Verification of Onsager's reciprocal relations for evaporation and condensation using non-equilibrium molecular dynamics

Non-equilibrium molecular dynamic (NEMD) simulations have been used to study heat and mass transfer across a vapor-liquid interface for a one-component system using a Lennard-Jones spline potential. It was confirmed that the relation between the surface tension and the surface temperature in the non-equilibrium system was the same as in equilibrium (local equilibrium). Interfacial transfer coefficients were evaluated for the surface, which expressed the heat and mass fluxes in temperature and chemical potential differences across the interfacial region (film). In this analysis it was assumed that the Onsager reciprocal relations were valid. In this paper we extend the number of simulations such that we can calculate all four interface film transfer coefficients along the whole liquid-vapor coexistence curve. We do this analysis both for the case where we use the measurable heat flux on the vapor side and for the case where we use the measurable heat flux on the liquid side. The most important result we found is that the coupling coefficients within the accuracy of the calculation are equal. This is the first verification of the validity of the Onsager relations for transport through a surface using molecular dynamics. The interfacial film transfer coefficients are found to be a function of the surface temperature alone. New expressions are given for the kinetic theory values of these coefficients which only depend on the surface temperature. The NEMD values were found to be in good agreement with these expressions.     

Effective kinetic phase diagrams

The composition of a solid solution that is growing at conditions well away from equilibrium is not prescribed by equilibrium thermodynamics, but is determined kinetically. It depends both on the surface kinetics and on the transport of mass and heat to and away from the solidification front. In previous work, we have formulated a model for the kinetic or nonequilibrium segregation taking place at the solidification front enabling the construction of kinetic phase diagrams, which gives the growth composition of a solid solution as a function of the liquid composition and undercooling at the surface. In the present work, we extend this model to include both mass and heat transport, giving rise to effective kinetic phase diagrams. An overview of the tendencies in the calculated effective kinetic phase diagrams is given by scanning a large part of the parameter space, covering different types of materials, including metals, semiconductors, and molecular systems. We find striking and characteric differences in the relative contribution of the various processes to the effective segregation. For molecular mixtures, interfacial undercooling and heat transport limitation can be expected to be much more important than for metal and semiconductor mixtures where mass transport limitation is dominant.     

Interface film resistivities for heat and mass transfers-integral relations verified by non-equilibrium molecular dynamics

Integral relations that predict interface film transfer coefficients for evaporation and condensation have recently been derived. According to these relations, all coefficients can be calculated for one-component systems, using the thermal resistivity and the enthalpy profile through the interface. The integral relations were tested in this work using nonequilibrium molecular dynamics simulations for argon-like particles and n-octane molecules. The simulations confirm the integral relations within the accuracy of the calculation for both systems. Evidence is presented for the existence of an excess thermal resistivity on the gas side of the surface, and the fact that this property is decisive for interface heat and mass transfer coefficients. The integral relations were used to predict the mass transfer coefficient for n- octane as a function of surface tension. The findings are important for modeling of one-component phase transitions.     

Microwave-driven zeolite-guest systems show athermal effects from nonequilibrium molecular dynamics

Nonequilibrium molecular dynamics simulations show that steady-state systems obtained by microwave heating are qualitatively different from those at thermal equilibrium. This difference arises because energy transfer from hotter to colder species is not efficient enough to equilibrate the distribution of energy. Under nonequilibrium conditions, we found that microwave radiation can selectively heat methanol in a binary mixture of methanol-benzene adsorbed in faujasite zeolite. The difference in steady-state temperatures follows the trend Tmethanol > Tbenzene > Tzeolite, which is qualitatively consistent with recent experimental results.     

Mixing rules for multicomponent mixture mass diffusion coefficients and thermal diffusion factors

Mixing rules are derived for mass diffusion coefficient and thermal diffusion factor matrices by developing compatibility conditions between the fluid mixture equations obtained from nonequilibrium thermodynamics and Grad's 13-moment kinetic theory. The mixing rules are shown to be in terms of the species mole fractions and binary processes. In particular, the thermal diffusion factors for binary mixtures obtained by the Chapman-Enskog expansion procedure are suitably generalized for many-component mixtures. Some practical aspects of the results are discussed including the utilization of these mixing rules for high pressure situations.     

Bead-bead interaction parameters in dissipative particle dynamics: relation to bead-size, solubility parameter, and surface tension

Dissipative particle dynamics (DPD) is a mesoscale modeling method for simulating equilibrium and dynamical properties of polymers in solution. The basic idea has been around for several decades in the form of bead-spring models. A few years ago, Groot and Warren established an important link between DPD and the Flory-Huggins chi-parameter theory for polymer solutions. We revisit the Groot-Warren theory and investigate the DPD interaction parameters as a function of bead size. In particular, we show a consistent scheme of computing the interfacial tension in a segregated binary mixture. Results for three systems chosen for illustration are in excellent agreement with experimental results. This opens the door for determining DPD interactions using interfacial tension as a fitting parameter.     

