External porosity

Chromatographic use of monolithic silica columns has been attracting considerable attention because they can potentially provide higher overall performance than particle-packed columns based on the variable external porosity and through-pore size/skeleton size ratios. These subjects have been recently reviewed with particular interests in fundamental properties, applications, or chemical modifications (Tanaka et al., 2001 Siouffi, 2003 Cabrera, 2004 Eeltink et al., 2004 Rieux et al., 2005). Commercially available monolithic silica columns at this time include conventional size columns (4.6 mm i.d., 1-10 cm), capillary columns (50-200 pm i.d., 15-30 cm), and preparative scale columns (25 mm i.d., 10 cm). 

External porosity is above 60% for conventional size columns prepared in a test tube (Al-Bokari et al., 2002), and above 80% for those prepared in a capillary. 

Gzil, R, Vervoort, N., Baron, G.V., Desmet, G. (2004). General rules for the optimal external porosity of LC supports. Anal. Chem. 76, 6707-6718. 

The lumped kinetic model can be obtained with further simplifications from the lumped pore model. We now ignore the presence of the intraparticle pores in which the mobile phase is stagnant. Thus, p = 0 and the external porosity becomes identical to the total bed porosity e. The mobile phase velocity in this model is the linear mobile phase velocity rather than the interstitial velocity u = L/Iq. There is now a single mass balance equation that is written in the same form as Equation 10.8. 

Effective length between the inlet and the detection window. Total length, 33.5 cm s External porosity... 

Assuming an external porosity of 0.4 for the laboratory column, the zero retention time associated to the pulse test is... 

To check the quality of the columns of the SMB pilot plant, a pulse test is performed on all the columns connected in series, the eluent flow rate being fixed to 4 liters/h. The total bed volume of the pilot plant being 2.016 liters, assuming an external porosity of 0.4, the zero retention time associated to... 

External porosity Mobile phase viscosity Column section... 

In this context, the SPM techniques (and especially STM and AFM) appear, a priori, ideally suited for the direct visualization of the porous structure of materials at scales which are not so readily accessible by other means (e.g., scaiming and transmission electron microscopies). However, the performance of such a task is confronted with two major limitations. The first one arises from the fact that detection with SPM is exclusively restricted to the outermost surface of the sample. Accordingly, this implies that only the most external porosity of the material can be probed, whereas no information on the bulk (inner) porosity, which might not be identical to the former, is revealed. The second drawback is related to the finite dimensions of the probing tip, which limits the size of the voids (pores) physically accessible (and thus detectable) by the tip on the sample surface. Obviously, pores significantly smaller than the tip diameter will pass uimoticed to the instrument when the surface is scanned. As a specific example, the tips normally employed in AFM are not sharp enough to provide access to the whole mesopore range (between 2 and 50 nm). 

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... 

Internal porosity. The total porosity, e or ej, is the volume fraction of the column that is available to the mobile phase. The external porosity, e, is the volume fraction of the column that is available to the mobile phase percolating through the bed while the internal or particle porosity, characterizes the volume available to the stagnant mobile phase. Chromatographers define the internal porosity of the column as the difference between the total and the external porosities. So, for chromatographers. 

This definition is more complex to use because it requires the actual knowledge of the external porosity that is difficult to measure directly. 

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. 

Such beds have obviously a bimodal pore size distribution (see Figure 5.2), with a mode of large pores that have an average size of the order of a quarter to a third of the particle diameter and extending between 10 and 50% of this diameter (see Figure 5.2a) and which corresponds to the interparticle space or external porosity of the bed [61]. The small pores are all smaller than 100 nm for the pack-... 

This noninvasive method could allow the differentiation between the various packing materials used in chromatography, a correlation between the chromatographic properties of these materials that are controlled by the mass transfer kinetics e.g., the coliunn efficiency) and the internal tortuosity and pore coimectivity of their particles. It could also provide an original, accurate, and independent method of determination of the mass transfer resistances, especially at high mobile phase velocities, and of the dependence of these properties on the internal and external porosities, on the average pore size and on the parameters of the pore size distributions. It could be possible to determine local fluctuations of the coliunn external porosity, of its external tortuosity, of the mobile phase velocity, of the axial and transverse dispersion coefficients, and of the parameters of the mass transfer kinetics discussed in the present work. Further studies along these lines are certainly warranted. 

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