Young equation modification

The importance of the solid-liquid interface in a host of applications has led to extensive study over the past 50 years. Certainly, the study of the solid-liquid interface is no easier than that of the solid-gas interface, and all the complexities noted in Section VIM are present. The surface structural and spectroscopic techniques presented in Chapter VIII are not generally applicable to liquids (note, however. Ref. 1). There is, perforce, some retreat to phenomenology, empirical rules, and semiempirical models. The central importance of the Young equation is evident even in its modification to treat surface heterogeneity or roughness. ... 

Contact angle between liquid and solid Yes (many goniometers and other methods) Yes (combination of Young equation with a theory for solid-liquid interfaces) Wetting, adhesion, characterization and modification of surfaces... 

Good, R.J, (1952). A thermodynamic derivation of Wenzel s modification of Young s equation contact angles Together with a theory of hysteresis. J. Am. Chem. Soc. 74, 5041-5042. 

Both roughness and heterogeneity may be present in real surfaces. In such a case, the correction factors defined by Equations (45) and (46) are both present. Although such modifications adapt Young s equation to nonideal surfaces, they introduce additional terms that are difficult to evaluate independently. Therefore the validity of Equation (44) continues to be questioned. 

It is important to remember the significance of irv. It refers specifically to the equilibrium between two surface states. There is a danger of confusing ttv with the equilibrium spreading pressure ire, introduced in Chapter 6. The latter is the pressure of the equilibrium film that exists in the presence of excess bulk material on the surface. It is the equilibrium spreading pressure that is involved in the modification of Young s equation (Equation (6.49)), for which a bulk phase is present on the substrate. For tetradecanol at 15°C, the equilibrium spreading pressure is about 4.5 10 2 N m so ire and irv are very different from one another. 

The yield stress in uniaxial tension is roughly proportional to Young s modulus. Equation 11.31 (with a relative standard deviation of 22% at T=298K, see Figure 11.11 for an illustration) is a slight modification of the original equation by Seitz [16], who used a proportionality constant of 0.025 instead of 0.028 based on the analysis of the data listed in Table 11.6. 

Young s modulus relaxation to occur between a value Eq at zero frequency, and a value E o at infinite frequency. The difference E o — Eq is the magnitude of the relaxation process. An empirical modification of the Zener model, known as the Cole-Cole equation, has the complex modulus equation... 

A stress-strain ellipse can be traced for sinusoidal deformations of a hard solid with the methods described previously after suitable modifications in the sample mounting. For example, the versatile apparatus of Philippoff described in Chapters 5 and 6 can be further modified for measurements of hard solids in flexure, using a configuration similar to that of (c) in Fig. 7-1. Configuration (a) is used by Koppelmann. The calculation of dynamic properties from equation 1 with both / and X2 sinusoidally varying is analogous to equations 19 and 20 of Chapter 5, except that now the two components of Young s modulus are determined ... 

Notably, all theories for estimating the interfacial tension have been subjected to severe criticism. All theories have limitations and they should be used with care. Despite the problems and uncertainties associated with the component theories, the solid surface energies calculated from contact angles with these theories are often of practical importance in studies of wetting phenomena, surface modification and adhesion, e.g. for developing correlations between the practical work of adhesion with the thermodynamic/reversible work of adhesion, i.e. the work of adhesion calculated from the Young-Dupre equation (or based on interfacial tensions). 

Equilibrium will occur when the presence of a surface-active agent does not lower Y any further. This concentration is typically at the critical micelle concentration [47]. Modification of fhe confacf angle (and fherefore emulsion sfability) can be achieved by a modification of the aqueous, oil, or solid phase so as to alter Yow, Yos, or Ysw- As described later, this can be achieved with the use of surfactants. The interfacial tension and surface tension are measurements of droplet deformation. Neither Ysw nor Yso can be directly measured, because the solid cannot be deformed. To solve Young s equation and to determine the solid/water and solid/oil interfacial surface tensions, the equation-of-state approach for interfacial surface tensions is required [48] ... 

On the basis of thermal shock fracture theory, the basic equation to predict thermal shock resistance is a well-known triaxial modification of Hooke s law to account for thermal strains during rapid cooling (Equation 38) (Zimmermann et al., 2008). The critical change in temperature, R, can be expressed in terms of the strength of the material (o). Young s modulus (E), Poisson s ratio (v) and coefficient of thermal expansion (a). The critical temperature difference, R, to represent thermal shock resistance predicts the maximum change in temperature that can occur without the initiation of cracks ... 

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