A family of time-staggered schemes for integrating hybrid DPD models for polymers: Algorithms and applications

We propose new schemes for integrating the stochastic differential equations of dissipative particle dynamics (DPD) in simulations of dilute polymer solutions. The hybrid DPD models consist of hard potentials that describe the microscopic dynamics of polymers and soft potentials that describe the mesoscopic dynamics of the solvent. In particular, we develop extensions to the velocity-Verlet and Lowe's approaches - two representative DPD time-integrators - following a subcycling procedure whereby the solvent is advanced with a timestep much larger than the one employed in the polymer time-integration. The introduction of relaxation parameters allows optimization studies for accuracy while maintaining the low computational complexity of standard DPD algorithms. We demonstrate through equilibrium simulations that a 10-fold gain in efficiency can be obtained with the time-staggered algorithms without loss of accuracy compared to the non-staggered schemes. We then apply the new approach to investigate the scaling response of polymers in equilibrium as well as the dynamics of λ-phage DNA molecules subjected to shear.

[1]  B. Forrest,et al.  Accelerated equilibration of polymer melts by time‐coarse‐graining , 1995 .

[2]  L. Verlet.  Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules , 1967 .

[3]  H. C. Andersen.  Molecular dynamics simulations at constant pressure and/or temperature , 1980 .

[4]  A. Malevanets,et al.  Solute molecular dynamics in a mesoscale solvent , 2000 .

[5]  Ronald G. Larson,et al.  Hydrodynamics of a DNA molecule in a flow field , 1997 .

[6]  T. Ala‐Nissila,et al.  Dynamics and scaling of two-dimensional polymers in a dilute solution. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  J. M. Yeomans,et al.  Dynamics of short polymer chains in solution , 2000 .

[8]  A. G. Schlijper,et al.  Computer simulation of dilute polymer solutions with the dissipative particle dynamics method , 1995 .

[9]  P. Nikunena,et al.  How would you integrate the equations of motion in dissipative particle dynamics simulations ? , 2003 .

[10]  P. Gennes.  Scaling Concepts in Polymer Physics , 1979 .

[11]  Eajf Frank Peters,et al.  Elimination of time step effects in DPD , 2004 .

[12]  山川 裕巳,et al.  Modern theory of polymer solutions , 1971 .

[13]  Douglas E. Smith,et al.  Single-polymer dynamics in steady shear flow. , 1999, Science.

[14]  Ronald G. Larson,et al.  Brownian dynamics simulations of single DNA molecules in shear flow , 2000 .

[15]  C. Brooks.  Computer simulation of liquids , 1989 .

[16]  Patrick S. Doyle,et al.  On the coarse-graining of polymers into bead-spring chains , 2004 .

[17]  Tony Shardlow,et al.  Splitting for Dissipative Particle Dynamics , 2002, SIAM J. Sci. Comput..

[18]  A. G. Schlijper,et al.  Effect of solvent quality on the conformation and relaxation of polymers via dissipative particle dynamics , 1997 .

[19]  R. Larson.  The Structure and Rheology of Complex Fluids , 1998 .

[20]  Ignacio Pagonabarraga,et al.  Self-consistent dissipative particle dynamics algorithm , 1998 .

[21]  Carlo Pierleoni,et al.  Molecular dynamics investigation of dynamic scaling for dilute polymer solutions in good solvent conditions , 1992 .

[22]  J. Koelman,et al.  Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics , 1992 .

[23]  A. Malevanets,et al.  Mesoscopic model for solvent dynamics , 1999 .

[24]  P. Español,et al.  Statistical Mechanics of Dissipative Particle Dynamics. , 1995 .

[25]  F. John,et al.  Stretching DNA , 2022 .

[26]  K. Schulten,et al.  Difficulties with multiple time stepping and fast multipole algorithm in molecular dynamics , 1997 .

[27]  Jesús A. Izaguirre,et al.  Verlet-I/R-RESPA/Impulse is Limited by Nonlinear Instabilities , 2003, SIAM J. Sci. Comput..

[28]  Gary Patterson,et al.  Physical Chemistry of Macromolecules , 2007 .

[29]  Juan J. de Pablo,et al.  Stochastic simulations of DNA in flow: Dynamics and the effects of hydrodynamic interactions , 2002 .

[30]  J. H. R. Clarke,et al.  The Temperature in Dissipative Particle Dynamics , 2000 .

[31]  Hiroshi Noguchi,et al.  Fluid vesicles with viscous membranes in shear flow. , 2004, Physical review letters.

[32]  Karttunen,et al.  Towards better integrators for dissipative particle dynamics simulations , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[33]  I. Vattulainen,et al.  How would you integrate the equations of motion in dissipative particle dynamics simulations , 2003 .

[34]  P. Ahlrichs,et al.  Simulation of a single polymer chain in solution by combining lattice Boltzmann and molecular dynamics , 1999, cond-mat/9905183.

[35]  P. B. Warren,et al.  DISSIPATIVE PARTICLE DYNAMICS : BRIDGING THE GAP BETWEEN ATOMISTIC AND MESOSCOPIC SIMULATION , 1997 .

[36]  C. Tanford.  Macromolecules , 1994, Nature.

[37]  Ole G Mouritsen,et al.  Artifacts in dynamical simulations of coarse-grained model lipid bilayers. , 2005, The Journal of chemical physics.

[38]  J. H. R. Clarke,et al.  A new algorithm for dissipative particle dynamics , 2001 .

[39]  G. Karniadakis,et al.  Spectral/hp Element Methods for Computational Fluid Dynamics , 2005 .

[40]  S. Edwards,et al.  The computer study of transport processes under extreme conditions , 1972 .

[41]  Michelle D. Wang,et al.  Estimating the persistence length of a worm-like chain molecule from force-extension measurements. , 1999, Biophysical journal.

[42]  Vasileios Symeonidis.  Numerical methods for multi-scale modeling of non-Newtonian flows , 2006 .

[43]  C. Lowe,et al.  An alternative approach to dissipative particle dynamics , 1999 .