We study the influence of the relative size of the reservoir on the adsorption isotherms of a fluid in disordered or inhomogeneous mesoporous solids. We consider both an atomistic model of a fluid in a simple, yet structured pore, whose adsorption isotherms are computed by molecular simulation, and a coarse-grained model for adsorption in a disordered mesoporous material, studied by a density functional approach in a local mean-field approximation. In both cases, the fluid inside the porous solid exchanges matter with a reservoir of gas that is at the same temperature and chemical potential and whose relative size can be varied, and the control parameter is the total number of molecules present in the porous sample and in the reservoir. Varying the relative sizes of the reservoir and the sample may change the shape of the hysteretic isotherms, leading to a "reentrant" behavior compared to the grand-canonical isotherm when the latter displays a jump in density. We relate these phenomena to the organization of the metastable states that are accessible for the adsorbed fluid at a given chemical potential or density.
In a recent paper [J. Chem. Phys. 127, 154701 (2007)], a multiscale approach was introduced which allowed the calculation of adsorption/desorption hysteresis for fluid confined in a single
We present a theoretical study of capillary condensation of fluids adsorbed in mesoporous disordered media. Combining mean-field density functional theory with a coarse-grained description in terms of a lattice-gas model allows us to investigate both the out-of-equilibrium (hysteresis) and the equilibrium behavior. We show that the main features of capillary condensation in disordered solids result from the appearance of a complex free-energy landscape with a large number of metastable states. We detail the numerical procedures for finding these states, and the presence or absence of transitio…
Soft porous crystals are flexible metal-organic frameworks that respond to physical stimuli such as temperature, pressure, and gas adsorption by large changes in their structure and unit cell volume. While they have attracted a lot of interest, molecular simulation methods that directly couple adsorption and large structural deformations in an efficient manner are still lacking. We propose here a new Monte Carlo simulation method based on non-Boltzmann sampling in (guest loading, volume) space using the Wang-Landau algorithm, and show that it can be used to fully characterize the adsorption pr…
The time dependency of the diffusion coefficient of particles in porous media is an efficient probe of their geometry. The analysis of this quantity, measured e.g. by nuclear magnetic resonance (PGSE-NMR), can provide rich information pertaining to porosity, pore size distribution, permeability and surface-to-volume ratio of porous materials. Nevertheless, in numerous if not all practical situations, transport is confined by walls where adsorption and desorption processes may occur. In this article, we derive explicitly the expression of the time-dependent diffusion coefficient between two con…
We propose a variation of the classical Szilard engine that uses a porous piston. Such an engine requires neither information about the position of the particle, nor the removal and subsequent insertion of the piston when resetting the engine to continue doing work by lifting a mass against a gravitational field. Though the engine operates in contact with a single thermal reservoir, the reset mechanism acts as a second reservoir, dissipating energy when a mass that has been lifted by the engine is removed to initiate a new operation cycle.
We present a numerical study of the structural correlations associated to gas adsorption/desorption in silica aerogels in order to provide a theoretical interpretation of scattering experiments. Following our earlier work, we use a coarse-grained lattice-gas description and determine the nonequilibrium behavior of the adsorbed gas within a local mean-field analysis. We focus on the differences between the adsorption and desorption mechanisms and their signature in the fluid-fluid and gel-fluid structure factors as a function of temperature. At low temperature, but still in the regime where the…
A new method for characterizing the deformable porous materials with non-critical adsorption probes is proposed. The mechanism is based on a driving the adsorbate through a sequence of constrained equilibrium states with the insertion isotherms forming a pseudo-critical point or a van der Waals-type loop. In the framework of a perturbation theory and Monte Carlo simulations we have found a link between the loop parameters and the host morphology. This allows one to characterize porous matrices through analyzing a shift of the pseudo-critical point and a shape of the pseudo-spinodals.
