Transport coefficients for ion and solvent coupling. The case of the lithium-ion battery electrolyte.

Transport properties are essential for the understanding and modeling of electrochemical cells, in particular complex systems like lithium-ion batteries. In this study, we demonstrate how a certain degree of freedom in the choice of variables allows us to efficiently determine a complete set of transport properties. We apply the entropy production invariance condition to different sets of electrolyte variables and obtain a general set of formulas. We demonstrate the application of these formulas to an electrolyte typical for lithium-ion batteries, 1M lithium hexafluoro-phosphate in a 1:1 wt. % mixture of ethylene and diethyl carbonates. While simplifications can be introduced, they provide inadequate predictions of conductivity and transport numbers, and we argue that a full matrix of Onsager coefficients is needed for adequate property predictions. Our findings highlight the importance of a complete set of transport coefficients for accurate modeling of complex electrochemical systems and the need for careful consideration of the choice of variables used to determine these properties.

Thermo-osmotic pressure and resistance to mass transport in a vapor-gap membrane.

We have investigated the transport of fluid through a vapor-gap membrane. The transport due to a membrane temperature difference was investigated under isobaric as well as non-isobaric conditions. Such a concept is relevant for water cleaning and power production purposes. A coarse-grained water model was used for modelling transport through pores of different diameters and lengths. The wall-fluid interactions were set so as to mimic hydrophobic interactions between water and membrane. The mass transport through the membrane scaled linearly with the applied temperature difference. Soret equilibria were obtained when the thermo-osmotic pressure was 18 bar K-1. The state of the Soret equilibrium did not depend on the pore size or pore length as expected. We show that the Soret equilibrium cannot be sustained by a gradient in vapor pressure. The fluxes of heat and mass were used to compute the total resistances to the transport of heat and mass.

Cooperative insertion of CO2 in diamine-appended metal-organic frameworks.

The process of carbon capture and sequestration has been proposed as a method of mitigating the build-up of greenhouse gases in the atmosphere. If implemented, the cost of electricity generated by a fossil fuel-burning power plant would rise substantially, owing to the expense of removing CO2 from the effluent stream. There is therefore an urgent need for more efficient gas separation technologies, such as those potentially offered by advanced solid adsorbents. Here we show that diamine-appended metal-organic frameworks can behave as 'phase-change' adsorbents, with unusual step-shaped CO2 adsorption isotherms that shift markedly with temperature. Results from spectroscopic, diffraction and computational studies show that the origin of the sharp adsorption step is an unprecedented cooperative process in which, above a metal-dependent threshold pressure, CO2 molecules insert into metal-amine bonds, inducing a reorganization of the amines into well-ordered chains of ammonium carbamate. As a consequence, large CO2 separation capacities can be achieved with small temperature swings, and regeneration energies appreciably lower than achievable with state-of-the-art aqueous amine solutions become feasible. The results provide a mechanistic framework for designing highly efficient adsorbents for removing CO2 from various gas mixtures, and yield insights into the conservation of Mg(2+) within the ribulose-1,5-bisphosphate carboxylase/oxygenase family of enzymes.

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 [Hill, J. Chem. Phys., 1962, 36, 3182], that the surface satisfies the thermodynamics of a flat surface as described by Gibbs [Gibbs, The Scientific Papers of J. Willard Gibbs, Volume 1, Thermodynamics, Ox Bow Press, Woodbridge, Connecticut, 1993]. The Small System Method (SSM), first derived by Schnell et al. [Schnell et al., J. Phys. Chem. B, 2011, 115, 10911], is extended and used to analyze simulation data on small systems of water. We simulate water as an example to illustrate the method, using TIP4P/2005 and other models, and compute the isothermal compressibility and thermodynamic factor. We are able to retrieve the experimental value of the bulk phase compressibility within 2%, and show that the compressibility of nanosized volumes increases by up to a factor of two as the number of molecules in the volume decreases. The value for a tetrahedron, cube, sphere, polygon, etc. can be predicted from the same scaling law, as long as second order effects (nook and corner effects) are negligible. Lastly, we propose a general formula for finite reservoir correction to fluctuations in subvolumes.

Nanoporous Materials Can Tune the Critical Point of a Pure Substance.

