Modelling and Simulation in Life and Materials Sciences
http://hdl.handle.net/20.500.11824/15
2023-09-30T12:23:26ZPartition Constant of Binary Mixtures for the Equilibrium between a Bulk and a Confined Phase
http://hdl.handle.net/20.500.11824/1585
Partition Constant of Binary Mixtures for the Equilibrium between a Bulk and a Confined Phase
Cortés, H.E.; Scherlis, D. A.; Factorovich, M. H.
It is well-known that the thermodynamic, kinetic and structural properties of fluids, and in particular of water and its solutions, can be drastically affected in nanospaces. A possible consequence of nanoscale confinement of a solution is the partial segregation of its components. Thereby, confinement in nanoporous materials (NPM) has been proposed as a means for the separation of mixtures. In fact, separation science can take great advantage of NPM due to the tunability of their properties as a function of nanostructure, morphology, pore size, and surface chemistry. Alcohol-water mixtures are in this context among the most relevant systems. However, a quantitative thermodynamic description allowing for the prediction of the segregation capabilities as a function of the material-solution characteristics is missing. In the present study we attempt to fill this vacancy, by contributing a thermodynamic treatment for the calculation of the partition coefficient in confinement. Combining the multilayer adsorption model for binary mixtures with the Young equation, we conclude that the liquid-vapor surface tension and the contact angle of the pure substances can be used to predict the separation ability of a particular material for a given mixture to a semiquantitative extent. Moreover, we develop a Kelvin-type equation that relates the partition coefficient to the radius of the pore, the contact angle, and the liquid-vapor surface tensions of the constituents. To assess the validity of our thermodynamic formulation, coarse grained molecular dynamics simulations were performed on models of alcohol-water mixtures confined in cylindrical pores. To this end, a coarse-grained amphiphilic molecule was parametrized to be used in conjunction with the mW potential for water. This amphiphilic model reproduces some of the properties of methanol such as enthalpy of vaporization and liquid-vapor surface tension, and the minimum of the excess enthalpy for the aqueous solution. The partition coefficient turns out to be highly dependent on the molar fraction, on the interaction between the components and the confining matrix, and on the radius of the pore. A remarkable agreement between the theory and the simulations is found for pores of radius larger than 15 Å.
2022-09-15T00:00:00ZExistence, Uniqueness, and Numerical Modeling of Wine Fermentation Based on Integro-Differential Equations
http://hdl.handle.net/20.500.11824/1502
Existence, Uniqueness, and Numerical Modeling of Wine Fermentation Based on Integro-Differential Equations
Schenk, C.; Schulz, V.
Predictive modeling is key for saving time and resources in manufacturing processes such as fermentation arising in food and chemical manufacturing. To make reliable predictions, realistic models representing the most important process features are required. Several models describing the white wine fermentation process already exist. However, all of these models lack a combination of features, such as the importance of oxygen at the beginning of the process, the consumption of sugar due to yeast activity, and the toxicity of alcohol on the yeast cells combined with the single-cell yeast dynamics. This work introduces a new population balance model representing all these features in one model. It is based on a system of highly nonlinear weakly hyperbolic partial/ordinary integro-differential equations which poses a number of theoretical and numerical challenges. This paper increases the understanding of the latter and of the process itself by combining theoretical with numerical investigations. Existence and uniqueness of solutions to a simplified problem are studied based on semigroup theory. For the numerical solution of the problem, a numerical methodology based on a finite volume scheme combined with a time implicit scheme is derived. The impact of the initial cell distribution on the dynamics is studied. The detailed model is compared to a simpler model based on ordinary differential equations. The observed differences for different initial cell distributions and distinct models turn out to be smaller than expected. The outcomes of this paper are specifically relevant for applied mathematicians, winemakers, and process engineers.
2022-01-01T00:00:00ZNumerical Regge pole analysis of resonance structures in state-to-state reactive differential cross sections
http://hdl.handle.net/20.500.11824/1491
Numerical Regge pole analysis of resonance structures in state-to-state reactive differential cross sections
Akhmatskaya, E.; Sokolovski, D.
This is the third (and the last) code in a collection of three programs [Sokolovski et al. (2011), Akhmatskaya et al. (2014)] dedicated to the analysis of numerical data, obtained in an accurate simulation of an atom-diatom chemical reaction. Our purpose is to provide a detailed description of a FORTRAN code for complex angular momentum (CAM) analysis of the resonance effects in reactive angular scattering [for CAM analysis of integral reactive cross sections see [Akhmatskaya et al. (2014)]. The code evaluates the contributions of a Regge trajectory (or trajectories) to a differential cross section in a specified range of energies. The contribution is computed with the help of the methods described in [Dobbyn et al. (1999), Sokolovski and Msezane (2004), Sokolovski et al. (2007)]. Regge pole positions and residues are obtained by analytically continuing S-matrix element, calculated numerically for the physical integer values of the total angular momentum, into the complex angular momentum plane using the PADE_II program [Sokolovski et al. (2011)]. The code represents a reactive scattering amplitude as a sum of the components corresponding to a rapid “direct” exchange of the atom, and the various scenarios in which the reactants form long-lived intermediate complexes, able to complete several rotations before breaking up into products. The package has been successfully tested on the representative models, as well as the F + H2→HF+H benchmark reaction. Several detailed examples are given in the text.
2022-04-19T00:00:00ZOn the interfacial lithium dynamics in Li7La3Zr2O12:poly(ethylene oxide) (LiTFSI) composite polymer-ceramic solid electrolytes under strong polymer phase confinement
http://hdl.handle.net/20.500.11824/1479
On the interfacial lithium dynamics in Li7La3Zr2O12:poly(ethylene oxide) (LiTFSI) composite polymer-ceramic solid electrolytes under strong polymer phase confinement
Rincón, M.; García, F.; Cortés, H.E.; Carrasco, J.; Akhmatskaya, E.
A better molecular-level understanding of Li+ diffusion through ceramic/polymer interfaces is key to designing high-performance composite solid-state electrolytes for all-solid-state batteries. By considering as a case study a composite electrolyte constituted by Li+ conductive Ga3+ doped-Li7La3Zr2O12 (LLZO) garnet fillers embedded within a poly(ethylene oxide) and lithium bis(trifluoromethanesulfonyl) imide polymer matrix (PEO(LiTFSI)), we investigate Li+ interfacial dynamics at conditions of high polymer confinement, with large filler particles in a fully amorphous polymer phase. Such confinement scenario is aimed to capture the conditions near the percolation threshold, at which conductivity enhancement is often reported. Using molecular dynamics simulations combined with the generalized shadow hybrid Monte Carlo method and umbrella sampling calculations, we explain why the hopping towards the polymer phase of the Li+ sitting on the LLZO surface is thermodynamically hindered while hopping of Li+ from the polymer to the LLZO is kinetically slowed-down by rigidified polymer near the interface. In addition, we demonstrate how the overlap of LLZO-bound polymer chains at high confinement leads to a decrease of Li+ diffusivity within the interstitial space. We put forward that these insights are relevant to interpreting the variation of ionic conductivity as a function of volume fraction and filler particle sizes also below the glass transition temperature of the polymer, at the typical operating conditions of lithium-ion batteries.
2022-05-27T00:00:00Z