Absorption, multicomponent systems

A detailed discussion for the design methods of plate and packed absorbers is beyond the scope of this chapter. Reference to Perry s hlandbook (50th edition), pp. 14-14-14-24 is recommended. Heat effects in gas absorption, multicomponent systems, and absorption with chemical reaction are fully discussed as well on pp. 14-24-14-31. 

Multicomponent Diffusion. In multicomponent systems, the binary diffusion coefficient has to be replaced by an effective or mean diffusivity Although its rigorous computation from the binary coefficients is difficult, it may be estimated by one of several methods (27—29). Any degree of counterdiffusion, including the two special cases "equimolar counterdiffusion" and "no counterdiffusion" treated above, may arise in multicomponent gas absorption. The influence of bulk flow of material through the films is corrected for by the film factor concept (28). It is based on a slightly different form of equation 13 ... 

FIG. 14-9 Graphical design method for multicomponent systems absorption of hiitane and heavier components in a soliite-free lean oil. 

According to Maxwell s law, the partial pressure gradient in a gas which is diffusing in a two-component mixture is proportional to the product of the molar concentrations of the two components multiplied by its mass transfer velocity relative to that of the second component. Show how this relationship can be adapted to apply to the absorption of a soluble gas from a multicomponent mixture in which the other gases are insoluble and obtain an effective diffusivity for the multicomponent system in terms of the binary diffusion coefficients. 

The squaraine rotaxanes based on the macrocycle 16b exhibit intense NIR absorption and emission maxima, and it should be possible to develop them into molecular probes for many types of photonic and bioimaging applications. In contrast, the squaraine fluorescence intensity is greatly diminished when the dye is encapsulated with macrocycle 18. The fluorescence is restored when a suitable anionic guest is used to displace the squaraine dye from a pseudorotaxane complex, which indicates that the multicomponent system might be applicable as a fluorescent anion sensor. 

In multicomponent systems A"0 can be written as a sum of the individual absorption coefficients A ot = 2TA , where each AT,(A ) depends in a different way on the wavelength. If one or more of the components are fluorescent, their excitation spectra are mutually attenuated by absorption filters of the other compounds. This effect is included in Eqs. (8.27) and (8.28) so that examples like that of Figure 8.4 can be quantified. The two fluorescent components are monomeric an aggregated pyrene, Mi and Mn. The fluorescence spectra of these species are clearly different from each other but the absorption spectra overlap strongly. Thus the excitation spectrum of the minority component M is totally distorted by the Mi filter (absorption maxima of Mi appear as a minima in the excitation spectrum ofM see Figure 8.4, top). In transparent samples this effect can be reduced by dilution. However, this method is not very efficient in scattering media as can be seen by solving Eqs. (8.27 and 8.28) for bSd — 0. Only the limit d 0 will produce the desired relation where fluorescence intensity and absorption coefficient of the fluorophore are linearly proportional to each other in a multicomponent system. 

The expression for the excess Gibbs energy is built up from the usual NRTL equation normalized by infinite dilution activity coefficients, the Pitzer-Debye-Hiickel expression and the Born equation. The first expression is used to represent the local interactions, whereas the second describes the contribution of the long-range ion-ion interactions. The Bom equation accounts for the Gibbs energy of the transfer of ionic species from the infinite dilution state in a mixed-solvent to a similar state in the aqueous phase [38, 39], In order to become applicable to reactive absorption, the Electrolyte NRTL model must be extended to multicomponent systems. The model parameters include pure component dielectric constants of non-aqueous solvents, Born radii of ionic species and NRTL interaction parameters (molecule-molecule, molecule-electrolyte and electrolyte-electrolyte pairs). 

Vapor-Liquid Equilibria for the Ammonia, Hydrogen, Nitrogen, Argon, Methane System (Fig. 4). Because of the great importance of absorption processes in synthesis loop engineering (see Section 4.5.6), these binary and multicomponent systems have been experimentally and theoretically reinvestigated several times. The updates are based mainly on thermodynamic relationships in combination with equations of state. 

A variety of other porphyrin-quinone-based multicomponent systems bearing four or more donor and acceptor moieties have been reported. For example, P-P-P-Q tetrad 53 and related compounds have been reported by Sessler and coworkers [64, 65, 73, 220, 232-236]. Fluorescence and time-resolved absorption experiments with 53 were interpreted in terms of rapid ( 10-ps) singlet-singlet energy transfer between the porphyrin units in the linear array and extremely fast (<350-fs) photo-induced electron transfer to the quinone from the proximal porphyrin excited singlet state to give a charge-separated species. 

Sauvage, J. P. Collin, J. P. Chambron, J. C. Guillerez, S. Coudret, C. Balzani, V. Barigelletti, F. Decola, L. Flamigni, L. Ruthenium(II) and osmium(II) bis(terpyridine) complexes in covalently linked multicomponent systems - synthesis, electrochemical behavior, absorption spectra, and photochemical and photophysical properties. Chem. Rev. 1994, 94, 993-1019. 

To decipher the number of ligands, F that bind to a metal, M, Job s method relies on the additive property of absorbance of species in solution. For a multicomponent system, absorbances, A, are additive for y non-interacting speciest with concentrations cy and molar absorptivities, sy, equation (3.14). 

There is ample experimental evidence to show that the efficiencies of different components in a multicomponent system are not all equal. The first clear statement of this fact can be found in a paper by Walter and Sherwood (1941) who, on the basis of an extensive experimental study of Murphree vapor and liquid efficiencies for absorption, desorption, and rectification operations, concluded The results indicate that different efficiencies should be used for each component in the design of absorbers for natural gasoline and refinery gases. Since the publication of their paper many others have provided additional data to confirm this view [see Krishna and Standart (1979) for a list of references]. We review some of these data below. 

Moreover, the mean polarizability approximation can yield highly accurate results for dispersion and optical anisotropy of crystalline solutions outside the absorption band. This is due to the fact that the concentration broadening in crystals of this type (with only van der Waals interactions between the molecules) does not affect the integral oscillator strength of a transition. The mean polarizability approximation served as the basis for the procedure developed by Obreimov for the analysis of the composition of multicomponent systems as applied to a wide variety of isotopic mixtures, both liquid and crystalline (for the details, see (20)). 

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