Systematic Dielectric and NMR Study of the Ionic Liquid 1‐Alkyl‐3‐Methyl Imidazolium

The dynamic behaviors of ionic liquid samples consisting of a series of 1‐alkyl‐3‐methylimidazolium cations and various counteranionic species are investigated systematically over a wide frequency range from 1 MHz to 20 GHz at room temperature using dielectric relaxation (DR) and nuclear magnetic resonance (NMR) spectroscopies. DR spectra for the ionic liquids are reasonably deconvoluted into two or three relaxation modes. The slowest relaxation times are strongly dependent upon sample viscosity and cation size, whereas the relaxation times of other modes are almost independent of these factors. We attribute the two slower relaxation modes to the rotational relaxation modes of the dipolar cations because the correlation times of the cations evaluated using longitudinal relaxation time (T₁ ¹³C NMR) measurements corresponded to the dielectric relaxation times. On the other hand, the fastest relaxation mode is presumably related to the inter‐ion motions of ion‐pairs formed between cationic and anionic species. In the case of the ionic liquid bis(trifluoromethanesulfonyl)imide, the system shows marked dielectric relaxation behavior due to rotational motion of dipolar anionic species in addition to the relaxation modes attributed to the dipolar cations.     

Molecular mobility of lyophilized poly(vinylpyrrolidone) and methylcellulose as determined by the laboratory and rotating frame spin-lattice relaxation times of 1H and 13C

Laboratory- and rotating- frame spin-lattice relaxation times (T(1) and T(1rho)) of (1)H and (13)C in lyophilized poly(vinylpyrrolidone) (PVP) and methylcellulose (MC) are determined to examine feasibility of using T(1) and T(1rho) as a measure of molecular motions on large time scales related to the storage stability of lyophilized formulations. The T(1rho) of proton and carbon was found to reflect the mobility of PVP and MC backbones, indicating that it is useful as a measure of large-time-scale molecular motions. In contrast to the T(1rho), the T(1) of proton measured in the same temperature range reflected the mobility of PVP and MC side chains. The T(1) of proton may be useful as a measure of local molecular motions on a smaller-time-scale, although the measurement is interfered by moisture under some conditions. The temperature dependence of T(1) and T(1rho) indicated that methylene in the MC molecule had much higher mobility than that in the dextran molecule, also indicated that methylene in the PVP side chain had a higher mobility than that in the MC side chain.     

Angular and frequency dependent spin relaxation study of liquid crystalline cyanobiphenyls

NMR field-cycling measurements of the Larmor frequency (v) and angular (Δ) dependences of the longitudinal proton spin relaxation time T₁ for the nematic liquid crystals 5CB and 8CB allow a more detailed analysis of the underlying molecular motions than data available previously. All T₁ (v, Δ) dispersion profiles essentially distinguish three frequency ranges where T₁ is governed by either local field effects, collective motions (director order fluctuations), or rotational and translational diffusion of individual molecules or molecular groups, respectively. The angular dependence supports and extends previous conclusions about the significance of the order fluctuation term at low (kHz) and high (MHz) Larmor frequencies; in addition it is the basis for the disentanglement of local field effects, which involve Jeener's dipolar relaxation, and of the sophisticated rotational relaxation models suggested in the literature by Dong, Nordio and Vold. It is found that Vold's third rate concept gives the best explanation of the measurements. The results on the rotational diffusion processes essentially agree with deuteron studies from the literature, but also reveal clear distinctions with regard to the anisotropy parameter σ, essentially due to the improved separation from the order fluctuation contribution.     

Conformation analysis and molecular mobility of ethylene and tetrafluoroethylene copolymer using solid-state 19F MAS and 1H --> 19F CP/MAS NMR spectroscopy

The changes in the conformation and molecular mobility accompanied by a phase transition in the crystalline domain were analyzed for ethylene (E) and tetrafluoroethylene (TFE) copolymer, ETFE, using variable-temperature (VT) solid-state 19F magic angle spinning (MAS) and 1H --> 19F cross-polarization (CP)/MAS NMR spectroscopy. The shifts of the signals for fluorines in TFE units to higher frequency and the continuing decrease and increase in the T1rho(F) values suggest that conformational exchange motions exist in the crystalline domain between 42 and 145 degrees C. Quantum chemical calculations of magnetic shielding constants showed that the high-frequency shift of TFE units should be induced by trans to gauche conformational changes at the CH2-CF2 linkage in the E-TFE unit. Although the 19F signals of the crystalline domain are substantially overlapped with those of the amorphous domain at ambient probe temperature (68 degrees C), they were successfully distinguished by using the dipolar filter and spin-lock pulse sequences at 145 degrees C. The dipolar coupling constants for the crystalline domain, which can be estimated by fitting the dipolar oscillation behaviors in the 1H --> 19F CP curve, showed a significant decrease with increasing temperature from 42 to 145 degrees C. This is due to the averaging of 1H-19F dipolar interactions originating from the molecular motion in the crystalline domain. The increase in molecular mobility in the crystalline domain was clearly shown by VT T1rho(F) and 1H --> 19F CP measurements in the phase transition temperature range.     

