Interfacial energy measurement

The technique of contact mechanics has also been applied to the direct mechanical determination of solid-fluid interfacial energies, and the results compare favorably with those obtained by contact angle measurements [19]. 

As mentioned earlier, the contact-mechanics-based experimental studies of interfacial adhesion primarily include (1) direct measurements of surface and interfacial energies of polymers and self-assembled monolayers (2) quantitative studies on the role of interfacial coupling agents in the adhesion of elastomers (3) adhesion of microparticles on surfaces and (4) adhesion of viscoelastic polymer particles. In these studies, a variety of experimental tools have been employed by different researchers. Each one of these tools offers certain advantages over the others. These experimental studies are reviewed in Section 4. 

Given the importance of surface and interfacial energies in determining the interfacial adhesion between materials, and the unreliability of the contact angle methods to predict the surface energetics of solids, it has become necessary to develop a new class of theoretical and experimental tools to measure the surface and interfacial energetics of solids. Thia new class of methods is based on the recent developments in the theories of contact mechanics, particularly the JKR theory. 

Measurements of surface and interfacial energies surface forces apparatus... 

SFA has been traditionally used to measure the forces between modified mica surfaces. Before the JKR theory was developed, Israelachvili and Tabor [57] measured the force versus distance (F vs. d) profile and pull-off force (Pf) between steric acid monolayers assembled on mica surfaces. The authors calculated the surface energy of these monolayers from the Hamaker constant determined from the F versus d data. In a later paper on the measurement of forces between surfaces immersed in a variety of electrolytic solutions, Israelachvili [93] reported that the interfacial energies in aqueous electrolytes varies over a wide range (0.01-10 mJ/m-). In this work Israelachvili found that the adhesion energies depended on pH, type of cation, and the crystallographic orientation of mica. 

As reviewed so far, the contact-mechanics-based techniques (JKR and SFA methods) have been effective in the understanding molecular level mechanisms related to the adhesion of elastomers and in measuring the surface and interfacial energies of polymers and self-assembled monolayers. The current work in this area is aimed at understanding contact induced interfacial rearrangements and the role of specific interactions. The recent progress of these studies is discussed in this section. 

Interfacial area measurement. Knowledge of the interfacial area is indispensable in modeling two-phase flow (Dejesus and Kawaji, 1990), which determines the interphase transfer of mass, momentum, and energy in steady and transient flow. Ultrasonic techniques are used for such measurements. Since there is no direct relationship between the measurement of ultrasonic transmission and the volumetric interfacial area in bubbly flow, some estimate of the average bubble size is necessary to permit access to the volumetric interfacial area (Delhaye, 1986). In bubbly flows with bubbles several millimeters in diameter and with high void fractions, Stravs and von Stocker (1985) were apparently the first, in 1981, to propose the use of pulsed, 1- to 10-MHz ultrasound for measuring interfacial area. Independently, Amblard et al. (1983) used the same technique but at frequencies lower than 1 MHz. The volumetric interfacial area, T, is defined by (Delhaye, 1986)... 

The above considerations show that the interfacial energy is of utmost importance in determining the thermodynamics and kinetics of the nucleation process. Unfortunately, however, there are considerable uncertainities on the values of interfacial free energies. Values determined from contact angle measurements are significantly lower than those determined from the dependence of solubility upon molar surface of the crystallites. Furthermore, reliable data on yes are lacking. 

Interfacial Tension. The interfacial energy a between a crystal and an aqueous solution cannot (at least in general) be measured by macroscopic methods. But it may be deduced from homogeneous nuclea-tion data (20-24). For the purpose of determining the edge energy Y = a CT one may either take the individual value determined on the actual substance (if it is determined) or use the general correlation with the solubility cs, expressed for instance by (10,18)... 

A very accurate measurement of Ccrjt would allow back-calculation of the surface energy for a given crystal. Because Ccrjt is dependent on the square of Y, such a measurement could be a very sensitive method of measuring interfacial energy at dislocation outcrops. The calculated interfacial energy from our experiments is 280+ 90 mJm- for the rhombohedral face of quartz at 300°C. Parks (10) estimated 25°C value of 360 + 30 mJm is well within the experimental error of our measurement. The best way to determine the value of Ccrjt would be to measure etch pit nucleation rate on... 

Several refinements of our experiments could test these theories further. By measuring etch pit densities as well as pit dimensions on sequentially-etched crystals, nucleation rate data and pit growth data could be collected, yielding information about the rate-limiting steps and mechanisms of dissolution. In addition, since the critical concentration is extremely dependent on surface energy of the crystal-water interface (Equation 4), careful measurement of Ccrit yields a precise measurement of Y. Our data indicates an interfacial energy of 280 + 90 mjm- for Arkansas quartz at 300°C, which compares well with Parks value of 360 mJm for 25°C (10). Similar experiments on other minerals could provide essential surface energy data. 

The experimental basis of sorption studies includes structural data (SANS, SAXS, USAXS), isopiestic vapor sorption isotherms,i and capillary isotherms, measured by the method of standard porosimetry. i 2-i44 Thermodynamic models for water uptake by vapor-equilibrated PEMs have been suggested by various groupThe models account for interfacial energies, elastic energies, and entropic contributions. They usually treat rate constants of interfacial water exchange and of bulk transport of water by diffusion and hydraulic permeation as empirical functions of temperature. 

Whilst certain of these methods involve measurements only at the liquid-vapour or liquid-liquid interfaces involved in the static methods we must usually consider besides the interfacial energy of the two fluids, that between each of them and a solid... 

Since it is relatively easy to transfer molecules from bulk liquid to the surface (e.g. shake or break up a droplet of water), the work done in this process can be measured and hence we can obtain the value of the surface energy of the liquid. This is, however, obviously not the case for solids (see later section). The diverse methods for measuring surface and interfacial energies of liquids generally depend on measuring either the pressure difference across a curved interface or the equilibrium (reversible) force required to extend the area of a surface, as above. The former method uses a fundamental equation for the pressure generated across any curved interface, namely the Laplace equation, which is derived in the following section. 

Energy of Adhesion. The interfacial energy between two mutually insoluble saturated liquids, A and B, is equal to the difference in the separately measured surface energies of each phase ... 

Of all local motions, v(r), of an interface that pass the same amount of volume from one side to the other, the motion that is normal to the interface with magnitude proportional to the weighted mean curvature, v f) oc /c7n, increases the interfacial energy the fastest. However, fastest depends on how distance is measured. How this distance metric alters the variational principles that generate the kinetic equations is discussed elsewhere [14]. 

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