Internal porosity definition

The resin internal porosity can be evaluated by using the definition of the hydraulic density (eq. 3.558) ... 

The Firestone flexometer method in D623 is not very specific. The standard test pieces are in the shape of a frustum of a rectangular pyramid but the use of any suitable shape is permitted when cut from products. The apparatus operates at 800 cycles/min and a range of compression loads and amplitudes of oscillation are possible, but no particular conditions are specified. The test piece is fatigued until a definite, but unspecified, decrease in the height of the test piece is reached, which is supposed to represent the onset of internal porosity. Parameters such as temperature rise and changes in compression are reported. 

In this book, we use alternately the chemical engineering and the chromatographic definitions of the internal porosity, the mobile phase and the equilibrium constant, depending on the choice made by the original authors whose work is discussed. We try to indicate clearly which definition has been used in each case. 

Note all the above definitions relate only to external surfaees internal area, due to porosity, requires further definition. 

If the solid is nonporous, VM is the space between the particles (the interparticle volume), but if it is porous, VM includes both the interparticle volume and the internal volume of the particles. (In some instances, the size of the pores in the solid may be too small to admit the analyte molecules, and thus the internal portions of the solid may not be accessible to the sample, but that is a complication we will ignore at present.) These two types of particle give rise to two definitions of porosity. 

The internal structure or polymorphic state represents the molecular arrangement within a crystal and is manifested in the form of a definite heat of fusion (AHf) value. External structure or crystal habit is the outer description of a crystal and is described by its length, width, thickness, and surface appearance (roughness, smoothness, and porosity). Crystal growth may be impeded by adjacent crystals growing simultaneously or contacting container walls. As a result, the development... 

In general (there are many exceptions), chemists and chemical engineers tend to use two different definitions for the mobile phase velocity and for the internal or particle porosity, and different units for the concentrations in the liquid and solid phases (see Section 2.3), hence different expressions for the equilibrium constant. While most papers dealing with the simple models derived from Eq. 2.2 do not need to distinguish between internal and external porosities (there is no... 

The apparent particle density, pp, is the ratio of the particle weight to the particle volume, or sum of the imaccessible volumes and the internal pore volume. This is the most practical definition. However, it carmot be as accurate as densities usually are because of the difficulty associated with defining accurately the external column porosity (see previous subsection),... 

The confusion that a combination of these different definitions can generate, together with the difficulties encoimtered in the determination of some of the column characteristics involved (particularly the internal and the external porosities) makes useful a careful consideration of these issues. Given the stage of sophistication that the modeling of chromatography has now reached, it is not possible to tolerate errors, confusions, or approximations in the definitions nor in the estimations of the critical parameters related to the porosities, the velocities, and the equilibrium constants, nor to accept that more errors be made in the estimation of these parameters than those that are always involved in any measurement process. 

In conclusion to this section on porosity of bulk powders, it seems that the indirect method of calculating its value from other powder properties, namely the bulk and particle densities, is adequate for most practical applications. The fact whether or not the porosity should include the internal pores of the particles is taken care of by selection of a suitable method for particle density measurement (section 2.4). Care must be taken to avoid a possible confusion between the definitions of porosity and void ratio. 

Since, ligand accessibility and template definition are maximal in stiff polymers, whilst good kinetics and rapid equilibration are favoured in flexible polymers, the choice of cross-linker must inevitably be a compromise [47], It should be pointed out that, in addition to the type and proportion of cross-linker involved, the porogenic solvent and method of polymerisation both also affect the macro structure of the polymer in terms of porosity and internal surface area. 

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