A quasi-elastic neutron scattering investigation of the hydrogen surface self diffusion on polymer electrolyte membrane fuel cell catalyst support.

International audience

Criteria for validity of thermodynamic equations from non-equilibrium molecular dynamics simulations.

International audience; The assumption of local equilibrium is validated in four different systems where heat and mass are transported. Mass fluxes up to 13kmol=m2 s and temperature gradients up to 1012 K=m were used. A two-component mixture, two vapor–liquid interfaces, a chemical reaction in a temperature gradient and gas adsorbed in zeolite were studied using non-equilibrium molecular dynamics simulations. In all cases, we verified that thermodynamic variables obeyed normal thermodynamic relations, with an accuracy better than 5%. The heat and mass fluxes, and the reaction rate were linearly related to the driving forces. Onsager's reciprocal relations were validated for two systems. Equ…

Thermodynamics of small systems embedded in a reservoir: a detailed analysis of finite size effects

International audience; We present a detailed study on the finite size scaling behaviour of thermodynamic properties for small systems of particles embedded in a reservoir. Previously, we derived that the leading finite size effects of thermodynamic properties for small systems scale with the inverse of the linear length of the small system, and we showed how this can be used to describe systems in the thermodynamic limit [Chem. Phys. Lett. 504, 199 (2011)]. This approach takes into account an effective surface energy, as a result of the non-periodic boundaries of the small embedded system. Deviations from the linear behaviour occur when the small system becomes very small, i.e. smaller tha…

Thermal effects during adsorption of n-butane on a slilicalite-1 membrane. A non-equilibrium molecular dynamics study

Abstract Non-equilibrium molecular dynamic (NEMD) simulations have been used to study the kinetics of adsorption of n-butane molecules in a silicalite membrane. We have chosen this simple well-known process to demonstrate that the process is characterized by two stages, both non-isothermal. In the first stage the large chemical driving force leads to a rapid uptake of n-butane in all the membrane and a simultaneous increase in the membrane temperature, explained by the large enthalpy of adsorption, Δ H = − 61.6 kJ / mol butane. A diffusion coefficient for transport across the external surface layer is calculated from the relaxation time; a value of 3.4 × 10 −9 m 2 / s is found. During the a…

Thermal Flux through a Surface of n-Octane. A Non-equilibrium Molecular Dynamics Study

We show using non-equilibrium molecular dynamics that there is local equilibrium in the surface when a two-phase fluid of n-octane is exposed to a large temperature gradient (10 8 K/m). The surface is defined according to Gibbs, and the transport across the surface is described with non-equilibrium thermodynamics. The structure of the surface in the presence of the gradient is the same as if the interface was in equilibrium, as measured by the variation across the surface of the pressure component that is parallel to the surface. The surface is in local equilibrium by this criterion and because the equation of state for the surface was unaltered by a large heat flux. The surface has a small…

Thermal Diffusion and Partial Molar Enthalpy Variations of n-Butane in Silicalite-1

International audience; We report for the first time the heat of transfer and the Soret coefficient for n-butane in silicalite-1. The heat of transfer was typically 10 kJ/mol. The Soret coefficient was typically 0.006 K−1 at 360 K. Both varied with the temperature and the concentration. The thermal conductivity of the crystal with butane adsorbed was 1.46 ±0.07 W/Km. Literature values of the isosteric enthalpy of adsorption, the concentration at saturation, and the diffusion coefficients were reproduced. Non-equilibrium molecular dynamics simulations were used to find these results, and a modified heat exchange algorithm, Soft-HEX, was developed for the purpose. Enthalpies of butane were al…

Fick diffusion coefficients of liquid mixtures directly obtained from equilibrium molecular dynamics.

