The twice-renormalized Rouse formalism of polymer dynamics: Segment diffusion, terminal relaxation, and nuclear spin-lattice relaxation

The twice-renormalized Rouse formalism, a refined version of Schweizer's renormalized Rouse treatment of chain dynamics in entangled polymers, is presented. The time scale of validity is extended to include the terminal chain relaxation and center-of-mass diffusion. In clear contrast to the laws concluded from other polymer dynamics concepts (such as the reptation (tube) model or the polymer mode-mode coupling formalism), the predictions perfectly coincide with all the results of recent spin-lattice relaxation dispersion and diffusion experiments as well as with computer simulations. On the other hand, the twice-renormalized Rouse formalism fails to explain the rubber-elastic plateau of stress relaxation. It is inferred that this is a consequence of the single-chain nature of the present approach not accounting for the fact that viscoelasticity is largely a manifestation of collective multichain modes. In the rigorous sense, no such multichain treatment has yet been established to our knowledge. The necessity to consider interchain cooperativity in any real comprehensive polymer dynamics theory is concluded from low-frequency spin-lattice relaxation data, which are shown to reflect fluctuations of long-distance intermolecular dipole-dipole interactions. © 2000 MAIK "Nauka/Interperiodica"

Polymer chain dynamics predicted by n-renormalized rouse models: Numerical studies

Features of the renormalized and twice renormalized Rouse models were examined numerically. Based on numerical evaluations of the generalized Langevin equation in renormalization approaches, nonexponential normal mode autocorrelation functions were derived, that can be described over two orders of magnitude by stretched exponential functions. The mode number dependence of the stretching parameter was evaluated. The consequences of the nonexponential correlation functions on dynamical properties are discussed. As a basis for predictions for the behavior of diffusion and spin-lattice relaxation dispersion, the time dependence of the mean-squared segment displacement and of the autocorrelation function of the segment tangential vector, respectively, were obtained taking into account finite chain lengths

The twice renormalized rouse formalism of polymer dynamics. Segment diffusion, terminal relaxation, and nuclear spin-lattice relaxation

The twice renormalized Rouse formalism, a refined version of Schweizer's renormalized Rouse treatment of chain dynamics in entangled polymers, is presented. The time scale of validity is extended including terminal chain relaxation and center-of-mass diffusion. In clear contrast to the laws concluded from other polymer dynamics concepts such as the reptation (tube) model or the polymer mode-mode coupling formalism, the predictions perfectly compare with all results of recent spin-lattice relaxation dispersion and diffusion experiments as well as computer simulations. On the other hand, the twice renormalized Rouse formalism fails to explain the rubber-elastic plateau of stress relaxation. It is inferred that this is a consequence of the single-chain nature of the present approach not accounting for the fact that viscoelasticity largely is a manifestation of collective many-chain modes. In the rigorous sense, no such multi-chain treatment has been established so far to our knowledge. The necessity to consider inter-chain cooperativity in any really comprehensive polymer dynamics theory is concluded from low-frequency spin-lattice relaxation data, which are shown to reflect fluctuations of long-distance intermolecular dipole-dipole interactions

Segment diffusion and nuclear magnetic resonance spin-lattice relaxation of polymer chains confined in tubes: Analytical treatment and Monte Carlo simulation of the crossover from Rouse to reptation dynamics

The dynamics of polymer chains in model tubes of variable diameter and varying chain and wall potentials was studied. The study was carried out using analytical treatment and Monte Carlo simulations of the crossover from Rouse to reptation dynamics. It was found that depending on the tube diameter, a crossover from Rouse to reptation behavior occurred

The confined-to-bulk dynamics transition of polymer melts in nanoscopic pores of solid matrices with varying pore diameter

The confinement of polymer melts in nanoscopic pores leads to chain dynamics significantly different from bulk behaviour. This so-called 'corset effect' occurs both above and below the critical molecular mass and induces dynamic features as predicted for reptation. The confined-to-bulk dynamics crossover is treated analytically on the basis of general thermodynamic relations connected to the fluctuation of the number of particles (Kuhn segments) in a given volume. Bulk behaviour is shown to occur only if the pore diameter complies with the limit dpore ≫ (b3/k BTκT )1/3RF ≈ 10R F , where b is the Kuhn segment length, κT the isothermal compressibility, T the temperature, kB the Boltzmann constant and RF the Flory radius. For smaller pores, the confined polymer chains reptate along their own contours in tubes with an effective diameter d ≈ √b2ρskBTκ T ≈ 0.5 nm, where ρs is the number density of Kuhn segments. From the theoretical point of view, the crucial factors on which the corset effect is based are (i) impenetrable pore walls, (ii) low compressibility and (iii) the uncrossability of polymer chains

