Shape of pores

Pore shape is a characteristic of pore geometry, which is important for fluid flow and especially multi-phase flow. It can be studied by analyzing three-dimensional images of the pore space [2, 3]. Also, long time diffusion coefficient measurements on rocks have been used to argue that the shapes of pores in many rocks are sheetlike and tube-like [16]. It has been shown in a recent study [57] that a combination of DDIF, mercury intrusion porosimetry and a simple analysis of two-dimensional thin-section images provides a characterization of pore shape (described below) from just the geometric properties. 

Affects shape of pores and thus fluid-flow patterns. 

Shapes of pores have a great effect on diffusion through them. They are greatly varied and usually cannot be observed directly for commercial materials. For theoretical comparisons they may be assumed parallel cylinders of some mean diameter. Diffusion experments also have been performed with parallel small capillaries. 

Depending on substrate orientation and formation condition, individual pores may have different shapes. The shape of the pores formed on (100) substrate is a square bounded by 011 planes with comers pointing to the <100> directions.14,77 The shape of individual pores formed on n-Si tends to change from circular to square to star-like and to dendrite-like with increasing potential.20 Low formation voltage tends to favour circular shape while high voltage favours star-like shape. Near perfect square shape of pores can be obtained for the PS formed on n-Si under certain conditions. 

The shape of pores can be square, dendritic, circular, and star-like. 

The size and shape of pores, and their distribution also contribute to the separation process. It is obvious that the pore size and pore volume influence markedly the specific surface area. 

Pores may be present as structural features (e. g. between domains) or as a result of aggregation of particles. They may also be the result of partial dehydroxylation (oxide hydroxides) or dissolution. Although the shapes of pores can be quite variable, there are some definite, basic forms. The commonest of these are 1) slit shaped, the walls of which may or may not be parallel 2) ink bottle which are closed upon all sides but one from which a narrow neck opens and 3) cylindrical. Upon partial dissolution, pores bounded by well-defined crystal planes (e. g. 102 in goethite) develop (Chap. 12). 

Figure 16.14 Cross section of equilibrium shape of pore on grain boundary as in...

Many catalysts are porous, a feature which greatly increases their surface area [48]. Pores above 50 nm in width are termed macropores, those with widths below 2 nm are called micropores, and those of intermediate size are mesopores. Not only the size but also the shape of pores can vary widely and common descriptions refer to open and closed cylinders, slits, cones, spheroidal cavities, and ink-bottle shapes. The type of pore can frequently be identified from the shape of the hysteresis loop in physical gas adsorption experiments [32, 49], The absence of hysteresis indicates that the pores are closed perfect cylinders, or that the solid is microporous or, indeed, non-... 

For a given state of the solid surface the eneTgy of immersion is simply proportional to the surface area available to the immersion liquid for any size and shape of pore. 

In order to convert the measured lifetimes into dimensions (and shapes) of the pores, additional information is required. A basic shape of pores has to be assumed. The single parameter (lifetime) is not sufficient to determine a three dimensional object. Here simple spherical shapes for isolated pores and channels (tubes) with circular cross sections are assumed. The diameter of the pores can be related to the classical mean free path ( ) of a particle in such objects of volume V and surface area f [46],... 

Results obtained by the above method could be presented in due form of summary volume curves or histograms. Such curves with adsorption or mercury porosimetry results are used together to calculate of volume distribution curves. More advanced analysis of density measurements results enable us determination of shape of pores. 

The bottom of pores is always eurved, varying from a shallowly eurved semicircle to an elongated eone depending on the formation conditions as pictured in Fig. 8 22 g 4 sjjows that the shape of pore bottoms, in terms of the ratio of... 

M. Brun, A. Lallemand, J.F. Quinson and C. Eyraud, A new method for the simultaneous determination of the size and shape of pores the thermoporometry. Thermochim. Acta, 21 (1977) 59. 

Compaction conditions affect the total pore volume and shape of pores for some materials. In general, pore volume is smaller for a catalyst granulated by a tabletting machine than that by a pellet press. Partial pore closure is possible for tablets having a very high crush strength. 

