Numerical study of dynamical properties of entangled polymer melts in terms of renormalized rouse models

The dynamic properties of n-renormalized Rouse models (n = 1, 2) were numerically investigated. Within two decay orders of magnitude, the damping of normal Rouse modes of a polymer chain was shown to be approximated by the stretched exponential function Cp(t) ∝ exp{- (t/τp*)βp}, where βp is the stretching parameter dependent on the number p of the Rouse mode and τp* is the characteristic decay time. The dependence of the stretching parameter on the mode number has a minimum. It was found that the nonexponential form of autocorrelation functions of the normal modes affects the dynamic characteristics of a polymer chain: the mean-square segment displacement 〈r2(t)〉nRR and the autocorrelation function of the tangential vector 〈b(t)b(0)〉NRR. In comparison with the Markov approximation, the 〈r2(t) 〉TRR and 〈b(t)b(0)〉TRR values in the twice-normalized Rouse model change over time at a lesser rate: ∝t 0.31 and ∝t-0.31 at times t ≪ τ p TRR, respectively. The effect of the finite dimensions of the polymer chain on the relaxation times of the normal modes was studied. Copyright © 2005 by Pleiades Publishing, Inc

Coherent Dynamic Structure Factor of a Polymer Chain Confined Into a Harmonic Radial Potential

The coherent dynamic structure factor of a single polymer chain is calculated based on the model of a Rouse polymer chain constrained (confined) by a harmonic radial potential and its behavior in different limiting cases is analyzed. The strength of confinement is characterized using an effective diameter of the harmonic radial potential as a model parameter. The method provides a reliable model to study the crossover between unconstrained (Rouse) and constrained dynamics

Numerical study of dynamical properties of entangled polymer melts in terms of renormalized rouse models

The dynamic properties of n-renormalized Rouse models (n = 1, 2) were numerically investigated. Within two decay orders of magnitude, the damping of normal Rouse modes of a polymer chain was shown to be approximated by the stretched exponential function Cp(t) ∝ exp{- (t/τp*)βp}, where βp is the stretching parameter dependent on the number p of the Rouse mode and τp* is the characteristic decay time. The dependence of the stretching parameter on the mode number has a minimum. It was found that the nonexponential form of autocorrelation functions of the normal modes affects the dynamic characteristics of a polymer chain: the mean-square segment displacement 〈r2(t)〉nRR and the autocorrelation function of the tangential vector 〈b(t)b(0)〉NRR. In comparison with the Markov approximation, the 〈r2(t) 〉TRR and 〈b(t)b(0)〉TRR values in the twice-normalized Rouse model change over time at a lesser rate: ∝t 0.31 and ∝t-0.31 at times t ≪ τ p TRR, respectively. The effect of the finite dimensions of the polymer chain on the relaxation times of the normal modes was studied. Copyright © 2005 by Pleiades Publishing, Inc

Numerical study of dynamical properties of entangled polymer melts in terms of renormalized rouse models

The dynamic properties of n-renormalized Rouse models (n = 1, 2) were numerically investigated. Within two decay orders of magnitude, the damping of normal Rouse modes of a polymer chain was shown to be approximated by the stretched exponential function Cp(t) ∝ exp{- (t/τp*)βp}, where βp is the stretching parameter dependent on the number p of the Rouse mode and τp* is the characteristic decay time. The dependence of the stretching parameter on the mode number has a minimum. It was found that the nonexponential form of autocorrelation functions of the normal modes affects the dynamic characteristics of a polymer chain: the mean-square segment displacement 〈r2(t)〉nRR and the autocorrelation function of the tangential vector 〈b(t)b(0)〉NRR. In comparison with the Markov approximation, the 〈r2(t) 〉TRR and 〈b(t)b(0)〉TRR values in the twice-normalized Rouse model change over time at a lesser rate: ∝t 0.31 and ∝t-0.31 at times t ≪ τ p TRR, respectively. The effect of the finite dimensions of the polymer chain on the relaxation times of the normal modes was studied. Copyright © 2005 by Pleiades Publishing, Inc

Numerical study of dynamical properties of entangled polymer melts in terms of renormalized rouse models

The dynamic properties of n-renormalized Rouse models (n = 1, 2) were numerically investigated. Within two decay orders of magnitude, the damping of normal Rouse modes of a polymer chain was shown to be approximated by the stretched exponential function Cp(t) ∝ exp{- (t/τp*)βp}, where βp is the stretching parameter dependent on the number p of the Rouse mode and τp* is the characteristic decay time. The dependence of the stretching parameter on the mode number has a minimum. It was found that the nonexponential form of autocorrelation functions of the normal modes affects the dynamic characteristics of a polymer chain: the mean-square segment displacement 〈r2(t)〉nRR and the autocorrelation function of the tangential vector 〈b(t)b(0)〉NRR. In comparison with the Markov approximation, the 〈r2(t) 〉TRR and 〈b(t)b(0)〉TRR values in the twice-normalized Rouse model change over time at a lesser rate: ∝t 0.31 and ∝t-0.31 at times t ≪ τ p TRR, respectively. The effect of the finite dimensions of the polymer chain on the relaxation times of the normal modes was studied. Copyright © 2005 by Pleiades Publishing, Inc

Direct Observation of confined Single Chain Dynamics by Neutron Scattering

Neutron spin echo has revealed the single chain dynamic structure factor of entangled polymer chains confined in cylindrical nanopores with chain dimensions either much larger or smaller than the lateral pore sizes. In both situations, a slowing down of the dynamics with respect to the bulk behavior is only observed at intermediate times. The results at long times provide a direct microscopic measurement of the entanglement distance under confinement. They constitute the first experimental microscopic evidence of the dilution of the total entanglement density in a polymer melt under strong confinement, a phenomenon that so far was hypothesized on the basis of various macroscopic observations