Langmuir isotherm, zeolite

Figure 5.19 shows an idealized form of the adsorption isotherm for physisorption on a nonporous or macroporous solid. At low pressures the surface is only partially occupied by the gas, until at higher pressures (point B on the curve) the monolayer is filled and the isotherm reaches a plateau. This part of the isotherm, from zero pressures to the point B, is equivalent to the Langmuir isotherm. At higher pressures a second layer starts to form, followed by unrestricted multilayer formation, which is in fact equivalent to condensation, i.e. formation of a liquid layer. In the jargon of physisorption (approved by lUPAC) this is a Type II adsorption isotherm. If a system contains predominantly micropores, i.e. a zeolite or an ultrahigh surface area carbon (>1000 m g ), multilayer formation is limited by the size of the pores. 

F or nonconstant diffusivity, a numerical solution of the conservation equations is generally required. In molecular sieve zeolites, when equilibrium is described by the Langmuir isotherm, the concentration dependence of the intracrystalline diffusivity can often be approximated by Eq. (16-72). The relevant rate equation is ... 

At a given temperature adsorption isotherms measure the number of adsorbed molecules as a function of pressure for the fluid that is in contact with the zeolite. The simplest form is the Langmuir isotherm which treats the zeolite as a collection of equivalent adsorption sites in the absence of adsorbate-adsorbate... 

A volume of 100 L of a solution containing 1000 ppm Pb2+ and minor amounts of other ions has to be treated. The desired final concentration is 100 ppm. The available adsorbent is a zeolite with a particle size of 1.3 mm, density of 2 g/cm3, and the REC is QM = 176 mg/g. Suppose that we have efficient agitation and solid diffusion is the controlling mechanism. Solid diffusion is about 6.4 X 10 1° cm2/s. Furthermore, the system obeys a favorable Langmuir isotherm with La = 0.03 and the maximum exchange level is qmm = 106 mg/g. 

Prediction of the breakthrough performance of molecular sieve adsorption columns requires solution of the appropriate mass-transfer rate equation with boundary conditions imposed by the differential fluid phase mass balance. For systems which obey a Langmuir isotherm and for which the controlling resistance to mass transfer is macropore or zeolitic diffusion, the set of nonlinear equations must be solved numerically. Solutions have been obtained for saturation and regeneration of molecular sieve adsorption columns. Predicted breakthrough curves are compared with experimental data for sorption of ethane and ethylene on type A zeolite, and the model satisfactorily describes column performance. Under comparable conditions, column regeneration is slower than saturation. This is a consequence of non-linearities of the system and does not imply any difference in intrinsic rate constants. 

This equation, with a constant value for D, has been shown to provide a satisfactory correlation of experimental diffusivity data for several zeolitic systems (6-8). For a system which obeys the Langmuir isotherm, Equation 5 becomes... 

The reversible Type I isotherm (Type I isotherms are sometimes referred to as Langmuir isotherms, but this nomenclature is not recommended) is concave to the p/pa axis and na approaches a limiting value as p/p° — 1. Type I isotherms are given by microporous solids having relatively small external surfaces (e.g. activated carbons, molecular sieve zeolites and certain porous oxides), the limiting uptake being governed by the accessible microporc volume rather than by the internal surface area. 

In general, adsorption isotherms obtained with this and other zeolitic substrates are of Brunauer s Type I, the simple hyperbolic form also known as the Langmuir isotherm. Consequently, the asymptotic limit of adsorption is used instead of the value of Vm normally derived from the BET evaluation of specific surface area. It is, of course, not possible to define exact monolayer or multilayer adsorption in these three-dimensional interconnected pore systems. 

Adsorption of single components in zeolites can often be described by a simple Langmuir isotherm, Eq. (18), or the Langmuir-Freundlich isotherm, Eq. (26) [50-52] ... 

Generally speaking, the single-gas flux through supported zeolite membranes, for a given temperature, depends on the sorption capacity of the gas on the zeolite pores and its equilibrium adsorption constant (Langmuir isotherm is often used to describe the relationship between the amount adsorbed and the gas-phase pressure), the gas diffusion coefficient, the thickness of the zeolite layer, the porosity of the support, and the pressure at the feed and permeate sides. 

The equilibrium relations that must be expected for a mixed sorbate, are relatively simple for localized sorbate particles on identical independent sites in a zeolite. The pure components (indices i, j) obey Langmuir isotherms, Eq. (11), and the sorption equilibrium of the mixture will be described by... 

Since it was also found that the Langmuir isotherm describes these water-zeolite systems approximately (51), the term d In cjd In a = dlnOjdlnp is equal to (1 — 0) and Eq. (37) is then equivalent to Eq. (31). 

Surface resistance effect factor defined in Eq. 19 A measure of the approach to saturation of the Langmuir isotherm cf. Baerlocher C, Meier WM, Olson DH (2001) Atlas of zeolite framework types, 5th edn. Elsevier, Amsterdam. 

Thus, for Langmuir isotherm the transport diffusivity increases as the loading inside the zeolite crystal increases. Stronger dependence with concentration can be observed if the isotherm takes the form of Volmer equation (Table 10.2-1). This stronger concentration dependence of the transport diffusivity in the case of Volmer isotherm equation is attributed to the mobility term in the Volmer equation. 

We estimated the N2 desorption characteristics from these zeolites under two idealized but common concepts of operation of PSA processes. They are (a) isothermal evacuation of an adsorbent column which is initially equilibrated with a binary gas mixture of N2 (yi=0,79) and O2 (y2=0.21), and (b) isothermal and isobaric desorption of pure N2 from an adsorbent column by flowing a stream of pure O2 (called purging) through the column. The adsorbers are initially at a pressure of one atmosphere and at a temperature of 30 C in both cases. Analytical model solutions are available for the above described desorption processes when they are carried out under local equilibrium conditions and when the adsorbates follow Langmuir isotherms [1,6]. 

After diffusion inside the zeolite the paraffin P is adsorbed on the metal (de) hydrogenation function. The concentration of the sorbed paraffin is given by the Langmuir isotherm... 

Figure 3.4 The adsorption of propane on a 5i4 zeolite apparently obeys a Langmuir isotherm (source Ruthven and Loughlin 1972).

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. 

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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