Correlation Time Τc Research Articles

μ+SR in amorphous spin glasses Pd75Fe5Si20 and Pd75Fe5P20

The zero-field muon spin relaxation functionGzz (t) has been measured as a function of reduced temperaturet=T/Tg in the amorphous metallic spin glasses Pd75Fe5Si20 and Pd75Fe5P20. The results are in qualitative agreement with earlier measurements on dilute alloy spin glasses, including an onset of static order belowTg and a [t/(t-1)]2 dependence of the correlation time τc aboveTg. Both samples have the same τc (t) aboveTg and almost identical static width ΔS→Δo≃43 μS−1) asT»0, but thet-dependence of Δs nearTg differs markedly.

Multiple-quantum NMR spectroscopy of S=3/2 spins in isotropic phase: A new probe for multiexponential relaxation

In nuclear magnetic resonance of quadrupolar spins with S≥3/2, it is shown that excitation and observation of multiple-quantum coherence is possible in the absence of scalar, dipolar, or quadrupolar splittings, in contrast to the widely accepted view that nonvanishing couplings are a prerequisite for the creation of multiple-quantum coherence. In the absence of splittings, multiple-quantum coherence can be excited because the longitudinal (‘‘T1’’) or transverse (‘‘T2’’) relaxation is multiexponential, which occurs if the motional correlation times τc are comparable to or larger than the inverse of the Larmor frequency (violation of the extreme narrowing approximation). Two experiments are described, which combine multiple-quantum filtration with conventional spin-echo and inversion-recovery sequences. For isotropic motion each experiment allows one to determine the motional correlation time without knowledge of the magnitude of the quadrupolar coupling constant.

Determination of very slow μ+ hop rates in Cu by LLF-μSRhop rates in Cu by LLF-μSR

Muon spin relaxation in low (weak) longitudinal magnetic field (LLF-μSR) provides a means of independently determining the static dipolar width Δ characterizing the μ+ lattice site and the correlation time τc for μ+ hopping, in a manner that is nearly model-independent for τc and especially accurate in the near-static limit (τc>τμ). The advantages of this method are illustrated by its application to muon hopping in Cu near the τc maximum around 50 K.

Statistics of dephasing perturbations and relaxational processes in a high-power optic field: application to free-induction decay

It is shown that the dependence of relaxational processes on radiation intensity associated with the finiteness of correlation time τc of relaxational perturbations is to a great extent defined by the statistics of these perturbations. Generalized master equations (GME’s) that take into account the nonvanishing correlation time τc are obtained by using the characteristic operator method. With the Gaussian statistics assumption for adiabatic perturbations causing a stochastic transition-frequency modulation, these GME’s are used to reveal the main features of the free-induction-decay rate dependence on radiation power. Good agreement with the experiment of DeVoe and Brewer [ Phys. Rev. Lett.50, 1263 ( 1983)] is obtained. Our preceding theory [ Opt. Commun.52, 279 ( 1984)] based on the correlation (Born) approximation closely agrees with the results of this paper at τc/T2 ≪ 1 and T1/T2 < 3.67.

Motional anisotropy‐induced unequal deuterium NMR spin‐lattice relaxation of 3α‐deuteriocholesterol and 3β‐deuterioepi‐cholesterol in solution as a measure of sterol motion about the molecular axis

AbstractDeuterium spin‐lattice relaxation (T1) data for 3α‐deuteriocholesterol and 3β‐deuterioepicholesterol in solution were obtained at 12.21 MHz as a function of solvent viscosity (η). The correlation times (τc) for both 3‐deuteriosterols varied in a linear fashion over the range of viscosities studied. The data showed that although both 3α‐deuteriocholesterol and 3β‐deuterioepicholesterol undergo rapid reorientations (τc ≈︁ 10−11s) in solution, the relaxation of the deuterium in 3β‐deuterioeholesterol was approximately 2.5 times faster than in 3β‐deuterioepicholesterol. These unequal rates of relaxation are due to the difference in the angles between the CD bond and the molecular axis for the two sterol isomers. An equation containing an angular‐dependent term was derived to analyze the T1 data further. The effective correlation times (τeff), thus calculated, converged for identical viscosities. In the case of 3α‐deuteriocholesterol, it was determined that rotation about the molecular axis comprised up to 60% of the motions relaxing the deuteron. The results show that for molecules having an inherent anisotropy and undergoing isotropic motions, it is possible to separate the portion of motion due to rotation about the molecular axis from other motions which contribute to the relaxation processes at a specific center.

