Reciprocal Times Research Articles

The temperature dependence of double-layer capacitance

The capacitance dispersion of two Hg/borax contacts was measured in the temperature range 15–50 °C at zero-charge potential using a previously described bridge (100 Hz–300 kHz). Increasing the temperature shifts the dispersion to higher frequencies and raises the low frequency limit. To obtain some idea of how to evaluate relaxation times from non-Debye dispersion curves, an inverse Fourier transformation into decay functions was made numerically. From logarithmic plots of the decay functions three relaxation times were extracted: one long time that was independent of temperature and electrolyte concentration and two much shorter times corresponding to relaxation of the double layer. The values of the shorter times are not very different and are probably caused by relaxing cations and anions. A numerical method was used for these times within the frequency domain, thereby neglecting the long time process. This approach leads to reciprocal times of the order of 10 kHz for the 0.02 M borax contact and to 100 kHz for the 0.2 M borax contact. When the logarithmic time data are plotted against reciprocal temperature an activation energy of about 20 kJ mol -1 is found. In addition, with the aid of an adsorption model described elsewhere the low frequency data yield an approximate value for the standard free enthalpy of adsorption.

Stopped-Flow Spectrophotometric Assay of Glycerol Permeation in Escherichia coli: Applicability and Limitations

The passive permeation and facilitated diffusion of glycerol in various strains of Escherichia coli have been studied by stopped-flow spectrophotometry. Contrary to the prediction for glycerol entry by simple diffusion, the reciprocal relaxation time (1/tau, s-1) for the passive permeation of glycerol in cells grown in the presence of glucose was not constant but decreased as the glycerol concentration increased above 100 mM. This anomaly was not due to refractive index differences or to the presence of residual levels of the glycerol facilitator protein in non-induced cells. Although reciprocal relaxation times for glycerol-induced E. coli exhibited the expected elevation relative to non-induced cells, a similar anomalous decrease 1/tar (s-1) with increasing glycerol concentration was observed. In addition, at early times after suspension in dilute buffer, the 1/tau (s-1) values obtained for induced or non-induced E. coli swelling in glycerol were considerably greater than for organisms incubated in dilute buffer for longer times. We concluded that either this spectrophotometric technique was not monitoring solely the permeation of glycerol into E. coli, or concentrations of glycerol above 100 mM significantly perturbed the structure of the E. coli cell envelope.

Effects of inorganic complexing on the toxicity of copper to Daphnia magna

Effects of carbonate-bicarbonate, orthophosphate, and pyrophosphate on the toxicity of copper (II) to Daphnia magna were studied at constant pH and total hardness. Mortality rates and reciprocal survival times were directly correlated with cupric (Cu 2+) and copper hydroxy (Cu(OH) n) ion activities as determined by equilibrium calculations. Toxicity was negatively related to activities of soluble copper carbonate (CuCO 3) and other complexes, and was found to be independent of dissolved copper or total copper concentrations.

Elementary processes in the interaction of serine protease with a possible transition state analog. Subtillisin-benzeneboronic acid system.

The interaction of benzeneboronic acid(BBA), a possible transition state analog, with subtilisin BPN' [EC 3.4.21.14] was studied by the temperature-jump method at various pH's, temperatures and in D2O as well as H2O. From analysis of the concentration dependence of the relaxation times, it was suggested that the subtillsin-BBA interactions consist of at least two elementary steps, a fast bimolecular association followed by a slow unimolecular process. Similar concentration dependence was observed at pH 6.1-6.7 at 25degrees. However, in D2O the reciprocal relaxation times generally decreased compared to those in H2O and became concentration-independent below pD 6.5. The relaxation times were influenced considerably by the temperature. From these results, the slow unimolecular process was assigned to the trigonal-tetrahedral interconversion of BBA at the active site of the enzyme.

Kinetics of conformational change during micelle formation in apolar media

AbstractAccording to previously developed ideas on the nucleation process of micelle formation the kinetics of the micellization of an ionic surfactant (Aerosol OT) was studied in various apolar solvents. The applied kinetic method utilizes the dielectric field effect due to a considerable variation of the reaction moment produced by the extensive compensation of the effective dipole moment of the monomers in the micelle. Rotational relaxations of about 120, 23 and 20 MHz in dioxane, benzene and cyclohexane solutions, respectively, were assigned to the expected premicellar aggregates (nuclei) and the micelles; in the latter solutions, however, orientational and chemical relaxation processes are superimposed. The analysis of the corresponding data yields a concentration dependence of the reciprocal relaxation times of the chemical process which conforms very satisfactorily to the corresponding theoretical plot derived from a model which assumes a conformational change between two premicellar states during the formation of the micelle.

