Hysteresis, sorption isotherm

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

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. 

Kapsalis, J.G. 1987. Influence of hysteresis and temperature on moisture sorption isotherms. In Water Activity Theory and Application to Foods (L.B. Rockland and L.R. Beuchat, eds), pp. 173-213. Dekker, New York. 

Hysteresis is observed not only in the sorption isotherms but also in calorimetric measurements of heat of wetting at different moisture contents, and it is thus a combined entropy and enthalpy phenomenon. A reliable explanation for this effect is not currently available, but there is speculation that it is due to the stresses which are induced as the cellulose swells. Since the swelling of cellulose is not completely reversible, mechanical recovery is incomplete and hysteresis will therefore be present both in the internal stress-strain curve of the sample, and also in the water adsorption isotherm. 

In many early experiments, hysteresis was observed for highly hydrophobic compounds such as PCBs (79, 80). Since the time to reach equilibrium can be quite long for strongly hydrophobic compounds, a solute may have never reached equilibrium during the sorption isotherm experiment. Consequently, Kj would be underestimated, which leads to the discrepancy between the sorption and desorption coefficients that was attributed to hysteresis. The case for hysteresis being an artifact is supported by recent data for tetrachlorobenzene (log K = 4.7), illustrating that sorption and desorption require approximately two days to reach equilibrium with approximately equal time constants (78). Finally, the diffusion model is consistent with the observation that the extent of hysteresis was inversely related to particle size (81). 

As discussed above, hysteresis loops can appear in sorption isotherms as result of different adsorption and desorption mechanisms arising in single pores. A porous material is usually built up of interconnected pores of irregular size and geometry. Even if the adsorption mechanism is reversible, hysteresis can still occur because of network effects which are now widely accepted as being a percolation problem [21, 81] associated with specific pore connectivities. Percolation theory for the description of connectivity-related phenomena was first introduced by Broad-bent et al. [88]. Following this approach, Seaton [89] has proposed a method for the determination of connectivity parameters from nitrogen sorption measurements. 

Retention of organic contaminants on subsurface solid phase constituents in general is not completely reversible, so that release isotherms differ from retention isotherms. As a consequence, the extent of sorption depends on the nature of the sorbent. Subsurface constituents as well as the types of bonding mechanisms between contaminants and the sohd phase are factors that control the release of adsorbed organic contaminants. Saltzman et al. (1972) demonstrated the influence of soil organic matter on the extent of hysteresis. Adsorption isotherms of parathion showed hysteresis (or apparent hysteresis) in its adsorption and desorption in a water solution. In contrast, smaller differences between the two processes were observed when the soils were pretreated with hydrogen peroxide (oxidized subsamples) to reduce initial organic matter content. The parathion content of the natural... 

Figure 7.11 Hysteresis of a moisture sorption isotherm (from Fennema, 1985).

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

Figure 7.42 Types of gas sorption isotherm - microporous solids are characterised by a type I isotherm. Type II corresponds to macroporous materials with point B being the point at which monolayer coverage is complete. Type III is similar to type II but with adsorbate-adsorbate interactions playing an important role. Type IV corresponds to mesoporous industrial materials with the hysteresis arising from capillary condensation. The limiting adsorption at high P/P0 is a characteristic feature. Type V is uncommon. It is related to type III with weak adsorbent-adsorbate interactions. Type VI represents multilayer adsorption onto a uniform, non-porous surface with each step size representing the layer capacity (reproduced by permission of IUPAC).

This equation has been successfully applied to many sorption and desorption reactions of dissolved metals and organic compounds. In the case of irreversible sorption (hysteresis), sorption and desorption isotherms are not identical. However, both sorption and desorption Freundlich isotherm equations can be substituted into the transport equation(2) ... 

Hygro-themo-chemo-mechanical behaviour of concrete is of great practical importance in many fields of civil engineering. Modelling these phenomena, especially in fresh concrete structures or concrete elements exposed to fire, is a complex problem. Several non-linear phenomena, like heat and mass sources associated with hydration or dehydration processes, phase changes, hysteresis of sorption isotherms, material properties dependent on moisture content, tem-... 