Carbon-13 chemical shift anisotropy in DNA bases from field dependence of solution NMR relaxation rates

Knowledge of (13)C chemical shift anisotropy (CSA) in nucleotide bases is important for the interpretation of solution-state NMR relaxation data in terms of local dynamic properties of DNA and RNA. Accurate knowledge of the CSA becomes particularly important at high magnetic fields, prerequisite for adequate spectral resolution in larger oligonucleotides. Measurement of (13)C relaxation rates of protonated carbons in the bases of the so-called Dickerson dodecamer, d(CGCGAATTCGCG)(2), at 500 and 800 MHz (1)H frequency, together with the previously characterized structure and diffusion tensor yields CSA values for C5 in C, C6 in C and T, C8 in A and G, and C2 in A that are closest to values previously reported on the basis of solid-state FIREMAT NMR measurements, and mostly larger than values obtained by in vacuo DFT calculations. Owing to the noncollinearity of dipolar and CSA interactions, interpretation of the NMR relaxation rates is particularly sensitive to anisotropy of rotational diffusion, and use of isotropic diffusion models can result in considerable errors.     

Mobility of solid tert-butyl alcohol studied by deuterium NMR

The molecular mobility of solid deuterated tert-butyl alcohol (TBA) has been studied over a broad temperature range (103–283 K) by means of solid-state 2H NMR spectroscopy, including both line shape and anisotropy of spin–lattice relaxation analyses. It has been found that, while the hydroxyl group of the TBA molecule is immobile on the 2H NMR time scale (τC > 10(–5) s), its butyl group is highly mobile. The mobility is represented by the rotation of the methyl [CD3] groups about their 3-fold axes (C3 rotational axis) and the rotation of the entire butyl [(CD3)3-C] fragment about its 3-fold axis (C3′ rotational axis). Numerical simulations of spectra line shapes reveal that the methyl groups and the butyl fragment exhibit three-site jump rotations about their symmetry axes C3 and C3′ in the temperature range of 103–133 K, with the activation energies and preexponential factors E1 = 21 ± 2 kJ/mol, k(01) = (2.6 ± 0.5) × 10(12) s(–1) and E2 = 16 ± 2 kJ/mol, k(02) = (1 ± 0.2) × 10(12) s(–1), respectively. Analysis of the anisotropy of spin–lattice relaxation has demonstrated that the reorientation mechanism of the butyl fragment changes to a free diffusion rotational mechanism above 173 K, while the rotational mechanism of the methyl groups remains the same. The values of the activation barriers for both rotations at T > 173 K have the values, which are similar to those at 103–133 K. This indicates that the interaction potential defining these motions remains unchanged. The obtained data demonstrate that the detailed analysis of both line shape and anisotropy of spin–lattice relaxation represents a powerful tool to follow the evolution of the molecular reorientation mechanisms in organic solids.     

Effect of water on the molecular mobility of sucrose and poly(vinylpyrrolidone) in a colyophilized formulation as measured by (13)C-NMR relaxation time

Individual molecular mobility of sucrose and poly(vinylpyrrolidone) (PVP) in a colyophilized mixture of 1 : 1 by weight has been determined by (13)C spin-lattice relaxation times in the laboratory frame (T(1)) and in the rotating frame (T(1 rho)) for systems containing absorbed water at various levels. The T(1) of the PVP pyrrolidone ring carbon increased with storage relative humidity (RH) in lyophilized PVP alone, indicating that the MHz-order motions of PVP side chain increased with storage RH. However, in the colyophilized mixture, the side chain motions of PVP did not change with storage RH, and showed similar mobility to sucrose. This may be caused by hydrogen bonding between the PVP ring carbonyl group and hydroxyl group of sucrose, as suggested by a previous FT-Raman study. The mid-kHz-order motions of sucrose in the sucrose-PVP mixture as determined by T(1 rho) did not increase with storage RH as much as in lyophilized sucrose alone. This suggests that the molecular mobility of sucrose decreases in the presence of PVP due to hydrogen bonding between the hydroxyl group of sucrose and the carbonyl group of PVP. Inhibition of sucrose crystallization by PVP in the presence of water appears to be linked to the effect of PVP on the molecular mobility of sucrose.     