Molecular simulations and NMR relaxometry experiments demonstrate that pure benzene or xylene confined in isoreticular metal-organic frameworks (IRMOFs) exhibit true vapor-liquid phase equilibria where the effective critical point may be reduced by tuning the structure of the MOF. Our results are consistent with vapor and liquid phases extending over many MOF unit cells. These results are counterintuitive since the MOF pore diameters are approximately the same length scale as the adsorbate molecules. As applications of these materials in catalysis, separations, and gas storage rely on the ability to tune the properties of adsorbed molecules, we anticipate that the ability to systematically control the critical point, thereby preparing spatially inhomogeneous local adsorbate densities, could add a new design tool for MOF applications.

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 obtained with the new method are in excellent agreement with those from previous methods. Especially for modeling chemical reactions, our method can be a valuable tool for determining reaction enthalpies directly from a single MD simulation.

Adsorption of an Ideal Gas on a Small Spherical Adsorbent.

The ideal gas model is an important and useful model in classical thermodynamics. This remains so for small systems. Molecules in a gas can be adsorbed on the surface of a sphere. Both the free gas molecules and the adsorbed molecules may be modeled as ideal for low densities. The adsorption energy, Us, plays an important role in the analysis. For small adsorbents this energy depends on the curvature of the adsorbent. We model the adsorbent as a sphere with surface area Ω=4πR2, where R is the radius of the sphere. We calculate the partition function for a grand canonical ensemble of two-dimensional adsorbed phases. When connected with the nanothermodynamic framework this gives us the relevant thermodynamic variables for the adsorbed phase controlled by the temperature T, surface area Ω, and chemical potential µ. The dependence of intensive variables on size may then be systematically investigated starting from the simplest model, namely the ideal adsorbed phase. This dependence is a characteristic feature of small systems which is naturally expressed by the subdivision potential of nanothermodynamics. For surface problems, the nanothermodynamic approach is different, but equivalent to Gibbs' surface thermodynamics. It is however a general approach to the thermodynamics of small systems, and may therefore be applied to systems that do not have well defined surfaces. It is therefore desirable and useful to improve our basic understanding of nanothermodynamics.

Cassie-Baxter and Wenzel States and the Effect of Interfaces on Transport Properties across Membranes.

Mass transfer across a liquid-repelling gas permeable membrane is influenced by the state(s) of the liquid-vapor interface(s) on the surface of the membrane, the pore geometry, and the solid-fluid interactions inside the membrane. By tuning the different local contributions, it is possible to enhance the temperature difference-driven mass flux across the membrane for a constant driving force. Non-equilibrium molecular dynamics simulations were used to simulate a temperature difference-driven mass flux through a gas permeable membrane with the evaporating liquid on one side and the condensing liquid on the other. Both sides were simulated for Wenzel- and Cassie-Baxter-like states. The interaction between the fluid and the solid inside the gas permeable membrane varied between the wetting angles of θ = 125° and θ = 103°. For a constant driving force, the Cassie-Baxter state led to an increased mass flux of almost 40% in comparison to the Wenzel state (given a small pore resistance). This difference was caused by an insufficient supply of vapor particles at the pore entrance in the Wenzel state. The difference between the Wenzel and Cassie-Baxter states decreased with increasing resistance of the pore. The condensing liquid-vapor interface area contributed in the same manner to the overall transport resistance as the evaporating liquid-vapor interface area. A higher repulsion between the fluid and the solid inside the membrane decreased the overall resistance.

Kirkwood-Buff Integrals Using Molecular Simulation: Estimation of Surface Effects.

Kirkwood-Buff (KB) integrals provide a connection between microscopic properties and thermodynamic properties of multicomponent fluids. The estimation of KB integrals using molecular simulations of finite systems requires accounting for finite size effects. In the small system method, properties of finite subvolumes with different sizes embedded in a larger volume can be used to extrapolate to macroscopic thermodynamic properties. KB integrals computed from small subvolumes scale with the inverse size of the system. This scaling was used to find KB integrals in the thermodynamic limit. To reduce numerical inaccuracies that arise from this extrapolation, alternative approaches were considered in this work. Three methods for computing KB integrals in the thermodynamic limit from information of radial distribution functions (RDFs) of finite systems were compared. These methods allowed for the computation of surface effects. KB integrals and surface terms in the thermodynamic limit were computed for Lennard-Jones (LJ) and Weeks-Chandler-Andersen (WCA) fluids. It was found that all three methods converge to the same value. The main differentiating factor was the speed of convergence with system size L. The method that required the smallest size was the one which exploited the scaling of the finite volume KB integral multiplied by L. The relationship between KB integrals and surface effects was studied for a range of densities.

