Size pores

Size exclusion effects can influence the measurement of chromatographic parameters in all types of liquid chromatography. Size exclusion effects occur because of the existence of pores in the stationary phase which are filled with mobile phase and are too small for large sample molecules to enter. The efficiency of the column is clearly influenced by these effects as the rate of equilibration between the mobile and stationary phases depends on the rate of diffusion of the sample molecules into the pores. As the length of the alkyl chain attached to the particles constituting the stationary phase is increased, the rate of diffusivity into the pores is decreased due to restricted access. It is thus clear that an optimum situation must be achieved whereby the access of the sample molecules to the stationary phase is 

Section 5.2.2.3 already described the pore size influence in combination with stationary phases. Therefore, only the particularly RP-relevant points are specified here. Normally, stationary phases between 100 and 300 A are used for peptides. The bigger pores, in particular, have the advantage of better accessibility. This is not only an advantage during chromatography, but also during the bonding. Due 

oxytocin, 3. angiotensin II, 4. neurotensin, 5. angiotensin I. Source Protein and Peptide Analysis and Purification, Vydac Reversed Phase Handbook, 5th edition, W.R. Grace, 2013. 

In addition to the classification described above, the real metric scale in form of nanometer, micrometer, and millimeter is often used particularly by materials scientists to characterize the pore size. To prevent misunderstandings with the IUPAC classification, we propose to use in these cases the expression always with the suffix meter, viz. nanometer, micrometer, and millimeter (sized) pores. 

Pellicular materials consist of a solid spherical bead of relatively large 

Long pores filled with stagnant mobile phase 

Chapter 3 Instrumentation for High-Performance Liquid Chromatography 

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For a single fluid flowing through a section of reservoir rock, Darcy showed that the superficial velocity of the fluid (u) is proportional to the pressure drop applied (the hydrodynamic pressure gradient), and inversely proportional to the viscosity of the fluid. The constant of proportionality is called the absolute permeability which is a rock property, and is dependent upon the pore size distribution. The superficial velocity is the average flowrate... 

SANS Small-angle neutron scattering [175, 176] Thermal or cold neutrons are scattered elastically or inelastically Incident-Beam Spectroscopy Surface vibrational states, pore size distribution suspension structure... 

The specific surface area of a solid is one of the first things that must be determined if any detailed physical chemical interpretation of its behavior as an adsorbent is to be possible. Such a determination can be made through adsorption studies themselves, and this aspect is taken up in the next chapter there are a number of other methods, however, that are summarized in the following material. Space does not permit a full discussion, and, in particular, the methods that really amount to a particle or pore size determination, such as optical and electron microscopy, x-ray or neutron diffraction, and permeability studies are largely omitted. 

The method to be described determines the pore size distribution in a porous material or compacted powder surface areas may be inferred from the results. 

A procedure that is more suitable for obtaining the actual distribution of pore sizes involves the use of a nonwetting liquid such as mercury—the contact angle on glass being about 140° (Table X-2) (but note Ref. 31). If all pores are equally accessible, only those will be filled for which... 

We have considered briefly the important macroscopic description of a solid adsorbent, namely, its speciflc surface area, its possible fractal nature, and if porous, its pore size distribution. In addition, it is important to know as much as possible about the microscopic structure of the surface, and contemporary surface spectroscopic and diffraction techniques, discussed in Chapter VIII, provide a good deal of such information (see also Refs. 55 and 56 for short general reviews, and the monograph by Somoijai [57]). Scanning tunneling microscopy (STM) and atomic force microscopy (AFT) are now widely used to obtain the structure of surfaces and of adsorbed layers on a molecular scale (see Chapter VIII, Section XVIII-2B, and Ref. 58). On a less informative and more statistical basis are site energy distributions (Section XVII-14) there is also the somewhat laige-scale type of structure due to surface imperfections and dislocations (Section VII-4D and Fig. XVIII-14). 

Below the critical temperature of the adsorbate, adsorption is generally multilayer in type, and the presence of pores may have the effect not only of limiting the possible number of layers of adsorbate (see Eq. XVII-65) but also of introducing capillary condensation phenomena. A wide range of porous adsorbents is now involved and usually having a broad distribution of pore sizes and shapes, unlike the zeolites. The most general characteristic of such adsorption systems is that of hysteresis as illustrated in Fig. XVII-27 and, more gener-... 

Brunauer and co-workers [211, 212] proposed a modelless method for obtaining pore size distributions no specific capillary shape is assumed. Use is made of the general thermodynamic relationship due to Kiselev [213]... 

Horvath G and Kawazoe K 1983 Method for oaloulation of effeotive pore size distribution in moleoular sieve oarbon J. Chem. Eng. Japan 16 470-5... 

