I recently read the book chapter on the assessment of mesoporosity from "Adsorption by Powders and Porous Solids" by Sing et al. and the remark was raised that in the case of a certain hysteresis loop as the attached isotherms show mesopore size analysis should not be undertaken. I yet have to understand why this is the case, and what mathematical/physical reason underlies this.
I discussed the isotherms with a technician and we concluded that there is not really any existence of micro- and mesopores (also, crystallite sizes are in the order 10-50 nm), and that most of the adsorption of nitrogen is due to interstices, fissures, interparticle voids (and the like) in the powder. If that is the case, I could picture that the BJH method commonly used for pore distribution analysis would provide a rather crude estimate, since it operates under the assumption of a particular pore type (e.g. cylindrical), but is that the reason for the remark raised by the earlier mentioned source?
Article Assessment of Mesoporosity
The main issue with H3 (referrd to as type B by Gregg and Sing) is (i) that closure step in the desorption isotherm due to some some of pore blocking, and so the desorption branch cannot be reliably used for pore size measurements and (ii) it most often does not correspond to internal pores of fixed geometry.
IUPAC say "There are two distinctive features of the Type H3 loop: (i) the adsorption branch resembles a Type II isotherm (ii) the lower limit of the desorption branch is normally located at the cavitation-induced p/p0. Loops
of this type are given by non-rigid aggregates of plate-like particles (e.g., certain clays) but also if the pore network consists of macropores which are not completely filled with pore condensate."
The above quote comes from IUPAC's excellent technical report, attached.
If the closure is actually due to small mesopore necks then the pore size is the size of the necks, but the volume is from the necks (which in the limit can be "2D windows" with no significant volume of their own) PLUS the large meso/macropores which are being blocked from emptying at their own equilibrium pressure. the cavitation referred to in the quote above is due to meso/macropores emptying through micropore space (including micropore windows). the two pore blockings can only be properly separated out by repeating the analysis with a different fluid/temperature, e.g. Ar/87K. The closure point will move if it's due to a property of the fluid and not pore size. Gregg and Sing's 2nd edition (1982, Academic Press) has nice examples of this (on type H3, montmorillonite) on page 132.
BJH is not particularly accurate since it underestimates the true pore size (and the error gets worse for smaller pores). So since desorption is probably ruled out in this instance, we have to deal with the adsorption branch and the fact that it does not represent an equilibrium transition but rather one that had to overcome a nucleation energy barrier (the reason for hysteresis in meso/macropores in the first place). Best option is to use DFT on the adsorption branch.
But in any case here, the isotherm does not plateau and as Robert Haaring suggests, the pore spaces are most likely voids and not particularly informative as a 'pore size distribution'. If you have the time and inclination, these spaces can be investigated by compression studies. The change in the isotherm for powders under compression is also given some consideration in Gregg and Sing, page 154-155.
BR
Dear Robert Haaring
Greetings
I read your question and you shold know there is in ASAP2020 BET
the Isothermal adsorption theory developed by Brunauer Emmett Teller (BET)
allows for the determination of the amount of gas to cover the solid surface with a single layer of gas molecules.. The quantity of gas adsorbed is usually expressed as its volume under standard conditions.
H3 non-rigid aggregates of plate-like particles (slit-shaped pores)
Utilizing BET analysis method; single condensation point (P/Po = 0.99) was used to find the pore volume and five points, 0.05
Dear Robert Haaring
Greetings
I read your question and you shold know there is in ASAP2020 BET
the Isothermal adsorption theory developed by Brunauer Emmett Teller (BET)
allows for the determination of the amount of gas to cover the solid surface with a single layer of gas molecules.. The quantity of gas adsorbed is usually expressed as its volume under standard conditions.
H3 non-rigid aggregates of plate-like particles (slit-shaped pores)
Utilizing BET analysis method; single condensation point (P/Po = 0.99) was used to find the pore volume and five points, 0.05
The main issue with H3 (referrd to as type B by Gregg and Sing) is (i) that closure step in the desorption isotherm due to some some of pore blocking, and so the desorption branch cannot be reliably used for pore size measurements and (ii) it most often does not correspond to internal pores of fixed geometry.
IUPAC say "There are two distinctive features of the Type H3 loop: (i) the adsorption branch resembles a Type II isotherm (ii) the lower limit of the desorption branch is normally located at the cavitation-induced p/p0. Loops
of this type are given by non-rigid aggregates of plate-like particles (e.g., certain clays) but also if the pore network consists of macropores which are not completely filled with pore condensate."
The above quote comes from IUPAC's excellent technical report, attached.
If the closure is actually due to small mesopore necks then the pore size is the size of the necks, but the volume is from the necks (which in the limit can be "2D windows" with no significant volume of their own) PLUS the large meso/macropores which are being blocked from emptying at their own equilibrium pressure. the cavitation referred to in the quote above is due to meso/macropores emptying through micropore space (including micropore windows). the two pore blockings can only be properly separated out by repeating the analysis with a different fluid/temperature, e.g. Ar/87K. The closure point will move if it's due to a property of the fluid and not pore size. Gregg and Sing's 2nd edition (1982, Academic Press) has nice examples of this (on type H3, montmorillonite) on page 132.
BJH is not particularly accurate since it underestimates the true pore size (and the error gets worse for smaller pores). So since desorption is probably ruled out in this instance, we have to deal with the adsorption branch and the fact that it does not represent an equilibrium transition but rather one that had to overcome a nucleation energy barrier (the reason for hysteresis in meso/macropores in the first place). Best option is to use DFT on the adsorption branch.
But in any case here, the isotherm does not plateau and as Robert Haaring suggests, the pore spaces are most likely voids and not particularly informative as a 'pore size distribution'. If you have the time and inclination, these spaces can be investigated by compression studies. The change in the isotherm for powders under compression is also given some consideration in Gregg and Sing, page 154-155.
BR
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