Modulus of surface elasticity

In Chapter 3 we will show that the modulus of surface elasticity is really quite a complex quantity. Whereas the flow properties of liquid/air and liquid/liquid interfaces are determined strongly by elastic forces, the solid/liquid interface is mainly related to wetting processes. 

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... 

Under dynamic conditions, where equilibrium between the surface and the film bulk cannot be realised, some specific elasticity properties are expressed. This is Marangoni s effect. Assuming that under such conditions there is an equilibrium only in some parts between the film bulk and its surface, it is possible to employ Eq. (7.6) for the material balance to calculate the modulus of elasticity. Hence, instead of the whole film volume, only the zone where equilibrium with the film surface is established, should be considered. The faster the process of film thinning, the smaller this volume is and the larger the modulus of film elasticity. In the limiting case, when it is completely impossible to achieve equilibrium between the film bulk and its surface, the elasticity of the adsorption surfactant layers takes place. 

It should be noted that the formula about the modulus of bulk elasticity of a foam refers to deformation at both compression and expansion. At large deformations, however, their effects differ significantly. When the foam is compressed the gas volume can be reduced so that to become comparable to the liquid volume. The expansion of a foam cannot be unlimited depending on its initial expansion ratio, the volume of the foam can increase only until the border pressure reaches a critical value (see Section 6.5.2). The latter is related to foam dispersity and surfactant adsorption, and decreases with the increase in surface area. 

Adsorbed gelatine molecules alone do not show a frequency dependence of surface elasticity (Fig. 6.19), which corresponds to a behaviour of an insoluble monolayers. The presence of surfactants changes the elastic and relaxation behaviour dramatically. With increasing SDS concentration the elasticity modulus (frequency independent plateau value of the elasticity) first increases and then decreases. The dynamic behaviour of the mixed adsorption layer changes from one completely formed by gelatine molecules to an adsorption layer completely controlled by surfactant molecules (Fig. 6.20). A similar behaviour can be observed for CTAB and a perfluorinated surfactant (Hempt et al. 1985). 

Shearer and Akers [5], Callaghan et al. [114] supposed that the mechanism involves elimination of surface tension gradients (see Section 4.4.3) as indicated by elimination of surface elasticity. These authors studied the effect of PDMSs on the surface elasticity of crude oil. PDMSs are used as antifoams to assist gas-oil separation during crude oil production and are apparently effective at the remarkably low concentration of 1 part per million (which presumably still exceeds the solubility limit). Callaghan et al. [114] find that PDMS diminishes the frequency-dependent dynamic dilational (elastic) modulus e = doAo (0/d In A(t) relative to that found for the uncontaminated oil. Here Oao(0 is the time-dependent air-crude oil surface tension, and A(t) is the area of a constrained element of air-crude oil surface subject to time-dependent dilation. The effect is more marked the higher the molecular weight (or viscosity) of the PDMS. This correlates with an enhanced antifoam effectiveness found with increase in molecular weight. 

Ultrasonic Microhardness. A new microhardness test using ultrasonic vibrations has been developed and offers some advantages over conventional microhardness tests that rely on physical measurement of the remaining indentation size (6). The ultrasonic method uses the DPH diamond indenter under a constant load of 7.8 N (800 gf) or less. The hardness number is derived from a comparison of the natural frequency of the diamond indenter when free or loaded. Knowledge of the modulus of elasticity of the material under test and a smooth surface finish is required. The technique is fast and direct-reading, making it useful for production testing of similarly shaped parts. 

Such nonequilihrium surface tension effects ate best described ia terms of dilatational moduh thanks to developments ia the theory and measurement of surface dilatational behavior. The complex dilatational modulus of a single surface is defined ia the same way as the Gibbs elasticity as ia equation 2 (the factor 2 is halved as only one surface is considered). 

The common tests are shown in Fig. 17.2. The obvious one is the simple tensile test (Fig. 17.2a). It measures the stress required to make the longest crack in the sample propagate unstably in the way shown in Fig. 17.3(a). But it is hard to do tensile tests on ceramics - they tend to break in the grips. It is much easier to measure the force required to break a beam in bending (Fig. 17.2b). The maximum tensile stress in the surface of the beam when it breaks is called the modulus of rupture, o for an elastic beam it is related to the maximum moment in the beam, M by... 