A complication arises because isotherms display hysteresis as shown in Fig. 7.17. Much has been written on the origin of these hysteresis cur xs, which provide information about the shape of pores. There are two extremes. Cylindrical or slit-shaped pores (Fig. 7.18a) give moderate hysteresis, such as Fig. 7.17a. The adsorption branch of the isotherm results from adsorbed layers on the cylindrical walls, which thicken until a miniscus forms. Applicability of the Kelvin equation to such a microscopic system is doubtful. Upon desorption, however, evaporation occurs at the larger miniscus and the Kelvin equation is valid. In this case, pore size distributions from the desorption branch arc recommended as more reliable. The other extreme... 

As the surface tension of the pore liquid was lowered in these experiments, the total pore volume increased. Nitrogen adsorption indicated that the pores also became larger. This is an inevitable outcome of maintaining constant surface area (from the definition of a cylinder, or any other shape of pore, pore volume must be proportional to pore area multiplied by pore diameter). The least active silica in the series, which had the lowest pore volume, also contained most of its volume within small pores (less than 60 A in diameter). In contrast, the most active samples, which were dried by organic solvent extraction, had the highest total pore volumes and most of that volume was inside much larger (meso) pores. 

BET Adsorption Data. A wealth of information about the size and shape of pores may be obtained from adsorption isotherms where the mols of nitrogen adsorbed on the membrane are measured as a function of pressure. However, the use of this techniques is not widespread due to the tedious regimen required in gas adsorption measurements. Further, the hysteresis effects make conclusions about pore-structure ambiguous. 

Ink Bottle Pore A description of one kind of shape of pore in a porous medium, in which a narrow throat is connected to a larger pore body. See also Porous Medium. 

Some authors have found that the shape of pores in activated carbons can play an important role in the catalytic process when it is used as support, in opposition to other solids with pores that are not slit shaped. This is the case for Laine et al. 

Theoretically the use of the desorption branch of the isotherm is applicable for materials with pores predominandy comprised of independent capillaries, because this was the system used for the deduction of the Kelvin equation. If bottle-hke pores are anticipated, where the Hquid in the narrow opening prevents evaporation of the condensate from larger compartments, it is better to calculate pore size distribution using the adsorption branch of the hysteresis loop. Since the shape of pores is usually a priori unknown, the selection of the adsorption or desorption branch of the hysteresis loop largely remains arbitrary. Concerning the choice between dWo/dD or dfFo/dlog(D) plots, which by definition are different functions, one may note that the difference may be small for materials with narrow pore size distribution, but become more significant for a broad and unsymmetrical pore size distribution. 

In the case of Fig. 7.27 the dWo/dD plot obtained from the adsorption branch characterizes a polymer with wide pore size distribution, with pores ranging from 17 to about 200 A. The same plot calculated from the desorption branch would indicate narrow pore size distribution, with pores having diameters from 17 to 60 A with two pseudo-maxima located between 40 and 50 A. A similar shape of pore distribution results from the dFFo/dlog(D) presentation of the desorption branch, while the dlTo/dlog(D) plot evaluated from the adsorption branch would indicate a wider pore size distribution, with pore diameters from 17 to 300 A and a noticeable predominance of pores with diameters of30—100 A. Thus, the desorption branch of the isotherm points to a narrower pore size distribution compared to results of the analysis of the nitrogen adsorption isotherm of the same polymer sample. 

In 1956, Selwood published the results of studies by the spin-echo method, in which the response of the nuclear magnetization to a series of pulses is measured, for methanol, ethanol, water, and n-hexane adsorbed on y-a l UBiina, silica-alumina, MnO, and CuO, all presumably diamagnetic materials ( ). He found for the proton relaxation time marked reductions over those in the liquid phase, but pointed out that many uncertainties remained, such as the effects of traces of paramagnetic impurities and of the shapes of pores in which the adsorbate molecules were located ... 

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