NMR field-cycling relaxation spectroscopy, transverse NMR relaxation, self-diffusion and zero-shear viscosity: Defect diffusion and reptation in non-glassy amorphous polymers

Abstract

Molecular weight and frequency dependences, respectively, of the nuclear magnetic relaxation times and the self-diffusion coefficient of polyethylene and polystyrene have been investigated over several orders of magnitude. The relation to viscous behaviour is established. A closed concept is developed. Conclusions are: a) The y-process in amorphous polyethylene can be described by the aid of the limited defect diffusion model. b) The fl-process in the same material is interpreted as limited reptation. The intensity function of this process depends on the amorphous content. c) The three-component description of chain fluctuations already presented in previous papers has been modified in order to account for the precise molecular weight dependences, which now have been measured. Especially we distinguish between internal and whole-chain reptation. A correlation function is derived, which predicts the right limiting behaviour inspite of its semi-empirical character. The three components can be identified by the frequency and molecular weight dependences of the nuclear magnetic relaxation times. d) The molecular weight dependences are subdivided by 3 (spin lattice relaxation), 2 (transverse relaxation), 1 (zero-shear viscosity) and 0 (self-diffusion coefficient) characteristic molecular weights (Me, MBo MA~ ). All of them can be derived as dynamic case transitions. Especially the classical critical molecular weight of the viscosity can be explained by the transition between tube fluctuations governed by internal and wholechain reptation, respectively. The assumption of a structural transition is unnecessary. e) A semi-empirical expression for the zero-shear viscosity is derived for the whole range of chain lengths. The analysis of the molecular weight dependences of the NMR relaxation times straightforwardly leads to those of the zero-shear viscosity. f) Using a NMR field-gradient method, it is shown again that the self-diffusion coefficients of both melt examples obey D ~ M~72~ g) Matrix effects predominantly are due to changes in the free volume.

Molecular Dynamics in Polymers

“…Nevertheless, there are systematic shortcomings of the model which will shortly be discussed in the following points outlining a number of discrepancies with experimental findings. law predicted for limit (IV) DE appears to be corroborated at first sight by early studies [67,[78][79][80]. However, there are a number of effects that may influence the outcome of such measurements.…”

“…Ref. [67] The experimental parameters are molecular mass M ¼ N K M K ð Þ , time (t), and angular frequency (o)…”

The chain length dependence of self-diffusion in melts of polyethylene and polystyrene

“…The measured echo attenuation plot is shown in Figure 5 together with the echo attenuation plots calculated numerically with Equation (4) Figure 6. For this sample the factors Ao(M) could be set constant since due to long nuclear relaxation times of polyethylene in this molar mass region [27,28] and the short measuring times (~1 = 3 ms and 32 = 50 ms in the stimulated echo experiment) the nuclear magnetic relaxation could be neglected.…”

Three‐dimensional water diffusion in impermeable cylindrical tubes: theory versus experiments

“…In polymer physics, macromolecular-sized cylindrical 'tubes' through which longchain polymers reptate (1) can be viewed as pores. Knowledge of the displacement distribution of monomers on the backbone of long-chain polymers, as well as the shape of this reptation tube, is useful in understanding polymer mobility (2). Finally, in materials engineering and biotechnology applications, morphological and microstructural features of porous materials determine transport of charge, mass, momentum, and heat, and are thus critical properties in applications ranging from catalysis (3) to water purification to tissue engineering (4).…”