Relaxation film elasticity

Figure IV-10 illustrates how F may vary with film pressure in a very complicated way although the v-a plots are relatively unstructured. The results correlated more with variations in film elasticity than with its viscosity and were explained qualitatively in terms of successive film structures with varying degrees of hydrogen bonding to the water substrate and varying degrees of structural regularity. Note the sensitivity of k to frequency a detailed study of the dispersion of k should give information about the characteristic relaxation times of various film structures.

As for Ge on Si [3], growth conditions are chosen which favor nucleation only on regions between the pores. With further deposition three-dimensional islands allow strain relaxation by elastic deformation, followed by island coalescence. The density of inter-island dislocations can be orders of magnitude less than in films grown on nonporous substrates. 

The initial (maximum) film tension after the expansion in the film stress-relaxation experiments can also be used to determine the film elasticity (7). A plot of the initial film tension versus the logarithm of the relative film expansion is shown in Fig. 5. For comparison, the initial single interfacial tensions obtained in the experiments with the respective single oil/water interface are also plotted. The film elasticity obtained from the top of the curve is equal, within experimental error, to twice the interfacial elasticity of the single interface. 

It was found that when the solution-cast films are stretched at temperature greater than Tg, liquid crystalline microdomains can support part of the elastic extension and, at the same time, deform to result in a long-range orientation of azobenzene mesogens. The liquid crystal orientation is retained in the relaxed film at r < Tg, which creates a thermoplastic elastomer whose glassy micro-... 

Once the previous loop had been completed a new pressure distribution was determined with the use of considerable under-relaxation. The elastic deformation was Chen re-evaluated and a new film shape was computed by the use of an over-relaxation procedure, before a new set of finite difference coefficients were determined. On every tenth cycle through the loop the Input load and integrated load were compared, allowing any discrepancy to be corrected by an adjustment of the central film thickness constant (H ). 

As the coherent film becomes thicker, it grows with essentially uniform elastic strain over most of the growth area. The strain energy per unit volume is constant consequently, over most of the growth area, the stored strain energy per unit area of interface increases linearly with film thickness beyond thicknesses of a few atomic dimensions. This increasing energy reservoir is available to drive various physical mechanisms for relaxation of elastic strain. 

Fukada and Sakurai (1971) measured the temperature dependence of df3 and df2 for a drawn and polarized PVDF film (Fig. 30). The relaxational behavior is somewhat masked by the rapid monotonic increase with increasing temperature on account of the decrease in the elastic modulus. Details of the curves, however, seem to indicate that d has a maximum at relaxational temperatures and, in accordance with this, d" has a maximum and a succeeding minimum at these temperatures. 

The mechanism of the equilibrium elasticity acts until it is possible to provide a surfactant re-partition between the exterior and interior of the film. In a NBF such a repartition is not possible and this mechanism of elasticity ceases to act. The elasticity properties of bilayer films, in which the hydrodynamic and adsorption processes are characterised with normal time of relaxation, are due to Marangoni effect in the insoluble adsorption layers. That is why stable foams with black films are very sensitive to different local disturbances (heating, vibration, etc.). 

The adsorbed surfactant film is assumed to control the mechanical-dynamical properties of the surface layers by virtue of its surface viscosity and elasticity. This concept may be true for thick films (>100 run) whereby intermolecular forces are less dominant (i.e., foam stability under dynamic conditions). Surface viscosity reflects the speed of the relaxation process which restores the equilibrium in the system after imposing a stress on it. Surface elasticity is a measure of the energy stored in the surface layer as a result of an external stress. 

The Gibbs elasticity, Eq, favors the formation of emulsion 1, because it slows the film thinning. On the other hand, increased surface diffusivity, D, decreases this effect, because it helps the interfacial tension gradients to relax, thus facilitating the formation... 

Insoluble monolayers on an aqueous substrate have been investigated by means of the capillary wave method for many years. Lucassen and Hansen (1966) in their pioneering work neglected the surface viscosity and considered only pure elastic films. Subsequent studies showed that the surface elasticity of real surface films is a complex quantity, and both the equilibrium surface properties and the kinetic coefficients of relaxation processes in the films influence the characteristics of surface waves. However, it has been discovered recently that the real situation is even more complicated and the macroscopic structure of surface films influences the dependency of the damping coefficient of capillary waves on the area per molecule (Miyano and Tamada 1992, 1993, Noskov and Zubkova 1995, Noskov et al. 1997, Chou and Nelson 1994, Chou et al. 1995, Noskov 1991, 1998, Huhnerfuss et al. this issue). Some peculiarities of the experimental data can be explained, if one takes into account the capillary wave scattering by two-dimensional particles (Noskov et al. 1997). 

Elastic properties of interface. The surface tension of the solution interface is less than the surface tension of the pure solvent interface. The difference is equal to the surface pressure of surfactant molecules [9, 109, 414], This does not contradict the fact that the films forming the skeleton of the foam possess increased strength and elasticity. The equilibrium surface layer of a pure liquid is ideally inelastic. Under the action of external forces, the free surface increases not because of extension (an increase in the distance between the molecules in the near-surface layer) but because new molecules are coming from the bulk. A decrease in the equilibrium tension as some amount of surfactant is added does not mean that the elasticity of the surface decreases, since this surface does not possess elastic properties under slow external actions. Nevertheless, we point out that even surfaces of pure liquids possess elastic properties [465] (dynamic surface tension [232]) under very rapid external actions whose characteristic time is less than the time of self-adsorption relaxation of the surface layer. This property must not depend on the existence of an adsorption layer of surfactant. At the same time, surfactants impart additional elastic properties to the surface both at low and high strain rates. 

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