Relaxation dependence

Both spin-lattice and spin-spin relaxation depend on rates of molecular motion, for relaxation results from the interaction of fluctuating magnetic fields set up by nuclei in the spin system and in the lattice. A quantitative theory of this dependence was given by Bloembergen et al., who obtained... 

The charge consumed by oxidation swelling under diffusion control, once the structure is relaxed, depends on the anodic potentials applied at each moment. The process can be quantified by Fick s law ... 

While the rate of change of dipolar interaction depends on t its magnitude depends only on the internuclear distance and is independent of t,. Thus the dipole-dipole relaxation depends on the molecular correlation time T the internuclear distance r, and the gyromagnetic ratios of the two nuclei, y and js -... 

Often the electronic spin states are not stationary with respect to the Mossbauer time scale but fluctuate and show transitions due to coupling to the vibrational states of the chemical environment (the lattice vibrations or phonons). The rate l/Tj of this spin-lattice relaxation depends among other variables on temperature and energy splitting (see also Appendix H). Alternatively, spin transitions can be caused by spin-spin interactions with rates 1/T2 that depend on the distance between the paramagnetic centers. In densely packed solids of inorganic compounds or concentrated solutions, the spin-spin relaxation may dominate the total spin relaxation 1/r = l/Ti + 1/+2 [104]. Whenever the relaxation time is comparable to the nuclear Larmor frequency S)A/h) or the rate of the nuclear decay ( 10 s ), the stationary solutions above do not apply and a dynamic model has to be invoked... 

Aime et al. took advantage of the different redox states of manganese and of the difference in the related relaxation properties to design a p02 responsive contrast agent. The adducts formed between Mn /Mnn tpps complexes and poly-P-cyclodex-trin have considerably different relaxivities depending on the redox state of the metal, itself determined by the partial oxygen pressure of the solution (tpps — 5,10,15,20-tetrakis-(p-sulfonato-phenyl porphinate) (243). 

Membrane depolarization typically results from an increase in Na+ conductance. In addition, mobilization of intracellular Ca2+ from the endoplasmic or sarcoplasmic reticulum and the influx of extracellular Ca2+ appear to be elicited by ACh acting on muscarinic receptors (see Ch. 22). The resulting increase in intracellular free Ca2+ is involved in activation of contractile, metabolic and secretory events. Stimulation of muscarinic receptors has been linked to changes in cyclic nucleotide concentrations. Reductions in cAMP concentrations and increases in cGMP concentrations are typical responses (see Ch. 21). These cyclic nucleotides may facilitate contraction or relaxation, depending on the particular tissue. Inhibitory responses also are associated with membrane hyperpolarization, and this is a consequence of an increased K+ conductance. Increases in K+ conductance may be mediated by a direct receptor linkage to a K+ channel or by increases in intracellular Ca2+, which in turn activate K+ channels. Mechanisms by which muscarinic receptors couple to multiple cellular responses are considered later. 

Due to the fact that cross-correlated relaxation depends linearly on the correlation time, it can be used to determine the conformation of ligands when bound to target molecules, provided that the off rate is fast enough to enable detection of the cross-correlated relaxation rate via the free ligand [33, 34]. The conditions under which such an experiment can be performed are similar to those found for transferred NOEs [35], and, for Kd values... 

It is important to note that the rate of solvent relaxation depends on the solvent viscosity. If the time required for the reorganization of solvent molecules around... 

Both, longitudinal and transverse relaxation of protons in tissue depend on the microstructure and on the chemical composition of several microscopic compartments. Relaxation properties are not necessarily constant for the diiferent compartments inside the cells (cytosol and cavities in cell organella) and in the extracellular space (interstitium and vessels). However, water exchange processes between the compartments are often fast enough to generate one effective relaxation time, which can be assessed by monoexponential fitting of the relaxation dependent data. 

The static ZFS, which is present in low-symmetry complexes, affects mainly the energy level fine structure. It is described by axial and rhombic components, D and E. Its effects on nuclear relaxation depend on two angles, 9 and cj), defining the position of the nucleus with respect to the ZFS principal tensor axes. Figure 23 shows the dispersion profiles for different values of S, D, E and 9. Many such examples are reported in Chapter 2. 

