(7v) Quantitatively Reliable Molecular Modeling and Simulation of Vapor-Liquid Equilibria

To reach the quantitative precision required in engineering applications, molecular force-field models need to be adjusted to experimental data for diverse thermodynamic properties. This implies the presence of multiple conflicting objectives in the optimization task, making it difficult to achieve an optimal agree­ment for the different properties with a single model parameterization. In the present work, this pro­blem is solved by computing and analysing the Pareto set, i.e. the set of all rational compromises between objectives, from which a user can choose the one which fits best to a particular application scenario.

For a variety of low-molecular fluids, two-center Lennard-Jones plus point-quadrupole (2CLJQ) and two-center Lennard-Jones plus point-dipole (2CLJD) models are applied to describe bulk and interfacial properties of pure-component vapor-liquid equilibria. Computing the surface tension at a high accuracy by molecular dynamics simulation requires a massively-parallel simulation environment with a numerically efficient long-range correction for planar interfaces [1, 2]. For this purpose, a highly scalable molecular dynamics code is used: ls1 mardyn [3]. Literature models, which were adjusted to bulk properties, but not to interfacial properties, are validated against the surface tension of real fluids. These models, on average, overestimate the surface tension by 15 to 20% [4, 5].

On this basis, the following optimization task is studied: For ten different pure fluids, the 2CLJQ model class is explored as a whole, and by computing the Pareto set, it is evaluated to what extent the vapor pressure, the liquid density, and the surface tension can be accurately modelled by one and the same model. In various cases, it is found that any pair of two out of the three pro­perties can be described by a 2CLJQ model with an accuracy close to the accumulated error from ex­periment and simulation, but it is impossible to reconcile all three properties to that level of accuracy [6].

It is computationally expensive to determine the Pareto set. Brute force methods usually cannot be ap­plied even for moderate dimensionalities of the objective and parameter spaces, whereas Monte Carlo methods often yield poor results. For the present study, two algorithms are combined: Sandwiching and hyperboxing. This is computationally efficient and enables a specification of the numerical error, illustrating that multicriteria optimization provides a versatile framework for developing thermodynamic models. User-friendly visualization techniques for the Pareto set are discussed, including a novel approach based on self-organizing patch plots [6].

[1] S. Werth, G. Rutkai, J. Vrabec, M. Horsch, and H. Hasse, Molecular Physics 112 (2014) 2227-2234.
[2] S. Werth, M. Horsch, and H. Hasse, Molecular Physics 113 (2015) 3750-3756.
[3] A. Heinecke, W. Eckhardt, M. Horsch, and H.-J. Bungartz, Supercomputing for Molecular Dynamics Simulations, Springer, Heidelberg (2015).
[4] S. Werth, K. Stöbener, P. Klein, K.-H. Küfer, M. Horsch, and H. Hasse, Chemical Engineering Science 121 (2015) 110-117.
[5] S. Werth, M. Horsch, and H. Hasse, Journal of Chemical Physics 144 (2016) 054702.
[6] K. Stöbener, P. Klein, M. Horsch, K. Küfer, and H. Hasse, Fluid Phase Equilibria 411 (2016) 33-42.

Research Interests:

Computational Molecular Engineering (see above).

Teaching Interests:  

Courses presently taught by Martin Horsch at the University of Kaiserslautern, Germany:

Molecular Thermodynamics (in German): Lecture covering statistical mechanics (ensemble, phase space, partition function, analytically tractable problems) as well as molecular modeling and simulation (Monte Carlo and molecular dynamics, computation of thermodynamic properties).

Molecular Simulation (in German): In this "computer laboratory" course, the students implement and apply molecular simulation methods under individual supervision. This is accompanied by a lecture concerning the simulation of phase equilibria (entropic quantities, Grand Equilibrium, interfacial properties) and non-equilibria (fluctuation and dissipation, transition states, work done by small systems), extending the knowledge from Molecular Thermodynamics.

Molecular Modeling (in English): Compact course within the international graduate school IRTG 2057 "Physical Modeling for Virtual Manufacturing Systems and Processes" (University of Kaiserslautern, UC Berkeley, and UC Davis), covering basic molecular modeling and simulation approaches and relating them to other methods in computational engineering.

Martin Horsch was positively evaluated as a Junior Professor in 2014, and following a training in didactics, he obtained the Rhineland-Palatinate Certificate for University Didactics in 2015. Preceding his faculty appointment, he served as a teaching assistant in Mechanical Engineering (Molecular Thermodynamics) and Computer Science (Theoretical Computer Science II and III) at the University of Stuttgart, and in Mechanical Engineering at the University of Paderborn (Thermodynamics II and Refrigeration Technology).