Adsorption isothermic conditions

Calculation of the SMB flowrates The criterion C + K - Cg<0. (Equation 10) equaling now approximately 0.22, the system is operating under nonlinear adsorption isotherm conditions. 

The specific adsorption of ions at the ITIES has been studied by Su et al. who have simulated the capacitance response for different adsorption isotherm conditions [77]. Figure 1.6 illustrates the effect of adsorption on the capacitances and potential distribution in the case of a potential dependent Langmuir isotherm for which the surface coverage is given by... 

Fig. XI-5. Adsorption isotherm from Ref. 61 for polystyrene on chrome in cyclohexane at the polymer theta condition. The polymer molecular weights x 10 are (-0) 11, (O) 67, (( )) 242, (( )) 762, and (O) 1340. Note that all the isotherms have a high-affinity form except for the two lowest molecular weights.

The adsorption isotherms are often Langmuirian in type (under conditions such that multilayer formation is not likely), and in the case of zeolites, both n and b vary with the cation present. At higher pressures, capillary condensation typically occurs, as discussed in the next section. Some N2 isotherms for M41S materials are shown in Fig. XVII-27 they are Langmuirian below P/P of about 0.2. In the case of a microporous carbon (prepared by carbonizing olive pits), the isotherms for He at 4.2 K and for N2 at 77 K were similar and Langmuirlike up to P/P near unity, but were fit to a modified Dubninin-Radushkevich (DR) equation (see Eq. XVII-75) to estimate micropore sizes around 40 A [186]. 

The hydration shell is formed with the increasing of the water content of the sample and the NA transforms from the unordered to A- and then to B form, in the case of DNA and DNA-like polynucleotides and salt concentrations similar to in vivo conditions. The reverse process, dehydration of NA, results in the reverse conformational transitions but they take place at the values of relative humidity (r.h.) less than the forward direction [12]. Thus, there is a conformational hysteresis over the hydration-dehydration loop. The adsorption isotherms of the NAs, i.e. the plots of the number of the adsorbed water molecules versus the r.h. of the sample at constant temperature, also demonstrate the hysteresis phenomena [13]. The hysteresis is i( producible and its value does not decrease for at least a week. 

Contemporary development of chromatography theory has tended to concentrate on dispersion in electro-chromatography and the treatment of column overload in preparative columns. Under overload conditions, the adsorption isotherm of the solute with respect to the stationary phase can be grossly nonlinear. One of the prime contributors in this research has been Guiochon and his co-workers, [27-30]. The form of the isotherm must be experimentally determined and, from the equilibrium data, and by the use of appropriate computer programs, it has been shown possible to calculate the theoretical profile of an overloaded peak. 

However, before proceeding with the description of simulation data, we would like to comment the theoretical background. Similarly to the previous example, in order to obtain the pair correlation function of matrix spheres we solve the common Ornstein-Zernike equation complemented by the PY closure. Next, we would like to consider the adsorption of a hard sphere fluid in a microporous environment provided by a disordered matrix of permeable species. The fluid to be adsorbed is considered at density pj = pj-Of. The equilibrium between an adsorbed fluid and its bulk counterpart (i.e., in the absence of the matrix) occurs at constant chemical potential. However, in the theoretical procedure we need to choose the value for the fluid density first, and calculate the chemical potential afterwards. The ROZ equations, (22) and (23), are applied to decribe the fluid-matrix and fluid-fluid correlations. These correlations are considered by using the PY closure, such that the ROZ equations take the Madden-Glandt form as in the previous example. The structural properties in terms of the pair correlation functions (the fluid-matrix function is of special interest for models with permeabihty) cannot represent the only issue to investigate. Moreover, to perform comparisons of the structure under different conditions we need to calculate the adsorption isotherms pf jSpf). The chemical potential of a... 

Table 9-3. Operating conditions for complete separation under Equilibrium Theory. Langmuir adsorption isotherms (see Fig. 9-8).

