Isotherms for sorption

Fig. 11 Sorption isotherms for water onto potato starch (0) and microcrystalline cellulose ( ). (Data adapted from Ref. 83.)...

Fig. 6 Water vapor sorption isotherms for poly(vinylpyrrolidone) at 60°C(+) 30°C (x) -20°C ( ) and -40°C (A). Data were taken from Oksanen and Zografi [71,75]. A 0 represents the calculated water contents necessary to depress Tg to the temperature of the isotherms.

Hageman, M. J., Possert, P., Bauer, J. M. Prediction and characterization of the water sorption isotherm for bovine somatropin recombinant. Journal of Agricultural Food Chemistry, 40(2), p. 342-347, 1992. 

Fig. 1. CO2 and methane sorption isotherms for the Lower Cretaceous Mannville Group high volatile bituminous B coal, Alberta. 

Typically, sorption isotherms are constructed for a single food ingredient or food system. An alternative approach is to plot the moisture content versus water activity (or relative vapor pressure) values for a variety of as is food ingredients and food systems. The result is a composite food isotherm (Figure 17). The composite isotherm fits the typical shape observed for a sorption isotherm for an individual food system, with a few products falling above or below the isotherm curve (chewing gum, honey, raisins, bread, and colby and cheddar cheeses). Slade and Levine (1991) were the first to construct such a plot using moisture content and aw values from van den... 

This can be related to the fact that the Si atoms substituting Al in the framework during the SiCl treatment originate outside the zeolite (i.e. from SiCl,), while in the steam/ acid treatment the corresponding silicon atoms originate in other parts of the zeolite crystals. This can also explain the absence of "secondary" pores in the material prepared with SiCl, as shown by sorption isotherms for different hydrocarbons (27). 

Sorption isotherms for relatively low concentrations of hydrophobic compounds (i.e., less than one half solubility) are relatively linear and may be estimated by the following equation ... 

To begin, it is essential to rationalize the equilibration of water within the membrane at AP = 0, APs = 0, j = 0, and = 0. The suggested scenario of membrane swelling is based on the interplay of capillary forces and polymer elasticity. In order to justify a scenario based on capillary condensation, isopiestic vapor sorption isotherms for Nafioni in Figure 6.9(a) are compared with data on pore size distributions in Figure 6.9(b) obtained by standard porosimetry.i In Figure 6.9(a), a simple fit function. 

Figure 3 Sorption isotherms for HA and its three esters. Solid lines are the model fitting of the experimental data.

The sorption of Pb(II) to C-S-H has been investigated by Moulin (1999) and Pointeau (2000). In fact XAFS studies indicate that, as for Zn(II), Pb(II) is adsoibed to the silicate chains within the C-S-H structure (Rose et al. 2000). Figure 7 shows sorption isotherms for C-S-H of different Ca Si ratios. It appears that sorption is greater at a lower Ca Si ratio. 

The sorption behaviour of a number of dairy products is known (Kinsella and Fox, 1986). Generally, whey powders exhibit sigmoidal sorption isotherms, although the characteristics of the isotherm are influenced by the composition and history of the sample. Examples of sorption isotherms for whey protein concentrate (WPC), dialysed WPC and its dialysate (principally lactose) are shown in Figure 7.13. At low aw values, sorption is due mainly to the proteins present. A sharp decrease is observed in the sorption isotherm of lactose at aw values between 0.35 and 0.50 (e.g. Figure 7.13). This sudden decrease in water sorption can be explained by the crystallization of amorphous lactose in the a-form, which contains one mole of water of crystallization per mole. Above aw values of about 0.6, water sorption is principally influenced by small molecular weight components (Figure 7.13). 

Despite some conflicting evidence (Kinsella and Fox, 1986), it appears that denaturation has little influence on the amount of water bound by whey proteins. However, other factors which may accompany denaturation (e.g. Maillard browning, association or aggregation of proteins) may alter protein sorption behaviour. Drying technique affects the water sorption characteristics of WPC. Freeze-dried and spray-dried WPC preparations bind more water at the monolayer level than do roller-, air- or vacuum-dried samples, apparently due to larger surface areas in the former. As discussed above, temperature also influences water sorption by whey protein preparations. The sorption isotherm for /Mactoglobulin is typical of many globular proteins. 

