Interdependence of motional processes in polymers: correlation functions for nmr relaxation

The roles of both anisotropic motion and the interdependence of multiple motions in leading to nonexponential correlation functions for NMR relaxation data are explored. A motional model is developed in which rotational motions of segments of various lengths are controlled by the formation and disappearance of a suitable conformation. Such a model gives correlation functions which can be made, through adjustment of parameters, to be almost identical to correlation functions from other, quite different, models. The ability of NMR relaxation data to identify unique motional models is thus questioned.     

Molecular dynamics and ordering of pyridine in its cyclophosphazene inclusion compound as evaluated by solid state 2H NMR spectroscopy

Variable temperature 2H NMR experiments (line shape analysis, relaxation studies) were carried out on the pyridine-d5-tris-(1,2-dioxyphenyl)-cyclotriphosphazene inclusion compound in the temperature range between 110-300 K. It is found that the pyridine guests are highly mobile throughout the whole temperature range covered here. The observation of three superimposed 2H NMR signals can be understood in terms of a particular (motionally averaged) orientation of the pyridine molecules, which is a consequence of the molecular symmetry of the pyridine guests and the imposed channel restrictions. The experimental data are consistent with a combined rotation on cone-small angle fluctuation model, which assumes a fast molecular reorientation between two superimposed cones with an opening angle for the inner cone between 59-73 degrees (angle of fluctuation between 1-3 degrees ). On the basis of this model assumption it is possible to reproduce both the experimental 2H NMR line shapes and the spin-lattice relaxation data in a quantitative way. The analysis of the partially relaxed spectra (inversion recovery experiments) yields the correlation times for this overall motional process. They follow an Arrhenius behavior from which an activation energy of 8.7 +/- 0.4 kJ mol(-1) is derived. The results are discussed in the framework of the published data for related systems.     

Effect of temperature and molecular weight on enthalpy relaxation in polystyrene

Isothermal enthalpy relaxation in polystyrene was measured as a function of temperature and molecular weight on a differential scanning calorimeter. Relaxation spectra were derived from the data and expressed as a distribution of relaxation times. For a given molecular weight the relaxation spectra at different temperatures could not be superimposed by a shift in time. The relaxation curves of samples of different molecular weights could be superimposed only when the difference between the temperature at which the relaxation was monitored (T_a) and their respective T_g was the same. The relaxation spectrum at any temperature for a given molecular weight was also expressed as a distribution of energies. The average energy represented by this distribution was associated with an activation energy required for the motion of a chemical repeat unit. The activation energy extracted from the temperature shift in the relaxation spectra corresponded to the motion of a statistical unit (Kuhn's segment) in polystyrene.     

De novo determination of bond orientations and order parameters from residual dipolar couplings with high accuracy

We report the de novo determination of 15N-1H bond orientations and motional order parameters for the protein ubiquitin with high accuracy based solely on NMR residual dipolar coupling measurements made in six distinct alignment media. The resulting bond orientations are in agreement with RDC-refined orientations of either solid or solution state coordinates to within approximately 2 degrees , which is also the estimated precision of the resulting orientations. The squared generalized order parameters, which reflect amplitudes of motion spanning the picosecond to millisecond time scales, exhibit a correlation with picosecond time scale order parameters derived from conventional NMR 15N spin relaxation methods. Provided that RDC measurements can be obtained using many different alignment media, this approach (called direct interpretation of dipolar couplings) may significantly impact the attainable accuracy and the molecular weight range accessible to NMR structure determination in the solution state, as well as provide a route for the study of motions occurring on the nanosecond to microsecond time scales, which have been traditionally difficult to study at atomic resolution.     