Solvent and temperature dependence of the phosphorescence decay time of hexacyanochromate (III)

The temperature dependence of the 2E g - 4A 2g phosphorescence of tetrabutylammonium hexacyanochromate (III) dissolved in various solvents has been measured within the liquid range of these solvents. In this limited temperature range, the reciprocal decay times obey Arrhenius relationship. From the absence of a solvent isotope effect, in ethanol and methanol and their monodeuterated analogues it is concluded that hydrogen bonds between the solvent and the complex ion do not provide promoting or accepting modes for the radiationless deactivation. The room temperature decay times have been found to correlate with the solvatochromic shift of the 4A 2 g − 4T 2 g absorption bands and with Dimroth's E T parameter. According to the selection rules for non-radiative decay a combination of CN stretching with either a Cr-C-N bending or a Cr-C stretching vibration is postulated as the promoting mode.

The reorientation of Cd 2+-vacancy and Pb 2+-vacancy complexes in KCl

The relaxation of Pb 2+-vacancy and Cd 2+-vacancy dipoles in purified KCl crystals was studied using a double crystal dc polarization method which self-corrects relaxation effects due to spurious causes. In the radius range from Cd 2+ to Ba 2+ these results and most others support Dreyfus' model. The reciprocal relaxation times for each impurity are given by τ −1 Cd =2.06x10 12 exp(−s0.64±0.01 eV) kT ; τ −1 Pb =1.19x10 13 exp(−0.69±0.01 eV) kT . It is also shown that the presence of H 2O or its products greatly perturb the relaxation times observed.

Time and consistency as measures of psychological distance.

Decision times, consistency measures, and their relationships were used to study stimulus-stimulus and subject-stimulus distance for two types of responses—single stimulus and paired comparisons, and two types of tasks—preference and judged complexity. Two assumptions based on Coombs' (1964) theory of data—that decision time is inversely related to distance and that both stimulus and ideal points have variability—led to the following predictions: (1) stimulus ordering from paired comparison judgments will be predictable from the ordering of decision times in single stimulus judgments; (2) more intransitive triads will occur in paired comparison preference judgments than paired comparison complexity judgments; and (3) complexity judgments will exhibit greater concordance than preference judgments. All three predictions were supported by data. Of three latency transformations investigated, standardized reciprocal times showed the highest correlation with difference in ranks in the paired comparison task.

DIGITAL PROCESSING OF REFRACTION DATA STUDY OF FIRST ARRIVALS*

AbstractIt has been necessary to resort to the use of “long‐line” refraction marine operations in certain areas where it proved impossible to eliminate singing from reflection records despite the number and variety of programs at our disposal for this purpose.Experience has shown that manual processing of offshore refraction records takes a disproportionate length of time in comparison with the surveys themselves, and this is incompatible with the requirements for choosing the site of an exploration well. It thus became necessary to find an “industrial approach” to the solution of this processing problem.It was apparent that automatic picking could also facilitate the interpretation of land refraction data, and that in the case of both marine and land work the interpretations would be more accurate when factors were taken into account which could not be considered when working without the aid of a digital computer.For these reasons a set of programs was developed for automatic picking and interpretation of refracted arrivals.The picking itself consists in searching for the maximum values of the normalized cross‐correlation functions of the traces with a “model” trace. The first results thus supplied are: “picked” times, intercept times, maximum values of the correlations, and the values of the tie constants between overlapping spreads.Next, the construction of the relative intercept time curves is performed; a statistical analysis of these curves then allows the determination of the offset distance.From these elements,⊙ either the delay time curve is produced, after ensuring correct reciprocal times by means of additional minor corrections.Such work is carried out in order to enable the geophysicist to gain a sound idea of the quality of the interpretation. To assist in this aim, part of the trace on both sides of the pick is plotted on the final documents. Valid groupings of several traces involving the same amount of refraction data are thus possible.⊙ or the refractor depth is constructed with the wavefront method, making use of the relative intercept times.Such a procedure, which is normally applied to first breaks, can also be used for later arrivals exhibiting slight interference and should represent an important step towards processing secondary arrivals with high interference.The development of this package, in response to a need which is shared by both SNPA and CGG, is the result of the joint efforts of the Geophysical Group of SNPA's Pau Research Center and CGG's Technical and Scientific Departments.

