Mixtures of protonated and deuterated polybutadiene and polydimethylsiloxane are studied by means of field-cycling (FC) 1H NMR relaxometry in order to analyze the intra- and intermolecular contributions to spin–lattice relaxation. They reflect reorientational and translational dynamics, respectively. Master curves in the susceptibility representation χ″(ωτs) are constructed by employing frequency–temperature superposition with τs denoting the segmental correlation time. The intermolecular contribution is dominating at low frequencies and allows extracting the segmental mean square displacement ⟨R 2(t)⟩, which reveals two power-law regimes. The one at short times agrees with t 0.5 predicted for the free Rouse regime and at long times a lower exponent is observed in fair agreement with t 0.25 expected for the constrained Rouse regime of the tube-reptation model. Concomitantly the reorientational rank-two correlation function C 2(t/τs) is obtained from the intramolecular part. Again two power-law regimes t –ε are identified for polybutadiene. The first agrees with t –1 of free Rouse dynamics whereas at long times ε = 0.49 is obtained. The latter is corroborated by the 2H relaxation of deuterated polybutadiene, yet, it does not agree with ε = 0.25 predicted for constrained Rouse dynamics. Thus, the relation C 2(t) ∝ ⟨R 2(t)⟩–1 as assumed by the tube-reptation model is not confirmed.

The segmental dynamics of 1,4-polybutadiene is investigated by means of electronic field cycling 1H NMR. The frequency dependence (dispersion) of the spin–lattice relaxation time is probed over a broad range of temperature (223–408 K), molecular mass (355 ≤ M (g/mol) ≤ 441 000), and frequency (200 Hz–30 MHz). The extremely low frequencies are accessed by employing a home-built compensation for earth and stray fields extending prior reports about 2 decades to lower frequencies. Applying frequency–temperature superposition yields master curves over 10 decades in frequency (or time), and after Fourier transform the full dipolar correlation function is traced over up to 8 decades in amplitude. Several relaxation regimes can be identified, and their power-law exponents are compared to the predictions of the Doi–Edwards tube-reptation model, namely the free Rouse (I) and the constrained Rouse regime (II). Whereas the predicted value of the power-law exponent of regime II is 0.25, we find that it depends on M and levels off at 0.32 for very high M = 441 000 ≈ 220M e (M e: entanglement molecular mass). This is in good agreement with recent results from double quantum 1H NMR and indicates that the actual onset of full reptation dynamics is strongly protracted.

Field-cycling and field-gradient 1H NMR experiments were combined to reveal the segmental mean-square displacement as a function of time for polydimethylsiloxane (PDMS) and polybutadiene (PB). Together, more than 10 decades in time are covered, and all four power-law regimes of the tube-reptation (TR) model are identified with exponents rather close to the predicted ones. Characteristic polymer properties like the tube diameter a 0, the Kuhn length b, the mean-square end-to-end distance ⟨R 0 2⟩, the segmental correlation time τs(T), the entanglement time τe(T), and the disengagement time τd(T) are estimated from the measurements and compared to results from literature. Concerning τd(T), fair agreement is found. In the case of τe, agreement with rheological data is achieved when the time constant is extracted from the minimum in the shear modulus G″(ω). Concerning the TR predictions the molar mass (M) dependence of τd is essentially reproduced. Yet, calculating τe from τd for PDMS yields agreement with experimental data while for PB it gets by 2 orders of magnitude too short. In no case τe is correctly reproduced from τs(T). Segmental and shortest Rouse times appear to coincide for PB, while in the case of PDMS the latter turns out to be longer by 1 decade.

Field-cycling (FC) 1H and 2H NMR relaxometry is applied to linear polybutadiene (PB) of different molar mass (M) in order to test current polymer theories. Applying earth field compensation, five decades in the frequency dependence of the spin–lattice relaxation rate T 1 –1(ν) = R 1(ν) are accessed (200 Hz - 30 MHz), and we focus on the crossover from Rouse to entanglement dynamics. A refined evaluation is presented, which avoids application of frequency–temperature superposition as well as Fourier transformation. Instead, the power-law exponent ε in the entanglement regime is directly determined from the susceptibility representation χNMR ″(ω) = ω/T 1(ω) ∝ ωε by a derivative method. Correspondingly, a power-law t –ε characterizes the decay in the time domain, i.e., the dipolar correlation function. For the total 1H relaxation, comprising intra- and intermolecular relaxation, a high-M exponent εtotal = 0.31 ± 0.03 is found. An isotope dilution experiment, which yields the intramolecular relaxation reflecting solely segmental reorientation, provides an exponent εintra = 0.44 ± 0.03. It agrees with that of FC 2H NMR (ε Q = 0.42 ± 0.03) probing only segmental reorientation. The fact that εintra > εtotal demonstrates the relevance of intermolecular relaxation in the entanglement regime (but not in the Rouse regime), and εintra is significantly higher than predicted by the tube-reptation (TR) model (εTR = 0.25) and, the latter being supported also by recent simulations. The ratio of inter- to intramolecular relaxation grows with decreasing frequency, again in contradiction to the TR model and results from double quantum 1H NMR. We conclude that no clear evidence of a tube is found on the microscopic level and the so-called return-to-origin hypothesis is not confirmed. Studying the influence of chain end dynamics by FC 1H NMR we compare differently chain end deuterated PB. For the dynamics of the central part of the polymer the exponent drops from εintra = 0.66 ± 0.03 down to εcent = 0.41 ± 0.03 for M = 29k which is very close to the high-M value εintra. Thus, the protracted transition to entanglement dynamics reported before is not found when the polymer center is probed; instead full entanglement dynamics appears to set in directly with M > M e .

A recent measurement of the hyperfine splitting in the ground state of Li-like ^{208}Bi^{80+} has established a "hyperfine puzzle"-the experimental result exhibits a 7σ deviation from the theoretical prediction [J. Ullmann et al., Nat. Commun. 8, 15484 (2017)NCAOBW2041-172310.1038/ncomms15484; J. P. Karr, Nat. Phys. 13, 533 (2017)NPAHAX1745-247310.1038/nphys4159]. We provide evidence that the discrepancy is caused by an inaccurate value of the tabulated nuclear magnetic moment (μ_{I}) of ^{209}Bi. We perform relativistic density functional theory and relativistic coupled cluster calculations of the shielding constant that should be used to extract the value of μ_{I}(^{209}Bi) and combine it with nuclear magnetic resonance measurements of Bi(NO_{3})_{3} in nitric acid solutions and of the hexafluoridobismuthate(V) BiF_{6}^{-} ion in acetonitrile. The result clearly reveals that μ_{I}(^{209}Bi) is much smaller than the tabulated value used previously. Applying the new magnetic moment shifts the theoretical prediction into agreement with experiment and resolves the hyperfine puzzle.