Elastic constants magnitude

Leadbetter AJ, Norris EK (1979) Molec Phys 38 669. There are different contributions which give rise to a broadening a of the molecular centre of mass distribution function f(z). The most important are the long-wave layer displacement thermal fluctuations and the individual motions of molecules having a random diffusive nature. The layer displacement amplitude depends on the magnitude of the elastic constants of smectics ... 

The thermal conductivity plateau has traditionally been considered by most workers as a separate issue from the TLS. In addition to the rapidly growing magnitude of phonon scattering at the plateau, an excess of density of states is observed in the form of the so-called bump in the heat capacity temperature dependence divided by T. The plateau is interesting from several perspectives. For one thing, it is nonuniversal if scaled by the elastic constants (say, co/)... 

However, if there are large variations in the elastic constants with pressure, this can seriously affect Pent by as much as an order of magnitude (Lam et al. 1984). 

For a nematic LC, the preferred orientation is one in which the director is parallel everywhere. Other orientations have a free-energy distribution that depends on the elastic constants, K /. The orientational elastic constants K, K22 and K33 determine respectively splay, twist and bend deformations. Values of elastic constants in LCs are around 10 N so that free-energy difference between different orientations is of the order of 5 x 10 J m the same order of magnitude as surface energy. A thin layer of LC sandwiched between two aligned surfaces therefore adopts an orientation determined by the surfaces. This fact forms the basis of most electrooptical effects in LCs. Display devices based on LCs are discussed in Chapter 7. 

The high viscosity of the PMMA damps out orientational contributions so that the yqeo that is measured is thought to be =60-90% electronic. This has been ascertained by measuring the electric field induced second harmonic generation (EFISH) below the Tg of the polymer. From this can be obtained the microscopic elastic constant, which can in turn be used to estimate the magnitude of the two orientational contributions to yQEO- Details are provided else where (13,16). 

Nevertheless, some conclusions may be drawn from the set of results presented here. First, with the notable exception of InN, the group III nitrides form a family of hard and incompressible materials. Their elastic moduli and bulk modulus are of the same order of magnitude as those of diamond. In diamond, the elastic constants are [49] Cu = 1076 GPa, Cn = 125 GPa and Cm = 577 GPa, and therefore, B = (Cn + 2Ci2)/3 = 442 GPa. In order to make the comparison with the wurtzite structured compounds, we will use the average compressional modulus as Cp = (Cu + C33)/2 and the average shear modulus as Cs = (Cu + Ci3)/2. The result of this comparison is shown in TABLE 8. 

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...

Therefore, switch-off times are independent of the field strength and directly dependent on material parameters, such as viscosity coefficients and elastic constants, and the cell configuration. Therefore, they are often three or four orders of magnitude larger than the switch-on times. However, sophisticated addressing techniques can produce much shorter combined response times ( on + off The nematic director should be inclined, e.g. 1° pretilt,... 

The application of an electric field above the threshold value results in a reorientation of the nematic liquid crystal mixture, if the nematic phase is of negative dielectric anisotropy. The optically active dopant then applies a torque to the nematic phase and causes a helical structure to be formed in the plane of the display. The guest dye molecules are also reoriented and, therefore, the display appears coloured in the activated pixels. Thus, a positive contrast display is produced of coloured information against a white background. The threshold voltage is dependent upon the elastic constants, the magnitude of the dielectric anisotropy, and the ratio of the cell gap to the chiral nematic pitch ... 

In piezoelectric media, the strain energy is multiplied by the factor (1 + due to piezoelectric stiffening of the elastic constants. Thus, the strain energy includes electrical stored energy in this case. To calculate the magnitude of the electrical energy density Ue independent of the strain energy, the relation... 

In this expression r is some combination of elastic constants ( 1q11 erg/cm ), b the magnitude of the Burger s vector of the dislocation, a the nearest neighbor distance in the crystal and... 

Vdues of the magnetic anisotropy are measured independently by n ans of the magnetic balance (58—60) and those of 22 are calculated (Table 3). The magnitude of ki2 is by far lower than elastic constants considered in defotmaticMis d ordinary solids. 

For small-molecule thermotropic smectic-A phases, typical values of two elastic constants are K 10 dyn and B 10 dyn/cm (Ostwald and Allain 1985). For lyotropic smectics, such as those made from surfactants in oil or water solvents, the layer compression modulus B can be much lower (see Chapter 12). From B and K, a length scale A. = ( 1 /B) 1 nm is defined it is called the permeation depth and its magnitude... 

High accuracy requires that systematic errors be minimized. These errors are chiefly of two kinds, those of a geometrical nature and those involved in the elastic-constant portion of the stress constant. The systematic errors cause an error in the measured stress which is proportional to the magnitude of the stress. 

Porosity is known to decrease the elastic moduli of ceramic materials (8-9). To estimate the magnitude of this effect for the current elastic constant measurements, we have used theories for the elastic modulus decrement due to spherical pores by Mackenzie (10) and Ledbetter and Datta (1 ) to calculate the "zero-porosity"... 

The dependence of the elastic modulus on protein concentration has been used to establish the framework of fractal geometry. Bremer et al. (1990) indicated that a cluster of protein molecules would possess a fractal nature if the power-law dependence exists between the amount of floes in the cluster and the radius of the cluster. In addition, the magnitude of this power, signified as the fractal dimension, D, would be below 3. The elastic constant of protein aggregates could be described as a function of the aggregate volume fraction ... 

For an external field pardlel to tlK helicoidal axis, the cholesteric pitch varies depending on the relative magnitudes of 22 and 33 (the bending elastic constant ) 53). 

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