Surface Adsorption Isotherms and Surface Excess Densities of n-Butane in Silicalite-1.

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

International audienceThe 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. Equipartition of kinetic energy applied to all directions. There was no need to invoke any dependence of the thermodynamic variables on the gradients. Away from global equilibrium, the local velocity distribution was found to deviate from the Maxwell distribution in the direction of transport. The deviation was in a form that is used by the Enskog method to solve the Boltzmann equation. New general criteria were formulated for thermodynamic state variables, P. In order to obey local equilibrium, the relative fluctuation in the state variable needs only to fulfill dP=Pt1= ffiffiffiffi N p , where N is the number of particles in the volume element. The variation of the variable in the direction of transport needs to fulfill DP=P ¼ ‘xrP=P51, where the length of the volume element in direction of transport, ‘x, is of the order of the diameter of a molecule. These criteria are much less restrictive than proposed earlier, and allows us to use thermodynamic equations in open volume elements with a surprisingly small number (8–18) of particles

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

International audienceNon-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, 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 m2/s is found. During the adsorption, a significant thermal driving force develops across the external surface of the membrane, which leads to an energy flux out of the membrane during the second stage. In this stage a thermal conductivity of 3.4 × 10−4 W/Km is calculated from the corresponding relaxation time for the surface, confirming that the thermal conduction is the rate-limiting step. The aim of this paper is to demonstrate that a thermal driving force must be taken into account in addition to a chemical driving force in the description of transport in nano-porous materials

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

International audienceThe transport properties of nano-porous materials determine their applicability, e.g. as separators or catalysts [1, 2]. Adsorption in zeolites is explained as a two-step process; adsorption to the external crystal surface and subsequent intra-crystalline diffusion [3]. Both steps have been considered to be isothermal [4, 5]. Here we show, using non-equilibrium molecular dynamics simulations of n-butane in silicalite [6] that a significant temperature change accompanies adsorption and intra-crystalline transport, and leads to a significant varying thermal driving force across the crystal surface, in agreement with the proposition of Ruthven et al. [7]. The butane flux into the crystal is caused in the first stage by a chemical potential difference. In the second stage the temperature of the zeolite decreases due to a thermal force across the surface. This slow reduction in the zeolite temperature induces a small butane uptake, that may help explain why equilibrium techniques give larger diffusion coefficients than non-equilibrium techniques [5]. Descriptions of transport in nano-porous materials [1, 8] need to include a thermal driving force

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

International audienceWe 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 adsorption as a function of the excess surface concentration and surface temperature, but in this case it is nearly constant, 55 kJ/ mol. An expression of the surface permeability is given and our results are in agreement with experimental observations. A further inspection of the surface regarded as a series of two resistances, showed that the gas side of the surface dominates completely the resistance to heat transfer, while the silicalite side determines the resistance to mass transfer and the value of the coupling coefficient. The coefficients were not sensitive to the surface structure, whether it was flat, or zig-zag textured. Interestingly, the surface excess concentration was negative for low pressures, underlining the importance of the surface as a barrier to transport. The findings may help reduce adsorption data from experiments on zeolites and other porous materials

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

International audienceWe 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 also determined. We use these results to give numerical proof for a recently proposed relation, that the heat of transfer plus the partial molar enthalpy of butane is constant at a given temperature. The proof is offered for a regime where the partial molar enthalpy can be approximated by the molar internal energy. This result may add to the understanding of the sign of the Soret coefficient. The technical importance of the heat of transfer is discussed

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

International audienceThe 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 Trans., 86, 1123 (1990)). Both steps have been considered to be isothermal (P. Kortunov, S. Vasenkov, C. Chmelik, J. Ka¨rger, D. Ruthven, J. Wloch. Influence of defects on the external crystal surface on molecular uptake into MFI-type zeolites. Chem. Mater., 16, 3552 (2004); J. Ka¨rger. Measurements of diffusion in zeolites—a never ending challenge? Adsorption, 9, 29 (2003)). Here we show, using non-equilibrium molecular dynamics simulations of n-butane in silicalite (J.M. Simon, A. Decrette, J.P. Bellat, J.M. Salazar. Kinetics of adsorption of n-butane on an aggregate of silicalite by transient non-equilibrium molecular dynamics. Mol. Simul., 30, 621 (2004)) that a significant temperature change accompanies adsorption and intra-crystalline transport, and leads to a significant varying thermal driving force across the crystal surface, in agreement with the proposition of Ruthven et al. (D.M. Ruthven, L.K. Lee. Kinetics of nonisothermal sorption: systems with bed diffusion control. AICHE J., 27, 654 (1981)). The butane flux into the crystal is caused in the first stage by a chemical potential difference. In the second stage the temperature of the zeolite decreases due to a thermal force across the surface. This slow reduction in the zeolite temperature induces a small butane uptake, that may help explain why equilibrium techniques give larger diffusion coefficients than non-equilibrium techniques (J. Ka¨rger. Measurements of diffusion in zeolites—a never ending challenge? Adsorption, 9, 29 (2003)). Descriptions of transport in nano-porous materials (J. Ka¨rger, D. Ruthven. Diffusion in zeolites, Wiley, New York (1991); R. Krishna, J. A. Wesselingh. The Maxwell–Stefan approach to mass transfer. Chem. Eng. Sci., 52, 861 (1997)) need to include a thermal driving force