Nuclear magnetic relaxation induced by exchange-mediated orientational randomization: Longitudinal relaxation dispersion for spin I = 1

The frequency dependence of the longitudinal relaxation rate, known as the magnetic relaxation dispersion (MRD), can provide a frequency-resolved characterization of molecular motions in complex biological and colloidal systems on time scales ranging from 1 ns to 100 μs. The conformational dynamics of immobilized proteins and other biopolymers can thus be probed in vitro or in vivo by exploiting internal water molecules or labile hydrogens that exchange with a dominant bulk water pool. Numerous water (1)H and (2)H MRD studies of such systems have been reported, but the widely different theoretical models currently used to analyze the MRD data have resulted in divergent views of the underlying molecular motions. We have argued that the essential mechanism responsible for the main dispersion is the exchange-mediated orientational randomization (EMOR) of anisotropic nuclear (electric quadrupole or magnetic dipole) couplings when internal water molecules or labile hydrogens escape from orientationally confining macromolecular sites. In the EMOR model, the exchange process is thus not just a means of mixing spin populations but it is also the direct cause of spin relaxation. Although the EMOR theory has been used in several studies to analyze water (2)H MRD data from immobilized biopolymers, the fully developed theory has not been described. Here, we present a comprehensive account of a generalized version of the EMOR theory for spin I = 1 nuclides like (2)H. As compared to a previously described version of the EMOR theory, the present version incorporates three generalizations that are all essential in applications to experimental data: (i) a biaxial (residual) electric field gradient tensor, (ii) direct and indirect effects of internal motions, and (iii) multiple sites with different exchange rates. In addition, we describe and assess different approximations to the exact EMOR theory that are useful in various regimes. In particular, we consider the experimentally important dilute regime, for which approximate analytical results are derived. As shown by the analytical expressions, and confirmed by exact numerical calculations, the dispersion is governed by the pure nuclear quadrupole resonance frequencies in the ultraslow-motion regime, where the relaxation rate also exhibits a much stronger dependence on the electric field gradient asymmetry than in the motional-narrowing regime.     

Nuclear spin relaxation in biaxial liquid crystal phases

The orientation-dependent spin-lattice relaxation rates for biaxial liquid crystal phases are given explicitly in terms of spectral densities J_mLm'L (ω) described by Berggren et al. (1993, J. chem. Phys., 99, 6180). It is recognized that the 'biaxial' spectral densities are not observed in biaxial phases unless the director is oriented away from the external magnetic field.     

Nuclear spin relaxation in biaxial liquid crystal phases

Abstract

The orientation-dependent spin-lattice relaxation rates for biaxial liquid crystal phases are given explicitly in terms of spectral densities J _mLm′L (ω) described by Berggren et al. (1993, J. chem. Phys., 99, 6180). It is recognized that the ‘biaxial’ spectral densities are not observed in biaxial phases unless the director is oriented away from the external magnetic field.     

Nuclear spin relaxation in poly(diethylsiloxane)

Earlier work showed that heating causes poly(diethylsiloxane) to undergo a first-order transition from a semicrystalline solid to a more mobile viscous—crystalline material. The latter is composed of two phases and analogies between polymer and liquid crystal morphology and behavior have been made. The viscous—crystalline phase in PDES appears to be unique since the literature is devoid of other documented examples. In this study, spin—lattice and spin—spin relaxation times were measured over a wide temperature range. They show a glass transition at 138°K, a crystal—crystal transition at 206°K, and a transition around 250°K which results from translational motion of the polymer chains with respect to each other. This motion is observed in the amorphous phase at a lower temperature than in the crystalline phase. Translational motion in the crystalline phase is observed on melting of the crystallites. The spin—spin data permitted monitoring of the molecular motions in each phase and the data suggest that these phases exert some influence on the molecular motions of each other. The viscous—crystalline phase in PDES may represent a unique model for studying and understanding “precrystalline” behavior and structure in amorphous solids.     

A phenomenological approach to relaxation in disordered systems

We propose a phenomenological approach to relaxation in disordered systems which is modelled after the well-known percolation behaviour. The approach shows an interesting behaviour of the time correlation function of relevant variables which is characterized by three temporal regimes, an initial exponential decay, a power-law regime and a stretched exponential decay for long times. We give some relevant examples of this behaviour in a wide variety of systems such as gels, microemulsions and glasses.     

