. Thus, in the limit of infinite chain size the hopping rates at a fixed value of the suitably defined Deborah number approach zero and the states are "frozen." We present the results that demonstrate this "ergodicity breaking."     

Adsorption/desorption hysteresis in inkbottle pores: a density functional theory and Monte Carlo simulation study

The mechanisms of adsorption and desorption in inkbottle-shaped pores are considered for lattice models using grand canonical mean field density functional theory and Monte Carlo simulation. We find that they depend significantly on the particular pore geometry, the nature of the fluid-solid interaction, and the temperature. We find two mechanisms for desorption. One mechanism involves the emptying of the main cavity even as the density of fluid in the necks remains high, a mechanism observed recently in studies of an off-lattice model of an inkbottle. The other is a simultaneous desorption from the entire pore space, behavior that is more closely related to the traditional picture of pore blocking in the inkbottle system.