Where the artifact comes from
The Washburn equation underlying MIP, d = −4γcosθ / P, relates the applied pressure to the diameter of a cylindrical pore that mercury can enter at that pressure. The implicit assumption is that every pore is an open, cylindrical channel: mercury reaches a given cavity by passing only through pores at least as wide as the cavity itself.
Real materials rarely satisfy that assumption. A concrete paste, a catalyst pellet, a sintered ceramic, or a lump of activated carbon contains a pore network: cavities of various sizes connected by narrower throats. To enter a wide cavity that is connected to the outside only through a narrow throat, mercury must first overcome the pressure required to enter the throat. At that pressure, the entire cavity fills in one event — and the instrument records that whole cavity volume as if it belonged to a pore the size of the throat.
The geometry that produces this is called an "ink-bottle" pore: a wide body with a narrow neck, like a classical ink bottle. The artifact applies more broadly than the literal geometry, though — any time a body is accessible only through narrower throats, the volume gets misassigned.
Net effect on the data: the intrusion curve is shifted to higher pressures (smaller apparent pore sizes), and the implied pore-size distribution overweights pore-throat sizes at the expense of cavity sizes. Total intruded volume is not affected — the same total mercury still enters — but how that volume is distributed across pore size is.
What the artifact is, and is not
The ink-bottle effect is sometimes confused with two other features of MIP data, so it is worth being precise about what counts.
It is not the same as mercury entrapment
Mercury entrapment refers to mercury that does not leave the sample on extrusion. The two phenomena are related — both arise from the same network geometry — but they are not the same. A sample can show ink-bottle behaviour on intrusion (a sharp step at the throat pressure) and still extrude all of its mercury given enough time. Conversely, entrapment can have other causes including chemical interaction between mercury and the sample.
It is not the same as compressibility
Compressibility shows up at the highest pressures as a smooth, continuous rise in apparent volume that has nothing to do with pore filling. The ink-bottle effect, by contrast, shows up as a sharp step at the throat pressure followed by a plateau, which is what makes it look like a real population of small pores. The two features can coexist on the same curve and the diagnostics for distinguishing them are different.
It is not unique to mercury
The same effect appears in gas adsorption, where it is one of the drivers of H2-class hysteresis loops. The desorption branch of an H2 loop shows the same kind of throat-controlled sudden release. The hysteresis-loops page covers that side.
Recognizing the ink-bottle effect on a real curve
The cleanest diagnostic is to run the full intrusion-extrusion cycle and look at the relationship between the two branches.
- Run intrusion to maximum pressure. The intrusion curve rises in steps that the Washburn equation translates into apparent pore sizes.
- Reduce pressure and record extrusion. On extrusion, mercury must un-bridge each cavity through the same throat geometry on the way out. Cavities behind narrow throats often release at significantly lower pressure than they entered.
- Compare the two branches. The horizontal offset between intrusion and extrusion at a given volume is the hysteresis. The larger the hysteresis, the more strongly the network's pore-throat / cavity geometry deviates from a simple cylindrical-pore model.
- Look for residual entrapment after extrusion. Mercury that does not return on extrusion has been trapped behind throats that re-bridge before the cavity empties.
A pure cylindrical pore network produces little to no hysteresis and little entrapment. A pronounced hysteresis loop on the intrusion-extrusion plot is direct evidence of network connectivity effects, of which the ink-bottle effect is the prototypical example.