Such degradation of the surface causes little effect on either flexural strength or flexural modulus of elasticity but the influence on the impact properties is more profound. In such instances the minute cracks form centres for crack initiation and samples struck on the face of samples opposite to the exposed surface show brittle behaviour. For example, a moulded disc which will withstand an impact of 12 ftlbf without fracture before weathering will still withstand this impact if struck on the exposed side but may resist impacts of only 0.75 ftlbf when struck on the unexposed face. 

As is true for macroscopic adhesion and mechanical testing experiments, nanoscale measurements do not a priori sense the intrinsic properties of surfaces or adhesive junctions. Instead, the measurements reflect a combination of interfacial chemistry (surface energy, covalent bonding), mechanics (elastic modulus, Poisson s ratio), and contact geometry (probe shape, radius). Furthermore, the probe/sample interaction may not only consist of elastic deformations, but may also include energy dissipation at the surface and/or in the bulk of the sample (or even within the measurement apparatus). Study of rate-dependent adhesion and mechanical properties is possible with both nanoindentation and... 

When a - 1 ( perfect adhesion) the elasticity modulus of the interphase decreases continuously from the fiber value to the matrix value, the interphase layer modulus being higher than that of the matrix. When a < 1, the interphase layer modulus assumes, some distance off the fiber surface, a minimum value smaller than the matrix value, and then increases tending asymptotically to the matrix modulus. 

There are different techniques that have been used for over a century to increase the modulus of elasticity of plastics. Orientation or the use of fillers and/or reinforcements such as RPs can modify the plastic. There is also the popular and extensively used approach of using geometrical design shapes that makes the best use of materials to improve stiffness even though it has a low modulus. Structural shapes that are applicable to all materials include shells, sandwich structures, and folded plate structures (Fig. 3-8). These widely used shapes employed include other shapes such as dimple sheet surfaces. They improve the flexural stiffness in one or more directions. 

Although hardness is a somewhat nebulous term, it can be defined in terms of the tensile modulus of elasticity. From a more practical side, it is usually characterized by a combination of three measurable parameters (1) scratch resistance (2) abrasion or mar resistance and (3) indentation under load. To measure scratch resistance or hardness, an approach is where a specimen is moved laterally under a loaded diamond point. The hardness value is expressed as the load divided by the width of the scratch. In other tests, especially in the paint industry, the surface is scratched with lead pencils of different hardnesses. The hardness of the surface is defined by the pencil hardness that first causes a visible scratch. Other tests include a sand-blast spray evaluation. 

Currently, there is a trend of low dielectric constant (low-k) interlevel dielectrics materials to replace Si02 for better mechanical character, thermal stability, and thermal conductivity [37,63,64]. The lower the k value is, the softer the material is, and therefore, there will be a big difference between the elastic modulus of metal and that of the low-k material. The dehiscence between the surfaces of copper and low-k material, the deformation and the rupture of copper wire will take place during CMP as shown in Fig. 28 [65]. 

The ratio (p/G) has the units of time and is known as the elastic time constant, te, of the material. Little information exists in the published literature on the rheomechanical parameters, p, and G for biomaterials. An exception is red blood cells for which the shear modulus of elasticity and viscosity have been measured by using micro-pipette techniques 166,68,70,72]. The shear modulus of elasticity data is usually given in units of N m and is sometimes compared with the interfacial tension of liquids. However, these properties are not the same. Interfacial tension originates from an imbalance of surface forces whereas the shear modulus of elasticity is an interaction force closely related to the slope of the force-distance plot (Fig. 3). Typical reported values of the shear modulus of elasticity and viscosity of red blood cells are 6 x 10 N m and 10 Pa s respectively 1701. Red blood cells typically have a mean length scale of the order of 7 pm, thus G is of the order of 10 N m and the elastic time constant (p/G) is of the order of 10 s. 

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