Numerical characterization of the density of metastable states within the hysteresis loop in disordered systems

International audienceAn improved approach is proposed to analyze the density of metastable states within any hysteresis loop, such as those observed in magnetic materials or for adsorption in porous materials. Except for a few analytically tractable models, most calculations have to be performed numerically on finite systems. The main points to be addressed thus concern the average over various material samples (the so-called realizations of the disorder), and the finite size analysis to estimate the thermodynamic limit. As an improvement of previously existing methods, it is proposed to introduce the Fourier transform of the density of metastable states (characteristic function). Its logarithm is shown to be additive and can straightforwardly be averaged over disorder. This procedure leads to a new definition of the complexity in finite size, giving the usual quenched complexity in the thermodynamic limit, while being better suited to performing finite size analysis. The calculations are illustrated on a molecular simulation based model for a simple fluid adsorbed in heterogeneous siliceous tubular pores mimicking mesoporous materials like MCM-41 or porous silicon. This approach is expected to be of general interest for hysteresis phenomena, including magnetic materials

Counting metastable states within the adsorption/desorption hysteresis loop: A molecular simulation study of confinement in heterogeneous pores

International audienceA molecular simulation approach has been used to model simple fluid adsorption in heterogeneous tubular pores mimicking mesoporous materials such as MCM-41 or porous silicon, allowing to determine the amount adsorbed as a function of the chemical potential. A hysteresis loop is observed in adsorption/desorption cycles, which is closely connected to the appearance of many metastable states. The density of these metastable states is studied in the-plane. Experimentally, the accessible metastable states are those that can be attained by the-path, i.e., a series of increasing or decreasing steps. One could also imagine using a quench from high temperature. Although the total density of metastable states is not directly accessible to experiments, it is of primary theoretical importance to understand the structure of metastable states in the hysteresis as determined experimentally. The disorder associated with the porous material realizations is accurately taken into account, and a systematic system size analysis is also performed in order to study the thermodynamic limit. It is shown that the quenched complexity is the relevant quantity to understand the hysteresis structure in the thermodynamic limit. It clearly exhibits a distinctive behavior depending on the distribution of heterogeneities characterizing the disorder in the pore. Some analogies can be found with the situation where an out-of-equilibrium transition appears, but careful examination of the data suggests another interpretation

Molecular simulation study of the heat capacity of metastable water between 100K and 300K

Molecular simulation study of the heat capacity of metastable water between 100K and 300K Molecular simulations have been used to study the heat capacity of metastable liquid water at low temperature adsorbed on a smooth surface. These calculations aim at modelling water properties measured by experiments performed on water films adsorbed on Vycor nanoporous silica at low temperature. In particular, the study focuses on the non-monotonous variation of the heat capacity around between 100 and 300 K

Elastic Compliance and Stiffness Matrix of the FCC Lennard-Jones Thin Films: Influence of Thickness and Temperature

International audienceThe face-centered cubic (fcc) Lennard-Jones crystal is used as a generic model of a solid to study the elastic properties of thin films as a function of thickness and temperature. The Monte Carlo algorithm is used to calculate the average deformations along the axes in the isostress–isothermal ensemble that mimics a real uniaxial loading experiment. Four independent parameters (tetragonal symmetry without shear) have been calculated for film thicknesses ranging from 4 to 12 atomic layers and for five reduced temperatures between 0 and 0.5 ε/kB, where ε is the energetic parameter of the Lennard-Jones potential and kB is Boltzmann’s constant. These parameters (Poisson’s ratio and moduli) give the compliance matrix, which is inverted to obtain the stiffness coefficients. It is shown that the three Poisson’s ratios exhibit a good linearity with the inverse of the film thickness, while this is not the case for the moduli and the compliance coefficients. Remarkably, the stiffness coefficients do exhibit a good linearity with the inverse of the film thickness, including the limiting value of infinite thickness (bulk solid) obtained by applying periodic boundary conditions in all directions. This linearity suggests to interpret the results in terms of a bulk + surface decomposition. However, the surface stiffness matrix deduced from the slopes has nonzero components along the out-of-plane direction—an unexpected observation in the framework of the surface stress theory

Adsorption-Induced Deformation of a Nanoporous Material: Influence of the Fluid-Adsorbent Interaction and Surface Freezing on the Pore-Load Modulus Measurement

Liquid adsorption in nanoporous materials induces their deformation due to strong capillary forces. The linear relationship between the liquid pressure and the solid strain (pore-load modulus) provides an experimental technique to determine the mechanical properties of nanosized solids. Puzzling experimental results have often been reported, leading to a severe reconsideration of the mechanical properties of the thin walls, the introduction of surface stresses, and the suggestion of a mutual influence of fluid adsorption and matrix deformation. This work presents a molecular simulation examination of the fundamentals of the pore-load measurement technique. The pore-load protocol is reproduced as in experiments by measuring the solid deformation in presence of the liquid ("numerical experiment"), and the result is compared to the expected mechanical response of the solid. Focusing on a single nanoplatelet mimicking silicon stiffness, we show that the pore-load protocol is valid as long as the liquid in the pores remains liquid. However, when an ordered layer can form at the solid surface, it significantly affects the pore-load measurement. It is shown that this may happen above the freezing point even for moderately strong fluid-solid interactions. This observation could help for the interpretation of experimental data, in particular in porous silicon, where the expected presence of atomically smooth surfaces could favor the formation of highly ordered fluid layers

Influence of Elastic Strains on the Adsorption Process in Porous Materials. An Experimental Approach

The experimental results presented in this paper show the influence of the elastic deformation of porous solids on the adsorption process. With p+-type porous silicon formed on highly boron doped (100) Si single crystal, we can make identical porous layers, either supported by or detached from the substrate. The pores are perpendicular to the substrate. The adsorption isotherms corresponding to these two layers are distinct. In the region preceding capillary condensation, the adsorbed amount is lower for the membrane than for the supported layer and the hysteresis loop is observed at higher pressure. We attribute this phenomenon to different elastic strains undergone by the two layers during the adsorption process. For the supported layer, the planes perpendicular to the substrate are constrained to have the same interatomic spacing as that of the substrate so that the elastic deformation is unilateral, at an atomic scale, and along the pore axis. When the substrate is removed, tridimensional deformations occur and the porous system can find a new configuration for the solid atoms which decreases the free energy of the system adsorbate-solid. This results in a decrease of the adsorbed amount and in an increase of the condensation pressure. The isotherms for the supported porous layers shift toward that of the membrane when the layer thickness is increased from 30 to 100 microns. This is due to the relaxation of the stress exerted by the substrate as a result of the breaking of Si-Si bonds at the interface between the substrate and the porous layer. The membrane is the relaxed state of the supported layer.Comment: Accepted in Langmui

Influence of reservoir size on the adsorption path in an ideal pore

International audienceWe consider the influence of the relative size of the gas reservoir on the states visited by a simple fluid adsorbed in a nanopore of ideal geometry (a slit). We focus on the intermediate states that appear in between the main hysteresis branches comprising gaslike and liquidlike states and we study the adsorption and desorption paths actually followed by the system as one changes the reservoir size. We find that these paths may display discontinuous sections associated with transitions between different nonuniform states. We also discuss the stability of the states in such situations

Effect of the reservoir size on gas adsorption in inhomogeneous porous media

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.Comment: 16 page