Dynamics of polymer chains confined into tubes: Scaling theory and Monte Carlo simulations

The crossover from chain dynamics described by the Rouse model to reptation behavior is studied for chains confined into straight tubes. Scaling considerations are presented for mean‐square displacements parallel and perpendicular to the tube, for the static structure factor, and for dynamic coherent and incoherent structure factors, taking excluded‐volume interactions into account. Monte Carlo calculations of long chains (from N=100 up to N=800 links) on the tetrahedral lattice in tubes with diameters in the range from d T =16 to d T =32 lattice spacings are presented and analyzed in terms of the scaling picture. While the scaling predictions are nicely confirmed, the simulations also reveal additional interesting features: (i) For intermediate wave vectors the structure factor exhibits (damped) oscillations. This behavior is discussed in terms of the analogy with a one‐dimensional harmonic ‘‘crystal’’ composed of blobs, and differs from the behavior of a nonconfined chain stretched to the same length. (ii) In the center of gravity system of the chain, the monomer displacements along the tube axis for monomers near the chain ends are very much larger than those near the chain center. We also give a preliminary discussion of consequences for the dynamics of melts, if they are modeled in terms of tubes following a random‐walk contour.

[1]  T. Fox,et al.  The viscosity of polymers and their concentrated solutions , 1968 .

[2]  William W. Graessley.  The Entanglement Concept in Polymer Rheology , 1974 .

[3]  S F Edwards,et al.  The statistical mechanics of polymerized material , 1967 .

[4]  P. Pincus.  Excluded Volume Effects and Stretched Polymer Chains , 1976 .

[5]  T. Kataoka,et al.  Viscosity of polydimethylsiloxane–pentamer systems , 1967 .

[6]  R. Ball,et al.  A real time neutron scattering experiment for the study of polymer dynamics , 1982 .

[7]  S. Edwards,et al.  Dynamics of concentrated polymer systems. Part 4.—Rheological properties , 1979 .

[8]  C. F. Curtiss,et al.  A kinetic theory for polymer melts. I. The equation for the single‐link orientational distribution function , 1981 .

[9]  W. Graessley.  Entangled linear, branched and network polymer systems — Molecular theories , 1982 .

[10]  Hiromi Yamakawa,et al.  Modern Theory of Polymer Solutions , 1971 .

[11]  S. Edwards,et al.  Screening concepts in polymer solution dynamics , 1982 .

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

[13]  S. Edwards,et al.  Polymer viscosity in concentrated solutions , 1974 .

[14]  S. Edwards,et al.  The effect of entanglements of diffusion in a polymer melt , 1973 .

[15]  L. Turban.  Conformation of confined macromolecular chains : cross-over between slit and capillary , 1984 .

[16]  A. Baumgärtner.  Glass transition of a polymer chain , 1980 .

[17]  P. Gennes,et al.  Statistics of macromolecular solutions trapped in small pores , 1977 .

[18]  V. J. Emery,et al.  One-dimensional fluctuations and the chain-ordering transformation in Hg/sub 3-delta/AsF/sub 6/ , 1978 .

[19]  J. Klein.  Translational diffusion in entangled polyethylene melts , 1981 .

[20]  Liliane Léger,et al.  Dynamics of Entangled Polymer Chains , 1982 .

[21]  P. G. de Gennes,et al.  Dynamics of Entangled Polymer Solutions. I. The Rouse Model , 1976 .

[22]  P. Gennes,et al.  Quasi-elastic scattering by dilute, ideal, polymer solutions: II. Effects of hydrodynamic interactions , 1967 .

[23]  Kurt Kremer,et al.  Dynamics of entangled flexible polymers. Monte Carlo simulations and their interpretation , 1983 .

[24]  J. Ferry.  Viscoelastic properties of polymers , 1961 .

[25]  J. D. Cloizeaux.  Polymer melt : reptation of a chain and viscosity , 1984 .

[26]  M. Kalos,et al.  Investigations of model polymers: Dynamics of melts and statics of a long chain in a dilute melt of shorter chains , 1982 .

[27]  G. Fleischer.  Self diffusion in melts of polystyrene and polyethylene measured by pulsed field gradient NMR , 1983 .

[28]  K. Osaki,et al.  Experimental Appraisal of the Doi-Edwards Theory for Polymer Rheology Based on the Data for Polystyrene Solutions , 1980 .

[29]  Kenneth E. Evans,et al.  Computer simulation of the dynamics of highly entangled polymers. Part 1.—Equilibrium dynamics , 1981 .

[30]  M. Doi.  Explanation for the 3.4 power law of viscosity of polymeric liquids on the basis of the tube model , 1981 .

[31]  K. Freed,et al.  Multiple scattering theory calculation of the concentration dependence of the tracer and cooperative friction coefficients for Gaussian polymer chains , 1983 .

[32]  K. Freed,et al.  Concentration dependence of the viscoelastic properties of polymer solutions , 1983 .

[33]  L. Léger,et al.  Self-Diffusion in Polymer Solutions: A Test for Scaling and Reptation , 1979 .

[34]  R. Needs.  Computer simulation of the effect of primitive path length fluctuations in the reptation model , 1984 .

[35]  K. Kawasaki,et al.  Application of field-theoretical renormalisation-group method to polymer dynamics , 1982 .

[36]  Kurt Kremer,et al.  Self-avoiding-walks (SAW's) on diluted lattices, a Monte Carlo analysis , 1981 .

[37]  S. Edwards,et al.  Entanglement interactions in polymers and the chain contour concentration , 1981 .

[38]  P. Gennes.  Coherent scattering by one reptating chain , 1981 .

[39]  W. Graessley.  Viscoelastic properties of entangled flexible polymers , 1983 .

[40]  Kurt Kremer,et al.  Adsorption of polymer chains at surfaces: Scaling and Monte Carlo analyses , 1982 .

[41]  Simulation of the brownian motion of macromolecular chains. I. Local motions and chain conformations , 1979 .

[42]  J. Noolandi,et al.  Non-equilibrium correlation function of a reptating chain , 1984 .

[43]  M. Daoud,et al.  Scattered Intensity by a Polymer Chain in a Sample with External Constraints , 1975 .

[44]  K. Binder,et al.  Richteret al.Respond , 1982 .

[45]  S. Edwards,et al.  Dynamics of concentrated polymer systems. Part 1.—Brownian motion in the equilibrium state , 1978 .

[46]  M. Huggins.  The Physical Properties of Polymers. , 1959 .

[47]  Kurt Kremer,et al.  Statics and dynamics of polymeric melts: a numerical analysis , 1983 .

[48]  Y. Oono,et al.  Renormalization group theory of transport properties of polymer solutions. I. Dilute solutions , 1983 .

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

[50]  P. Gennes.  Dynamics of Entangled Polymer Solutions. II. Inclusion of Hydrodynamic Interactions , 1976 .

[51]  P. Gennes.  Reptation of a Polymer Chain in the Presence of Fixed Obstacles , 1971 .

[52]  Kurt Kremer,et al.  Collapse transition and crossover scaling for self-avoiding walks on the diamond lattice , 1982 .

[53]  P. Gennes,et al.  Dynamics of confined polymer chains , 1977 .

[54]  M. Doi.  Viscoelasticity of concentrated solutions of stiff polymers , 1983 .

[55]  G. Ronca.  Frequency spectrum and dynamic correlations of concentrated polymer liquids , 1983 .