Three dimensional phase growth

Jeong, J.-H., N. Goldenfeld, and J. Dantzig. 2001. Phase field model for three dimensional dendritic growth with fluid flow. Phys. Rev. E 64 041602. 

R. Yamamoto and K Nakanishi, Computer Simulation of Vapor-liquid Phase Separation in two- and three-dimensional Fluids Growth Law of Domain Size, Phys. Rev. B 49 (1994) 14958-14966 II. Domain Structure, Phys. Rev. B 51... 

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. 

The self-assembly of natural and synthetic multifunctional unimers occurs, in fact, by a combination of classical molecular recognition and growth mechanisms. Self-assembled, reversible structures include linear, helical, columnar, and tubular polymers micelles monolayers and three-dimensional phases and networks. Self-assembled systems based on an interplay between covalent chains and supramolecular interactions are also important. Typical examples are side-chain SPs (Chapter 5), host-guest polymeric composites and dendrimers (Chapters 2 and 7), polymers with mechanical bonds (Chapter 8), and block copolymers (Chapters 9-11). 

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). 

In most carbon and graphite processes, the initial polymerization reactions occur in the Hquid state. The subsequent stages of crystal growth, heteroatom elimination, and molecular ordering occur in the soHd phase. The result is the development of a three-dimensional graphite stmcture. 

A continuous lipidic cubic phase is obtained by mixing a long-chain lipid such as monoolein with a small amount of water. The result is a highly viscous state where the lipids are packed in curved continuous bilayers extending in three dimensions and which are interpenetrated by communicating aqueous channels. Crystallization of incorporated proteins starts inside the lipid phase and growth is achieved by lateral diffusion of the protein molecules to the nucleation sites. This system has recently been used to obtain three-dimensional crystals 20 x 20 x 8 pm in size of the membrane protein bacteriorhodopsin, which diffracted to 2 A resolution using a microfocus beam at the European Synchrotron Radiation Facility. 

The growth of vanadium oxide overlayers on Rh(l 11) converges after a number of intermediate stages to the formation of a three-dimensional bulk-like epitaxial V203 film [90], which is oriented with the (0 0 01) plane of its corundum structure parallel to the Rh(l 1 1) substrate surface. The V203 phase is the thermodynamically stable... 

Polymer crystallization is usually divided into two separate processes primary nucleation and crystal growth [1]. The primary nucleation typically occurs in three-dimensional (3D) homogeneous disordered phases such as the melt or solution. The elementary process involved is a molecular transformation from a random-coil to a compact chain-folded crystallite induced by the changes in ambient temperature, pH, etc. Many uncertainties (the presence of various contaminations) and experimental difficulties have long hindered quantitative investigation of the primary nucleation. However, there are many works in the literature on the early events of crystallization by var-... 

Despite the vast quantity of data on electropolymerization, relatively little is known about the processes involved in the deposition of oligomers (polymers) on the electrode, that is, the heterogeneous phase transition. Research - voltammetric, potential, and current step experiments - has concentrated largely on the induction stage of film formation of PPy [6, 51], PTh [21, 52], and PANI [53]. In all these studies, it has been overlooked that electropolymerization is not comparable with the electrocrystallization of inorganic metallic phases and oxide films [54]. Thus, two-or three-dimensional growth mechanisms have been postulated on the basis that the initial deposition steps involve one- or two-electron transfers of a soluted species and the subsequent formation of ad-molecules at the electrode surface, which may form clusters and nuclei through surface diffusion. These phenomena are still unresolved. 

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