Why hysteresis happens at all
In a mesopore, condensation on uptake and evaporation on release do not necessarily occur at the same relative pressure. Two effects drive the difference. First, condensation in a cylindrical pore is delayed beyond the equilibrium relative pressure because the metastable adsorbate film must overcome the activation barrier to nucleate a meniscus — a kinetic effect. Second, the geometry of the meniscus on emptying is different from the geometry on filling, especially when the pore has a constricted neck or is part of a connected network — a thermodynamic effect.
The combination is what produces the loop. The loop's shape — how steep the branches are, where the closure point sits, and whether the branches are parallel — encodes the underlying pore geometry. The IUPAC 2015 Technical Report on physisorption is the authoritative classification.
Reading the loop: a generic procedure
Before assigning a class, look at three features of the loop:
- Steepness of the branches. Are both adsorption and desorption branches near-vertical at a single pressure (narrow, well-defined pore size), or are they spread out (broad pore size distribution)?
- Parallelism. Do the branches run roughly parallel to each other across the pressure range, or does one branch drop sharply while the other is gentle?
- Closure point. Where does the loop close at the bottom? A sharp closure at relative pressure ~0.42 (for nitrogen at 77 K) is a tell-tale sign of cavitation rather than capillary evaporation.
Together these three features place the loop in one of the five IUPAC classes.
The five canonical classes
H1 — cylindrical-like, narrow distribution
Steep, parallel adsorption and desorption branches over a narrow pressure range. Both branches are near-vertical, so the pore size distribution is narrow.
Typical pore geometry: uniform cylindrical or near-cylindrical mesopores in a well-ordered, weakly connected network. Common in templated mesoporous silicas (MCM-41 family, SBA-15), some controlled-pore glasses, and certain templated carbons.
What it tells you: the pore size derived from a Kelvin-equation analysis (BJH, or DFT) is meaningful, with relatively little ambiguity between branches.
H2 — ink-bottle / network effects
An asymmetric loop, often with a relatively gentle adsorption branch and a much steeper desorption branch. The desorption branch frequently shows a sharp drop at a low relative pressure even when there is little or no corresponding feature on adsorption.
Typical pore geometry: pores connected through narrow constrictions ("ink-bottle" pores), pore networks with restricted access, or solids with significant pore-blocking effects. Common in some silica gels, mesoporous metal oxides, and cement pastes.
Sub-classes: the IUPAC 2015 report further distinguishes H2(a) (steep, sharp desorption drop — classic pore-blocking) and H2(b) (broader desorption drop — broader distribution of neck sizes).
What it tells you: the adsorption branch is a more reliable input to a Kelvin / BJH analysis than the desorption branch, because the desorption branch reflects neck size rather than cavity size. Many BJH analyses therefore prefer the adsorption branch when an H2 shape is present.
H3 — aggregates of plate-like particles
An open, almost wedge-shaped loop that does not exhibit a Type IV plateau and often shows continued uptake near saturation pressure. The loop is open in the sense that the desorption branch does not close cleanly at low pressure, or closes only at the lower limit of the hysteresis range.
Typical pore geometry: non-rigid aggregates of plate-like particles forming slit-shaped pores, or macroporous solids with poorly defined mesoporosity. Common in clays, layered double hydroxides, and many graphite-derived materials.
What it tells you: the meaningful pore-size descriptor is the slit width, not a cylindrical pore radius. Conventional BJH analysis on a cylindrical-pore model is not appropriate; use a slit-pore DFT model where one is available.
H4 — mixed micro- and mesoporous slits
An H4 loop sits between H3 and H2: still slit-shaped in character but with a more pronounced uptake step at low relative pressure that signals the presence of micropores in addition to the mesopore network.
Typical pore geometry: aggregates of plate-like particles with significant micropore content. Common in many activated carbons, micro-mesoporous zeolites, and some pillared clays.
What it tells you: the analysis must explicitly account for micropores — the t-plot, α-s plot, or DFT methods covered on the gas-adsorption methodology page are needed alongside any mesopore analysis.
H5 — partially open / partially blocked pore networks
Less common than H1–H4. Characterized by a pronounced step on adsorption with a steep desorption branch at lower relative pressure, suggesting that part of the pore network is open and part is accessible only through narrow necks.
Typical pore geometry: certain templated and de-templated mesoporous structures with partially blocked channels, or some dual-pore-system solids.
What it tells you: a single Kelvin / BJH analysis may be misleading; the isotherm is signalling that two distinct pore populations are contributing differently to adsorption and desorption. DFT analysis with an appropriately structured kernel is the safer route.
The cavitation-induced step at p/p₀ ≈ 0.42 (nitrogen at 77 K)
One feature deserves special mention because it is a frequent source of misinterpretation: a sharp drop on the desorption branch at relative pressure around 0.42 for nitrogen at 77 K (or around 0.38 for argon at 87 K). This drop is not a real pore-size feature. It is the cavitation limit — below this relative pressure, the metastable adsorbate liquid in any neck or cavity becomes mechanically unstable and evaporates regardless of the actual pore geometry.
If your isotherm has this drop and you interpret it through a Kelvin / BJH analysis applied to the desorption branch, you will see a spurious peak in the pore-size distribution at around 4 nm that does not correspond to a real population of pores. The IUPAC 2015 recommendations advise using the adsorption branch when the desorption branch passes through the cavitation region, exactly to avoid this artifact.
Quick-reference table
| Loop | Shape signature | Pore geometry suggested | Best analysis branch |
|---|---|---|---|
| H1 | Steep, parallel branches | Uniform cylindrical mesopores | Either; BJH/DFT both work |
| H2 | Asymmetric, sharper desorption | Ink-bottle / pore-blocking network | Adsorption branch (avoid neck artifact) |
| H3 | Open wedge, no plateau | Slit pores in plate-like aggregates | Slit-pore DFT, not cylindrical BJH |
| H4 | Slit-like + low-p uptake step | Micro + meso slit pores | t-plot or DFT for micro; care for meso |
| H5 | Adsorption step + steep desorption | Partially blocked / dual-population | DFT with appropriate kernel |
Common mistakes when reading hysteresis
- Forcing every loop into H1. Many published BJH distributions are computed on the desorption branch of an H2 loop and report a spurious narrow peak at 4 nm. The peak is the cavitation step, not a real pore population.
- Applying a cylindrical-pore model to H3/H4 loops. The pore geometry is wrong by construction; a slit-pore model gives a more meaningful pore-size descriptor.
- Ignoring the adsorption branch. When the desorption branch is unreliable (H2, H5, or cavitation-affected loops), the adsorption branch is the better input even though many older procedures default to desorption.
- Reading hysteresis on a sample that was not properly degassed. Residual water can cause apparent "hysteresis" that is really just hysteresis of water adsorption on top of the adsorbing gas. The first defence is in sample preparation.
Connecting hysteresis to method choice
The hysteresis class is also informative for method-selection decisions covered elsewhere on this site:
- If the loop is H3 or H4 with significant low-pressure uptake, the sample has substantial micropore content; the nitrogen vs. argon comparison covers when argon at 87 K is the better adsorbate for resolving narrow micropores.
- If the loop is H2 with strong pore-blocking, complementary mercury intrusion can separately characterize the macropore tail and validate that the gas adsorption peak is real.
- If the sample is a membrane or filter and the question is functional pore size rather than total porosity, the porosimetry-vs-porometry comparison is the correct first stop — capillary flow porometry, not gas adsorption, is the appropriate technique.