Results at a glance
| Reported value | How it is obtained | Notes |
|---|---|---|
| Total intrusion volume (mL/g) | Mercury volume intruded from the filling pressure to the maximum pressure, blank-corrected, per gram | Includes interparticle voids in powders |
| Bulk (envelope) density | m / Vbulk; Vbulk = penetrometer volume − mercury volume at the filling pressure | At ~0.5 psia mercury bridges openings larger than ~360 μm |
| Apparent (skeletal) density | m / (Vbulk − Vintruded) at the highest pressure | Excludes pores < ~3 nm and closed pores |
| Porosity (%) | Vintruded / Vbulk × 100 | Open porosity in the measured size window |
| Median pore diameter (volume) | Diameter at 50 % of total intrusion | Most robust single size |
| Median pore diameter (area) | Diameter at 50 % of cumulative pore area | Smaller than the volume median |
| Average pore diameter (4V/A) | 4 × total volume / total pore area | Area from the pressure–volume integral |
| Total pore area | Rootare–Prenzlow: A = −(1/γcosθ) ∫ P dV, reported at the maximum pressure (e.g. ~60,000 psia) | Assumes no pore-shape model but is sensitive to the high-pressure end |
Worked example
A 1.000 g piece of sintered ceramic gives a bulk density of 1.60 g/mL and a total intrusion volume of 0.250 mL/g.
- Bulk volume = 1.000 / 1.60 = 0.625 mL.
- Porosity = 0.250 / 0.625 = 40 % (or 0.250 × 1.60 = 0.40).
- Skeletal volume = 0.625 − 0.250 = 0.375 mL, so apparent skeletal density = 1.000 / 0.375 = 2.67 g/mL.
- Check: 1 − 1.60/2.67 = 0.40 ✓.
If the true density of the ceramic phase is higher than 2.67 g/mL, the difference points to closed pores or pores below ~3 nm that mercury cannot reach.
Reading the curves
Cumulative intrusion vs. pressure or diameter
Steep steps mark pore entrance sizes that hold much of the volume. A rise at the very lowest pressures in a powder is usually mercury filling the gaps between particles, not pores inside them.
Log differential intrusion (dV/dlogD)
Peaks give the dominant entrance sizes. In powders a bimodal curve is typical: the large-diameter peak is interparticle space and the small-diameter peak intraparticle porosity. Choose a cut-off diameter between the two before quoting intraparticle porosity.
Extrusion curve and entrapment
The gap between intrusion and extrusion, and the mercury left in the sample at the end, reflect pore-throat/body geometry. Large entrapment points to ink-bottle pores.
Checks before you trust the numbers
- Stem volume used should be within roughly 25–90 % of the penetrometer capillary. Outside that band the volume resolution is poor or the stem runs out.
- Blank correction must have been applied; otherwise mercury and instrument compression appear as fake nanopore volume at high pressure.
- Sample compression. A smooth, featureless rise at the highest pressures, with no extrusion hysteresis, can be the sample compressing.
- Conformance. For rough or irregular particles, mercury filling surface irregularities at low pressure is sometimes subtracted (conformance correction). Report whether this was done.
- Constants. Note the contact angle and surface tension used. Changing θ from 130° to 140° shifts every diameter by about 19 %.
Writing it up
A complete description includes the instrument pressure range, the equilibration criterion, γ and θ, sample mass and form, drying conditions, whether blank and conformance corrections were applied, and which interparticle cut-off was used for powders. ISO 15901-1 lists the items to report.
Related guides
- The Washburn equation
- Mercury intrusion porosimetry method guide
- Average pore diameter (4V/A)
- MIP vs. gas adsorption
Frequently asked questions
How is porosity calculated from mercury intrusion?
Porosity = total intrusion volume per gram × bulk density, or equivalently 1 − ρ_bulk/ρ_skeletal. For example, 0.25 mL/g × 1.60 g/mL = 0.40, i.e. 40 % porosity.
Can mercury intrusion detect closed pores?
No. Mercury only enters pores connected to the outside. Closed pores count as solid, so the MIP skeletal density is lower than the true density. Comparing with helium pycnometry on a finely ground sample gives an estimate of closed porosity.
What is log differential intrusion (mL/g)?
dV/dlogD: the intruded volume in each pressure step divided by the change in log of pore diameter. It is plotted on a log diameter axis so peaks show the dominant pore entrance sizes and the area under the curve stays proportional to volume.
What is the difference between median pore diameter by volume and by area?
The volume median is the diameter at which half the total intrusion volume has entered. The area median is where half the cumulative pore area is reached. Small pores carry most of the area, so the area median is always smaller.