Rod-like colloids and polymers in shear flow: a multi-particle-collision dynamics study

The effect of the hydrodynamic interaction on the dynamics of flexible and rod-like polymers in solution is investigated. The solvent is simulated by the multi-particle-collision dynamics (MPCD) algorithm, a mesoscale simulation technique. The dynamics of the solvent is studied and the self-diffusion coefficient is calculated as a function of the mean free path of a particle. At small mean free paths, the hydrodynamic interaction strongly influences the dynamics of the fluid particles. This solvent model is then coupled to a molecular dynamics simulation algorithm. We obtain excellent agreement between our simulation results for a flexible polymer and the predictions of Zimm theory. The study of the translational diffusion coefficient of rod-like polymers confirms the predicted chain-length dependence. In addition, we study the influence of shear on the structural properties of rod-like polymers. For shear rates exceeding the rotational relaxation time, the rod-like molecule aligns with the shear flow, leading to an orientational symmetry breaking transverse to the flow direction. The comparison of the obtained shear rate dependencies with theoretical predictions exhibits significant deviations. The properties of the orientational tensor and the rotational velocity are discussed in detail as a function of shear rate.

[1]  P. E. Rouse A Theory of the Linear Viscoelastic Properties of Dilute Solutions of Coiling Polymers , 1953 .

[2]  B. Zimm Dynamics of Polymer Molecules in Dilute Solution: Viscoelasticity, Flow Birefringence and Dielectric Loss , 1956 .

[3]  H. Janeschitz-Kriegl Flow birefringence of elastico-viscous polymer systems , 1969 .

[4]  E. Merrill,et al.  Conformation of polyisobutylene in dilute solution subjected to a hydrodynamic shear field , 1969 .

[5]  A. Peterlin Optical Effects in Flow , 1976 .

[6]  J. García de la Torre,et al.  Hydrodynamic properties of complex, rigid, biological macromolecules: theory and applications , 1981, Quarterly Reviews of Biophysics.

[7]  Y. Pomeau,et al.  Lattice-gas automata for the Navier-Stokes equation. , 1986, Physical review letters.

[8]  S. Edwards,et al.  The Theory of Polymer Dynamics , 1986 .

[9]  S. Hess Rheological properties via nonequilibrium molecular dynamics: From simple towards polymeric liquids , 1987 .

[10]  J. Banavar,et al.  Computer Simulation of Liquids , 1988 .

[11]  Zanetti,et al.  Use of the Boltzmann equation to simulate lattice gas automata. , 1988, Physical review letters.

[12]  R. Oberthür,et al.  Shear induced deformation of polystyrene in dilute solution from SANS , 1989 .

[13]  Ryckaert,et al.  Relaxation of a single chain molecule in good solvent conditions by molecular-dynamics simulation. , 1991, Physical review letters.

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

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

[16]  R. Benzi,et al.  The lattice Boltzmann equation: theory and applications , 1992 .

[17]  A. Ladd Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results , 1993, Journal of Fluid Mechanics.

[18]  Roland G. Winkler,et al.  MODELS AND EQUILIBRIUM PROPERTIES OF STIFF MOLECULAR CHAINS , 1994 .

[19]  J. Ryckaert,et al.  Deformation and Orientation of Flexible Polymers in Solution under Shear Flow: A New Picture for Intermediate Reduced Shear Rates , 1995 .

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

[21]  A. Szeri A deformation tensor model of liquid crystalline polymers , 1995 .

[22]  J. Springer,et al.  Light-scattering studies on the dynamics of long-chain macromolecules in shear flow , 1995 .

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

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

[25]  R. Winkler,et al.  Collapse of Polyelectrolyte Macromolecules by Counterion Condensation and Ion Pair Formation: A Molecular Dynamics Simulation Study , 1998 .

[26]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[27]  Burkhard Dünweg,et al.  Lattice Boltzmann Simulation of Polymer-Solvent Systems , 1998 .

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

[29]  Martin Kröger,et al.  Structure and dynamics of dilute polymer solutions under shear flow via nonequilibrium molecular dynamics , 1999 .

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

[31]  N. A. Spenley Scaling laws for polymers in dissipative particle dynamics , 2000 .

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

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

[34]  Geometry and dynamics of a nematic liquid crystal in a uniform shear flow , 2001 .

[35]  Pep Español,et al.  Large scale and mesoscopic hydrodynamics for dissipative particle dynamics , 2001 .

[36]  T. Ihle,et al.  Stochastic rotation dynamics: a Galilean-invariant mesoscopic model for fluid flow. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  T. Ihle,et al.  Erratum: Multi-particle collision dynamics: Flow around a circular and a square cylinder , 2001, cond-mat/0110148.

[38]  S. Hess,et al.  Rotation and deformation of a finitely extendable flexible polymer molecule in a steady shear flow , 2002 .

[39]  S. Hess,et al.  Chaotic and regular shear-induced orientational dynamics of nematic liquid crystals , 2002 .

[40]  G. Gompper,et al.  Mesoscopic solvent simulations: multiparticle-collision dynamics of three-dimensional flows. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  A Lamura,et al.  Numerical study of the flow around a cylinder using multi-particle collision dynamics , 2002, The European physical journal. E, Soft matter.

[42]  T Ihle,et al.  Stochastic rotation dynamics. I. Formalism, Galilean invariance, and Green-Kubo relations. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  G. Gompper,et al.  Erratum: Mesoscopic solvent simulations: Multiparticle-collision dynamics of three-dimensional flows [Phys. Rev. E 66, 036702 (2002)] , 2003 .

[44]  T Ihle,et al.  Transport coefficients for stochastic rotation dynamics in three dimensions. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[45]  T Ihle,et al.  Stochastic rotation dynamics. II. Transport coefficients, numerics, and long-time tails. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[46]  M. Fukugita,et al.  Erratum: Light hadron spectroscopy with two flavors of dynamical quarks on the lattice [Phys. Rev. D 65, 054505 (2002)] , 2003 .

[47]  J. F. Ryder,et al.  Transport coefficients of a mesoscopic fluid dynamics model , 2003, cond-mat/0302451.