Nuclear spin relaxation of mesogenic fluids in spherical microcavities

We discuss the nuclear spin relaxation resulting from molecular translational diffusion of a liquid crystal in the isotropic phase confined to spherical microcavities. The relaxation is induced by the time modulation of spin interactions as molecules diffuse between the ordered surface layer into the isotropic interior volume and back. The calculated spin-lattice relaxation rate T(1) (-1) shows three distinct dispersion regimes: a plateau at the lowest frequencies, practically independent of the size of the cavity, an intermediate power-law dispersion regime with an exponent between -0.7 and -1, depending on the spatial profile of the order parameter and cavity radius, and at frequencies above 1 MHz a strong dispersion tending toward the quadratic dependence of the relaxation rate on the Larmor frequency in the high-frequency limit. The pretransitional increase in T(1) (-1) depends drastically on the Larmor frequency. The frequency and temperature dependences of T(1) (-1) yield not only information on the magnitude of the surface order parameter, but also on its spatial profile, revealing the type of liquid-crystal-substrate interactions. Apart from thermotropic liquid crystals in the isotropic phase, this analysis can be also applied to other fluids in porous media.     

High resolution NMR study of T1 magnetic relaxation dispersion. II. Influence of spin-spin couplings on the longitudinal spin relaxation dispersion in multispin systems

Effects of scalar spin-spin interactions on the nuclear magnetic relaxation dispersion (NMRD) of coupled multispin systems were analyzed. Taking spin systems of increasing complexity we demonstrated pronounced influence of the intramolecular spin-spin couplings on the NMRD of protons. First, at low magnetic fields where there is strong coupling of spins the apparent relaxation times of the coupled spins become equal. Second, there are new features, which appear at the positions of the nuclear spin level anticrossings. Finally, in coupled spin systems there can be a coherent contribution to the relaxation kinetics present at low magnetic fields. All these peculiarities caused by spin-spin interactions are superimposed on the features in NMRD, which are conditioned by changes of the motional regime. Neglecting the effects of couplings may lead to misinterpretation of the NMRD curves and significant errors in determining the correlation times of molecular motion. Experimental results presented are in good agreement with theoretical calculations.     

Formation of anisotropic polymer colloids by disparate relaxation times

We show that coupling between a fast and a slow relaxation time causes the spontaneous formation of protrusions in colloids made of cross-linked polymers. The volume of the protrusions can be controlled by adjusting the ratio between the relaxation times. This, in principle, results in particles with levels of anisotropy that can be made "to order".     

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.     

Proton spin lattice relaxation times in biological tissues Water and lipid role

Abstract

The multiphase model of water present in biological tissues derives mainly from the N.M.R. observation of a fraction of non-freezing water in biological tissues which is attributable to the water bound to macromolecules. Studies of this problem rule out completely the lipids as the source of the NMR signal. Our studies on nuclear spin lattice relaxation times of human and animal tissues have been made to understand if other contributions to the N.M.R. signal are present in addition to that coming from the water protons. We have measured directly by the N.M.R. method the relative water and lipid content and the relaxation time T ₁ as a function of the water content which was varied by controlled dehydration. The results show clearly that lipids contribute actively to the N.M.R. signal and the fast relaxation time T ₁ which is of the order of 100 ms in all biological tissues is related to the lipids. In view of these experimental observations we think that it is opportune to reconsider critically all the determinations of the ‘bound water’ made by the freezing procedure with the N.M.R. technique, and dedicate more attention to the lipids of biological membranes.     

Geometrical information from 13C spin lattice relaxation times of salicylaldehyde

¹³C NMR spin-lattice relaxation times and nuclear overhauser-enhancement factors of salicylaldehyde and salicylaldehyde-d₁, under conditions of proton noise decoupling were measured to explore the possibilities of using relaxation time measurements to obtain geometrical information. The distances from the hydroxyproton to the two quarternary carbons were obtained in good agreement with microwave data.     

Nuclear spin relaxation dynamics of 13CO2 sorbed in polyisobutene rubber

Recently we presented the dynamics of ¹³CO₂ molecules sorbed in silicone rubber (PDMS) ascertained from spin relaxation experiments. Results of a similar investigation for ¹³CO₂ sorbed in polyisobutene (PIB) are presented in this report. The spin-lattice and spin-spin relaxation times as well as nuclear Overhauser enhancements (NOE) were determined as a function of temperature and Larmor frequency. The relaxation mechanisms found to be important for ¹³CO₂/PIB system are intermolecular dipole-dipole relaxation and chemical shift anisotropy with a minor contribution from spin rotation relaxation. We have determined the parameters which characterize correlation times for ¹³CO₂ collisional motion, rotational motion, and translational motions in the PIB. The self-diffusion coefficient of 5.15 × 10^?8 cm²/s obtained from the nuclear magnetic resonance (NMR) data is close to the literature value of the mutual diffusion coefficient of CO₂ in PIB at 300 K obtained from permeability measurements. In contrast to the case of CO₂/PDMS in which a broad distribution (characterized by a fractional exponential correlation function of the Williams-Watts type with α = 0.58) is observed, a sharp distribution with a fractional exponent, α, of 0.99 is found for the CO₂/PIB system. Instead of assuming an Arrhenius type temperature dependence, we used a Williams-Landel-Ferry type temperature dependence and found it to be better suited to describe the behavior of this system. PIB is a densely packed “strong” chain polymer which responds gradually to the temperature variation and gas sorption. In contrast PDMS is a relatively loosely packed “fragile” polymer with a propensity to exhibit rapid dynamic responses to the temperature change and gas sorption. © 1993 John Wiley & Sons, Inc.     

