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

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

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

On the Thermodynamics and Experimental Control of Twinning in Metal Nanocrystals

International audienceThis work demonstrates a new strategy for controlling the evolution of twin defects in metal nanocrystals by simply following thermodynamic principles. With Ag nanocrystals supported on amorphous SiO2 as a typical example, we establish that twin defects can be rationally generated by equilibrating nanoparticles of different sizes through heating and then cooling. We validate that Ag nanocrystals with icosahedral, decahedral, and single‐crystal structures are favored at sizes below 7 nm, between 7 and 11 nm, and greater than 11 nm, respectively. This trend is then rationalized by computational studies based on density functional theory and molecular dynamics, which show that the excess free energy for the three equilibrium structures correlate strongly with particle size. This work not only highlights the importance of thermodynamic control but also adds another synthetic method to the ever‐expanding toolbox used for generating metal nanocrystals with desired properties.

Bridge function for the dipolar fluid from simulation

International audienceThe exact bridge function of the Lennard-Jones dipolar (Stockmayer) fluid is extracted from Monte Carlo simulation data. The projections g mnl (r) onto rotational invariants of the non-spherically symmetric pair distribution function g(r,) are accumulated during simulation. Making intensive use of anisotropic integral equation techniques, the molecular Ornstein-Zernike equation is then inverted in order to derive the direct correlation function c mnl (r), the cavity function y mnl (r), the negative excess potential of mean force lny| mnl (r), and the bridge function b mnl (r) projections. b(r,) presents strong, non-universal anisotropies at high dipolar coupling. This simulation data analysis may serve as reference and guide for approximated bridge function theories of dipolar fluids and is a valuable step towards the case of more refined, nonlinear water-like geometries

Finite-size corrections in simulation of dipolar fluids

International audienceMonte Carlo simulations of dipolar fluids are performed at different numbers of particles N=100-4000. For each size of the cubic cell, the non-spherically symmetric pair distribution function g(r,) is accumulated in terms of projections g mnl (r) onto rotational invariants. The observed N dependence is in very good agreement with the theoretical predictions for the finite-size corrections of different origins: the explicit corrections due to the absence of fluctuations in the number of particles within the canonical simulation and the implicit corrections due to the coupling between the environment around a given particle and that around its images in the neighboring cells. The latter dominate in fluids of strong dipolar coupling characterized by low compressibility and high dielectric constant. The ability to clean with great precision the simulation data from these corrections combined with the use of very powerful anisotropic integral equation techniques means that exact correlation functions both in real and Fourier spaces, Kirkwood-Buff integrals and bridge functions can be derived from box sizes as small as N≈100, even with existing long-range tails. In presence of dielectric discontinuity with the external medium surrounding the central box and its replica within the Ewald treatment of the coulombic interactions, the 1/N dependence of the g mnl (r) is shown to disagree with the, yet well-accepted, prediction of the literature