Field-cycling 31P and 1H NMR relaxometry studying the reorientational dynamics of glass forming organophosphates.

We apply field-cycling (FC) 31P nuclear magnetic resonance (NMR) to access the reorientational susceptibility of two glass formers, m-tricresyl phosphate (m-TCP) and tri-butyl phosphate (TBP). Although FC 31P studies are still instrumentally demanding, together with FC 1H data, they provide site-resolved information. A crossover from dipolar relaxation at low frequencies to relaxation determined by chemical shift anisotropy at high frequencies and probed by conventional NMR is identified. A comparison is made between dielectric (DS) and depolarized light scattering (DLS) relaxation spectra demonstrating similar behavior close to Tg, including an excess wing contribution for m-TCP. The time constants of 31P NMR and DLS, probing the molecular core, agree. The 1H data monitoring the dynamics of the phenyl groups yield slightly shorter correlation times. At high temperatures, the DS relaxation spectra show a bimodal character: a fast component in agreement with 1H data, and a slow component much slower than 31P NMR and DLS suggest. We discuss the possible origins of the slow component. All time constants tend to merge toward Tg. Hence, we propose that site-specific dynamics disappear and a common α-relaxation establishes near Tg. In addition, we compare the diffusion coefficient D(T) determined by FC and static field gradient 1H NMR. Concerning TBP, we present FC 31P data of both α- and ß-processes. Regarding the latter, we compare the DS and NMR susceptibility on absolute scale, yielding a significantly stronger ß-relaxation in the 31P NMR spectra.

NMR Relaxometry: The Canonical Case Glycerol.

We present a quantitative description of the proton spin-lattice relaxation rate R1(T,ω) of glycerol including temperatures from 191 to 360 K and a frequency range 10 kHz < ω/2π < 20 MHz covered by the field-cycling technique. The analysis encompasses the data compiled by Noack and co-workers in 1971, so far, the most complete data set (10 kHz > ω/2π < 117 MHz). Applying frequency-temperature superposition, master curves are constructed extending over 15 decades in frequency/time. They are described by contributions reflecting translational and rotational dynamics mediated by inter- and intramolecular relaxation pathways. The rotational part of the spectral density/susceptibility shows high similarity with those reported by dielectric spectroscopy or photon correlation spectroscopy (PCS). In addition to a Cole-Davidson-like peak, a high-frequency "excess wing" has to be accounted for. Quantitative agreement with the PCS susceptibility is found which probes the same order of the rotational correlation function. The translational contribution is reproduced by applying the force-free hard sphere model, describing diffusion of dipolarly coupled spin systems. Rotational and translational time constants are compared to those from other techniques. Our approach is paradigmatic for the analysis of spin relaxation in glass-forming liquids. It also solves long-standing deficiencies regarding the analyses of deuteron relaxation. Moreover, the case of glycerol is special as its large separation of translation and rotation dynamics, probably because of its hydrogen bond network, is not found in nonassociated liquids.

The dynamics of the plastically crystalline phase of cyanoadamantane revisited by NMR line shape analysis and field-cycling relaxometry.

The dynamics of cyanoadamantane (CN-ADA) in its plastically crystalline phase encompasses three processes: overall tumbling of the rigid molecule, rotation around the molecular symmetry axis, and vacancy diffusion. This makes CN-ADA a prototypical case to be studied by field-cycling as well as by conventional NMR relaxometry. Data are collected from 430 K down to about 4 K and frequencies in the range of 10 kHz-56 MHz are covered. The overall tumbling is interpreted as a cooperative jump process preceding along the orthogonal axis of the cubic lattice and exhibiting a temperature independent non-Lorentzian spectral density. Consequently, a master curve is constructed, which yields model-independent correlation times, which agree well with those reported in the literature. It can be interpolated by a Cole-Davidson function with a width parameter ßCD = 0.83. The uniaxial rotation persisting in the glassy crystal (T < Tg = 170 K) is governed by a broad distribution of activation energies, g(E). In this case, the standard master curve construction applied for the overall tumbling, for example, fails, as the actually probed distribution of correlation times G(ln τ) strongly changes with temperature. We suggest a scaling method that generally applies for the case that a relaxation process is determined by a distribution of thermally activated processes. Frequency as well as temperature dependence of the relaxation rate can be used to reconstruct g(E). In addition, g(E) is extracted from the proton line-shape, which was measured down to 4 K. Vacancy diffusion governs the relaxation dispersion at highest temperatures; yet, a quantitative analysis is not possible due to instrumental limitations.

Scaling analysis of the viscoelastic response of linear polymers.

Viscoelastic response in terms of the complex shear modulus G*(ω) of the linear polymers poly(ethylene-alt-propylene), poly(isoprene), and poly(butadiene) is studied for molar masses (M) from 3k up to 1000k and over a wide temperature range starting from the glass transition temperature Tg (174 K-373 K). Master curves G'(ωτα) and G″(ωτα) are constructed for the polymer-specific relaxation. Segmental relaxation occurring close to Tg is independently addressed by single spectra. Altogether, viscoelastic response is effectively studied over 14 decades in frequency. The structural relaxation time τα used for scaling is taken from dielectric spectra. We suggest a derivative method for identifying the different power-law regimes and their exponents along G″(ωτα) ∝ ωε″. The exponent ε″ = ε″(ωτα) ≡ d ln G″(ωτα)/d ln(ωτα) reveals more details compared to conventional analyses and displays high similarity among the polymers. Within a simple scaling model, the original tube-reptation model is extended to include contour length fluctuations (CLFs). The model reproduces all signatures of the quantitative theory by Likhtman and McLeish. The characteristic times and power-law exponents are rediscovered in ε″(ωτα). The high-frequency flank of the terminal relaxation closely follows the prediction for CLF (ε″ = -0.25), i.e., G″(ω) ∝ ω-0.21±0.02. At lower frequencies, a second regime with lower exponent ε″ is observed signaling the crossover to coherent reptation. Application of the full Likhtman-McLeish calculation provides a quantitative interpolation of ε″(ωτα) at frequencies below those of the Rouse regime. The derivative method also allows identifying the entanglement time τe. However, as the exponent in the Rouse regime (ωτe > 1) varies along εeRouse = 0.66 ± 0.04 (off the Rouse prediction εRouse = 0.5) and that at ωτe < 1 is similar, only a weak manifestation of the crossover at τe is found at highest M. Yet, calculating τe/τα= (M/Mo)2, we find good agreement among the polymers when discussing ε″(ωτe). The terminal relaxation time τt is directly read off from ε″(ωτα). Plotting τt/τe as a function of Z = M/Me, we find universal behavior as predicted by the TR model. The M dependence crosses over from an exponent significantly larger than 3.0 at intermediate M to an exponent approaching 3.0 at highest M in agreement with previous reports. The frequency of the minimum in G″(ωτα) scales as τmin ∝ M1.0±0.1. An M-independent frequency marks the crossover to glassy relaxation at the highest frequencies. Independent of the amplitude of G″(ω), which may be related to sample-to-sample differences, the derivative method is a versatile tool to provide a detailed phenomenological analysis of the viscoelastic response of complex liquids.

Perspectives of Deuteron Field-Cycling NMR Relaxometry for Probing Molecular Dynamics in Soft Matter.

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.