Contribution to understanding of the molecular dynamics in liquids

The dielectric relaxation spectroscopy is used for studying the orientational molecular dynamics in the isotropic (I) and nematic (N) phases of two mesogenic liquids composed of the molecules of similar structure and length, but of an essentially different polarity: n-heptylcyanobiphenyl, C(7)H(15)PhPhCN, 7CB (molecular dipole moment mu approximately 5D) and 4-(trans-4'-n-hexylcyclohexyl)isothiocyanatobenzene, C(6)H(13)CyHxPhNCS, 6CHBT (mu approximately 2.5D); advantageously, the temperatures of the I-N phase transition for the two compounds are very close to each other (T(NI) = 316.6 +/- 0.2 K). It is shown that regardless of the differences in polarity of 7CB and 6CHBT molecules and their abilities in dipolar aggregation, the values and temperature dependences of the relaxation time (corresponding to the rotational diffusion of the molecules around their short axis) are very close to each other, in both the isotropic and nematic phases of the liquids studied. Therefore, the data show that the dielectric relaxation processes occurring in dipolar liquids in the isotropic and nematic states lead through the rotational diffusion of individual molecules and the diffusion seems to be not influenced by the intermolecular interactions.     

Generalized gaussian model for uniaxial rotational motion: application to the calculation of spectroscopic responses

An exact model aimed at describing uniaxial rotational motions, based on a rotational adapted Gaussian statistics, is presented. In its simplest form, it depends on only two parameters, an order parameter which can vary from 1 (perfect order) to 0 (isotropic diffusion) and a time-dependent correlation parameter rho which varies from 1 to 0 between initial and infinite times. This model yields closed form expressions for the correlation functions relevant to the main spectroscopic techniques (dielectric absorption, light and neutron scattering, NMR line shape, spin-lattice relaxation, etc.) for all values of the two parameters. According to the functional form postulated for rho(t), in particular forms decaying as power laws at long times, one obtains shapes for the spectroscopic correlation functions and spectra that are similar to those experimentally observed in a large variety of complex systems (liquid crystals, polymers, gels, and amorphous and glassy materials), especially in confined geometries, which often resemble "stretched" exponentials. A simple way to introduce time coherent effects through a modification of rho(t) is proposed. Examples of theoretical correlation functions and spectra are presented. Important remarks concerning the application of this model to the analysis of real data are made. This model is the rotational analogue of the Gaussian translational model developed recently (Volino et al. J. Phys. Chem B 2006, 110, 11217).     

Model-free approach to the dynamic interpretation of residual dipolar couplings in globular proteins.

The effects of internal motions on residual dipolar NMR couplings of proteins partially aligned in a liquid-crystalline environment are analyzed using a 10 ns molecular dynamics (MD) computer simulation of ubiquitin. For a set of alignment tensors with different orientations and rhombicities, MD-averaged dipolar couplings are determined and subsequently interpreted for different scenarios in terms of effective alignment tensors, average orientations of dipolar vectors, and intramolecular reorientational vector distributions. Analytical relationships are derived that reflect similarities and differences between motional scaling of dipolar couplings and scaling of dipolar relaxation data (NMR order parameters). Application of the self-consistent procedure presented here to dipolar coupling measurements of biomolecules aligned in different liquid-crystalline media should allow one to extract in a "model-free" way average orientations of dipolar vectors and specific aspects of their motions.     

Low-frequency cooperative dynamics in L-, D-, and DL-alanine crystals: a 13C and 15N cross-polarization magic-angle-spinning NMR study

Knowledge of the dynamical changes in molecular configurations in various amino acid structures over a wide range of time scales is important since such changes may influence the structural transformations and the diverse biological functionalities of proteins. Using the temperature dependence of the rotating-frame NMR spin-lattice relaxation times T(1rho) of protons as a probe, we have investigated the low-frequency (approximately 60-100 kHz) dynamics in the crystal structures of L-, D-, and DL- alanine (C(12)H(28)O(8)N(4)) polymorphs. The proton relaxation times T(1rho) were obtained from (13)C <-- (1)H and (15)N <-- (1)H cross-polarization magic-angle-spinning NMR experiments over a temperature range of 192-342 K. The data reveal that the time scales of these low-frequency dynamical processes are distinctly different from the localized, high-frequency rotational motion of methyl and amine groups. The strongly asymmetric T(1rho) versus temperature curves and the subtle dynamical differences between the DL-alanine and the L- and d-enantiomorphs indicate that these low-frequency processes are cooperative in nature and are sensitive to molecular packing.     

