Hysteresis in sorption

Figure 1-13 Ink Bottle Theory of Hysteresis in Sorption. Source From T.P. Labuza, Sorption Phenomena in Foods, Food Technol, Vol. 22, pp. 263-272, 1968.

The conventional inverse gas chromatography (IGC) is based on equations that assume equilibrium is established during the course o the chromatograph. Consequently, those stationary phases that exhibit marked hysteresis in sorption/desorption give IGC sorption data at considerable variance with long-term gravimetric methods. A modified frontal procedure was developed that avoids the assumption of equilibrium to enable studies of interaction kinetics of gas phase components with a stationary phase, such as a biopolymer, having entropic as well as enthalpic relations affected by concentration shifts and time dependent parameters. 

Qualitative explanations for the hysteresis in sorption for cellulosic materials have been advanced. Urquhart [23] hypothesized that hysteresis could be caused by a differential availability of hydroxyl groups in cellulose during the adsorption and desorption branches of the RH cycle. A second explanation for hysteresis stems from the observed plasticity of the cellulose gels, which swells upon adsorption. Desorption results in some irreversible (plastic) deformation, which results in a higher moisture content of the structure as compared to the adsorption process. His theory postulated that the lost work during a stress strain cycle is equal to the lost work represented by the hysteresis loop between two relative humidity levels. 

Fig. 39.4 (a) Gas sorption isotherm of 2b at 296 K for N2, Air, O2 and CO2 (b) SectiMial views of dimaeric capsule formed from 2, two calixarenes are colored blue and red while sectiOTied surface kept yellow with green methane molecules, (c) Sorption of acetylene and CO2 at room temperature (d) Hysteresis in sorption and desorption isotherm of acetylene (Reproduced with permission from publisher Refs. [16,26b, 23b]. Copyright 2004,2005, and 2006, Wiley-VCH and Royal Society of Chemistry)... 

Sorbed pesticides are not available for transport, but if water having lower pesticide concentration moves through the soil layer, pesticide is desorbed from the soil surface until a new equiUbrium is reached. Thus, the kinetics of sorption and desorption relative to the water conductivity rates determine the actual rate of pesticide transport. At high rates of water flow, chances are greater that sorption and desorption reactions may not reach equihbrium (64). NonequiUbrium models may describe sorption and desorption better under these circumstances. The prediction of herbicide concentration in the soil solution is further compHcated by hysteresis in the sorption—desorption isotherms. Both sorption and dispersion contribute to the substantial retention of herbicide found behind the initial front in typical breakthrough curves and to the depth distribution of residues. 

The amounts of water absorbed as function of relative water vapor pressure (relative humidity) for HA and its esters are reported in Tables 1-4. HA absorbed the highest amount of water at all humidity levels compared to its esters. The ethyl ester (Hyaff ) absorbs more water than the other two, and the dodecyl ester (Hyaff73) absorbs more water than the benzyl ester (Hyaffll). A small percentage of water absorption hysteresis, between sorption and desorption, was found for the four different materials analyzed. No significant differences in the percentage of hysteresis was found among the HA and the three esters. 

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. 

Apparent hysteresis occurs mainly when complete equilibrium is not reached. Diffusion into the solid matrix or into micropores of aggregates is considered a main cause of apparent hysteresis. In a transitory state, sorption occurs concurrently with desorption and the concentration of contaminant in the liquid phase is erroneously low because some fraction is associated with sorption. 

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... 

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-... 

If sorption was entirely reversible, an isotherm can be obtained by connecting the origin to the first desorption point. The slope of the line (6671/kg) represents the partition coefficient, if the partitioning was entirely reversible. It is quite clear that the adsorption and desorption pathways are quite different, and that considerable hysteresis in desorption exists. A linear fit of data in the desorption cycle yields a slope equivalent to a partition coefficient for the loosely bound fraction which we represent as K 1// 1 and is 1661/kg in the present case. Extrapolating back on this slope suggests that approximately 1,204 13 pg/g of the HCBD is tightly bound to the soil and may desorb only very slowly (months... 

York, P. Analysis of moisture sorption hysteresis in hard gelatin capsules, maize starch, and maize starch drug powder mixtures. J. Pharm. Sci. 1981, 33, 269-273. 

