Vycor, diffusion

Surface diffusion has been extensively studied in literature. An overview of experimental data is given in Table 6.1. Okazaki, Tamon and Toei (1981), for example, measured the transport of propane through Vycor glass with a pore radius of 3.5 nm at 303 K and variable pressure (see Table 6.1). The corrected gas phase permeability was 0.69 m -m/m -h-bar, while the surface permeability was 0.55 m -m/m -h-bar, and so almost as large as the gas phase permeability (Table 6.1). It is clear from Table 6.1, that the effects of surface diffusion, especially at moderate temperatures, can be pronounced. At higher temperatures, adsorption decreases and it can be expected that surface diffusion will become less pronounced. 

Fig. 2 shows the spectrum as a function of time of HP xenon diffusing into porous Vycor glass, which has interconnecting pores of 42A diameter. The experiment in this case was done in batch mode, where a previously collected volume of HP xenon is passed into the sample space in a static NMR probe containing the Vycor sample. The spectrum was collected with a series of pulses with small tip angles so as not to destroy the magnetization of the HP xenon. The experiment is started even before there is gas in the sample space so that... 

Figure 2. Time dependence of 129Xe NMR spectrum (left) and intensity (inset) as HP Xe diffuses into a cylinder of porous Vycor glass (right). The stronger line close to 0 ppm is due to Xe gas.

In smaller pores where the majority of the molecules are in the proximity of the walls, the presence of an immobile superficial layer limits even more the diffusion coefficient by reducing the effective pore diameter as a result in saturated Vycor (pore size 29 A) the movement of particles is about two times slower than the one in bulk phase, while in MCM-41-S (pore diameter 25 A) and MCM-48-S (pore diameter 22 A) the movement of particles is about four to ten times slower. The limit case is an in-file diffusion process, where particles are unable to pass each other in a channel. 

Kainourgiakis ME, Kikkinides ES, Stubos AK, Kanellopoulos NK. (1999) Simulation of self-diffusion of point-like and finite-size tracers in stochastically reconstructed Vycor porous glasses. J Chem Phys 111 2735-2743. 

The orientationally averaged effective diffusivity of He in the reconstructed Vycor structure (dry or wet), is calculated from the mean-square displacement , of a statistically sufficient number of identical particles injected in the void space of the medium, according to ... 

Tables 1 and 2 give respectively for hydrated protein h = 0.4) and for 25% hydrated Vycor the values of the diffusion cofficients T io ai A or confined water as compared with the diffusion coefficient Dj of bulk water, together with the residence times Tq and the H-bond lifetimes Xj as a function of temperature.

For hydrated protein (Table 1), the values obtained for Aocai lower than those of bulk water they are close to those obtained at the same temperature for 25% H20-hydrated Vycor (Table 2), which demonstrates the influence of the hydrophilic groups on the water molecules when one reaches a monolayer coverage. This shows that the diffusive motion of water molecules is strongly retarded by interactions with a protein surface. 

Okubo et al. [40,41] treated Vycor glass membranes with tetra-ethoxysilane which was initially adsorbed and finally decomposed on the pore wall by heat treatment. The pore size was expected to be decreased by this treatment. As a result of this modification the permeation decreased and the permeation as a function of temperature increased (compared with that of the non-modified glass) for the gases He, O2, N2, Ar, H2 and CO2 and became activated. The authors argue that surface diffusion carmot explain this result and suggest that the modified system is in the transition region of Knudsen to molecular sieving (micropore diffusion). 

Example 11-5 Vycor (porous silica) appears to have a pore system with fewer interconnections than alumina. The pore system is monodisperse, with the somewhat unusual combination of a small mean pore radius (45 A) and a low porosity 0.31. Vycor may be much closer to an assembly of individual voids than to an assembly of particles surrounded by void spaces. Since the random-pore model is based on the assembly-of-particles concept, it is instructive to see how it applies to Vycor. Rao and Smith measured an effective diffusivity for hydrogen of 0.0029 cm /sec in Vycor. The apparatus was similar to that shown in Fig. 11-1, and data were obtained using an H2-N2 system at 25°C and 1 atm. Predict the effective diffusivity by the random-pore model. 

Diffusion rates for the H2-N2 system were measured by Rao and Smith for a cylindrical Vycor (porous-glass) pellet 0.25 in. long and 0.56 in. in diameter, at 25°C and 1 atm pressure. A constant-pressure apparatus such as that shown in Fig. 11-1 was used. The Vycor had a mean pore radius of 45 A, so that diffusion was by the Knudsen mechanism. The diffusion rates were small with respect to the flow rates of the pure gases on either side of the pellet. The average diffusion rate of hydrogen for a number of runs was 0.44 cm min (25°C, 1 atm). The porosity of the Vycor was 0.304. 

The permeabilities of oxygen through the Vycor were constant with the pressure difference and decreased with the square root of the temperature (figure not included). So the main mechanism for gas permeation is Knudsen diffusion. However, the permeabilities of oxygen through the V20s-coated catalytic membrane were deviated from Knudsen diffusion. As the partial oxidation proceeded, the... 

In the above sections, we have amply shown that capillary condensation occurs in the contact zones of elementary particles and the shape of isotherms measured up to a = 1 is determined by existing pore distributions of the porous materials. In addition, it has been shown by sorption methods that porous Vycor glass and Neobead C-5 are ideal porous bodies consisting of spherical elementary particles arranged in characteristic types of packing. Based on these idealized models, we have calculated the effective diffusion coefficients in these porous bodies. 

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