A clearer picture of the sorption of water vapour by montmorillonite was obtained by Cases et al. (1992). Their adsorption-desorption isotherms of water on sodium montmorillonite are shown in Figure 11.7. The wavy nature of the adsorption and desorption branches (At and Dlr respectively) of the full hysteresis loop in Figure 11.7 is evidently similar to that of the water isotherm in Figure 11.6 and is indicative of a complex mechanism. However, it was established that the scale of the hysteresis loop depended on the maximum relative pressure reached before the pressure was reduced. This dependency is illustrated by the appearance of the partial sorption isotherms also plotted in Figure 11.7. Here, a small hysteresis loop (desorption branch D3) was the result of (p/p°)ma < 0.25, in contrast to much larger loop (desorption branch D2) when the adsorption was taken to (p/p°)max = 0.35. 

Water sorption isotherms for hep show marked hysteresis. Powers and Brownyard (P20) found that, while it was difficult to obtain reproducible desorption curves, the low-pressure part of the water vapour resorption curve varied little with w/c ratio, between different Portland cements, or, if allowance was made for the contents of unreacted cement, with the degree of hydration. This was their main direct evidence for the conclusion (Section 8.2.1) that the properties of the hydration product considered in their model were essentially independent of these variables. However, the water sorption iostherms obtained by different investigators have varied considerably (e.g. Refs P20 and S79), and it is not clear to what extent the above conclusion would stand had different desorption conditions been used. 

It is possible, and perhaps generally believed, that the high reproducibility of an isotherm justihes the extraction of thermodynamic values from data that show hysteresis. However, hysteresis would still be a source of systematic error in the values. There is a poorly documented impression that small samples or thin films display less hysteresis. Hysteresis was not found for the heat capacity isotherm (Yang and Rupley, 1979), which may he taken as support for the view that meaningful free-energy information also can be derived from sorption isotherms. 

It is the scope of the present work to investigate the potential of the CPSM model [8,9], to simulate composite gas sorption isotherms exhibiting or not hysteresis and hence the evaluation of a unified pore size distribution (PSD) covering both the micro-and meso-pore range. Additionally, micropore volume and surface areas will be calculated via the integration... 

The pore condensation hysteresis of two fluids (CHF3 and C2F6) in mesoporous silicas with open cylindrical pores of uniform size (MCM-41 and SBA-15), and in a silica with large cellular mesopores which are accessible only via micropores or narrow mesopores, has been studied over a wide temperature range up to the critical point of the fluids. From the sorption isotherms in MCM-41 and SBA-15 the hysteresis onset-temperapore 7h and the corresponding pore condensation pressure plpo)H was determined for several materials of different pore radius R. 

For the material with cellular pores the temperature dependence of the lower closure point pressure (plpo)i. was measured over a wide temperature range. It is found that in a hysteresis phase diagram (ptpo vs. 777i) the locus of (p/po)H and of the closure point-pressure p po)h almost coincide. Thus it appears that this locus represents a universal border line between sorption isotherms with and without hysteresis loop. 

The texture properties of the ultrathin porous glass membranes prepared in our laboratory were initially characterized by the equilibrium based methods nitrogen gas adsorption and mercury porosimetry. The nitrogen sorption isotherms of two membranes are shown in Fig. 1. The fully reversible isotherm of the membrane in Fig. 1 (A) can be classified as a type I isotherm according to the lUPAC nomenclature which is characteristic for microporous materials. The membrane in Fig. 1 (B) shows a typical type IV isotherm shape with hysteresis of type FIl (lUPAC classification). This indicates the presence of fairly uniform mesopores. The texture characteristics of selected porous glass membranes are summarized in Tab. 1. The variable texture demanded the application of various characterization techniques and methods of evaluation. 

Fig. 3 is an example of a Type II sorption isotherm with hysteresis. Although the etiology of hysteresis has been the subject of many discussions,the phenomena usually can be attributed to... 

Moisture Sorption Isotherms. Green wood loses moisture to the atmosphere and approaches a moisture content designated as the equilibrium moisture content (EMC) for the particular atmospheric conditions. The EMC is a function of relative humidity, temperature, previous exposure history (hysteresis), species, and other miscellaneous factors. 

Sorption hysteresis in wood is beneficial from the viewpoint of wood utilization. This is because wood exposed to cyclic humidity conditions shows smaller changes in moisture content for given humidity changes than would be the case if there were no hysteresis (2J). Sorption hysteresis reduces the effective slope dM/dH of the sorption isotherm and the dimensional changes associated with humidity changes. 

When wood below the fiber-saturation point interacts with water, heat is evolved, and there are changes in the free energy and entropy of the sorbed water. Furthermore, the wood exerts swelling forces that can be measured. These effects can be treated by classical thermodynamic methods although moisture sorption by wood is not a perfectly reversible process because sorption hysteresis is involved, as was pointed out in the section on Moisture Sorption Isotherms (p. 136). 

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