A first example is represented by the Mn(III)/Mn(II) redox switch. The complexes of Mn(II) and Mn(III) with the water-soluble tetraphenylsulpho-nate porphyrin (TPPS, Chart 13) display significantly different ri values at low magnetic field strength (lower than 1 MHz), but very similar values at the fields currently used in the clinical practice (> 10 MHz) (141). However, the longer electronic relaxation rates of the Mn(II) complex makes its relaxivity dependent on the rotational mobility of the chelate. In fact, upon interacting with a poly-p-cyclodextrin, a 4-fold enhancement of the relaxivity of [Mn(H)-TPPS(H20)2] at 20 MHz has been detected, whereas little effect has been observed for the Mn(III)-complex. The ability of the Mn(II)/Mn(III)... 

A route for designing Gd(HI) complexes whose relaxivity depends on the presence of lactate, is provided by the ability shown by some hexa- or hepta-coordinate chelates to form ternary complexes with a wide array of anionic species (154-161). The interaction between the coordinatively unsatured metal complex and lactate involves the displacement of two water molecules coordinated to Gd(III) ion with the two donor atoms of the substrate, thus leading to a marked decrease in the relaxivity. Lactate is a good ligand for Gd(IH) ion because it can form a stable 5-membered ring by using the hydroxo and carboxylic oxygen donor atoms (Fig. 19). 

The purpose of this section is to review the parameters influencing the proton relaxation of a nanomagnet suspension. It will include an analysis of NMRD profiles, which provide the relaxivity dependence with the external held, expressed in proton Larmor frequency units. 

The maximum of relaxivity is proportional to the squared saturation magnetization of the crystal. The low field relaxivity depends on the anisotropy, and the presence of a low field dispersion indicates a low anisotropy energy. 

Carbon-13 relaxation depends predominantly on intramolecular contributions, whereas proton relaxation is sensitive to inter-molecular as well as intramolecular interactions. However, by use of isotope dilution— the two types of interactions may be separated. Studies utilizing both nuclei can thus yield complimentary information. 

In Chapter 12 the layered perovskite, La2Ni04 (65917), was used as an example of a structure which displays lattice-induced strain. This compound is typical of the large class of perovskite-related structures. All show some degree of lattice-induced strain and, because the mechanism of relaxation depends on the details... 

No explicit temperature dependence is included in the equations for R m and Rim, except for cases where Curie spin relaxation is the dominant term (Section 3.6). In the latter case, Curie paramagnetism has a T x dependence and therefore relaxation depends on T 2. The effect of temperature on linewidths determined by Curie relaxation is dramatic also because of the xr dependence on temperature, as shown in Eq. (3.8). All the correlation times modulating the electron-nucleus coupling, either contact or dipolar, are generally temperature dependent, although in different ways, and their variation will therefore be reflected in the values of Rim and Rim-... 

D spectra are in principle possible for heteronuclei coupled by either dipolar or scalar interactions. However, the magnetic moments of heteronuclei are sizably smaller than that of the proton, and since cross relaxation depends on the square of the magnetic moment it appears that this is a serious limitation for the observation of NOESY or ROESY cross peaks. However, as already discussed, in scalar-coupled systems the relevant coherences build up with sin(nJ/jt). Since Jjj in directly bound 13C- H and l5N- H moieties is of the order of 102 Hz, as opposed to about 10 Hz between proton pairs, it is conceivable that scalar correlation experiments are successful. Heterocorrelated spectra have the advantage of allowing one to detect signals of protons attached to carbons or nitrogens when they are within a crowded envelope. 

Wang, L., Fritton, S.P., et al. (1999) Fluid pressure relaxation depends upon osteonal microstructure modeling of an oscillatory bending experiment. Journal of Biomechanics 32 663-672... 

The water-promoted hydrolyses of a bicyclic amide, l-azabicyclo[2.2.2]octan-2-one (87), and a planar analogue, l,4-dimethylpiperidin-2-one (88), were studied using density functional theory in conjunction with a continuum dielectric method to introduce bulk solvent effects. The aim of these studies was to reveal how the twisting of the C-N bond affects the neutral hydrolysis of amides. The results predict important rate accelerations of the neutral hydrolysis of amides when the C-N bond is highly twisted, the corresponding barrier relaxation depending on the specific reaction pathway and transition state involved.85... 

Watanabe (1999, p. 1354) has deducted that, according to experimental data for polystyrene/polystyrene blends, when the matrix is a weakly entangled system, terminal time of relaxation depends on the lengths of macromolecules as... 

More precisely, the magnetic relaxation depends on the variable of gelation, i.e., the density of crosslinks, and is closely related to the modulus of elasticity, E, on the one hand and to the swelling ratio, Qm, on the other hand. Long polybutadiene chains are currently randomly crosslinked, using sulfur they can serve to illustrate the NMR approach to the characterisation of vulcanised polymers. It has been shown that the... 

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