Exact evaluation of the effect of an arbitrary mean flow in kinematic dynamo theory

An exact derivation is given of the dynamo equation in the presence of an arbitrary incompressible mean flow v0. A mixed representation is used specifying v0 in terms of a Lagrangian displacement, while Eulerian coordinates are employed for the turbulent velocity v superimposed on v0.When the first-order-smoothing approximation is made (FOSA; valid when the turbulent velocity v has a short correlation time τc) the usual dynamo equation is recovered, except that the turbulent velocity v in the tensors αis and βisk is replaced by . The bar represents the effect of advection and is expressed solely in terms of the Lagrangian coordinate specifying the mean flow v0. Thus the intuitive idea is confirmed that dynamo action depends only on velocity correlation functions measured at a point comoving with the mean flow. The result admits easy evaluation in actual model situations. This is illustrated with an example tailored to the solar dynamo. A shear in v0 causes a (kinematic) anisotropy in the tensors αis and βisk. This can be a large effect, which comes on top of the intrinsic (dynamical) anisotropy in the velocity correlation functions. Subsequently, the analysis is extended beyond FOSA up to arbitrary order, relevant for long correlation times τc on the basis of the work of Van Kampen (1974). It is shown that the same formalism is also applicable to the problem of turbulent transport of a scalar.Conditions for applicability of the work are (1) very large magnetic Reynolds number, (2) incompressible flows v and v0, (3) stationary mean flow v0, and (4) correlation time τc [Lt ] period of the dynamo.

Molecular dynamics and interactions of human ceruloplasmin: A spin labelling study

Ceruloplasmin, a paramagnetic copper-containing protein, has been spin labelled with different nitroxide spin labels in order to study its molecular dynamics and to gain further information about its interaction with other biosystems. Spin labelling with a maleimide derivative resulted in an electron spin resonance spectrum which was a superposition of two different absorptions due to paramagnetic species in different microenvironments. The first one, a three-line isotropic spectrum, is due to a fast-moving spin label (with a rotational correlation time τc≃10-9s); the second one is an anisotropic, asymmetrical signal arising from an immobilized spin in a slow-motion domain (τc=10-7). The assumption of a spherical shape for the molecule provided, through the Stokes-Einstein relation, an estimate of the molecular-radius value consistent with smallangle neutron scattering measurements. The interaction with other biosystems, as deduced from the protein molecule dynamics, is discussed.

Poly(O-acyl-hydroxy-L-proline) IV. Studies of Molecular Motions in Poly(O-acetyl, butyryl, hexanoyl, dodecanoyl, and benzoyl-hydroxy-L-proline) Films by the Spin Probe Technique

The molecular motion in poly(O-acetyl (Ac), butyryl (But), hexanoyl (Cap), dodecanoyl (Lau), and benzoyl (Bz)-hydroxy-L-proline (Hyp)) films was investigated by ESR measurements with 2,2,6,6-tetramethyl-4-hydroxypiperidine-1-oxyl (TEMPO) as the spin probe. As the length of acyl side chains increased, the temperature at which the separation of the outer extrema of ESR spectra reached 50 gausses (T50) decreased. The rotational correlation times (τc) obtained from the ESR spectra at −70°C for series of polymers were nearly the same. The values of τc at 130°C decreased with an increase in the acyl side chain length until the number of carbon atoms in the acyl chains reached 6. The activation energies of TEMPO in the polymers were less than 3 kcal mol−1 at low temperatures. At high temperatures, the activation energies of poly(O-Ac-Hyp) and poly(O-Bz-Hyp) differed scarcely from those at low temperatures. The activation energies of poly(O-But-Hyp), poly(O-Cap-Hyp), and poly(O-Lau-Hyp) were enhanced and particularly that of poly(O-Cap-Hyp), exceeding 10 kcal mol−1.