A methodology for computing Fick diffusivities directly from equilibrium molecular dynamics (MD) simulations is presented and validated for acetone-methanol and acetone-tetrachloromethane liquid mixtures. Fick diffusivities are obtained from Maxwell-Stefan (MS) diffusivities and the so-called thermodynamic factor. MS diffusivities describe the friction between different components, while the thermodynamic factor is the concentration derivative of the activity describing the deviation from ideal mixing behavior. It is important to note that all mutual diffusion experiments measure Fick diffusion coefficients, while molecular simulation provides MS diffusivities. The required thermodynamic fa…

Quasi-elastic Neutron Scattering Investigation of the Hydrogen Surface Self-Diffusion on Polymer Electrolyte Membrane Fuel Cell Catalyst Support

International audience; Quasi-elastic neutron scattering (QENS) measurements have been performed to investigate the surface selfdiffusion of hydrogen molecules. A monolayer of molecular hydrogen was adsorbed on a carbon material commonly used in polymer electrolyte membrane fuel cells, called XC-72. QENS spectra were recorded at the time-of-flight spectrometer IN5 at Institut Laue-Langevin (ILL) in Grenoble at 40, 50, 60, and 70 K. By using the Chudley & Elliott model for jump diffusion, we found the diffusion coefficient at each temperature. The logarithm of the diffusion coefficient was plotted versus the inverse of the temperature to give the coefficient in the Arrhenius equation. From t…

Finite-size effects of Kirkwood–Buff integrals from molecular simulations

The modelling of thermodynamic properties of liquids from local density fluctuations is relevant to many chemical and biological processes. The Kirkwood–Buff (KB) theory connects the microscopic structure of isotropic liquids with macroscopic properties such as partial derivatives of activity coefficients, partial molar volumes and compressibilities. Originally, KB integrals were formulated for open and infinite systems which are difficult to access with standard Molecular Dynamics (MD) simulations. Recently, KB integrals for finite and open systems were formulated (J Phys Chem Lett. 2013;4:235). From the scaling of KB integrals for finite subvolumes, embedded in larger reservoirs, with the…

Integral relations, a simplified method to find interfacial resistivities for heat and mass transfer.

International audience; Integral relations were used to predict interface film transfer coefficients for evaporation and condensation. According to these, all coefficients can be calculated for one-component systems, using the thermal resistivity and the enthalpy profile through the interface. The expressions were verified in earlier work using non-equilibrium molecular dynamics simulations for argon-like particles, which interacted with a short-range Lennard-Jones (LJ) spline potential, which becomes zero at about 1.7 times the LJ-diameter. In this paper we verify the validity of these relations for a long-range LJ spline potential which becomes zero at 2.5 times the diameter. In an earlie…

Transfer coefficients for the liquid–vapor interface of a two-component mixture

Abstract We present the excess entropy production for heat and mass transport across an interface of a non-ideal two-component mixture, using as interface variables the excess densities proposed by Gibbs. With the help of these variables we define the interface as an autonomous system in local equilibrium and study its transport properties. The entropy production determines the conjugate fluxes and forces, and equivalent forms are given. The forms contain finite differences of intensive variables into and across the surface as driving forces. These expressions for the fluxes serve as boundary conditions for integration across heterogeneous systems that are far from global equilibrium. The r…

Size and shape effects on the thermodynamic properties of nanoscale volumes of water

Small systems are known to deviate from the classical thermodynamic description, among other things due to their large surface area to volume ratio compared to corresponding big systems. As a consequence, extensive thermodynamic properties are no longer proportional to the volume, but are instead higher order functions of size and shape. We investigate such functions for second moments of probability distributions of fluctuating properties in the grand-canonical ensemble, focusing specifically on the volume and surface terms of Hadwiger's theorem, explained in Klain, Mathematika, 1995, 42, 329–339. We resolve the shape dependence of the surface term and show, using Hill's nanothermodynamics…

Defining the local temperature of adsorbed argon in a nanoporous zeolitic membrane. A molecular dynamics study.

