The mobility of the polymer chains depends on many parameters: the structure of the molecules (chemical bonds), branching of chains, molecular weight, and the external parameters as temperature and pressure. Liquid NMR spectroscopy can help assess the mobility of the molecules. But it is not applicable for polymers with high molecular weight and height viscosity of melt. In this case it is better to use a solid-state NMR.
You can find necessary information in works of de Gennes, Doi and Edwards:
G.de Gennes, Diffusion controled reactions in polymer melts, Radiation Physics and Chemistry 22 (1977) 193-196 http://dx.doi.org/10.1016/0146-5724(83)90203-0
M. Doi, Molecular theory of the viscoelāstic properties of concentrated polymer solutions, Chemical Physics Letters. 26 (1974) 269-272 http://dx.doi.org/10.1016/0009-2614(74)85412-6
S.F Edwards, Dynamics of polymers in solution and melts, Polymer, 26 (1985) 163-168 http://dx.doi.org/10.1016/0032-3861(85)90025-4
The mobility of the polymer chains depends on many parameters: the structure of the molecules (chemical bonds), branching of chains, molecular weight, and the external parameters as temperature and pressure. Liquid NMR spectroscopy can help assess the mobility of the molecules. But it is not applicable for polymers with high molecular weight and height viscosity of melt. In this case it is better to use a solid-state NMR.
You can find necessary information in works of de Gennes, Doi and Edwards:
G.de Gennes, Diffusion controled reactions in polymer melts, Radiation Physics and Chemistry 22 (1977) 193-196 http://dx.doi.org/10.1016/0146-5724(83)90203-0
M. Doi, Molecular theory of the viscoelāstic properties of concentrated polymer solutions, Chemical Physics Letters. 26 (1974) 269-272 http://dx.doi.org/10.1016/0009-2614(74)85412-6
S.F Edwards, Dynamics of polymers in solution and melts, Polymer, 26 (1985) 163-168 http://dx.doi.org/10.1016/0032-3861(85)90025-4
As Fedor mentioned the relaxation time depends on the molecular parameters, temperature and time. In general, faster molecular mobility results in the shorter relaxation time. So, increasing the molecular weight, degree of branching, cross-link density, size of the side groups and decreasing temperature increases the relaxation time by decreasing the molecular mobility. For more information about this subject, you may want to look at the book "Relaxation Phenomena in Polymers" by Matsuoka.
To determine the relaxation time, in solid state, you can use DMA. In the melt state, rheological analysis is the tool. You can use frequency sweep and/or creep-recovery test to determine the relaxation time. You can first do the frequency sweep test and if you couldn't observe the relaxation phenomenon of your polymer in the studied range, then you can apply some methods that are used to extend the frequency range. I prepared a short review on some of those methods about 3 years ago, you can find it in the attachment.
There are many ways to measure the mobility. One is to produce a mono-polar device by placing the polymer between two metals. Then you can perform experiments like DIT (dark injection transients) or SCLC (space charge limited currents). CELIV (charge extraction with linearly increasing voltage) may also be an option.
Some people have already tried to measure relaxation time with photo-celiv. But I doubt that this is accurate. To do it properly you need numerical simulation.
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It is possible to measure (at least qualitatively) both of them by molecular dynamic simulation. Even after doing experiment, MD helps you to address the cause of the data you have obtained.