Dissipative Particle Dynamics via Molecular Dynamics
Immobilisation Science Laboratory, Department of Materials Science and Engineering University of Sheffield, Sheffield, S1 3JD, UK
E-mail: k.travis@sheffield.ac.uk
Received:
Received: 21 July 2017; revised: 02 August 2017; accepted: 04 August 2017; published online: 30 September 2017
DOI: 10.12921/cmst.2017.0000033
Abstract:
We demonstrate that the main features of DPD may be obtained using molecular dynamics employing a determin- istic thermostat. This apparent isomorphism holds as long as the MD pair potentials are sufficiently smooth and short ranged, which gives rise to a quadratic equation of state (pressure as a function of density). This is advantageous because it avoids the need to use stochastic forces, enabling a wider choice of integration algorithms, involves fully time reversible motion equations and offers a simpler algorithm to achieve the same objective. The isomorphism is explored and shown to hold in 2 and 3 physical dimensions as well as for binary and ternary systems for two different choices of pair potential. The mapping between DPD and Hildebrand’s regular solution theory (a consequence of the quadratic equation of state) is extended to multicomponent mixtures. The procedure for parametrization of MD (identical to that of DPD) is outlined and illustrated for a equimolar binary mixture of SnI4 and isooctane (2,2,4-trimethylpentane).
Key words:
dissipative particle dynamics, molecular dynamics, phase equilibria
References:
[1] P.J. Hoogerbrugge, J.M.V.A. Koelman, Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics, Europhys. Lett. 19, 155 (1992).
[2] P. Español, P.B. Warren, Statistical Mechanics of Dissipative Particle Dynamics, Europhys. Lett. 30, 191 (1995).
[3] R.D. Groot, P.B. Warren, Dissipative Particle Dynamics: Bridging the gap between atomistic and mesoscopic simulation, J. Chem. Phys. 107, 4423 (1997).
[4] R.D. Groot, Electrostatic interactions in dissipative particle dynamics – simulation of polyelectrolytes and anionic surfactants, J. Chem. Phys. 118, 11265 (2003).
[5] M. González-Melchor, Electrostatic interactions in dissipative particle dynamics using the Ewald sums, E. Mayoral, M.E. Velázquez, J. Alejandre, J. Chem. Phys. 125, 224107 (2006).
[6] R.D. Groot, Mesoscopic Simulation of Polymer-Surfactant Aggregation, Langmuir 16, 7493 (2000).
[7] F. Goujon, P. Malfreyt, D.J. Tildesley, Mesoscopic simulation of entanglements using dissipative particle dynamics: application to polymer brushes, J. Chem. Phys. 129, 034902 (2008).
[8] S. Jury, P. Bladon, M. Cates, S. Krishna, M. Hagen, N. Ruddock, P. Warren, Simulation of amphiphilic mesophases using dissipative particle dynamics, PCCP 1, 2051 (1999).
[9] J. Shillcock, R. Lipowsky, Visualizing soft matter: mesoscopic simulations of membranes, vesicles and nanoparticles, BioPhys. Rev. and Lett. 2, 33 (2007).
[10] N.S. Martys, Study of dissipative particle dynamics based approach for modelling suspensions, J. Rheol. 49, 401 (2005).
[11] I. Pagonabarraga, D. Frenkel, Dissipative particle dynamics for interacting systems, J. Chem. Phys. 115, 5015 (2001).
[12] I.V. Pivkin, G.E. Karniadakis, Coarse-graining limits in open and wall-bounded dissipative particle dynamics systems, J. Chem. Phys. 124, 184101 (2006).
[13] C.P. Lowe, An alternative approach to dissipative particle dynamics, Europhys. Lett. 47, 145 (1999).
[14] B. Hafskjold, C.C. Liew, W. Shinoda, Can such long time steps really be used in dissipative particle dynamics simulations?, Mol. Simul. 30, 879 (2004).
[15] M. Ndao, J. Devemy, A. Ghoufi, P. Malfreyt, Coarse-Graining the Liquid–Liquid Interfaces with the MARTINI Force Field: How Is the Interfacial Tension Reproduced?, J. Chem. Theory Comput. 11, 3818 (2015).
[16] K.P. Travis, M. Bankhead, K. Good, S.L. Owens, New parametrization method for dissipative particle dynamics, J. Chem. Phys. 127, 014109 (2007).
[17] D.A. McQuarrie, Statistical Mechanics (Harper Collins, New York) 1976.
[18] A. Maiti, S. McGrother, Bead–bead interaction parameters in dissipative particle dynamics: Relation to bead-size, solubility parameter, and surface tension, J. Chem. Phys. 120, 1594 (2004).
[19] J.A. Beattie, Methods for the Thermodynamic Correlation of High Pressure Gas Equilibria with the Properties of Pure Gases, Chem. Rev. (Washington D.C.) 18, 359 (1936).
[20] J.H. Hildebrand, R.L. Scott, The Solubility of non-electrolytes, 3rd Ed. (Reinhold, New York, 1950).
[21] J.H. Hildebrand, G.R. Negishi, Solubility XV. Solubility of liquid and solid Stannic Iodidein Silicon Tetrachloride,JACS,59,339-341(1937).