Equilibrium calculations of viscosity and thermal conductivity across a solid-liquid interface using boundary fluctuations

We calculate viscosity and thermal conductivity in systems of Lennard-Jones particles consisting of coexisting solid and liquid with different interface wetting properties using the recently developed equilibrium boundary fluctuation theory. We compare the slip length and equivalent liquid length obtained from these calculations with those obtained from nonequilibrium molecular dynamics. The equilibrium and nonequilibrium calculations of the slip length and the sum of the thermal equivalent lengths are in good agreement. We conclude that for both interfacial properties, the nonequilibrium simulations were probing the linear response. The significant dependence of the intrinsic equivalence length on the interfacial temperature difference used to generate the thermal gradient is explained as a consequence of the different thermodynamic states of the two interfaces.     

Structuring of a disperse system of ethylene-chlorine complexes in a nonequilibrium vitreous film at liquid helium temperatures

A two-component vitreous, structurally nonequilibrium reaction mixture is considered as an open thermodynamic system of a set of molecules in the gas phase at room temperature. The system is subjected to external action via the rapid transfer of gases in a vitreous film below the vitrification temperature. After the first structuring in the film’s formation, a second structuring that consisted of initiating a set of complexes is attained within the released phase of complexes in the process of structural self-organization. It is found that laser photolysis of the solid-phase reaction mixture is a structure-sensitive diagnostic tool for states of nonequilibrium glass. It is concluded that the change from explosive to stationary kinetic behavior during photolysis is due to the second structuring, the accelerated attainment of which is a product of thermal annealing.     

Testing the accuracy of correlations for multicomponent mass transport of adsorbed gases in metal-organic frameworks: diffusion of H2/CH4 mixtures in CuBTC

Mass transport of chemical mixtures in nanoporous materials is important in applications such as membrane separations, but measuring diffusion of mixtures experimentally is challenging. Methods that can predict multicomponent diffusion coefficients from single-component data can be extremely useful if these methods are known to be accurate. We present the first test of a method of this kind for molecules adsorbed in a metal-organic framework (MOF). Specifically, we examine the method proposed by Skoulidas, Sholl, and Krishna (SSK) ( Langmuir, 2003, 19, 7977) by comparing predictions made with this method to molecular simulations of mixture transport of H 2/CH 4 mixtures in CuBTC. These calculations provide the first direct information on mixture transport of any species in a MOF. The predictions of the SSK approach are in good agreement with our direct simulations of binary diffusion, suggesting that this approach may be a powerful one for examining multicomponent diffusion in MOFs. We also use our molecular simulation data to test the ideal adsorbed solution theory method for predicting binary adsorption isotherms and a method for predicting mixture self-diffusion coefficients.     

Dynamics and kinetics of heat transfer at the interface of model diamond [111] nanosurfaces

A molecular dynamics simulation was performed to study the effect of an applied force on heat transfer at the interface of model diamond [111] nanosurfaces. The force was applied to a small, hot nanosurface at 800, 1000, or 1200 K brought into contact with a larger, colder nanosurface at 300 K. The relaxation of the initial nonequilibrium interfacial force occurs on a subpicosecond time scale, much shorter than that required for heat transfer. Heat transfer occurs with exponential kinetics and a rate constant that increases linearly with the interfacial force according to 7 x 10(-4) ps(-1)/nN. This rate constant only increases by at most 10% as the temperature of the hot surface is increased from 800 to 1200 K. Replacing the interfacial H-atoms on both surfaces by D atoms also has a very small effect on the heat transfer. However, if one nanosurface has H atoms on its interface and the other nanosurface's interface has D atoms, then there is a marked 25% decrease in the rate constant for heat transfer. Increasing the size of the hot surface, and, thus, the interfacial contact area, increases the rate of heat transfer but not the rate constant. For the same interfacial force, different anharmonic models for the nanosurfaces' potential energy function give the same heat transfer rate constant. The possibility of quantum effects for heat transfer across the diamond interface is considered.     

Kinetic Study of the Aggregation of Colloids Immersed in a Binary Mixture of Polymers

Summary: We consider an assembly of colloidal particles, which are immersed in a binary mixture of polymers. At temperatures close to the critical point of the free mixture, the fluctuations of the composition induce a critical Casimir force between colloids. This force naturally depends on their distance and it is responsible for the colloidal aggregation. In this paper, we propose to study the kinetics of such a transition leading colloids from a dispersed phase (gas) to a dense one (liquid). This kinetics is studied through the relaxation rate, which is a function of the transfer wave-vector.     

Nonequilibrium inertial dynamics of colloidal systems

We consider the properties of a one-dimensional fluid of Brownian inertial hard-core particles, whose microscopic dynamics is partially damped by a heat bath. Direct interactions among the particles are represented as binary, instantaneous elastic collisions. Collisions with the heat bath are accounted for by a Fokker-Planck collision operator, whereas direct collisions among the particles are treated by a well known method of kinetic theory, the revised Enskog theory. By means of a time multiple time-scale method we derive the evolution equation for the average density. Remarkably, for large values of the friction parameter and/or of the mass of the particles we obtain the same equation as the one derived within the dynamic density functional theory (DDF). In addition, at moderate values of the friction constant, the present method allows to study the inertial effects not accounted for by DDF method. Finally, a numerical test of these corrections is provided.     