Thermal noise in double injection diodes operating in the insulator regime

Thermal noise calculations, based on the Langevin procedure, are given for a double injection diode operating in the insulator regime. The frequency range is restricted to frequencies smaller than the reciprocal free carrier transit times. It turns out that at high frequencies the spectral density of the ac short circuit current fluctuations can be described by Nyquist's formula. At low frequencies an additional term, proportional to (1+ω 2τ 2) −1 was found, where τ is the hole life time. The low frequency thermal noise level may be some orders of magnitude larger than the level at high frequencies. It is shown that in general the frequency dependent term will be masked by generation recombination noise. A special case is indicated where those contributions become comparable.

Relaxation Spectra and Association Constants of 1:1 Charge-Transfer Complexes

The possibility of determining the association constant of a 1:1 charge-transfer complex AB in solution from the concentration dependence of the relaxation time is discussed. If small quantities of termolecular complexes A2B and AB2 are also present there will be two additional relaxation times corresponding to the decomposition rate constants of these complexes. It is shown that if A and B are aromatic molecules whose two sides act completely independently so as to form an infinite series of sandwich complexes (model 3), then the usual relaxation techniques would detect only one relaxation time whose concentration dependence would be indistinguishable from that of a system containing only one complex, AB. If such a system were mistakenly assumed to contain only one complex AB, relaxation methods would lead to the correct value for the dissociation rate constant of AB but to an association rate constant equal to half the true value. The association constant found would thus be equal to half its true value, just as if it had been determined spectrophotometrically. The complete relaxation spectrum of model 3 and the corresponding normal reaction coordinates were calculated; the reciprocal relaxation times form three infinite series, the spacing in each series being twice the dissociation rate constant of AB. If the rate constants of reactions involving isolated molecules of A or B differ slightly from those of the corresponding reactions involving complexes of A and B, then perturbation theory shows that in principle three relaxation times, instead of one, should be observable; in practice, difficulties would arise since these relaxation times are all of similar magnitude.

Phonon-Electron Scattering inn-Type Ge at Low Temperatures

The role of phonon-electron interaction in the thermal transport properties of $n$-type Ge crystals has been investigated for different situations provided by the large variation of the donor electron concentration from 6.1\ifmmode\times\else\texttimes\fi{}${10}^{15}$ to 2.5\ifmmode\times\else\texttimes\fi{}${10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. Assuming the additivity of the reciprocal relaxation times and incorporating the electron-phonon scattering relaxation time in the expression for the combined relaxation time, Callaway's theory has been used to calculate the phonon conductivity of the different Sb- and As-doped Ge crystals in the temperature range 1-150\ifmmode^\circ\else\textdegree\fi{}K. If one takes into account the temperature dependence of the reduced Fermi potential and the density-of-states effective mass, Ziman's scattering can explain the phonon conductivity of the samples for which the donor electron concentration is higher than ${10}^{17}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ and impurity levels merge with the conduction band. The large decrease in the phonon conductivity with increasing donor electron concentration is explained in terms of the increase in the deformation potential. A plot of the deformation-potential constant against the electron concentration shows a linear relationship. Carruthers's scattering, for which phonons are scattered as a result of virtual transitions of the donor electrons between the ground state and the threefold degenerate first excited state, is found to be more appropriate for those samples for which the donor electron concentration is less than ${10}^{17}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. Values of the shear deformation potential as obtained from the phonon conductivity data are found to lie between 17.83 and 27.91 eV. Carruthers' scattering is also appropriate for the compensated samples, which confirms Fritzsche's suggestion that for materials with sufficiently high donor concentration, compensation by acceptors may bring the donor levels from the conduction band to a position in the energy gap.

Proton relaxation times in7LiCl and6LiCl solutions

Measurements of the proton spin-lattice relaxation times have been made as a function of concentration and temperature in aqueous solutions of 7LiCl and 6LiCl. The difference in the relaxation times for two isotopic solutions of the same concentration and temperature is small, corresponding to a difference n reciprocal relaxation times of 0·004 sec-1. c at 25°c, where c is the molarity of the solutions. This value decreases with increasing temperature. It is shown that the difference in relaxation times arises solely from the magnetic dipole interaction between the 7Li ion nucleus and water protons. The concept of a long-lived, rigid hydrated complex around the Li ion is shown to be inconsistent with the results.

