Diffusion in Liquids: Equilibrium Molecular Simulations and Predictive Engineering Models

The aim of this thesis is to study multicomponent diffusion in liquids using Molecular Dynamics (MD) simulations. Diffusion plays an important role in mass transport processes. In binary systems, mass transfer processes have been studied extensively using both experiments and molecular simulations. From a practical point of view, systems consisting more than two components are more interesting. However, experimental and simulation data on transport diffusion for such systems are scarce. Therefore, a more detailed knowledge on mass transfer in multicomponent systems is required. The presence of multiple components in a system introduces difficulties in studying diffusion in experiments. Investigating the concentration dependence of diffusion coefficients seriously increases the required experimental effort. In this thesis, we will use MD simulation based on classical force fields to study multicomponent diffusion in liquids. Diffusion can be described using both Fick and Maxwell- Stefan (MS) diffusion coefficients. Experiments provide Fick diffusion coefficients while simulations usually provide MS diffusion coefficients. Fick and MS diffusivities are related via the matrix of thermodynamic factors. A brief survey on methods for studying liquid diffusion and their limitations is presented in chapter 1 In chapter 2, we study the diffusion in the ternary system n-hexane-cyclohexanetoluene. The existing models for predicting MS diffusivities at finite concentrations (i:e: the Vignes equation) as well as the predictions at infinite dilution (i:e: predictions of Ðxk!1 i j using the so-called WK, KT, VKB, DKB and RS models) are tested using MD simulations. We find that (1) the Vignes equation only results in reasonable predictions for MS diffusivities yielding differences of 13% compared to the actual diffusion coefficients; (2) the best predictive model (the KT model) for calculating MS diffusivities at infinite dilution results in differences of 8% compared to the actual diffusion coefficients. It is important to note that the differences of 8% can be a coincidence since KT model is empirical and does not have a theoretical basis. This limitation makes KT model unreliable for other systems. To overcome the difficulties in predicting ternary MS diffusivities at infinite dilution (i:e: Ðxk!1 i j ), we derive the so-called LBV model based on the Onsager relations. MS diffusivities at infinite dilution can be expressed in terms of binary and pure component self-diffusivities and integrals over velocity cross-correlation functions. By neglecting the latter terms, we obtain the LBV model. In chapter 3, the LBV model is validated for WCA fluids and the ternary systems n-hexane-cyclohexane-toluene and methanol-ethanol-water. We find that: (1) for ideal mixtures i:e: the WCA system, as well as the n-hexane-cyclohexane-toluene system, the LBV model is accurate and superior compared to the existing models for predicting ternary MS diffusivities at infinite dilution (i:e: the WK, KT, VKB, DKB and RS models); (2) in mixtures containing associating components, i:e: the ethanol-methanol-water system, the LBV model indicates that in this system the integrals over velocity cross-correlation functions are important and cannot be neglected. Moreover, the LBV model provides an explanation why the MS diffusivity describing the friction between adsorbed components in a porous material is usually very large. In chapter 4, we focus on describing the values of MS diffusivities at finite concentration. A multicomponent Darken model for describing the concentration dependence of MS diffusivities is derived from linear response theory and the Onsager relations. In addition, a predictive model for the required self-diffusivities in the mixture is proposed leading to the so-called predictive Darken-LBV model. We compare our novel models to the existing generalized Vignes equation and the generalized Darken equation. Two systems are considered: (1) ternary and quaternary WCA systems; (2) the ternary system n-hexane-cyclohexane-toluene. Our results show that in all studied systems, our predictive Darken-LBV equation describes the concentration dependence better than the existing models. The physically-based Darken-LBV model provides a sound and robust framework for prediction of MS diffusion coefficients in multicomponent mixtures. In chapter 5, diffusion in more complex ionic liquid (IL) systems are investigated. Previous research reported in literature has largely focused on self-diffusion in ILs. For practical applications, mutual (transport) diffusion is by far more important than self-diffusion. We compute the MS diffusivities in binary systems containing 1-alkyl- 3- methylimidazolium chloride (CnmimCl), water and/or dimethyl sulfoxide (DMSO). The dependence of MS diffusivities on mixture composition are investigated. Our results show that: (1) For solutions of ILs in water and DMSO, self-diffusivities decrease strongly with increasing IL concentration. For the system DMSO-IL, an exponential decay is observed for this; (2) For both water-IL and DMSO-IL, MS diffusivities vary by a factor of 10 within the concentration range which is still significantly smaller than the variation of the self diffusivities; (3) The MS diffusivities of the investigated IL are almost independent of the alkyl chain length; (4) ILs stay in a form of isolated ions in CnmimCl-H2O mixtures, however, dissociation into ions is much less observed in CnmimCl-DMSO systems. This has a large effect on the concentration dependence of MS diffusivities; (5) The LBV model for predicting the MS diffusivity at infinite dilution described in chapter 3 suggests that velocity cross-correlation functions in ionic liquids cannot be neglected and that the dissociation of ILs into ion pairs has a very strong influence on diffusion. In experiments, Fick diffusion coefficients are measured and molecular simulation usually provides MS diffusivities. These approaches are related via the matrix of thermodynamic factors which is usually known only with large uncertainties. This leaves a gap between theory and application. In chapter 6, we introduce a consistent and efficient framework for the determination of Fick diffusivities in liquid mixtures directly from equilibrium MD simulations by calculating both the thermodynamic factor and the MS diffusivity. 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 based on a consistent molecular picture. In chapter 7, we validate our method for computing Fick diffusivities using equilibrium MD simulations for the ternary system chloroform - acetone - methanol. Even though a simple molecular model is used (i:e: rigid molecules that interact by Lennard-Jones and electrostatic interactions), the computed thermodynamic factors are in close agreement with experiments. Validation data for diffusion coefficients is only available for two binary sub-systems. In these binary systems, MD results and experiments do agree well. For the ternary system, the computed thermodynamic factors using Molecular Dynamics simulation are in excellent agreement with experimental data and better than the ones obtained from COSMO-SAC calculations. Therefore, we expect that the computed Fick diffusivities should also be comparable with experiments. Our results suggest that the presented approach allows for an efficient and consistent prediction of multicomponent Fick diffusion coefficients from MD simulations. Now, a tool for guiding experiments and interpreting multicomponent mass transfer is available