The "corset effect" of spin-lattice relaxation in polymer melts confined in nanoporous media

Linear polyethylene oxides with molecular weights Mw of 1665 and 10170 confined in pores with variable diameters in a solid methacrylate matrix were studied by proton field-cycling nuclear magnetic resonance relaxometry. The pore diameter was varied in the range of 9-57 nm. In all cases, the spin-lattice relaxation time shows a frequency dependence close to T1 ∝ ν3/4 in the range of ν = 3·10 -1-2·101 MHz as predicted by the tube-reptation model. This proton T1 dispersion essentially reproduces that found in a previous deuteron study (R. Kimmich, R.-O. Seitter, U. Beginn, M. Möller, N. Fatkullin: Chem. Phys. Lett. 307, 147, 1999). As a feature particularly characteristic for reptation, this finding suggests that reptation is the dominating chain dynamics mechanism under pore confinement in the corresponding time range. The absolute values of the spin-lattice relaxation times indicate that the diameter of the effective tubes in which reptation occurs is much smaller than the pore diameters on the time scale of spin-lattice relaxation experiments. An estimation leads to a value d* ∼ 0.5 nm. The impenetrability of the solid pore walls, the uncrossability of polymer chains (·excluded volume·) and the low value of the compressibility in polymer melts create the ·corset effect· which reduces the lateral motions of polymer chains to a microscopic scale of only a few tenths of a nanometer

Polymer chain dynamics predicted by n-renormalized rouse models: Numerical studies

Features of the renormalized and twice renormalized Rouse models were examined numerically. Based on numerical evaluations of the generalized Langevin equation in renormalization approaches, nonexponential normal mode autocorrelation functions were derived, that can be described over two orders of magnitude by stretched exponential functions. The mode number dependence of the stretching parameter was evaluated. The consequences of the nonexponential correlation functions on dynamical properties are discussed. As a basis for predictions for the behavior of diffusion and spin-lattice relaxation dispersion, the time dependence of the mean-squared segment displacement and of the autocorrelation function of the segment tangential vector, respectively, were obtained taking into account finite chain lengths

The twice renormalized rouse formalism of polymer dynamics. Segment diffusion, terminal relaxation, and nuclear spin-lattice relaxation

The twice renormalized Rouse formalism, a refined version of Schweizer's renormalized Rouse treatment of chain dynamics in entangled polymers, is presented. The time scale of validity is extended including terminal chain relaxation and center-of-mass diffusion. In clear contrast to the laws concluded from other polymer dynamics concepts such as the reptation (tube) model or the polymer mode-mode coupling formalism, the predictions perfectly compare with all results of recent spin-lattice relaxation dispersion and diffusion experiments as well as computer simulations. On the other hand, the twice renormalized Rouse formalism fails to explain the rubber-elastic plateau of stress relaxation. It is inferred that this is a consequence of the single-chain nature of the present approach not accounting for the fact that viscoelasticity largely is a manifestation of collective many-chain modes. In the rigorous sense, no such multi-chain treatment has been established so far to our knowledge. The necessity to consider inter-chain cooperativity in any really comprehensive polymer dynamics theory is concluded from low-frequency spin-lattice relaxation data, which are shown to reflect fluctuations of long-distance intermolecular dipole-dipole interactions

The twice-renormalized Rouse formalism of polymer dynamics: Segment diffusion, terminal relaxation, and nuclear spin-lattice relaxation

The twice-renormalized Rouse formalism, a refined version of Schweizer's renormalized Rouse treatment of chain dynamics in entangled polymers, is presented. The time scale of validity is extended to include the terminal chain relaxation and center-of-mass diffusion. In clear contrast to the laws concluded from other polymer dynamics concepts (such as the reptation (tube) model or the polymer mode-mode coupling formalism), the predictions perfectly coincide with all the results of recent spin-lattice relaxation dispersion and diffusion experiments as well as with computer simulations. On the other hand, the twice-renormalized Rouse formalism fails to explain the rubber-elastic plateau of stress relaxation. It is inferred that this is a consequence of the single-chain nature of the present approach not accounting for the fact that viscoelasticity is largely a manifestation of collective multichain modes. In the rigorous sense, no such multichain treatment has yet been established to our knowledge. The necessity to consider interchain cooperativity in any real comprehensive polymer dynamics theory is concluded from low-frequency spin-lattice relaxation data, which are shown to reflect fluctuations of long-distance intermolecular dipole-dipole interactions. © 2000 MAIK "Nauka/Interperiodica"