Dual-site Langmuir isotherm

In this chapter we present the results of computer simulations of lineeir cind branched alkcines in the zeolite Silicalite. We focus on the development of the model and a detailed comparison with experimental data for the linear and brcinched alkcines. In addition we demonstrate that these isotherms can be described quantitatively with a dual-site Langmuir isotherm. 

The adsorption behavior of branched alkanes in Silicalite is completely different from linear alkanes. Branched alkanes are preferentially adsorbed at the intersections of Silicalite, which is due to larger available space for the branch at the intersections. At a loading of 4 molecules per unit cell Silicalite, all intersections are occupied. Additional molecules will have to reside in the channel interiors. As this is energetically unfavorable, an additioncd driving force is needed to force the molecules into the channel interiors. This is the cause of the inflection in the isotherm, which has also been obtained experimentally for Silicalite. All isotherms can be described well using a dual-site Langmuir isotherm. 

Fundamentals of sorption and sorption kinetics by zeohtes are described and analyzed in the first Chapter which was written by D. M. Ruthven. It includes the treatment of the sorption equilibrium in microporous sohds as described by basic laws as well as the discussion of appropriate models such as the Ideal Langmuir Model for mono- and multi-component systems, the Dual-Site Langmuir Model, the Unilan and Toth Model, and the Simphfied Statistical Model. Similarly, the Gibbs Adsorption Isotherm, the Dubinin-Polanyi Theory, and the Ideal Adsorbed Solution Theory are discussed. With respect to sorption kinetics, the cases of self-diffusion and transport diffusion are discriminated, their relationship is analyzed and, in this context, the Maxwell-Stefan Model discussed. Finally, basic aspects of measurements of micropore diffusion both under equilibrium and non-equilibrium conditions are elucidated. The important role of micropore diffusion in separation and catalytic processes is illustrated. 

Carbonization seems to be an effective method to adjust the pore size of PAF-1 to increase the gas selectivity. PAF-1-450 (PAF-1 carbonized at 450 °C), with a narrow micropore distribution of 0.8 nm, shows obvious increased CO2 sorption. Besides, on the basis of single component isotherm data, the dual-site Langmuir-Freundlich adsorption model-based lAST prediction indicates that the CO2/N2 adsorption selectivity may be as high as 209 at a 15 85 CO2 N2 ratio. Also, the CO2/CH4 adsorption selectivity should be in the range of 7.8-9.8 at a 15 85 C02 CH4 ratio at 0adsorption selectivity could be about 392 at 273 K and 1 bar for the 20 80 CO2 H2 mixture (Figure 10.2). ... 

The simulated isotherms for 2-methylalkanes at 300K temperature are shown in figure 4.19. The continuous lines in this figure are fits of the CBMC simulations using the dual-site Langmuir model which will be discussed in section 4.6. 

Fitting of simulated isotherms with dual-site Langmuir model... 

There is an important advantage in being able to describe the inflection behavior accurately with the help of the dual-site Langmuir model (DSL) this is because it would then be possible to predict the mixture isotherm from only pure component data. For single components, we have... 

We see from figures 5.2-5.4 that the simulated isotherms conform very well to the mixture rule II based on the dual-site Langmuir model. For alkanes with carbon atoms in the 5-7 range, we need to set up the mixture rule considering the total Silicalite matrix (including sites A and B) as one entity. This is because the branched alkanes do not easily occupy site B (channel interiors) and for some pressure range the channel interiors are completely devoid of the branched isomers. The simulated isotherm for the 50%-50% mixture of butane-isobutane behaves differently, however. Neither mixture rule, I or II, is completely successful. An average of the two mixture rules, on the other hand, is very successful. 

Figure 5.7 Pure component and 50%-50% mixture isotherms at 362K in Silicalite. The open square and circle symbols represent the CBMC simulations for (1) n-Cg and (2) 3MP respectively. The continuous and dashed lines are the dual-site Langmuir (DSL) fits with the parameter values determined only from pure component CBMC simulation data. The dual-site Langmuir parameter values are for n-Cg 0ia = 4, 0ib = 4, kiA = 0.07Pa kiB = 2 x and for...

The mixture isotherms can be predicted quite accurately by applying the appropriate mixture rule to the dual-site Langmuir model. This model allows the mixture isotherm to be predicted purely on the basis of the parameters describing the isotherms of the pure components, linear and branched alkane. 

Earlier work on the application of the concept of dual mode sorption and diffusion to glassy polymer-gas systems has been reviewed in detail 6) and important aspects of more recent work have been dealt with in more recent reviews 7 10). Eq. (5) was first applied by Michaels et al U). Sorption in the polymer matrix and in the specific sorption sites was represented by linear (Henry s law) and Langmuir isotherms respectively so that Sj in Eq. (5) is given by... 

In glassy polymers the interactions of the penetrant molecules with the polymer matrix differ from one sorption site to another. A limiting description of the interaction distribution is known imder the name of the dual-sorption model [59, 60]. In this model, the concentration of the penetrant molecules consists of two parts. One obeys Henry s law and the other a Langmuir isotherm ... 

Gases B, C, and D experience single-site adsorption on the catalyst, and surface coverage is described by the classic Langmuir isotherm 0, = KiPi v. Dual-site chemical reaction on the surface equilibrates on the time scale of the adsorption of reactant A. Hence,... 

Single-site surface coverage by CO and methanol is described by a classic Langmuir isotherm, whereas H2 requires modification for dual-site dissociative adsorption. Hence,... 

Chapter 5 describes the adsorption of 50%-50% mixtures of linecir and branched alkanes on Silicalite. We find that at low pressures, both linear as well as brcinched molecules are adsorbed. At high pressures, there will be a competition between these molecules because the space in the zeolite is limited. At these pressures, linear alkanes are adsorbed cinywhere in the zeolite while branched alkanes are only adsorbed at the intersections. Branched alkanes disturb the structure of the linear ones. Therefore, the system can gain entropy when the branched molecules cire completely squeezed out of the zeolite. This process occurs for 50%-50% mixtures of i-Cs-n-C5, i-Cg-u-Cg en i-Cj-n-Cy. These mixture isotherms are well described by a dual-site binciry Langmuir isotherm. 

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