Surface elasticity

Force curve gives the relationship between the z-piezo displacement and the cantilever deflection as shown in Figure 21.10b. When a cantilever approaches to a stiff sample surface, cantilever deflection. A, is equal to the z-piezo displacement, z — Zo- The value of zo is defined as the position where the tip-sample contact is realized. On the other hand, z-piezo displacement becomes larger to achieve the preset trigger value (set point) of the cantilever deflection in the case of an elastic sample due to the deformation of the sample itself. In other words, we can obtain information about a sample deformation, 8, from the force-distance curve of the elastic surface by the following relationship ... 

It is probable that numerous interfacial parameters are involved (surface tension, spontaneous curvature, Gibbs elasticity, surface forces) and differ from one system to the other, according the nature of the surfactants and of the dispersed phase. Only systematic measurements of > will allow going beyond empirics. Besides the numerous fundamental questions, it is also necessary to measure practical reason, which is predicting the emulsion lifetime. This remains a serious challenge for anyone working in the field of emulsions because of the polydisperse and complex evolution of the droplet size distribution. Finally, it is clear that the mean-field approaches adopted to measure > are acceptable as long as the droplet polydispersity remains quite low (P < 50%) and that more elaborate models are required for very polydisperse systems to account for the spatial fiuctuations in the droplet distribution. 

Dransfeld, K. and Salzmann, E. (1970). Excitation, detection and attenuation of high-frequency elastic surface waves. In Physical acoustics VII (ed. W. P. Mason and R. N. Thurston), pp. 260-83. Academic Press, New York. [117]... 

Foaming capability relates to both foam formation and foam persistence. Surface tension lowering is necessary, but not sufficient. Other important factors include surface elasticity, surface viscosity, and disjoining pressure [303], Considering stabil-... 

The stability of foams in constraining media, such as porous media, is much more complicated. Some combination of surface elasticity, surface viscosity and disjoining pressure is still needed, but the specific requirements for an effective foam in porous media remain elusive, partly because little relevant information is available and partly because what information there is appears to be somewhat conflicting. For example, both direct [304] and inverse [305] correlations have been found between surface elasticity and foam stability and performance in porous media. Overall, it is generally found that the effectiveness of foams in porous media is not reliably predicted based on bulk physical properties or on bulk foam measurements. Instead, it tends to be more useful to study the foaming properties in porous media at various laboratory scales micro-, meso-, and macro-scale. 

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...

Further increases in elasticity lead to the next limit of the minimum velocity for a perfectly elastic surface film. Here, the mode coupling leads to the case when the transverse motion is favored at the expense of lateral motion that is now practically stopped. Treating this case as a departure from the infinite lateral modulus case, Limit V, expressions for co0 and a are given as follows. 

The limit is when s = ico ic -> oo in the case of a purely viscous film with d = 0. Putting it differently, the lateral modulus is a complex quantity, = (j + icon (Eq. 18), hence the infinite limit must apply not only to the purely elastic surface film, k = 0, but also to the purely viscous surface film, d = 0. The dynamics are then closely related to those of a surface with the... 

In Fig. 24 a polar plot with all four polymers is displayed. PHcMA (C4 side chain) follows the profile of an almost purely elastic surface film whereas chains with longer side chains follow that of progressively more viscous pro-... 

K. Dransfeld and E. Saizmann, Excitation, Detection and Attenuation of High-Frequency Elastic Surface Waves, Physical Acoustic Principles and Methods, Vol. VII, Academic Press, New York, 1970, p. 219. 

Equations [3.6.16 and 17] define the interfacial viscous and elastic components if surfaces are deformed by shear. Their counterparts refer to deformation by dilation (extension), or compression. Now we are concerned with relative extensions AAI A, or, infinitesimally, d In A. As before, for purely elastic surfaces the following two options should be considered (a) there is a network-type elasticity, as in a two-dimensional gel and (b) such a skin is absent elasticity is of the Gibbs... 

Striking evidence of phenomena that are clearly dependent on the formation of a superficial layer across the crystal surface is provided [67] by a microscopic examination of the changes that occur during the dehydration of cleaved single crystals of a-NiS04.6H20. DSC observations (4 K min ) between 400 and 415 K detected a series of small endotherms, identified from observations as bubble development with swelling of a relatively impermeable and elastic surface layer. 

As in the case of the planar bilayer, the energy of this elastic surface can be assigned a Hamiltonian [46,48] ... 

The earliest available hydrodynamic theory of water wave damping by elastic surface films was published by Lamb (1895). He refers to Reynolds (1880) and the experiments by Aitken (see Scott 1979, Giles and Forrester 1970), but prior publication of the detailed theory is not indicated. All but the outline of the theory was omitted from later editions of this book, and it is likely that Lamb assumed that damping was greatest with an inextensible film, and that intermediate elasticities, therefore, had less effect (cited after Scott 1979). This conclusion was shown by Dorrestein (1951) to be incorrect. The paper by Levich (1940) was the first to present in detail the linearised hydrodynamics of waves on a water surface with surface dilational elasticity. The only cases considered in detail concern insoluble films, and represent the clean and incompressible-film-covered surface. A detailed treatment of the hydrodynamic theory of surface waves, including the effect of an elastic surface film, was published by Levich in 1962. In addition, the damping caused by dissolved surface-active material was considered. Further laboratory experiments performed until 1978 were briefly reviewed by Scott (1979). 

Fig. 3.26. Schematic of a purely elastic and visco-elastic surface, after Lucassen (1968)...

Fig. 13.15), so as to resemble the surface of a latex particle. The two rubber cylinders, A and B, were mounted vertically, one above the other. The upper cylinder was held fixed during the experiment whereas the position of the lower cylinder could be moved up and down by a micrometer drive unit (D). Moving the cylinder A up towards B, after polymer had been adsorbed onto the poly(methyl methacrylate) surfaces, distorted the soft, elastic surfaces in the centi region, resulting in flat discs in the zone of interaction. The distance of separation between the surfaces was measured by multiple beam interferometry. The applied pressure caused an equilibrium contact area to be formed, the magnitude of which could also be determined interferometrically. The relationship between contact area and the equilibrium pressure was established by direct calibration. In this fashion, the equilibrium pressure could be measured for a given distance of separation. 

In addition to parameters commonly used in many applications, this chapter includes some dD descriptors and molecular pD models that are not found in the standard computational chemistry literature. This is the case, for instance, for the topological and geometrical analyses of elastic chains and elastic surfaces. Their inclusion aims at giving the reader a broader perspective on the tools used in other related fields. 

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