No abstract

No abstract

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.

Poly­(propylene glycol), poly­(isoprene), and poly­(dimethlyl siloxane) (PDMS) of different molecular masses M are investigated by field-cycling 1H NMR relaxometry to monitor the crossover from segmental dynamics, to Rouse and entanglement dynamics. The spin–lattice relaxation dispersions T 1(ω) obtained at different temperatures (160 K – 400 K) are converted to the susceptibility representation χ″ DD (ω) = ω/T 1(ω). Applying frequency–temperature superposition, the data are merged to provide master curves χ″ DD (ωτ s ) with τ s = τ s (T) being the segmental correlation times. Combining them with those from dielectric spectroscopy about 12 decades in time are covered. A similar M dependence of χ″ DD (ωτ s ) is observed for all polymers (t ≫ τ s ) and comparison with dielectric normal mode spectra is carried out. In the case of PDMS showing particularities at t ≈ τ s we attempt to separate intra- and intermolecular relaxation contributions. Transformation into time domain yields the dipolar correlation function C DD (t/τ s ) which covers up to six decades in amplitude and eight decades in time. Whereas glassy dynamics is observed at shortest times, the correlation function closely follows C DD (t) ∝ t –1 at intermediate times as predicted by the Rouse theory. For longer times and high M entanglement sets in yielding C DD (t) ∝ t –ε with ε (<1) being M-dependent. As for the previously studied poly­(butadiene), a highly protracted transition to full reptation is observed.

Field Cycling Nuclear Magnetic Resonance (FC NMR) relaxation studies are reported for three ionic liquids: 1-ethyl-3- methylimidazolium thiocyanate (EMIM-SCN, 220-258 K), 1-butyl-3-methylimidazolium tetrafluoroborate (BMIM-BF4, 243-318 K), and 1-butyl-3-methylimidazolium hexafluorophosphate (BMIM-PF6, 258-323 K). The dispersion of (1)H spin-lattice relaxation rate R1(ω) is measured in the frequency range of 10 kHz-20 MHz, and the studies are complemented by (19)F spin-lattice relaxation measurements on BMIM-PF6 in the corresponding frequency range. From the (1)H relaxation results self-diffusion coefficients for the cation in EMIM-SCN, BMIM-BF4, and BMIM-PF6 are determined. This is done by performing an analysis considering all relevant intra- and intermolecular relaxation contributions to the (1)H spin-lattice relaxation as well as by benefiting from the universal low-frequency dispersion law characteristic of Fickian diffusion which yields, at low frequencies, a linear dependence of R1 on square root of frequency. From the (19)F relaxation both anion and cation diffusion coefficients are determined for BMIM-PF6. The diffusion coefficients obtained from FC NMR relaxometry are in good agreement with results reported from pulsed- field-gradient NMR. This shows that NMR relaxometry can be considered as an alternative route of determining diffusion coefficients of both cations and anions in ionic liquids.

The enhancement of the spin-lattice relaxation rate for nuclear spins in a ligand bound to a paramagnetic metal ion [known as the paramagnetic relaxation enhancement (PRE)] arises primarily through the dipole-dipole (DD) interaction between the nuclear spins and the electron spins. In solution, the DD interaction is modulated mostly by reorientation of the nuclear spin-electron spin axis and by electron spin relaxation. Calculations of the PRE are in general complicated, mainly because the electron spin interacts so strongly with the other degrees of freedom that its relaxation cannot be described by second-order perturbation theory or the Redfield theory. Three approaches to resolve this problem exist in the literature: The so-called slow-motion theory, originating from Swedish groups [Benetis et al., Mol. Phys. 48, 329 (1983); Kowalewski et al., Adv. Inorg. Chem. 57, (2005); Larsson et al., J. Chem. Phys. 101, 1116 (1994); T. Nilsson et al., J. Magn. Reson. 154, 269 (2002)] and two different methods based on simulations of the dynamics of electron spin in time domain, developed in Grenoble [Fries and Belorizky, J. Chem. Phys. 126, 204503 (2007); Rast et al., ibid. 115, 7554 (2001)] and Ann Arbor [Abernathy and Sharp, J. Chem. Phys. 106, 9032 (1997); Schaefle and Sharp, ibid. 121, 5387 (2004); Schaefle and Sharp, J. Magn. Reson. 176, 160 (2005)], respectively. In this paper, we report a numerical comparison of the three methods for a large variety of parameter sets, meant to correspond to large and small complexes of gadolinium(III) and of nickel(II). It is found that the agreement between the Swedish and the Grenoble approaches is very good for practically all parameter sets, while the predictions of the Ann Arbor model are similar in a number of the calculations but deviate significantly in others, reflecting in part differences in the treatment of electron spin relaxation. The origins of the discrepancies are discussed briefly.

By application of the field-cycling technique, we measure the dispersion of the (1)H nuclear magnetic resonance (NMR) spin-lattice relaxation time T(1)(ω) for a series of molecular liquids. We demonstrate that such NMR relaxometry studies can be used for determining diffusion coefficients. A broad frequency range of 10 kHz-20 MHz is covered. By scanning T(1)(ω) one directly probes the spectral density of the diffusion processes. The value of the diffusion coefficient D can be determined from a linear dependence of the (1)H spin-lattice relaxation rate on the square root of the frequency at which it is measured. The power of this method lies in its simplicity, which allows one to determine D(T) independently of the diffusive model. The results obtained are in very good agreement with those of field gradient NMR methods.