Study of internal ring rotation and molecular reorientation in the liquid crystal 5O.7 by deuterium N.M.R. spectroscopy

The spectral densities of motion were determined by deuterium N.M.R. relaxation measurements in the nematic, smectic A and smectic C phases of 4-n-pentyloxybenzylidene-d₁-4'-heptylaniline and 4-n-pentyloxybenzylidene-4'-heptylaniline-2,3,5,6-d₄. By examining two atomic sites on a 5O.7 molecule, we were able to gain information on the reorientation motion and internal rotation of the aniline ring. It was also found that director fluctuations make some contribution to the spectral density J₁ (ω). We use the superimposed rotations model to account for the internal ring motion and the small step rotational diffusion model for the molecular reorientation. The derived rotational diffusion constants for the spinning and tumbling motions appear to give physically plausible activation energies in the mesophases of 5O.7.     

Off-resonance R(1rho) NMR studies of exchange dynamics in proteins with low spin-lock fields: an application to a Fyn SH3 domain

An (15)N NMR R(1rho) relaxation experiment is presented for the measurement of millisecond time scale exchange processes in proteins. On- and off-resonance R(1rho) relaxation profiles are recorded one residue at a time using a series of one-dimensional experiments in concert with selective Hartmann-Hahn polarization transfers. The experiment can be performed using low spin-lock field strengths (values as low as 25 Hz have been tested), with excellent alignment of magnetization along the effective field achieved. Additionally, suppression of the effects of cross-correlated relaxation between dipolar and chemical shift anisotropy interactions and (1)H-(15)N scalar coupled evolution is straightforward to implement, independent of the strength of the (15)N spin-locking field. The methodology is applied to study the folding of a G48M mutant of the Fyn SH3 domain that has been characterized previously by CPMG dispersion experiments. It is demonstrated through experiment that off-resonance R(1rho) data measured at a single magnetic field and one or more spin-lock field strengths, with amplitudes on the order of the rate of exchange, allow a complete characterization of a two-site exchange process. This is possible even in the case of slow exchange on the NMR time scale, where complementary approaches involving CPMG-based experiments fail. Advantages of this methodology in relation to other approaches are described.     

Ishtar: An interactive system for quantitative investigation on dipolar and quadrupolar spin-lattice relaxation

Within the model of anisotropic rotational diffusion, the quantitative treatment of dipolar and quadrupolar spin-lattice relaxation provides valuable information about molecular structures and molecular associations. When quadrupolar relaxation is involved, the title program calculates: (1) the electric field gradient tensor (EFGT) which is diagonalized; (2) the assymetry parameter, the components of the principal axes of the EFGT in the molecular frame of reference and the quadrupole coupling constant; and (3) the rotational diffusion constants which are iteratively determined from the experimental quadrupolar relaxation times. Analogously, for dipolar relaxation ISHTAR calculates the tensor of inertia, the diagonalization of which leads to diffusion constants and free rotor correlation times and the rotational diffusion constants from the experimental spectral densities.     

Molecular motion of isolated linear alkanes in nanochannels

The mobility of a series of linear alkanes in their inclusion compound with tris(o-phenylenedioxy)spirotriphosphazene is studied by high-resolution carbon-proton magic-angle spinning solid-state NMR spectroscopy. Two different carbon-proton dipolar recoupling experiments are compared with respect to their ability to yield precise site-specific, motion-averaged dipolar coupling constants. The most accurate results are obtained by analysis of extrema positions in Lee-Goldburg cross-polarization build-up curves. We present a comprehensive collection of coupling constants, which evidence a rotational motion of the all-trans chains around the channel axis, with some further averaging due to additional fluctuations, as previously found for alkanes in other host matrices such as urea. The order parameter increases toward the inner parts of the chains, and is largely independent of chain length. Notably, chains in a TPP host are not more ordered than in urea, even though the average TPP channel diameter is reported to be smaller. Significantly decreased order is found for highly filled short-alkane samples, which is interpreted in terms of an increased rate of mutual collisions. From residual dipolar couplings as well as carbon chemical shifts, we derive similar amounts of gauche conformers. Translational motions along the channels are further studied by proton double-quantum spectroscopy, which probes guest-host dipolar couplings. The extent of local-scale lateral motion is again correlated with the sample filling, and is a weak function of temperature, as expected from a case in which highly restricted single-file diffusion should dominate the mobility. Characteristic effects of sample aging are apparent in all our experiments.     

