Total adsorption isotherm

Equation (2-52) is the total adsorption isotherm derived from experimentally measurable excess isotherm using the model of adsorption process obtained from the analysis of the experimental isotherm profile. 

Integration of the single-pore isotherms over the PSD produced the total adsorption isotherm for the model carbon, which can be compared with the experimental data. This comparison is shown in Figure 4. 

If we assume that (i) expression (23) defines the local function, x ](y, B) associated with the definite B value and (ii) B is a continuous variable, then the total adsorption isotherm takes a general form similar to that expressed by Eq. (1). 

Here, K denotes the r.h.s. of Eq. (79) and A = Uo/kT is an heterogeneity factor which increases with increasing heterogeneity of the adsorbing surface. Homogeneous surfaces correspond to A = 0. At patchwise surfaces Eq. (80) should be solved numerically with respect to 0, and the total adsorption isotherm is determined again numerically from Eqs. (81) and (82). 

Figure 15.2 Total adsorption isotherms for (9, 9) nanotube arrays with two different lattice spacings and diEFerent charges on each carbon atom. (Reprinted with permission from Ref. [51] Copyright 1999 by the American Institute of Physics.)...

Q)A on random surfaces or g = (1 - 20 <)/4 on patchwise surfaces. At a random surface the sites of different adsorption energy are randomly distributed over the lattice, whereas at a patchwise surface the sites of equal energy are present in groups. The total adsorption isotherm may be calculated from... 

The total adsorption isotherm can be expressed as an average of the local isotherm... 

In Fig. 3, the total adsorption isotherms calculated for various topographies are presented. One can conclude that even for the surface consisting of the same number of different adsorption sites ( 1 = S2= 0.5), their distribution on the surface is an important feature of the system and affects the adsorption equilibrium considerably. A sequence of adsorption isotherms calculated for various topographies depends on the pressure region. 

When the total adsorption isotherm is known, the partial adsorption isotherms can be calculated from the following relation ... 

Fig. 4.11 (o) Adsorption isotherm for (i) a powder made up of nonporous particles (ii) a solid which is wholly microporous (iii) a powder with the same external surface as in (i) but made up of microporous particles having a total micropore volume given by the plateau of isotherm (ii). The adsorption is expressed in arbitrary units, (b) t-Plots corresponding to isotherms (i) and (iii). The o,-plots are similar, except for the scale of... 

Characterization. When siHca gel is used as an adsorbent, the pore stmcture determines the gel adsorption capacity. Pores are characterized by specific surface area, specific pore volume (total volume of pores per gram of solid), average pore diameter, pore size distribution, and the degree to which entrance to larger pores is restricted by smaller pores. These parameters are derived from measuring vapor adsorption isotherms, mercury intmsion, low angle x-ray scattering, electron microscopy, gas permeabiHty, ion or molecule exclusion, or the volume of imbibed Hquid (1). 

The water removal mechanism is adsorption, which is the mechanism for ad Class 4 drying agents. The capacity of such materials is often shown in the form of adsorption isotherms as depicted in Figures 9a and 9b. The initial adsorption mechanism at low concentrations of water is beheved to occur by monolayer coverage of water on the adsorption sites. As more water is adsorbed, successive layers are added until condensation or capidary action takes place at water saturation levels greater than about 70% relative humidity. At saturation, ad the pores are fided and the total amount of water adsorbed, expressed as a Hquid, represents the pore volume of the adsorbent. 

Oxide-supported metals constitute one of the most important classes of heterogeneous catalysts, and for this reason they have been investigated by many techniques adsorption isotherms, IR of chemisorbed molecules, electron microscopy, EXAFS, etc. Flowever, the fact that they have been studied by so many methods proves that no one technique is totally satisfactory. 

The competitive adsorption isotherms were determined experimentally for the separation of chiral epoxide enantiomers at 25 °C by the adsorption-desorption method [37]. A mass balance allows the knowledge of the concentration of each component retained in the particle, q, in equilibrium with the feed concentration, < In fact includes both the adsorbed phase concentration and the concentration in the fluid inside pores. This overall retained concentration is used to be consistent with the models presented for the SMB simulations based on homogeneous particles. The bed porosity was taken as = 0.4 since the total porosity was measured as Ej = 0.67 and the particle porosity of microcrystalline cellulose triacetate is p = 0.45 [38]. This procedure provides one point of the adsorption isotherm for each component (Cp q. The determination of the complete isotherm will require a set of experiments using different feed concentrations. To support the measured isotherms, a dynamic method of frontal chromatography is implemented based on the analysis of the response curves to a step change in feed concentration (adsorption) followed by the desorption of the column with pure eluent. It is well known that often the selectivity factor decreases with the increase of the concentration of chiral species and therefore the linear -i- Langmuir competitive isotherm was used ... 