EPR spin probe study of polymer associative systems

Molecular dynamics of polyacrylamide gels, polymeric micelles and hydrogel of polyacrylic acid and macrodiisocyanate was investigated by the ESR spectroscopy of spin probes. The local mobility in network junction of polyacrylamide gels is found to be essentially slower than that in the micelles created by the low molecular weight detergents and does not depend on the amount and length of hydrophobic groups (C9 or C12) in the polymer chain. The immersion of 10-30 mol.% of ionic monomers into the polymer chain (sodium acrylate) influences insufficiently on the local mobility of network junctions. In aqueous solutions, polystyrene-block-poly-(N-ethyl-4-vinylpyridinium bromide) block copolymers create polymeric micelles. The local mobility in the polystyrene core of the micelles is about twice as much as that in the solid polystyrene. Partially swellable polymer network in aqueous solutions was synthesized from polyacrylic acid and macrodiisocyanate. The local mobility in hydrophobic regions of the gel is substantially lower than that in the hydrophilic regions. It was concluded that the hydrophobic and hydrophilic regions and the local dynamics of them dictate practical application of the polymer associative systems.     

Optical relaxation in organic disordered systems submitted to photochemical and non-photochemical hole-burning

The temperature dependence of the homogeneous linewidth (Γ_hom) of S₁ ← S₀ 0-0 transitions of organic amorphous systems undergoing either photochemical or non-photochemical hole-burning from 4.2 down to 0.3 K is presented. In all cases Γ_hom follows a T^1.3 dependence, and extrapolates to or actually reaches the lifetime-limited value of the guest. An estimate of the relative guest-host coupling strengths is made.     

An efficient Monte Carlo method to calculate nuclear spin relaxation times in complex molecules

An efficient Monte Carlo method to calculate nuclear spin relaxation times and nuclear Overhauser enhancements in complex molecules based on the convolution of power spectra for independent processes is proposed and applied to analyze the ¹³C T₁ distribution in poly(N-hexy-4-vinylpyridinium) bromide.     

Recent progress in EPR study of spin labeled polymers and spin probed polymer systems

The EPR technique is commonly used for the detection and characterization of paramagnetic centers in chemical science. This method can provides a lot of information, such as identity, structure, dynamics, interaction, orientation, glass transition temperature, adsorption behavior, functionality, phase behavior, nano-inhomogeneities, and conformation of the free-radical portion of the polymer chain. Most polymers intrinsically possess diamagnetic properties, so in order to study polymers with EPR, paramagnetic centers need to be incorporated into the polymer systems. Spin labeling and spin probing are main methods of covalently attaching paramagnetic centers to polymer chains or embedding them in polymer matrices through non-covalent interactions, respectively. Spin labeling and spin probing techniques for polymers and polymer systems (especially with nitroxide radicals) have also been studied, which have a profound impact on polymer science. This review focuses on the continuous wave EPR technique and introduces the recent advances in spin labeled polymers and spin probed polymer systems in EPR research.     

Nuclear spin relaxation due to chemical shift anisotropy of gas-phase 129Xe

Nuclear spin relaxation provides detailed dynamical information on molecular systems and materials. Here, first-principles modeling of the chemical shift anisotropy (CSA) relaxation time for the prototypic monoatomic (129)Xe gas is carried out, both complementing and predicting the results of NMR measurements. Our approach is based on molecular dynamics simulations combined with pre-parametrized ab initio binary nuclear shielding tensors, an "NMR force field". By using the Redfield relaxation formalism, the simulated CSA time correlation functions lead to spectral density functions that, for the first time, quantitatively determine the experimental spin-lattice relaxation times T(1). The quality requirements on both the Xe-Xe interaction potential and binary shielding tensor are investigated in the context of CSA T(1). Persistent dimers Xe(2) are found to be responsible for the CSA relaxation mechanism in the low-density limit of the gas, completely in line with the earlier experimental findings.