Hydrogen nuclear spin relaxation in hydrogen-ice clathrate

H2 in D2O ice clathrate has been studied by hydrogen NMR. In a previous report, the H2 line shape was shown to be due to incompletely averaged intramolecular dipolar interactions. Here the relaxation times T1, T1rho, and T2 are reported. T1 passes through a minimum at 10 K, indicating that the rotational transition rate Gamma between the three sublevels of J = 1 passes through the resonance frequency at this temperature. On the cold side, T1 varies as T(-2.6); on the hot side, the rate T1(-1) varies as T(-2) plus a constant (due to paramagnetic impurities). These indicate a two-phonon process drives the rotational transitions Gamma. The spin-echo T2 is nearly independent of temperature and in reasonable agreement with the Van Vleck intermolecular H2-H2 second moment. T1rho deviates from the expected T1rho = T1 behavior above 85 K, revealing an additional slow-motion source of relaxation. The deviation is driven by the hopping of H2 between large cages. Ortho-para conversion is measured to be much slower in the clathrate than in the bulk solid, reflecting the greater distances between the H2 molecules.     

Determination of the rotational diffusion tensor of porphycene by 13C and 1H spin relaxation methods

The longitudinal (13)C and (1)H relaxation rates were determined in porphycene in CD(2)Cl(2) solution. These data, augmented by (13)C{(1)H} NOE enhancements were numerically analyzed to evaluate the rotational diffusion tensor of the molecule and the vibrational correction for the one-bond (13)C-(1)H dipolar couplings. The (13)C and (1)H relaxation data seem to be consistent with each other, and the emerging picture of the rotational dynamics of porphycene compares well with the results that can be found in the literature.     

Practical route to relative diffusion coefficients and electronic relaxation rates of paramagnetic metal complexes in solution by model-independent outer-sphere NMRD. Potentiality for MRI contrast agents

The relaxation of electronic spins S of paramagnetic species is studied by the field-dependence of the longitudinal, transverse, and longitudinal in the rotating frame relaxation rates R1, R2, and R1rho of nuclear spins I carried by dissolved probe solutes. The method rests on the model-independent low-frequency dispersions of the outer-sphere (OS) paramagnetic relaxation enhancement (PRE) of these rates due to the three-dimensional relative diffusion of the complex with respect to the probe solute. We propose simple analytical formulas to calculate these enhancements in terms of the relative diffusion coefficient D, the longitudinal electronic relaxation time T1e, and the time integral of the time correlation function of the I-S dipolar magnetic interaction. In the domain of vanishing magnetic field, these parameters can be derived from the low-frequency dispersion of R1 thanks to sensitivity improvements of fast field-cycling nuclear relaxometers. At medium field, we present various approaches to obtain these parameters by combining the rates R1, R2, and R1rho. The method is illustrated by a careful study of the proton PREs of deuterated water HOD, methanol CH3OD, and tert-butyl alcohol (CH3)3COD in heavy water in the presence of a recently reported nonacoordinate Gd(III) complex. The exceptionally slow electronic relaxation of the Gd(III) spin in this complex is confirmed and used to test the accuracy of the method through the self-consistency of the low- and medium-field results. The study of molecular diffusion at a few nanometer scale and of the electronic spin relaxation of other complexed metal ions is discussed.     

A solid-state NMR study of the fast and slow dynamics of collagen fibrils at varying hydration levels

We report solid-state NMR investigations of the effect of temperature and hydration on the molecular mobility of collagen isolated from bovine achilles tendon. (13)C cross-polarization magic angle spinning (MAS) experiments were performed on samples at natural abundance, using NMR methods that detect motionally averaged dipolar interactions and chemical shift anisotropies and also slow reorientational processes. Fast motions with correlation times much shorter than 40 micro s scale dipolar couplings and chemical shift anisotropies of the carbon sites in collagen. These motionally averaged anisotropic interactions provide a measure of the amplitudes of the segmental motions expressed by a molecular order parameter. The data reveal that increasing hydration has a much stronger effect on the amplitude of the molecular processes than increasing temperature. In particular, the Cgamma carbons of the hydroxyproline residues exhibit a strong dependence of the amplitude of motion on the hydration level. This could be correlated with the effect of hydration on the hydrogen bonding structure in collagen, for which this residue is known to play a crucial role. The applicability of 1D MAS exchange experiments to investigate motions on the millisecond time-scale is discussed and first results are presented. Slow motions with correlation times of the order of milliseconds have also been detected for hydrated collagen.