A successive fine-graining scheme for predicting the rheological properties of dilute polymer solutions

A new method for refining the predictions of a finitely extensible bead-spring chain model with hydrodynamic interactions is introduced. The suggested successive fine-graining procedure involves the representation of a long but finite macromolecule of NK Kuhn steps with a coarse-grained bead-spring chain model, and subsequently "fine graining" the representation by progressively increasing the number of beads, N. Extrapolating the results obtained using exact Brownian dynamics simulations for several values of N to the limit N−1→NK, leads to improved estimates for the behavior of the actual polymer chains. The extrapolated results for the extensional viscosity are found to be in good agreement with the recent experimental observations of Gupta et al. (2000). The scaling of the extensional viscosity with molecular weight is also examined.

[1]  G. Batchelor,et al.  Slender-body theory for particles of arbitrary cross-section in Stokes flow , 1970, Journal of Fluid Mechanics.

[2]  R. Gupta,et al.  Measurement of extensional viscosity of polymer solutions , 1991 .

[3]  G. McKinley,et al.  FILAMENT-STRETCHING RHEOMETRY OF COMPLEX FLUIDS , 2002 .

[4]  Bamin Khomami,et al.  Brownian dynamics simulations of bead-rod and bead-spring chains: numerical algorithms and coarse-graining issues , 2002 .

[5]  J. H. Cifre,et al.  Kinetic aspects of the coil-stretch transition of polymer chains in dilute solution under extensional flow , 2001 .

[6]  H. C. Öttinger.  A model of dilute polymer solutions with hydrodynamic interaction and finite extensibility. I. Basic equations and series expansions , 1987 .

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

[8]  T. McLeish.  Dynamics of polymeric liquids, Vol. 2: kinetic theory, 2nd ed. by R.B. Bird, C.F. Curtiss, R.C. Armstrong and O. Hassager, John Wiley and Sons, New York, NY, 1987, ISBN 0-471-01596-2, 437 pp., $65.00. , 1989 .

[9]  E. Hinch.  Uncoiling a polymer molecule in a strong extensional flow , 1994 .

[10]  T. Sridhar,et al.  A filament stretching device for measurement of extensional viscosity , 1993 .

[11]  H. Fujita,et al.  Excluded-volume effects in dilute polymer solutions. 11. Tests of the two-parameter theory for radius of gyration and intrinsic viscosity , 1981 .

[12]  R. Prabhakar,et al.  Multiplicative separation of the influences of excluded volume, hydrodynamic interactions and finite extensibility on the rheological properties of dilute polymer solutions , 2004 .

[13]  H. Fujita,et al.  Flory's Viscosity Factor for the System Polystyrene + Cyclohexane at 34.5 °C , 1980 .

[14]  P. de Gennes,et al.  POLYMER PHYSICS: Molecular Individualism , 1997 .

[15]  Ronald G. Larson,et al.  Modeling hydrodynamic interaction in Brownian dynamics: simulations of extensional flows of dilute solutions of DNA and polystyrene , 2003 .

[16]  U. S. Agarwal.  Effect of initial conformation, flow strength, and hydrodynamic interaction on polymer molecules in extensional flows , 2000 .

[17]  H. C. Öttinger.  Generalized Zimm model for dilute polymer solutions under theta conditions , 1987 .

[18]  Hiromi Yamakawa,et al.  Transport Properties of Polymer Chains in Dilute Solution: Hydrodynamic Interaction , 1970 .

[19]  D E Smith,et al.  Single polymer dynamics in an elongational flow. , 1997, Science.

[20]  Nikos Hadjichristidis,et al.  Molecular Weight Dependence of Hydrodynamic and Thermodynamic Properties for Well‐Defined Linear Polymers in Solution , 1994 .

[21]  R. Larson,et al.  Deformation-dependent hydrodynamic interaction in flows of dilute polymer solutions , 1988 .

[22]  O. Hassager,et al.  Kinetic theory and rheology of bead‐rod models for macromolecular solutions. I. Equilibrium and steady flow properties , 1974 .

[23]  Douglas E. Smith,et al.  Response of flexible polymers to a sudden elongational flow , 1998, Science.

[24]  H. C. Öttinger,et al.  A model of dilute polymer solutions with hydrodynamic interaction and finite extensibility. II. Shear flows , 1988 .

[25]  H. C. Oettinger,et al.  Calculation of various universal properties for dilute polymer solutions undergoing shear flow , 1991 .

[26]  J Ravi Prakash.  Rouse Chains with Excluded Volume Interactions: Linear Viscoelasticity , 2001 .

[27]  T. Sridhar.  An overview of the project M1 , 1990 .

[28]  Ronald G. Larson,et al.  Brownian dynamics simulations of dilute polystyrene solutions , 2000 .

[29]  K. Osaki.  A Revised Version of the Intergrodifferential Equation in the Zimm Theory for Polymer Solution Dynamics , 1972 .

[30]  Y. Rabin,et al.  Renormalization-group calculation of viscometric functions based on conventional polymer kinetic theory , 1989 .

[31]  K. Ahn,et al.  Bead-spring chain model for the dynamics of dilute polymer solutions , 1992 .

[32]  A. Mchugh,et al.  A discussion of shear-thickening in bead-spring models , 1990 .

[33]  Translational diffusion of polymer chains with excluded volume and hydrodynamic interactions by Brownian dynamics simulation , 2003, cond-mat/0301583.

[34]  S. Prager,et al.  Variational Treatment of Hydrodynamic Interaction in Polymers , 1969 .

[35]  Rahul K Gupta,et al.  Extensional viscosity of dilute polystyrene solutions: Effect of concentration and molecular weight , 2000 .

[36]  Daniel N. Ostrov,et al.  A finitely extensible bead-spring chain model for dilute polymer solutions , 1991 .

[37]  K. Ahn,et al.  Bead-spring chain model for the dynamics of dilute polymer solutions: Part 2. Comparisons with experimental data , 1993 .

[38]  R. Larson,et al.  Brownian dynamics simulations of a DNA molecule in an extensional flow field , 1999 .

[39]  M. Denn,et al.  Monte Carlo simulation of steady extensional flows , 2004 .

[40]  H. R. Warner,et al.  Kinetic Theory and Rheology of Dilute Suspensions of Finitely Extendible Dumbbells , 1972 .

[41]  Manuel Laso,et al.  Variance reduced Brownian simulation of a bead-spring chain under steady shear flow considering hydrodynamic interaction effects , 2000 .

[42]  C. F. Curtiss,et al.  Dynamics of Polymeric Liquids, Volume 1: Fluid Mechanics , 1987 .

[43]  L. Schäfer.  Excluded Volume Effects in Polymer Solutions , 1999 .