Interface deformation, elastic properties

While the macroscopic concepts of hardness, adhesion, friction, and slide have evolved over the last two centuries, atomic level understanding of the mechanical properties of surfaces eluded researchers. The discovery of the atomic force microscope in recent years promises to change this state of affairs. Being able to measure forces as small as 10 newton or as large as 10 newton [5] over a very small surface area (few atoms) and by simultaneously providing atomic spatial resolution, this technique permits the study of deformation (elastic and plastic), hardness, and friction on the atomic scale. The buried interface between moving solid surfaces can be studied with spectroscopic techniques on the molecular level. Study of the mechanical properties of interfaces is, again, a frontier research area of surface chemistry. 

The heat that is generated in cutting a uniform sample (usually by means of a grinding wheel consisting of grit embedded in rubber) can cause plastic deformation of the coal surface and thereby affect the plastic properties. Water used to cool the grinding interface and to carry away particles may be absorbed by the coal and affect the elastic properties. Furthermore, discontinuities in the coal structure give a wide sample-to-sample variation. 

The results of fracture tests of adhesive bonds are almost never independent of the experimental geometry because the presence of the interface with its discontinuity in elastic properties ensures that the stress field at the interface depends on both the external loading and the elastic properties mismatch as discussed in chapters on hard adhesives. However, soft adhesives have the added complication to dissipate energy, not only in a restricted plastic zone near the interface, but over a large volume, often the entire volume of the sample. This means that there is a very strong coupling between the boundary conditions of the test (thickness of the layer, size of the probe and stiffness of the probe) and the observed deformation mechanisms. 

The width of the relaxation zone R, which is the thickness of the kinetic interface , may differ considerably from other lengths characterizing other properties of an interface (e.g., space charge width, elastic deformation width). 

Vogler 31) developed a mathematical model to derive semiquantitative kinetic parameters interpreted in terms of transport and adsorption of surfactants at the interface. The model was fitted to experimental time-dependent interfacial tension, and empirical models of concentration-de-pendent interfacial tension were compared to theoretical expressions for time-dependent surfactant concentration. Adamczyk (32) theoretically related the mechanical properties of the interface to the adsorption kinetics of surfactants by introducing the compositional surface elasticity, which was defined as the proportionality coefficient between arbitrary surface deformations and the resulting surface concentrations. Although the expressions to describe the adsorption process differed from one another, it was demonstrated that the time-dependent interfacial tensions mirrored the change of surface-active substances at the interface. 

The possible development of gradients in the components of the interfacial stress tensor due to flow of an adjacent fluid implies that the momentum flux caused by the the flow of liquid at one side of the interface does not have to be completely transported across the interface to the second fluid but may (partly or completely) be compensated in the interface. The extent to which this is possible depends on the rheological properties of the interface. For small shear stresses the interface may behave elastically or viscoelastically. For an elastic interfacial layer the structure remains coherent the layer will only deform, while for a viscoelastic one it may or may not start to flow. The latter case has been observed for elastic networks (e.g. for proteins) that remciln intact, but inside the meshes of which liquid can flow leading to energy dissipation. At large stresses the structure may yield or fracture (collapse), leading to an increased flow. 

This relation describes not only periodic deformations of a liquid surface. Using methods of integral transformations it is possible to show that the dynamic surface elasticity is a fundamental surface property and its value determines the system response to a small arbitrary surface dilation [161]. With this method it is also possible to determine the dynamic elasticity of liquid-liquid interfaces where the surfactant is soluble in both adjacent phases [133]. Moreover, similar transformations lead to an expression for the dynamic surface elasticity for the case when the mechanism of the slow step of micellisation is determined by scheme (5.185) or for frequencies corresponding to the fast step of micellisation [133,134]. However, as stated above, it is the slow process which mainly influences the adsorption kinetics from micellar solutions. 

A foam is a dispersion of gas bubbles in a relatively small volume of a liquid or solid continuous phase. Liquid foams consist of gas bubbles separated by thin liquid films. It is not possible to make a foam from pure water the bubbles disappear as soon as they are created. However, if surface active molecules, such as soap, emulsifiers or certain proteins, are present they adsorb to the gas-liquid interfaces and stabilize the bubbles. Solid foams, e.g. bread, sponge cake or lava, have solid walls between the gas bubbles. Liquid foams have unusual macroscopic properties that arise from the physical chemistry of bubble interfaces and the structure formed by the packing of the gas bubbles. For small, gentle deformations they behave like an elastic solid and, when deformed more, they can flow like a liquid. When the pressure or temperature is changed, their volume changes approximately according to the ideal gas law (PF/r= constant). Thus, foams exhibit features of all three fundamental states of matter. In ice cream, the gas phase volume is relatively low for a foam (about 50%), so the bubbles do not come into contact, and therefore are spherical. Some foams, for example bubble bath. 

In Chapter 17, we discuss rheological properties, in particular viscosity and elasticity, of colloidal systems. These properties are at the basis of quality characteristics such as strength, pliancy, fluidity, texture, and other mechanical properties of various materials and products. In addition to bulk rheology, rheological features of interfaces are discussed. Interfacial rheological behavior is crucial for the existence of deformable dispersed particles in emulsions and foams. Emulsions and foams, notably their formation and stabilization, are considered in more detail in Chapter 18. 

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