1H and13C nuclear magnetic relaxation and local dynamics of lysozyme and synthetic polypeptides

The combined analysis of¹H and¹³C NMR relaxation data in solid lysozyme and some typical homopolypeptides was carried out by using “model-free” approach. Three types of relaxation transitions (γ’, γ and β) were revealed in the temperature range investigated. The microdynamical parameters of these motions were determined. From the comparison of these parameters with those of selected synthetic polymers it follows that the molecular motions in proteins and synthetic polymers are of the same nature. All these motions show pronounced anisotropic character. In the investigated temperature range no molecular motions corresponding to α-relaxation (liquid-like) transition were revealed. The hydration effects on parameters of the motions in proteins were considered. The most pronounced effect takes place for β-transition. The effect of Brownian rotation of protein molecule in solution on measured correlation function of local motions was also discussed.     

Nuclear magnetic relaxation and dynamics of biopolymers

A model is proposed in which the NMR relaxation dispersion profiles of biomolecule water solutions are interpreted in terms of magnetic field fluctuations due to the backbone vibrations involving the biopolymer paramagnetic nuclei. This model, which takes into account the experimental evidence which has appeared in the literature for a “fractal-like” density of vibrational state for the protein backbone, has been used to fit some experimental NMR relaxation profiles of biomolecule water solutions. The results obtained are discussed critically in connection with the data reported in the related literature.     

Nuclear magnetic relaxation without spin diffusion in polymers at interfaces

We consider theoretically the possibility of solid state NMR experiments with frozen linear polymer chains at interfaces. Three different cases are studied, namely, when the macromolecules are grafted on the surface, when they are adsorbed, and when they are very strongly adsorbed from a melt that is subsequently washed by a good solvent. The latter case is somewhat intermediate between the two former ones. For each case, we consider the relaxation when paramagnetic centers are located on the surface. We show that the shape of the relaxation curves depends critically on the monomer concentration profile, and exhibits characteristic power-law variations.     

Measuring surface and bulk relaxation in glassy polymers

We present a comprehensive study of gold nanoparticle embedding into polystyrene (PS) surfaces at temperatures ranging from T _g + 8 K to T _g − 83 K and times as long as 10⁵ minutes. This range in times and temperatures allows the first concurrent observation of and differentiation between surface and bulk behavior in the 20nm region nearest the free surface of the polymer film. Of particular importance is the temperature region near the bulk glass transition temperature where both surface and bulk processes can be measured. The results indicate that for the case of PS, enhanced surface mobility only exists at temperatures near or below the bulk T _g value. The surface relaxation times are only weakly temperature dependent and near T _g , the enhanced mobility extends less than 10nm into the bulk of the film. The results suggest that both the concept of a “surface glass transition” and the use of glass transition temperatures to measure local mobility near interfaces may not universally apply to all polymers. The results can also be used to make a quantitative connection to molecular dynamics simulations of polymer films and surfaces.     

Monte Carlo simulation of polymers in solution and bulk

The behavior of polymers in solution depends on both temperature and concentration. At least four different regions of the concentration-temperature plane exist in which the physical properties are fundamentally different. These regions are known as the dilute good solvent, theta solvent, semidilute, and concentrated regions. In this investigation, Monte Carlo simulations were performed in order to examine how properties change in going from one region to another. Two series of simulations were performed. In the first series, properties were studied as a function of concentration so that crossover from dilute, to semidilute, and then to concentrated was obtained. In the concentrated or bulk region, it was found that the second and fourth moments of the end-to-end distance were characteristic of ideal chains (without excluded volume), consistent with neutron scattering results. In the semidilute region, the concentration dependence of the mean square end-to-end distance was not in agreement with scaling theory. In the second series of simulations, the temperature was changed for an isolated chain (zero concentration limit), so that crossover from good solvent to theta solvent behavior was obtained. Over the chain length range studies (10–300), no evidence was seen for the existence of “thermal blobs.” In addition, expansion of the average internal conformation over the expected result was observed and found to be increasingly important as the temperature increases from the theta temperature.     

Nuclear quadrupolar spin-lattice relaxation in the amorphous state

It is proposed that the nuclear quadrupole spin-lattice relaxation in glasses is due to interaction of solitons with the nuclear quadrupole moment. The magnitude of the interaction is estimated and the resulting temperature dependence of the spin-lattice relaxation time is compared to experiment.     

