Related to Relaxation

Two avenues were explored to find the relationship between LC20 dephosphorylation and smooth muscle relaxation correlation and kinetic analysis. 

In canine tracheal muscles contracted with 1 jjlM methacholine, at 37°C, and relaxed with 0.4 jjlM atro-pin or 40 pM forskolin, myosin phosphorylation and force decayed simultaneously (de Lanerolle, 1988). In rabbit tracheal smooth muscle stimulated with carbachol, at 37°C, LC20 dephosphorylation occurred at about the same rate as the decline in stress 

The experiments on intact muscles, unlike those on skinned fibers, agree with the concept that relaxation of contracted smooth muscle is associated with LC20 dephosphorylation (Stull et al., 1991 Hartshorne and Kawamura, 1992 Somlyo and Somlyo, 1994). 

In kinetic analysis, the rate constants of both the dephosphorylation and relaxation were determined in several cases in bovine tracheal muscle after 15 s of electrical stimulation, at 37°C, LC20 was dephosphory-lated with an apparent first-order rate constant (fc) of 

26 s i, whereas k for relaxation was 0.13 s i (Kamm and Stull, 1985a) in histamine-treated rhythmically contracting porcine carotid arteries, at 37°C, the k values were 0.17 and 0.02 s i, respectively (Driska et ah, 

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If we denote as s the relative error of a particular relaxation rate estimate (or, for that matter, of any quantity related to relaxation-rates), the above discussion can be summed up by the following formula... 

Quantitative measurements in NMR are based on the area of the signals present in the spectrum. Signal areas can be produced as numerical values proportional to the area or, on less modern instruments, from the integration plots that are superimposed on the spectrum (Fig. 9.1). For the proton, the precision obtained in area measurements does not exceed l % even if continuous wave instruments are used at slow scanning speeds. In l3C NMR, it is preferable to add a relaxation reagent in order to avoid saturation related to relaxation times that alter the intensity of the signal. Using the molar ratios that are easily accessible from the spectrum, it is possible to deduce concentrations. 

The parameters a and are not necessarily real, and bl can even be negative. The properties of continued fractions in relation to relaxation operators are described in Chapter III. 

Again, only few results are related to relaxation of metal nuclei in clusters. T values have been reported only for Co [21,28] and range between 1 ms and 50 ps. Linewidths, directly related to the spin-spin relaxation, are sometimes given for quadrupolar nuclei Co [29-31], Cu [32], Mo [33,34]. Relaxation times have been used for structural determination [21] or for the investigation of the dynamic behaviour of clusters [28] no special use of the linewidth is reported, however. 

Another problem related to relaxation in solids is the following. Thus, one thing is the disappearance of the magnetization (M) in the x-y plane (the... 

A noteworthy finding has been that all the materials show two distinct relaxation dynamics, a fast and a slow relaxation [60]. The fast mode corresponds to relaxation of bulky polymer molecules, while the slow mode is related to relaxation of the filler structure with much longer time scales. As silica particles are physically connected with adsorbed polymer molecules, the formed polymer-particle network is a temporary physical network. On a long time scale, relaxation of this network occurs when immobilized polymer molecules connecting silica particles become free, via dissociation from silica particles or disentanglement from other immobilized polymer molecules. 

Hunt, A., An explanation for the Kauzmann paradox and its relation to relaxation-times, J. Non-Cryst Solids, 175, 129-136 (1994). 

Dlnbek, G., Kilbnrn, D., Bondarenko, V., Pionteck, J., Kranse-Rehberg, R., and Alam, M. A., Characterization of free volume in amorphons materials by PALS in relation to relaxation phenomena, in 24th Arbeitskreistagung Nichtkristalline Structuren of DGK, Jena, Germany, Sept. 2003. 

These characteristie features originate from the interaction between the electron spin and the nuclear spins and with other surrounding electron spins. It is well known that paramagnetie relaxation kinetics of radical species is closely related to relaxation phenomena of polymers. The electron spin echo (ESE) method can for example directly observe the relaxation behavior of electron spins. 

Abstract Measurements of temperature dependent ESR spectra of spin labels trapped in the polymer matrices is very effective for the evaluation of molecular mobility (molecular motion) of polymer chains. We can characterize the molecular motion of the particular sites in different region by the ESR method. It is possible to detect the mobility of polymer material at the segment or atomic level. ESR studies help to relate the features of the nanometer scale to macroscopic properties of the polymer materials. We present examples of spin labeling studies in the polymer science to help readers new to the field understand how and for what areas the method is effective. In the first part, we give a simple review of the spin labeling method and present applications in the polymer physics related to relaxation phenomena in various systems. In the second part applications to biopolymer system are introduced to help the clarification of various mechanisms of bio-membranes. 

There are other physical measurements which reflect molecular mobility and can be related to relaxation times and friction coefficients similar to those which characterize the rates of viscoelastic relaxations. Although such phenomena are outside the scope of this book, they are mentioned here because in some cases their dependence on temperature and other variables can be described by reduced variables and, by means of equation 49 or modifications of it, free volume parameters can be deduced which are closely related to those obtained from viscoelastic data. These include measurements of dispersion of the dielectric constant, nuclear magnetic resonance relaxation, diffusion of small molecules through polymers, and diffusion-controlled aspects of crystallization and polymerization. 

Polyvinyl fluoride has a number of transitions below the melting temperature, the values of which depend on the measurement techniques. The lower glass transition occurs at -15 to -20°C and is believed to relate to relaxation free from restraint by crystallites. The upper glass transition ranges from 40 to 50°C, apparently due to amorphous regions under restraint by crystalhtes.1 1 Yet another transition occurs at -80°C because of short-chain amorphous relaxation and another at 150°C associated with premelting intracrystalline relaxation. 

There is an ongoing attempt to find a proper function that fits the viscoelastic property data and to calculate the strength of mechanical relaxation and parameters related to relaxation and its distribution. The method used to describe linear viscoelastic behavior by these mathematical models is described in detail in the monograph by Tschoegel [179]. There is an example of the analysis of viscoelastic behavior data obtained using this method where the sol-gel transition of a gellan aqueous solution was the subject [180]. 

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