Surface elastic constants measurement

R286 D. G. Cory, R. Laflamme, E. Knill, L. Viola, T. F. Havel, N, Boulant, G. Boutis, E. Fortunato, S. Lloyd, R. Martinez, C. Negrevergne, M. Pravia, Y. Sharf, G. Teklemariam, Y. S. Weinstein and W. H. Zurek, NMR Based Quantum Information Processing Achievements and Prospects , Forschr. Phys., 2000, 48, 875 R287 G. P. Crawford, Measurement of Surface Elastic Constants , EMIS Datarev. Ser., 2000,25, 230... 

The effect of surface elastic constants on the nematic director configurations is of basic interest for the elastic theory of liquid crystals and plays a critical role in those device applications where the nematic is confined to a curved geometry. The saddle-splay surface elastic constant, K24, and the splay-bend surface elastic constant, K13, defied measurement for more than sixty years, since the pioneering work of Oseen, who made the first steps toward the elastic theory of liquid crystals. 

Measurements of the saddle-splay surface elastic constant, K24, and the splay-bend surface elastic constant, K13, were first introduced by Oseen [1] in 1933 from a phenomenological viewpoint, and later by Nehring and Saupe [2] from a molecular standpoint. These constants tend to be neglected in conventional elastic continuum treatments for fixed boundary conditions because they do not ent the Euler-Lagrange equation for bulk equilibrium. Experimental determination of tiie two surface elastic constants is undoubtedly a difficult task, since their effects are hard to discriminate from those of ordinary sur ce anchoring [3]. 

By measuring V z), which includes examining the reflectance function of solid material, measuring the phase velocity and attenuation of leaky surface acoustic waves at the liquid-specimen boundary, the SAM can be used indetermining the elastic constants of the material. 

Fig. 5 Dependency of the measured shell spring constant on speed the speed of the AFM probe deforming the surface is varied over 3 orders of magnitude which results, within the accuracy of the measurement, in no change of the elastic constants...

The chosen technique was X-ray diffraction that is widely used for non-destructive surface measurement of applied and residual stresses. Stress analysis relies on the determination of the lattice strain using the interplanar spacing as a gauge by measuring the peak shifts in a fixed O-direction for different /-tilt of the sample [3]. Stresses are calculated from measured strains using diffraction elastic constants which were calculated theoretically. As the Co phase takes up a certain amount of W and transforms after cooling into a solid solution with a variable W content, the measurements were limited to the WC phase. 

The simplest method of measuring the three elastic constants of a nematic liquid crystal is by studying the deformations due to an external magnetic field (Freedericksz and Tsvetkov, Zocher ). The geometry has to be so chosen that the orienting effect of the field conflicts with the orientations imposed by the surfaces with which the liquid crystal is in contact. To develop a static theory of such deformations we apply the equation of... 

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