Slow motion

As the motion of the spin label is slowed, the lines gradually broaden. When the correlation time is 3 x 10 s the spectrum suddenly changes from a motionally narrowed to a slow-motion one. The spectrum then remains essentially the same except that the distance between the low and high field extrema increases with increasing correlation time until the rigid limit is reached. 

The most rigorous method of determining in this regibn is by computer simulation [IS, 16]. The variable input parameters of correlation time and line width are varied until a good match between the computed and the observed spectra is obtained. Anisotropic rotation and various rotational diffusion models can be accommodated by this method. In many cases, however, simpler methods based on analysis of the outer extrema, either their inward shift from the rigid limit or their line width, are adequate. Such methods have been extensively reviewed elsewhere [1,15,17,18]. 

It is important for all of these methods to choose an appropriate diffusion model for the system. It has been shown that the ratio of the shifts of the high and low field extrema (AHJAHj) with change in Aff, is sensitive to the mode of reorientation of the nitroxide, and so can be used in the choice of diffusion model [19]. 

For correlation times longer than 10 s, the technique of saturation transfer (ST) ESR spectroscopy must be used [20]. In this technique, either the first harmonic of the dispersion or the second harmonic of the absorption signal, as opposed to the usud first derivative ESR espectrum, is obsoved. The shapes of these spectra are sensitive to changes in the correlation time in the ran 10 10 s. As for the slow-motion spectra, correlation times are calculated by 

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In the example of pressure-volume work in die previous section, the adiabatic reversible process consisted simply of the sufficiently slow motion of an adiabatic wall as a result of an infinitesimal pressure difference. The work done on the system during an infinitesimal reversible change in volume is then -pdVand one can write equation (A2.1.11) in the fomi... 

For very fast reactions, as they are accessible to investigation by pico- and femtosecond laser spectroscopy, the separation of time scales into slow motion along the reaction path and fast relaxation of other degrees of freedom in most cases is no longer possible and it is necessary to consider dynamical models, which are not the topic of this section. But often the temperature, solvent or pressure dependence of reaction rate... 

Bruno G and Freed J 1974 ESR llneshapes and saturation In the slow motional region ELDOR Chem. Phys. Lett, pp 328-32... 

QCMD describes a coupling of the fast motions of a quantum particle to the slow motions of a classical particle. In order to classify the types of coupled motion we eventually have to deal with, we first analyze the case of an extremely heavy classical particle, i.e., the limit M —> oo or, better, m/M 0. In this adiabatic limit , the classical motion is so slow in comparison with the quantal motion that it cannot induce an excitation of the quantum system. That means, that the populations 6k t) = of the... 

The range of aeeuraey of this separation ean be understood by eonsidering the differenees in time seales that relate to eleetronie motions and nuelear motions under ordinary eireumstanees. In most atoms and moleeules, the eleetrons orbit the nuelei at speeds mueh in exeess of even the fastest nuelear motions (the vibrations). As a result, the eleetrons ean adjust quiekly to the slow motions of the nuelei. This means it should be possible to develop a model in whieh the eleetrons follow smoothly as the nuelei vibrate and rotate. 

When the friction coefficient is set to zero, HyperChem performs regular molecular dynamics, and one should use a time step that is appropriate for a molecular dynamics run. With larger values of the friction coefficient, larger time steps can be used. This is because the solution to the Langevin equation in effect separates the motions of the atoms into two time scales the short-time (fast) motions, like bond stretches, which are approximated, and longtime (slow) motions, such as torsional motions, which are accurately evaluated. As one increases the friction coefficient, the short-time motions become more approximate, and thus it is less important to have a small timestep. 

Theatrical Pyrotechnics or Special Effects. Many spectacular visual and audible effects are produced for stage presentations of both music and drama, and many motion pictures and television shows incorporate pyrotechnic and explosive special effects to Hven up the presentation. These spectacular effects are a combination of pyrotechnics, explosives, combustion, and electronics. After the effects are filmed or videotaped, they are often enhanced by slow-motion replay and by the addition of more exciting noise. A real explosion is over in milliseconds, and hence there is a need for electronic enhancement to create a more spectacular effect on the screen. 

