Determination of statistically reliable transport diffusivities from molecular dynamics simulation

Keffer, David J.; Edwards, Brian J.; Adhangale, Parag

doi:10.1016/j.jnnfm.2004.01.014

Cited by 26 publications

(35 citation statements)

References 23 publications

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“…In all simulations, at least 1000 points along the trajectory were saved. From simulations one could only obtain statistically reliable MSDs of about half of the time of the simulation, before the diminishing amount of data in the correlation function rendered the rest of the MSD unacceptably noisy [27]. Therefore we calculated the selfdiffusivity coefficients in a range of observation times running from t sim /4 to t sim /2, where t sim is the simulation duration.…”

Section: Confined Random Walk Simulationsmentioning

confidence: 99%

Applications of a general random-walk theory for confined diffusion

et al. 2011

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A general random walk theory for diffusion in the presence of nanoscale confinement is developed and applied. The random-walk theory contains two parameters describing confinement: a cage size and a cage-to-cage hopping probability. The theory captures the correct nonlinear dependence of the mean square displacement (MSD) on observation time for intermediate times. Because of its simplicity, the theory also requires modest computational requirements and is thus able to simulate systems with very low diffusivities for sufficiently long time to reach the infinite-time-limit regime where the Einstein relation can be used to extract the self-diffusivity. The theory is applied to three practical cases in which the degree of order in confinement varies. The three systems include diffusion of (i) polyatomic molecules in metal organic frameworks, (ii) water in proton exchange membranes, and (iii) liquid and glassy iron. For all three cases, the comparison between theory and the results of molecular dynamics (MD) simulations indicates that the theory can describe the observed diffusion behavior with a small fraction of the computational expense. The confined-random-walk theory fit to the MSDs of very short MD simulations is capable of accurately reproducing the MSDs of much longer MD simulations. Furthermore, the values of the parameter for cage size correspond to the physical dimensions of the systems and the cage-to-cage hopping probability corresponds to the activation barrier for diffusion, indicating that the two parameters in the theory are not simply fitted values but correspond to real properties of the physical system.

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Section: Confined Random Walk Simulationsmentioning

confidence: 99%

Applications of a general random-walk theory for confined diffusion

et al. 2011

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“…MaxwellStefan diffusivities can be computed directly from molecular simulations [5][6][7][8][9][10][11][12][13][14][15] and predictive models for Ð ij are available that work reasonably well for systems in which molecules do not strongly interact [7]. It is possible to relate both Fick's law and the MaxwellStefan theory, since they both describe the same diffusion process [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

A direct method for calculating thermodynamic factors for liquid mixtures using the Permuted Widom test particle insertion method

et al. 2012

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Understanding mass transport in liquids by mutual diffusion is an important topic for many applications in chemical engineering. The reason for this is that diffusion is often the rate limiting step in chemical reactors and separators. In multicomponent liquid mixtures, transport diffusion can be described by both generalized Fick's law and the Maxwell-Stefan theory. The Maxwell-Stefan and Fick approaches in an n-component system are related by the so-called thermodynamic factor [R. Taylor and H.A. Kooijman, Chem. Eng. Commun, 102, 87 (1991)]. As Fick diffusivities can be measured in experiments and Maxwell-Stefan diffusivities can be obtained from molecular simulations/theory, the thermodynamic factors bridge the gap between experiments and molecular simulations/theory. It is therefore desirable to be able to compute thermodynamic factors from molecular simulations. Unfortunately, presently used simulation techniques for computing thermodynamic factors are inefficient and often require numerical differentiation of simulation results. In this work, we propose a modified version of the Widom test-particle method to compute thermodynamic factors from a single simulation. This method is found to be more efficient than the conventional Widom test particle insertion method combined with numerical differentiation of simulation results. The approach is tested for binary systems consisting of Lennard-Jones particles. The thermodynamic factors computed from the simulation and from numerically differentiating the activity coefficients obtained from the conventional Widom test particle insertion method are in excellent agreement.

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“…• Newtonian Keffer et al (2004) Due to the limitations of the accessible time frames, transport coefficients (viscosities, diffusivities) are calculated at very high shear rates far beyond those applicable experimentally…”

Section: Rheologymentioning

confidence: 99%

In Silico Prediction of Food Properties: A Multiscale Perspective

2022

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Several open software packages have popularized modeling and simulation strategies at the food product scale. Food processing and key digestion steps can be described in 3D using the principles of continuum mechanics. However, compared to other branches of engineering, the necessary transport, mechanical, chemical, and thermodynamic properties have been insufficiently tabulated and documented. Natural variability, accented by food evolution during processing and deconstruction, requires considering composition and structure-dependent properties. This review presents practical approaches where the premises for modeling and simulation start at a so-called “microscopic” scale where constituents or phase properties are known. The concept of microscopic or ground scale is shown to be very flexible from atoms to cellular structures. Zooming in on spatial details tends to increase the overall cost of simulations and the integration over food regions or time scales. The independence of scales facilitates the reuse of calculations and makes multiscale modeling capable of meeting food manufacturing needs. On one hand, new image-modeling strategies without equations or meshes are emerging. On the other hand, complex notions such as compositional effects, multiphase organization, and non-equilibrium thermodynamics are naturally incorporated in models without linearization or simplifications. Multiscale method’s applicability to hierarchically predict food properties is discussed with comprehensive examples relevant to food science, engineering and packaging. Entropy-driven properties such as transport and sorption are emphasized to illustrate how microscopic details bring new degrees of freedom to explore food-specific concepts such as safety, bioavailability, shelf-life and food formulation. Routes for performing spatial and temporal homogenization with and without chemical details are developed. Creating a community sharing computational codes, force fields, and generic food structures is the next step and should be encouraged. This paper provides a framework for the transfer of results from other fields and the development of methods specific to the food domain.

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Determination of statistically reliable transport diffusivities from molecular dynamics simulation

Cited by 26 publications

References 23 publications

Applications of a general random-walk theory for confined diffusion

Applications of a general random-walk theory for confined diffusion

A direct method for calculating thermodynamic factors for liquid mixtures using the Permuted Widom test particle insertion method

In Silico Prediction of Food Properties: A Multiscale Perspective

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