(571c) A New Theory for Adsorbate Specific Volumes and Saturation Loadings on 4A, 5A and 13X Zeolites

Adsorbate data for nitrogen and xenon on three zeolites, 4A, 5A, and 13X, reduces to one dimensionless plot in the supercritical region (which we have named the superT_CAR region, where T_CAR is the critical adsorbate reduced temperature) having a slope of -1 and intercept 0.6356. This equation is derived through consideration of the theory of adsorbate specific volumes and saturation loadings on 4A, 5A and 13X zeolites and application to the saturation loading data for nitrogen and xenon. Saturation loadings are observed to be linear in the supercritical region for these zeolites. The exponential expansivity equation of Ozawa et al¹ is linearized to model this data. Dimensionless equations for q_max and adsorbate specific volumes are derived for this linear equation. Adsorption q_max data for nitrogen on 4A, 5A, and 13X and xenon on 5A and 13X zeolite is optimized for the adsorbate specific volume expansivity factor and plotted on one straight line.

THEORY

The coefficient of expansion of a liquid is defined in equation 1. Assuming α is constant as noted by Dubinin and Astakhov⁷, this may be integrated to give equation 2 where V_b, the normal boiling point temperature, T_b and the specific volume of the liquid at T_b are constants of integration. This may be written for an adsorbate as in equation 3 where Ω is the coefficient of expansion of the adsorbate, and V_ads is the specific volume of the adsorbate at temperature T. Ozawa et al.¹ provide a value of 0.0025 for Ω for adsorption for the characteristic curves in the Polanyi theory.

The saturation loading, q_max (g/100gZ) and V_ads are interchangeable for zeolites using the equation 4 where the right-hand side are well-known crystallographic properties of the zeolites. Substituting this into Equation 3 gives equation 5.

Data for these equations may be found in the NIST website under search, more options, and Thermophysical Properties of Fluid Systems. The value of 100 ε_Z/ρ_Z for the three zeolites 4A, 5A, and 13X are 24.24, 27.97, 31.75 cc/ 100gZ respectively for the α or large cavity⁸.

Plots of Equation 5 for the three zeolites are curves as may be observed in Figures 1 and 2 in the Results section. However, the adsorption data is linear for these zeolites in Figures 1 and 2. This suggests that the exponential in Equation 5 should be linearized to give equation 6. Approximating T_b as 0.61 T_C, Equation 6 may be rearranged to give equation 7. This equation may also be written in terms of specific volumes as shown in equation 8.

The left-hand side of Equations 7 and 8 are dimensionless numbers. The term V_b/V_adsΩT_c is the dimensionless specific volume group for the adsorbate. To calculate V_ads, knowledge of V_b and Ω as a function of zeolite type, saturation temperature and saturation pressure between the boiling point and the critical point temperature are required. Similarly, the term q_maxρ_zV_b/100ε_zΩT_c is a dimensionless saturation loading group. To calculate q_max, knowledge of the framework voidage for the α or large cage, density, and saturation temperature and saturation pressure between the boiling point and the critical point temperature are required. Equations 7 and 8 are the dimensionless groups for saturation loading or specific volume and a plot of these equations will have a slope of -1 for all species, but each species will have different intercepts (1/ΩT_C +0.61).

A further refinement of Equations 7 and 8 is to move the term 1/ΩT_C from the right-hand side to the left-hand side of the equations, giving equations 9 and 10. These equations imply that all the adsorbent data for q_max or V_ads for all the zeolites should collapse onto one line with an approximate intercept of 0.61 and slope of -1.

A further refinement of Equations 9 and 10 is to replace the numeral 0.61 by T_bR = T_b/T_C, the ratio of the normal boiling point temperature to the critical temperature. This ratio lies between 0.57 to 0.64 for most species. This is more accurate for a single species but loses the simplicity of Equations 9 and 10 for multiple species.

RESULTS

Experimental data for saturation loadings of nitrogen and xenon on the zeolites 4A, 5A and 13X are reported in our papers^2-6 and are plotted in Figures 1 and 2. The data in the supercritical region is linear. The subcritical region below T_C = 1 calculated using the Rackett equation for density and framework properties of the zeolites are shown as curves using the appropriate equation in the paper by Abouelnasr and Loughlin⁵. Plots of equation 3 for Ozawa et al’s¹ model are shown as curves for all systems. It is clear that these plots do not fit the data.

The calculation of the linear plots by Equations 6-10 requires values of V_b and T_b at any saturation pressure be determined by optimizing for the appropriate value of W. This was done by using the NIST website under isobaric conditions. The procedure was to select individual saturation pressures, determine T_b and V_b at each saturation pressure, and minimize the sum of squares difference between the experimental data points and theoretical points to determine the appropriate value for Ω.

The optimized values for the 5 systems are reported in reference 8. The values of the expansivity parameter W for the adsorbed phases vary from 0.001377 to 0.004175 for the different systems and are significantly different from the value of 0.0025 used by Ozawa et al¹. The straight-line fits shown in Figures 1 and 2 are calculated from these optimized values and are in good agreement with the experimental data.

A plot of the data for all 5 systems for equations 7 and 8 is displayed in Figure 3. The data is parallel with a slope of -1 for all systems and with intercepts close to the predicted values. When the data is plotted as f(q_max) or g(V_ads) versus T_R, the data all collapse onto one line with slope of -1 and intercept of 0.6356 as illustrated in Figure 4. The intercept varies from 0.61 due to the preponderance of the data for either sorbate.

CONCLUSIONS

The q_max adsorbate data or specific volume adsorbate data for xenon and nitrogen on zeolites 4A, 5A an13X may be represented by two dimensionless groups involving q_max and V_ads. When these dimensionless groups are plotted against T_R, the experimental data fall on parallel lines with intercepts (1/ΩT_C + 0.61). When 1/ΩT_C is subtracted from the dimensionless groups, the experimental data all fall on one straight line with a slope of -1 and an intercept of 0.6356.

ACKNOWLEDGEMENTS

The authors wish to acknowledge the support of the American University of Sharjah and, Georgia Institute of Technology in the development of this paper.

REFERENCES

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