Surface-controlled growth

In both the equations for surface controlled growth rates we find... 

Figure 9. (a) Fits of Z(r) data (solid circles from TEM and open circles from SAXS) of uncapped ZnO nanorods to the Ostwald ripening (I3) model (solid curve), (b) Fits of Z(r) data (3olid circles from TEM and open circles from SAXS) of PVP-capped ZnO nanorods to the Ostwaid ripening (Z3) model (broken curve) and mixed diffusion-surface control growth (Z3 + Z2) model (solid curve). 

Fig. 15. Reaction model of the formation of ZrOj colloids covered by mediacrylic acid (ma) through a surface-controlled growth process...

Figure 3 Concept of ALD window, or temperature region for surface-controlled growth...

Nieminen M, Sajavaara T, Rauhala E, Putkonen M, Niinisto L. Surface-controlled growth of LaAlOs thin films by atomic layer epitaxy. J Mater Chem 2001 11 2340-5. 

Reactions of the general type A + B -> AB may proceed by a nucleation and diffusion-controlled growth process. Welch [111] discusses one possible mechanism whereby A is accepted as solid solution into crystalline B and reacts to precipitate AB product preferentially in the vicinity of the interface with A, since the concentration is expected to be greatest here. There may be an initial induction period during solid solution formation prior to the onset of product phase precipitation. Nuclei of AB are subsequently produced at surfaces of particles of B and growth may occur with or without maintained nucleation. 

Dehydration reactions are typically both endothermic and reversible. Reported kinetic characteristics for water release show various a—time relationships and rate control has been ascribed to either interface reactions or to diffusion processes. Where water elimination occurs at an interface, this may be characterized by (i) rapid, and perhaps complete, initial nucleation on some or all surfaces [212,213], followed by advance of the coherent interface thus generated, (ii) nucleation at specific surface sites [208], perhaps maintained during reaction [426], followed by growth or (iii) (exceptionally) water elimination at existing crystal surfaces without growth [62]. 

A more detailed picture of the temperature dependence of the growth is given in Figure 2.4, where the island density is plotted as a function of temperature. It can be seen that only in the temperature range from 207 to 288 K the growth is perfectly template controlled and the number of islands matches the number of available nucleation sites. This illustrates the importance of kinetic control for the creation of ordered model catalysts by a template-controlled process. Obviously, there has to be a subtle balance between the adatom mobility on the surface and the density of template sites (traps) to allow a template-controlled growth. We will show more examples of this phenomenon below. 

That not only an increased interaction energy at the traps can be responsible for a template-controlled growth but also an anisotropy of the surface diffusion... 

Before we discuss the template-controlled growth of model catalysts in more detail, we will have to consider a few aspects of STM imaging of these systems. This will be crucial for the characterization of the model catalyst surfaces. 

We define the linear growth rate Vg as the linear velocity of displacement of a crystal face relative to some fixed point in the crystal. vg may be known as a function of c and c , derived from the theory of transport control, and as a function of c and cs as well, derived from the theory of surface control. Then c may be eliminated by equating the two mathematical expressions... 

Fick s diffusion laws, depending on the shape of the liquid as determined by the particle surfaces (1,31-33). However, in such systems the rate of depletion of a supersaturated solution by diffusion controlled growth would be very fast, and if the rate is actually slow (measurable) the rate control is likely to be a surface process. 

If the transport process is rate-determining, the rate is controlled by the diffusion coefficient of the migrating species. There are several models that describe diffusion-controlled processes. A useful model has been proposed for a reaction occurring at the interface between two solid phases A and B [290]. This model can work for both solids and compressed liquids because it doesn t take into account the crystalline environment but only the diffusion coefficient. This model was initially developed for planar interface reactions, and then it was applied by lander [291] to powdered compacts. The starting point is the so-called parabolic law, describing the bulk-diffusion-controlled growth of a product layer in a unidirectional process, occurring on a planar interface where the reaction surface remains constant ... 

Matyjaszewski K, Miller PJ, ShuklaN, Immarapom B, Gelman A, LuokalaBB, Siclovan TM, Kickelbick G, Valiant T, Hoffmann H, Pakula T (1999) Polymers at interfaces using atom transfer radical polymerization in the controlled growth of homopolymers and block copolymers from silicon surfaces in the absence of untethered sacrificial initiator Macromolecules 32 8716-8724... 

The influence of surface tension on the diffusion-controlled growth or... 

---