Film elasticity coefficient

The film elasticity roots retrieved from the data presented in Figure 5 are shown in Figure 6. One should note that the two roots tend to each other at concentrations corresponding to the maxima of the damping coefficients. We assume that a transition of the film elasticity values from one root to another should occur. It will give us a smooth dependence of the elasticity on concentration with a continuous derivative of the elasticity on concentration, which is reasonable from a physical point of view. If to assume the elasticity as one of the roots in the whole concentration range, then the derivative of the retrieved elasticity will have a step-like behaviour at concentrations of the damping maxima. 

Usually, a ferroelectric thin film sample fabricated by the sol-gel method is coated on a substrate, which is much thicker than the film. The piezoelectric constant, 433, of the thin film sample can be measured by the static (or quasi-static) method and the electromechanical coupling factor 33 can be calculated from the known dielectric constant and the elastic coefficients 3. It is hard to measure a thin film/substrate system by a dynamic method, e.g., the transportation line method, because the vibrator is a thin film/substrate system and the major vibration is caused by the substrate, not by the film. 

Several types of spontaneous periodic director pattern yield information about elastic coefficients. Static stripe textures, as described by Lonberg and Meyer [45], appear in polymer nematics if the twist/splay ratio below the critical value of 0.303. Calculations of director fields and the influence of elastic constants and external fields on the appearance of these periodic patterns have been performed by several authors (e.g. [49-51]). In nematic cells with different anchoring conditions at the upper and lower cell plates (hybrid cells), other types of striped texture appear these are similar in nature, but involve different director deformations and elastic coefficients. For a description of various types of static periodic texture and their relationship to elastic coefficients see, for example, Lavren-tovich and Pergamenshchik [52]. In thin hybrid aligned films, a critical thickness is observed below which the director align-... 

A number of friction studies have been carried out on organic polymers in recent years. Coefficients of friction are for the most part in the normal range, with values about as expected from Eq. XII-5. The detailed results show some serious complications, however. First, n is very dependent on load, as illustrated in Fig. XlI-5, for a copolymer of hexafluoroethylene and hexafluoropropylene [31], and evidently the area of contact is determined more by elastic than by plastic deformation. The difference between static and kinetic coefficients of friction was attributed to transfer of an oriented film of polymer to the steel rider during sliding and to low adhesion between this film and the polymer surface. Tetrafluoroethylene (Telfon) has a low coefficient of friction, around 0.1, and in a detailed study, this lower coefficient and other differences were attributed to the rather smooth molecular profile of the Teflon molecule [32]. 

CNT can markedly reinforce polystyrene rod and epoxy thin film by forming CNT/polystyrene (PS) and CNT/epoxy composites (Wong et al., 2003). Molecular mechanics simulations and elasticity calculations clearly showed that, in the absence of chemical bonding between CNT and the matrix, the non-covalent bond interactions including electrostatic and van der Waals forces result in CNT-polymer interfacial shear stress (at OK) of about 138 and 186MPa, respectively, for CNT/ epoxy and CNT/PS, which are about an order of magnitude higher than microfiber-reinforced composites, the reason should attribute to intimate contact between the two solid phases at the molecular scale. Local non-uniformity of CNTs and mismatch of the coefficients of thermal expansions between CNT and polymer matrix may also promote the stress transfer between CNTs and polymer matrix. 

The elastic properties of the substrate can be determined more accurately than those of the film. Hence, in principle, the magnetoelastic coupling parameter By-2 can be determined more accurately than the magnetostriction coefficient ky-2. An analogous conclusion can be drawn with respect to bending experiments (see e.g. section 3.1 the magnetoelastic cantilever method). 

Fig. 13. Effect of the solvent solubility parameter 8 on the linear coefficient of thermal expansion 3 (1) and modulus of elasticity E (2) of films of linear SBS thermoelastoplastics with 28.3% PS obtained from solutions. The solvent is indicated on the abscissa axis I — n-heptane, II — tetra-hydrofurane, III — benzene, IV — chlorobenzene 119)...

Figure 24. A comparison of the data obtained from a range of surface rheological measurements of samples of /3-lg as a function of Tween 20 concentration. ( ), The surface diffusion coefficient of FITC-jS-lg (0.2 mg/ml) at the interfaces of a/w thin films (X), the surface shear viscosity of /3-lg (0.01 mg/ml) at the o/w interface after 5 hours adsorption ( ), the surface dilational elasticity and (o) the dilational loss modulus of /3-lg (0.2 mg/ml).

Due to the chain architecture and the large size of the macromolecules, the wetting behaviour of polymer liquids can be different from that of simple liquids. The effect becomes particularly strong when the dimension of the liquid phase, e.g. film thickness and droplet diameter, approaches the dimension of the polymer coil. In addition to the spreading coefficient and the surface pressure effects, entropic elasticity of the polymer chain provides a strong contribution to the free energy for a constant volume V0=Ad ... 

The main issue is to attempt to provide a better interpretation of the results in terms of skin parameters. The friction coefficient depends on several parameters microrelief, vertical pressure, skin elastic properties, hydration of the surface, presence (or not) of a greasy film at the interface between skin and the measuring pad, nature of the pad. Several publications describe the influence of all these parameters on the measurement of friction coefficients but results are only qualitative because of the complexity of the phenomenon. 

Fig. 4 General solution for the dispersion equation on water at 25 °C. The damping coefficient a vs. the real capillary wave frequency o> , for isopleths of constant dynamic dilation elasticity ed (solid radial curves), and dilational viscosity k (dashed circular curves). The plot was generated for a reference subphase at k = 32431 m 1, ad = 71.97 mN m-1, /i = 0mNsm 1, p = 997.0kgm 3, jj = 0.894mPas and g = 9.80ms 2. The limits correspond to I = Pure Liquid Limit, II = Maximum Velocity Limit for a Purely Elastic Surface Film, III = Maximum Damping Coefficient for the same, IV = Minimum Velocity Limit, V = Surface Film with an Infinite Lateral Modulus and VI = Maximum Damping Coefficient for a Perfectly Viscous Surface Film...

In this relation, a and a, are the thermal expansion coefficients of the substrate and film. These depend on the temperature T. If the film is homogeneous and elastically isotropic, the in plane thermoelastic stress is expressed by ... 

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