Composite adsorption isotherms

It is important to note that the experimentally defined or apparent adsorption no AN 2/, while it gives F, does not give the amount of component 2 in the adsorbed layer Only in dilute solution where N 2 0 and = 1 is this true. The adsorption isotherm, F plotted against N2, is thus a composite isotherm or, as it is sometimes called, the isotherm of composition change. 

Equation XI-27 shows that F can be viewed as related to the difference between the individual adsorption isotherms of components 1 and 2. Figure XI-9 [140] shows the composite isotherms resulting from various combinations of individual ones. Note in particular Fig. XI-9a, which shows that even in the absence of adsorption of component 1, that of component 2 must go through a maximum (due to the N[ factor in Eq. XI-27), and that in all other cases the apparent adsorption of component 2 will be negative in concentrated solution. 

More often, however, microporosity is associated with an appreciable external surface, or with mesoporosity, or with both. The effect of microporosity on the isotherm will be seen from Fig. 4.11(a) and Fig. 4.12(a). In Fig. 4.11(a) curve (i) refers to a powder made up of nonporous particles and curve (ii) to a solid which is wholly microporous. However, if the particles of the powder are microporous (the total micropore volume being given by the plateau of curve (ii)), the isotherm will assume the form of curve (iii), obtained by summing curves (i) and (ii). Like isotherm (i), the composite isotherm is of Type II, but because of the contribution from the Type 1 isotherm, it has a steep initial portion the relative enhancement of adsorption in the low-pressure region will be reflected in a significantly increased value of the BET c-constant and a shortened linear branch of the BET plot. 

Even so, it is of interest to calculate the BET monolayer capacity from the composite isotherm of Fig. 5.12(b). Though the isotherm did not conform very closely to the BET equation, the isosteric net heat of adsorption was... 

Figure 2 shows us the N2 adsorption-desorption isotherm of Beta/montmorillonite composite. At low relative pressure a sharp adsorption of nitrogen indicates the existence of large amount of micropore. The hysteresis shown in figure 2 is ascribed to type H4 which usually can be observed on layered clay and other materials [2], It is obvious that part of the pore structure in montmorillonite is still preserved after calcination under high temperature and the following hydrothermal crystallization. 

Figure 2. N2 adsorption-desorption isotherm of Beta/montmorillonite composite...

The N2 adsorption-desorption isotherms of dried chitosan gel and chitosan-zeolite composites are reported in Figure 4 (a). Dried chitosan gels present a surface area lower than 5 m2 g"1 and virtually no porosity, the evaporation of water having brought about the coalescence of the polymer fibrils. The composites with a small amount of zeolites (less than 8 % for the zeolite X composite) present a type 4 isotherm leaning towards... 

Figure 4. (a) Adsorption-desorption isotherms of N2 at -196°C of 80°C-outgassed (empty squares) chitosan, (filled trangles) zeolite X-chitosan composite from in-situ zeolite synthesis and (empty triangles) zeolite Y-chitosan composite from encapsulation of the zeolite in the gelling chitosan. (b) Scanning electron micrographs of a calcined zeolite-chitosan bead prepared by zeolitisation of a silica-chitosan composite. 

When a specific feed composition is given, the constraints on m1 and m4 as well as the complete separation region in the (m2, m3) plane can be determined,since these depend only on the parameters of the adsorption equilibrium isotherms and the feed composition itself. Based on these values an operating point can be selected, i. e. a set of four values of = 1,..., 4 fulfilling the complete separation requirements. Since the flow rate ratios are dimensionless groups combining column volumes, flow rates and switching intervals, the constraints on the flow rate ratios are independent of the size and productivity of the SMB unit. 

Adsorption Isotherm Measurements and Site-Selective Thermodynamics. For heterogeneous surfaces like CSPs, the adsorption isotherms are usually composite isotherms and often a Bi-Langmuir model (Equation 1.15) describes reasonably well the adsorption behavior [54]. 

The second concept that has to be considered is that of absolute adsorption or adsorption of an individual component. This can be considered as the true adsorption isotherm for a given component that refers to the actual quantity of that component present in the adsorbed phase as opposed to its relative excess relative to the bulk liquid. It is a surface concentration. From a practical point of view, the main interest lies in resolving the composite isotherm into individual isotherms. To do this, the introduction of the concept of a Gibbs dividing surface is necessary. Figure 10.6 shows the concept of the surface phase model. 

