Rheology of hydroxypropylcellulose solutions

The rheology of hydroxypropylcellulose (HPC)—acetic acid solutions was investigated by using a cone-and-plate rheometer and a capillary rheometer, for polymer concentrations ranging from 10 to 80%. Isotropic solutions exhibit a Newtonian plateau followed at higher shear rates by a pseudoplastic zone. The apparent viscosity varies as C^5.2 if concentration C is less than 27% and as C¹³ for 27% < C < 30%. A biphasic interval (isotropic and cholesteric phases) exists between 30 and 35%. A maximum in viscosity is observed at C = 30%, the height of the viscosity peak being a decreasing function of shear rate. Anisotropic solutions are strongly viscoelastic. Both isotropic and anisotropic solutions give results (apparent viscosity, first normal-stress difference, relaxation time, etc.) which are not in good agreement with Doi's theory. This is understandable since the HPC chain cannot be modeled by a rigid rod. Upon heating, anisotropic HPC—acetic acid solutions undergo an anisotropic to isotropic phase transition which is easily detected by a maximum in the temperature dependence of the first normal-stress difference and of the apparent viscosity.     

Scalar relaxation of homonuclear multiple-quantum coherences and relative signs of 14N-1H spin-spin coupling constants in E-N-phenylformamide

Homonuclear multiple-quantum NMR relaxation rates for E-N-phenylformamide, whose interesting part consists of two protons A and M differently coupled to a rapidly relaxing ¹⁴N nucleus are reported. The zero- and double-quantum linewidths depend on the cross correlation spectral densities and allow the determination of ¹J and ²J¹⁴N-¹H spin-spin coupling constants and their relative signs. We show that the two coupling constants have the same signs and are likely to be positive. Note that only one of the resonances of the AM pair needs to be significantly broadened due to scalar interactions in order for the cross correlation spectral density to become important for the multiple-quantum relaxation rates.     

Low density spectrum of transverse NMR in molecular gases. Application to hydrogen

The low density behaviour of the spectral lineshape function associated with the relaxation of the transverse components of the nuclear magnetization of a homonuclear diatomic gas of spin $\text{1}\text{2}$ nuclei is studied from the point of view of a recent kinetic theory approach to NMR in molecular gases. It is shown that as a critical density is approached (from above), the relaxation (in time-domain) passes over from exponential to non-exponential behaviour. For the special case in which the spin—rotation relaxation mechanism predominates, an analytic solution to the problem has been given, while for molecular hydrogen which has, in addition to the aforementioned mechanism, dipolar relaxation, the behaviour of the lineshape function has been obtained numerically. The critical density at which the relaxation passes from exponential to nonexponential in H₂ is found to be of the order of 3 × 10^?3 amagats which lies, at present, still outside experimental accessibility. One important consequence of this result is that the traditional Abragam formula for the transverse relaxation time T₂ is clearly seen to be invalid below ≈ 5 × 10^?3 amagats.     

Spin—rotational relaxation study of molecular reorientation in the presence of internal extended rotational diffusion

Molecular reorientation in the presence of internal rotation is investigated and an analytical expression for the spin—rotational rate of a nucleus attached to the internal rotor is obtained in terms of the internal angular-momentum correlation time. A model of a symmetric-top molecule undergoing anisotropic rotational diffusion is extended to include a modified extended diffusion of internal rotation. The result is applied to liquid toluene and the internal angular-momentum correlation time is evaluated from the ¹³C nuclear spin—rotational relaxation rate of the methyl carbon. A comparison with the previous result on the dipole—dipole relaxation data is made and the consistency of the present theory is discussed.     

Carbon-13 spin–lattice relaxation of tropane alkaloids. Anisotropic rotational motion of tropine and pseudotropine

The ¹³C spin–lattice relaxation times of tropine and pseudotropine have been measured in CDCl₃ as a function of concentration. The same relative increase in concentration serves to increase the relaxation rates much less in the region 0.9–5.0 wt.% than in the region 5.0–14.3 wt.%. The rotational diffusion coefficients have been calculated from the relaxation data using Woessner's anisotropic rotational diffusion model. Reorientation of both molecules is shown to be moderately anisotropic. The principal axes of the rotational diffusion tensor in the symmetry plane of both molecules are rotationally shifted from the principal axes of the moment of inertia tensor of the free molecules, and the main rotational axis is parallel with a line passing through the centre of mass of the molecule and the nitrogen atom.     