[22] L.D. Gelb, E.A. Müller, Location of phase equilibria by temperature-quench molecular dynamics simulations, Fluid Phase Equilib. 203, 1 (2002).
We demonstrate that the main features of DPD may be obtained using molecular dynamics employing a determin- istic thermostat. This apparent isomorphism holds as long as the MD pair potentials are sufficiently smooth and short ranged, which gives rise to a quadratic equation of state (pressure as a function of density). This is advantageous because it avoids the need to use stochastic forces, enabling a wider choice of integration algorithms, involves fully time reversible motion equations and offers a simpler algorithm to achieve the same objective. The isomorphism is explored and shown to hold in 2 and 3 physical dimensions as well as for binary and ternary systems for two different choices of pair potential. The mapping between DPD and Hildebrand’s regular solution theory (a consequence of the quadratic equation of state) is extended to multicomponent mixtures. The procedure for parametrization of MD (identical to that of DPD) is outlined and illustrated for a equimolar binary mixture of SnI4 and isooctane (2,2,4-trimethylpentane).
Key words:
dissipative particle dynamics, molecular dynamics, phase equilibria
References:
[1] P.J. Hoogerbrugge, J.M.V.A. Koelman, Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics, Europhys. Lett. 19, 155 (1992).
[2] P. Español, P.B. Warren, Statistical Mechanics of Dissipative Particle Dynamics, Europhys. Lett. 30, 191 (1995).
[3] R.D. Groot, P.B. Warren, Dissipative Particle Dynamics: Bridging the gap between atomistic and mesoscopic simulation, J. Chem. Phys. 107, 4423 (1997).
[4] R.D. Groot, Electrostatic interactions in dissipative particle dynamics – simulation of polyelectrolytes and anionic surfactants, J. Chem. Phys. 118, 11265 (2003).
[5] M. González-Melchor, Electrostatic interactions in dissipative particle dynamics using the Ewald sums, E. Mayoral, M.E. Velázquez, J. Alejandre, J. Chem. Phys. 125, 224107 (2006).
[6] R.D. Groot, Mesoscopic Simulation of Polymer-Surfactant Aggregation, Langmuir 16, 7493 (2000).
[7] F. Goujon, P. Malfreyt, D.J. Tildesley, Mesoscopic simulation of entanglements using dissipative particle dynamics: application to polymer brushes, J. Chem. Phys. 129, 034902 (2008).
[8] S. Jury, P. Bladon, M. Cates, S. Krishna, M. Hagen, N. Ruddock, P. Warren, Simulation of amphiphilic mesophases using dissipative particle dynamics, PCCP 1, 2051 (1999).
[9] J. Shillcock, R. Lipowsky, Visualizing soft matter: mesoscopic simulations of membranes, vesicles and nanoparticles, BioPhys. Rev. and Lett. 2, 33 (2007).
[10] N.S. Martys, Study of dissipative particle dynamics based approach for modelling suspensions, J. Rheol. 49, 401 (2005).
[11] I. Pagonabarraga, D. Frenkel, Dissipative particle dynamics for interacting systems, J. Chem. Phys. 115, 5015 (2001).
[12] I.V. Pivkin, G.E. Karniadakis, Coarse-graining limits in open and wall-bounded dissipative particle dynamics systems, J. Chem. Phys. 124, 184101 (2006).
[13] C.P. Lowe, An alternative approach to dissipative particle dynamics, Europhys. Lett. 47, 145 (1999).
[14] B. Hafskjold, C.C. Liew, W. Shinoda, Can such long time steps really be used in dissipative particle dynamics simulations?, Mol. Simul. 30, 879 (2004).
[15] M. Ndao, J. Devemy, A. Ghoufi, P. Malfreyt, Coarse-Graining the Liquid–Liquid Interfaces with the MARTINI Force Field: How Is the Interfacial Tension Reproduced?, J. Chem. Theory Comput. 11, 3818 (2015).
[16] K.P. Travis, M. Bankhead, K. Good, S.L. Owens, New parametrization method for dissipative particle dynamics, J. Chem. Phys. 127, 014109 (2007).
[17] D.A. McQuarrie, Statistical Mechanics (Harper Collins, New York) 1976.
[18] A. Maiti, S. McGrother, Bead–bead interaction parameters in dissipative particle dynamics: Relation to bead-size, solubility parameter, and surface tension, J. Chem. Phys. 120, 1594 (2004).
[19] J.A. Beattie, Methods for the Thermodynamic Correlation of High Pressure Gas Equilibria with the Properties of Pure Gases, Chem. Rev. (Washington D.C.) 18, 359 (1936).
[20] J.H. Hildebrand, R.L. Scott, The Solubility of non-electrolytes, 3rd Ed. (Reinhold, New York, 1950).
[21] J.H. Hildebrand, G.R. Negishi, Solubility XV. Solubility of liquid and solid Stannic Iodidein Silicon Tetrachloride,JACS,59,339-341(1937).
[22] L.D. Gelb, E.A. Müller, Location of phase equilibria by temperature-quench molecular dynamics simulations, Fluid Phase Equilib. 203, 1 (2002).