Rotational correlation times of a nitroxide spin probe in low temperature matrices determined by saturation transfer ESR: Their correlation to dynamic behavior of radiation products

Rotational correlation times τc of the spin probe, di-tert-butyl nitroxide, in several organic solvents cooled to temperatures lower than their melting points have been measured using a saturation transfer (ST) ESR technique. Since the ST spectra changed markedly depending on microwave power, we have introduced a scaled ST parameter to eliminate this effect. The temperature dependence of τc in a noncrystalline phase can be described by the Arrhenius relation. The activation energies are 17.6 kJ mol−1 for methanol containing 5% water, 20.8 kJ mol−1 for ethanol, and 18.9 kJ mol−1 for n-propanol. The values are close to the activation energies reported for the solvation and decay rates of electrons in the solvents. The rotational correlation time can be expressed in terms of a viscosity using the Stokes–Einstein equation. However, a macroscopic viscosity fails to reproduce the observed τc, especially at low temperatures. On the other hand, we have evaluated the solvation rate of an electron in n-propanol and the diffusion coefficients of radicals in methanol and 3-methylpentane on the basis of the tentative viscosity derived from τc using the same expression. The results are in good agreement with the experimental data. The temperature and phase dependences of τc will also be discussed.

Thermotropic ionic liquid crystals. II. 1H and 23Na NMR study of the smectic mesophase of molten sodium n-butyrate and sodium isovalerate

The 1H and 23Na NMR studies of smectic ionic mesophases of molten sodium n-butyrate and sodium isovalerate are reported over the temperature range of the stability of the liquid crystalline phases. The 1H spin-lattice relaxation times T1 at ν0=9.2, 24.3, and 60 MHz for the anions of both the systems are interpreted in terms of diffusion intermolecular relaxation mechanism. The predicted anion diffusion coefficients are in agreement with those measured directly by spin-echo technique and indicate that the anion diffuses rapidly. In contrast to the T1 relaxation mechanism the results obtained for the proton relaxation times in the rotating coordinate frame T1ρ indicate that the order-fluctuation relaxation mechanism determines the frequency dispersion of T1ρ. The analysis of the T1ρ data provides an approximate measure of the order parameter S as a function of temperature. Fourier transform spectra of the 23Na transitions show that the electric field gradient (EFG) at the Na+ ion is nonaveraged and of such a strength as to produce a second order quadrupole effect in the spectra of the central transition. From the first-order splitting, the quadrupole coupling constant (QCC) is obtained as a function of temperature. The gradual temperature change of QCC demonstrates that only a single liquid crystalline phase exists over the temperature interval of the stability of the smectic mesophase. Using approximate analysis the correlation time τc for the EFG fluctuation is obtained from the 23Na T1 data for the melts of both sodium n-butyrate and sodium isovalerate.

NMR investigations of dynamical processes in orientationally ordered and disordered NaCN, RbCN and CsCN

The nuclear spin lattice relaxation timeT 1 of the23Na,85Rb,87Rb,133Cs,14N nuclei is measured in NaCN, RbCN and CsCN as a function of temperature below and above the ferroelastic phase transition temperatureT c. BelowT c the behaviour ofT 1 of the alkali nuclei renders possible to determine the flip frequency of the CN molecules and its temperature dependence. AboveT c from the14NT 1 the correlation time τc of the rotational motions of the CN molecules and its temperature dependence is determined. An empirical rule is verified demonstrating that atT c the correlation times take nearly the same values for all cyanides. For the high and low temperature phases one obtains atT c about τc=5·10−13s and τc=5·10−11s, respectively. The results are discussed with respect to the mechanism of the phase transition.

Measurement of the hyperfine interaction of free75As ions In H2, He, Ne, Kr and Xe buffer environments and estimate of clolision cross sections in the eV and meV energy region

With the time-integral perturbed angular correlation (TIPAC) method the pressure dependence of the perturbation of the 121.1–279.5 keV γ-γ cascade in75As has been investigated using gaseous H275Se sources in different buffer environments. The obtained attenuation coefficients G22 (∞) in the range of 0.55 to 1.0 were fitted with a theoretical stochastic model. In the region of low density, where the correlation time τC is large compared to the lifetime τ of the intermediate level of the nucleus, charge transfer collision cross sections have been evaluated between 8.1·10−16 cm2 for He, 1.3·10−14 cm2 for Xe and 1.8·10−14 cm2 for the molecular H2 buffer gas. For increasing densities of the buffer gases the correlation time τC became small compared to the intermediate lifetime τ. The main effect in this region is the depolarization, and we found cross sections between 5.2·10−15 cm2 for He, 8.7·10−14 cm2 for Xe and 1.2·10−13 cm2 for the H2 buffer gas.

Effect of Fluctuation on Plane Front Propagation in Bistable Nonequilibrium Systems

AbstractA theory of front propagation in bistable stochastic media is developed. The effect of fluctuations is twofold: 1) they lead to random variations of the front shape. 2) they result in random motion of the front positions. Its general expression for the dispersion of the position for arbitrary stochastic noises with spatial correlation length lc and correlation time τc is given. For rate functions with cubic nonlinearities the dispersion formula is further analysed.