Nuclear spin relaxation of sodium cations in bacteriophage Pf1 solutions

The nuclear magnetic resonance (NMR) spectra for the I=3/2 23Na cation dissolved into filamentous bacteriophage Pf1 solutions display line splittings and relaxation times consistent with an interaction between the 23Na nuclear quadrupole moment and the electric field gradient produced by the negatively charged Pf1 particles. The 23Na NMR line splittings and relaxation rates corresponding to magnetization recovery and single, double, and triple quantum coherence decays are measured in Pf1 solutions and compared to theoretical values. The deviation of the observed dc spectral density J0 from the equal first harmonic J(omega0) and second harmonic J(2omega0) values as J(omega0)=J(2omega0) not equal to J0 in these solutions suggests that ion migration in the electric field gradient of the Pf1 particles produces an anisotropic relaxation mechanism. Correlation functions and thus spectral densities for this process are calculated from solutions to the Fokker-Planck equation for radial motion in an electric potential and used to estimate measured relaxation rates. Appropriate electric potentials are generated from the solutions to the Poisson-Boltzmann equation for a charged Pf1 particle in aqueous phase, functions that lead to theoretical estimates of NMR line splittings consistent with experimental observations.     

Temperature- and solvation-dependent dynamics of liquid sulfur dioxide studied through the ultrafast optical Kerr effect

The ultrafast dynamics of liquid sulphur dioxide have been studied over a wide temperature range and in solution. The optically heterodyne-detected and spatially masked optical Kerr effect (OKE) has been used to record the anisotropic and isotropic third-order responses, respectively. Analysis of the anisotropic response reveals two components, an ultrafast nonexponential relaxation and a slower exponential relaxation. The slower component is well described by the Stokes-Einstein-Debye equation for diffusive orientational relaxation. The simple form of the temperature dependence and the agreement between collective (OKE) and single molecule (e.g., NMR) measurements of the orientational relaxation time suggests that orientational pair correlation is not significant in this liquid. The relative contributions of intermolecular interaction-induced and single-molecule orientational dynamics to the ultrafast part of the spectral density are discussed. Single-molecule librational-orientational dynamics appear to dominate the ultrafast OKE response of liquid SO2. The temperature-dependent OKE data are transformed to the frequency domain to yield the Raman spectral density for the low-frequency intermolecular modes. These are bimodal with the lowest-frequency component arising from diffusive orientational relaxation and a higher-frequency component connected with the ultrafast time-domain response. This component is characterized by a shift to higher frequency at lower temperature. This result is analyzed in terms of a harmonic librational oscillator model, which describes the data accurately. The observed spectral shifts with temperature are ascribed to increasing intermolecular interactions with increasing liquid density. Overall, the dynamics of liquid SO2 are found to be well described in terms of molecular orientational relaxation which is controlled over every relevant time range by intermolecular interactions.     

Studies of Molecular Motions of Ocotillol-Type Saponins in Solution by ~(13)C Nuclear Magnetic Relaxation

In this paper, the fully anisotropicoverall tumbling motions and side groups internal rotation of ocotillol-type saponins separated from the leaves of Panax Quidquefolium L. are investigated by ~(13)C nuclear magnetic relaxation. The fully anisotropic overall tumbling motion model with methyl conformation jumps internal rotation among three equivalent sites is presented, and the spectral density function of this model is derived. The rotation rates for overall tumbling motions to ocotillol-type saponins (OTS) are computed by Woessner's fully anisotropic overall tumbling motion model, and the internal rotation rate and barrier for side groups in OTS are calculated using free diffusion internal rotation model, restriction diffusion internal rotation model and conformation jumps internal rotation model, respectively.     

