Sorption isotherm, 5.25

In a sorption process, a species from a fluid phase binds to the surface of (in the case of adsorption) or in the interior of (for absorption) another condensed phase. Thus, one can find sorption of gas molecules to liquids, adsorption of gas molecules to the surface of liquids or solids, or sorption of solute species (ions or molecules) from solution to solid particles. An adsorption isotherm or, more generally, a sorption isotherm, is an equilibrium relationship between the activity (or fugacity) of the species to be bound, the sorbate, in the bulk phase and the activity of the bound sorbate. The process can be regarded formally as a chemical reaction, for example, in the case of adsorption from aqueous solution 

A necessary consistency check of a water sorption model is the calculation of vapor sorption isotherms. Equation 2.49 gives A V/Vb as a function of oo.c- The input for the calculation includes the environmental parameters T, P, P ), materials parameters (sr, G, PsQ-) probability density distribution n (ao). The value of t]c can be 

In order to simplify the calculation, a modified version of liquation 2.49 is used  

The insensitivity of water sorption and swelling to P should not be seen as an argument for neglecting pressure driven flux mechanisms in models of PEM 

Eigure 2.26 compares calculated water sorption isotherms to two independent sets of experimental data for Nafion (Maldonado et al., 2012 Zawodzinski et al., 1991). A fixed amount of surface water is subtracted in experimental isotherms, since the theory describes bulk-like water only. After this modification, the agreement that can be achieved is good. 

FIGURE 2.26 Left Sorption isotherm from theory with the statistical distribution of the surface charge density as input. Comparison with exp. data in (Zawodzinski et al., 1991) (dark grey dots) and (Maldonado et al., 2012) (light grey dots). Right Microscopic statistical distributions of pore size and pressure (left to right P /P = 0.25, 0.5, 0.75, and 0.90). 

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Nonideal asymmetrical chromatographic bands showing (a) fronting and (b) tailing. Also depicted are the corresponding sorption isotherms showing the relationship between the concentration of solute in the stationary phase as a function of its concentration in the mobile phase. 

Fig. 3. Sorption isotherms of water on textile fibers at 25°C 0, wool x viscose D, silk O, cotton V, acetate A nylon.

Sorption Modeling. Pesticide sorption is characterized by describing sorption isotherms using the Freundhch equation, S = Kj, where S is the pesticide sorbed concentration, C is the pesticide solution concentration after equdibration, and fy and N are constants. Although other equations have been used, the Freundhch has satisfactodly described experimental sorption results for a wide range of pesticides in a variety of sods. The value of N is usually <1 and between 0.75 and 0.95, which indicates that pesticides are proportionally more sorbed at low solution concentration than at high solution concentration. 

Fig. 6. Sorption and desorption of ima2ethapyr on (a) Sassfras sandy loam and (b) Webster clay loam (45) Q — sorption isotherm,...

Indirect methods of estimating sorption have been used when actual measurement of sorption isotherm is impossible (44). For instance, sorption coefficients have been estimated from soil organic carbon and a specific surface of soil, and from semiempidcal equations using pesticide properties. 

For glassy polymers, sorption isotherms are more complex and hysteresis oetween the pressurization and depressurization steps may... 

Generally the above expressions adequately describe sorption isotherms of the type reported in Fig. 1, giving good agreement with experimental results in non-... 

Fig. 3. Water sorption isotherms of poIy(trans-3,4-dihydroxytetrahydiopyran-6,2-diyloxy-methylene) 24 and its related polymers at 20 °C.

Fig. 10. Sorption isotherms of different polyamides. At 20 °C. o, 67 , nylon-4 o. nylon-6 ----, wool ----, silk58)...

Igwe, C.J. and Abia, A.A., Equilibrium sorption isotherm studies of Cd(II), Pb(II) and Zn(II) ions detoxification from wastewater using unmodified and EDTA-modified maize husk, Electronic Journal of Biotechnology, 10 (4), 536-548, 2007. 

Schechter, R.S., Wade, U.H., and Uingrave, J.A. "Sorption Isotherm Hysteresis and Turbidity Phenomena in Mesoporous Media," J. Colloid Sci.. Manuscript 4880-2. 

Without any doubt, the zeolite framework porous characteristics (micropores sizes and topology) largely govern the zeolite properties and their industrial applications. Nevertheless for some zeolite uses, as for instance, host materials for confined phases, the zeolite inner surface characteristics should be precised to understand their influence on such low dimensionality sorbed systems. In that paper, we present illustrative examples of zeolite inner surface influence on confined methane phases. Our investigation extends from relatively complex zeolite inner surface types (as for MOR structural types) to the model inner surface ones (well illustrated by the AFI zeolite type). Sorption isotherm measurements associated with neutron diffraction experiments are used in the present study. 

Qads.(max) = 5.7 molecules by unit cell). Generally speaking, Qacis.(max) is closely related to the molecular size, as it is observed for the other molecular species. Secondly, as shown on Figure 5, sorption isotherm sub-step observation could be another signature of zeolite inner surface influence. Such isotherm sub-step reflects a phase transition existence between a fluid phase and a solid phase stabilized by the inner surface sorption sites. 

Figure 1. Methane sorption isotherms measured at T = 77.35 K on four different AlP04-5 zeolite samples S(l), S(2), S(3) and S(4).

The same study has been performed concerning the methane / ZSM-12 zeolite system. The neutron diffractograms, measured for different methane loadings of ZSM-12 zeolite, are represented on figure 9. In addition, a methane calibration sorption isotherm... 

Figure 10. Methane calibration sorption isotherm measured at T = 78 K during the neutron diffraction experiment.

Figure 3. Nitrogen sorption isotherms, DFT pore size distributions (inset) and XRD patterns (inset) of MCM-41-IBU obtained after different immersion times...

In the case of MCM-41-REF, N2 sorption isotherms (figure 4) reveal that the same mesopores occlusion occurs between 2 and 9 hours, but, at variance with MCM-41-IBU, the temporary opening of mesopore between 24 and 27 hours is not observed and the occlusion continues over 170 hours. We suggest that the entrapped molecules play a role in the temporary opening of the pores in MCM-41-IBU between 24 and 27 hours of immersion. 

Pigna M, Colombo C, Violante A (2003) Competitive sorption of arsenate and phosphate on synthetic hematites (in Italian). Proceedings XXI Congress of Societa Italiana Chimica Agraria SICA (Ancona), pp 70-76 Quirk JP (1955) Significance of surface area calculated from water vapour sorption isotherms by use of the B. E. T. equation. Soil Sci 80 423-430 Rancourt DG, Fortin D, Pichler T, Lamarche G (2001) Mineralogical characterization of a natural As-rich hydrous ferric oxide coprecipitate formed by mining hydrothermal fluids and seawater. Am Mineral 86 834-851 Raven K, Jain A, Loeppert, RH (1998) Arsenite and arsenate adsorption on ferrihydrite kinetics, equilibrium, and adsorption envelopes. Environ Sci Technol 32 344-349... 

Captina silt loam pH 4.97 McLaurin sandy loam pH 4.43, batch equilibrium, Walton et al. 1992) 1.75 (average of 5 soils, sorption isotherms by batch equilibrium method-GC, Xing et al. 1994)... 

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