What Does Chi Theory Say about Hysteresis

Hysteresis is undoubtedly a real phenomenon. It has been widely reported and reproducibly observed. The BdB theory and the theories that propose a switch from 2D to 3D meniscus are capable of explaining it, although whether they calculate it properly is open to question. It is unclear whether this is an experimental problem, that is a matter of kinetics, or not. X theory does not explain hysteresis except for the following caveat. This caveat should be taken into account for any calculation that may be attempted. 

Referring to the data by Qiao et ai., in the untransformed isotherm there appears to be hysteresis for nearly all the samples. However in the analysis it should be noticed that the for adsorption is nearly the same as that for desorption, indicating no hysteresis. Thus in the plots of versus Ax, instead of x, the adsorption data and the desorption data coincide. This is true for all the samples except the largest pore size sample, C-22 (which interestingly enough has a pore size just exceeding the value specified by the BdB theory where one should observe hysteresis). Even for sample C-22 in the plot versus instead of x, the hysteresis is considerably less - about half. The absence of hysteresis on a Ax plot for all samples except C-22 and the decrease in the hysteresis for C-22 would indicate that the value of increases from the adsorption branch to the desorption branch. 

There are several explanations for this phenomenon, one of which is that the adsorption process eliminates pre-adsorbed gases which would artificially lower the adsorption energy. Adsorbed gases such as CO or H2 are very difficult to avoid even in very good ultrahigh vacuums. 

To illustrate the decreased amount of hysteresis, the data of sample C-22 for adsorption are modified by shifting the PIP value by an energy amount required by the difference in of the adsorption versus desorption. 

Thus an untransformed plot of energy corrected adsorption may be obtained to compare with the desorption branch. The plot so obtained along with the original adsorption and desorption data is illustrated in Fig. 112. Although this explains some of the hysteresis, it does not explain all of the hysteresis. The use of the nearly half-power relationship mentioned with respect to Eq. (197), or using 1 in place of 2 in Eq. (196), overestimates the hysteresis by a considerable amount and does not explain the total absence of hysteresis for the other samples. The BdB theory also considerably overestimates the magnitude of the hysteresis. 

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