Molecular Reorientational Dynamics of the Neat Ionic Liquid 1‐Butyl‐3‐methylimidazolium Hexafluorophosphate by Measurement of 13C Nuclear Magnetic Relaxation Data

The reorientational dynamics of the ionic liquid 1butyl‐3‐methylimidazolium hexafluorophosphate ([BMIM]PF₆) were studied over a wide range of temperatures by measurement of ¹³C spin–lattice relaxation rates and NOE factors. The reorientational dynamics were evaluated by performing fits to the experimental relaxation data. Thus, the overall reorientational motion was described by a Cole–Davidson spectral density with a Vogel–Fulcher–Tammann temperature dependence of the correlation times. The reorientational motion of the butyl chain was modelled by a combination of the latter model for the overall motion with a Bloembergen–Purcell–Pound spectral density and an Arrhenius temperature dependence for the internal motion. Except for C2 in the aromatic ring, an additional reduction of the spectral density by the Lipari–Szabo model had to be employed. This reduction is a consequence of fast molecular motions before the rotational diffusion process becomes effective. The C2 atom did not exhibit this reduction, because the librational motion of the corresponding C2? H vector is severely hindered due to hydrogen bonding with the hexafluorophosphate anion. The observed dynamic features of the [BMIM]⁺ cation confirm quantum‐chemical structures obtained in a former study.     

Two-stage model for molecular orientational relaxation in liquid crystals

Abstract

The molecular reorientation in anisotropic fluids is considered as twostage process—fast single molecule rotation in the volume restricted by close neighbours and slow collective relaxation of the local surrounding. The theoretical results are applied to explain the discrepancy between the rotational diffusion coefficients D_⊥ ^r obtained by infrared bandshape analysis and polarized fluorescence techniques.     

Intermolecular Interactions and Protein Dynamics by Solid‐State NMR Spectroscopy

Understanding the dynamics of interacting proteins is a crucial step toward describing many biophysical processes. Here we investigate the backbone dynamics for protein GB1 in two different assemblies: crystalline GB1 and the precipitated GB1–antibody complex with a molecular weight of more than 300 kDa. We perform these measurements on samples containing as little as eight nanomoles of GB1. From measurements of site‐specific ¹⁵N relaxation rates including relaxation dispersion we obtain snapshots of dynamics spanning nine orders of magnitude in terms of the time scale. A comparison of measurements for GB1 in either environment reveals that while many of the dynamic features of the protein are conserved between them (in particular for the fast picosecond–nanosecond motions), much greater differences occur for slow motions with motions in the >500 ns range being more prevalent in the complex. The data suggest that GB1 can potentially undergo a small‐amplitude overall anisotropic motion sampling the interaction interface in the complex.     

Anisotropy of local relaxation properties of macromolecules. Spin-lattice relaxation of 13C nuclei,the nuclear overhauser effect and the estimation of parameters of an equivalent ellipsoid for kinetic segments of polymer chains

The expressions for the functions of spectral density at different orientations of the components of the internuclear vector with respect to the chain backbone, the frequency dependences of the spin-lattice relaxation time of ¹³C nuclei (T_1C) and the values of the nuclear Overhauser effect (NOE) were obtained for the tetrahedral lattice model of a polymer chain with three-unit kinetic elements. It was shown that peculiar features of the behavior of T_1C and NOE reflect the characteristic properties of the spectra of relaxation (correlation) times for “longitudinal” and “transverse” components of the internuclear vector. It was established that in the range of relatively short times of the relaxation spectrum the dynamics of an anisotropic kinetic segment of the chain may be described with the aid of a simple model of an elongated ellipsoid of rotation with an axial ratio of about 10. It is shown that the equivalent-ellipsoid model leads to significant differences from a more specific model of chain dynamics when a broad frequency range is considered.     

Viscoelastic properties of liquid crystal polymers: Collective motions and nuclear spin relaxation

Transverse deuterium (²H) nuclear spin relaxation experiments have been performed on a ²H labelled main chain liquid crystal polymer. Relaxation rates are determined as a function of temperature and pulse frequency using a modified Carr-Purcell-Meiboom-Gill pulse train. The results are analysed in terms of a hydrodynamic model for fluctuations of the liquid crystal director. Analytic expressions are employed which relate the transverse spin relaxation rate to the anisotropic viscoelastic parameters of the polymer and allow estimates to be obtained for the effective viscosity and average elastic constant of the polymer. The molecular weight dependence of the viscoelastic parameters has been investigated and is found to be consistent with theoretical predictions for highly extended liquid crystal polymers.     

