Three-dimensional phase formation

In the fourth part of the book the problem of three-dimensional phase formation and growth by overpotential deposition (OPD) is presented. Thermodynamic and kinetic aspects are considered. The atomistic approach is discussed and illustrated on bare and UPD modified substrates. 

A fiorther advantage of electrochemical in-situ SPM studies of two- and three-dimensional phase formation processes is the possibility of controlling accurately the supersaturation or undersaturation, Ap, which can be correlated, in the absence of other kinetic hindrances with overpotential and underpotential, respectively [11] ... 

We must note that equation (2.9) represents a very general formula for/ and can be applied to any particular case of two-dimensional or three-dimensional phase formation, both on a like and on a foreign substrate, if ct)+ and fii ate expressed through appropriate physical quantities. 

The fundamental behaviour of stationary phase materials is related to their solubility-interaction properties. A hydrophobic phase acts as a partner to a hydrophobic interaction. An ionic phase acts as a partner for ion-ion interactions, and surface metal ions as a partner for ligand complex formation. A chiral phase partners chiral recognition, and specific three-dimensional phases partner affinity interactions. 

Chrysikopoulos CV,Lee KY (1998) Contaminant transport resulting from multicomponent phase liquid pool dissolution in three-dimensional subsurface formations. J Contam Hydrol 31 1-21... 

As the amount of metal cation or anion sorbed on a surface (surface coverage or loading, which is affected by the pH at which sorption occurs) increases, sorption can proceed from mononuclear adsorption to surface precipitation (a three-dimensional phase). There are several thermodynamic reasons for surface precipitate formation (1) the solid surface may lower the energy of nucleation by providing sterically similar sites (McBride, 1991) (2) the activity of the surface precipitate is less than 1 (Sposito, 1986) and (3) the solubility of the surface precipitate is lowered because the dielectric constant of the solution near the surface is less than that of the bulk solution (O Day et al., 1994). There are... 

It has been noted above that phase separation in thermoplastics is a common occurrence when two or more polymers are mixed and that miscibility is the uncommon event. This is exploited in toughening of thermosets by elastomers when phase separation occurs during the reaction that leads to three-dimensional network formation. If macroscopic phase separation is not desired then it is possible to achieve a different microscopic morphology and in some cases maintain some features of miscibility... 

The formation of two- and three-dimensional phases on electrode surfaces is a topic of central importance in interfacial electrochemistry. It is of relevance not only to hmdamental problems, such as the formation of ionic and molecular adsorbate films, but also to areas of great technological interest, such as thin-film deposition, self-assembly of monolayers, and passivation. So far, phase formation in electrochemical systems has been studied predominantly by kinetic measurements using electrochemical or spectroscopic techniques. In order to understand and control these processes as well as the resulting interface structure better, however, improved... 

Cells are often implanted or seeded into an artificial structure capable of supporting three-dimensional tissue formation. These structures, typically called scaffolds, are often critical, both ex vivo as well as in vivo, to recapitulating the in vivo milieu and allowing cells to influence their own microenvironments. Scaffolds usually serve at least one of the following purposes (i) allow cell attachment and migration, (ii) deliver and retain cells and biochemical factors, (iii) enable diffusion of vital cell nutrients and expressed products, and (iv) exert certain mechanical and biological influences to modify the behavior of the cell phase. 

Stabilization of the Cellular State. The increase in surface area corresponding to the formation of many ceUs in the plastic phase is accompanied by an increase in the free energy of the system hence the foamed state is inherently unstable. Methods of stabilizing this foamed state can be classified as chemical, eg, the polymerization of a fluid resin into a three-dimensional thermoset polymer, or physical, eg, the cooling of an expanded thermoplastic polymer to a temperature below its second-order transition temperature or its crystalline melting point to prevent polymer flow. 

Production of net-shape siUca (qv) components serves as an example of sol—gel processing methods. A siUca gel may be formed by network growth from an array of discrete coUoidal particles (method 1) or by formation of an intercoimected three-dimensional network by the simultaneous hydrolysis and polycondensation of a chemical precursor (methods 2 and 3). When the pore Hquid is removed as a gas phase from the intercoimected soHd gel network under supercritical conditions (critical-point drying, method 2), the soHd network does not coUapse and a low density aerogel is produced. Aerogels can have pore volumes as large as 98% and densities as low as 80 kg/m (12,19). 

Because of the expanded scale and need to describe additional physical and chemical processes, the development of acid deposition and regional oxidant models has lagged behind that of urban-scale photochemical models. An additional step up in scale and complexity, the development of analytical models of pollutant dynamics in the stratosphere is also behind that of ground-level oxidant models, in part because of the central role of heterogeneous chemistry in the stratospheric ozone depletion problem. In general, atmospheric Hquid-phase chemistry and especially heterogeneous chemistry are less well understood than gas-phase reactions such as those that dorninate the formation of ozone in urban areas. Development of three-dimensional models that treat both the dynamics and chemistry of the stratosphere in detail is an ongoing research problem. 

At higher temperatures, other degrees of freedom than the radius R must also be considered in the fluctuation. However, this becomes critical only near the critical point where the system goes through a phase transition of second order. The nucleation arrangement described here is for heterogeneous or two-dimensional nucleation on a flat surface. In the bulk, there is also the formation of a three-dimensional nucleation, but its rate is smaller ... 

For rigid-chain crystallizable polymers, spontaneous transition into the nematic phase is accompanied by crystallization intermolecular interactions should lead to the formation of a three-dimensional ordered crystalline phase. 

In each of the composition diagrams in Fig. 14.2, the numbers represent a series of reactions run at a defined composition and temperature. These are isometric sulfur slices through three-dimensional K/P/RE/S quaternary phase diagrams. As just one example of what we have studied. Table 14.1 identifies the compositions at each point and the resulting phase(s). We have rigorously studied how phase formation is dependent upon the compositions of reactions for the rare-earth elements Y, Eu, and La and we have also discovered key structural relationships between the rare-earth elements, indicating a significant dependence on rare-earth and alkali-metal size for sulfides and selenides. 

Johans et al. derived a model for diffusion-controlled electrodeposition at liquid-liquid interface taking into account the development of diffusion fields in both phases [91]. The current transients exhibited rising portions followed by planar diffusion-controlled decay. These features are very similar to those commonly observed in three-dimensional nucleation of metals onto solid electrodes [173-175]. The authors reduced aqueous ammonium tetrachloropalladate by butylferrocene in DCE. The experimental transients were in good agreement with the theoretical ones. The nucleation rate was considered to depend exponentially on the applied potential and a one-electron step was found to be rate determining. The results were taken to confirm the absence of preferential nucleation sites at the liquid-liquid interface. Other nucleation work at the liquid-liquid interface has described the formation of two-dimensional metallic films with rather interesting fractal shapes [176]. 

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