Pores measurement

Step 3. Transport within a catalyst pore is usually modeled as a one-dimensional diffusion process. The pore is assumed to be straight and to have length The concentration inside the pore is ai =ai(l,r,z) where I is the position inside the pore measured from the external surface of the catalyst particle. See Figure 10.2. There is no convection inside the pore, and the diameter of the pore is assumed to be so small that there are no concentration gradients in the radial direction. The governing equation is an ODE. 

Fig.3.1.9 (a) The adsorption-desorption isotherm (circles, right axis) and the self-diffusion coefficients D (triangles, left axis) for cyclohexane in porous silicon with 3.6-nm pore diameter as a function of the relative vapor pressure z = P/PS1 where Ps is the saturated vapor pressure, (b) The self-diffusion coefficients D for acetone (squares) and cyclohexane (triangles) as a function of the concentration 0 of molecules in pores measured on the adsorption (open symbols) and the desorption (filled symbols) branches. 

Porous silicon was discovered over 35 years ago by Uhlir.28 The porous material is created by electrochemical dissolution in HF-based electrolytes. Hydrofluoric acid, on its own, etches single-crystal Si extremely slowly, at a rate of only nanometers per hour. However, passing an electric current between the acid electrolyte and the Si sample speeds up the process considerably, leaving an array of deep narrow pores that generally run perpendicular to the Si surface. Pores measuring only nanometers across, but micrometers deep, have been achieved under specific etching conditions. 

It is to be hoped that future calculations will attempt to predict the diffusion coefficients of solutes in narrow pores. Measurements in such systems are extremely difficult to carry out and recent experiments in an admittedly broad pore (a 2 mm diameter capillary) are therefore of particular interest. Liukkonen and co-workers [61] found that the diffusion coefficient of NaCl in a dilute aqueous solution was 75% greater at the walls of this capillary than in the bulk solution, a result in line with the phenomenon of "surface conductivity [62]. Yet this finding clearly runs counter to the trend in the self-diffusion calculations in much narrower pores. It rather looks at this stage as if electrolytes near polar walls behave quite differently from non-electrolytes. 

Fermentation and Biochemical Engineering Handbook Table 13. Water Soluble Standard Samples for Pore Measurements J... 

A similar approach has been used by Celanese Corp. to make Celegard . an expanded polypropylene membrane (see Figure 2.4). The stretching creates elongated pores measuring 0.02 by 0.20 ju or 0.04 by 0.40 ju. The low flow rates of this membrane limit applications primarily to battery separators and airvents. 

Small pores measurements of pore size distributions revealed that from all supports studied, only Merck 40 has a considerable portion of small pores (about 50% of the surface is in pores with a size < 4nm). Possibly, the lower selectivity (ee 86.8-89.8%) obtained with this support may be a consequence of tight caging of immobilized cateilyst molecules. The lower activity observed with high loading (ligand Im) indicates that a dense coating of small pores with ligand molecules can reduce or even block mass transport. 

Metal clusters in zeolites. Zeolite NaY-supported Ir4(CO),2 was prepared by direct deposition onto the outside surface of the zeolite crystals and alternatively by reductive carbonylation of IrfCOjjfacac) sorbed in its pores. Measurements of infrared and EXAFS spectra during the formation of the entrapped metal carbonyl clusters gave evidence of reaction intermediates, suggested to be These... 

Figure 4.4. Possible configuration of adsorbate molecules in a slit-shaped adsorbent pore measuring between 2 to 3 adsorbate molecular diameters in width (Rege and Yang, 2000, with permission).

Morris, C. A., C.-C. Chen, and L. A. Baker, Transport of redox probes through single pores measured by scanning electrochemical-scanning ion conductance microscopy (SECM-SICM), Awa/ysr, Vol. 2012 pp. 2933-2938. 

The above calculation should yield the correct answer under equilibrium conditions, which is often not obtained. Modifying the Kelvin equation (51) by eliminating the factor 2 for the adsorption branch has often been suggested. This assumes that the cylindrical adsorption does not coUapse from the ends or from constrictions of the capillaries but rather from the sides. There are reasons to assume either one. Hysteresis is a big problem for meso-pore measurements, and research by many groups on this subject is ongoing. 

However, it must be noted that this approximated, although excellent for small pores measuring less than twice the adsorbate diameter, fails for larger-sized pores [57]. 

Havard and Wilson [77] describe pore measurement on meso-porous silica surface area standard powders. They presented pore size distributions based on the modeUess method and the Kelvin equation based on open ended cylinders and spheres with co-ordination numbers of 4, 6 and 8. The isotherm can be used to calibrate BET apparatus over the whole range (samples are available from the British National Physical Laboratory). 

Molecular size prevents the diffusion of protein molecules through membranes whose pores measure less than a few millimicrons, as for example coUodium, parchment, and cellophane, while small molecules and ions can pass through. This fact is put to use in dialysis in order to separate salts from proteins. 

Galvanostatic transient for Ni dissolution in saturated NiClj solution with potential increase after the induction time X and the ohmic drop in pores measured by superimposed fast short additional galvanostatic transients. (From Strehblow, H.-H. and Wenners, ]., Electrochim. Acta, 22,421,1977.)... 

Fig. 7. Pore quality plotted as a function of various parameters, a) Pore quality vs. surface area/cc of pore (measured by single point BET technique) for MWX samples, b) Pore quality vs. porosity for all samples, c) Pore quality vs. permeability for all samples.

---