Interconnecting pores

As Everett points out, however, the analogy of a pore as a narrownecked bottle is over-specialized, and in practice a series of interconnected pore spaces rather than discrete bottles is more likely. The progress of capillary condensation and evaporation in pores of this kind (cf. Fig. 3.13) has been discussed by de Boer, and more recently by Everett. ... 

The internal structure of the catalyst particle is often of a complex labyrinth-like nature, with interconnected pores of a multiplicity of shapes and sizes, In some cases, the pore size may be less than the mean free path of the molecules, and both molecular and Knudsen diffusion may occur simultaneously. Furthermore, the average length of the diffusion path will be extended as a result of the tortuousity of the channels. In view of the difficulty of precisely defining the pore structure, the particle is assumed to be pseudo-homogeneous in composition, and the diffusion process is characterised by an effective diffusivity D, (equation 10.8). 

EDI), and water to produce a group of biodegradable PU foams. The interconnected pores varied in size from 10 to 2 mm in diameter. Rabbit bone-marrow stromal cells cultured on the materials for up to 30 days formed multilayers of confluent cells and were phenotypically similar to those grown on tissue culture PS. It supported the adherence and proliferation of both bone-marrow stromal cells and chondrocytes in vitro. In subdermal implants the investigators found that the material showed infiltration of both vascular cells and connective tissue. 

Microporous. Microporous membranes are characterized by interconnected pores, which are small, but large in comparison to the size of small molecules. If the pores are of the order of size of the molecules for at least some of the components in the feed mixture, the diffusion of those components will be hindered, resulting in a separation. Molecules of size larger than the pores will be prevented from diffusing through the pores by virtue of a sieving effect. 

It is interesting to observe that a fair correlation can be found between the pore size evaluated by the Washbum-Laplace model and the pore size evaluated by the BJH model of nitrogen adsorption in the case of SBA-15 [12] and other materials with interconnected pores [13], In the case of gas adsorption, the surface defects are filled at a lower pressure and do not affect the pressure of capillary condensation [10]. However, the BJH model does not take into account the effects of curvature on condensation and systematically underevaluates the size of the mesopores [7, 14]. 

The first phase in the process is the formation of the sol . A sol is a colloidal suspension of solid particles in a liquid. Colloids are solid particles with diameters of 1-100 nm. After a certain period, the colloidal particles and condensed silica species link to form a gel - an interconnected, rigid network with pores of submicrometer dimensions and polymeric chains whose average length is greater than one micrometer. After the sol-gel transition, the solvent phase is removed from the interconnected pore network. If removed by conventional drying such as evaporation, so-called xerogels are obtained, if removed via supercritical evacuation, the product is an aerogel . 

The catalyst used for the conversion of methanol to gasoline is based on a new class of shape-selective zeolites (105-108), known as ZSM-5 zeolites, with structures distinctly different from other well-known zeolites. Apparently, the pore dimensions of the ZSM-5 zeolites are intermediate between those of wide-pore faujasites (ca. 10 A) and very narrow-pore zeolites such as Zeolite A and erionite (ca. 5 A) (109). The available structural data indicate a lattice of interconnecting pores all having approximately the same diameter (101). Hydrocarbon formation... 

For bone substitutes, it is very important that bioceramics have a considerable degree of porosity and particularly interconnected pores so that living bone grows rapidly into the pores. Special bone remodeling cells called osteoclasts and osteoblasts play an extremely important part of the process of rebuilding or repairing the bone. 

The first model of porous space as a 2D lattice of interconnected pores with a variation of randomness and branchness was offered by Fatt [220], He used a network of resistors as an analog PS. Further, similar approaches were applied in a number of publications (see, e.g., Refs. [221-223]). Later Ksenjheck [224] used a 3D variant of such a model (simple cubic lattice with coordination number 6, formed from crossed cylindrical capillaries of different radii) for modeling MP with randomized psd. The plausible results were obtained in these works, but the quantitative consent with the experiment has not been achieved. 

The observed small and interconnected pores are expected to perform as electrodes of supercapacitors. Cyclic voltammetry (CV) and galvanostatic charge/discharge curves were used to characterize the capacitive properties the resulting data in simple acid (1 mol L 1 II2S0/() are shown in Fig. 7.11. 

However, this porosity takes into account all the open pores—even those that are not connected between each other, which are useless in fuel cell operation. Therefore, the effective porosity, which counts only the interconnected pores, is more critical when determining the optimal diffusion layer in a fuel cell. This porosity can be determined by using volume filtration techniques. For example, a porous sample is immersed in a liquid that does not enter inside the pores (e.g., mercury at low pressures) and then the total volume of the material can be determined. Next, the specimen is put inside a container of known volume that contains an inert gas, and the changed pressure is recorded. After this, a second evacuated chamber of known volume is connected to the system, and the new pressure is recorded. With these pressures and the ideal gas law, the volume of open pores and thus the effective porosity can be determined [195]. 

Figure 2.1. Schematic representation of main types of pore structures and membranes. A and B homogeneous unsupported straight pores C supported asymmetric, interconnected pores D a photograph of a membrane of the type (c). (SCT-support+y-AljOj top layer UT Twente)...

The separator pore structure is usually very complex. It consists of a porous network of interconnected pores, which are filled with liquid electrolyte. A complete description of the pore structure would require a very intricate model. Simulations are only practically possible if the structure is represented by a simplified quasi-continuum involving a few param-... 

As discussed above, hysteresis loops can appear in sorption isotherms as result of different adsorption and desorption mechanisms arising in single pores. A porous material is usually built up of interconnected pores of irregular size and geometry. Even if the adsorption mechanism is reversible, hysteresis can still occur because of network effects which are now widely accepted as being a percolation problem [21, 81] associated with specific pore connectivities. Percolation theory for the description of connectivity-related phenomena was first introduced by Broad-bent et al. [88]. Following this approach, Seaton [89] has proposed a method for the determination of connectivity parameters from nitrogen sorption measurements. 

Emulsion derived foams prepared via the concentrated emulsion pathway are characterized by highly interconnected pores, thus offering density values as low as 0.02 g/cm and a relatively narrow size distribution in the pm-range resulting from a thermodynamically stable system. This principle allows for the synthesis of organic as well as inorganic foams that offer a wide range of appHcations [20, 21]. Recently such technique has been applied to form injectable siloxane foams where the emulsified liquid was removed supercritically in order to avoid pore collapse [22]. 

In contrast to the highly interconnected pores mentioned previously, closed pores can also be obtained by microemulsion polymerization if the initial volume fraction of the dispersed phase is kept lower than 30%. Recently two systems have been reported where the polymerization of the continuous phase and the subsequent removal of the Hquid dispersed phase resulted in the formation... 

Polymeric membranes with highly interconnected pores have been produced commercially for more than 30 years based on a phase inversion process. These... 

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