Determination of relaxation times

Direct determination of relaxation time through viscoelastic studies (all mechanical properties involve this important parameter). 

Knowing and p (or k), the relaxation time (r) can be estimated. The determination of relaxation time allows the rate of charge dissipation to be calculated for any process obeying Ohm s law. 

T, 0.1 MPa) condition to be calculated, t is then known for any P and T corresponding to an ambient pressure value of TV. This method is quite powerful because it allows determination of relaxation times for any thermodynamic condition T, P, or V) provided only that the same value of T had been measured at ambient pressure. 

Both find their origin in the spin-echo sequence, devised hy Hahn in 1952 and used for the determination of relaxation times. 

Evaluation and Determination of Relaxation Times and Rate Constants in Single-Step Systems 70 Pressure-Jump (p-Jump) Relaxation 71 Historical Perspective 71 Pressure-Jump Apparatus 72... 

Evaluation and Determination of Relaxation Times and Rate Constants in Single-Step Systems... 

While the methods mentioned allow determination of relaxation times of all 29Si signals in one experiment, it is sometimes useful to employ selective versions of the experiments, e.g., to differentiate possible relaxation mechanisms358,359. 

Determination of relaxation time and correlation time of carbon atoms by means of NMR spectroscopy. 

Signals with different multiplicities Multiplet pattern Determination of Relaxation time... 

K. A. Christensen, D. M. Grant, E. M. Schulman, and C. Walling, Optimal determination of relaxation times of Fourier transform nuclear magnetic resonance. Determination of spin-lattice relaxation times in chemically polarized species, J. Phys. Chem. 78, 1971-1977 (1974). 

Fig. 6. (A) A 270 MHz 180°-t-90° inversion recovery determination of relaxation times in an endo-exo isomeric mixture of (T -allyl)Fe(CO)3l. The value of rfor each trace is the delay (seconds) between the 180° and 90° pulse. The doublets with the greater spacing at 2.33 and 3.788 are assigned to the anti protons of the exo and endo isomers, respectively. Those at 3.69 and 4.158 are assigned to the syn resonances. The central proton resonances are at lower field. These traces demonstrate that the relaxation times for the syn and anti protons in both isomers are equal.

E. Special pulse methods in FTNMR (Determination of relaxation times, solvent peak suppression etc.)... 

Kinetic applications of relaxation phenomena result from their time dependent nature. From measurements of line widths, line shapes, and direct determinations of relaxation times, many fast chemical reactions (/j < ca. 1 s) can be studied (sect. 4.22). Slower processes (t > ca. 60 s)... 

Din2] Coherence effects on ENDOR line shapes, determination of relaxation times T, T, ) This value is in better agreement with calculated C splitting than 0.550 which is possible too. ) Determination of the components of the axially symmetric g-tensor. 

The invention of the surface coil and the development of NMR probes containing life-support systems have made it possible to observe high-energy phosphates in intact tissues and whole organisms. P NMR has been used for the safe, noninvasive detection of disease states in tissues without risk to the patient. Metabolic products soluble in the cytoplasm of skeletal muscle, heart, kidney, brain, and eye have all been qualitatively observed and identified. With the appropriate use of standards, determination of relaxation times, and performance of the necessary instrument calibrations, quantitative results can be comparable to those obtained in wet-chemical assays. The protonation/deprotonation equilibrium of phosphates influences the P chemical shift, facilitating the noninvasive determination of tissue pFi. 

Table 16.3 Step-by-step instructions on the determination of relaxation time using DSC Method 1 (82)...

The first two quantities allow determination of relaxation times of corresponding objects in the model (bonds and chains) and the last two allow determination of diffusion constants. Chain length dependencies of the self-diffusion constant and of the relaxation times of bonds and chains are presented in Fig. 3. These results show that the dynamic behavior of... 

Although this modulation method permits qualitative measurements of x effects, especially determination of relaxation times, quantitative evaluation of is not possible, due to the infinite number of modulation harmonics with iU-defined relative amplitudes caused by the trapezoidal modulation form provided by a chopper blade [106]. 

The crosslinked network formed during photolysis of polymers can not be identified by usual methods, such as FTIR or molecular weight measurements. nuclear magnetic resonance ( C NMR) is a useful technique for detecting new types of carbon atoms formed in the crosslinking. Some studies with NMR are based on the determination of relaxation times spin-lattice... 

Overall, these two techniques permit the determination of relaxation times in the range 0.5 ts to 0.3 ns. They have been used extensively at the early stage of kinetic studies of micellar solutions for the study of the exchange process of surfactants with a relatively short alkyl chain and, more recently, for the study of novel surfactants, including gemini (dimeric) surfactants. They have also been used for the study of phase transition in vesicle systems. 

Many other data processing techniques are used to extract useful information from experimental NMR spectra. Signal intensities compiled by peak picking may be fitted to an exponential or Gaussian function, as in the determination of relaxation times and... 

There are several different methods for determining the elastic properties of flexible homopolymers. One simple method is the determination of relaxation time. As presented in Chapters 3 and 4, the relaxation time(s) appearing in constitutive equations represents the elastic nature of polymers. Simply put, the larger the relaxation time(s) of a polymer, the greater is its fluid elasticity. It is then not difficult to surmise that the relaxation time(s) of a polymer would depend on temperature and perhaps on the extent of applied shear rate. However, the continuum theory presented in Chapter 3 does not reveal how the relaxation time(s) might vary with temperature, whereas the molecular theory presented in Chapter 4 does. 

Finally, we will only mention the ultrasonic absorption relaxation method which is, in fact, several different experimental techniques that permit the determination of relaxation times in the range 10 to 5 X 10 sec. Several of the dissociation field effect results in Table II have been confirmed by this method, and much new data on ligand substitution of alkali metal complexes have also been acquired by ultrasonic techniques (Eigen, 1963). Eigen and Tamm (1962) have thoroughly reviewed the role these techniques have played in revealing the mechanism of fast consecutive substitution reactions in metal complexes. 

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