Other hysteresis theories

Intrusion-extrusion hysteresis has been attributed to ink-bottle shaped pores. In pores of this type intrusion cannot occur until sufficient pressure is attained to force mercury into the narrow neck, whereupon the entire pore will fill. However, on depressurization the wide-pore body cannot empty until a lower pressure is reached, leaving entrapped mercury in the wide inner portion. The ink-bottle model ignores several factors which may reduce it to an untenable concept. These include the following  

All porous samples exhibit hysteresis. This would require that every porous material contains pores which are ink-bottle in shape. 

Porosimetry curves exhibit various shapes. If hysteresis were caused by ink-bottle pores only one shape hysteresis curve should be observed. 

Regardless of the maximum pressure attained, depressurization always results in hysteresis. This would imply that ink-bottle pores are distributed over the entire range of pore sizes. Therefore, pores with very wide entrances would have to possess even wider inner cavities. 

Intrusion into and extrusion out of the volume between packed spheres, where the openings are wider than the interior, show hysteresis. 

---

Nearly all of the data are collected at room temperature, and there is no accepted method for correcting them to other temperatures. Far fewer data have been collected for sorption of anions than for cations. The theory does not account for the kinetics of sorption reactions nor the hysteresis commonly observed between the adsorption and desorption of a strongly bound ion. Finally, much work remains to be done before the results of laboratory experiments performed on simple mineral-water systems can be applied to the study of complex soils. 

These and other theories may each describe a unique condition leading to hysteresis and indeed there may be no single mechanism which can universally explain the phenomenon. 

Computer modelling of physisorption hysteresis is simplified if it is assumed that pore filling occurs reversibly (i.e. in accordance with the Kelvin equation) along the adsorption branch of the loop. Percolation theory has been applied by Mason (1988), Seaton (1991), Liu et al., (1993, 1994), Lopez-Ramon et al., (1997) and others (Zhdanov et al.,1987 Neimark 1991). One approach is to picture the pore space as a three-dimensional network (or lattice) of cavities and necks. If the total neck volume is relatively small, the location of the adsorption branch should be mainly determined by the cavity size distribution. On the other hand, if the evaporation process is controlled by percolation, the location of the desorption branch is determined by the network coordination number and neck size distribution. 

Analysis of behavior in single pores is certainly an excellent place to start an understanding of adsorption hysteresis. On the other hand, real porous materials eu e in most cases not simply described in terms of single pore behavior. At the very least a distribution of pores of different sizes should be contemplated. The first analysis of hysteresis loops using a theory of adsorption in single pores together with a pore size distribution was the independent domain theory of Everett and coworkers (Everett, 1967). The most sophisticated application of this kind of approach was made by Ball and Evans (1989) who used density functional theory for adsorption in a distribution of cylindrical pores and compared the hysteresis loops obtained with those for xenon adsorbed in Vycor glass. 

In the Bueehe-Halpin theory the necessity of a strong filler-rubber bond follows naturally from the requirement of a low creep compliance. On the other hand the hysteresis criterion of failure, Eq. (32), does not make the need for filler-rubber adhesion immediately obvious. It is clear, however, that Hb cannot exceed Ub. In absence of a strong filler-rubber bond, the stress will never attain a high value the only way for Ub to become large would be for eb to increase considerably. There is no reason, however, why under these conditions eb should be much greater than in the unfilled rubber at the same test conditions and, in any case, it will be limited by the so-called ultimate elongation . This is the maximum value of eh on the failure envelope and is a fundamental property of polymeric networks. The ultimate extension ratio is given by theory (2/7) as the square root of the number of statistical links per network chain, n,... 

The whole phenomenology of phase behavior and emulsion inversion was interpreted wifli a butterfly catastrophe model with amazing quahtative matching between theory and experiment. The phase behavior model used the Maxwell convention which allows the system to split into several states, i.e., phases at equilibrium. On the other hand, the emulsion-type model allows for only one state (emulsion type) at the time, with eventually catastrophic transition and hysteresis, according to the perfect delay convention. The fact that the same model potential permits the interpretation of the phase behavior and of the emulsion inver sion (204, 206) is a symptomatic hint that both phe-nomenologies are linked, probably through formulation and water/oil composition which are two of the four manipula-ble parameters in the butterfly catastrophe potential. 

In later years various observations were published throwing doubt as to the correctness of Zsigmondy s theory. Numerous sorption isotherms on silica gel were found not showing any hysteresis at all. Sometimes water yielded isotherms of the type discussed hereabove and other substances, sorbed on the same gel sample, did not. ... 

Although this approach seems to yield satisfactory agreement with the JKR theory for experiments in which the load on the sample is increased with time, very often a substantial hysteresis is found when the sample is unloaded. The origin of this hysteresis is not fixlly understood and may well be different for different situations. In one set of experiments hysteresis was attributed to interfacial chemical reactions (Silberzan et al. 1994), whereas in other cases the hysteresis has been associated with physical interpenetration of the network by dangling chains (Brown 1993, Creton et al. 1994b, Deruelle et al. 1995). 

---