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42201-AC9
Application of Beyond Equilibrium Molecular Dynamics Simulation to Generate Statistically Reliable Mass Transport Properties
In this work, our goal was to develop a practical, reliable and computationally efficient method for determining mass transport coefficients (Fickian diffusivities) from molecular dynamics simulation that are intrinsically compatible with continuum-level descriptions of mass transport. To achieve this end, we began with a description of the mass, composition and momentum balances of a binary Lennard-Jones liquid under isothermal conditions. It is a relatively straightforward procedure to provide the temperature, diffusivity and viscosity and plot the steady-state density, mass fraction and velocity profiles. However, if these profiles are to be mapped onto a molecular-level simulation, then they must be periodic. In the absence of any external forces, the only boundary conditions that yield a periodic system are those in which all of the profiles are constant. This default case is unacceptable since it will not allow us to observe any diffusional effect. Therefore, we created an implemented a fictitious potential field that generated a sinusoidal profile on the density of component A. While the density of A was now both variable and periodic, the density and velocity were now not periodic. We then iteratively determined a potential field acting on component B that resulted in periodic density and velocity as well. At this point, we have a system in the presence of an artificial external field that has non-constant but periodic profiles in the density, composition and velocity. It is crucial to understand that the variation in composition, required to extract a diffusivity, necessarily mandates a variation in density and velocity, thus significantly complicating the system, in terms of imposing this profile on a molecular-level simulation.
One of the key issues at the macroscopic level of description is that the net (or laboratory) velocity of component A is composed of a convective (or center-of-mass) component, a diffusive component, and a component due to the external field. It is necessary to carefully isolate each of these contributions because, in the molecular dynamics simulation, we will require peculiar velocities of each individual particle in order to compute the temperature via the equipartition theorem. We must also separate the diffusive component from all other components so that we can extract a diffusivity from the MD simulation. We have carefully performed this decomposition of velocities so that all of the pieces (lab, convective, diffusive, external and peculiar) are individually known.
We then proceeded to the molecular-level simulations, in which we performed molecular dynamics simulation in the NVT ensemble. Since all of the continuum level equations were rendered in dimensionless form, it was a straightforward procedure to impose the two external potential fields in the simulation. These external fields, while artificial, are the same as were used in the macroscopic simulations. They, therefore, should generate the same profiles at the molecular-level as they did at the macroscopic level. Our procedure was to measure the composition gradient and the diffusive flux directly from the MD simulations and to determine the diffusivity by inserting these properties into Fick's Law. If the diffusivity matched that used in the macroscopic simulation, then the procedure was self-consistent. Otherwise, we would iterate and resolve the macroscopic simulation using the new diffusivity delivered by the MD simulation.
At present we are dealing with technical details associated with the fact that our macroscopic system was not exactly periodic, only approximately periodic due to the iterative nature in which the external potential field on B was determined. This slight aperiodicity which appeared to be insignificant at the macroscopic scale, appears to be important at the molecular-level. We are working to obtain a more periodic curve so that we can extract reliable diffusivities from the MD simulations.
Four people have participated in this work, the PI, David Keffer, a graduate student, Ruichang Xiong, and two undergraduate researchers, Rebecca Empting and Ian Morris. For the graduate student and the two undergraduate researchers, this project has taught them numerous skills, including (i) the solution of combined mass and momentum balances at the continuum level, (ii) molecular dynamics simulation, (iii) how to program, and (iv) how to perform research in an objective and methodical procedure so that one can answer the questions that have been posed. All three of the students have grown terrifically in competence during the past year, due to their activity on this project.
Once perfected, this method will provide a completely integrated multiscale (continuum/molecular) procedure for the self-consistent and statistically reliable generation of Fickian diffusivities, which was the project goal.