Linear case This case is met when the adsorption isotherm is considered linear, which means operation under diluted conditions. Taking into account the saturation capacities of the CSP, this behavior is usually met for concentrations around or below 1 g for separation of enantiomers. 

The dissolution of passive films, and hence the corrosion rate, is controlled by a chemical activation step. In contrast to the enhancement of the rate of dissolution by OH ions under film-free conditions, the rate of dissolution of the passive film is increased by increasing the ion concentration, and the rate of corrosion in film-forming conditions such as near-neutral solutions follows the empirical Freundlich adsorption isotherm ... 

The conformity to laws of adsorption, in particular their thermodynamic fundamentals, is independent of whether a water-air or a water-apolar oil interface is considered, provided that the surfactant is soluble only in one phase. If the oil phase in a liquid two-phase system is apolar, this condition is valid for many surfactants. Thus, all surfactants with an adequate solubility in water are almost insoluble in the hydrocarbon phase. If this condition is not met, e.g., in the system water-amyl alcohol, the thermodynamically based adsorption isotherms are more complicated to set up [39]. 

A quantitative analysis [34], based on the adsorption isotherms and the intercrystalline porosity, yielded the remarkable result that a satisfactory fit between the experimental data and the estimates of Aong-range = Pinter Anter following Eqs. (3.1.11) and (3.1.12) only lead to coinciding results for tortuosity factors a differing under the conditions of Knudsen diffusion (low temperatures) and bulk-diffusion (high temperatures) by a factor of at least 3. Similar results have recently been obtained by dynamic Monte Carlo simulations [39—41]. 

The basic assumption of the Langmuir adsorption isotherm is that the adsorbed molecules do not interact. This condition is not always fulfilled for adsorption, particularly on electrodes. The Frumkin adsorption isotherm includes interaction between molecules in the adsorption film,... 

Limited available data on adsorption under simulated deep-well conditions are best described by the formula however, the disadvantage of all adsorption isotherms applies. 

This chapter reports the results from transient experiments (mainly, TPD or TPSR) coupled with on-line analysis of reaction mixture at the outlet of a well-stirred reactor. It means that the gas composition detected at the outlet of the reactor is in contact with the catalyst inside the reactor. Catalytic runs in isothermal conditions were also proceeded in order to avoid strong adsorptions of reactants or intermediates. 

Monkiedje et al. [10] investigated the fate of niclosamide in aquatic system both under laboratory and field conditions. The octanol/watcr partition coefficient (Kaw) of niclosamide was 5.880 x 10 4. Adsorption isotherm studies indicated that the Freundlich parameters (K, n) for niclosamide were 0.02 and 4.93, respectively, for powder activated carbon (PAC), and 9.85 x 10 5 and 2.81, respectively, for silt loam soil. The adsorption coefficient (Aoc) for the drug was 0.02 for PAC, and 4.34 x 10-3 for the same soil. Hydrolysis of niclosamide occurred in distilled water buffer at pH above 7. No photolysis of the drug was observed in water after exposure to long-wave UV light for 4 h. Similarly, neither chemically volatilized from water following 5 h of sample aeration. Under field conditions, niclosamide persisted in ponds for over 14 days. The half-life of niclosamide was 3.40 days. 

Rhaman and coworkers [112,113] studied the adsorption of lipase on [MgAl] LDH and its biocatalytic activity for butyl oleate synthesis. They demonstrated that up to 277 and 531 mgg-1 of lipase were adsorbed on [MgAl-N03] and [MgAl-Dodecylsulfate] LDH, respectively, showing the highest adsorption capacity of the anionic clays compared to smectite or inorganic phosphate. Recently, we reported the adsorption isotherms of urease on [ZnRAl] LDH under various experimental conditions (pH, buffer) [117]. The kinetic study showed the fast adsorption process (less than 60 min) (Figure 15.3). 

Figure 2. Adsorption isotherms for equilibrium (top curve) and nonequilibrium conditions. Molecular weight 1x10, charge density 95%. Nonequilibrium, open symbols G = 1800 s 1, closed symbol G = 8000 s-1.

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