Spheres, growth

Zhang G, Schwartz JB, Schnaare RL, Sugita ET, Wigent RJ. Kinetics of sphere growth in marumerization. J China Pharm Univ 1990 21(2) 73-76. 

Stdber W, Fink A and Bohn E 1968 Controlled growth of monodisperse silioa spheres in the mioron size range J. Colloid Interface Sol. 26 62-9... 

Rouw P W and de Kruif C G 1989 Adhesive hard-sphere colloidal dispersions fractal structures and fractal growth in silica dispersions Phys. Rev. A 39 5399-408... 

Lonally, the templates were chosen by trial and error or exhaustive enumeration. A itafional method named ZEBEDDE (ZEolites By Evolutionary De novo DEsign) en developed to try to introduce some rationale into the selection of templates et al. 1996 Willock et al. 1997]. The templates are grown within the zeolite by an iterative inside-out approach, starting from a seed molecule. At each jn an action is randomly selected from a list that includes the addition of new (from a library of fragments), random translation or rotation, random bond rota-ing formation or energy minimisation of the template. A cost function based on erlap of van der Waals spheres is used to control the growth of the template ale ... 

Fig. 7.13, this shifts the vacancy—represented by the square-in the coordination sphere of the titanium to a different site. Syndiotactic regulation occurs if the next addition takes place via this newly created vacancy. In this case the monomer and the growing chain occupy alternating coordination sites in successive steps. For the more common isotactic growth the polymer chain must migrate back to its original position. 

The composition, properties, and size of soot particles collected from flame products vary considerably with flame conditions and growth time. Typically the C—H atomic ratio ranges from two to five and the particles consist of kregular chains or clusters of tiny spheres 10—40 nm in diameter with overall dimensions of perhaps 200 nm, although some may agglomerate further to much larger sizes. 

Crystals are ubiquitous. They vary enormously in form, size and shape, partly refleeting their internal strueture, partly their growth history. Partiele size and shape are quantified by use of eharaeteristie dimensions and shape faetors that, in eombination, permit ealeulation of important properties sueh as partiele volume (mass) and surfaee area. Relating them to the shape of ideal partieles, e.g. the sphere often approximates real partieles. Similarly, the size of a mass of partieles ean be expressed in terms of a eharaeteristie mean and spread. The voidage of a mass of partieles is influeneed by both these quantities. It will be shown in subsequent ehapters that these partiele eharaeteristies ean have a determining effeet on both their proeessing behaviour and properties in appli-eation. They are therefore very important for the proeess engineer or seientist to measure, prediet and eontrol in a partieulate erystallization proeess system. 

An intrinsic surface is built up between both phases in coexistence at a first-order phase transition. For the hard sphere crystal-melt interface [51] density, pressure and stress profiles were calculated, showing that the transition from crystal to fluid occurs over a narrow range of only two to three crystal layers. Crystal growth rate constants of a Lennard-Jones (100) surface [52] were calculated from the fluctuations of interfaces. There is evidence for bcc ordering at the surface of a critical fee nucleus [53]. 

Alder and Wainwright gave MD treatments of particles whose pair potential was very simple, typically the square well potential and the hard sphere potential. Rahman (1964) simulated liquid argon in 1964, and the subject has shown exponential growth since then. The 1970s saw a transition from atomic systems... 

The formation of a 3D lattice does not need any external forces. It is due to van der Waals attraction forces and to repulsive hard-sphere interactions. These forces are isotropic, and the particle arrangement is achieved by increasing the density of the pseudo-crystal, which tends to have a close-packed structure. This imposes the arrangement in a hexagonal network of the monolayer. The growth in 3D could follow either an HC or FCC struc-... 

By defining spheres which are nucleated at time, x, the time of growth becomes (t - x). If we now define Xext as the extrinsic amount per nucleus before growth steirts (note that it is not a radius in fact, it is the same x given in Ap.3.5.), then we have ... 

J. Lu.ssenhop and R. Fogel, Soil invertebrates are concentrated on roots. The Rhizo-sphere und Plant Growth (D. L. Keiser and P. B. Cregan, eds.), Kluwer Academic Publishers, Boston. 1991. p. 111. 

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