Nonexponential Character Research Articles

Nestabil'nost' protona i neeksponentsial'nost' zakona raspada

Nestabil'nost' protona i neeksponentsial'nost' zakona raspada

Nuclear magnetic resonance transverse relaxation in muscle water

The origin of the nonexponentiality of proton spin echoes of skeletal muscle has been carefully examined. It is shown that the slowly decaying part of the proton spin echoes is not due to extracellular water. First, for muscle from mice with in vivo deuteration, the deuteron spin echoes were also nonexponential, but the slowly decaying part had a larger weighing factor. Second, for glycerinated muscle in which cell membranes were disrupted, the proton spin echoes were similar to those in intact muscle. Third, the nonexponentiality of the proton spin echoes in intact muscle increased when postmortem rigor set in. Finally, when the lifetimes of extracellular water and intracellular water were taken into account in the exchange, it was found that the two types of water would not give two resolvable exponentials with the observed decay constants. It is suggested that the unusually short T2's and the nonexponential character of the spin echoes of proton and deuteron in muscle water are mainly due to hydrogen exchange between water and functional groups in the protein filaments. These groups have large dipolar or quadrupolar splittings, and undergo hydrogen exchange with water at intermediate rates. The exchange processes and their effects on the spin echoes are pH-dependent. The dependence of transverse relaxation of pH was observed in glycerinated rabbit psoas muscle fibers.

Nonexponential proton relaxation from cross-correlation in dissolved poly(2,6-dimethyl-1,4-phenylene oxide)

The methyl proton spin-lattice relaxation of poly(2,6-dimethyl-1,4-phenylene oxide) dissolved in CDCl 3 is strongly nonexponential at long times, but this behavior can be quantitatively accounted for by the cross-correlation descriptions of Hubbard and Werbelow and Marshall in combination with a dynamic model for local motions in randomly coiled polymer chains. The pronounced nonexponential decay stems from rapid anisotropic methyl group rotation, which is much faster than the other motions modulating the dipole-dipole interaction. An estimate of the correlation time for methyl group rotation is obtained by simulating the nonexponential character of the return to equilibrium, yielding values of 2 to 15 psec. The uncertainty in these values is rather high, a factor of 5, since three different exponential time constants describe the return to equilibrium; the difficulties associated with such a fitting procedure are well known. The initial spin-lattice relaxation is almost free of cross-correlation effects and independent of the value of the correlation time for methyl group rotation as long as it is short. This permits an analysis of the other motions contributing to relaxation.

Disk and spheroidal components of external galaxies: an overview

A brief review of current theoretical views on how disk and spheroidal galaxies form and evolve provides the background for a summary of recent optical observations of external galaxies. Primary emphasis is placed on a discussion of the large-scale distribution and chemical composition of the stellar and gaseous constituents of relatively isolated galaxies. New studies of halo and disk surface-brightness distributions in spiral and SO galaxies are summarized. The “missing mass” in galactic halos, the relationship between disk size and luminosity, the nonexponential character of disk light distributions and very low-surface-brightness disk systems are highlighted in this section. Next discussed are observations which may provide insight into the factors which regulate the star-forming history of galactic disks and the post-astration appearance of spiral galaxies. Finally, the observed properties of relatively isolated disk galaxies are compared with those located in dense groups. It appears from this comparison that environment plays a significant role in governing the evolutionary history of a galaxy.

Flourescence decay characteristics of Tb 3+-activated phosphates under H 2-VUV laser excitation

Non-exponential flourescence decays from the trivalent terbium 5D 4 state of Tb x Y 1− x PO 4 were observed under the H 2-VUV laser (7.75 eV) excitation. The non-exponential character was ascribed to exciton-exciton annihilation resulting from high excitation density at the surface of the phosphors. Dependence of the annihilation coefficients upon x was explained by a random walk diffusion model.

The nonexponential character of the Zeeman relaxation of reorienting methyl groups in solids

If the rapid reorientations of methyl groups in solids are the dominant relaxation mechanisms, it is theoretically found that the Zeeman system is dynamically coupled to the so-called rotational polarization system, resulting in a nonexponential Zeeman relaxation. Though this result has been confirmed experimentally, in many samples within measuring error an exponential Zeeman relaxation has been observed. In order to decide whether or not this is contradictory to the theory the degree of nonexponentiality has been further investigated in this paper. It is shown that the nonexponential character depends stronly on the following parameters: (i) the way in which the spin system is prepared for the observation of the Zeeman relaxation, (ii) the number of protons not belonging to the methyl groups, (iii) the relaxation due to the intermethyl dipolar interactions, and (iv) the temperature. It is found that under specific conditions the observed relaxation can become almost exponential. The corresponding time constant, however, can differ considerably from that predicted by the usual spin temperature theory. Therefore, the interpretation of the experiments with this theory can lead to incorrect values of the different parameters characterizing the relaxation process. The various results have been illustrated with experiments on polycrystalline samples of 2,6-dimethylphenol, methylcyanide, 2-methylpiperazine, and 1,4-dimethoxy-2,6-dimethylbenzene.

