New equations for the physical adsorption of gases on solids have been developed based on the vacancy solution model of adsorption in conjunction with the Flory-Huggins activity coefficient equations. The isotherm equation contains three regression parameters: a Henry's law constant, the limiting amount of adsorption, and a gas-solid interaction term. Pure-gas data over a range of temperature can be correlated using only five parameters. Gas-mixture equilibria can be predicted using only the parameters obtained from the pure-gas data. Pure-component, binary, and ternary adsorption equilibrium data on activated carbons, silica, and zeolites over a wide range of conditions have been used to evaluate the model. The results show that, except for a few systems, this model predicts gas-mixture equilibria better than any other model. SCOPEIn order to exploit the physical adsorption of gases in separation processes, quantitative characterization of the multicomponent adsorption equilibria are needed as functions of temperature and pressure. Experimental multicomponent adsorption data are difficult and tinie-consuming to obtain; therefore, a reliable method of predicting multicomponent equilibria at various temperatures and pressures from purecomponent adsorption data, and if necessary binary mixture data, would be preferred. Suwanayuen and Danner (1980a, b) proposed a vacancy solution model using the Wilson model for the activity coefficients. Although this approach has been successful for the prediction of isothermal multicomponent equilibria from single-gas isotherms alone, it fails to explicitly include the effect of temperature. Also, the equations in the Suwanayuen and Danner (S&D) model are complex, and it is often difficult to obtain physically significant parameters from the regression of limited isothermal data sets.The objective of this work was to develop a new gas adsorption model based on vacancy solution theory which corrects the deficiencies inherent in the S&D model and surpasses it in accuracy. Any new model should account for nonideal behavior in the adsorbed phase including the adsorbate-adsorbate interactions and should predict the temperature dependency of the equilibria as well as the pressure and compositional dependencies. The model should be flexible enough to allow the use of binary data to characterize the adsorbate-adsorbate interactions if such data are available and if such binary parameters are needed. Preferably the model should include a method of estimating these adsorbate-adsorbate parameters, thus eliminating the need for the binary data which are seldom available and difficult to obtain experimentally. The model presented in this paper meets these criteria. CONCLUSIONS AND SIGNIFICANCEA new model for pure-and multicomponent gas adsorption is developed based on the vacancy solution theory as presented by Suwanayuen and Danner (1980a, b). Activity coefficients based on a Flory-Huggins type expression have been introduced to account for the nonideality in the adsorbed phase. By regress...

The vacancy solution model of adsorption which uses an activity coefficient equation of the Wilson form has been improved (1) by incorporating temperature dependency into the model, and (2) The vacancy solution model (VSM) of adsorption has been nurtured with one primary objective in mind: to facilitate the prediction of multicomponent adsorption equilibria from pure-component data. Because of the difficulty of obtaining gas-mixture adsorption data experimentally, a predictive scheme is needed. To be useful, the procedure must include a method of interpolating and extrapolating to different temperatures and pressures. If, on the other hand, binary adsorption data are available, it is important to use this information as effectively as possible when predicting multicomponent systems. Suwanayuen and Danner (1980a,b) presented a form of the VSM based on the Wilson activity coefficient equation, incorporating no temperature dependency and having two independent adsorbate-adsorbate interaction parameters. Cochran et al. (1985) introduced the Flory-Huggins activity coefficient into the VSM, incorporated temperature dependency, and reduced the number of binary interaction parameters. They were able to predict gas-mixture adsorption equilibria quite well for many systems using only pure-gas data. However, a number of systems involving zeolites led to less than satisfactory results. Furthermore, no significant improvements were attained by regressing a binary interaction parameter from the binary adsorption data.In an attempt to improve the predictions for zeolite systems, temperature dependence has been introduced into the Wilson form of the VSM and the number of binary regression parameters has been reduced. This modified Wilson form and the Flory-Huggins form of the VSM are examined in terms of their abilities to correlate or predict binary and ternary equilibria with and without parameters extracted from the binary data. CONCLUSIONS AND SIGNIFICANCETemperature dependency has been introduced into the Wilson form of the vacancy solution model. This allows purecomponent isotherms to be predicted at temperatures where no data are available, and gas-mixture adsorption equilibria to be predicted within this expanded temperature range. A relationship between the two adsorbate-adsorbate binary interaction parameters has been developed. Thus the number of regression parameters that must be determined is decreased with no reduction in the accuracy of the method.When pure-component isotherms are available at a number of temperatures, the temperature-dependent model should be used in preference to the isothermal model. In this way the regressed parameters attain more reasonable values. If only pure-component data are available, the Flory-Huggins form of the vacancy solution model should be used to predict gasmixture adsorption equilibria. If binary data are also available, predictions of the binary equilibria using only the puregas data with the Flory-Huggins form should be compared to the data. If these predictions are accurat...

The thermodynamic and structural properties of purely repulsive hard-core Yukawa particles in the fluid state are determined through Monte Carlo simulation and modeled using perturbation theory and integral equation theory in the mean spherical approximation (MSA). Systems of particles with Yukawa screening lengths of 1.8, 3.0, and 5.0 are examined with results compared to variations of MSA and perturbation theory. Thermodynamic properties were predicted well by both theories in the fluid region up to the fluid-solid phase boundary. Further, we found that a simplified exponential version of the MSA is the most accurate at predicting radial distribution function at contact. Radial distribution function of repulsive hard-core Yukawa particles are also reported. The results show that methods based on MSA and perturbation theory that are typically applied to the attractive hard-core Yukawa potential can also be extended to the purely repulsive hard-core Yukawa potential.

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A perturbed chain equation of state for the solid phase has been derived. Although the equation is general with respect to intermolecular potential, we incorporate the Lennard-Jones potential in this work in order to compare results from the model with available Monte Carlo simulation data. Two forms of the radial distribution function for the hard-sphere solid chain reference state are used in the model. First, a theoretically rigorous approach is taken by using a correlation of actual solid-phase Monte Carlo hard-sphere chain data for the radial distribution function. This results in good agreement with the Monte Carlo data only at high density. Second, a simple extended-density approximation was used for the radial distribution function. This second approach was found to work well across the entire density range including the vicinity of the solid-fluid equilibrium.

Monte Carlo simulation is used to generate the radial distribution function of freely jointed tangent-bonded hard-sphere chains in the disordered solid phase for chain lengths of three, four, six, and eight segments. The data are used to create an accurate analytical expression of the total radial distribution function of the hard-sphere chains that covers a density range from the solidification point up to a packing fraction of 0.71. It is envisioned that the correlation will help further progress toward molecular thermodynamic treatment of the solid phase in general and toward perturbed chain theories for the solid phase, in particular.

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