Interfacial pressure

Fig. 9. Residual stresses owing to thermal expansion mismatch between a particle with radius a and thermal expansion coefficient and a matrix with thermal expansion coefficient The stresses illustrated here are for and P is the interfacial pressure.

The log of the reciprocal of the bulk concentration of surfactant (C in mol/ L) necessary to produce a surface or interfacial pressure of 20 raN/m, log( 1 / On= 20 i e > a 20 mN/m reduction in the surface or interfacial tension, is considered a measure of the efficiency of a surfactant. The effectiveness of surface tension reduction is the maximum effect the surfactant can produce irrespective of concentration, (rccmc = [y]0 - y), where [y]0 is the surface tension of the pure solvent and y is the surface tension of the surfactant solution at its cmc. 

In Eq. (5.26), Tt is the interfacial pressure of the aqueous-organic system, equal to (Yo - Y) e to the difference between the interfacial tensions without the extractant (Yo) and the extractant at concentration c (y)], c is the bulk organic concentration of the extractant, and is the number of adsorbed molecules of the extractant at the interface. The shape of a typical n vs. In c curve is shown in Fig. 5.4 rii can be evaluated from the value of the slopes of the curve at each c. However, great care must be exercised when evaluating interfacial concentrations from the slopes of the curves because Eq. (5.26) is only an ideal law, and many systems do not conform to this ideal behavior, even when the solutions are very dilute. Here, the proportionality constant between dHld In c and is different from kT. Nevertheless, Eq. (5.26) can still be used to derive information on the bulk organic concentration necessary to achieve an interface completely saturated with extractant molecules (i.e., a constant interfacial concentration). According to Eq. (5.26), the occurrence of a constant interfacial concentration is indicated by a constant slope in a 11 vs. In c plot. Therefore, the value of c at which the plot n vs. In c becomes rectilinear can be taken as the bulk concentration of the extractant required to fully saturate the interface. 

Fig. 5.4 Typical interfacial pressure (If) vs. logarithm of bulk organic concentration (log c) plotted for an extractant exhibiting surface-active properties.

It is interesting to note that Umax, when calculated by the above equations, may exceed the maximum surface or interfacial pressure to which the film can, in practice, be subjected. The absorbed film will then desorb or crumple, or it may rather suddenly be shed to the rear of the drop as a filament or, if the interfacial tension is very close to zero, as emulsion. The drop may thus, on suddenly losing its surface film, accelerate again, as has indeed been noted (without explanation) by Terjesen. For the same reason, drops larger than given by some critical radius, may have a calculated greater than the adsorbed film can maintain, and hence will rise or fall with virtually no retardation, though drops below this critical size will be retarded to the velocity expected for solid spheres (70). 

The interfacial tension of mixed adsorbed films of 1-octadecanol and dodecylammonium chloride has been measured as a function of temperature at various bulk concentrations under atmospheric pressure. The transition interfacial pressure of 1-octadecanol film has been observed to increase with the addition of dodecylammonium chloride and then to disappear. The interfacial pressure vs mean area per adsorbed molecule curves have been illustrated at a constant mole fraction of adsorbed molecules. With the aid of the thermodynamic treatment developed previously, we find that the mutual interaction between 1-octadecanol and dodecylammonium chloride molecules in the expanded state is similar in magnitude to the interaction between the scime kind of film-forming molecules. 

The interfacial pressure II vs the mean area per adsorbed molecule A curves are useful to make clear the film behavior. By making use of Figures 2 and 4, we can obtain the II vs A curves at constant m as shown in Figure 6(a), where II and A are defined, respectively, by... 

Figure 6. (a) Interfacial pressure vs mean area per molecule... 

Pavlovskaya, G., Semenova, M., Tsapkina, E., Tolstoguzov V. (1993). The influence of dextran on the interfacial pressure of adsorbing layers of 1 IS globulin Viciafaba at the planar w-decane/aqueous solution interface. Food Hydrocolloids, 7, 1-10. 

In line with the Gibbs adsorption equation (equation 3.33 in chapter 3), the presence of thermodynamically unfavourable interactions causes an increase in protein surface activity at the planar oil-water interface (or air-water interface). As illustrated in Figure 7.5 for the case of legumin adsorption at the n-decane-water interface (Antipova et al., 1997), there is observed to be an increase in the rate of protein adsorption, and also in the value of the steady-state interfacial pressure n. (For the definition of this latter quantity, the reader is referred to the footnote on p. 96.)... 