Explanation of spin-lattice relaxation rates of spin labels obtained with multifrequency saturation recovery EPR

Electron paramagnetic resonance (EPR) pulsed saturation recovery (pSR) measurements of spin-lattice relaxation rates have been made on nitroxide-containing fatty acids embedded in lipid bilayers by Hyde and co-workers. The data have been collected for a number of spin-labeled fatty acids at several microwave spectrometer frequencies (from 2 to 35 GHz). We compare these spin-lattice relaxation rates to those predicted by the Redfield theory incorporating several mechanisms. The dominant relaxation mechanism at low spectrometer frequencies is the electron-nuclear dipolar (END) process, with spin rotation (SR), chemical shift anisotropy (CSA), and a generalized spin diffusion (GSD) mechanism all contributing. The use of a wide range of spectrometer frequencies makes clear that the dynamics cannot be modeled adequately by rigid-body isotropic rotational motion. The dynamics of rigid-body anisotropic rotational motion is sufficient to explain the experimental relaxation rates within the experimental error. More refined models of the motion could have been considered, and our analysis does not rule them out. However, the results demonstrate that measurements at only two suitably chosen spectrometer frequencies are sufficient to distinguish anisotropic from isotropic motion. The results presented demonstrate that the principal mechanisms responsible for anisotropically driven spin-lattice relaxation are well understood in the liquids regime.     

Temperature dependence of rotational correlation times in tribromobenzene

The ¹³C relaxation times and nuclear Overhauser enhancements of the protonated carbons in 1,3,5-tribromobenzene were measured as a function of temperature in the solvent benzene-d₆. Rotational correlation times, τ_C(CH), calculated by the Microviscosity/Free Rotor and Hu-Zwanzig “slip” models are substantially below the measured values. In contrast, correlation times predicted by the Hynes—Kapral—Weinberg model are in near quantitative agreement with experiment at all temperatures studied.     

Exciton dynamics in molecular crystals from line shape analysis. Spectral moment analysis of the origin region of the 4000 Å transition of crystal anthracene

A spectral moment analysis of the line shape function ω?₂(ω) in the region of the (0—0) band of the 4000 ŹB_2u ← ¹A_g transition in crystal anthracene at various temperatures is performed. The data are compared with the predictions of three coupling models, viz., weak exciton—photon with weak exciton—phonon coupling, strong exciton—photon with weak exciton—phonon coupling, weak exciton—photon with strong exciton—phonon coupling. The terms contributing to each spectral moment for each model are rendered explicit. The experimental data indicate that the exciton—intermolecular phonon coupling is primarily weak. The exciton interacts with optical phonons of about 90 cm^-1 frequency with a coupling strength of about 140 cm^-1 , a value near that predicted by a weak coupling model. The coupling strength is nearly the same irrespective of whether the exciton is created by b- or a-polarized light probably indicative of the importance of higher multipole contributions to the coupling although the existence of strong interband scattering could affect that suggestion. The coupling parameters g_op and g_ac are about 10^-1 and 10^-4 respectively.     

Rotational Dynamics of Adamantanecarboxylic Acid in Complex with β-cyclodextrin

The reorientation of 1-adamantanecarboxylic acid (AdCA) within the β-cyclodextrin (β-CD) cavity is investigated by means of multiple-field ¹³C NMR relaxation. The dissociation constant describing the complexation equilibrium is determined using translational diffusion measurements for the guest during a titration by the host in D₂O/DMSO solvent mixture. The changes in apparent diffusion properties of AdCA during the titration are at 25 °C well described assuming the formation of a 1:1 complex, whereas at 0 °C the data indicate the presence of a 2:1 (guest:host) complex. The ¹³C NMR relaxation parameters for the AdCA molecule bound inside the β-CD cavity are extracted. Despite the high association constant, indicating a strong interaction between the two molecules, the guest molecule is quite mobile. The reorientation of the bound AdCA at 25 °C can be described by either the Lipari–Szabo or the axially symmetric rotational diffusion model. The motion is extremely anisotropic: the adamantyl group rotates fast around the β-CD symmetry axis, inside its cylindrical cavity. At lower temperature, the relaxation properties are no longer possible to explain using these models. Instead, the data are analyzed using extended, three-step spectral density of Clore et al. [J. Am. Chem. Soc. 112, 4989 (1990)].     

