Elastic constants molecular structure dependence

The switching time r of a TN cell depends mostly on the rotational viscosity which can be influenced by molecular design, and on the elastic splay constant Kp, the correlation of with molecular structure remains quite elusive. 

Interpretation of mechanical measurements in terms of molecular structure was until fairly recently confined essentially to identification of the temperatures of the major viscoelastic relaxations through extensional or torsional dynamic mechanical studies. Now, however, investigations of the elastic constants and their temperature dependence—allied with dynamic mechanical, creep and both wide and small angle X-ray diffraction— are yielding fairly detailed pictures of the interrelation of the crystalline and less well ordered regions of some oriented solid polymers. 

Temperature dependence of the optical threshold voltage Vth is a dominant factor in the figure of merit (M), It is worth analyzing the relations between AV, or and LC material properties, or molecular structures. Concerning physical constants, viz, dielectric anisotropy and elastic constant, both of which govern the threshold voltage of LC, we made some investigation of temperature dependence of V h for each LC in relation to that of ECH ... 

The behavior of weakly twisted structures depends on the relative values of the elastic constants in (5.3) and (5.4). As we shall see in the next section, splay and bend distortions are often relaxed by twist. It is therefore important to know the elastic constants for different types of deformations these constants are specified by molecular structures and interactions. 

Elasticity is a macroscopic property of matter defined as the ratio of an applied static stress (force per unit area) to the strain or deformation produced in the material the dynamic response of a material to stress is determined by its viscosity. In this section we give a simplified formulation of the theory of torsional elasticity and how it applies to liquid crystals. The elastic properties of liquid crystals are perhaps their most characteristic feature, since the response to torsional stress is directly related to the orientational anisotropy of the material. An important aspect of elastic properties is that they depend on intermolecular interactions, and for liquid crystals the elastic constants depend on the two fundamental structural features of these mesophases anisotropy and orientational order. The dependence of torsional elastic constants on intermolecular interactions is explained, and some models which enable elastic constants to be related to molecular properties are described. The important area of field-induced elastic deformations is introduced, since these are the basis for most electro-optic liquid crystal display devices. 

The configuration of molecular directors within a spherical micro-droplet depends on the boundary conditions imposed by the surrounding material, on the temperature and the elastic constants of the liquid crystal and on the strength of the external electric or magnetic fields. If the splay, twist and bend elastic constants are almost equal, the structure is, in the absence of external fields, either ... 

Fig. 1.3 (a) Dependence of the splay/bend elastic constant ratio iaa/Ai i of different nematic liquid crystals on molecular structural elements versus normalized (reduced) temperature TfTc. (b) Odd-even dependence of the material properties of a homologous stales of Odi CPS alkenyl liquid crystals on side-chain double-bond position d (i = 3,4,5,7)... 

The dependence of the elastic constants on the chemical constitution of the mesogens, i.e. the attached functional groups ete., has not been systematically investigated. There are a number of pap that discuss the relationship between the physical propoties, including elastic constants, of nematics and the molecular structure of the mesogens [36,37]. It seons likely that the effect of changes of structure... 

Experimentally, as indicated in Fig. 12.13, we find that D/Dq depends on the shear stress at the wall xw (a flow variable) and the molecular weight distribution (MWD) (a structural variable) (22). The length-to-diameter ratio of the capillary (a geometric variable) also influences D/Dq. The swelling ratio at constant xw decreases exponentially with increasing L/Dq and becomes constant for L/Dq > 30. The reason for this decrease can be explained qualitatively as follows. Extrudate swelling is related to the ability of polymer melts and solutions to undergo delayed elastic strain recovery, as discussed in... 

The cases considered above, when the reaction rate is restricted by the distribution of elastic stresses in the polymer, do not describe in full the kinetics of complex multistage tribochemical reactions in pol3Tuers. The limiting stage may happen to be the displacement of reacting particles, formation of a new friction surface and so on. The reaction velocity constant may vary during the friction process as it depends upon the pol3mier permolecular structure, molecular-mass distribution and other factors. 

Continuum shell models used to study the CNT properties and showed similarities between MD simulations of macroscopic shell model. Because of the neglecting the discrete nature of the CNT geometry in this method, it has shown that mechanical properties of CNTs were strongly dependent on atomic structure of the tubes and like the curvature and chirality effects, the mechanical behavior of CNTs cannot be calculated in an isotropic shell model. Different from common shell model, which is constmcted as an isotropic continuum shell with constant elastic properties for SWCNTs, the MBASM model can predict the chirality induced anisotropic effects on some mechanical behaviors of CNTs by incorporating molecular and continuum mechanics solutions. One of the other theory is shallow shell theories, this theory are not accurate for CNT analysis because of CNT is a... 

The boundaries between spherulites resemble grain boundaries these grain boundary zones are enriched in low molecular weight material, impurities, chain ends, and defects. The deformation and strength of such a composite structure naturally depend on the compliances of all of its components. In such a composite large compliances (small constants of elasticity) have to be assigned to the cohesion across... 

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