Gels pore size distribution

The method of immobilization of the SO, the nature of the matrix (organic polymer, silica gel, pore size distribution) and hence the flexibility and accessibility of coordination positions for SA molecules to the > Cu( II) SO moiety are crucial. 

The large majority of activated alumina products are derived from activation of aluminum hydroxide, rehydrated alumina, or pseudoboehmite gel. Other commerical methods to produce specialty activated aluminas are roasting of aluminum chloride [7446-70-0], AIQ calcination of precursors such as ammonium alum [7784-25-0], AlH2NOgS2. Processing is tailored to optimize one or more of the product properties such as surface area, purity, pore size distribution, particle size, shape, or strength. 

Characterization. When siHca gel is used as an adsorbent, the pore stmcture determines the gel adsorption capacity. Pores are characterized by specific surface area, specific pore volume (total volume of pores per gram of solid), average pore diameter, pore size distribution, and the degree to which entrance to larger pores is restricted by smaller pores. These parameters are derived from measuring vapor adsorption isotherms, mercury intmsion, low angle x-ray scattering, electron microscopy, gas permeabiHty, ion or molecule exclusion, or the volume of imbibed Hquid (1). 

Generally, optimizing the selectivity by choosing a gel medium of suitable pore size and pore size distribution is the single most important parameter. Examples of the effect of pore size on the separation of a protein mixture are given in Fig. 2.15. The gain in selectivity may then be traded for speed and/ or sample load. However, if the selectivity is limited, other parameters such as eluent velocity, column length, and sample load need to be optimized to yield the separation required. 

The selectivity of a gel, defined by the incremental increase in distribution coefficient for an incremental decrease in solute size, is related to the width of the pore size distribution of the gel. A narrow pore size distribution will typically have a separation range of one decade in solute size, which corresponds to roughly three decades in protein molecular mass (Hagel, 1988). However, the largest selectivity obtainable is the one where the solute of interest is either totally excluded (which is achieved when the solute size is of the same order as the pore size) or totally included (as for a very small solute) and the impurities differ more than a decade in size from the target solute. In this case, a gel of suitable pore size may be found and the separation carried out as a desalting step. This is very favorable from an operational point of view (see later). 

The advantage of sol-gel technology is the ability to produce a highly pure y-alumina and zirconia membrane at medium temperatures, about 700 °C, with a uniform pore size distribution in a thin film. However, the membrane is sensitive to heat treatment, resulting in cracking on the film layer. A successful crack-free product was produced, but it needed special care and time for suitable heat curing. Only y-alumina membrane have the disadvantage of poor chemical and thermal stability. 

In a further study, Rill et al. [325] developed a model of gel permeation chromatography that included a bimodal pore stracture. The smallest mode in the pore-size distribution represents the basic background polyacrylamide pore structure of about 1-mn mean radius, and the second mode was around 5 nm, i.e., in the range of size of the molecular templates. The introduction of this second pore structure was found to substantially improve the peak resolution for molecules with molecular sizes in the range of the pore size. 

Gel filtration chromatography has been extensively used to determine pore-size distributions of polymeric gels (in particle form). These models generally do not consider details of the shape of the pores, but rather they may consider a distribution of effective average pore sizes. Rodbard [326,327] reviews the various models for pore-size distributions. These include the uniform-pore models of Porath, Squire, and Ostrowski discussed earlier, the Gaussian pore distribution and its approximation developed by Ackers and Henn [3,155,156], the log-normal distribution, and the logistic distribution. 

Silica gels with mean pore diameters of 5-15 nm and surface areas of 150-600 m /g have been preferred for the separation of low molecular weight samples, while silica gels with pore diameters greater than 30 nm are preferred for the separation, of biopolymers to avoid restricting the accessibility of the solutes to the stationary phase [15,16,29,34]. Ideally, the pore size distribution should be narrow and symmetrical about the mean value. Micropores are particularly undesirable as they may give rise to size-exclusion effects or irreversible adsorption due to... 

The major design concept of polymer monoliths for separation media is the realization of the hierarchical porous structure of mesopores (2-50 nm in diameter) and macropores (larger than 50 nm in diameter). The mesopores provide retentive sites and macropores flow-through channels for effective mobile-phase transport and solute transfer between the mobile phase and the stationary phase. Preparation methods of such monolithic polymers with bimodal pore sizes were disclosed in a US patent (Frechet and Svec, 1994). The two modes of pore-size distribution were characterized with the smaller sized pores ranging less than 200 nm and the larger sized pores greater than 600 nm. In the case of silica monoliths, the concept of hierarchy of pore structures is more clearly realized in the preparation by sol-gel processes followed by mesopore formation (Minakuchi et al., 1996). 

J.H. Harreld, T. Ebina, N. Tsubo, and G. Stocky, Manipulation of pore size distributions in silica and ormosil gels dried under ambient pressure conditions. J. Non-Cryst. Solids 298, 241—251 (2002). 

Figure 5.5 shows the variation of the pore size distribution as a function of cycles of surface-modification-based N2 adsorption isotherms. The pore size decreases with the modification cycle number. The reduction of the mesopore size for each cycle should be about twice the single-layer thickness. Accordingly, the effective singlelayer thickness is about 6 to 7 A based on the above BET measurements. This value is close to those estimated from the frequency changes of a quartz crystal balance for ultrathin fihns prepared by the surface sol-gel process on 2-D substrates." " ... 

Characteristic microstructural properties of TiOj membranes produced in this way are given in Table 2.5. Mean pore diameters of 4-5 nm were obtained after heat treatment at T < 500°C. The pore size distribution was narrow in this case and the particle size in the membrane layer was about 5 nm. Anderson et al. (1988) discuss sol/gel chemistry and the formation of nonsupported titania membranes using the colloidal suspension synthesis of the type mentioned above. The particle size in the colloidal dispersion increased with the H/Ti ratio from 80 nm (H /Ti = 0.4, minimum gelling volume) to 140 nm (H /Ti " — 1.0). The membranes, thus prepared, had microstructural characteristics similar to those reported in Table 2.5 and are composed mainly of 20 nm anatase particles. Considerable problems were encountered in membrane synthesis with the polymeric gel route. Anderson et al. (1988) report that clear polymeric sols without precipitates could be produced using initial water concentrations up to 16 mole per mole Ti. Transparent gels could be obtained only when the molar ratio of H2O to Ti is < 4. Gels with up to 12 wt.% T1O2 could be produced provided a low pH is used (H /Ti + < 0.025). 

Hgure 3.9. Dynamic pore size distributions of (a) two sol-gel alumina membranes and (b) two anodized alumina membranes (Fain 1990). 

Figure 16. The pore-size distribution for sol—gel-derived birnessite Na(5Mn02 20 as processed into three pore-solid nanoarchitectures xerogel, ambigel, and aerogel. Distributions are derived from N2 physisorption measurements and calculated on the basis of a cylindrical pore model. (Reprinted with permission from ref 175. Copyright 2001 American Chemical Society.)...

Here Cp is the accessible pore volume fraction of the gel which is a fijnction of the pore size distribution as well as the size of a polymer molecule. The value of p is given by Equation 3 ... 

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