Structural parameter relaxation and pucker mode—internal mode coupling in the four-ring molecules cyclobutanol,cyclobutylfluoride and cyclobutylchloride

The present work is directed towards the investigation of the pucker—internal rotation modes of cyclobutanol and cyclobutanol-OD by the aid of a semirigid two-dimensional model. Based on spherical four-ring coordinates and general geometrical relations expressing wagging, twisting and rocking coordinates for CH₂ and CHX groups, experimental rotational constants of cyclobutanol, cyclobutylfluoride and cyclobutylchloride in the ground and excited pucker states are analyzed in terms of a two-dimensional four- ring pucker model with structural relaxation of CH₂ and CHX groups concerted with the ring puckering angles. The rotational data are found to be satisfactorily described by a one-dimensional ring pucker model including structural relaxation of the rocking angles of the CHX and the CH₂ groups. Then results of extended SCF computations (4-31G level) of the puckering—internal rotation potential of cyclobutanol are presented. These emphasize again the importance of structural relaxation of bond length and rocking type coordinates of the corner groups concerted with the puckering angle and serve as a basis for numerical solution of the two-dimensional pucker—internal rotation problem within the framework of a semirigid model. Predicted transitions and energy eigenstates will be correlated with far i.r. spectral data of cyclobutanol and cyclobutanol-OD observed in the 30–300 cm⁻¹ range and will be interpreted in terms of an alternative assignment, whose relation to an earlier analysis will finally be discussed.     

Laser-induced-fluorescence study of A Na/Na2 free jet. II. State-dependent effective inelastic cross sections for rotational and vibrational relaxation

Laser-induced-fluorescence measurements along the jet axis are used to study the relaxation of Na₂ molecules in a Na/Na₂ expansion. From the fluorescence intensity, the evolution of the occupancies of several vibration—rotation levels of the Na₂ ground state is obtained. The whole relevant region along the jet axis is covered: from the equilibrium region close to the nozzle down to the downstream part of the jet, where the internal-state distribution is non-Boltzmann and “frozen”. The relaxation of Na₂ molecules is analysed using first-order relaxation equations. Vibrational and rotational relaxation are treated separately by means of similar equations but with different inelastic cross sections determining the relaxation rates. The evolution of the vibrational levels can be described by means of a single effective cross section of = 100 Ų; the rotational cross sections are strongly J-state dependent and range from = 250 to 15 Ų, for J = 13-55.     

A carbon-13 study of relaxation in the mesophases of 5O·7 and the 5CB homologous series

Abstract

Carbon-13 spin-lattice relaxation times of the protonated ring carbons have been measured at 22·6 MHz in the nematic and all four smectic phases of 5O·7 (4-n-pentyloxybenzylidene-4′-n-heptylaniline). Dong has obtained the deuterium spectral densities J ₁ and J ₂ at 15·4MHz for the deuterated aniline ring of 5O·7-d ₄, and has presented and applied a theory in which the spectral densities are expressed in terms of the diffusion constants D∥ and D?. His results are used to calculate ¹³C relaxation times from the spectral densities J ₀, J ₁ and J ₂. The calculated ¹³C spin-lattice relaxation times are then compared with our experimental values to test the theory. The ¹³C spin-lattice relaxation times of all the resolved resonances in the various phases of the first four members of the 5CB homologous series have been published previously. Dong has also published an analysis of 5CB deuterium data, and we use his results for the diffusion constants D∥ and D? to calculate ¹³C relaxation times of the protonated aromatic carbons of 5CB, 6CB, 7CB and 8CB. The ¹³C relaxation times of the unprotonated aromatic carbons of the 5CB series are calculated in the manner of Wittebort et al., but using the spectral density expressions developed by Dong. The calculated ¹³C spin-lattice relaxation times of the 5CB homologous series are then compared with our experimental values to test the theory for the protonated and unprotonated ring carbons.