Surface elastic moduli tension

The surface rheological properties of the /3-lg/Tween 20 system at the macroscopic a/w interface were examined by a third method, namely surface dilation [40]. Sample data obtained are presented in Figure 24. The surface dilational modulus, (E) of a liquid is the ratio between the small change in surface tension (Ay) and the small change in surface area (AlnA). The surface dilational modulus is a complex quantity. The real part of the modulus is the storage modulus, e (often referred to as the surface dilational elasticity, Ed). The imaginary part is the loss modulus, e , which is related to the product of the surface dilational viscosity and the radial frequency ( jdu). 

A Models to describe microparticles with a core/shell structure. Diametrical compression has been used to measure the mechanical response of many biological materials. A particular application has been cells, which may be considered to have a core/shell structure. However, until recently testing did not fully integrate experimental results and appropriate numerical models. Initial attempts to extract elastic modulus data from compression testing were based on measuring the contact area between the surface and the cell, the applied force and the principal radii of curvature at the point of contact (Cole, 1932 Hiramoto, 1963). From this it was possible to obtain elastic modulus and surface tension data. The major difficulty with this method was obtaining accurate measurements of the contact area. 

Bianko and Marmur [99] have developed a new technique for the measurement of Gibbs elasticity of foam films. In order to exclude the effect of the mass transfer of the surfactant, the stretching of an isolated soap bubble is used. The surface tension needed for the calculation of the elasticity modulus is determined by the pressure in the bubble and the radius of curvature. The modulus obtained are considerably lower than those derived by the technique of Prins et al. [95]. 

MeC adsorbs at the air water interface leading to a decrease in the surface tension. An equilibrium state is only reached at very long times, due to the high molecular mass of methylcellulose. The layer which is present at the interface at equilibrium is almost purely elastic with a large dilational elastic modulus. The value of the excluded volume critical exponent extracted from the E-n curve indicates that the air-water interface is not a good solvent for the polymer. 

The relationship between the force, Fc, the surface tension, a, (which in this case represents the work required to form a new interface), crack length, /, thickness, h, width, d, and Young s elasticity modulus, E, of the cleaved layer... 

Film Elasticity The differential change in surface tension of a surface film with relative change in area. Also termed surface elasticity, dilata-tional elasticity, areal elasticity, compressional modulus, surface dilata-tional modulus, or modulus of surface elasticity. For fluid films, the surface tension of one surface is used. The Gibbs film (surface) elasticity is the equilibrium value. If the surface tension is dynamic (time-dependent) in character, then for nonequilibrium values, the term Marangoni film... 

It seems instructive to discuss the nature of the minima in the plots of Fig. 2.10. For CioEOg at the water/hexane interface the elasticity modulus attains a minimum at n = 25 mN/m. This can be explained by the influence of the surface pressure on the composition of the surface layer comprised of surfactant molecules capable to adsorb in two states, see Fig. 2.11. Moreover, at n > 11 mN/m for the water/hexane interface, and H > 7 mN/m for the water/air interface, the adsorption in state 1 starts to decrease significantly. At the same time, adsorption in state 2 increases continuously as usual - with increasing pressure the adsorption becomes higher. As the changes of adsorption in states 1 and 2 are opposite to each other, the resulting changes in the total adsorption and surface tension are small. 

The above analysis of the viscoelastic behaviour for adsorption layers of a reorientable surfactant leads to important conclusions. It is seen that the most important prerequisite for a realistic prediction of the elastic properties is the adequacy of the theoretical model used to describe the equilibrium adsorption of the surfactant. For example, when we use the von Szyszkowski-Langmuir equation instead of the reorientation model to describe the interfacial tension isotherm, this rather minor difference drastically affects the elasticity modulus of the surface layer. The elasticity modulus, therefore, can be regarded to as a much more sensitive parameter to find the correct equation of state and adsorption isotherm, rather than the surface or interfacial tension. Therefore the study of viscoelastic properties can give much more insight into the nature of subtle phenomena, like reorientation, aggregation etc. 

Some consequences which result from the proposed models of equilibrium surface layers are of special practical importance for rheological and dynamic surface phenomena. For example, the rate of surface tension decrease for the diffusion-controlled adsorption mechanism depends on whether the molecules imdergo reorientation or aggregation processes in the surface layer. This will be explained in detail in Chapter 4. It is shown that the elasticity modulus of surfactant layers is very sensitive to the reorientation of adsorbed molecules. For protein surface layers there are restructuring processes at the surface that determine adsorption/desorption rates and a number of other dynamic and mechanical properties of interfacial layers. 

While the tilt is a measure of the dilational elasticity, the thickness is proportional to the exchange of matter rate, sometimes named dilational viscosity. The ellipse thickness corresponds to the phase shift between the generated area oscillation and the surface tension response. With increasing frequencies the thickness decreases while the tilt angle increases up to a final value of representing the dilational elasticity modulus So. 

In the general case the phase of oscillations of the surface tension and the phase of periodical alterations of the surface area do not coincide. Then it is convenient to use complex numbers in order to describe the oscillations, and to consider two components of the surface elasticity, the surface storage modulus z, and the surface loss modulus ct... 

X10. The next three rows present the viscosity rj, the surface tension, and its tenqterature dependence, in the liquid state. The next properties are the coefficient of linear thermal expansion a and the sound velocity, both in the solid and in the liquid state. A number of quantities are tabulated for the presentation of the elastic properties. For isotropic materials, we list the volume compressihility k = —(l/V)(dV/dP), and in some cases also its reciprocal value, the bulk modulus (or compression modulus) the elastic modulus (or Young s modulus) E the shear modulus G and the Poisson number (or Poisson s ratio) fj,. Hooke s law, which expresses the linear relation between the strain s and the stress a in terms of Young s modulus, reads a = Ee. For monocrystalline materials, the components of the elastic compliance tensor s and the components of the elastic stiffness tensor c are given. The elastic compliance tensor s and the elastic stiffness tensor c are both defined by the generalized forms of Hooke s law, a = ce and e = sa. At the end of the list, the tensile strength, the Vickers hardness, and the Mohs hardness are given for some elements. 

Most hard amorphous polymers under tension show brittle fracture. The strength, ct, is determined under the Griffith equation (Equation (1.3)) by the fracture surface energy, y, which in turn mostly depends on the energy absorbed by the plastic deformation and void formation (crazing) that occurs immediately at the tip of the crack. E is the elastic modulus and c is the crack length ... 

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