Growth faces

PV growth faces similar challenges, since deregulation is likely to lower the cost of electric power from natural gas and coal. 

Fig. 2.2. A diamond-shaped crystal showing four sectors and the folds lying parallel to the (110) growth faces...

Fig. 3.7. Some of the common twins seen for polyethylene. Continuous and dashed lines depict (110) and (100) growth faces respectively...

Fig. 3.14. The profile of a lamellar growth face which may be obtained by using moving boundary conditions. The boundaries move with a constant velocity, h...

It is a condition of the Mansfield model that steps are not in principle obstructed from travelling across the entire growth face. This leads to a substrate length on (200) of polyethylene very much larger than that predicted for (110) ( (110) 50 nm). 

Fig. 4.1a-c. Various types of roughness which may occur on the growth face of a lamella (The details of the polymer are not shown), a All growth units are complete stems which are of the same length, b Stems may be of differing lengths, c Growth units are only parts of complete stems... 

Fig. 4.2a, b. Configurations of molecules which are unfavourable to further growth, a The growth face of a lamella is shown, on which a molecule has deposited but is prevented from reaching the length required for stability by other attachments elsewhere, b Two examples of possible cross-sections perpendicular to the growth front. The outermost depositions must be removed before further growth of the stable crystal... 

A very recent application of the two-dimensional model has been to the crystallization of a random copolymer [171]. The units trying to attach to the growth face are either crystallizable A s or non-crystallizable B s with a Poisson probability based on the comonomer concentration in the melt. This means that the on rate becomes thickness dependent with the effect of a depletion of crystallizable material with increasing thickness. This leads to a maximum lamellar thickness and further to a melting point depression much larger than that obtained by the Flory [172] equilibrium treatment. 

FIGURE 11 Synthesized high-quality diamond crystals, showing their typical growth faces. 

Doubts about the impact on crystallization of such processes have already been raised by the present author in a paper that, very gracefully, Gert Strobl allowed to be published in parallel with his own contribution that presented a different viewpoint [8]. In that paper, the preeminence of a more classical nucleation and growth scheme (Fig. 1) was advocated crystallization is viewed as a more sequential process in which incoming stems probe the crystal growth face and are accepted if they fulfill the correct criteria. If not, the incoming stems are rejected or must undertake conformational adjustments. In other words, the classical nucleation and growth process can be seen as dominated or controlled by the crystal (substrate structure, or... 

The structural relationship of this face with the substrate (Fig. 5b) illustrates the selection mechanisms that are at play during deposition of each and every incoming stem on a foreign crystalline substrate, and also, by extension, on the growth face of the polymer itself. 

Abstract Recent extensive experimental work and the limited theoretical studies of the phenomenon of self-poisoning of the crystal growth face are reviewed. The effect arises from incorrect but nearly stable stem attachments which obstruct productive growth. Experimental data on the temperature and concentration dependence of growth rates and... 

V Rate of step propagation on a crystal growth face (often also referred to as g)... 

Fig. 18 The model of elementary steps as used in the rate equation and Monte Carlo simulation treatments that reproduced the self-poisoning minimum. A cross-section (row of stems) normal to the growth face is shown. There are three elementary steps differing in their barrier and driving force attachment (rate A) and detachment (rate B) of segments equal to half the chain length, and partial detachment of an extended chain (rate C). The key self-poisoning condition is that attachment of the second half of an extended chain is allowed only if m = 1, i.e. an extended chain cannot deposit onto a folded chain (from [49] by permission of the American Institute of Physics)...

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. 

Fig. 26 Schematic view of the growth face of an extended-chain lamellar crystal poisoned by stems of half the chain length. The row-of-stems model can be applied with the row perpendicular to the growth face, as in the previous rough growth models to describe retardation of i (rowp), or parallel to the growth face to describe retardation of v (row q). (From [29], by permission of American Chemical Society)...

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