Dubinin adsorption

Determination of the Micropore Volume 6.7.3.1 Dubinin Adsorption Isotherm Equation... 

The Dubinin adsorption isotherm equation is a good tool for the measurement of the micropore volume. This isotherm can be deduced with the help of Dubinin s theory of volume filling, and Polanyi s adsorption potential [11,26], The Dubinin adsorption isotherm equation has the following form [11]... 

It is possible, as well, to express the Dubinin adsorption isotherm equation in linear form... 

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... 

Wood, G O., "Affinity Coefficients of the Polanyi/Dubinin Adsorption Isotherm Equations a Review with Compilations and Correlations," Carbon. 2001 39 343 356. 

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]. 

Adsorption isotherms in the micropore region may start off looking like one of the high BET c-value curves of Fig. XVII-10, but will then level off much like a Langmuir isotherm (Fig. XVII-3) as the pores fill and the surface area available for further adsorption greatly diminishes. The BET-type equation for adsorption limited to n layers (Eq. XVII-65) will sometimes fit this type of behavior. Currently, however, more use is made of the Dubinin-Raduschkevich or DR equation. Tliis is Eq. XVII-75, but now put in the form... 

Show that 5config = 0 for adsorption obeying the Dubinin equation (Eq. XVn-75). 

For other adsorptives the experimental evidence, though less plentiful than with nitrogen, supports the view that at a given temperature the lower closure point is never situated below a critical relative pressure which is characteristic of the adsorptive. Thus, for benzene at 298 K Dubinin noted a value of 017 on active carbons, and on active charcoals Everett and Whitton found 0-19 other values, at 298 K, are 0-20 on alumina xerogel, 0-20-0-22 on titania xerogel and 017-0-20 on ammonium silicomolybdate. Carbon tetrachloride at 298 K gives indication of a minimum closure point at 0-20-0-25 on a number of solids including... 

These various considerations led Pierce, Wiley and Smith in 1949, and independently, Dubinin, to postulate that in very fine pores the mechanism of adsorption is pore filling rather than surface coverage. Thus the plateau of the Type 1 isotherm represents the filling up of the pores with adsorbate by a process similar to but not identical with capillary condensation, rather than a layer-by-layer building up of a film on the pore walls. 

Fig. 4.6 Plat of the net differential heat of adsorption q — qj against the relative adsorption n/no.j, where H(,.2 is the adsorption at p/p° = 0-2. (A) active carbon (B) carbon black. (After Dubinin.)...

According to Dubinin s ideas, the process involved is volume filling of the micropores rather than layer-by-layer adsorption on the pore walls. A second parameter is therefore the degree of filling of the micropores, defined by... 

Fig. 4.17 Plot of log,o(n/(mmol g ) against logfo (p7p) for the adsorption of benzene at 20°C on a series of progressively activated carbons prepared from sucrose. (Courtesy Dubinin.)...

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. 

Parkyns and Quinn [20] showed a linear relationship between methane uptake at 25 C, 3.4 MPa and the Dubinin-Radushkievich micropore volume from 77 K nitrogen adsorption for porous carbons,... 

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... 

The curve showing as a function of the relative pressure is called the isotherm, since the measurement is conducted at a constant temperature. Fig. 3.42 shows an adsorption isotherm of a so-called type IV (see Dubinin and Astakhov, 1971) isotherm material. This type of isotherm is very common. 

The specific surface area of the fresh and used catalysts was measured by nitrogen adsorption method (Sorptometer 1900, Carlo Erba Instruments). The catalysts were outgassed at 473 K prior to the measurements and the Dubinin equation was used to calculate the specific surface area. The acidity of investigated samples was measured by infrared spectroscopy (ATI Mattson FTIR) by using pyridine (>99.5%, a.r.) as a probe molecule for qualitative and quantitative determination of both Bronstcd and Lewis acid sites (further denoted as BAS and LAS). The amounts of BAS and LAS were calculated from the intensities of corresponding spectral bands by using the molar extinction coefficients reported by Emeis (23). Full details of the acidity measurements are provided elsewhere (22). 

Porosity characteristics were determined by N2 adsorption-desorption at 77 K (Dubinin method) with a Thermoquest Sorptomatic 1990. Powder samples were outgassed (10 4 Torr) and heated to 450°C before each test. 

Dual nickel, 9 820—821 Dual-pressure processes, in nitric acid production, 17 175, 177, 179 Dual-solvent fractional extraction, 10 760 Dual Ziegler catalysts, for LLDPE production, 20 191 Dubinin-Radushkevich adsorption isotherm, 1 626, 627 Dubnium (Db), l 492t Ductile (nodular) iron, 14 522 Ductile brittle transition temperature (DBTT), 13 487 Ductile cast iron, 22 518—519 Ductile fracture, as failure mechanism, 26 983 Ductile iron... 

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