Discrete Relaxation Times in Neutron Thermalization

On the basis of the Van Hove theory, an analysis is given of those properties of the neutron-scattering law which influence the decay constants (the reciprocal relaxation times) in neutron thermalization. It is shown how the known differences in the long-time behavior of the correlation functions for a gas, a liquid, and a solid are reflected in the different behavior of the differential cross sections at low energies. This behavior ultimately determines the general character of the spectrum of decay constants for a uniform neutron distribution in an infinite medium. For a gaseous moderator, either there is an infinite set of discrete decay constants, strongly accumulating towards the lower limit ${\ensuremath{\lambda}}^{*}=min[v\ensuremath{\Sigma}(v)]$ of the continuous spectrum, or else the spectrum below ${\ensuremath{\lambda}}^{*}$ is empty altogether. On the other hand, for a solid, the set of discrete decay constants is always finite, or possibly empty. The liquid appears to allow, in principle, all three possibilities, but normally the spectrum is expected to resemble that of a solid. In any case, the existence of the lowest decay constant ${\ensuremath{\lambda}}_{0}$ (and hence the existence of an infinite set for a gas) is trivial whenever absorption is absent or of the $\frac{1}{v}$ kind. Only an absorption rate $v{\ensuremath{\Sigma}}_{a}(v)$ which strongly increased in the small-$v$ region could cause the complete disappearance of the discrete spectrum. In this event any initial neutron distribution slowly evolves towards a singular distribution containing a $\ensuremath{\delta}(v)$ term, or some weaker singularity, and the decay rate approaches ${\ensuremath{\lambda}}^{*}$.

The transfer of vibrational energy between molecules

Ultrasonic dispersion measurements have been made in mixtures of SF 6 + CHClF 2 , extending over the whole concentration range. All mixtures showed a single dispersion zone corresponding to relaxation of the whole of the vibrational energy of both components, with approximately quadratic dependence of reciprocal relaxation time on molar concentration. A quantitative interpretation is based on the assumption that the vibrational energy of the whole system is maintained in continuous equilibrium by rapid near-resonant transfer of vibrational energy between the 344 cm -1 mode of SF 6 and the 369 cm -1 mode of CHClF 2 . The collision number for this transfer is estimated as Z AB ~ 50, which is lower than the collision numbers for homomolecular deactivation of SF 6 (Z 10 = 1005) and CHClF 2 (Z 10 = 122). This behaviour is contrasted with that of mixtures previously investigated, which showed double dispersion with linear concentration dependence of reciprocal relaxation times. A quantitative reinterpretation of these is based on the assumption of a near-resonant vibration-vibration transfer, with a rate intermediate between the homomolecular deactivation rates of the two pure components. Values of Z AB ranging from 5 to 110 are estimated for these systems. The significance of the available values of Z AB for vibration-vibration transfer is discussed, and their general pattern, in relation to the vibrational frequencies of the exchanging modes, is shown to be in accord with the quantum-mechanical theory of Schwartz, Slawsky & Herzfeld.

Line-Broadening of Cyclotron Resonance due to Lattice and Neutral Impurity Scattering in Silicon and Germanium

The relaxation times for electrons in germanium and silicon were measured from the half-width of the cyclotron resonance line at 6 mm wavelength over the temperature range from 1.6° to 20°K for the specimens of different impurity concentration. Above 3°K the reciprocal relaxation times for electrons in high purity specimens are 1/τ 0 =3.6×10 8 T 3/2 sec -1 for germanium and 1/τ 0 =2.6×10 8 T 3/2 sec -1 for silicon, respecitively. These results show that the acoustical lattice scattering is predominant in this region. For impure specimens, deviation from the T 3/2 -dependence was observed at low temperatures. This deviation is due to neutral impurity scattering. The applicability of Erginsoy's formula for neutral impurity scattering was examined. It was found that the conventional Erginsoy,s formula corrected for chemical shift agrees fairly well with the experimental results.

Sound Dispersion in Substituted Methane—Inert Gas Mixtures

Binary halomethane—noble gas mixtures were examined ultrasonically. The methanes used were CF4, CHF3, and CCl2F2 and the noble gases were Ar, Ne, and He. Results obtained show that the reciprocal relaxation times for these mixtures vary linearly with the concentration. Also, Ar—X collisions are less effective, He—X collisions are much more effective, and Ne—X collisions differ little from X—X collisions in vibrational energy transfer. X represents the dispersive gas. Theoretical values of Z10AB, the mean collision lifetime of an A molecule in an otherwise pure gas of B molecules, were calculated according to the Schwartz, Slawsky, and Herzfeld theory. Intermolecular potentials appropriate for the treatment of the data were examined, and it was found that the Lennard-Jones 6:12 potential was appropriate for the noble gases, and the 7:28 form was appropriate for the halomethanes.