Chemical composition of fresh HTs was determined in a Perkin Elmer Mod. OPTIMA 3200 Dual Vision by inductively coupled plasma atomic emission spectrometry (ICP-AES). The crystalline structure of the solids was studied by X-ray diffraction (XRD) using a Siemens D-500 diffractometer equipped with a CuKa radiation source. The average crystal sizes were calculated from the (003) and (110) reflections employing the Debye-Scherrer equation. Textural properties of calcined HTs (at 500°C/4h) were analyzed by N2 adsorption-desorption isotherms on an AUTOSORB-I, prior to analysis the samples were outgassed in vacuum (10 Torr) at 300°C for 5 h. The specific surface areas were calculated by using the Brunauer-... 

Fig. 4. N2 adsorption-desorption isotherms of (a) sample 11, (b) sample III, and (c) sample IV, and pore size distribution of (a ) sample II, (b1) sample III, and (c ) sample IV of micro-mesoporous composite materials.

The new composite (SC-155) and some of its precursors and derivatives were characterized by LOI (loss on ignition), XRD ( X ray diffraction), 1R (infrared spectra), BET specific surface area, nitrogen adsorption desorption isotherms, pore size distribution (mercury porosimetry), dynamic methylene blue adsorption and SEM (Scanning Electron... 

Analysis of the Composite Isotherm for the Adsorption of a Strong Electrolyte from Its Aqueous Solution onto a Solid... 

Many attempts have been made to obtain the micropore capacity by the analysis of composite isotherms. The calculation of the micropore volume, up(mic), from np(mic) is almost invariably based on the assumption that the adsorbate in the micropores has the same density as the adsorptive in the liquid state at the operational... 

It is the first step in the construction of so-called composite isotherms describing the adsorption on surfaces containing k different adsorption sites. For example,... 

The application of the composite isotherms enables us to model the ion exchange on heterogeneous surfaces, such as rocks and soils. When the structure and composition of the sorbent is well known, we can choose the most probable site affinity distribution function. If not, it is desirable to fit the composite isotherm by different models. The just-described four isotherms provide an opportunity for this. In addition, when adsorption and ion exchange can take place simultaneously, adsorption and ion-exchange isotherms and site distribution functions can be combined (Cernik et al. 1996). 

In Table 2 the textural properties of all the composites heat-treated at 150°, 500°C and 850°C are presented. The sample designation is the same as that used for the raw materials with the addition of the letter m to indicate that the results refer to monolith composites. The total pore volume is the sum of the micro- and mesopore volumes (0-2 nm and 2-50 nm) calculated from the corresponding nitrogen adsorption/desorption isotherms, and the macroporosity (50 nm - 100 pm) determined from MIP, respectively. The threshold diameter was that at which in the MIP analysis there was a sudden upswing in the cumulative volume curve where a large part of the porous network became filled. This pore size can be considered as that which controls any transport phenomena through the solid sample. 

In this work, nickel oxides are prepared by dehydration under vacuum (10 torr) at moderate temperatures (200-300 ) of a pure nickel hydroxide. The hydroxide itself is prepared by the steam distillation of a solution of reagent grade Ni(NOs)2 in an excess of aqueous ammonia (22). As has been shown (22), this method yields Ni(OH)2 containing less than 0.08% of NHs and N2O6. When dried at about 60°, the product has the composition NiO, 1.05 H2O and its BET surface area amounts to 34 m /gm. The external aspect is that of a fine crystalline powder and not of a gel. There are no small-diameter pores in the hydroxide particles since the adsorption-desorption isotherm of nitrogen at —195° does not present an hysteresis loop. The X-ray diagram is that of a well-crystalized nickel hydroxide. 

Figure 15.7 Comparison between experimental and calculated band profiles of 2-phenylethanol in gradient elution. Experimental conditions mobile phase flow rate 1 mL/min. initial mobile phase composition 10% ACN in water column temperature 40°C column dead volume Vq = 2.71 mL. Concentration of the sample solution Cq = 132.5 mmol/L. Gradient, 2% ACN/min. Experimental band profiles (square symbols) and profiles calculated using a composite isotherm (linear plus Langmuir terms), taking into account (solid line) or not (dotted line) the adsorption of ACN on the stationary phase, (a) Injection volume, Vj = 4 mL sample size, 0.53 mmol, loading ratio, 29 molecule per 100 bonded groups, (b) Injection volume, Vj = 6 mL sample size, 0.80 mmol, loading ratio, 43 molecule per 100 bonded groups. Reproduced with permission from M.Z. El Fallah and G. Guiochon, Anal. Chem., 63 (1991) 2244 (Fig. 8). ( 1991, American Chemical Society.

The composite isotherms of hexane, benzene and dioxane adsorption from their mixture on silica are presented on Fig. 1. The isotherms of adsorption are expressed by projections of the same adsorption lines on concentration triangle. 

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