Quantitative Description of Pore Structures

It is useful at this stage to define pore structure and terminology. Here again we mainly follow the recommendations for the characterisation of porous solids recently proposed by lUPAC [5,9]. 

Porosity is defined as the fraction e of the total volume of the sample which is attributed to the pores detected by the method used 

The specific surface area is defined as the accessible area of solid surface per unit mass of material. It is also dependant on the method employed and the size of the probe used (e.g. adsorbate, molecular probe, wavelength of radiation, etc.). The recorded value will also depend on the assumptions inherent in the simplified models applied to interpret experimental data. This consideration is of particular significance for materials containing micropores. 

This definition is based on different physical adsorption phenomena of gases in pores of different size. Adsorption interactions of adsorbates are stronger in micropores and modify the bulk properties (density, surface tension) of the adsorbed fluids. The maximum size of ultramicropores corresponds to the bilayer thickness of nitrogen molecules adsorbed on a solid surface (2 x 0.354 nm). 

Usually the pores in a material do not have the same size but exist as a distribution of size which can be wide or sharp. We can characterise a film by a nominal or an absolute pore size. In fact this definition rather characterises the size of the particles or molecules retained by the layer. Pore size distribution is classically represented by the derivatives dSp/dfp or dUp/drp as a function of Fp (pore radius) where Sp and Vp are respectively the wall area and volume of the pores. The size in question is here the radius, which implies that the pores are known to be, or assumed to be, cylindrical. In other cases, Fp should be replaced by the width. 

---

In this section these relationships will be explored in more detail with particular emphasis on the porous properties of membranes and their characterisation. Firstly we will present the general definitions and terminology used to describe porous media. The origin of porosity in inorganic materials will also be outlined and related to a quantitative description of pore structures in... 

The measurement of the permeability of non adsorbed gases is classically used to determine the range of pore size in membranes (macro, meso or micropores). Indeed by plotting the permeability as a function of gas pressure, a straight line is usually obtained whose slope gives an indication of the gas transport mechanism in the membrane. A quantitative description of pore structure can be attempted from the results. 

---