Equilibrium properties of the reaction H2⇌ 2H by classical molecular dynamics simulations

We have developed a classical molecular dynamics model for the hydrogen dissociation reaction, containing two- and three-particle potentials derived by Kohen, Tully and Stillinger. Two fluid densities were investigated for a wide range of temperatures, and 11 fluid densities were considered for one temperature. We report the temperature range where the degree of reaction is significant, and also where a stable molecule dominates the population in the energy landscape. The three-particle potential, which is essential for the reaction model and seldom studied, together with the two-particle interaction lead to a large effective excluded volume diameter of the molecules in the molecular fluid.…

Thermodynamic Characterization Of Two Layers Of CO2 On A Graphite Surface

We find by examination of density profiles that carbon dioxide adsorbs on graphite in two distinct layers. We report the activity coefficient, entropy and enthalpy for CO2 in each layer using a convenient computational method, the Small System Method, thereby extending this method to surfaces. This opens up the possibility to study thermodynamic properties for a wide range of surface phenomena. © 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Thermodynamic properties of a liquid–vapor interface in a two-component system

Abstract We report a complete set of thermodynamic properties of the interface layer between liquid and vapor two-component mixtures, using molecular dynamics. The mixtures consist of particles which have identical masses and diameters and interact with a long-range Lennard-Jones spline potential. The potential depths in dimensionless units for like interactions is 1 (for component 1) and 0.8 (for component 2). The surface excess entropy decreases when the temperature increases, so the surface has a negative excess heat capacity. This is a consequence of the fact that the surface tension decreases to zero at the critical point, proportional to ( T C , i − T ) 2 ν . The surface entropy decre…

The reaction enthalpy of hydrogen dissociation calculated with the Small System Method from simulation of molecular fluctuations.

We show how we can find the enthalpy of a chemical reaction under non-ideal conditions using the Small System Method to sample molecular dynamics simulation data for fluctuating variables. This method, created with Hill's thermodynamic analysis, is used to find properties in the thermodynamic limit, such as thermodynamic correction factors, partial enthalpies, volumes, heat capacities and compressibility. The values in the thermodynamic limit at (T,V, μj) are then easily transformed into other ensembles, (T,V,Nj) and (T,P,Nj), where the last ensemble gives the partial molar properties which are of interest to chemists. The dissociation of hydrogen from molecules to atoms was used as a conve…

Transfer coefficients for evaporation of a system with a Lennard-Jones long-range spline potential

International audience; Surface transfer coefficients are determined by nonequilibrium molecular dynamics simulations for a Lennard-Jones fluid with a long-range spline potential. In earlier work A. Røsjorde et al., J. Colloid Interface Sci. 240, 355 2001; J. Xu et al., ibid. 299, 452 2006, using a short-range Lennard-Jones spline potential, it was found that the resistivity coefficients to heat and mass transfer agreed rather well with the values predicted by kinetic theory. For the long-range Lennard-Jones spline potential considered in this paper we find significant discrepancies from the values predicted by kinetic theory. In particular the coupling coefficient, and as a consequence the…

Integral relations for mass and heat transport through a liquid-vapour interface; A molecular dynamics study.

Fick Diffusion Coefficients in Ternary Liquid Systems from Equilibrium Molecular Dynamics Simulations

An approach for computing Fick diffusivities directly from equilibrium molecular dynamics (MD) simulations is presented and demonstrated for a ternary chloroform–acetone–methanol liquid mixture. In our approach, Fick diffusivities are calculated from the Maxwell–Stefan (MS) diffusivities and the so-called matrix of thermodynamic factors. MS diffusivities describe the friction between different molecular species and can be directly computed from MD simulations. The thermodynamic factor describes the deviation from ideal mixing behavior and is difficult to extract from both experiments and simulations. Here, we show that the thermodynamic factor in ternary systems can be obtained from density…

Calculating thermodynamic properties from fluctuations at small scales.

