Hopping Molecules

Fig. 5. Surface diffusion of the rigid rodlike molecule 4-trans-2-(pyrid-4-yl-vinyl) benzoic acid on Pd(110). In (a) and (b) two consecutive STM images taken at 361 K are shown which demonstrate the 1-dim motion. Arrows indicate molecules whose position changed circles mark fractionally imaged molecules moving under the STM tip in the course of the measurement, (c) Model for the flat adsorption geometry explaining the two observed molecular orientations in the STM data. The length of the molecule is 12.5 A. (d) Arrhenius plot of single molecule hopping rates [75].

We imagine molecules hopping erratically between mobile and stationary phases. The hops represent random steps forward and backward with respect to the zone center. Equation 9.12 shows that plate height H for such a process is proportional to transfer or equilibration time teqi in agreement with our conclusions based on nonequilibrium considerations. 

Let me give you another example. What happens when a laser beam is striking a molecular surface I have found out that the laser can heat the surface at a very rapid rate of about 10 -10 degrees per second. Of course, this does not last long otherwise, we would have a thermonuclear reaction But even for a millionth of a second, the temperature jump is huge, and the molecules hop off the surface into the gas phase, often without fragmenting. Then we come in with a second laser and we ionize those molecules that absorb a particular color of that second laser. Because we now have ions, we can do time-of-flight mass spectrometry. Laser-desorption/laser-ionization mass spectrometry is an invention of ours, and many other people have worked on this technique too. 

Within this general scheme, there is much flexibility in the kind of stationary and mobile phases that may be used, but the basic principles of separation remain the same. Consider a molecule dissolved in the mobile phase flowing over the stationary phase. If the solvent (mobile phase) is moving at a velocity Vs, then the solute molecule will be carried along at the same speed. If, however, the solute molecule partitions into, or binds to, the stationary phase, then for the fraction of the time it spends in the stationary phase - it will remain stationary. Consequently, as the molecule hops back and forth between the two phases, its rate of flow will be reduced depending on how much time it spends in the stationary phase. 

The mechanisms of diffusion in these two systems (gas and liquid) are different and unrelated diffusion in gases is the result of the collision process, whereas that in liquids is an activated process (Bird et al., 1960). Diffusion in microp-orous materials is neither gaseous nor liquid diffusion. The closest case for such diffusion is surface diffusion, where molecules hop within the surface force field (see review by Kapoor et al., 1989b). Pick s law is used for both application (in modeling of adsorption processes) and experimental measurement of diffusion. Extensive reviews are available on diffusion in microporous materials and zeolites (Karger and Ruthven, 1992 Do, 1998). A lucid discussion on the nonlinear, and in some cases peculiar, phenomena in zeolite diffusion was given... 

Theories from two extremely different points of view have been proposed to determine the relation between 0,9 and velocity U. They differ in the way the friction is calculated. In hydrodynamic theories, the dissipation is assumed to take place very close to the TCL mainly through viscous forces on the other hand, in the molecular model proposed by Blake the dissipation is mostly associated with molecules hopping at the molecular edge of the contact line. 

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