Conformational flexibility of the group B meningococcal polysaccharide in solution

To elucidate the role of secondary structure in the immune response against alpha(2-->8)-linked polysialic acid, the capsular polysaccharide of Group B meningococci, we have investigated its solution dynamics by using specific models of molecular motion and hydrodynamic modeling to interpret experimental NMR data. (13)C-[(1)H] NMR relaxation times and steady-state NOE enhancements were measured for two aqueous solutions of alpha(2-->8)-linked sialic acid polysaccharides. Each contained a unique distribution of polysaccharide chain lengths, with average lengths estimated at 40 or 400 residues. Models for rigid molecule tumbling, including two based on helical conformations proposed for the polysaccharide,(31) could not explain the NMR measurements. In general for these helices, the correlation times for their overall tumbling that best account for the NMR data correspond to polysaccharide chains between 9 and 18 residues in length, far short of the average lengths estimated for either solution. The effects of internal motions incorporated into these helices was modeled with an effective correlation time representing helix tumbling as well as internal motion. This modeling demonstrated that even with extreme amounts of internal motion, "flexible helices" of 25 residues or more still could not produce the NMR measurements. All data are consistent with internal and segmental motions dominating the nuclear magnetic relaxation of the polysaccharide and not molecular tumbling. Statistical distributions of correlation times have been found specifically for the pyranose rings, linkage groups, and methoxy groups that can account for the measured relaxation times and NOE enhancements. The distributions suggest that considerable flexibility attends the polysaccharide in solution, and the ranges of motional frequencies for the linkage groups and pyranose rings are comparable. We conclude that the Group B meningococcal polysaccharide is a random coil chain in solution, and therefore, does not have antigenic epitopes dependent upon a rigid, ordered conformation.     

Dynamics of junction point motions in model network polymers

³¹P solid-state exchange 2D NMR and spin-lattice relaxation times (T₁^P) have been used to investigate the motion of a crosslink unit in model networks. The networks were formed from tris(4-isocyanatophenyl) thiophosphate with telechelic poly(propylene glycol) or poly(tetrahydrofuran). From the variation of the 2D NMR pattern with temperature and mix time, the motion of the crosslink is identified as Brownian reorientational diffusion. Good simulations of the spectra were obtained using the Williams-Watts distribution of correlation times. The temperature dependence of the crosslink motion follows the WLF equation. The parameters derived from the NMR data are sufficient to describe the temperature dependence and breadth of both the dielectric and mechanical loss associated with the glass transition. The T₁^P relaxation data fitted equally well to the Cole-Cole or the Williams-Watts relaxation functions. The motion of the crosslinks can be described quantitatively by the activation energies and the coupling parameters.     

2H nuclear magnetic resonance study on the molecular motion in cyanoadamantane. II. Orientationally ordered and glassy crystalline phase

The orientationally ordered crystalline and glassy plastically crystalline phase of cyanoadamantane were investigated using (2)H NMR. Solid-echo line shape, two-dimensional spectrum, and spin-lattice relaxation were analyzed. In both phases, the molecules display solely a rotation around the molecular C(3) symmetry axis. For the orientationally ordered phase, a single correlation time characterizes the motion, and the time constant shows an Arrhenius temperature dependence. In contrast, a broad distribution G[ln(tau)] of correlation times is observed for the glassy plastically crystalline phase that leads to characteristically different NMR features such as "two-phase" spectra and pronounced nonexponential relaxation. The distribution G[ln(tau)] can be derived from a temperature independent distribution of activation energies g(E(a)), with its mean value lying significantly below the activation energy corresponding to the ordered phase. Thus, the molecular uniaxial rotation proves to be a sensitive probe for the energy landscape of the orientationally disordered glassy crystalline phase of cyanoadamantane.     

Dynamics by solid-state NMR: detailed study of ibuprofen Na salt and comparison with ibuprofen

The various internal rotations and interconformational jumps of the Na-salt form of ibuprofen in the solid state were characterized in detail by means of the simultaneous analysis of a variety of low- and high-resolution NMR experiments aimed at measuring several (13)C and (1)H spectral and relaxation properties at different temperatures and frequencies. The results were first qualitatively analyzed to identify the motions of the different molecular fragments and to assign them to specific frequency regimes (slow, <10(3) Hz; intermediate, 10(3)-10(6) Hz; and fast, >10(6) Hz). Subsequently, a simultaneous fit of the experimental data sets most sensitive to each frequency range was performed by using suitable motional models, thus obtaining, for each motion, correlation times and activation energies. The motions so characterized were: the rotations of the three methyl groups and of the isobutyl group, occurring in the fast regime, and the π-flip of the phenyl ring, belonging to the intermediate motional regime. The results obtained for the Na-salt form were compared with those of the acidic form of ibuprofen, previously obtained from a similar solid-state NMR approach: despite the very similar chemical structure of the two compounds, their dynamic properties in the solid state are noticeably different.     

