Nucleation pores

Assume first that the interfacial tensions of the curved and planar parts are the same. The free energy balance of the nucleation pore in a liquid film states that ... 

Consider again eqn. (7.25). The first term on the right-hand side is proportional to the hole surface area and is the interfacial tension contribution. The second term is proportional to the hole perimeter and is therefore the line tension contribution. (The third term is constant for constant film thickness b and can be incorporated into the pre-exponent.) The alternative way to model the film rupture is to present the free energy of the nucleation pore as the sum of the line and surface tension terms ... 

Nucleation Pore in Multilamellar-covered Emulsion Films... 

Qualitative examples abound. Perfect crystals of sodium carbonate, sulfate, or phosphate may be kept for years without efflorescing, although if scratched, they begin to do so immediately. Too strongly heated or burned lime or plaster of Paris takes up the first traces of water only with difficulty. Reactions of this type tend to be autocat-alytic. The initial rate is slow, due to the absence of the necessary linear interface, but the rate accelerates as more and more product is formed. See Refs. 147-153 for other examples. Ruckenstein [154] has discussed a kinetic model based on nucleation theory. There is certainly evidence that patches of product may be present, as in the oxidation of Mo(lOO) surfaces [155], and that surface defects are important [156]. There may be catalysis thus reaction VII-27 is catalyzed by water vapor [157]. A topotactic reaction is one where the product or products retain the external crystalline shape of the reactant crystal [158]. More often, however, there is a complicated morphology with pitting, cracking, and pore formation, as with calcium carbonate [159]. 

The formation of a liquid phase from the vapour at any pressure below saturation cannot occur in the absence of a solid surface which serves to nucleate the process. Within a pore, the adsorbed film acts as a nucleus upon which condensation can take place when the relative pressure reaches the figure given by the Kelvin equation. In the converse process of evaporation, the problem of nucleation does not arise the liquid phase is already present and evaporation can occur spontaneously from the meniscus as soon as the pressure is low enough. It is because the processes of condensation and evaporation do not necessarily take place as exact reverses of each other that hysteresis can arise. 

The variant of the cylindrical model which has played a prominent part in the development of the subject is the ink-bottle , composed of a cylindrical pore closed one end and with a narrow neck at the other (Fig. 3.12(a)). The course of events is different according as the core radius r of the body is greater or less than twice the core radius r of the neck. Nucleation to give a hemispherical meniscus, can occur at the base B at the relative pressure p/p°)i = exp( —2K/r ) but a meniscus originating in the neck is necessarily cylindrical so that its formation would need the pressure (P/P°)n = exp(-K/r ). If now r /r, < 2, (p/p ), is lower than p/p°)n, so that condensation will commence at the base B and will All the whole pore, neck as well as body, at the relative pressure exp( —2K/r ). Evaporation from the full pore will commence from the hemispherical meniscus in the neck at the relative pressure p/p°) = cxp(-2K/r ) and will continue till the core of the body is also empty, since the pressure is already lower than the equilibrium value (p/p°)i) for evaporation from the body. Thus the adsorption branch of the loop leads to values of the core radius of the body, and the desorption branch to values of the core radius of the neck. 

Both the cone-shaped and the wedge-like pore give rise to simple, hysteresis-free behaviour. The meniscus is nucleated at the apex of the cone (Fig. 3.14(a)) or at the intersection of the two planes of the wedge (Fig. 3.14(b)), giving a spherical meniscus in the first case and a cylindrical one in the second. In both systems the process of evaporation is the exact reverse of that of condensation, and hysteresis is therefore absent. 

Fig. 4. Diagram of the two-step process to manufacture nucleation track membranes, (a) Polycarbonate film is exposed to charged particles in a nuclear reactor, (b) Tracks left by particles are preferentially etched into uniform cylindrical pores (8).

Another method to synthesize hollow nanocapsules involves the use of nanoparticle templates as the core, growing a shell around them, then subsequently removing the core by dissolution [30-32]. Although this approach is reminiscent of the sacrificial core method, the nanoparticles are first trapped and aligned in membrane pores by vacuum filtration rather than coated while in aqueous solution. The nanoparticles are employed as templates for polymer nucleation and growth Polymerization of a conducting polymer around the nanoparticles results in polymer-coated particles and, following dissolution of the core particles, hollow polymer nanocapsules are obtained. 