We show how density and energy fluctuations of small nonperiodic systems embedded in a reservoir can be used to determine macroscopic thermodynamic properties like the enthalpy density and the thermodynamic correction factor. For mixtures, the same formalism leads to a very convenient method to obtain so-called total correlation function integrals, also often referred to as Kirkwood-Buff integrals. Using finite size scaling, the properties obtained for small systems can be extrapolated to the macroscopic system limit provided that the system is sufficiently far from the critical point. As derived in our previous work (Chem. Phys. Lett. 2011, 504, 199-201), the finite size scaling is signifi…

The heat of transfer in a chemical reaction at equilibrium.

International audience; We study a reacting mixture (2F $ F2) in a temperature gradient. We had previously used boundary-driven non-equilibrium molecular dynamics (NEMD) simulations to study this system, and found that the reaction was close to local chemical equilibrium in temperature gradients up to 1012 K/m. Using the condition of local chemical equilibrium, we show that the heat of transfer of the reacting mixture is equal to minus the enthalpy of the reaction. The fact that the sign of the heat of transfer is determined by the type of reaction adds insight to the discussion of the origin of the sign

Kirkwood-Buff Integrals for Finite Volumes.

Exact expressions for finite-volume Kirkwood−Buff (KB) integrals are derived for hyperspheres in one, two, and three dimensions. These integrals scale linearly with inverse system size. From this, accurate estimates of KB integrals for infinite systems are obtained, and it is shown that they converge much better than the traditional expressions. We show that this approach is very suitable for the computation of KB integrals from molecular dynamics simulations, as we obtain KB integrals for open systems by simulating closed systems.

Numerical evidence for a thermal driving force during adsorption of butane in silicalite.

International audience; The transport properties of nano-porous materials determine their applicability, e.g. as separators or catalysts (J. Ka¨rger, D. Ruthven. Diffusion in zeolites, Wiley, New York (1991); L.V.C. Rees, D. Shen. Adsorption of gases in zeolite molecular sieves. In Introduction to Zeolite Science and Practice, Studies in surface science and catalysis, H.V.C. van Bekkum, E.M. Flanigen, P.A. Jacobs, J.C. Jansen (Eds.), vol. 137, pp. 579–631, Elsevier, Amsterdam (2001)). Adsorption in zeolites is explained as a two-step process; adsorption to the external crystal surface and subsequent intra-crystalline diffusion (R. M. Barrer. Porous crystal membranes. J. Chem. Soc. Faraday T…

Calculation of the chemical potential and the activity coefficient of two layers of CO2 adsorbed on a graphite surface.

We study the adsorption of carbon dioxide at a graphite surface using the new Small System Method, and find that for the temperature range between 300 K and 550 K most relevant for CO2 separation; adsorption takes place in two distinct thermodynamic layers defined according to Gibbs. We calculate the chemical potential and the activity coefficient of both layers directly from the simulations. Based on thermodynamic relations, the entropy and enthalpy of the CO2 adsorbed layers are also obtained. Their values indicate that there is a trade-off between entropy and enthalpy when a molecule chooses for one of the two layers. The first layer is a densely packed monolayer of relatively constant e…

Surface Self-Diffusion and Mean Displacement of Hydrogen on Graphite and a PEM Fuel Cell Catalyst Support

International audience; Quasielastic neutron scattering (QENS) measurements together with equilibrium molecular dynamic (EMD) simulations have been performed to investigate the surface interaction between hydrogen molecules and a carbon material commonly used in polymer electrolyte membrane fuel cells (PEMFC), called XC-72. Half a monolayer of molecular hydrogen was adsorbed on to the carbon material at 2 K. QENS spectra were recorded at the time-of-flight spectrometer IN5 at 40, 45, 50, 60, 70, 80, and 90 K. Simultaneously the pressure was measured as a function of time to monitor the equilibrium surface coverage at each temperature. By using the Chudley and Elliott model for jump diffusio…

Partial molar enthalpies and reaction enthalpies from equilibrium molecular dynamics simulation

