Rotational kinetics and relaxation time

Experimental data on nitrogen obtained from spin-lattice relaxation time (Ti) in [71] also show that tj is monotonically reduced with condensation. Furthermore, when a gas turns into a liquid or when a liquid changes to the solid state, no breaks occur (Fig. 1.17). The change in density within the temperature interval under analysis is also shown in Fig. 1.17 for comparison. It cannot be ruled out that condensation of the medium results in increase in rotational relaxation rate primarily due to decrease in free volume. In the rigid sphere model used in [72] for nitrogen, this phenomenon is taken into account by introducing the factor g(ri) into the angular momentum relaxation rate 

This expression was shown to be valid for hard sphere systems of arbitrary density. Moreover, the free-path distribution scaled by A = (uto) is nearly density-independent and almost the same as in the limit of zero density [74]. 

Of course, the effect of excluded volume is opposite and greatly exceeds that shown in Fig. 1.10, which is produced by uncorrelated collective interaction. Unfortunately, neither of them results in sign-alternating behaviour of angular or translational momentum correlation functions. This does not have a simple explanation either in gas-like or solid-like models of liquids. As is clearly seen from MD calculations, even in 

The hypothesis proposed in [76] implies that collective effects change the collisional event statistics in a hard sphere liquid. The collisional distribution tp(t) dt is assumed to deviate from the famous Poissonian law i/ (t) = exp (—t/To)/r0 corresponding to the flow of events being uniform in time. The distribution 

If the molecule moves without hindrance in a rigid-walled enclosure (the free enclosure ), as assumed in free volume theories, then rattling back and forth is a free vibration, which could be considered as coherent in such a cell. The transfer time between opposite sides of the cell t0 is roughly the inverse frequency of the vibration. The maximum in the free-path distribution was found theoretically in many cells of different shape [74]. In model distribution (1.121) it appears at a 2 and shifts to t0 at a - oo (Fig. 1.18). At y — 1 coherent vibration in a cell turns into translational velocity oscillation as well as a molecular libration (Fig. 1.19). 

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However, the NMR properties of solid-phase methane are very complex, due to subtle effects associated with the permutation symmetry of the nuclear spin set and molecular rotational tunnelling.55 Nuclear spin states ltotai = 0 (irred. repr. E), 1 (T) and 2 (A) are observed. The situation is made more complicated since, as the solids are cooled and the individual molecules go from rotation to oscillation, several crystal phases become available, and slow transitions between them take place. Much work has been done in the last century on this problem, including use of deuterated versions of methane for example see Refs. 56-59. Much detail has emerged from NMR lineshape analysis and relaxation time measurements, and kinetic studies. For example, the second moment of the 13C resonance is found to be caused by intermolecular proton-carbon spin-spin interaction.60 Thus proton inequivalence within the methane molecules is created. 

Within physical chemistry, the long-lasting interest in IR spectroscopy lies in structural and dynamical characterization. Fligh resolution vibration-rotation spectroscopy in the gas phase reveals bond lengths, bond angles, molecular symmetry and force constants. Time-resolved IR spectroscopy characterizes reaction kinetics, vibrational lifetimes and relaxation processes. 

The nmr data for this type of motion are direct and the motion clearly involves rotation about bonds in the millisecond time scale range. However. less direct evidence for motion comes from other techniques such as fluorescence depolarization, 02 diffusion, hydrogen exchange kinetics, and nmr relaxation times (see Ref. 4). The extent of this motion is not yet easy to define, but this evidence points to motion in the nanosecond time scale range. It is tempting to see the motion in this time scale as bond oscillations rather than rotations. To put it in a different way, on this time scale the side chains have some freedom to move with respect to each other but not normally to undergo substantial bond rotation. Table IV summarizes some references for motion of different types. Additionally, nmr relaxation studies suggest that the backbone or main chain of a protein is more restricted than that of the side chains. 

In several previous papers, the possible existence of thermal anomalies was suggested on the basis of such properties as the density of water, specific heat, viscosity, dielectric constant, transverse proton spin relaxation time, index of refraction, infrared absorption, and others. Furthermore, based on other published data, we have suggested the existence of kinks in the properties of many aqueous solutions of both electrolytes and nonelectrolytes. Thus, solubility anomalies have been demonstrated repeatedly as have anomalies in such diverse properties as partial molal volumes of the alkali halides, in specific optical rotation for a number of reducing sugars, and in some kinetic data. Anomalies have also been demonstrated in a surface and interfacial properties of aqueous systems ranging from the surface tension of pure water to interfacial tensions (such as between n-hexane or n-decane and water) and in the surface tension and surface potentials of aqueous solutions. Further, anomalies have been observed in solid-water interface properties, such as the zeta potential and other interfacial parameters. 

The departure of the Perrin equation from linearity may be considered more generally. A curvature convex to the T/rj axis may result from the complete kinetic dissociation of rigid units or from increased rotational freedom within the polypeptide chain 26, 32, 65, 66, 68). A curvature concave to the T/rj axis may occur whenever more than one rotational relaxation time is present and may be detected when the two rotational relaxation times differ by more than fivefold 65). The initial slope, for small values of T/tj, depends upon the harmonic mean of the relaxation times involved and is determined practically by the shorter one. Such curvature has been reported in studies with DNS-labeled polyvinylamine and poly-p-amino-styrene 22, 33, 64). By applying a theory which deals with the case of an emitting group which has only one degree of rotational freedom, Gottlieb and Wahl 33) concluded that the rotations activated by temperature in... 

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