Decision criteria: when to worry, when to ignore
Not every measurement needs to correct for the ink-bottle effect. The decision depends on what the data is being used for.
| Use case | Worry about ink-bottle? | Why |
|---|---|---|
| Total porosity / total intruded volume | No | Total volume is preserved; only its distribution by pore size is affected. |
| Threshold-pressure / pore-throat size for transport | No — this is the throat size | For permeability and capillary-pressure curves, the apparent throat size is the relevant quantity. |
| True cavity-size distribution | Yes | The MIP-derived "pore size distribution" understates cavity sizes wherever throats are present. |
| Comparing two materials with similar throat structures | Often acceptable | The artifact is similar in both samples and largely cancels. |
| Comparing two materials with different throat structures | Yes | Differences in apparent pore size may reflect throat-size differences, not cavity-size differences. |
What to do about it
1. Use the intrusion-extrusion hysteresis as a diagnostic
Quantify the hysteresis. The difference between intrusion and extrusion volume at fixed pressure, integrated across the loop, is a direct measure of how much volume sits behind throats. If the loop is small, the cylindrical-pore reading of the intrusion curve is reasonable. If the loop is large, treat the apparent pore-size distribution as a throat-size distribution rather than a cavity-size distribution.
2. Combine with gas adsorption
Gas adsorption (BET / BJH / DFT) on the same sample senses cavities directly through capillary condensation. Where the BJH desorption branch and the MIP intrusion curve assign volume differently across pore size, the discrepancy is informative: the BJH adsorption branch typically reads cavity sizes, while the MIP intrusion reads throat sizes. The MIP vs. gas adsorption comparison covers when the overlap between the two methods is useful.
3. Use a network-aware analysis
Pore-network modelling and percolation-based MIP inversion methods exist that try to recover the cavity-size distribution from the intrusion-extrusion data and any independent cavity information. These are active research methods and require model assumptions; they are appropriate where the cavity-size distribution is needed quantitatively, not as a routine substitute for the standard analysis.
4. Cross-check with imaging
Where it is feasible, micro-CT, FIB-SEM, or other 3D imaging techniques can directly measure both throat and cavity sizes on the same sample. They are slower and more expensive than MIP, but they are the most direct ground truth.
A worked example
Consider a hypothetical cement paste in which spherical hydration cavities of ~2 µm diameter are connected to the surface only through ~50 nm capillary throats. The Washburn equation, with mercury surface tension 485 mN/m and contact angle 130°, gives:
- For 50 nm throats: applied pressure ~25 MPa.
- For 2 µm cavities (taken in isolation): applied pressure ~0.6 MPa.
In a sample that contains both, mercury would intrude the freely accessible 2 µm features at ~0.6 MPa but the cavities behind throats would not fill until ~25 MPa — producing a sharp step at 25 MPa and a plateau in between. The instrument's standard reduction would assign all of that step to a "50 nm pore" population, even though the actual cavity diameters are 40× larger. On extrusion, the 2 µm cavities release at much lower pressure than they entered, producing strong hysteresis and likely some entrapment.
Use the Washburn pore-size calculator to convert specific test pressures to equivalent pore diameters for your own data.
Common-mistakes checklist
- Reporting the apparent MIP pore-size distribution as a cavity-size distribution in materials with strong network effects (cement pastes, many activated carbons, hierarchical catalysts).
- Comparing two materials' "median pore size" from MIP without checking that their pore networks have similar throat-to-cavity ratios.
- Mistaking the throat-pressure step for a real population of small pores. The volume in the step is real, but the pore size assigned to it is not.
- Ignoring extrusion data. Without the extrusion branch you have no direct evidence of network effects on the curve. Extrusion is also where mercury entrapment is quantified.
- Confusing ink-bottle hysteresis with sample compressibility. The two have different fixes — compressibility is corrected with a blank, ink-bottle behaviour is interpreted with the extrusion branch.
- Not preparing the sample properly. Residual water, loose powder, or inconsistent consolidation produce their own artifacts that look superficially similar; see the sample preparation page.
How this connects to the rest of the site
The MIP methodology page covers the underlying Washburn relation and the standard intrusion procedure (Mercury Intrusion Porosimetry). The MIP vs. gas adsorption comparison covers when the two methods are best run together to triangulate cavity vs. throat sizes. The hysteresis-loops page covers the analogous artifact in gas adsorption, where pore-blocking shows up as an H2 loop. And the sample preparation page covers the upstream issues that can mimic ink-bottle behaviour without involving the network at all.