Molecular reorientation with internal extended rotational diffusion in liquids

An extended diffusion model is applied to describe the internal rotation about the figure axis of a symmetric top molecule whose overall reorientation is undergoing anisotropic rotational diffusion. An explicit analytical expression for the internal correlation time τ(k)int as a function of the angular momentum correlation time τj is obtained. The overall reorientational correlation time τc in the presence of the internal extended diffusional rotation is also obtained analytically as a function of τ(j). This expression is free from any restriction on the range of validity for τj.(AIP)

1H‐nmr comparative studies of polynucleotides: Conformation and dynamic structure of polyribo(uridylic) and polyribo(cytidylic) acids in neutral solution

AbstractThe conformation and the dynamic structure of single‐stranded poly(U) and poly(C) in neutral aqueous solution have been investigated by 1H‐nmr at two different frequencies (90 and 250 MHz) and at various temperatures. Measurements of proton chemical shifts, coupling constants JH‐H, and proton relaxation times, T1, T2, versus temperature show a striking difference in conformation and in dynamic structure between the two polynucleotides studied. The temperature effect on δ and JH‐H is found to be substantial for poly(C) and insignificant for poly(U). The S conformer is favored in poly(U), whereas the N conformer strongly predominates in poly(C) (≃90%), similar to the case for RNAs. These results suggest that single‐stranded poly(C) probably possesses a helical or partial helical structure, whereas poly(U) shows a clear preference for the random coil, in agreement with the optical results. The local motions of the ribose and base were studied at various temperatures by measurements on the relaxation times at 90 and 250 MHz. For a given temperature between 22 and 72°C, the ratio T1(90)/T1(250) is practically the same for all poly(U) protons, indicating that in this temperature interval the ribose base unit of poly(U) undergoes an isotropic motion characterized by a single correlation time τc. Above 52°C, poly(C) exhibits a dynamic structure similar to poly(U). Below this temperature, poly(C) exists in an equilibrium between randomly coiled and single‐stranded helix forms. This situation is characterized by a strong cross‐relaxation effect and T1 values corresponding to a relatively short apparent correlation time. An activation energy of 4 kcal/mol was determined for the motion of the ribose–base unit in both single‐stranded polynucleotides.

Vibrational dephasing by bonding interaction in liquids

Two models for vibrational dephasing by the bonding interactions in liquids are presented for a two component mixture; one is based on a semiclassical trajectory theory with a Morse potential, and the other is based on a quantum mechanical calculation using the Lennard-Jones-Devonshire cell model. The results are compared with those from isolated binary collision theory. It is found that the bonding interaction broadens the isotropic Raman width by increasing both the mean square vibrational frequency shift and the vibrational frequency correlation time τc, corresponding to the lifetime of the environment about a probe molecule. As τc increases with increasing bonding energy, slow fluctuation of the vibrational frequency may give rise to a distribution of vibrational frequencies to inhomogeneously broadened bands.

Studies with a hydrophobic, spin-labeled virucidal agent.

A spin-labeled virucidal agent was synthesized, purified, and tested for its activity against the enveloped bacterial virus phi6 and herpes simplex virus. This compound, designated BPN, inactivated greater than 99% of phi6 and herpes simplex virus in vitro at concentrations as low as 0.1 mM. Detailed studies were carried out on the mechanism of inactivation of phi6 by BPN. These studies revealed that treatment of phi6 by BPN specifically removes a single envelope protein that is considered to be responsible for adsorption of the virus to the host cell. Related experiments with the phi6 host, Pseudomonas phaseolicola strain HB10Y, showed that this organism is insensitive to the effects of BPN. The basis for the differential sensitivity of phi6 to BPN, in comparison to the host cell, was investigated by electron spin resonance techniques. It was found that, for phi6, HB10Y, and their extracted phospholipids, BPN is localized in the hydrocarbon zones of the membrane bilayer. However, in the case of phi6, the rotational mobility of BPN is much reduced in comparison to that in HB10Y and the phospholipid preparations. Furthermore, an Arrhenius plot of rotational correlation time (tau(c)) showed a marked discontinuity in slope at 31 degrees C in the case of phi6, but not for the other samples studied. This suggests a strong interaction between the phi6 envelope proteins and the lipid domains in which BPN is localized. Calculations based on the known lipid and protein composition of phi6 indicate that there is an absence of "free-lipid" pools in the viral envelope. It is suggested that BPN localizes in free-lipid pools of cell membranes, where its presence is of little or no consequence, but that in phi6 the BPN perturbs the hydrophobic interactions between phospholipids and proteins in the envelope.