Analysis of Structural Relaxation in Glass Using Rate Heating Data

A method was developed to determine the kinetic parameters controlling structural relaxation in the glass transition region from data acquired during continuous heating or cooling. The nonexponential character of the relaxation is accounted for by assuming an equilibrium isothermal relaxation function of the form exp [−(t/Toe)ß], where Toe is a relaxation time and 0<β1. The data are linearized using the method of Narayanaswamy, and the continuous temperature variation during heating or cooling is dealt with by invoking the superposition principle. The analysis yields the kinetic parameters A, the relaxation‐time preexponential term; Δh★, the relaxation‐time activation enthalpy; x, a term describing the relative effects of temperature and structure on the rate of relaxation; and β. The method was applied to analysis of the variation of the enthalpy of vitreous B2O3 during rate heating through the transition region following rate cooling through the same region at a variety of rates.

On the relationship between molecular structure and proton magnetic relaxation in polyethylene melts

A study has been made of relaxation mechanisms of longitudinal and transverse proton magnetization in PE melts. It was found that the transverse relaxation is of a non-exponential character, the mean relaxation time 〈T2〉 depending on molecular weight, polydispersity and short chain branching. Empirical equations have been derived, correlating 〈T2〉 with Mη for linear PE, and it was found that 〈T2〉 rises as the number of methyl branches increases. It is suggested that degrees of polydispersity of the samples could be characterized by the parameter 〈T2〉2/〈T22〉.

Luminescence and triplet decay in quinoxaline vapors

The effects of the gas pressure on the quinoxaline triplet state kinetics and luminescence yields were studied in the 10 −3 −10 torr pressure range. The non-exponential character of the fluorescence decay and long fluorescence lifetimes, previously reported, are confirmed. The collision-free lifetime of the “hot” triplet state measured by triplet—triplet absorption kinetics and by phosphorescence collisional induction is of the order of 100 μs, much longer than the long-fluorescence decay times (0.5–70 μs). The results are discussed on the basis of a model involving anharmonic coupling between triplet levels strongly and weakly coupled to the singlet.

Pulsed NMR studies of 17O from H2 17O in frog striated muscle.

Abstract Whole striated muscles from the frog were bathed in Ringer's solution enriched with 8–14% H 2 17 O until the isotope compositions of the water in the muscle and bathing media were identical. The spin-lattice relaxation time ( T 1 ) was determined by pulsed NMR techniques. In fresh preparations, the longitudinal relaxation rate was found to be non-exponential, both at 20–22°C and at 2–3°C, reflecting the presence of a heterogeneity of populations of water molecules. With deterioration of the muscle samples over the 1–3 days of observation, the non-exponential character of the longitudinal relaxation became progressively less apparent; eventually, T 1 could be characterized by a single exponential. T 1 was also examined as a function of the total muscle water, during the course of progressive evacuation of water; the data are consistent with the concept that the enhanced rates of longitudinal relaxation in muscle arise from rapid exchanges between free and bound fractions of water.

New evidence supporting energy transfer between photosynthetic units.

Abstract The non-exponential character of the fluorescence induction observed in presence of 3-(3,4-dichlorophenyl)-1,1-dimethylurea or at low temperature has been previously interpreted in terms of energy transfer between photosynthetic units. Alternative hypotheses have been recently proposed and this problem is discussed on the basis of new experimental results. Several independent methods are used to decrease the concentration of photoactive centers. If the inactive centres are blocked in a non-quenching form, one observes that the number of photons collected per active center increases up to a factor of 3 as the concentration of active centres decreases. However, if the inactive centres are blocked in a quenching form, the number of photons collected per active center remains independent of the concentration of the active centers. From the experiments described in this paper, one can conclude: 1. 1. Each center includes only one photoactive chlorophyll. 2. 2. Energy transfer occurs between three and probably more connected photosynthetic units. 3. 3. One must assume that the photosynthetic units are not identical. This heterogeneity may be due to their size or some structural features.

Stochastic Model of Molecular Relaxation

A simple stochastic model is used to show that the time autocorrelation function which determines dynamic susceptibility is generally nonexponential. The nonexponential character is caused by environmental fluctuations which arise in ordinary Brownian motion. Some computations of dynamic susceptibility are presented which indicate the kind of experimental results anticipated for substances which conform to this model.

Spin Relaxation and Line Width in Alkali Metal Vapors

Relaxation constants ${T}_{1}$ and ${T}_{2}$ have been computed for experiments involving optical pumping and optical detection in alkali metal vapor. The calculations have been performed for several possible spin relaxation mechanisms; namely, magnetic dipole, electric quadrupole, spin exchange, and the optical pumping process itself. For all of these mechanisms a reorientation experiment will approximately predict a spin resonance line width (equivalent to the statement ${T}_{1}\ensuremath{\approx}{T}_{2}$ for spin-\textonehalf{} particles.) However, a spin reorientation experiment of the type originally performed by Dehmelt, employing circularly polarized light, gives approximate results because of the nonexponential character of the reorientation. A more suitable experiment is one employing hyperfine population differences and unpolarized light.