Translational motion conclusions

In this chapter we describe the various stages of the factorisation process. Following the separation of translational motion by reference of the particles coordinates to the molecular centre of mass, we separate off the rotational motion by referring coordinates to an axis system which rotates with the molecule (the so-called molecule-fixed axis system). Finally, we separate off the electronic motion to the best of our ability by invoking the Born-Oppenheimer approximation when the electronic wave function is obtained on the assumption that the nuclei are at a fixed separation R. Some empirical discussion of the involvement of electron spin, in either Hund s case (a) or (b), is also included. In conclusion we consider how the effects of external electric or magnetic fields are modified by the various transformations. 

Simulations of C NMR lineshapes have shown that experimental spectra that appear to result from a superposition of two different lines (cf. Fig. 15) can be explained by the above-mentioned molecular jump model. Analogous conclusions were drawn from macroscopic sorption kinetic data (82). From the experimental C NMR lineshapes, a mean residence time tj of 20 and 150 p-s for a concentration of six molecules per u.c. at 250 and 200 K, respectively, was derived. Provided that these jumps detected in C NMR spectroscopy are accompanied by a translational motion of the molecules, it is possible to derive self-diffusivities D from the mean residence times. Assuming the diffusion path of a migrating molecule as a sum of individual activated jumps, for isotropic systems the relation (P) = 6Dtj is valid, where (P) denotes the mean square jump length. Following experimental and theoretical studies on the preferential sorption sites of benzene molecules in the MFI framework (83-90), in our estimate the mean distance between adjacent sorption sites is assumed to be 1 nm. 

The conclusion to be drawn from all of these calculations is that the translational motion of the nitrogen molecule can be described classically. The energy of the molecule is essentially continuous,... 

The continuous nature of the emission is associated with the variable quantities of energy that are taken up by the translational motion of the molecules of stannic and stannous chloride which move off in opposite directions. Such a conclusion is obviously verifiable by the use of crossed molecular beam techniques (see Section 3). 

This expression shows that the difference decreases as the length L of the box increases and that it becomes zero when the walls are infinitely far apart (Fig. 9.19). Atoms and molecules free to move in laboratory-sized vessels may therefore be treated as though their translational energy is not quantized, because L is so large. The expression also shows that the separation decreases as the mass of the particle increases. Particles of macroscopic mass (like balls and planets and even minute specks of dust) behave as though their translational motion is unquantized. Both these conclusions are true in general ... 

It is easy to realize that this spectator model can account for the observation that very little of the reaction exoergicity is released as translational energy of the products. The Cl atom approaches the HI molecule with a particular momentum and captures the H. But the H atom is so light that the momentum of the 1 atom is left nearly unchanged, and so too is that of the Cl atom, which is part of the HCl product. But if energy is to be conserved without altering the translational motion, it follows that the exoergicity of the reaction mnst be deposited in the internal motion of the HCl. The quantitative version of our conclusion is the subject of Problem B. Here we proceed to look for additional experimental evidence that can lend support to the model. 

In conclusion, it is useful to note that the structure of the formulas of the kinematics and dynamics of rotational motion relative to a fixed axis have the same structure as formulas of translation motion. One has only to substitute all translational characteristics with rotational ones. This analogy can be seen in Table 1.1. 

Classical trajectory studies of the association reactions M+ + H20 and M+ + D20 with M = Li, Na, K (Hase et al. 1992 Hase and Feng 1981 Swamy and Hase 1982,1984), Li+(H20) + H20 (Swamy and Hase 1984), Li+ + (CH3)20 (Swamy and Hase 1984 Vande Linde and Hase 1988), and Cl- + CH3C1 (Vande Linde and Hase 1990a,b) are particularly relevant to cluster dynamics. In these studies, the occurrence of multiple inner turning points in the time dependence of the association radial coordinate was taken as the criterion for complex formation. A critical issue (Herbst 1982) is whether the collisions transfer enough energy from translation to internal motions to result in association. Comparison of association probabilities from various studies leads to the conclusion that softer and/or floppier ions and molecules that have low frequency vibrations typically recombine the most efficiently. Thus, it has been found that Li+ + (CH3)20 association is more likely than Li+ + H20 association, and similarly H20 association with Li(H20)+ is more likely than with the bare cation Li+. The authors found a nonmonotonic dependence of association probability on the assumed HaO bend frequency and also a dependence on the impact parameter, the rotational temperature, and the orientation of the H20 dipole during the collision. 

Extensive investigations on the effects of ultrasound at various frequencies on the 7j of H, i3C, and l4N in a variety of liquids and liquid mixtures have been conducted by Homer and Patel [12,16] only the main conclusions of this work will be outlined. While changes to 7j were observed when ultrasound in the MHz region was used, no effect was observed using low frequency ultrasound at 20 kHz. The changes in 7j were observed only for liquid mixtures. This suggests that ultrasound causes relative motion of different molecular species, and that it modifies the translational contribution to the relaxation process. 

However, measurement of water mobility in multicomponent, multi-domained systems is not so simple. In food systems, water may be associated with different domains that control its local molecular motions. Within a specific timeframe, water molecules may migrate between two domains (of two different local mobilities). If the migration rate is slow (due to kinetic barriers) with respect to the experimental observable time frame, then the system experimental data would report multiple components in terms of water mobility. If another system has a reduced kinetic barrier, translational exchange between domains is rapid within the timeframe of the experiment. In this case, the data obtained would only report seemingly one water population (with one average mobility) leading to a misleading conclusion. Because most dynamic experiments are limited by the instrumental timeframe, it is important to select the appropriate instrument for the... 

The introductory discussion on thermal analysis begins with a brief outline of the history of the understanding of heat and temperature. Heat is obviously a macroscopic quantity. One can feel its effect directly with one s senses. The microscopic origin of heat, the origin on a molecular scale, rests with the motion of the molecules of matter discussed in Sect. 2.3. The translation, rotation, internal rotation, and vibration of molecules are the cause of heat. Temperature, in turn, is more difficult to comprehend. It is the intensive parameter of heat. Before we can arrive at this conclusion, several aspects of heat and temperature must be considered. A short description based on experiments is given in Sects. 2.1.5 and 2.1.4 and more details are found in Sects. 4.2 and 4.1. 

Uniaxially oriented n-CsjH, Tm = 71.8) has been studied at temperatures of 66 C and 67 "C (c-phase) where some line-broadening occurs. The motion observed is composed of rotational and translational components. A comparison of the spectra with theoretical scattering laws predicted by different models leads to the conclusion that translational jumps in the chain direction, jump distance 1.27 A, and rotational 180 jumps take place independently the frequency of the former is Vt = (2.6 0.4)x 10 s and of the latter F, = (5 2) x 10 s . These studies have been extended to include the D-phase . ... 

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