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1 results

  • 8 - Microscopic Models of Brownian Motion

  • Radek Erban, University of Oxford, S. Jonathan Chapman, University of Oxford
  • Book:
    Stochastic Modelling of Reaction–Diffusion Processes
    Published online:
    04 November 2019
    Print publication:
    30 January 2020, pp 226-267

  • Summary

    This chapter presents microscopic models of diffusion (Brownian motion). The discussed diffusion models explicitly describe the dynamics of solvent molecules. Such molecular dynamics models provide many more details than the models discussed in Chapter 4 (which simply postulate that the diffusing molecule is subject to a random force) and can be used to assess the accuracy of the stochastic diffusion models from Chapter 4. The analysis starts with theoretical solvent models, including a simple “one-particle” description of the solvent (heat bath), which is used to introduce the generalized Langevin equation and the generalized fluctuation–dissipation theorem. Analytical insights are provided by theoretical models with short- and long-range interactions. The chapter concludes with less analytically tractable, but more realistic, computational models, introducing molecular dynamics (molecular mechanics) and applying it to the Lennard-Jones fluid and to simulations of ions in aquatic solutions.