Starch has been classified as a moderately hygroscopic material.f Water sorption studies have been conducted using static methods (saturated salt solutions in closed chambers) modified inverse frontal gas chromatography, and automated moisture balance systems. " The isotherms are typically type II curves exhibiting hysteresis, as shown in Fig. 5. Hysteresis in starch samples has been attributed to intra- and... 

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. 

Skaar, C. Moisture Sorption Hysteresis in Wood Proc., Symposium on Wood Moisture Content, Temperature and Humidity Relationships, U.S. For. Serv. For. Prod. Lab., Madison, WI 1979. 

Finally, we can analyze the sorption hysteresis in terms of the change in structural arrangement in the molecular network (24) noted for similar systems where swelling-shrinking occur on sorption-desorption. The concept of a yielding coal structure is quite valid in view of the comprehensive work to show that swelling and shrinking are appreciable (even for CO2 and CH4 sorption) (23, 25, 26). 

These results indicate that the shape of sorption isotherms of pure fluids on MCM-48 silicas, i.e. the occurence of pore condensation and sorption hysteresis as well as details of the hysteresis loop depend on the pore size and temperature. The observed hysteresis loops are of type HI, indicating that networking effects are not dominant for sorption hysteresis in the MCM-48 silica materials studied here, despite the fact that MCM-48 consists of a unique three dimensional pore network. 

Methods for determining sorption isotherms by gas chromatography have been published by various authorsQ,-, ). The methods used have been elution and frontal chromatography. The first combines sorption and desorption so that any hysteresis in the equilibrium transport from gas to stationary phase and back to the gas phase can produce corresponding errors. The Kiselev-Yashin equation, as shown in Figure 1,... 

The use of frontal chromatography would appear to avoid the errors produced by hysteresis in that the sorption and desorption processes can be separated in time. An extensive study of this method for water sorption, using freeze-dried coffee as a... 

Theoretical isotherms calculated for regularly packed spheres look encouraging. In spite of simplifying assumptions, we obtained a qualitative agreement with experimental isotherms, mainly narrow sorption hysteresis in the regions close to p/Po - 1- Total pore volumes depend strongly on the choice of n (coordination number). More detailed analysis, allowing for polydisperslty of both r and n, is required for quantitative interpretation of Isotherms. 

McEnaney, B. (1974). Low pressure hysteresis in the sorption of carbon tetrachloride vapour on polymer carbon. J. Chem. Soc. Faraday Trans. I, 70, 84—94. 

Liu, H., Zhang, L., and Seaton, N. (1993). Analysis of sorption hysteresis in mesoporous solids using a pore network model. J. Colloid Interface Sci., 156, 285-93. 

The water uptake data are presented in Figure 51.1, which shows that polymorph A adsorbs greater quantities of water vapor than polymorph B under all conditions of temperature and RH investigated. In general, sorption isotherms of form A also exhibit more pronoimced hysteresis than form B. A notable exception is the 45°C isotherm, where the two crystal forms show similar and quite pronounced hysteresis. In fact, the profiles obtained at 45°C are suggestive of condensation taking place at that temperature. 

As we pointed out above, metastability is manifest as hysteresis in a sorption isotherm (like the one plotted in Fig. 5.9). Metastabihty involves a range of finite width As around the true transition point over which for the same T and fj, p (sz) is a double-valued function. To distinguish the metastable from the thermodynamically (i.e., globally) stable phase one needs to compare w for the two states pertaining to different brandies of the sorption isotherm at the same p, and [see Eq. (1.68)]. The branch having lowest uj is the globally stable phase the other one is only metastable. In Fig. 5.9 we plot only data for thermodynamically stable phases identified according to this... 

Consider now adsorbed molecular or ionic species that are, practically speaking, immobilized in the soil. Unless the soil is extremely acid, metals such as Cu, Cr, and Pb fall into this category. Also, certain anions such as phosphate bond so strongly on minerals that they too behave as immobile elements. The property that all of these ions have in common is that their sorption isotherms are not reversible within a time scale relevant to soil processes the adsorption (forward) isotherm is usually approximated closely by a Langmuir function of the strong-affinity type, but the desorptioii (backward) isotherm deviates markedly from the adsorption isotherm. This kind of nonequilibrium behavior, depicted in Figure 9.6, is sometimes referred to as hysteresis. Possible reasons for hysteresis in chemisorption are discussed in Chapter 4. 

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