Nucleation, branching

Keywords Nanofiber Nucleation Branching Fiber network Additive... 

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. 

Type V isotherms of water on carbon display a considerable variety of detail, as may be gathered from the representative examples collected in Fig. 5.14. Hysteresis is invariably present, but in some cases there are well defined loops (Fig. 5.14(b). (t ), (capillary-condensed water. Extreme low-pressure hysteresis, as in Fig. 5.14(c) is very probably due to penetration effects of the kind discussed in Chapter 4. 

Lipson (1943, 1944), who had examined a copper-nickeMron ternary alloy. A few years ago, on an occasion in honour of Mats Hillert, Cahn (1991) mapped out in masterly fashion the history of the spinodal concept and its establishment as a widespread alternative mechanism to classical nucleation in phase transformations, specially of the solid-solid variety. An excellent, up-to-date account of the present status of the theory of spinodal decomposition and its relation to experiment and to other branches of physics is by Binder (1991). The Hillert/Cahn/Hilliard theory has also proved particularly useful to modern polymer physicists concerned with structure control in polymer blends, since that theory was first applied to these materials in 1979 (see outline by Kyu 1993). 

A natural mechanism for the local reduction of cell spacings (or creation of a new cell) is either a nucleation in one of the grooves (the liquid is supercooled) or, even more likely, the formation of a new cell out of a side branch in such a groove. Alternatively, tip-splitting of a cell may give the same result [121]. 

Gamer and Hailes [462] postulated a chain branching reaction in the decomposition of mercury fulminate, since the values of n( 10—20) were larger than could be considered consistent with power law equation [eqn. (2)] obedience. If the rate of nucleation is constant (0 = 1 for the generation of a new nuclei at a large number of sites, N0) and there is a constant rate of branching of existing nuclei (ftB), the nucleation law is... 

The strongly acceleratory character of the exponential law cannot be maintained indefinitely during any real reaction. Sooner or later the consumption of reactant must result in a diminution in reaction rate. (This behaviour is analogous to the change from power law to Avrami—Erofe ev equation obedience as a consequence of overlap of compact nuclei.) To incorporate due allowance for this effect, the nucleation law may be expanded to include an initiation term (kKN0), a branching term (k N) and a termination term [ftT(a)], in which the designation is intended to emphasize that the rate of termination is a function of a, viz. 

Fig. 16. Graphical representation of Arrhenius parameters for the low temperature decomposition of ammonium perchlorate (pelleted, orthorhombic, o, and cubic, , forms). Compensation behaviour is observed. Data from Jacobs and Ng [452]. N = nucleation, B = branching, G = growth processes.

Before discussing the effect of short-chain branching on the kinetics of crystallization process, it is necessary to revisit the theory of secondary nucleation and the concept of regimes as given by Lauritzen and Hoffmann... 

Figure 17 Effect of branching on the secondary nucleation and linear growth rates from the work of Lambert and Phillips [58]. The effect of branching on the Regime l-ll transition can also be seen. Reprinted with permission from Lambert and Phillips [58]. Copyright 1994, American Chemical Society.

Fragments MFs and nucleates assembly, regulated by Ca2+ Binds actin monomers and regulates MF assembly Binds actin monomers, inhibits MF formation, regulated by selected signal transduction pathways Nucleation of actin MF assembly in cortex and initiation of MF branches... 

To summarize, in the present scenario pure hadronic stars having a central pressure larger than the static transition pressure for the formation of the Q -phase are metastable to the decay (conversion) to a more compact stellar configuration in which deconfined quark matter is present (i. e., HyS or SS). These metastable HS have a mean-life time which is related to the nucleation time to form the first critical-size drop of deconfined matter in their interior (the actual mean-life time of the HS will depend on the mass accretion or on the spin-down rate which modifies the nucleation time via an explicit time dependence of the stellar central pressure). We define as critical mass Mcr of the metastable HS, the value of the gravitational mass for which the nucleation time is equal to one year Mcr = Miis t = lyr). Pure hadronic stars with Mh > Mcr are very unlikely to be observed. Mcr plays the role of an effective maximum mass for the hadronic branch of compact stars. While the Oppenheimer-Volkov maximum mass Mhs,max (Oppenheimer Volkov 1939) is determined by the overall stiffness of the EOS for hadronic matter, the value of Mcr will depend in addition on the bulk properties of the EOS for quark matter and on the properties at the interface between the confined and deconfined phases of matter (e.g., the surface tension a). 

B11 < B < l>1. Now, in addition to pure HS, there is a new branch of compact stars, the hybrid stars but the nucleation time r(MHs,max) to form a droplet of Q -matter in the maximum mass hadronic star, is of the same order or much larger than the age of the Universe. Therefore, it is extremely unlikely to populate the hybrid star branch. Once again, the compact star we can observe are, in this case, pure HS. 

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