We present a new molecular simulation technique for determining partial molar enthalpies in mixtures of gases and liquids from single simulations, without relying on particle insertions, deletions, or identity changes. The method can also be applied to systems with chemical reactions. We demonstrate our method for binary mixtures of Weeks-Chandler-Anderson particles by comparing with conventional simulation techniques, as well as for a simple model that mimics a chemical reaction. The method considers small subsystems inside a large reservoir (i.e., the simulation box), and uses the construction of Hill to compute properties in the thermodynamic limit from small-scale fluctuations. Results …

Thermodynamics of a small system in a μT reservoir

Abstract Due to advances in experimental techniques operating at the nanoscale, it is possible to compute properties from density fluctuations by studying ‘snapshots’ of particle configurations. Thermodynamics on a small scale is different from thermodynamics in bulk systems. We show how the molar enthalpy h and the inverse thermodynamic correction factor Γ - 1 depend on system size and how these properties can be computed from fluctuations at the nanoscale. We find a 1/ L finite size effect for all thermodynamic quantities for a small system in contact with a reservoir, where L is the length of the system in a single dimension.

Criteria for validity of thermodynamic equations from non-equilibrium molecular dynamics simulations

Abstract The assumption of local equilibrium is validated in four different systems where heat and mass are transported. Mass fluxes up to 13 kmol / m 2 s and temperature gradients up to 10 12 K / m were used. A two-component mixture, two vapor–liquid interfaces, a chemical reaction in a temperature gradient and gas adsorbed in zeolite were studied using non-equilibrium molecular dynamics simulations. In all cases, we verified that thermodynamic variables obeyed normal thermodynamic relations, with an accuracy better than 5%. The heat and mass fluxes, and the reaction rate were linearly related to the driving forces. Onsager's reciprocal relations were validated for two systems. Equipartiti…

How to apply the Kirkwood–Buff theory to individual species in salt solutions

It is generally assumed that the Kirkwood–Buff (KB) theory cannot be applied to anions and cations individually in a solution, as one cannot simulate this system in an open ensemble due to the electroneutrality constraint. By applying our recently derived KB theory for closed systems, we show that one does have access to single-ion properties in Molecular Dynamics. Our findings are supported by simulations for a model of a salt solution in which particles interact with WCA potentials, as well as for the NaCl/water system using the Particle Mesh Ewald technique for electrostatics.

Transport properties of 2F = F2 in a temperature gradient as studied by molecular dynamics simulations

International audience; We calculate transport properties of a reacting mixture of F and F2 from results of nonequilibrium molecular dynamics simulations. The reaction investigated is controlled by thermal diffusion and is close to local chemical equilibrium. The simulations show that a formulation of the transport problem in terms of classical non-equilibrium thermodynamics theory is sound. The chemical reaction has a large effect on the magnitude and temperature dependence of the thermal conductivity and the interdiffusion coefficient. The increase in the thermal conductivity in the presence of the chemical reaction, can be understood as a response to an imposed temperature gradient, whic…

Transport coefficients of n-butane into and through the surface of silicalite-1 from non-equilibrium molecular dynamics study

We have studied coupled heat and mass transfer of n-butane through a membrane of silicalite-1. A description of the surface was given using non-equilibrium thermodynamics, and transport coefficients were determined. Three independent coefficients were found for the whole surface: the resistance to heat transfer, the coupling coefficient and the resistance to mass transfer. These coefficients were defined in stationary state. All resistances are significant, and show that the surface acts as a barrier to transport. A new scheme was devised to find the enthalpy of adsorption, from two particular coupling coefficients, namely the measurable heats of transfer. The method yields the enthalpy of …

Bridging scales with thermodynamics: from nano to macro

We have recently developed a method to calculate thermodynamic properties of macroscopic systems by extrapolating properties of systems of molecular dimensions. Appropriate scaling laws for small systems were derived using the method for small systems thermodynamics of Hill, considering surface and nook energies in small systems of varying sizes. Given certain conditions, Hill's method provides the same systematic basis for small systems as conventional thermodynamics does for large systems. We show how the method can be used to compute thermodynamic data for the macroscopic limit from knowledge of fluctuations in the small system. The rapid and precise method offers an alternative to curre…