Pore branching

As illustrated in Fig. 8.19(5), individual pores, depending on the formation conditions, may propagate straight in the preferred direction with very little branehing or with formation of side pores, hi general, the conditions that favor the formation of small pores 

FIGURE 8.34. Preferential growth of pores n-Si misoriented 35° from (100) surface with back illumination. After Ronnebeck et 

TABLE 8.4. Shape of Individual Pore Bottoms Observed for the PS Formed under Different Conditions 

The degree of branching and interpore connection, similar to pore diameter, depends strongly on doping concentration. The most highly connected PS is found in the PS of lowly doped p type and the micro PS of illuminated n-Si, on which the pores are extremely small, less than a few nanometers. On the other hand, well-separated and straight pores are generally found on moderately or lowly doped n-Si. Under certain 

FIGURE 8.35. Straight pores with smooth wall formed on -Si in the dark in 2% HF at 6 V.  

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Morphology, which is determined by the distribution of materials in space, is the least quantifiable aspect of a material. It is thus very difficult to characterize morphology of PS, which has extremely rich details with respect to the range of variations in pore size, shape, orientation, branch, interconnection, and distribution. Qualitatively, the diverse morphological features of PS reported in the literature can be summarized by Figure 9 with respect to four major different aspects pore orientation, fill of macro pores, branching, and depth variation of a PS layer. 

Foam (5) is a collection of gas bubbles with sizes ranging from microscopic to infinite for a continuous gas path. These bubbles are dispersed in a connected liquid phase and separated either by lamellae, thin liquid films, or by liquid slugs. The average bubble density, related to foam texture, most strongly influences gas mobility. Bubbles can be created or divided in pore necks by capillary snap-off, and they can also divide upon entering pore branchings (5). Moreover, the bubbles can coalesce due to instability of lamellae or change size because of diffusion, evaporation, or condensation (5,8). Often, only a fraction of foam flows as some gas flow is blocked by stationary lamellae (4). 

Now consider the total material flux in a porous solid. We postulate a thoroughly cross-linked main pore network with singly attached dead-end pore branches. 

Fig. 1 shows the porous silicon structures formed on different silicon wafers. Porous silicon on p-type wafer is characteri d by a sponge-like structure with pore wall thickness of 2-4 nm and 5-6 rnn for wafers with resistivity of 12 and 0.03 Q cm, respectively (Fig. la,b). Porous silicon on n-type silicon (0.01 Q cm) shows a branch-like structure (Fig. lc,d). In this case mother pores branch out and form the daughter pores. The pore wall thickness is 7-10 nm for porous silicon anodized with the light exposition (Fig. Ic) and 15-20 nm for porous silicon anodized without the light exposition (Fig. Id). 

A single pore is evidently an oversimplified model of a catalyst particle A relatively stralghtforvard extension, accounting up to a certain extent for the pore size distribution, is the parallel pore model. This is still unsatisfactory with complex, multilayered catalysts and/or when blockage by metal or coke deposition occurs For such cases the location of the blockage matters and pore branching and types of interconnection between pores become of importance. 

The concept of template-assisted fabrication of nanowires is further illustrated in Fig. 30 where the pore branching created by hierarchical fabrication techniques (section 2.3) is mirrored by the branched pore structure developed in the metal nanowires, in this case copper nanowires. Provided there is clear passage for the plating solution, it is simple... 

This is a somewhat more advanced model and demonstrates the multiplicity of size of porosity that may exist within a porous carbon from micro to macroporosity (Figure 3.2). It suggests the possibility of transport of material (usually an adsorbate gas) through the widest of pores (the trunk) to the narrowest of pores (branches and twigs). 

Transitional pores have an effective radius between 16 and 2000 A and they can contribute a BET surface area of20-70 g h The effective radius of micro-pores is less than 20 A and can constitute 95% of the total specific BET area. The pore structure has the following pattern the macropores open out to the external surface of the particle, transitional pores branch off from macropores, and micropores, in turn, branch off from the transitional pores. 

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