They considered that cement formation was the result of an acid-base reaction leading to the formation of hydrates by a through-solution mechanism, by nucleation and precipitation from pore fluids. Two phases were found in the matrix, one amorphous and the other crystalline. The crystalline phase was newberyite. Finch Sharp concluded that the amorphous phase was a hydrated form of aluminium orthophosphate, AIPO4, which almost certainly contained magnesiiun. They ruled out a pure AlP04.nH20, for they considered that the reaction could not be represented by the equation... 

A series of observations in different areas of the specimen have unambiguously evidenced the presence of a porous structure. Moreover, it has been observed that the density of pores is higher where the particle density is reduced, suggesting that the particles nucleate on the pores of the substrate and that the pores, which are not filled, are not completely reduced in the final thermal process. 

The most developed and widely used approach to electroporation and membrane rupture views pore formation as a result of large nonlinear fluctuations, rather than loss of stability for small (linear) fluctuations. This theory of electroporation has been intensively reviewed [68-70], and we will discuss it only briefly. The approach is similar to the theory of crystal defect formation or to the phenomenology of nucleation in first-order phase transitions. The idea of applying this approach to pore formation in bimolecular free films can be traced back to the work of Deryagin and Gutop [71]. 

A (3 fibril formation an identifiable nucleating species has yet be isolated. Direct observation has been made difficult by the small size of the (3 peptide, which has an effective hydrodynamic radius of 4 nm [98-100], and by the apparent low abundance of nucleating species due to the low probability of their formation. Such species would be formally akin to an enzyme transition state that is usually kinetically inferred or sometimes trapped with certain kinds of inhibitor. In disaggregated, ultrafiltered (20 nm pore size) preparations, less than 1% of the molar peptide concentration is inferred to be present as seeds or nuclei determined by the kinetics of fibril formation [101]. 

The capacitance determined from the initial slopes of the charging curve is about 10/a F/cm2. Taking the dielectric permittivity as 9.0, one could calculate that initially (at the OCP) an oxide layer of the barrier type existed, which was about 0.6 nm thick. A Tafelian dependence of the extrapolated initial potential on current density, with slopes of the order of 700-1000 mV/decade, indicates transport control in the oxide film. The subsequent rise of potential resembles that of barrier-layer formation. Indeed, the inverse field, calculated as the ratio between the change of oxide film thickness (calculated from Faraday s law) and the change of potential, was found to be about 1.3 nm/V, which is in the usual range. The maximum and the subsequent decay to a steady state resemble the behavior associated with pore nucleation and growth. Hence, one could conclude that the same inhomogeneity which leads to pore formation results in the localized attack in halide solutions. 

Muller, M. and Schick, M. (1996). Structure and nucleation of pores in polymeric bilayers a Monte Carlo simulation, J. Chem. Phys., 105, 8282-8292. 

The polymerization temperature, through its effects on the kinetics of polymerization, is a particularly effective means of control, allowing the preparation of macroporous polymers with different pore size distributions from a single composition of the polymerization mixture. The effect of the temperature can be readily explained in terms of the nucleation rates, and the shift in pore size distribution induced by changes in the polymerization temperature can be accounted for by the difference in the number of nuclei that result from these changes [61,62]. For example, while the sharp maximum of the pore size distribution profile for monoliths prepared at a temperature of 70 °C is close to 1000 nm, a very broad pore size distribution curve spanning from 10 to 1000 nm with no distinct maximum is typical for monolith prepared from the same mixture at 130°C [63]. 

Let us assume that the total surface of an electrode is in an active state, which supports dissolution, prior to anodization. The application of a constant anodic current density may now lead to formation of a passive film at certain spots of the surface. This increases the local current density across the remaining unpassivated regions. If a certain value of current density or bias exists at which dissolution occurs continuously without passivation the passivated regions will grow until this value is reached at the unpassivated spots. These remaining spots now become pore tips. This is a hypothetical scenario that illustrates how the initial, homogeneously unpassivated electrode develops pore nucleation sites. Passive film formation is crucial for pore nucleation and pore growth in metal electrodes like aluminum [Wi3, He7], but it is not relevant for the formation of PS. 

The process described above is expected to produce a random distribution of active and passive spots on the electrode interface. But the electrode surface may also be artificially patterned prior to anodization in order to form nucleation centers for pore growth. This may be a lithographically formed pattern in said passive film or a predetermined pattern of depressions in the electrode material itself, which become pore tips upon subsequent anodization. The latter case applies to silicon electrodes and is discussed in detail in Chapter 9, which is devoted to macropore formation in silicon electrodes. 

---