Microscopic boundary layer effects

Recently, Hynes et al. [221, 222] have pointed out that continuum models of rotational relaxation become unreliable when the molecule of interest rotates in a solvent comprising molecules of similar size. To improve on the model, they considered a sphere to be surrounded by a first co-ordination shell of solvent molecules. All these were taken as rough spheres, that is hard spheres which reverse their relative velocity (normal and tangential components) on impulsive collision. Of specific interest are CCI4 and SF. The test sphere and its boundary layer is surrounded by a hydrodynamic continuum. To model this, Hynes et al. used linearised hydrodynamic equations for the solvent with a modified boundary condition between solvent and test molecule, which relates the rotational stress on the test sphere to the angular velocity of the sphere. A coefficient of proportionality, 3, is introduced as a slip coefficient (j3 0 

Very close correspondence was found between this diffusion coefficient and that from the molecular dynamics calculations of O Dell and Berne [234], 

Liquids with low viscosity or large 3 (high density or efficient momentum transfer across the boundary layer) have a rotational diffusion coefficient close to that of the Debye equation [220], eqn. (110). For viscous liquids, the rotational diffusion coefficient tends to saturate to a viscosity-independent value. Tanabe [235] has found perdeuterobenzene rotational diffusion to be well described by the Hynes et al. theory [221, 222]. 

Finally, it may be noted that the rotational relaxation time, r ot of eqn. (108) is reduced by (1 + 3tj/)3) times when considering the rotational relaxation of spheres. When test molecules of shapes far from spherical are considered, liquid is displaced by rotation (paddle wheel effect) and the Debye or Perrin theory should be a better approximation. 

---

J. T. Hynes, R. Kapral, and M. Weinberg, /. Chem. Phys., 67, 3256 (1977). Microscopic Boundary Layer Effects and Rough Sphere Rotation. 

Although the non-slip boundary condition has been remarkably successful in reproducing the characteristics of liquid flow on the macroscopic scale, its application for a description of Hquid dynamics in microscopic liquid layers is questionable. A number of experimental [45-52] and theoretical [53,54] studies suggest the possibility of slippage at soUd-Hquid interfaces. Recent reviews [55-57] summarize the results of these works. Here we focus on the effect of slippage on the QCM response. 

This reformulation in terms of diffusive propagation and microscopic dynamics in the boundary layer is reminiscent of Noyes s encounter formulation that we briefly described earlier. Now each diffusive encounter is interrupted by sequences of collisions and very short excursions into the fluid. The analysis of nonhydrodynamic effects on the rate kernel can, therefore, be discussed naturally in terms of the encounter formalism. 

As a final point, we note that typical surfaces are usually not crystalline but instead are covered by amorphous layers. These layers are much rougher at the atomic scale than the model crystalline surfaces that one would typically use for computational convenience or for fundamental research. The additional roughness at the microscopic level from disorder increases the friction between surfaces considerably, even when they are separated by a boundary lubricant.15 Flowever, no systematic studies have been performed to explore the effect of roughness on boundary-lubricated systems, and only a few attempts have been made to investigate dissipation mechanisms in the amorphous layers under sliding conditions from an atomistic point of view. 

Surface diffusion can be studied with a wide variety of methods using both macroscopic and microscopic techniques of great diversity.98 Basically three methods can be used. One measures the time dependence of the concentration profile of diffusing atoms, one the time correlation of the concentration fluctuations, or the fluctuations of the number of diffusion atoms within a specified area, and one the mean square displacement, or the second moment, of a diffusing atom. When macroscopic techniques are used to study surface diffusion, diffusion parameters are usually derived from the rate of change of the shape of a sharply structured microscopic object, or from the rate of advancement of a sharply defined boundary of an adsorption layer, produced either by using a shadowed deposition method or by fast pulsed-laser thermal desorption of an area covered with an adsorbed species. The derived diffusion parameters really describe the overall effect of many different atomic steps, such as the formation of adatoms from kink sites, ledge sites... 

Looking at a crystal layer with a microscope shows that it consists of crystals which are separated by grain boundaries (Fig. 8.2-14). Along these grain boundaries and also within the crystals, mother liquor can be included. Therefore, further decrease of the cleaning effect is obtained in real crystal layers compared to the thermodynamically possible. Wintermantel (1986) was able to show that this influence of the morphology of the crystals can be correlated to the dimensionless parameter... 

---