Density, adsorbed phase

Adsorbed Phase Density. Taking into account that isosteres and saturated vapor pressure curves are linear for coordinates In p vs. T l, Bering and Dubinin s method (16) allowed us to derive p vs. T by Equation 6, along an isostere. Neglecting the dependence of p on q relative to that of p on T, according to a classical assumption, we obtained p = f(T) with adjustable parameters. 

According to the classical assumption that the adsorbed phase density... 

It is clear that the calculation of gas—solid virial coefficients is very difficult, so that only the first few of them could be evaluated. This means that the model will be useful only at low values of the adsorbed phase density. But on the other hand, the most important effects of heterogeneity can be seen for the low-pressure part of the adsorption isotherm. 

Fig. 3. Adsorbed-phase density of hydrogen in slit pores at 77 K from GCMC simulations.

Fig. 4. Theoretical relationships between adsorbed-phase density for pure hydrogen and accessible pore volume for different mass uptakes. The dotted vertical line is the density for liquid hydrogen.

However, the pore volume for the AC-1 carbon in this work is 0.66 cm g, estimated by N2 adsorption at 77 K. It would therefore seem impossible for this carbon to have an uptake of about 7 wt%, since the adsorbed-phase density is equal or less than the density of liquid hydrogen (Fig. 4). Therefore, it is reasonable to suspeet that there are some pores not accessible to N2 at 77 K in the carbons. But these pores may still he accessible to pure H2 since the smallest slit pore accessible to N2 is 0.58 nm while H2 can access a slit pore with a pore size of 0.52 nm. Accordingly, we propose a pore blocking mechanism as follows. 

Evaluating the adsorbed phase density based on the linear section of the isothem n° versus p, plot [17]... 

It is clear from the previous discussion that there seems to be an end in the high-pressure direction for supercritical adsorption. However, adsorbed-phase density is the decisive factor for the existence of this end. The state of adsorbate at the end provides the standard state of the supercritical adsorbed phase just like the saturated liquid, which is the end state of adsorbate in the subcritical adsorption. Therefore, the end state has to be precisely defined. It is a serious challenge to define the end state precisely. The three ways to determine the end state summarized in the previous section cannot be considered thermodynamically rigorous. It has been acknowledged that the location of the cusplike maximum is not far from the critical density of gas, and a linear section, from which the end state can also be evaluated, follows the maximum. Therefore, the adsorbed-phase density at the end state must be intimately related to the critical density. Case studies [57,59,106] show that the density of the adsorbed phase ranges... 

Fig. XVII-13. Variation of the density with the adsorbed phase according to the potential theory.

Density of adsorbed phase/(gcm ) nonane, 0-72 nitrogen, 0-81 carbon dioxide, 110. 

Enhancement of gas storage capacity through adsorption occins when the overall storage density is increased above that of the normal gas density at a given pressure. The adsorbed phase has a greater density than the gas phase in equilibrium with it. However, enhancement in a storage system of fixed volume can only happen if a greater amount of gas is adsorbed compared to the volume of gas displaced by the adsorbent volume. 

From isotherm measurements, usually earried out on small quantities of adsorbent, the methane uptake per unit mass of adsorbent is obtained. Sinee storage in a fixed volnme is dependent on the uptake per unit volume of adsorbent and not on the uptake per unit mass of adsorbent, it is neeessary to eonvert the mass uptake to a volume uptake. In this way an estimate of the possible storage capacity of an adsorbent can be made. To do this, the mass uptake has to be multiplied by the density of the adsorbent. Ihis density, for a powdered or granular material, should be the packing (bulk) density of the adsorbent, or the piece density if the adsorbent is in the form of a monolith. Thus a carbon adsorbent which adsorbs 150 mg methane per gram at 3.5 MPa and has a packed density of 0.50 g/ml, would store 75 g methane per liter plus any methane which is in the gas phase in the void or macropore volume. This can be multiplied by 1.5 to convert to the more popular unit, V/V. 

The mass concentration x can be related to the volume of adsorbed phase V by an assumed density of adsorbed phase r ... 

For a gas-like adsorbed phase x(z) is elose to 1 in the entire pore, whereas for a liquid-hke phase x(z) exhibits a layered strueture. The oseillations in x(z) follow ehanges in the loeal density, though they are mueh less pronouneed. Inside the pore, x(z) is elose to 0.4. Obviously, when the bulk density inereases, the ratio x(z) inside the pore deereases. 

Axial coordinate, m Solid phase density, g/m3 Void fraction of adsorbent bed... 

Solid phase concentration of adsorbate i, mols i / g solid Gas phase density, mols/m3... 

Attempts have been made, using helium, to measure the density of the adsorbed phase 108-110) to try to find out whether the films are to be thought of as gaslike or liquidlike. The volume of the adsorbent was determined before adsorption, and then after a known amount of gas had been adsorbed. It was concluded 109) that the adsorption of helium, although small, was finite, introducing uncertainty in the results. Furthermore, while the concept of density is useful when multilayers are considered, it is not necessarily so at coverages less than unity. 

An analytical method for applying Polanyi s theory at temperatures near the critical temperature of the adsorbate is described. The procedure involves the Cohen-Kisarov equation for the characteristic curve as well as extrapolated values from the physical properties of the liquid. This method was adequate for adsorption on various molecular sieves. The range of temperature, where this method is valid, is discussed. The Dubinin-Rad/ush-kevich equation was a limiting case of the Cohen-Kisarov s equation. From the value of the integral molar entropy of adsorption, the adsorbed phase appears to have less freedom than the compressed phase of same density. 

Let q (expressed in cm3 NTP/gram of adsorbent) be the corresponding adsorbed amount, p (gram/cm3) the density of the adsorbed phase, and Vm (cm3 NTP/gram of adsorbate) the specific volume of the gaseous phase under normal conditions (1 atm, 0°C). The volume W (cm3/gram of adsorbent) occupied by the adsorbed phase is then expressed by ... 

Adsorbed Phase Entropy. Since Equations 7 and 8 can accurately describe the relationship between q, T, and p, we may use them to calculate the integral molar entropy of the adsorbed phase. At temperatures significantly lower than critical for the adsorbate, the entropy of the adsorbed phase is usually compared with the entropy of the liquid at same temperature in order to compare the freedom of each phase. Because our experimental domain was higher, we shall make this comparison with the gaseous phase compressed to the same density p as determined by Equation 8. 

Numerical values of Ss were obtained after replacing ps by fs according to Lewis method. Figure 5 shows that the entropy of the adsorbed phase always lies below that for gaseous phase compressed to the same density. Thus the adsorbed phase is more localized and has less freedom than the compressed phase. 

Figure 5. Comparison of the integral entropy of the adsorbed phase (solid lines) with the entropy of the gaseous phase of same density (dashed lines)...

In the range of validity of our method, integral molar entropies were easily computed by the appropriate equations and showed a loss of freedom for the adsorbed phase with respect to the compressed phase of same density. 

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