On the possible manifestation of harmonic-anharmonic dynamical transition in glassy media in electron paramagnetic resonance of nitroxide spin probes

Continuous wave (cw) electron paramagnetic resonance (EPR) and echo-detected (ED) EPR were applied to study molecular motions of nitroxide spin probes in glassy glycerol and o-terphenyl. A linear decrease with increasing temperature of the total splitting in the cw EPR line shape was observed at low temperatures in both solvents. Above some temperature points the temperature dependencies become sharper. Within the model of molecular librations, this behavior is in qualitative and quantitative agreement with the numerical data on neutron scattering and Mossbauer absorption for molecular glasses and biomolecules, where temperature dependence of the mean-squared amplitude of the vibrational motion was obtained. In analogy with these data the departure from linear temperature dependence in cw EPR may be ascribed to the transition from harmonic to anharmonic motion (this transition is called dynamical transition). ED EPR spectra were found to change drastically above 195 K in glycerol and above 245 K in o-terphenyl, indicating the appearance of anisotropic transverse spin relaxation. This appearance may also be attributed to the dynamical transition as an estimation shows the anisotropic relaxation rates for harmonic and anharmonic librational motions and because these temperature points correspond well to those known from neutron scattering for these solvents. The low sensitivity of ED EPR to harmonic motion and its high sensitivity to the anharmonic one suggests that ED EPR may serve as a sensitive tool to detect dynamical transition in glasses and biomolecules.     

Reorientational dynamics of p-sulfonatocalix[4]arene and of its La(III) complex in water

The reorientational dynamics of p-sulfonatocalix[4]arene and of its La(III) complex in deuterated water were studied by 1H NMR longitudinal relaxation rates. It is shown that the relaxation is purely dipolar in the non-extreme narrowing regime. The distance between the geminal protons could be determined from the NMR data, giving good agreement with the values generally used in correlation time calculations. The correlation times show an Arrhenius behaviour in good agreement with previously reported data from 13C measurements for a similar uncomplexed calixarene. The Arrhenius energies of activation are identical for the uncomplexed and the complexed calixarenes, suggesting a reorientational motion strongly dependent on the structure of the water cage around the complex. This is also in agreement with a complexation of the La(III) cation in the second sphere of solvation of the sulfonate groups, as shown by molecular dynamics simulations.     

Pulsed NMR study of molecular motion in the uncured diglycidyl ether of bisphenol-A

The diglycidyl ether of bisphenol-A, an uncured epoxy resin, has been studied by pulsed NMR. Values of the proton relaxation times T₁, T_1p, and T₂ have been measured over the temperature range from ?160 to 200°C. The resin was studied in its monomeric form and in two mixtures containing higher oligomers. The relaxation times are interpreted in terms of the molecular motion in the resins. The motion responsible for relaxation in the solid monomer form is thought to be methyl group reorientation at low temperatures and general molecular motion at high temperatures. The motions are characterized by activation energies of 5 kcal/mole and 33 kcal/mole, respectively. The solid mixtures exhibit similar effects to the monomer, but an additional relaxation mechanism is observed which is attributed to segmental motion. This motion is characterized by an activation energy of 12–15 kcal/mole. The self-diffusion coefficient was measured in the liquid monomer, and the activation energy for self-diffusion is found to be 11 kcal/mole.     

Molecular motions of tactic poly(2-hydroxyethyl methacrylate) in solutions studied by 13C-NMR relaxation measurement

The spin-lattice relaxation time and the nuclear Overhauser enhancement were measured using Bruker AM 300 spectrometer operating at 75.5 MHz for ¹³C to investigate the molecular motional characteristics and its tacticity effect for tactic poly(2-hydroxyethyl methacrylate) (PHEMA) as a function of temperature in dimethyl sulfoxide and methanol solvents. The observed relaxation data have been analyzed for both backbone motion and methyl internal rotation according to the log-χ² distribution model and the diamond-lattice model. The correlation times thus obtained for the molecular motions show that isotactic PHEMA is more flexible than syndiotactic counterpart. The syndiotactic PHEMA seems to have intramolecular hydrogen bonding which restricts the motion of C-2 carbon at temperatures below 35°C, whereas the isotactic one indicated no hydrogen bonding at all temperatures examined in this study. The methyl group of isotactic PHEMA shows a greater degree of freedom for the internal rotation than that of syndiotactic one. From the temperature dependence of correlation times, the activation energies for both backbone segmental motion and methyl internal rotation are obtained. The activation energies, 20 kJ/mol for backbone motion and 19 kJ/mol for methyl internal rotation, for isotactic PHEMA are substantially lower than the corresponding activation energies of 30 and 32 kJ/mol obtained for syndiotactic one. An examination of these energies indicates that methyl side group and backbone motions in tactic PHEMA are linked together.     