Nuclear magnetic relaxation induced by the relaxation of electron spins

A physical mechanism responsible for the relaxation of nuclear spins coupled by the hyperfine interaction to relaxed electron spins in materials with spin ordering is proposed. The rate of such induced nuclear spin relaxation is proportional to the dynamic shift of the nuclear magnetic resonance (NMR) frequency. Therefore, its maximum effect on the NMR signal should be expected in the case of nuclear spin waves existing in the system. Our estimates demonstrate that the induced relaxation can be much more efficient than that occurring due to the Bloch mechanism. Moreover, there is a qualitative difference between the induced and Bloch relaxations. The dynamics of nuclear spin sublattices under conditions of the induced relaxation is reduced to the rotation of m₁ and m₂ vectors without any changes in their lengths (m ₁ ² (t) = m ₂ ² (t) = m ₀ ² (t)= const). This means that the excitation of NMR signals by the resonant magnetic field does not change the temperature T _n of the nuclear spin system. This is a manifestation of the qualitative difference between the induced and Bloch relaxations. Indeed, for the latter, the increase in T _n accompanying the saturation of NMR signals is the dominant effect.     

13C NMR relaxation and computational study of anisole and derivatives in the solution state

¹³C NMR spin–lattice relaxation times and nuclear Overhauser effects were measured at several temperatures for the methoxyl methyl carbon and the phenyl ring carbons in neat samples and in dilute cyclohexane solution for anisole, 4‐methylanisole, and 4‐chloroanisole. Similar measurements were made for 2‐methylanisole, 2‐methyl‐4‐bromoanisole, and 2,4,6‐trimethylanisole in dilute cyclohexane solution. Density functional theory (DFT) computations were performed on anisole, 4‐chloroanisole and 2,4,6‐trimethylanisole to obtain the minimum energy structures and the potential energy barriers to the internal rotations of the methoxyl group. The shortest distance between a methoxyl methyl hydrogen and the ortho hydrogen in anisole is 1.920 Å. The DFT results point to steric interactions that arise thereof as the principal source of the energy barriers to the internal rotation of the methyl or of the methoxyl group. The carbon relaxation data are consistent with the existence of noncovalent intermolecular interaction, especially π ? π stacking interaction. The nuclear magnetic resonance and DFT results are discussed with reference to the rotational characteristics of the methoxyl methyl and the anisotropy in the reorientational motion of anisole and its derivatives in dilute cyclohexane solution. Copyright © 2012 John Wiley & Sons, Ltd.     

Nuclear magnetic relaxation,correlation time spectrum,and molecular dynamics in a linear polymer

The pulsed nuclear magnetic resonance (NMR) method at a proton frequency of 25 MHz at temperatures of 22–160°C is used to detect the transverse magnetization decay in polyisoprene rubbers with various molecular masses, to determine the NMR damping time T ₂, and to measure spin-lattice relaxation time T ₁ and time T _2eff of damping of solid-echo signals under the action of a sequence of MW-4 pulses modified by introducing 180° pulses. The dispersion dependences of T _2eff obtained for each temperature are combined into one using the temperature-frequency equivalence principle. On the basis of the combined dispersion dependence of T _2eff and the data on T ₂ and T ₁, the correlation time spectrum of molecular movements is constructed. Analysis of the shape of this spectrum shows that the dynamics of polymer molecules can be described in the first approximation by the Doi-Edwards tube-reptation model.     

Ground state energy of dilute magnetic alloys

The ground state energy of dilute magnetic alloys as described by thes-d-exchange Hamiltonian is calculated within the Nagaoka-Suhl theory. For integral impurity spinS it is shown that for positive coupling constantγ the energy is a holomorphic function ofγ. For negative coupling one obtains an additional singular contribution of the form (?1) ^s?1 e ^1/γ (γ<0). As this changes sign for different integral s-values, the interpretation of the singular part as a binding energy suggested previously does no longer hold. For half integral spin the energy is a singular function for bothγ>0. The singularities are not as elementary as in the case of integral spinS, but are rather related to those of the exponential integral function. In particular, forγ>0 the origin (γ=0) is a branch point. Earlier variational calculations are compared with our new results.     

