Relaxation time experimentally defined

The relaxation time constant defined by Eqn. 47 and the steady-state distribution of charges q(V, oo)/0nuK (which is equal to a/( + )) represent two expressions for a and in terms of measurable experimental quantities. Therefore it is possible to evaluate the rate constants at any given potential V. The results showed that the rate constants are exponential functions of and that the energy differences governing the rate constants are. to a first approximation, linearly dependent on the membrane potential. 

It is important to realize that the relaxation times might depend on some factors that are properties of the atom or molecule itself and on others that are related to its environment. Thus rotational spectra of gases have linewidths (related to the rotational relaxation times) that depend on the mean times between coUisions for the molecules, which in turn depend on the gas pressure. In liquids, the collision lifetimes are much shorter, and so rotational energy is effectively non-quantized. On the other hand, if the probability of collisions is reduced, as in a molecular beam, we can increase the relaxation time, reduce linewidths, and so improve resolution. Of course, the relaxation time only defines a minimum width of spectral lines, which may be broadened by other experimental factors. 

The possibility of experimental investigation is, of course, restricted to systems with particular ligand partition, where the number of isomers is not too big. The aim of such investigations is to obtain information about the relative probabilities of the five mechanisms which have been defined, till now, on symmetry grounds only. We think that a comparison of the experimental spectra of relaxation times with the various possible theoretical ones (see Table 3) should furnish answers to that question, provided the assumptions of the model are a good description of the physical system. 

In studies of superparamagnetic relaxation the blocking temperature is defined as the temperature at which the relaxation time equals the time scale of the experimental technique. Thus, the blocking temperature is not uniquely defined, but depends on the experimental technique that is used for the study of superparamagnetic relaxation. In Mossbauer spectroscopy studies of samples with a broad distribution of relaxation times, the average blocking temperature is commonly defined as the temperature where half of the spectral area is in a sextet and half of it is in a singlet or a doublet form. 

Although the idea of generating 2D correlation spectra was introduced several decades ago in the field of NMR [1008], extension to other areas of spectroscopy has been slow. This is essentially on account of the time-scale. Characteristic times associated with typical molecular vibrations probed by IR are of the order of picoseconds, which is many orders of magnitude shorter than the relaxation times in NMR. Consequently, the standard approach used successfully in 2D NMR, i.e. multiple-pulse excitations of a system, followed by detection and subsequent double Fourier transformation of a series of free-induction decay signals [1009], is not readily applicable to conventional IR experiments. A very different experimental approach is therefore required. The approach for generation of 2D IR spectra defined by two independent wavenumbers is based on the detection of various relaxation processes, which are much slower than vibrational relaxations but are closely associated with molecular-scale phenomena. These slower relaxation processes can be studied with a conventional... 

Time resolution of the enthalpy changes is often possible and depends on a number of experimental parameters, such as the characteristics of the transducer (oscillation frequency and relaxation time) and the acoustic transit time of the system, za, which can be defined by ra = r0/ua where r0 is the radius of the irradiated sample, and va is the speed of sound in the liquid. The observed voltage response of the transducer, V (t) is given by the convolution of the time-dependent heat source, H (t) and the instrument response function,... 

Where p defines the shape of the hole energy spectrum. The relaxation time x in Equation 3 is treated as a function of temperature, nonequilibrium glassy state (5), crosslink density and applied stresses instead of as an experimental constant in the Kohlrausch-Williams-Watts function. The macroscopic (global) relaxation time x is related to that of the local state (A) by x = x = i a which results in (11)... 

We can get a first approximation of the physical nature of a material from its response time. For a Maxwell element, the relaxation time is the time required for the stress in a stress-strain experiment to decay to 1/e or 0.37 of its initial value. A material with a low relaxation time flows easily so it shows relatively rapid stress decay. Thus, whether a viscoelastic material behaves as a solid or fluid is indicated by its response time and the experimental timescale or observation time. This observation was first made by Marcus Reiner who defined the ratio of the material response time to the experimental timescale as the Deborah Number, Dn-Presumably the name was derived by Reiner from the Biblical quote in Judges 5, Song of Deborah, where it says The mountains flowed before the Lord. ... 

Powell et al. give an excellent review of several approaches to interpret the frequency dependence of Tle and T2e in these systems [71]. One convenient approach is that developed by Hudson and Lewis [72], who showed that the eigenvalues of the relaxation matrix R as defined in Bloch-Wangsness-Red-field (BWR) theory [73] are functions of rv and the experimental frequency co, and are related to the relaxation time T2ei of the i-th allowed electron spin transition by the expression ... 

This analysis is, however, a little bit partial. We would like to notice that a model like that of the system of Eq. (1.7) can also be interpreted as a model of classical activation. The relaxation time defined by Eq. (5.5) would then be interpreted as a sort of activation time, that is, the time required for a starting point condition extremely favorable for the escape from a well. An experimenter aiming at activating a chemical reaction process would be greatly disappointed if the activation time were infinite ... 

This approach for the development of multiple-pulse sequences is only practical if a large number of sequences can be assessed in a short period of time. The final assessment of the quality of a multiple-pulse sequence must always be based on experiments. However, for the optimization of multiple-pulse sequences, experimental approaches are, in general, too slow and too expensive (instrument time ). An attractive alternative to experiments at the spectrometer is formed by numerical simulations, that is, experiments in the computer. In simulations it is also possible to take relaxation and experimental imperfections such as phase errors or rf inhomogeneity into account. In addition to the direct translation of a laboratory experiment into a computer experiment, it is possible to numerically assess the properties of a multiple-pulse sequence on several abstract levels, for example, based on the created effective Hamiltonian. If simple necessary conditions can be defined for a multiple-pulse sequence with the... 

Ice samples have a main dispersion induced by reorientation of the water molecules and proton conduction with movement of the point defects. Here, we discuss values of the relaxation time r of the main dispersion of ice samples reported in the literature and measured by the present authors. For convenience in experimental measurements, we define two classification of ice sample as bulk ice and ice particle aggregates corresponding to two types of growth, liquid phase growth and vapor phase growth. 

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