Carbon‐13 NMR measurments of polybutadiene local dynamics in dilute solution: Further evidence for non‐Kramers' behavior

Abstract

The local segmental dynamics of cis‐polybutadiene in dilute solutions have been investigated using natural abundance 13C NMR spectroscopy. The time integral of the CH orientation autocorrelation function 〈σ〉 is extracted from T1 measurements in five solvents covering a viscosity range of two decades. The hydrodynamic Kramers' equation, which is generally assumed to be appropriate for local polymer dynamics in dilute solution, cannot describe these results. 〈σ〉 is found to depend upon the solvent viscosity η raised to the 0.33 power whether η is varied by changing the temperature or the solvent. This apparent power law behavior has been observed for other polymers in dilute solution and can be rationalized if the solvent is viewed as viscoelastic. This view is supported by experimental results which show that local polymer dynamics can occur as much as an order of magnitude faster than solvent reorientation. Trends for a mixed microstructure polybutadiene are similar to those of cis‐polybutadiene. © 1994 John Wiley & Sons, Inc.

Viscosity Dependence of Polystyrene Local Dynamics in Dilute Solution

“…The α values for PVC and PNMA are model dependent and have undetermined error bars. α is obtained from the following references: cis -PB, ref ; PI, ref ; 1,2-PB, ref ; PVC(poly(vinyl chloride)), ref ; PS, this work; PNMA (poly(1-naphthylmethyl acrylate)), ref . The line is drawn to guide the eye. …”

“…This theory predicts that these dynamics have a linear dependence on solvent viscosity. Recent work − has shown that Kramers' theory is not applicable for at least some polymers. Instead of a linear dependence on solvent viscosity, local polymer relaxation times are found to have an apparent power law dependence.…”

“…Instead of a linear dependence on solvent viscosity, local polymer relaxation times are found to have an apparent power law dependence. The use of Kramers' theory where it is not applicable can lead to serious errors in the determination of the potential energy barrier between different conformational states. , This potential energy barrier has been postulated to be one of the most important parameters determining T g for bulk polymers.…”

Deuterium NMR Characterization of 1,2-Polybutadiene Local Dynamics in Dilute Solution

“…( ) = G(t) dt (4) T\ is inversely proportional to ( ) in the extreme narrowing regime: Y = § Ae2qQlhf(o) (5) One criterion for the extreme narrowing region is that T\ is independent of the Larmor frequency. Another criterion often used is that T\ = T2.…”

“…It has previously been argued that the problem is unlikely to be caused by the high friction assumption41 or by the use of Stokes' law to connect friction and viscosity.4 The most likely explanation for the failure of eq 6 lies in the derivation of the Kramers' equation from the Langevin equation. 4 The Langevin equation is an approximate description of a system which is accurate only if there exists a significant separation of time scales between system and bath dynamics. In this problem, the polymer chain is the system and the solvent is the bath.…”