Effects of temperature, pore dimensions and adsorbate on the transition from pore blocking to cavitation in an ink-bottle pore
Introduction
Hysteresis associated with capillary condensation and evaporation in porous materials has been the subject of immense interest for over 100 years [1], especially the search for the controlling mechanisms of adsorption and desorption. Adsorption in mesopores gives rise to hysteresis when the temperature is less than the critical hysteresis temperature and pore size is greater than a critical value [2], [3].
Materials such as activated carbon, porous glass and silica gel consist of interconnected networks of pores of various shape and size, and their experimental isotherms can exhibit single or double steps in the hysteresis loop [2], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18]. When hysteresis shows two distinct steps, the first, at lower pressure, is associated with condensation and evaporation in the smaller pores and the second with the same processes in wider pores. If the adsorbate–adsorbent system is wetting, adsorption proceeds by molecular layering, followed by condensation when both ends of a pore are exposed to the bulk surroundings, or by the advance of a meniscus from the closed end if one end of the pore is closed. Desorption, on the other hand, takes place by two processes which occur in conjunction: (1) the withdrawal of menisci from the pore mouth, and (2) the stretching of the condensed fluid in the interior region to a pressure where bubbles (cavities) appear in the adsorbate. When the first process dominates, the desorption mechanism is described as pore blocking, and as cavitation if stretching of the condensed fluid reaches the stability limit before the menisci have travelled to the pore interior. Both modes of evaporation can be illustrated by simulations using a simple ink-bottle pore model by tuning the neck size [19], [20], [21], [22], [23]. For a given adsorbate–adsorbent pair and temperature, the mechanism of desorption changes from pore-blocking to cavitation as the neck size decreases [20], [21], [22], [23], [24]. The cavitation pressure is a fluid property only when the cavity is large, typically greater than 7 nm for argon adsorption at 87 K, but is dependent on the cavity size for smaller cavities, because of the the overlap of adsorbent potential from closely spaced pore walls creates a stabilization effect [25], [26]. The neck length can affect evaporation in an interesting way: Even when the neck size is smaller than the value at which cavitation normally occurs, evaporation can switch to pore blocking when the neck is very short; the shorter the neck, the greater the desorption pressure. While the cavity size affects the cavitation pressure for small cavities and the neck dimensions (width and length) affect the governing mechanism for desorption, temperature can also affect the desorption mechanism, which changes from pore blocking to cavitation at high temperature, because stretching of the condensed fluid in the cavity, overrides the process of meniscus withdrawal. This has been observed both experimentally and theoretically [4], [7], [11]. The change of evaporation mechanism for a given adsorbent, can also switch from pore blocking to cavitation as the pressure is reduced, and this change depends strongly on the pore structure and temperature [11], [18], [27]. Finally, the adsorbate molecule can also affect the desorption mechanism; for example Reichenbach and co-worker [11] observed pore blocking for argon adsorption in porous glass at 77 K, but found cavitation to be the mechanism for nitrogen at the same temperature.
Despite numerous simulation studies, there is still no systematic investigation into the effects of pore dimensions, temperature and adsorbate on the switch in the mechanism of desorption, from pore blocking to cavitation, in ink-bottle pores. It is the objective of this paper to fill this gap.
Section snippets
Fluid–fluid potential model
Argon was modelled as a single Lennard Jones (LJ) site and the 2CLJ + 3q N2 (two LJ sites and three partial charges) model was chosen for nitrogen [28]. Their molecular parameters are listed in Table 1.
Fluid–solid potential model
A graphitic ink-bottle pore, with planar walls, connected to a gas reservoir via a neck is shown in Fig. 1. We used the Bojan-Steele equation [29], [30], [31] to calculate the fluid–solid potential energy with a 0.34 nm spacing between the two adjacent graphite layers, which are finite in the y
Ar adsorption at less than the critical hysteresis temperature
We first investigate argon adsorption in an ink-bottle pore whose cavity width is 3 nm and neck width is 2.3 nm. Note that in this small cavity and the force per unit area exerted by the cavitation pressure is less than the tensile strength of the bulk fluid because of the stabilization of the condensed fluid by the external field from the adsorbent. The lengths of the cavity and the neck were 10 nm. Fig. 2 shows the isotherms for temperatures from 60 K to 150 K. For ease of discussion, we define in
Conclusions
We have used grand canonical Monte Carlo simulation to investigate the transition from pore blocking to cavitation in the desorption branch of argon and nitrogen isotherms in carbonaceous ink-bottle pores. The transition temperature is found to increase with (i) increasing width of the pore neck, (ii) a decrease in neck length for very short necks (for longer necks, the transition temperature is insensitive to the length), (iii) a stronger holding potential for the adsorbate.
Argon adsorption in
Acknowledgement
This project was supported by the Australian Research Council.
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