Radial growth

Suppose we define the rate of radial growth of the crystalline disks as r. Then disks originating from all nuclei within a distance rt of an arbitrary point, say, point X in Fig. 4.6a, will reach that point in an elapsed time t. If the average concentration of nuclei in the plane is N (per unit area), then the average number of fronts F which converge on x in tliis time interval is... 

From microscopic measurements of the rates of nucleation and of growth of particles of barium metal product, Wischin [201] observed that the number of nuclei present increased as the third power (—2.5—3.5) of time and that the isothermal rate of radial growth of visible nuclei was constant. During the early stages of reaction, the acceleratory region of the a—time plot obeyed the power law [eqn. (2)] with 6 temperature coefficients of these processes were used by Wischin [201]... 

After a critically sized nucleus is formed, it starts to grow. Under the same hypothesis stated above for chronoamperometric growth, and taking into account that the radial growth of each cylinder occurs at the same time that the overpotential (tj) rises owing to the potential sweep (o) ... 

In this paper, TiCU was oxidized in the flow reactor at various temperature and gas flow rate. The wall scales were characterized by scan electron microscopy and X-ray diffraction. The effects of reactor wall surface state, radial growth of scale layer and reactor axial temperature distribution on scaling formation were discussed. At the same time, the mechanism of scaling on the reactor wall was explored furthermore. 

Mogi, 1., Okubo, S. and Nakagawa, Y. (1995) Dense radial growth of silver metal leavesin a high magnetic field. J. Phys. Soc. Jpn., 60, 3200-3202. 

Under internal pressure a vessel will expand slightly. The radial growth can be calculated from the elastic strain in the radial direction. The principal strains in a two-dimensional system are related to the principal stresses by ... 

Recently, the Okada group described a new class of polymerization systems [43] oligoglycopeptide-type sugar-balls were obtained by a radial growth polymerization (RGP) of a-amino acid AT-carboxyanhydrides with PAMAM dendrimers of different generations. 

K. Aoi, K. Tsutsumiuchi, A. Yamamoto, and M. Okada, Globular carbohydrate macromolecule sugar balls 3. Radial-growth polymerization of sugar-substituted x-amino acid N-carboxyanhydrides (glyco-NCAs) with a dendritic initiator, Tetrahedron, 53 (1997) 15415-15427. 

Yoshikawa, H. Myelin-associated oligodendrocytic basic protein modulates the arrangement of radial growth of the axon and the radial component of myelin. Med. Electron Microsc. 34,160-164, 2001. 

They therefore finally appear as polyhedra. Because of their radial growth the fibrillar or lamellar crystals have only little space-filling ability as they move away from the central nucleus. Typically for spherulitic structures, an irregular noncrystallo-graphic branching usually at small angles can be observed. 

Figure 5.9 shows the time evolution of the radii of selected 2D spherulites from Fig. 5.8. We observe that the process is non-linear and accelerated, (fR/df > 0. It is also interesting to notice that, at a given time, the radial growth velocity Ur = dR/dt (slope) is nearly the same for all spherulites, which implies that it depends on the deposition time and certainly not on the radius of the spherulites. In the case discussed here the thickness of the film is increasing with time because of continuous exposure to the molecular beam. The non-linearity is more pronounced at the beginning of the experiment (roughly between 250 and 350 s) and the velocity nearly tends towards an asymptotic value, so that 2D spherulites that are formed last show almost linear growth.

The observed non-linear radial growth of the spherulites can be described in terms of a thickness-dependent growth law given by the expression ... 

The height and growth rate from the vapour phase are assumed to be identical for both amorphous and crystalline phases. Taking into account only the in-plane radial growth resulting from the lateral incorporation of amorphous material, the number dA of molecules incorporated into the crystalline spheruhte contained in a volume dV is Qr 2n Rh t) dR, where dR represents the increase of the radius and... 

TaUe nL Radial Growth of A, flavus as a Percent of Control After Two Days in Contact with Some Selected Volatiles (Adapted from 79)... 

Radial growth (cm) of the fungus in a Petii plate on solid medium Mean SD for 3 replicates/tested level. 

Time Cone Vc for Isotropic, Time-Dependent Growth Rate R t). The time cone s geometry is given by simple relations. For isotropic (i.e., radial) growth, at time t the radius of a transformed region nucleated at an earlier time r is given by... 

Weisel, J. W., Nagaswami, C., and Makowski, L. (1987). Twisting of fibrin fibers limits their radial growth. Proc. Natl. Acad. Sci. USA 84, 8991-8995. 

A solute (additive) can be located in reverse micelles in different solubilization sites in the water core, in the interfacial region or in the bulk solvent. Solubilization into the water cores increases the inner volume at constant interfacial area, resulting in radial growth. If the micelle is too small to receive a solute molecule without deformation, e.g., at low water content, a segregation occurs between small free molecules and the large objects which are covered with surfactant (Chatenay et al., 1987 Encinas and Lissi, 1986 Pileni et al., 1985). 

The models used to describe self-poisoning kinetics (Figs. 18 and 19) are based on Sadler s row of stems normal to the growth face ( radial growth ). However, it can be equally applied to step propagation, i.e. tangential growth [29,61]. The two types of rows, to both of which the models in Sect. 4.1 could be applied, are schematically illustrated in Fig. 26. 

TABLE 2. Radial growth inhibition data of arylstannanes (ED50, mgl , errors given in paren-thesis)a73 74... 

---