It is very well known to be a hysteresis due to capillary condensation in mesopores. From the modelling of such hysteresis, you can calculate the mesopore size distribution, for example using the BJH method but not only. Any software associated to automatic adsorption apparatuses allows this.

Alain

This due to a capillary condensation within mesopores and macropores in the adsorbent which take places at higher relative pressure, showing adsorption-desorption for N2 over adsorbent.

Sorption process varies depending on the size of the pores. As the size of the pore increases from micro(2>d>50 nm), the relative pressure to fill the pores will also increase. In case of microporous materials, you can see maximum N2 sorption (mostly monolayer) at low pressures, hence a steep rise in the curve near 0.1 P/P0,  Whereas in mesopores, at first, monolayer coverage occurs followed by multilayer filling and consecutively capillary condensation.

However as the width of the mesopore increases (~2 nm / M41s,  ~ 6 nm /- SBA-15 and ~10 nm / - FDU-12), it requires more pressure to completely fill these wider mesopores, since multilayer adsorption occurs on low energy sites (uni/bilayers) away from the wall. Hence the maximum N2 adsorption/desorption is at high pressure region and hence hysteresis shifts towards high P/P0 regions

pore size of your material can be around 11-12 nm

Thanks all for your answers. I have attached the image of a typical isotherm (type I and type IV isotherm). Please comment on it. Whether inter-particle porosity can give this type of hysteresis loop in sample?

Yes, Intercrystalline voids can give such type of hysteresis. However intercrystalline pores of the crystals must be uniform and in the mesopore dimensions. Intracrystalline pores of a modified zeolite can also give such isotherm. I'm attaching an article FYI.

It has similar data resembling your isotherms. it clearly indicates the intra and intercrystalline mesoporosity in modified zeolites. wish you all the best narasimman

This is a typical type I - type IV combination of isotherms, showing a micro-mesoporous material, i.e. presenting both well developed microporosity (and narrow one) and some mesopores. Modelling the isotherm will give you the mesopore size distribution, then you can see whether the mesopore size corresponds or not to the spacing betwen grains. If not, this is an intrinsic mesoporosity. Mesoporosity can correspond to intergranualr voids, but this happens mainly with very fine powders made of well calibrated grains. Otherwise, intergranular voids are too big and can't be seen by adsorption.

Alain

Thank you Mr. Rajesh K. Parsapur for your very useful information. 

Dr. Alain Celzard, Thank you for your information. I will model my isotherm as you suggested.

The appearance of hysteresis due to the presence of mesopores (of whatever origin) has been well addressed. But I'd like to add something regarding as to why does filling/emptying of mesopores give rise to hysteresis in the first place?

Filling of mesopores (capillary condensation) is preceded by multilayer adsorption on the pore walls. As the relative pressure increases the general assumption (in calculating pore size from Kelvin-based equations like BJH) is that the empty "core" of the pore fills at the calculated Kelvin radius. However, this is mechanistically incorrect. For the gas to condense in the pore space it must first generate a stable liquid nucleus, and there exists a nucleation activation energy barrier to overcome.  This causes delayed condensation at a relative pressure higher than that predicted by Kelvin-based models. The adsorption curve of mesopores therefore, does NOT represent an equilibrium transition (bulk liquid in equilibrium with the gas phase). The multilayers do not represent a bulk liquid.

Emptying (capillary evaporation) occurs from a pre-existing liquid meniscus at the mouth of the pore and is therefore reasonably modeled by the Kelvin equation. Of course only the core evaporates leaving multilayers on the walls. Desorption from mesopores (so long as they are not only accessible through micropore-sized paths) IS an equilibrium transition because the bulk liquid does already exist in the pore.

Applying the BJH equation to adsorption and desorption data therefore will produce DIFFERENT results even for the commonly encountered H1 type hysteresis (more or less parallel expect for the "ends" that close asymptotically), the pore size distribution from adsorption being shifted to higher values compared to that from the desorption branch.  Both cannot be correct. BJH has its own additional problem of underestimating pore sizes anyway. So in certain cases the adsorption-shift and under-sizing seemingly offset each other to produce a reasonably accurate answer. Not through good science but lucky coincidence. If you don't have an appropriate DFT (density function theory) model for the sample in question, then one can make a semi-objective choice between adsorption and desorption for BJH pore size.  this is done by comparing both cumulative BJH surface areas with the BET surface area. the one with the better match can be said to be the better choice. Always remember NOT to include data points below P/Po 0.35 in a BJH calculation, as mesopore filling via capillary condensation does not take place at those pressures.

Type H2 hysteresis (triangular with a very steep desorption branch compared to adsorption) has yet more issues; the desorption branch here being controlled by evaporation from a distribution of small mesopore "necks" within the overall mesopore distribution.

I hope that adds to the general understanding of the hysteresis phenomenon.

I have a question regarding negative slope for adsorption curve. It would be great if some of the experts ( Alain Celzard Rajesh K. Parsapur Martin A Thomas Chitrakshi Goel Nady Fathy ) in this conversation could help me. The question is posted in the following link:

https://www.researchgate.net/post/Why_N2_adsorption_isotherm_has_negative_slope?view=5bbc293a979fdca1287e146d

I am using porous material for the BET analysis and the free space difference is negative (-0.0984 cm3) is there something wrong with the machine or the used protocol?

The isotherm also didn't close. What is the reason for the open-loop in N2-Adsorption/Desorption isotherm? I didn't use the filler tube and my sample is in the form of solid chunks is that causing a problem?