In milk powders, the caseins are the principal water sorbants at low and intermediate values of aw. The water sorption characteristics of the caseins are influenced by their micellar state, their tendency towards self-association, their degree of phosphorylation and their ability to swell. Sorption isotherms for casein micelles and sodium caseinate (Figure 7.14) are generally sigmoidal. However, isotherms of sodium caseinate show a marked increase at aw between 0.75 and 0.95. This has been attributed to the... 

Figure 7.14 Sorption isotherm for casein micelles (A) and sodium caseinate (B) at 24°C, pH 7...

Huang et al. (1997) measured sorption isotherms for phenanthrene on 21 soils and sediments. All isotherms were nonlinear with Freundlich exponents n,- (Eq. 9-1) between 0.65 and 0.9. For example, for a topsoil (Chelsea 1) and for a lake sediment (EPA-23), interpolating the isotherm data yields the following observed sorbed concentrations, Cis, in equilibrium with dissolved concentrations, Ciw, of 1 /zg L-1 and 100 /zg-L-1, respectively ... 

Xia and Ball (1999) measured sorption isotherms for a series of chlorinated benzenes and PAHs for an aquitard material (foc = 0.015 kg oc kg-1 solid) from a formation believed to date to the middle to late Miocene. Hence, compared to soils or recent sediment POM, the organic matter present in this aquitard material can be assumed to be fairly mature and/or contain char particles from prehistoric fires. A nonlinear isotherm was found for TeCB (fitting Eq. 9-2) and the following Freundlich parameters were reported XreCBF = 128(mg g 1)(mg mL 1) "T CBand "TeCB = 0.80. For partitioning of TeCB to this material (linear part of the isotherm at higher concentrations), the authors found a Kioc value of 4.2 x 104 L kg oc. 

Figure 11.6 Sorption isotherms for two kinds of nonionic organic compounds from aqueous solutions to suspended kaolinite (a) slightly monopolar compound, pyrene, showing a linear isotherm up to its solubility (Backhus, 1990), and (b) monopolar compound, 1,3,5-trinitrobenzene, showing a hyperbolic isotherm (Had-erlein et al., 1996).

Figure 11.9 Sorption isotherms for some charged organic compounds interacting with natural solids (a) quinolinium cation on a subsoil of /oc = 0.024 and cation exchange capacity of 84 mmol/kg (Zachara et al., 1986), ( >) anilinium cation on a surface soil with /oc = 0.013 and cation exchange capacity of 112 mmol/kg (Lee et al., 1997), and (c) sorption of 4-(2,4-dichloro-phe-noxy)-butyrate anion on a sediment with/oc = 0.015 and unknown anion exchange capacity (Jafvert, 1990).

Thus, in terms of a, the sorption isotherm for osmotically ideal solutions is of Type III in Brunauer s classification (29) and reduces to Henry s law for (Mi/M2)a< 1. 

The difference between IGC and conventional analytical gas-solid chromatography is the adsorption of a known adsorptive mobile phase (vapour) on an unknown adsorbent stationary phase (solid state sample). Depending on experiment setup, IGC can be used at finite or infinite dilution concentrations of the adsorptive mobile phase. The latter method is excellent for the determination of surface energetics and heat of sorption of particulate materials [3]. With IGC at finite dilution, it is possible to measure sorption isotherms for the determination of surface area and porosity [4], The benefits of using dynamic techniques are faster equilibrium times at ambient temperatures. 

Fig. 7. Mixed gas sorption isotherms for PMMA-C02> C2H4 in terms of fugacities f, at fC02 = 1.50 + 0.05 atm, T = 35 °C. Experimental data ( ) in comparison with lines calculated from pure...

Figure A2.2.1 Water activity stability map (adapted form Labuza, 1970). A representation of a typical sorption isotherm for food materials and of the effects of water activity on the relative reaction rates of several chemical processes, as well as the growth of microorganisms, in foods are shown.

Figure A2.3.3 Sorption isotherm for typical food product showing hysteresis. Reprinted from Rahman and Labuza (1999), courtesy of Marcel Dekker.

The grain size distributions of the two batches of SMZ were determined by sieve analysis. Chromate and PCE sorption isotherms for each batch of SMZ were prepared using methods described earlier (Li and Bowman 1997 Li and Bowman 1998). 

Table 4. Parameters of the HOC sorption isotherms for sorbed surfactants. 

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