Calculation of the Spectrum of Chemical Relaxation Times for a General Reaction Mechanism

AbstractA simple formalism is developed in which the determinantal equation for the reciprocal relaxation times of a reaction mechanism can be written down immediately from an inspection of the elementary chemical reactions in the mechanism. The reactions in the mechanism may be of any order; parallel reaction paths may be included. The determinantal equation can be solved for the relaxation times using the simple formalism and the expressions in terms of rate constants and equilibrium concentrations obtained at the end of the procedure. If the reactions are not thermodynamically independent then the order of the determinantal equation can be reduced directly in a simple way to that corresponding to the number of thermodynamically independent reactions. The procedure and the various approximational techniques are illustrated by a number of detailed examples.A number of general results are derived. It is pointed out that for kinetically elementary reactions, the matrix of Onsager coefficients is diagonal. The diagonal element is proportional to the exchange rate of the elementary reaction. It is shown that the transformation to normal coordinates can be done by using a product of a diagonal matrix and an orthogonal matrix. This simplifies the inversion of the transformation considerably. For systems with thermodynamically dependent reactions the explicit form of the time independent coordinates is derived. Some general relations between the elements of the transformation matrix are also derived.

Lattice Thermal Conductivity of Disordered Semiconductor Alloys at High Temperatures

The high-temperature thermal conductivity of a disordered semiconductor alloy is derived using the Klemens-Callaway theory. It is assumed that the reciprocal relaxation times depend on frequency $\ensuremath{\omega}$ as ${\ensuremath{\omega}}^{4}$ for strain and mass point defects and as ${\ensuremath{\omega}}^{2}$ for normal and umklapp three-phonon anharmonic processes. The thermal conductivity is expressed in terms of the lattice parameters and mean atomic weights of the alloy and its constituents. Agreement is obtained between theory and published experimental data on Ge-Si alloys at temperatures 300-1200\ifmmode^\circ\else\textdegree\fi{}K, and on (Ga,In)As alloys at 300\ifmmode^\circ\else\textdegree\fi{}K, using the value 2.5 for the ratio of umklapp to normal relaxation times. It is found that the large thermal resistivity of Ge-Si alloys is predominantly due to mass defect scattering, whereas that of (Ga,In)As alloys is mainly due to strain scattering.

Cholesterol and mevalonate metabolism: a time course study in vivo

SUMMARY Within 30 minutes after injecting ~~-mevalonate-2-C1~ into young rats, the total body nonsaponifiable fraction contained 47.6% of the biologically active Cz4-mevalonate. Time course data suggest that at this time utilization of tracer MVA was essentially complete. Urinary radioactivity accounted for slightly more than one-half of the dose. The metabolism of nonsaponifiable fractions of liver and gut may be related by two processes having similar but reciprocal half times. Kidney tissue was found to contain the greater part of the radioactivity previously associated with carcass nonsaDonifiable fractions. A small but consistent amount of label was found in the saponifiable fractions. The problem of cholesterol and fatty acid biosynthesis, transport, and turnover has been under investigation in this laboratory for some time (1 to 5), the larger part of these studies having been made with acetate-l-C14 as the labeling agent. The mult,iple pathways available for acetate metabolism tend to obscure the information desired on any single pathway, particularly if the time periods involved allow for recycling of the tracer. It appears well established that mevalonic acid (MVA) is a unique and a more direct precursor of squalene and cholesterol in mammalian systems (6 to 15) than is acetate. While most of these studies have been made with homogenates, we have compared acetate and mevalonate as tracers in a liver slice system (l). In the homogenate and liver slice systems, using C14-acetate and C14-mevalonate as tracers, it is possible to obtain definitive information largely on biosynthetic pathways. We have shown that the in vivo and in vitro methods are not directly comparable for studies on cholesterol metabolism (16), and that both in vivo cholesterol transport and turnover may be important facets of cholesterol metabolism (2). The present experiments were designed to utilize the more selective labeling of cholesterol by mevalonate in studies on cholesterol biosynthesis and turnover in