In studies of the thermodynamics of fluids confined in porous materials, a particularly interesting observed effect is that of adsorption-desorption hysteresis at subcritical temperature. This effect was observed and remarked upon nearly a century ago[1] and has been a point of discussion and, occasionally, contention ever since. An early explanation of hysteresis based on macroscopic thermodynamics, the Kelvin-Cohan relationship, proposed that the effect resulted from the formation of different gas-liquid menisci during the respective adsorption and desorption processes[2]. Later investigations linked hysteresis to fluid metastability and confirmed this argument via statistical mechanical means.
Based on the Kelvin-Cohan relationship, it was long assumed that hysteresis would not occur in a closed-end pore because the meniscus would be identically structured in the adsorption and desorption processes[2]. Some molecular simulations suggested the existence of hysteresis in a closed-end pore, but the uncertainty in the data precluded a firm conclusion[3]. More recent work by Do and coworkers has more confidently revealed the existence of hysteresis in closed-end pores of various shapes[4] via molecular simulations. Despite these results, disagreement over the existence of hysteresis in closed-end pores still persists in the field.
In the present work, we examine adsorption-desorption hysteresis in closed-end pores using flat-histogram Monte Carlo methods, in particular hybrid Wang-Landau/Transition-matrix Monte Carlo simulation. As we demonstrated recently[5], TMMC can easily and accurately compute adsorption isotherms exhibiting hysteresis including identification of the metastable regions, with high confidence. We now apply this method to adsorption in closed-end pores to revisit the results of Do and coworkers, as well as examining the purported metastable regions via ensemble macrostate probability distributions and free energy analyses.
[1] F. Rouquerol, J. Rouquerol, and K. Singh, Adsorption by Powders and Porous Solids, Academic Press: London, 1999.
[2] L. H. Cohan, J. Am. Chem. Soc., 60:433, (1938).
[3] L. D. Gelb, Mol. Phys, 100:2049, (2002).
[4] C. Fan, D. D. Do, and D. Nicholson, J. Colloid Int. Sci., 405:201, (2013).; Y. Zeng et al., J. Phys. Chem. C, 118:25496, (2014).
[5] D. W. Siderius and V. K. Shen, J. Phys. Chem. C, 117:5861, (2013).
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