The widths of the narrow Lorentzians representing slow motions in the plane and perpendicular to the plane of the bilayer are compared in Ligures 11a and 11b, respectively. Lor the in-plane motion, the MD values for Q = 0.5 A agree well with the experimental results, but the increase with Q is significantly overestimated in the simulation compared to the experimental values. This suggests that the slower component of the in-plane motion in the simulation is too fast at short distances. On the other hand, the MD line widths for the slower component of the out-of-plane motion agree well with the experimental results at 30% hydration. As in the case of the LISL, the simulation predicts a slight anisotropy not seen in the experimental data. 

Fein-arbeit, /. fine or delicate work (Metal.) refining, -aufspaltung, /. fine separation, -bau, m. fine structure, -bewegung, /. (Micros., etc.) slow motion, fine adjustment, feinblasig, a. having minute bubbles or blisters. Fein-blech, n. (Metal.) thin plate, sheet. 

Fig. 32 shows a stepwise separation of broad zones of thiamine mono- and diphosphate on a CS-KU-2 cellosorbent. The dynamic criteria (A and A.) predict the zones limited by sharp boundaries with a complete yield of the components at pH 4.9 for thiamine diphosphate and at pH 6.5 for thiamine monophosphate. It is noteworthy that the criterion A predetermines the slow motion ot the thiamine... 

We have thus the following representation of the phenomenon (Fig. 6-10) on the arc AB the motion is slow at the point B the representative point ceases to follow the curve F(x) and its horizontal velocity becomes very large, bringing it to the point C at which a slow motion begins on the arc CD, followed by another jump DC, and so on. 

The dramatic slowing down of molecular motions is seen explicitly in a vast area of different probes of liquid local structures. Slow motion is evident in viscosity, dielectric relaxation, frequency-dependent ionic conductance, and in the speed of crystallization itself. In all cases, the temperature dependence of the generic relaxation time obeys to a reasonable, but not perfect, approximation the empirical Vogel-Fulcher law ... 

The operational variants in tongue movement so far detected, are a simple extension/retraction and oscillations — occurring singly or as multiple bouts Fig. 7.3(a) the latter type can be divided into those with slow motion and those of normal duration (Toubeau, 1994). 

There is a second relaxation process, called spin-spin (or transverse) relaxation, at a rate controlled by the spin-spin relaxation time T2. It governs the evolution of the xy magnetisation toward its equilibrium value, which is zero. In the fluid state with fast motion and extreme narrowing 7) and T2 are equal in the solid state with slow motion and full line broadening T2 becomes much shorter than 7). The so-called 180° pulse which inverts the spin population present immediately prior to the pulse is important for the accurate determination of T and the true T2 value. The spin-spin relaxation time calculated from the experimental line widths is called T2 the ideal NMR line shape is Lorentzian and its FWHH is controlled by T2. Unlike chemical shifts and spin-spin coupling constants, relaxation times are not directly related to molecular structure, but depend on molecular mobility. 

TABLE 1 The suppressed temperature Ts at which 13C NMR peak intensities are most suppressed in the presence of slow motions (°C)... 

B.R. Patyal, R.H. Crepeau, D. Gamliel and J.H. Freed, Two-dimensional Fourier transform ESR in the slow-motional and rigid limits SECSY-ESR, Chem. Phys. Lett., 1990, 175, 445. 

The direction of slow motion can be found from normal-mode diagonalization. However, such a procedure would require, for a system of N particles, cal-... 

The slurry was pasted on a copper foil at slow motion (<2.54 cm/s) using an automatic draw down coater available from Paul N. Gardner Co. of Pompano Beach, FL, USA) and the electrode was dried for a day under vacuum at 120°C. After this drying step, the density of the coating was adjusted to 1.45-1.55 g/cc through calendaring operation. 

Goldman, S.A., Bruno, G.V., and Freed, J.H. 1972. Estimating slow-motional rotational correlation times for nitroxides by electron spin resonance. The Journal of Physical Chemistry 76 1858-1860. 

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