What BJH does
Barrett, Joyner and Halenda (1951) treated the pores as open cylinders. As pressure falls along an isotherm branch, two things happen. Liquid evaporates from the cores of pores of a certain size, and the adsorbed film on the walls of already-emptied pores gets thinner. The method subtracts the film-thinning volume from each pressure step and assigns the rest to pores of the size given by the Kelvin equation.
The two equations behind it
1. Kelvin equation (core radius)
For nitrogen at 77.35 K (γ = 8.85 mN/m, molar volume of the liquid VL = 34.68 cm³/mol, hemispherical meniscus, zero contact angle) this simplifies to rK [nm] ≈ 0.954 / ln(p₀/p).
2. Statistical film thickness t
The pore radius is the core radius plus the adsorbed film: rp = rK + t. Two thickness curves are common for nitrogen:
Halsey: t [Å] = 3.54 · [5 / ln(p₀/p)]⅓
| p/p₀ | rK (nm) | t, Harkins–Jura (nm) | Pore diameter D = 2(rK+t) |
|---|---|---|---|
| 0.42 | 1.10 | 0.58 | 3.4 nm |
| 0.50 | 1.38 | 0.65 | 4.1 nm |
| 0.60 | 1.87 | 0.74 | 5.2 nm |
| 0.70 | 2.68 | 0.86 | 7.1 nm |
| 0.80 | 4.28 | 1.03 | 10.6 nm |
| 0.90 | 9.06 | 1.32 | 20.8 nm |
| 0.95 | 18.6 | 1.58 | 40 nm |
| 0.99 | 95 | 1.9 | ≈ 190 nm |
The table shows the practical window. Below p/p₀ ≈ 0.4 the Kelvin picture no longer applies. Above ≈ 0.99 the pressure resolution is too coarse to separate sizes. BJH therefore covers mesopores and small macropores, roughly 2 to 200 nm in diameter.
The calculation step by step
- Start at the highest relative pressure, with all pores filled.
- For each pressure step, compute the Kelvin radius and film thickness at the old and new pressure.
- Subtract the volume released by thinning of the film in pores already emptied.
- Convert the remaining gas volume to liquid volume (× 0.0015468 for N₂ from cm³ STP) and assign it to pores of the mean size for that interval, using the cylinder geometry to go from core volume to pore volume.
- Keep track of the wall area of all emptied pores so that later film-thinning corrections are correct.
- Report the incremental volume, cumulative volume, and dV/dD or dV/dlogD versus pore diameter.
When the film-thinning correction becomes larger than the measured volume change, software either sets the increment to zero or stops the calculation. This often happens at the low-pressure end. It signals that the model no longer fits, often because of micropores.
Adsorption or desorption branch?
| Isotherm / loop | Recommended branch | Why |
|---|---|---|
| Type IV(a), H1 | Either; desorption is closer to equilibrium | Open, uniform pores: branches give consistent sizes. Adsorption-branch BJH slightly overestimates size because condensation is delayed. |
| H2(a), H2(b) | Adsorption | Desorption is controlled by neck size (pore blocking) or cavitation. |
| Any loop closing sharply at p/p₀ ≈ 0.42–0.45 | Adsorption | The desorption drop is cavitation; BJH turns it into a false peak around 3.5–4 nm. |
| H3, H4 | Use with caution; prefer slit-pore DFT | Slit-shaped pores between plates violate the cylinder assumption. |
| Type I (microporous) | Not applicable | The Kelvin equation fails below ~2 nm; use t-plot, DR or DFT. |
Reading a BJH report
- BJH cumulative pore volume — total volume of pores inside the stated diameter window (instrument software often uses 1.7–300 nm). It is smaller than the single-point total pore volume when micropores or large macropores are present.
- BJH cumulative surface area — wall area of those pores. It should be similar to the BET area for purely mesoporous samples; a much lower value suggests micropores.
- BJH average pore diameter — 4V/A using the BJH volume and area (see 4V/A guide).
- dV/dlogD peak — the mode of the pore-size distribution. The peak position matters more than the peak height.
Known limitations
- For pores narrower than about 10 nm, BJH underestimates the size by roughly 20–30 % compared with NLDFT on ordered materials (IUPAC 2015).
- It assumes rigid, cylindrical, unconnected pores.
- The result depends on the thickness equation chosen; report it.
- ISO 15901-2:2022 covers both the classical (BJH-type) and DFT methods for nanopores.
How to describe it in a methods section
A complete description names the adsorbate and temperature, the degassing conditions, the branch used, the thickness equation and the diameter range. For example: “Pore size distributions were calculated from the adsorption branch of the N₂ isotherm (77 K) using the BJH method with the Harkins–Jura thickness equation; the total pore volume was taken at p/p₀ = 0.99.”
Related guides
- Hysteresis loops H1–H5
- IUPAC isotherm types I–VI
- Gas adsorption method guide (BET, BJH, DFT)
- BET surface area calculation
Frequently asked questions
Should BJH be calculated from the adsorption or the desorption branch?
For H1 loops either branch gives similar results. For H2 loops, or whenever the desorption branch shows the sharp drop at p/p₀ ≈ 0.42–0.45 (N₂, 77 K), use the adsorption branch: the desorption branch then reflects neck sizes or cavitation, not pore bodies.
Can BJH measure micropores?
No. BJH relies on the Kelvin equation, which breaks down below about 2 nm. Micropores are evaluated with the t-plot, Dubinin–Radushkevich or DFT methods.
What is dV/dlogD?
It is the pore volume in each size interval divided by the width of that interval on a logarithmic scale. Plotting dV/dlogD rather than dV/dD keeps the area under the curve proportional to volume when the x-axis is logarithmic.
Why is there a sharp BJH peak near 3.5–4 nm in many papers?
On the desorption branch, nitrogen at 77 K cavitates at p/p₀ ≈ 0.42–0.45 regardless of pore size. BJH converts that sudden drop into a narrow peak at roughly 3.5–4 nm, which is an artifact, not a real pore population.