Dubinin adsorption models

Dubinin adsorption models have been used to calculate carbon micropore distributions from experimental isotherm measurements of a number of adsorbates, including nitrogen [120-122], carbon dioxide [122,123], methane [123], and several other organic molecules [124]. It is has generally been... 

Now let us overview the theoretical adsorption models for characterization of the pore structures according to the pore size range. For physical adsorption of the gas molecules on such microporous solids as activated carbons and zeolites, Dubinin and Radushkevich95 developed an empirical equation, which describes the volume filling process in the micropores. Their theory incorporates earlier work by Polanyi96 in regard to the adsorption potential Ad defined as... 

The methods depend on the theoretical treatment which is used. A majority of them are based on the Generalised Adsorption Isotherm (GAI) also called the Integral Adsorption Equation (LAE). The more recent approaches use the Monte Carlo simulations or the density functional theory to calculate the local adsorption isotherm. The analytical form of the pore size distribution function (PSD) is not a priori assumed. It is determined using the regularization method [1,2,3]. Older methods use the Dubinin-Radushkevich or the Dubinin-Astakhov models as kernel with a gaussian or a gamma-type function for the pore size distribution. In some cases, the generalised adsorption equation can be solved analytically and the parameters of the PSD appear directly in the isotherm equation [4,5,6]. Other methods which do not rely on the GAI concept are sometimes used the MP and the Horvath-Kawazoe (H-K) methods are the most well known [7,8]. 

For a carbonaceous material, the higher the steam percentage (in volume) in the gas stream, the lower its Phe adsorption capacity. The isotherms shape suggests that the presence of moisture in the gas stream seems to avoid the multilayer adsorption. The best model to fit the Phe adsorption capacities on carbonaceous materials is the Dubinin-Radushkevich model. 

Since lAST-based calculations require a precise description of pure component adsorption data, especially in the low coverage range, Freundlich, Langmuir, Toth and Dubinin-Astakhov models were compared. 

Two principal semiempirical adsorption models have enjoyed widespread use for adsorbent PSD characterization the Horvath-Kawazoe (HK) method [19] and its derivatives, and approaches based upon the ideas of Dubinin [20] for modeling micropore distributions. Each of these methodologies is considered in turn. 

In the Dubiiiin-Radushkevitch (DR) equation [115], an adsorption model derived from a concept of Dubinin [20] based on Polanyi potential theory, the fluid volume V adsorbed in micropores at pressure P is represented empirically as... 

The adsorption isotherm of microporous adsorbents have often been modeled by the Dubinin-Astakhov model. In this approach, which is based on a so-called pore-filling of an adsorbent by a subcritical gas (T < T ), the total adsorbed density is expressed as ... 

Sobolik, J.L. Ludlow, D.K., and Hessevick, W.L.. Parametric sensitivity comparison of the BET and Dubinin-Radushkevich models for determining char surface area bv carbon dioxide adsorption. Fuel, 71(10), 1195-1202(1992). 

The POLANYI-DUBININ adsorption potential theory is used to characterize the micropore network of zeolites (ref. 10). An isotherm at a given temperature T (expressed in volume adsorbed per activated zeolite mass unit, W, as a function of the relative pressure p/Pq) is treated in the DUBININ-RADUSHKEVICH model (ref. 11) (denoted D-R) in the linear form log W = f[(Tlog Po/p) ] ... 

The first term on the right is the common inverse cube law, the second is taken to be the empirically more important form for moderate film thickness (and also conforms to the polarization model, Section XVII-7C), and the last term allows for structural perturbation in the adsorbed film relative to bulk liquid adsorbate. In effect, the vapor pressure of a thin multilayer film is taken to be P and to relax toward P as the film thickens. The equation has been useful in relating adsorption isotherms to contact angle behavior (see Section X-7). Roy and Halsey [73] have used a similar equation earlier, Halsey [74] allowed for surface heterogeneity by assuming a distribution of Uq values in Eq. XVII-79. Dubinin s equation (Eq. XVII-75) has been mentioned another variant has been used by Bonnetain and co-workers [7S]. 

These procedures proposed by Dubinin and by Stoeckli arc, as yet, in the pioneer stage. Before they can be regarded as established as a means of evaluating pore size distribution, a wide-ranging study is needed, involving model micropore systems contained in a variety of chemical substances. The relationship between the structural constant B and the actual dimensions of the micropores, together with their distribution, would have to be demonstrated. The micropore volume would need to be evaluated independently from the known structure of the solid, or by the nonane pre-adsorption method, or with the aid of a range of molecular probes. 

Having chosen a suitable refrigerant, the best adsorbent must be found. Zeolites, silica gels and chemical adsorbents have been used as well as carbons, but this chapter will concentrate on the carbon adsorbents. An indication as to the range of cop s that can be expected and the influence of the type of carbon used can be obtained by modelling the perfonnance of carbons with a range of adsorption parameters. For this purpose it is preferable to use the Dubinin-Raduschkevich... 

Abstract To design an adsorption cartridge, it is necessary to be able to predict the service life as a function of several parameters. This prediction needs a model of the breakthrough curve of the toxic from the activated carbon bed. The most popular equation is the Wheeler-Jonas equation. We study the properties of this equation and show that it satisfies the constant pattern behaviour of travelling adsorption fronts. We compare this equation with other models of chemical engineering, mainly the linear driving force (LDF) approximation. It is shown that the different models lead to a different service life. And thus it is very important to choose the proper model. The LDF model has more physical significance and is recommended in combination with Dubinin-Radushkevitch (DR) isotherm even if no analytical solution exists. A numerical solution of the system equation must be used. 

Semiernpirical Isotherm Models. Some of these models have been shown to have some thermodynamic inconsistencies and should be used with due care. They include models based on the Polanyi adsorption potential (Dubinin-Radushkevich, Dubinin-Astakhov, Radke-Prausnitz, Toth, UNI LAN. and BET). 

Other -more complicated- models to evaluate the microporous volume exist. The Dubinin-Radushkevich model46,47,48,49 is based on thermodynamical considerations concerning the process of micropore filling. Full discussion of this model is beyond the scope of this book. The reader is referred to the standard work of Gregg and Sing50 on adsorption for a detailed treatment. 

Many other equilibrium relationships have been applied to model sorption. For example, the Langmuir (Eq.44) and the Polanyi-Dubinin (Eq.45) isotherms have been widely applied to adsorption in zeolites [9] ... 

Garrot B., Couderc G., Simonot-Grange M.-H., and Stoeckli F., Co-adsorption of 1,2-dichloroethane and l-bromo,2-chloroethane on zeolite ZSM-5 ftom the liquid and vapour phases, using the Myers-Prausnitz-Dubinin model, Microporous and Mesoporous Materials 52 (2002) pp. 199-206. 

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