Nuclear magnetic resonance and relaxation in liquid zinc

Measurements of the Knight shift K and the nuclear spin-lattice relaxation rate $\text{(}\text{1}\text{T}{}_{\mathrm{l}}\text{)}$ of Zn⁶⁷ are reported for liquid Zn. Measurements of K extend from 409°C (supercooled) to 700°C; measurements of $\text{(}\text{1}\text{T}{}_{\mathrm{l}}\text{)}$ cover the range 425 – 620°C. The Knight shift shows a weak positive temperature dependence attributed to thermal expansion. The reciprocal enhancement factor of the Korringa relation K(α) is found to increase with temperature from .77 ± .04 to .82 ± .04 in the range 425 – 620°C. The quadrupolar contribution to the relaxation rate was concluded to be very small with an estimated upper limit given by $\text{(}\text{1}\text{T}{}_{\mathrm{l}}\text{)}{}_{\mathrm{Q}}\text{≤ 15 sec.}{}^{\mathrm{-l}}$     

Spin diffusion and relaxation in dilute magnetic alloys: Electron-electron interaction

Diffusion and relaxation of conduction electrons is studied without making the usual approximation that the spin-orbit scattering be smaller than the impurity potential scattering. Renormalization of impurity vertices by the electron-electron interaction reduces the potential, enhances the s-d, but does not affect the spin-orbit scattering cross-section.     

Nuclear spin-lattice relaxation of dilute Mn in Cu,Ag, and Au

We have developed a new method of determining nuclear spinlattice relaxation times of dilute impurity nuclei in non-magnetic host metals. Direct measurement of these extremely rapid relaxation times has hitherto been difficult. The present method is based on fast pulsed heating of a sample containing oriented radioactive nuclei and is applicable to a wide range of impurity-host combinations and over a large range of applied magnetic fields. Results are presented for extremely dilute Mn in noble metal hosts.     

Nuclear spin-lattice relaxation in the mixed state of superconducting niobium

Pulsed NMR measurements of the spin-lattice relaxation timeT ₁ have been carried out in niobium metal, in order to investigate the elementary excitation spectrum in the superconducting mixed state. The dependences ofT ₁ on temperature, external field, and mean free path were determined. The results below ～5°K were in agreement with the theory of field-induced gapless superconductivity. The best fit was obtained with a scale factor 0.35±0.2, in agreement with recent ultrasonic attenuation results. Anomalously fast relaxation was observed above ～5°K, which could not be interpreted in terms of the present theory of thermal vortex fluctuations.     

Non-equilibrium relaxation and tumbling times of polymers in semidilute solution

The end-over-end tumbling dynamics of individual polymers in dilute and semidilute solutions is studied under shear flow by large-scale mesoscale hydrodynamic simulations. End-to-end vector relaxation times are determined along the flow, gradient, and vorticity directions. Along the flow and gradient directions, the correlation functions decay exponentially with sinusoidal modulations at short times. In dilute solution, the decay times of the various directions are very similar. However, in semidilute solutions, the relaxation behaviors are rather different along the various directions, with the longest relaxation time in the vorticity direction and the shortest time in the flow direction. The various relaxation times exhibit a power-law shear-rate dependence with the exponent -?2/3 at high shear rates. Quantitatively, the relaxation times are equal to the tumbling times extracted from cross-correlation functions of fluctuations of radius-of-gyration components along the flow and gradient direction.     

Nuclear magnetic resonance and spin relaxation in biological systems

Proton nuclear spin-lattice relaxation in biological systems is generally distinguished from that in inorganic systems such as rocks by the presence of locally disordered macromolecular environments. Rapid exchange of readily observed labile small molecules among differently oriented macromolecular sites generally nearly averages the spectral anisotropies in the small molecule resonances. The biological tissue is generally distinguished from the inorganic matrix by the presence of a significant population of protons in the solid components that are well connected by dipolar spin couplings. Magnetic coupling between the solid and the liquid components generally dominates the magnetic field dependence of the spin-lattice relaxation rates observed in the small molecule components which is generally described by a power law in the Larmor frequency. Recent theory involving a modification of the spin-phonon class of relaxation mechanism provides a quantitative understanding of these data in terms of the dynamics of the chain molecules generally present in the solid spin systems, folded proteins for example.     

Nuclear quadrupolar relaxation and the dynamics of pairs of atoms in liquids

We have developed a model calculation for the electrical field gradient correlation function on a probe atom in the liquid, c_EFG(t)=20(0)V₂₀(t)>. In this model, symmetry of the liquid is introduced explicitly and the distribution function for therelative coordinate r_i(t) between the probe atom and particle i is calculated using Smoluchowski's diffusion equation with a mean force potential Φ(r)=k_BT In g(r). The results for c_EFG(t) can be characterized by two correlation times, , the shorter one being responsible for the small values of R_Q in pure liquid metals, the longer one producing the increase of R_Q in alloys. Also good agreement is found with recent results for c_efg(t) from molecular dynamics studies.