Adsorption phenomena from solutions onto sohd surfaces have been one of the important subjects in colloid and surface chemistry. Sophisticated application of adsorption has been demonstrated recently in the formation of self-assembhng monolayers and multilayers on various substrates [4,7], However, only a limited number of researchers have been devoted to the study of adsorption in binary hquid systems. The adsorption isotherm and colloidal stabihty measmement have been the main tools for these studies. The molecular level of characterization is needed to elucidate the phenomenon. We have employed the combination of smface forces measmement and Fomier transform infrared spectroscopy in attenuated total reflection (FTIR-ATR) to study the preferential (selective) adsorption of alcohol (methanol, ethanol, and propanol) onto glass surfaces from their binary mixtures with cyclohexane. Om studies have demonstrated the cluster formation of alcohol adsorbed on the surfaces and the long-range attraction associated with such adsorption. We may call these clusters macroclusters, because the thickness of the adsorbed alcohol layer is about 15 mn, which is quite large compared to the size of the alcohol. The following describes the results for the ethanol-cycohexane mixtures [10],... 

The principle underlying surface area measurements is simple physisorb an inert gas such as argon or nitrogen and determine how many molecules are needed to form a complete monolayer. As, for example, the N2 molecule occupies 0.162 nm at 77 K, the total surface area follows directly. Although this sounds straightforward, in practice molecules may adsorb beyond the monolayer to form multilayers. In addition, the molecules may condense in small pores. In fact, the narrower the pores, the easier N2 will condense in them. This phenomenon of capillary pore condensation, as described by the Kelvin equation, can be used to determine the types of pores and their size distribution inside a system. But first we need to know more about adsorption isotherms of physisorbed species. Thus, we will derive the isotherm of Brunauer Emmett and Teller, usually called BET isotherm. 

Figure 2. Hydrogen adsorption and desorption Isotherms for rhodium catalysts. Solid lines denote total adsorption and dashed lines denote reversible adsorption. The meaning of symbols Is as follows ...

Fig. 8. The adsorption of hydrogen on copper-nickel catalysts as a function of the copper content. The circles represent the total amount of hydrogen adsorbed at room temperature at 10-cm pressure. The triangles represent the amount of strongly adsorbed hydrogen, i.e., the amount not removed by a 10-min evacuation at room temperature following the completion of the initial adsorption isotherm. The amount of strongly adsorbed hydrogen is determined as the difference between the initial isotherm and a subsequent isotherm obtained after a 10-min evacuation (74).

Chemical composition was determined by elemental analysis, by means of a Varian Liberty 200 ICP spectrometer. X-ray powder diffraction (XRD) patterns were collected on a Philips PW 1820 powder diffractometer, using the Ni-filtered C Ka radiation (A, = 1.5406 A). BET surface area and pore size distribution were determined from N2 adsorption isotherms at 77 K (Thermofinnigan Sorptomatic 1990 apparatus, sample out gassing at 573 K for 24 h). Surface acidity was analysed by microcalorimetry at 353 K, using NH3 as probe molecule. Calorimetric runs were performed in a Tian-Calvet heat flow calorimeter (Setaram). Main physico-chemical properties and the total acidity of the catalysts are reported in Table 1. 

Some direct comparisons of the present model with the published results of Fleer and Scheutjens (13) are given in Figures 2 and 3. In the comparison of the adsorption isotherms, shown in Figure 2, the amount adsorbed is represented by the number of equivalent monolayers g (total number of segments in molecules bound to the surface) defined by... 

Adsorption occurs on the microscopic level, with molecules of adsorbate sticking to the atoms on the surface of the substrate (in this case, the pan). In practice, it is rare for each and every adsorption site to have a dye molecule adsorbed to it. The coverage is only fractional. We give the name isotherm to the fraction of the total adsorption sites occupied by adsorbate. An isotherm is denoted with the Greek symbol 0 (theta). 

Total suspended particulates (TSP), 1 798 Toth adsorption isotherm, 1 626, 627 Toughening... 

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