Macroscopic interfacial separation

It is clear that if the criterion (la) or (3a) holds for interfacial separation before fibril drawing (whether on account of AG being small or Oy being large) then there will not be a large dissipation of energy,, per unit advance of the macroscopic separation front, and there will be very little work for the applied force to do. So the force required to open up an interfacial crack, in brittle separation, will be small ... 

In a Winsor I or Winsor II system (generally called saturated droplet type microemulsions), the interfacial tension, a, of the droplets can be related to the (measurable) macroscopic interfacial tension, y, of the flat interface separating the microemulsion and the excess phase by... 

The force given by Eq. (10), when summed over all the filaments that are present at a particular instant, is equal to the macroscopic force of adhesion. But this will be true only if the force, Eq. (10), is less than the force required for interfacial separation, which we will now examine in detail. 

Finally, we may look at the theory that we have developed from the viewpoint of catastrophe theory. Filament rupture is intrinsically a catastrophe, and so is interfacial separation. The peeling of a pressure-sensitive tape and the propagation of a fracture front are macroscopically continuous processes, but the change in behavior of individual filaments or fibers in the separation front is discontinuous either they detach from the solid or they rupture. Thus, the microscopic course of events is subject to a bifurcation, i.e., a choice between two catastrophes. 

Even though this contribution is always negative, the total capacity must be positive - otherwise the capacitor would accumulate charge spontaneously. Thus Eq. (17.4) is only valid if f > rjm, so that there is no electronic overlap between the two plates. Similarly the use of a macroscopic dielectric constant in Eq. (17.5) presupposes a plate separation of macroscopic dimensions, and again the total capacity is positive. Only unphysical models or bad mathematical approximations can produce negative interfacial capacities, which enjoyed a brief spell of fame under the name of the Cooper-Harrison catastrophe [2]. 

Additionally, some properties unique to both systems may result. The majority of homopolymer blends are immiscible with one another and often experience poor interfacial adhesion between the separate phases. Since block copolymers are covalently linked together, macroscopic incompatibility at the interface is minimized. The macroscopic incompatibility of a two-polymer blend may be eliminated by the addition of a block copolymer derived from the two systems. Hence, copolymers can be used to strengthen blends of immiscible polymers by serving as emulsifiers (7-9). 

Workers have shown theoretically that this effect can be caused both at the microstructural level (due to tunneling of the current near the TPB) as well as on a macroscopic level when the electrode is not perfectly electronically conductive and the current collector makes only intermittent contact. ° Fleig and Maier further showed that current constriction can have a distortional effect on the frequency response (impedance), which is sensitive to the relative importance of the surface vs bulk path. In particular, they showed that unlike the bulk electrolyte resistance, the constriction resistance can appear at frequencies overlapping the interfacial impedance. Thus, the effect can be hard to separate experimentally from interfacial electrochemical-kinetic resistances, particularly when one considers that many of the same microstructural parameters influencing the electrochemical kinetics (TPB area, contact area) also influence the current constriction. 

A significant difference between the interfacial events occurring here and those in previous studies, is that the earlier work always involved macroscopic separation of surfaces. Here, the fiber and matrix remain in relatively intimate contact after debonding, which very likely influences the intensity and time dependence of the resulting emission. For example, we expect possible quenching mechanisms involving the nearby surfaces and gases in the narrow void created by the broken interface, which would tend to reduce the intensity and duration (decay) after a separation event. 

Other macroscopic properties that in principle can be measured are the excess density and the excess compressibility of the interfacial liquid. These excess quantities can be positive or negative and follow from a comparison of the corresponding quantities in systems with the liquid and solid separated. Alternatively, liquid behaviour in pores can be studied. An example of this kind has been given by Derjaguin ) who claims that water in narrow pores of silica gel or Aerosil does not exhibit the typical thermal expansion minimum at 4 C because of structural changes near the surface. Ldring and Findenegg ) studied surface excesses dilatometrically. 

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