Relaxation time Subject

Variation of the relaxation times subject to x = 1 /T is shown in Fig. 6.3. It is really monotonic, and after the Q-branch collapse it can be describe by a very simple formula... 

Other properties of association colloids that have been studied include calorimetric measurements of the heat of micelle formation (about 6 kcal/mol for a nonionic species, see Ref. 188) and the effect of high pressure (which decreases the aggregation number [189], but may raise the CMC [190]). Fast relaxation methods (rapid flow mixing, pressure-jump, temperature-jump) tend to reveal two relaxation times t and f2, the interpretation of which has been subject to much disagreement—see Ref. 191. A fast process of fi - 1 msec may represent the rate of addition to or dissociation from a micelle of individual monomer units, and a slow process of ti < 100 msec may represent the rate of total dissociation of a micelle (192 see also Refs. 193-195). 

Dielectric Behavior of Adsorbed Water. Determination of the dielectric absorption of adsorbed water can yield conclusions similar to those from proton NMR studies and there is a considerable, although older literature on the subject. Figure XVI-7 illustrates how the dielectric constant for adsorbed water varies with the frequency used as well as with the degree of surface coverage. A characteristic relaxation time r can be estimated... 

The calculated results are demonstrated in Figs. 7a and 7b [25, 33). The system maintained at T—1.85 is subject to down quenching with a temperature step AT = 0.05 and isothermal aging is followed at each temperature to equilibrate the system. After reaching the equilibrium at T =1.5, the operation is reversed up to T =1.85. In Fig. 7a, one sees that the resultant relaxation time is shortened with decreasing temperature and... 

On the other hand, NMR spectra appear in general as the average of the spectra of the two spin states [36, 153]. This observation determines an upper limit for the spin-state lifetime shorter than the nuclear spin relaxation time Tl = l/ktH < lO s. In general, therefore, either the superposition or the average of the particular spectroscopic properties of the two spin states is observed, subject to the relative magnitude of lifetime of the excited spectroscopic state and the rate of spin-state conversion. The rate /clh is thus estimated... 

These nuclei (and they form by far the majority of the NMR-active nuclei ) are subject to relaxation mechanisms which involve interactions with the quadrupole moment. The relaxation times Tj and T2 (T2 is a second relaxation variable called the spin-spin relaxation time) of such nuclei are very short, so that very broad NMR lines are normally observed. The relaxation times, and the linewidths, depend on the symmetry of the electronic environment. If the charge distribution is spherically symmetrical the lines are sharp, but if it is ellipsoidal they are broad. 

It is emphasized that revealing the dynamics as well as the structure (or conformation) based on several types of spin-relaxation times is undoubtedly a unique and indispensable means, only available from NMR techniques at ambient temperature of physiological significance. Usually, the structure data themselves are available also from X-ray diffraction studies in a more refined manner. Indeed, better structural data can be obtained at lower temperature by preventing the unnecessary molecular fluctuations, which are major subjects in this chapter, since structural data can be seriously deteriorated for domains where dynamics are predominant even in the 2D or 3D crystalline state or proteoliposome at ambient temperature. It should be also taken into account that the solubilization of membrane proteins in detergents is an alternative means to study structure in solution NMR. However, it is not always able faithfully to mimick the biomembrane environment, because the interface structure is not always the same between the bilayer and detergent system. This typically occurs in the case of PLC-81(1-140) described in Section 4.2.4 and other types of peptide systems. 

An HM-HEC monolayer at the air/aqueous interface was formed by adsorption from an aqueous solution of the polymer placed in the Langmuir trough overnight. In "stress-jump" experiments, HM-HEC monolayers were placed under rapid compression to a large degree and surface pressure was measured as a function of time after compression was stopped. (The compressional "jumps" required a minute or two to complete, and in some cases were on the order of the polymer monolayer relaxation times. See later section for discussion). In hysteresis experiments, the adsorbed monolayers were subjected to continuous compression-expansion cycles at a specific speed, while surface pressure was determined as a function of surface area. 

First, consider the solvent. The characterization of the solute-solvent coupling by a relaxation time is based on analogy to Brownian motion, and the relaxation time is called the frictional relaxational time Xp. It is the relaxation time for momentum decay of a Brownian motion in the solute coordinate of interest when it interacts with the solvent under consideration. If we call the subject solute coordinate s, then the component of frictional force along this coordinate may be written as... 

Fig. 1. Top Scheme of an inversion recovery experiment 5rielding the longitudinal relaxation time (inversion is achieved by mean of the (re) radiofrequency (rf) pulse, schematized by a filled vertical rectangle). Free induction decays (fid represented by a damped sine function) resulting from the (x/2) read pulse are subjected to a Fourier transform and lead to a series of spectra corresponding to the different t values (evolution period). Spectra are generally displayed with a shift between two consecutive values of t. The analysis of the amplitude evaluation of each peak from — Mq to Mq provides an accurate evaluation of T. Bottom the example concerns carbon-13 Tl of irans-crotonaldehyde with the following values (from left to right) 20.5 s, 19.8 s, 23.3 s, and 19.3 s.

Fig. 8. Evolution of the longitudinal and transverse relaxation times (Ti and T2, respectively) as a function of (for a fixed measurement frequency Vo = 400 MHz) assuming that the considered spin is subjected to random fields whose correlation function is proportional to being the correlation time. Notice the continuous...

The second role of the chemical exchange phenomena can be seen in Eq. (2) the exchange lifetime competes with the in-complex nuclear spin-lattice relaxation time and can become a limiting factor in the attainable PRE. This aspect of the problem is highly relevant in practical consideration in the case of Gd(III) complexes as a potential contrast agent, because the water exchange in these systems is not too fast. This issue is considered to be outside of the scope of this article and we refer to recent literature on the subject 5,160) and to other contributions in this volume. 

Any NMR field-cycling (FC) relaxometry experiment presumes that the sample is subject to a magnetic field of various intensities for time intervals of varying durations. More specifically, between the various intervals of a relaxation-time measurement, the external magnetic field induction... 

As an example of potential clinical application of the proposed theoretical model, preliminary results of a phase I clinical trial are described below. We estimated the values of relaxation time and ratio Max/Max in adolescents with different results of endoscopy. We found that the mean relaxation time was significantly longer in subjects with a severe gastric and duodenal inflammation, namely, with ulcers and erosions compared to a healthy control group (p<0.05). The exhaled air of patients with milder forms of the disease and of the control group caused faster sensor relaxation after their interaction (Table 7.1). 

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