We combine field-cycling (FC) relaxometry and molecular dynamics (MD) simulations to study the rotational and translational dynamics associated with the glassy slowdown of glycerol. The 1H NMR spin-lattice relaxation rates R1(ω) probed in the FC measurements for different isotope-labelled compounds are computed from the MD trajectories for broad frequency and temperature ranges. We find high correspondence between experiment and simulation. Concerning the rotational motion, we observe that the aliphatic and hydroxyl groups show similar correlation times but different stretching parameters, while the overall reorientation associated with the structural relaxation remains largely isotropic. Additional analysis of the simulation results reveals that transitions between different molecular configurations are slow on the time scale of the structural relaxation at least at sufficiently high temperatures, indicating that glycerol rotates at a rigid entity, but the reorientation is slower for elongated than for compact conformers. The translational contribution to R1(ω) is well described by the force-free hard sphere model. At sufficiently low frequencies, universal square-root laws provide access to the molecular diffusion coefficients. In both experiment and simulation, the time scales of the rotational and translational motions show an unusually large separation, which is at variance with the Stokes–Einstein–Debye relation. To further explore this effect, we investigate the structure and dynamics on various length scales in the simulations. We observe that a prepeak in the static structure factor S(q), which is related to a local segregation of aliphatic and hydroxyl groups, is accompanied by a peak in the correlation times τ(q) from coherent scattering functions.
Due to the single-particle character of the quadrupolar interaction in molecular systems, (2)H NMR poses a unique method for probing reorientational dynamics. Spin-lattice relaxation gives access to the spectral density, and its frequency dependency can be monitored by field-cycling (FC) techniques. However, most FC NMR studies employ (1)H; the use of (2)H is still rare. We report on the application of (2)H FC NMR for investigating the dynamics in molecular liquids and polymers. Commercial as well as home-built relaxometers are employed accessing a frequency range from 30 Hz to 6 MHz. Due to low gyromagnetic ratio, high coupling constants, and finite FC switching times, current (2)H FC NMR does not reach the dispersion region in liquids (toluene and glycerol), yet good agreement with the results from conventional high-field (HF) relaxation studies is demonstrated. The pronounced difference at low frequencies between (2)H and (1)H FC NMR data shows the relevance of intermolecular relaxation in the case of (1)H NMR. In the case of the polymers polybutadiene and poly(ethylene-alt-propylene), very similar relaxation dispersion is observed and attributed to Rouse and entanglement dynamics. Combination with HF (2)H relaxation data via applying frequency-temperature superposition allows the reconstruction of the full spectral density reflecting both polymer as well as glassy dynamics. Transformation into the time domain yields the reorientational correlation function C2(t) extending over nine decades in time with a long-time power law, C2(t) ∝ t(-0.45±0.05), which does not conform to the prediction of the tube-reptation model, for which ∝ t(-0.25) is expected. Entanglement sets in below C2(t = τe) ≅ S(2) = 0.001, where τe is the entanglement time and S the corresponding order parameter. Finally, we discuss the future prospects of the (2)H FC NMR technique.
We investigate complex structure-dynamics relations in glass-forming ionic liquids comprising 1-alkyl-3-methylimidazolium cations and bis(trifluoromethylsulfonyl)imide anions. In doing so, we exploit the microheterogeneous structures emerging when the alkyl length is increased in the range n = 1–12 and use that 1H and 2H NMR give information about cation dynamics, while 19F NMR reports on anion motions. Furthermore, we combine spin-lattice relaxation analysis, including field-cycling relaxometry, with stimulated-echo experiments to follow reorientation dynamics related to structural relaxation in wide dynamic ranges and we apply static field gradients to probe translational diffusion. The resulting correlation times τ and diffusion coefficients D show Vogel-Fulcher-Tammann temperature dependence. Moreover, they indicate a moderate slowdown of both cation and anion dynamics with increasing alkyl length n. However, the relative diffusivities of the ionic species depend on the cation size, where cations are more mobile for n < 6 and anions for n > 6. Finally, we relate rotational and translational motions in the framework of the Stokes-Einstein-Debye (SED) approach. We find that the SED relation is obeyed for anion dynamics in all samples, while it breaks down for cation dynamics when n is increased. The origin of this SED breakdown is shown to differ fundamentally from that reported previously for conventional glass formers. We argue that an emergence of cation clusters causes a retardation of cation diffusion relative to cation reorientation upon cooling, i.e., the studied ionic liquids show a complex interplay of structural and dynamical properties.
Spin-lattice relaxation rates R 1 (ω,T), probed via highfield and field-cycling nuclear magnetic resonance (NMR), are used to test the validity of frequency−temperature superposition (FTS) for the reorientation dynamics in viscous liquids. For several liquids, FTS is found to apply so that master curves can be generated. The susceptibility spectra are highly similar to those obtained from depolarized light scattering (DLS) and reveal an excess wing. Where FTS works, two approaches are suggested to access the susceptibility: (i) a plot of deuteron R 1 (T) vs the spin−spin relaxation rate R 2 (T) and (ii) a plot of R 1 (T) vs an independently measured reference time τ ref (T). Using single-frequency scans, (i) allows one to extract the relaxation stretching as well as the NMR coupling constant. Surveying 26 data sets, we find Kohlrausch functions with exponents 0.39 < β K ≤ 0.67. Plots of the spin−spin relaxation rate R 2 rescaled by the NMR coupling constantas a function of temperature allow one to test how well site-specific NMR relaxations couple to a given reference process. Upon cooling of flexible molecule liquids, the sitespecific dynamics is found to merge, suggesting that near T g the molecules reorient essentially as a rigid entity. This presents a possible resolution for the much lower stretching parameters reported here at high temperatures that contrast with the ones that were reported to be universal in a recent DLS study close to T g . Our analysis underlines that deuteron relaxation is a uniquely powerful tool to probe single-particle reorientation.
We combine 1 H, 7 Li, and 19 F NMR methods to selectively investigate polymer, cation, and anion dynamics in polymer electrolytes on various length and time scales and over broad temperature ranges. By mixing unentangled poly(propylene glycol) (PPG) with lithium perchlorate (LiClO 4 ) or lithium bis-(trifluoromethylsulfonyl)imide (LiTFSI), fully disordered samples are obtained at all studied concentrations. In static field gradient diffusometry, we observe that the longrange motion of all components slows down when the salt concentration is increased, but the effect is more prominent for PPG−LiClO 4 than PPG−LiTFSI electrolytes and, in general, differs for the respective components. The self-diffusion coefficients D of polymer and ions have essentially temperature-independent ratios, where cations are less mobile than anions and do not show Arrhenius temperature dependence. To ascertain short-range motions in broad dynamic ranges, spin−lattice relaxation studies, including field-cycling relaxometry, are combined with stimulated-echo experiments. We show that rate and heterogeneity of local lithium and polymer dynamics depend on the salt content. For intermediate salt concentrations, the segmental motion even exhibits bimodal distributions of correlation times τ, implying structures with salt-rich and salt-depleted regions. Relating diffusion coefficients D and correlation times τ, we find that the lithium ion transport is strongly coupled to polymer segmental motion even in polymer electrolytes with micro-heterogeneous salt distributions. Finally, field-cycling susceptibilities reveal that Rouse dynamics is important not only for the reorganization of polymer chains but also for the transport of lithium ions.
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