Nuclear Magnetic Resonance Relaxivities: Investigations of Ultrahigh‐Spin Lanthanide Clusters from 10 MHz to 1.4 GHz

Paramagnetic relaxation enhancement is often explored in magnetic resonance imaging in terms of contrast agents and in biomolecular nuclear magnetic resonance (NMR) spectroscopy for structure determination. New ultrahigh‐spin clusters are investigated with respect to their NMR relaxation properties. As their molecular size and therefore motional correlation times as well as their electronic properties differ significantly from those of conventional contrast agents, questions about a comprehensive characterization arise. The relaxivity was studied by field‐dependent longitudinal and transverse NMR relaxometry of aqueous solutions containing Fe^III₁₀Dy^III₁₀ ultrahigh‐spin clusters (spin ground state 100/2). The high‐field limit was extended to 32.9 T by using a 24 MW resistive magnet and an ultrahigh‐frequency NMR setup. Interesting relaxation dispersions were observed; the relaxivities increase up to the highest available fields, which indicates a complex interplay of electronic and molecular correlation times.     

Isotropic reorientations of fullerene C70 triplet molecules in solid glassy matrices revealed by light-induced electron paramagnetic resonance

Continuous-wave X-band electron paramagnetic resonance (EPR) of fullerene C(70) molecules excited to a triplet state by continuous light illumination was studied in molecular glasses of o-terphenyl and cis/trans-decaline and in the glassy polymers polymethylmethacrylate (PMMA) and polystyrene (PS). Above ～100 K, a distinct narrowing of EPR lineshape of the triplet was observed, which was very similar for all systems studied. EPR lineshape was simulated reasonably well within a framework of a simple model of random jumps, which implies that the C(70) molecule performs isotropic orientational motion by sudden jumps of arbitrary angles. In simulations, a single correlation time τ(c) was used, varying in the range of 10(-7)-10(-8) s. Near and below 100 K electron spin echo (ESE) signals were also obtained which were found to decay exponentially. Correlation times τ(c) obtained from simulation of the EPR spectra in the slow-motion limit (τ(c) close to 10(-7) s) turned out to be in good agreement with the phase memory times T(M) of the ESE decay, which additionally supports the employed simple model. The observed motional effects provide evidence that the nanostructure of the solid glassy media of different origins is soft enough to allow a large asymmetric C(70) molecule to reorient rapidly. Except for the EPR spectra of the triplet, in the center of the spectra, a small admixture of a narrow line was also observed; its possible nature is briefly discussed.     

Sensitivity of 2H NMR spectroscopy to motional models: proteins and highly viscous liquids as examples

In order to study to what extent mechanisms of molecular motion can be unambiguously revealed by (2)H NMR spectroscopy, (2)H spectra for proteins (chicken villin protein headpiece HP36, selectively methyl-deuterated at leucine-69, C(δ) D(3)) and binary systems of high viscosity (benzene-d(6) in tricresyl phosphate) have been carefully analyzed as illustrative examples (the spectra are taken from the literature). In the first case, a model of restricted diffusion mediated by jumps between rotameric orientations has been tested against jump- and free diffusion models which describe rotational motion combined with jump dynamics. It has been found that the set of (2)H spectra of methyl-deuterated at leucine-69 chicken villin protein headpiece HP36 can be consistently explained by different motional models as well as by a gaussian distribution of correlation times assuming isotropic rotation (simple brownian diffusion model). The last finding shows that when the possible distribution of correlation times is not very broad one might not be able to distinguish between heterogeneous and homogenous (but more complex) dynamics by analyzing (2)H lineshapes. For benzene-d(6) in tricresyl phosphate, the dynamics is heterogeneous and it has been demonstrated that a gaussian distribution of correlation times reproduces well the experimental lineshapes, while for a Cole-Davidson distribution the agreement is somewhat worse. For inquires into the sensitivity of quadrupolar NMR spectral analysis (by "quadrupolar NMR spectroscopy we understand NMR spectroscopy of nuclei possessing quadrupole moment), the recently presented theoretical approach [Kruk et al., J. Chem. Phys. 135, 224511 (2011)] has been used as it allows simulating quadrupolar spectra for arbitrary motional conditions by employing the stochastic Liouville equation.     