Phonon thermal conductivity in nanolaminated composite metals via molecular dynamics

We use nonequilibrium molecular dynamics to characterize the phonon contribution to thermal conduction of Al nanostructures and the role of interfaces in metallic nanocomposites. We characterize the lattice thermal conductivity of pure Al samples as a function of size and temperature from which we obtain, using kinetic theory, the temperature dependence of the phonon mean free path. We also calculated the thermal conductivity of AlAl* and AlNi nanolaminate composites (where Al* differs from Al only in its mass) for various periodic sizes and compositions as well as the associated interfacial thermal resistivities (ITRs). We find that simple, additive models provide good estimates of the thermal conductivities of the nanocomposites in terms of those of the individual components and interfaces if size effects on the behavior of the individual components are considered. The additive models provide important insight to the decrease in thermal conductivity of the nanolaminates as their periodicity (thickness of a bilayer) is reduced to a size comparable with the phonon mean free path and break down when this characteristic size is reduced further. At this point the system can be regarded as homogeneous and the conductivity increases with decreasing periodicity of the laminates. We also observe that the ITR depends on the direction of the heat flux; this is the first molecular level characterization of such thermal diode behavior in a realistic three dimensional material.     

Equilibrium and nonequilibrium molecular dynamics simulations of the thermal conductivity of molten alkali halides

The thermal conductivity of molten NaCl and KCl was calculated through the Evans-Gillan nonequilibrium molecular dynamics (NEMD) algorithm and Green-Kubo equilibrium molecular dynamics (EMD) simulations. The EMD simulations were performed for a "binary" ionic mixture and the NEMD simulations assumed a pure system for reasons discussed in this work. The cross thermoelectric coefficient obtained from Green-Kubo EMD simulations is discussed in terms of the homogeneous thermoelectric power or Seebeck coefficient of these materials. The thermal conductivity obtained from NEMD simulations is found to be in very good agreement with that obtained through Green-Kubo EMD simulations for a binary ionic mixture. This result points to a possible cancellation between the neglected "partial enthalpy" contribution to the heat flux associated with the interdiffusion of one species through the other and that part of the thermal conductivity related to the coupled fluxes of charge and heat in "binary" ionic mixtures.     

Kinetics of Ge(IV) Extraction Using a Microstructured Membrane Contactor

For hydrometallurgical metal extraction, the mass transfer by diffusion is additionally coupled with a chemical reaction of the metal ion with the extractant molecule, usually at the interface. Consequently, the kinetics is either limited by diffusion or chemical reaction (or both, respectively, in a mixed regime). Conventional methods for determining the extraction kinetics often lead to a misinterpretation, especially for fast reactions, and an isolated view of the interfacial reaction is restricted. With a new microcontactor setup, it is possible to perform a comprehensive kinetic analysis with very low sample volumes compared to established methods. Additionally, it is possible to quantify all individual mass transfer resistances and identify the extraction regime with the developed mass transfer model. The chemical reaction part is investigated isolated, to derive rate laws and kinetic constants. The methodology is discussed for the extraction of Ge(IV) from aqueous solutions with the two extractants 5,8‐diethyl‐7‐hydroxydodecan‐6‐oxime (LIX 63) and 7‐(4‐ethyl‐1‐methyloctyl)‐8‐hydroxyquinoline (Kelex 100). It was found that the extraction with LIX 63 is reaction limited and with Kelex 100 the reaction resistance is in the same order of magnitude as the diffusion resistances. The obtained results provide fundamental kinetic data for the design of solvent extraction equipment.     

A Heterogeneous Multiscale Dynamic Model for Simulation of Catalytic Reforming Reactors

The present work aims to establish a generic reforming reaction scheme to evaluate the performance of catalytic reforming systems with the aid of a one‐dimensional heterogeneous dynamic model. The novelty of the numerical model stems from the direct inclusion of interphase (fluid‐to‐particle surface), intraparticle (within particle), and intrareactor heat and mass transport resistances under transient conditions. The developed model accounts for the multicomponent gas mixture physicochemical properties and correlations for calculating mass and heat transfer coefficients. Effective macroscopic properties within the particle are calculated by incorporating diffusivities and conductivities of the porous network characteristics accounting for Knudsen and molecular transport as well as tortuosity and porosity of the overall porous path. The industrial case of a steam‐methane reforming multitubular reactor was studied as the most representative case of the generic reaction scheme, with all mass/energy resistances present under severe pressure and temperature conditions. It was shown that there are notable diffusional limitations within the particle, whereas there are also temperature and partial pressure gradients due to the heat and mass transport resistances in the particle film layer. It is further demonstrated that the proposed model can be utilized as a versatile design tool for catalytic reactor development and optimization.