Osmotic adsorption isotherm equation

One more isotherm equation that could be helpful for the determination of the micropore volume is the osmotic isotherm of adsorption. Within the framework of the osmotic theory of adsorption, the adsorption process in a microporous adsorbent is regarded as the osmotic equilibrium between two solutions (vacancy plus molecules) of different concentrations. One of these solutions is generated in the micropores, and the other in the gas phase, and the function of the solvent is carried out by the vacancies that is, by vacuum [26], Subsequently, if we suppose that adsorption in a micropore system could be described as an osmotic process, where vacuum, that is, the vacancies are the solvent, and the adsorbed molecules the solute, it is possible then, by applying the methods of thermodynamics to the above described model, to obtain the so-called osmotic isotherm adsorption equation [55]  

Equation 6.21a reduces, for B = 1, to a Langmuir-type isotherm equation describing a volume filling  

Equation 5.21a is known in literature [10] as the Sips or Bradleys isotherm equation. This isotherm equation describes fairly well the experimental data of adsorption in zeolites and other microporous materials [26], The linear form of the osmotic equation can be expressed as follows 

The fitting process of the osmotic isotherm equation can be also carried out with the help of a nonlinear regression method [54], 

FIGURE 6.12 Linear osmotic plot with B = 0.5 of the adsorption data of NH3 at 300K in a magnesium homoionic CMT zeolite. 

---

As can be seen by comparison with the adsorption isotherm equation [Eq. (5)] of linear polymers, the last term of Eq. (20) is due to the crosslinking of the gel. Since the term can be rewritten as follows, it can be seen that this is due to the osmotic pressure caused by the difference in macrocounter ions in and out of the gel ... 

Virial Isotherm Equation. No isotherm equation based on idealized physical models provides a generally valid description of experimental isotherms in gas-zeolite systems (19). Instead (6, 20, 21, 22) one may make the assumption that in any gas-sorbent mixture the sorbed fluid exerts a surface pressure (adsorption thermodynamics), a mean hydrostatic stress intensity, Ps (volume filling of micropores), or that there is an osmotic pressure, w (solution thermodynamics) and that these pressures are related to the appropriate concentrations, C, by equations of polynomial (virial) form, illustrated by Equation 3 for osmotic pressure ... 

In Figure 6.12 [2,25], the plot of the linear form of the osmotic isotherm equation, with B = 0.5, using adsorption data of NH3 adsorbed at 300 K in an homoionic magnesium natural zeolite sample labeled CMT (see Table 4.1), is shown. The adsorption data reported in Figure 6.12 were determined volumetrically in a Pyrex glass vacuum system, previously described in the case of the Dubinin equation [25,31], With this plot, it is possible to calculate the maximum adsorption capacity of this zeolite, which is m = Na = 5.07mmol/g and b = UK = -0.92 (Torr)05. 

---