The nature of the NADP complex with manganese(II) ions as studied by proton and phosphorus magnetic resonance

Proton and phosphorus magnetic resonance techniques have been applied to study the conformation of the complex formed between Mn(II) ions and nicotinamide adenine dinucleotide phosphate (NADP) in aqueous solutions at a pH of 7.5 and 20 °C. The dipolar correlation time (τc) for the Mn(II)–NADP complex at 20 °C was calculated to be 1.7 × 10−10 s, based on the measurement of proton longitudinal relaxation time ratios and a literature value of τc for nicotinamide adenine dinucleotide (NAD). The τc, as well as the 1H and 31P relaxation data together with the measured stability constant for this complex, were used to calculate the distances from the 1H and 31P nuclei to the Mn(II) ion. These distances are 3.8 Å to A8, 5.0 Å to A2, 4.5 Å to A1′, 5.3 Å to N2, 5.4 Å to N6, 5.5 Å to N5, 5.8 Å to N1′, and 6.3 Å to N4. The distances to the linkage 31P nuclei are 3.7 Å, and 3.3 Å to the adenosine ribose 2′-phosphate. Based on these distances, a model is proposed for the Mn(II)–NADP complex. In this complex, the Mn(II) ion is bonded to the oxygens of all three phosphates, and the adenine and nicotinamide bases are 7–8 Å apart and parallel. Hence the Mn(II) ion is located between and to one side of the two bases but is distinctly closer to the adenine base. The adenine base is in the anti conformation, whereas the nicotinamide moiety can be either syn or anti. Hence there is little or no close stacking of the two bases in the complex. The addition of Mg(II) ions to a solution of free NADP caused no observable shift of the aromatic proton peaks, indicating no differences in shielding effects. Hence the rings are probably similarly oriented in both free NADP and the metal–NADP complex. Effects on the transverse relaxation rates due to the paramagnetic metal ion (T2p−1) were also measured from the 31P linewidths as a function of temperature. The lifetime of the metal ion in the complex is 4.0 ± 0.5 × 10−6 s and ΔH≠ for the exchange process is 13.7 ± 0.5 kcal/mol.

Interactions of long-chain aldehydes with luciferase. A carbon-13 nuclear magnetic resonance study

The interaction of long-chain aldehydes with bacterial luciferase has been studied by 13C NMR spectroscopy of natural-abundance and 13C-enriched 1-dodecanal. At high substrate/enzyme ratios, the spin-spin relaxation rates of C(1)-C(3) are faster than for the other carbons and are in the order C(1) greater than C(2) greater than C(3). The aldehyde is strongly bound in the active site along the entire length of the alkyl chain with the strongest interaction at the CHO group. At low substrate/enzyme ratios, interactions are apparent at C(10), which are removed upon denaturation of the enzyme. Spin-spin and spin-lattice relaxation rates were measured for odd-carbon 13C-enriched 1-dodecanal in the presence of luciferase. From the ratios of T1/T2 a single value of (1.8 +/- 0.7) X 10(-8) s was calculated for the rotational correlation time tc for the complex.

A nuclear magnetic resonance study of pyridoxal phosphate – metal ion interactions. II. Binding of manganese(II)

The line width and spin–lattice relaxation rates of phosphorus and proton nuclei in PLP have been measured as a function of temperature in the presence of Mn(II) using pulsed nmr methods. The T1M of 31P in PLP-Mn(II) is very close to the T1M values of β- and γ-phosphorus atoms in ATP–Mn(II) at ∼40 °C. The T1 data of 31P and 1H have been interpreted in terms of the dipolar interaction between the electron and nuclear spins. With the assumption that the Mn(II) interacts directly with the phosphate of PLP the rotational correlation time τc at 38 °C was calculated to be 7.6 × 10−10 s from phosphorus T1 data. This τc value was subsequently used to calculate metal–proton distances from proton T1 and T2 data. The results lead to the conclusion that the phosphate-bound metal interacts directly with the aldehyde oxygen in a 1:1 PLP–Mn(II) complex. The linewidth of the 13C resonances of PLP in the presence of Mn(II) supports this conclusion. The structure assigned for PLP–Mn(II) complex is in conformity with the structure for PLP-Co(II) complex.