Two-Phase Equilibrium Conditions in Nanopores.

It is known that thermodynamic properties of a system change upon confinement. To know how, is important for modelling of porous media. We propose to use Hill's systematic thermodynamic analysis of confined systems to describe two-phase equilibrium in a nanopore. The integral pressure, as defined by the compression energy of a small volume, is then central. We show that the integral pressure is constant along a slit pore with a liquid and vapor in equilibrium, when Young and Young-Laplace's laws apply. The integral pressure of a bulk fluid in a slit pore at mechanical equilibrium can be understood as the average tangential pressure inside the pore. The pressure at mechanical equilibrium, now named differential pressure, is the average of the trace of the mechanical pressure tensor divided by three as before. Using molecular dynamics simulations, we computed the integral and differential pressures, p ^ and p, respectively, analysing the data with a growing-core methodology. The value of the bulk pressure was confirmed by Gibbs ensemble Monte Carlo simulations. The pressure difference times the volume, V, is the subdivision potential of Hill, ( p - p ^ ) V = ϵ . The combined simulation results confirm that the integral pressure is constant along the pore, and that ϵ / V scales with the inverse pore width. This scaling law will be useful for prediction of thermodynamic properties of confined systems in more complicated geometries.

Correction: CO2 induced phase transitions in diamine-appended metal-organic frameworks.

[This corrects the article DOI: 10.1039/C5SC01828E.].

CO2 induced phase transitions in diamine-appended metal-organic frameworks.

Using a combination of density functional theory and lattice models, we study the effect of CO2 adsorption in an amine functionalized metal-organic framework. These materials exhibit a step in the adsorption isotherm indicative of a phase change. The pressure at which this step occurs is not only temperature dependent but is also metal center dependent. Likewise, the heats of adsorption vary depending on the metal center. Herein we demonstrate via quantum chemical calculations that the amines should not be considered firmly anchored to the framework and we explore the mechanism for CO2 adsorption. An ammonium carbamate species is formed via the insertion of CO2 into the M-Namine bonds. Furthermore, we translate the quantum chemical results into isotherms using a coarse grained Monte Carlo simulation technique and show that this adsorption mechanism can explain the characteristic step observed in the experimental isotherm while a previously proposed mechanism cannot. Furthermore, metal analogues have been explored and the CO2 binding energies show a strong metal dependence corresponding to the M-Namine bond strength. We show that this difference can be exploited to tune the pressure at which the step in the isotherm occurs. Additionally, the mmen-Ni2(dobpdc) framework shows Langmuir like behavior, and our simulations show how this can be explained by competitive adsorption between the new model and a previously proposed model.

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.

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 significant and depends on 1/L, where L is the length of the small system in one dimension. By considering a reservoir with an ensemble of embedded small systems, we can use the scaling arising from surface effects to determine properties for macroscopic systems by extrapolation. We demonstrate this method for the WCA and LJ fluids, as well a for a heterogeneous system, i.e., argon adsorbed in silicalite-1 zeolite.

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 factor to convert MS into Fick diffusivities and vice versa, however, is usually difficult to extract from both simulations and experiments leaving a gap between theory and application. Here, we employ our novel method to compute the thermodynamic factor from small-scale density fluctuations in equilibrium MD simulations [Chem. Phys. Lett.2011, 504, 199-201]. Previously, this method was developed and validated for molecules with single interaction sites only. In this work, we applied this method to acetone-methanol and acetone-tetrachloromethane liquid mixtures and show that the method also works well in these more complex systems. This provides the missing step to extract Fick diffusion coefficients directly from equilibrium MD simulations. The computed Fick diffusivities of acetone-methanol and acetone-tetrachloromethane mixtures are in excellent agreement with experimental values. The suggested framework thus provides an efficient route to model diffusion in liquids on the basis of a consistent molecular picture.