Computer simulation was used to study the random sequential adsorption of identical discorectangles onto a continuous plane . The problem was analyzed for a wide range of discorectangle aspect ratios ($\varepsilon \in [1;100]$). We studied anisotropic deposition, i.e., the orientations of the deposited particles were uniformly distributed within some interval such that the particles were preferentially aligned along a given direction. The kinetics of the changes in the packing density $φ$ found at different values of $S_0$ are discussed. Partial ordering of the discorectangles significantly af…
Random sequential adsorption of spheres on a wavy surface was studied. It was determined how surface structure influences random packing properties such as the packing fraction, the kinetics of packing growth, and the two-particle density correlation function. Until the substrate varies within the range one order of magnitude smaller than the particle's diameter, the properties of the packings obtained do not differ significantly from those on a flat surface. On the other hand, for the higher amplitude of unevenness, the packing fraction, low-density growth kinetics, and the density autocorrel…
In this paper we propose the Ising model to study the propagation of water in 2 dimensional (2D) petroleum reservoir in which each bond between its pores has the probability $p$ of being activated. We analyze the water movement pattern in porous media described by Darcy equations by focusing on its geometrical objects. Using Schramm-Loewner evolution (SLE) technique we numerically show that at $p=p_c\simeq 0.59$, this model lies within the Ising universality class with the diffusivity parameter $κ=3$ and the fractal dimension $D_f=\frac{11}{8}$. We introduce a self-organized critical model in …
We study isothermal transport of a nonelectrolyte binary fluid mixture, which lies in the homogeneous phase near the demixing critical point, through a capillary tube connecting two reservoirs. Usually, one component is preferentially adsorbed onto the tube wall, and the adsorption becomes significant owing to large osmotic susceptibility. The mixture flowing out of the tube is rich in the preferred component when flow is driven by the pressure difference between the reservoirs. When flow is driven by the mass-fraction difference, the total mass flow occurs in the presence of the preferential …
Many resources, such as oil, gas, or water, are extracted from porous soils and their exploration is often shared among different companies or nations. We show that the effective shares can be obtained by invading the porous medium simultaneously with various fluids. Partitioning a volume in two parts requires one division surface while the simultaneous boundary between three parts consists of lines. We identify and characterize these lines, showing that they form a fractal set consisting of a single thread spanning the medium and a surrounding cloud of loops. While the spanning thread has fra…
Cooperative adsorption of gases by porous frameworks permits more efficient uptake and removal than does the more usual non-cooperative (Langmuir-type) adsorption. Cooperativity, signaled by a step-like isotherm, is usually attributed to a phase transition of the framework. However, the class of metal-organic frameworks mmen-M$_2$(dobpdc) exhibit cooperative adsorption of CO2 but show no evidence of a phase transition. Here we show how cooperativity emerges in these frameworks in the absence of a phase transition. We use a combination of quantum and statistical mechanics to show that cooperati…
A classical density functional theory (cDFT) based on the PC-SAFT equation of state is proposed for the calculation of adsorption equilibria of pure substances and their mixtures in covalent organic frameworks (COFs). Adsorption isotherms of methane, ethane, n-butane and nitrogen in the COFs TpPa-1 and 2,3-DhaTph are calculated and compared to results from grand canonical Monte Carlo (GCMC) simulations. Mixture adsorption is investigated for the methane/ethane and methane/n-butane binary systems. Excellent agreement between PC-SAFT DFT and GCMC is obtained for all adsorption isotherms up to pr…
We present here exact results for a one-dimensional gas, or fluid, of hard-sphere particles with attractive boundaries. The particles, which can exchange with a bulk reservoir, mediate an interaction between the boundaries. A two-dimensional lattice of such one-dimensional gas `columns' represents a discrete approximation of a three-dimensional gas of particles between two surfaces. The effective particle-mediated interaction potential of the boundaries, or surfaces, is calculated from the grand-canonical partition function of the one-dimensional gas of particles, which is an extension of the …