Self-assembling of phenothiazine compounds investigated by small-angle X-ray scattering and electron paramagnetic resonance spectroscopy

Small-angle X-ray scattering (SAXS) and electron paramagnetic resonance (EPR) have been carried out to investigate the structure of the self-aggregates of two phenothiazine drugs, chlorpromazine (CPZ) and trifluoperazine (TFP), in aqueous solution. In the SAXS studies, drug solutions of 20 and 60 mM, at pH 4.0 and 7.0, were investigated and the best data fittings were achieved assuming several different particle form factors with a homogeneous electron density distribution in respect to the water environment. Because of the limitation of scattering intensity in the q range above 0.15 A(-1), precise determination of the aggregate shape was not possible and all of the tested models for ellipsoids, cylinders, or parallelepipeds fitted the experimental data equally well. The SAXS data allows inferring, however, that CPZ molecules might self-assemble in a basis set of an orthorhombic cell, remaining as nanocrystallites in solution. Such nanocrystals are composed of a small number of unit cells (up to 10, in c-direction), with CPZ aggregation numbers of 60-80. EPR spectra of 5- and 16-doxyl stearic acids bound to the aggregates were analyzed through simulation, and the dynamic and magnetic parameters were obtained. The phenothiazine concentration in EPR experiments was in the range of 5-60 mM. Critical aggregation concentration of TFP is lower than that for CPZ, consistent with a higher hydrophobicity of TFP. At acidic pH 4.0 a significant residual motion of the nitroxide relative to the aggregate is observed, and the EPR spectra and corresponding parameters are similar to those reported for aqueous surfactant micelles. However, at pH 6.5 a significant motional restriction is observed, and the nitroxide rotational correlation times correlate very well with those estimated for the whole aggregated particle from SAXS data. This implies that the aggregate is densely packed at this pH and that the nitroxide is tightly bound to it producing a strongly immobilized EPR spectrum. Besides that, at pH 6.5 the differences in motional restriction observed between 5- and 16-DSA are small, which is different from that observed for aqueous surfactant micelles.     

Study of relaxation rates of stable paramagnetic centers in gamma-irradiated alanine

The stable L-alanine radical induced by gamma-irradiation was examined by electron paramagnetic resonance (EPR), transfer saturation EPR and electron nuclear double resonance (ENDOR) in the temperature region of fast motion of the methyl group (180-320 K). From the obtained spectral line broadening and spectral intensity the correlation time for the methyl rotation was estimated. The complex processes determining the relaxation rate were examined in the same temperature interval. It was shown that important contributions to the relaxation rate arise from non-secular and pseudo-secular types of contributions. The non-secular contribution involves intramolecular dynamics while the pseudo-secular contribution originates from intermolecular motions. The obtained values for the dynamical parameters have been compared with those obtained by pulse EPR methods and by proton nuclear magnetic resonance (NMR) on undamaged crystals.     

Diglycidyl ether of bisphenol-A with 4,4′-methylenedianiline: A pulsed NMR study of the curing process

The curing process, during which the monomeric diglycidyl ether of bisphenol-A is cured with 4,4′-methylenedianiline, has been studied by pulsed NMR. Values of the proton relaxation times T₁, T_1ρ, and T₂ have been measured as a function of time as the resin system cures at constant temperature. The relaxation times are interpreted in terms of the decrease in general molecular motion which results from the cure. Plots of correlation frequency versus time for the constant-temperature cure were constructed for three temperatures. It is shown that these three plots can be represented by a reduced curve. With certain simplifying assumptions, the shape of this reduced curve. With certain simplifying assumptions, the shape of this reduced curve can be accounted for in terms of the chemical rate constant and an exponent relating molecular weight to viscosity. The activation energy for the cure is estimated to be 11.7 kcal/mole.