Figure 7.5 Effect of the character of the interactions between dextran and legunhn on the time-dependent interfacial pressure jc of the adsorbed layer of legumin at the planar o-decane-watcr interface (o) 0.001 wt% legumin alone, and ( ) 0.001 wt% legumin + 2 wt% dextran. (a) Thennodynanhcally unfavourable interaction pH = 7.0, ionic strength = 0.01 M (dextran A/w = 48 kDa). (b) Thermodynamically favourable interaction pH = 7.8, ionic strength = 0.01 M (dextran A/w = 270 kDa).

Interfacial pressure th, the change in interfacial tension as a result of sorption (usually positive adsorption) of the surface-active material. It may be regarded as a measure of the tendency of adsorbed species at the interface (or biface) to enlarge the area occupied by the BLM. 

Since the technique developed during this investigation differs from the classical methods for studying films at interfaces, a brief consideration of traditional techniques seems desirable. In general, the interfacial tension of films (e.g., insoluble monolayers) at interfaces is not measured as such. Instead, the so-called interfacial pressure is determined, which is given by ... 

At an air/water interface, the two-dimensional interfacial pressure (IT) can be easily monitored using an instrumented Langmuir trough. The initial adsorption rate at a clean surface is simply the rate of diffusion... 

A similar experiment to that noted above can be performed, but now let the interface be populated by a molecular layer at constant n and known interface electrical potential. A molecule adsorbing at such an interface must do work against the electrical potential barrier, as well as against the interfacial pressure. We get... 

FIGURE 1.8. (a) Schematic representation of the device used to study capillary surface instabilities. A polymer-air bilayer of thicknesses /ip and /ia, respectively, is formed by two planar silicon wafer held at a separation d by spacers. A capillary instability with wavelength k = 27t/q is observed upon applying a voltage U or a temperature difference AT. (b) Dispersion relation (prediction of Eq. (1.6)). While all modes are damped (r < 0) in the absence of an interfacial pressure pei, the application of an interfacial force gradient leads to the amplification of a range of k-values, with /.m the maximally amplified mode. 

The frequency dependent derivation of Jq and p is somewhat lengthy and is therefore discussed here only qualitatively (see [36] for a full discussion). Essentially, one has to write the heat flux and the pressure at the polymer-air interface in terms of reflectivities and transmittances of all three interfaces (all of which are a function of the phonon frequency). The total heat-flux and interfacial pressure are then obtained in a self-consistent way by an integration over the Debye density of states [36],... 

This leads to a rather simple scaling form of the interfacial pressure... 

Considering the interfacial pressure model, the flow rates should be between the higher and lower limits. APpiow can be evaluated by considering the pressure loss in the microchannels. Assuming that the pressure at the opened outlet is atmospheric pressure, Patm, then the pressure P of each phase from the pressure loss AP is expressed as follows ... 

The liquid-liquid interface formed between two immissible liquids is an extremely thin mixed-liquid state with about one nanometer thickness, in which the properties such as cohesive energy density, electrical potential, dielectric constant, and viscosity are drastically changing from those of bulk phases. Solute molecules adsorbed at the interface can behave like a 2D gas, liquid, or solid depending on the interfacial pressure, or interfacial concentration. But microscopically, the interfacial molecules exhibit local inhomogeneity. Therefore, various specific chemical phenomena, which are rarely observed in bulk liquid phases, can be observed at liquid-liquid interfaces [1-3]. However, the nature of the liquid-liquid interface and its chemical function are still less understood. These situations are mainly due to the lack of experimental methods required for the determination of the chemical species adsorbed at the interface and for the measurement of chemical reaction rates at the interface [4,5]. Recently, some new methods were invented in our laboratory [6], which brought a breakthrough in the study of interfacial reactions. 

INTERFACIAL PRESSURE MEASUREMENTS AT CHEMICAL MECHANICAL POLISHING INTERFACES... 

Volume 11 mainly dealt with interfaces of solids. For such systems, the adsorption of molecules and ions is the primary phenomenon. Interfaclal tensions cannot generally be measured, although interfacial pressures are obtainable from adsorption isotherms using Gibbs law. 

At very low molecular densities, i.e. at very low Interfacial pressures, the mono-layer exhibits gaseous behaviour. The molecules are far apart, but, unlike in a three-dimensional gas, they are not completely disordered. Because of their amphi-polar nature, the molecules exhibit a preferential orientation relative to the surface-normal. As stated in sec. 3.1, the interfacial pressure exerted by an ideally dilute monolayer is equivalent to the osmotic pressure of an ideal three-dimensional solution. Ideal gaseous monolayer behaviour means obe3dng relation [3.1.1]. 

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