Anotlier standard metliod is to use a (high-speed) centrifuge to sediment tire colloids, replace tire supernatant and redisperse tire particles. Provided tire particles are well stabilized in tire solvent, tliis allows for a rigorous purification. Larger objects, such as particle aggregates, can be fractionated off because tliey settle first. A tliird metliod is (ultra)filtration, whereby larger impurities can be retained, particularly using membrane filters witli accurately defined pore sizes. 

Physical properties affecting catalyst perfoniiance include tlie surface area, pore volume and pore size distribution (section B1.26). These properties regulate tlie tradeoff between tlie rate of tlie catalytic reaction on tlie internal surface and tlie rate of transport (e.g., by diffusion) of tlie reactant molecules into tlie pores and tlie product molecules out of tlie pores tlie higher tlie internal area of tlie catalytic material per unit volume, tlie higher the rate of tlie reaction... 

At the present time there exist no flux relations wich a completely sound cheoretical basis, capable of describing transport in porous media over the whole range of pressures or pore sizes. All involve empiricism to a greater or less degree, or are based on a physically unrealistic representation of the structure of the porous medium. Existing models fall into two main classes in the first the medium is modeled as a network of interconnected capillaries, while in the second it is represented by an assembly of stationary obstacles dispersed in the gas on a molecular scale. The first type of model is closely related to the physical structure of the medium, but its development is hampered by the lack of a solution to the problem of transport in a capillary whose diameter is comparable to mean free path lengths in the gas mixture. The second type of model is more tenuously related to the real medium but more tractable theoretically. 

Despite the fact Chat there are no analogs of void fraction or pore size in the model, by varying the proportion of dust particles dispersed among the gas molecules it is possible to move from a situation where most momentum transfer occurs in collisions between pairs of gas molecules, Co one where the principal momentum transfer is between gas molecules and the dust. Thus one might hope to obtain at least a physically reasonable form for the flux relations, over the whole range from bulk diffusion to Knudsen streaming. 

The relation between the dusty gas model and the physical structure of a real porous medium is rather obscure. Since the dusty gas model does not even contain any explicit representation of the void fraction, it certainly cannot be adjusted to reflect features of the pore size distributions of different porous media. For example, porous catalysts often show a strongly bimodal pore size distribution, and their flux relations might be expected to reflect this, but the dusty gas model can respond only to changes in the... 

Che pore size distribution and Che pore geometry. Condition (iil). For isobaric diffusion in a binary mixture Che flux vectors of Che two species must satisfy Graham s relation... 

The simplest way of introducing Che pore size distribution into the model is to permit just two possible sizes--Tnlcropores and macropotes--and this simple pore size distribution is not wholly unrealistic, since pelleted materials are prepared by compressing powder particles which are themselves porous on a much smaller scale. The small pores within the powder grains are then the micropores, while the interstices between adjacent grains form the macropores. An early and well known model due to Wakao and Smith [32] represents such a material by the Idealized structure shown in Figure 8,2,... 

Of course, these shortcomings of the Wakao-Smith flux relations induced by the use of equations (8.7) and (8.8) can be removed by replacing these with the corresponding dusty gas model equations, whose validity is not restricted to isobaric systems. However, since the influence of a strongly bidisperse pore size distribution can now be accounted for more simply within the class of smooth field models proposed by Feng and Stewart [49], it is hardly worthwhile pursuing this."... 

Case (b). The CorCuosity factor is independent of pore size, the pore... 

Case (c). The pore size distribution is strictly bimodal, with macropores... 

The pore size distribution function (a) appears parametrically in the flux relations of Feng and Stewart, so their models certainly cannot be completely predictive in nature unless this distribution is known. It is... 

Hugo s approach can be extended without difficulty to apply throughout the whole range of pore sizes, but to accomplish this a specific and complete flux model must be used. To be definite we will assume that the dusty gas model is adequate, but the same reasoning could be applied to certain other models if necessary. The relevant flux relations are now equations (5.4). Applied to the radial flux components In one of our three simple geometries they take the form... 

This argument is sound if we imagine Che number of active sites per unit surface area to remain constant as the pore size is changed. However, if the number of active sites per unit pellet volume remains constant, will be independent of d, and then 1/ d. Neither of these re-... 

As a consequence of this, i enever bulk dlffusional resistance domin ates Knudsen diffusional resistance, so that 1, it follows that fi 1 also, and hence viscous flow dominates Knudsen streaming. Thus when we physically approach the limit of bulk diffusion control, by increasing the pore sizes or the pressure, we must simultaneously approach the limit of viscous flow. This justifies a statement made in Chapter 5. 

To prevent this flow, the pressure on the hotter side must be larger than the pressure on the colder side. The required pressure difference depends on the nature of the gas, its mean pressure and absolute temperature, the relation between its density and the pore size, and the temperature difference. However, it does not depend on the thickness of the plate. 

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