Brownian Dynamics Simulations of Polymers and Soft Matter

  • Patrick S. Doyle
  • Patrick T. Underhill


The Brownian dynamics (BD) simulation technique is a mesoscopic method in which explicit solvent molecules are replaced instead by a stochastic force. The technique takes advantage of the fact that there is a large separation in time scales between the rapid motion of solvent molecules and the more sluggish motion of polymers or colloids. The ability to coarse-grain out these fast modes of the solvent allows one to simulate much larger time scales than in a molecular dynamics simulation. At the core of a Brownian dynamics simulation is a stochastic differential equation which is integrated forward in time to create trajectories of molecules. Time enters naturally into the scheme allowing for the study of the temporal evolution and dynamics of complex fluids (e.g., polymers, large proteins, DNA molecules and colloidal solutions). Hydrodynamic and body forces, such as magnetic or electric fields, can be added in a straightforward way. Brownian dynamics simulations are particularly well suited to studying the structure and rheology of complex fluids in hydrodynamic flows and other nonequilibrium situations.


Hydrodynamic Interaction Persistence Length Brownian Dynamic Brownian Dynamic Simulation Rigid Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    H.C. Ottinger, Stochastic Processes in Polymeric Fluids, Springer-Verlag, New York, 1996.Google Scholar
  2. [2]
    M. Fixman, “Construction of Langevin forces in the simulation of hydrodynamic interaction”, Macromolecules, 19, 1204, 1986.CrossRefADSGoogle Scholar
  3. [3]
    D.C. Morse, “Theory of constrained Brownian motion”, Adv. Chem. Phys., 128, 65, 2004.CrossRefGoogle Scholar
  4. [4]
    R.B. Bird, C.F. Curtiss, R.C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, Volume 2, 2nd edn., Wiley, New York, 1987.Google Scholar
  5. [5]
    C.-C. Hsieh, L. Li, and R.G. Larson, “Modeling hydrodynamic interaction in Brownian dynamics: simulations of extensional flows of dilute solutions of DNA and polystyrene”, J. Non-Newtonian Fluid Mech., 113, 147, 2003.MATHCrossRefGoogle Scholar
  6. [6]
    E. Marko and E.D. Siggia, “Stretching DNA”, Macromolecules, 28, 8759, 1995.CrossRefADSGoogle Scholar
  7. [7]
    P.T. Underhill and P.S. Doyle, “On the coarse-graining of polymers into bead-spring chains”, J. Non-Newtonian Fluid Mech., 122, 3, 2004.MATHCrossRefGoogle Scholar
  8. [8]
    H. Yamakawa, Helical Wormlike Chains in Polymer Solutions, Springer, Berlin, 1997.Google Scholar
  9. [9]
    A. Montesi, M. Pasquali, and F.C. MacKintosh, “Collapse of a semiflexible polymer in poor solvent”, Phys. Rev. E, 69, 021916, 2004.CrossRefADSGoogle Scholar
  10. [10]
    P.S. Grassia, E.J. Hinch, and L.C. Nitsche, “Computer simulations of Brownian motion of complex systems”, J. Fluid Mech., 282, 373, 1995.MATHCrossRefMathSciNetADSGoogle Scholar
  11. [11]
    P.S. Doyle, A.P. Gast, and E.S.G. Shaqfeh, “Dynamic simulation of freely draining flexible polymers in steady linear flows”, J. Fluid Mech., 334, 251, 1997.MATHCrossRefADSGoogle Scholar
  12. [12]
    S. Chu, “Biology and polymer physics at the single molecule level”, Phil. Trans. R. Soc. Lond. A, 361, 689, 2003.CrossRefADSGoogle Scholar
  13. [13]
    P.S. Doyle, B. Ladoux, and J.L. Viovy, “Dynamics of a tethered polymer in shear flow”, Phys. Rev. Lett., 84, 4769, 2000.CrossRefADSGoogle Scholar
  14. [14]
    R.G. Larson, H. Hu, D.E. Smith, and S. Chu, “Brownian dynamics simulations of DNA molecules in an extensional flow field”, J. Rheol., 43, 267, 1999.CrossRefADSGoogle Scholar
  15. [15]
    C.M. Schroeder, H.P. Babcock, E.S.G. Shaqfeh, and S. Chu, “Observation of polymer hysteresis in extensional flow”, Science, 3001, 1515, 2003.CrossRefADSGoogle Scholar
  16. [16]
    R.M. Jendrejack, D.C. Schwartz, J.J. de Pablo, and M.D. Graham, “Shearinduced migration in flowing polymer solutions: simulation of long-chain DNA in microchannels”, J. Chem. Phys., 120, 2513, 2004.CrossRefADSGoogle Scholar
  17. [17]
    G.H. McKinley and T. Sridhar, “Filament stretching rheometry of complex fluids”, Annu. Rev. Fluid Mech., 34, 375, 2002.CrossRefMathSciNetADSGoogle Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • Patrick S. Doyle
    • 1
  • Patrick T. Underhill
    • 1
  1. 1.Department of Chemical EngineeringMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations