Relaxation process correlation

Relaxation Process Correlation by Glass Transition Temperature... 

Werbelow L G 1996 Relaxation processes cross correlation and interference terms Encyclopedia of Nuclear Magnetic Resonance ed D M Grant and R K Harris (Chichester Wiley) pp 4072-8... 

Parvalbumin (Fig 1) is a cytosolic protein expressed in fast-twitch skeletal muscles and in the nervous system. In muscles, parvalbumin controls the relaxation process. In the CNS, parvalbumin, expressed in a subpopulation of GABAergic neurons, is correlated with their firing rates, protecting the cells from Ca2+ overload. 

Macromolecular fluctuations are characterized by correlation times which are closely related to the underlined relaxation processes. Such relaxation times can be evaluated by classical trajectory simulations using... 

Because non-adiabatic collisions induce transitions between rotational levels, these levels do not participate in the relaxation process independently as in (1.11), but are correlated with each other. The degree of correlation is determined by the kernel of Eq. (1.3). A one-parameter model for such a kernel adopted in Eq. (1.6) meets the requirement formulated in (1.2). Mathematically it is suitable to solve integral equation (1.2) in a general way. The form of the kernel in Eq. (1.6) was first proposed by Keilson and Storer to describe the relaxation of the translational velocity [10]. Later it was employed in a number of other problems [24, 25], including the one under discussion [26, 27]. 

Luminescence lifetime spectroscopy. In addition to the nanosecond lifetime measurements that are now rather routine, lifetime measurements on a femtosecond time scale are being attained with the intensity correlation method (124), which is an indirect technique for investigating the dynamics of excited states in the time frame of the laser pulse itself. The sample is excited with two laser pulse trains of equal amplitude and frequencies nl and n2 and the time-integrated luminescence at the difference frequency (nl - n2 ) is measured as a function of the relative pulse delay. Hochstrasser (125) has measured inertial motions of rotating molecules in condensed phases on time scales shorter than the collision time, allowing insight into relaxation processes following molecular collisions. 

In addition to the dipole-dipole relaxation processes, which depend on the strength and frequency of the fluctuating magnetic fields around the nuclei, there are other factors that affect nOe (a) the intrinsic nature of the nuclei I and S, (b) the internuclear distance (r,s) between them, and (c) the rate of tumbling of the relevant segment of the molecule in which the nuclei 1 and S are present (i.e., the effective molecular correlation time, Tf). 

In order for relaxation to occur through Wj, the magnetic field fluctuations need to correspond to the Larmor precession frequency of the nuclei, while relaxation via requires field fluctuations at double the Larmor frequency. To produce such field fluctuations, the tumbling rate should be the reciprocal of the molecular correlation time, i.e., f), so most efficient relaxation occurs only when voT, approaches 1. In very small, rapidly tumbling molecules, such as methanol, the concentration of the fluctuating magnetic fields spectral density) at the Larmor frequency is very low, so the relaxation processes Wj and do not occur efficiently and the nuclei of such molecules can accordingly relax very slowly. Such molecules have... 

For the simulation a correlation time 1 =0.1 ns is assumed for two protons at cOo=600MHz. (B) Maximum transfer efficiency for an isolated proton spin pair calculated using only dipolar relaxation processes. Note the sign change for the NOE cross-relaxation at cOo Uc=l -12. 

The effectiveness of a crude oil demulsifier is correlated with the lowering of the shear viscosity and the dynamic tension gradient of the oil-water interface. The interfacial tension relaxation occurs faster with an effective demulsifier [1714]. Short relaxation times imply that interfacial tension gradients at slow film thinning are suppressed. Electron spin resonance experiments with labeled demulsifiers indicate that the demulsifiers form reverse micellelike clusters in the bulk oil [1275]. The slow unclustering of the demulsifier at the interface appears to be the rate-determining step in the tension relaxation process. 

Investigation of water motion in AOT reverse micelles determining the solvent correlation function, C i), was first reported by Sarkar et al. [29]. They obtained time-resolved fluorescence measurements of C480 in an AOT reverse micellar solution with time resolution of > 50 ps and observed solvent relaxation rates with time constants ranging from 1.7 to 12 ns. They also attributed these dynamical changes to relaxation processes of water molecules in various environments of the water pool. In a similar study investigating the deuterium isotope effect on solvent motion in AOT reverse micelles. Das et al. [37] reported that the solvation dynamics of D2O is 1.5 times slower than H2O motion. 

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... 

The double commutator [[g, Tr /) (/], Tlp q may form new operators different from Q, and some of these new operators may not even be physical observables. When the double commutator conserves the operator Q, one speaks of the auto-correlation mechanism. Otherwise, one speaks of the cross-relaxation process. In other words, cross-relaxation is independent of the nature of the relaxation mechanism, but involves the interconversion between different operators. To facilitate such a possibility, it is desirable to write the density operator in terms of a complete set of orthogonal basis... 

Classical studies of the relaxation processes, caused by translational diffusion, have been presented in the early days by Abragam (18), Torrey (136) and Pfeifer (137). Abragam (18) found, by solving the diffusion equation, the following form of the correlation function for the stochastic function Z>o under translational diffusion of two spins 1/2 ... 

For a spin-1/2 nucleus, such as carbon-13, the relaxation is often dominated by the dipole-dipole interaction with directly bonded proton(s). As mentioned in the theory section, the longitudinal relaxation in such a system deviates in general from the simple description based on Bloch equations. The complication - the transfer of magnetization from one spin to another - is usually referred to as cross-relaxation. The cross-relaxation process is conveniently described within the framework of the extended Solomon equations. If cross-correlation effects can be neglected or suitably eliminated, the longitudinal dipole-dipole relaxation of two coupled spins, such... 

A surprising aspect of SD is how rapidly C i) in highly polar solvents decays relative to other relaxation processes such as reorientation of solvent dipoles. This very rapid time scale cannot be ascribed to dynamical solvent-solvent correlations, which, as illustrated in Fig. 6, are modest even for the longest ranged A . Thus the key to imderstanding the reasons for the rapid decay of C i) is in examining how solvent-solvent correlations contribute to it and to what extent their contributions can be accounted for in terms of static correlations measured by ((5A ) ), Eq. (32). The initial cmvature of C(t), which characterizes its short-time Gaussian-like behavior is often characterized in terms of the solvation frequency co o/v... 

NMR spectroscopy provides spin-lattice (ri) and spin-spin (Tj) relaxation times. Making appropriate assumptions with regard to the magnetic interactions responsible for the relaxation process, these relaxation times can be related to molecular motions. Since nuclear spin relaxation results from all processes which cause a fluctuation in the magnetic field at the nucleus, the correlation function will generally correspond to more than one kind of motion involving all possible interactions. The equations for the relaxation times are generally of the form... 

The previous discussion shows that the relaxation processes emerge from the quantum dynamics under appropriate circumstances leading to the formation of time-dependent quasiclassical parts in the observable quantities. Let us add that quasiclassical and semiclassical methods have been recently applied to the optical response of quantum systems in several works [65, 66] where the relation to the Liouville formulation of quantum mechanics has been discussed, without however pointing out the existence of Liouvillian resonances as we discussed here above. The connection between the property of chaos and n-time correlation functions or the nth-order response of a system in multiple-pulse experiments has also been discussed [67, 68]. 

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