Adsorbents density

A variety of experimental data has been found to fit the Langmuir equation reasonably well. Data are generally plotted according to the linear form, Eq. XVn-9, to obtain the constants b and n from the best fitting straight line. The specific surface area, E, can then be obtained from Eq. XVII-10. A widely used practice is to take to be the molecular area of the adsorbate, estimated from liquid or solid adsorbate densities. On the other hand, the Langmuir model is cast around the concept of adsorption sites, whose spacing one would suppose to be characteristic of the adsorbent. See Section XVII-5B for an additional discussion of the problem. 

A quantity of interest in many studies of surfaees and interfaees is tire eoneentration of adsorbed atomie or moleeular speeies. The SHG/SFG teelmique has been found to be a usefid probe of adsorbate density for a wide range of interfaees. The surfaee sensitivity afforded by the method is illustrated by the results of figure Bl.5.9 [72]. These data show the dramatie ehange in SH response from a elean surfaee of silieon upon adsorption of a fraetion of a monolayer of atomie hydrogen. 

We now consider how one extracts quantitative infonnation about die surface or interface adsorbate coverage from such SHG data. In many circumstances, it is possible to adopt a purely phenomenological approach one calibrates the nonlinear response as a fiinction of surface coverage in a preliminary set of experiments and then makes use of this calibration in subsequent investigations. Such an approach may, for example, be appropriate for studies of adsorption kinetics where the interest lies in die temporal evolution of the surface adsorbate density N. ... 

Before leavmg this topic, we would like to touch on two related points. The first concerns the possibility of an absolute detemiination of the surface adsorbate density. Equation BT5.43 would suggest that one might use... 

The models of Matranga, Myers and Glandt [22] and Tan and Gubbins [23] for supercritical methane adsorption on carbon using a slit shaped pore have shown the importance of pore width on adsorbate density. An estimate of the pore width distribution has been recognized as a valuable tool in evaluating adsorbents. Several methods have been reported for obtaining pore size distributions, (PSDs), some of which are discussed below. 

We conclude, from the results given above, that both the ROZ-PY and ROZ-HNC theories are sufficiently successful for the description of the pair distribution functions of fluid particles in different disordered matrices. It seems that at a low adsorbed density the PY closure is preferable, whereas... 

Figure 6.22. Adsorption of an atom on a d metal. The valence electron of the adsorbate, initially at 12 eV above the bottom of the metal band, interacts both weakly with a broad sp band and strongly with a narrow d band located between 9 and 12 eV. Note the significant splitting of the adsorbate density of states into bonding and antibonding orbitals of Ha( ) due to the interaction with the d band.

Ming L., Anzhong G., et al. Determination of adsorbate density from supercriticl gas adsorption equilibria data. 2003 Carbon 41(3) 585-588. 

True adsorbent volume. Vft. The weight of the adsorbent packing divided by adsorbent density. 

L = length of carbon rod 7) = viscosity of water at 25 C and 95 C p =mean adsorbate density = X/V where a X = grams adsorbed per gram of carbon and V = micropore volume per gram of carbon... 

If the attractive force of the adsorbent for the gas molecules is relatively strong and pairwise additive and varies inversely as the square of the distance between adsorbate and adsorbent molecules, then when the adsorbate density is at all large, wac must be large, since both adsorbate and adsorbent will be attracted to their mutual center of gravity. In this case the pressure acting on the outside surface of the whole system will be less than the pressure of either of the parts— i.e., P may approach zero while both pva and pvc are large and positive. 

Therefore, in this particular case, Aj(u)) provides a direct measure of the density of occupied states at the adsorbate, lmGaa(co — coo), if there is no pronounced structure in the density of final states and if the variation of the matrix element (J t a) with the final state energy can be neglected over the width of the adsorbate density of states function. The angular distribution of Aj(m) is determined by the matrix element f r a and reflects the symmetry of the adsorbate orbital. 

Values of apparent specific micropore volume, vp, of VPI-5 evaluated from the uptakes determined by Kenny et al. (1992) of various adsorptives at p/pa = 0.4 are recorded in Table 12.7. As before, the adsorbate densities are assumed equal to the respective liquid densities at the operational temperatures. Also included in Table 12.7 are values of vp derived from the measurements of Davis etal. (1989b), Schmidt et al. (1992) and Reichert et al. (1994). The complexity of the behaviour of VPI-5 is... 

In the original HK model, the density of the condensed phase in a pore is set equal to the liquid adsorbate density pi if the bulk gas pressure is greater than the filling pressure given by... 

The adsorbent density ps =ps( is set equal to the density of graphite, for which y0is =5.2. 

For bulk gas pressures P adsorbed fluid density is a fiactional amount of the adsorbate density at saturation conditions, as given by the following equation ... 

The adsorbate density after wetting is thus calculated as the product of the adsorbate density at maximum loading and the fi action of pore volume occupied by the monolayer. Equation (11) assumes that the film has the same molar volume as the condensed fluid, and that at the onset of condensation, the adsorbed fluid on each pore wall has a thickness equal to a. 

Figure 3. Variation of friction factor with density at potential minimum, obtained at temperatures of 150 K and 177 K. Inset depicts predicted and measured streaming velocity profile at adsorbed density...

A new approach based on a combination of the non-local density functional theory and the Bender equation of state was successfully applied to high-pressure (up to SO MPa) argon, nitrogen, methane and helium adsorption. The approach allows reliably determining pore size distribution and adsorbent density, and most importantly it does not require helium experiments to determine the skeletal density. 

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