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The t-Plot Method for Micropore Analysis

The t-plot (Lippens and de Boer, 1965) compares a sample's isotherm with the adsorbed-film thickness on a non-porous reference. It separates micropore volume from the surface outside the micropores. It is the standard way to report "micropore volume" and "external surface area" alongside BET.

Published: October 4, 2026

The idea

On a non-porous surface, the adsorbed amount is proportional to the statistical thickness t of the film. Plot the sample's adsorbed volume against t (taken from a reference curve at the same p/p₀):

  • A straight line through the origin means no micropores. The slope gives the total surface area.
  • A straight line with a positive intercept means micropores filled before the multilayer region. The intercept is the micropore volume and the slope the external (non-micropore) area.
  • Upward deviation at larger t means capillary condensation in mesopores.

Thickness equations for nitrogen at 77 K

Harkins–Jura: t [Å] = [13.99 / (0.034 − log₁₀(p/p₀))]½
Halsey: t [Å] = 3.54 · [5 / ln(p₀/p)]⅓
Carbon black STSA (ASTM D6556): t [Å] = 0.88 (p/p₀)² + 6.45 (p/p₀) + 2.98

Harkins–Jura is common for oxides, and the STSA equation is standard for carbon blacks and widely used for carbons. The thickness curve should match the surface chemistry of the sample, and the choice changes the answer, so report it.

Converting slope and intercept

Vmicro [cm³/g] = intercept [cm³ STP/g] × 0.0015468
Sext [m²/g] = 15.47 × slope [cm³ STP g⁻¹ Å⁻¹]

The factor 15.47 comes from converting gas volume to liquid volume (0.0015468 cm³ per cm³ STP) and dividing by a film thickness of 1 Å (10⁻¹⁰ m).

Worked example

A nitrogen isotherm on an activated carbon gives, in the t-range 3.5–5.0 Å (Harkins–Jura), a straight line V = 4.0·t + 120 (V in cm³ STP/g, t in Å). The BET area is 650 m²/g.

  1. Micropore volume = 120 × 0.0015468 = 0.186 cm³/g.
  2. External surface area = 15.47 × 4.0 = 62 m²/g.
  3. “Micropore area” (comparative) = 650 − 62 = 588 m²/g.

Choosing the fitting range

  • Pick a region that is clearly linear, above the end of micropore filling and below the onset of capillary condensation.
  • Instrument defaults (often 3.5–5.0 Å) are a starting point, not a rule. Check the plot.
  • Use enough points (at least four or five) and report the range used.

Alternatives

  • αs-plot — uses a reference isotherm normalised at p/p₀ = 0.4 instead of a thickness equation, which avoids assuming a film thickness.
  • Dubinin–Radushkevich — micropore volume from the low-pressure part of the isotherm, common for carbons and for CO₂ at 273 K.
  • NLDFT / QSDFT — full micropore size distribution; best with argon at 87 K (see nitrogen vs. argon).

Related guides

Frequently asked questions

How do I calculate micropore volume from a t-plot?

Fit a straight line to the linear part of the V vs. t plot that lies above micropore filling (often t ≈ 0.35–0.5 nm for N₂). The positive y-intercept, in cm³ STP/g, multiplied by 0.0015468 gives the micropore volume in cm³/g of liquid nitrogen.

How is external surface area obtained?

From the slope of the same line: S_ext [m²/g] = 15.47 × slope, with V in cm³ STP/g and t in Å (or 1547 × slope with t in nm).

What does a negative t-plot intercept mean?

No measurable micropore volume, or a poorly chosen fitting range or thickness equation. Report it as no detectable micropores rather than a negative volume.

Is micropore area = BET area − external area meaningful?

It is widely reported, but for micropores the BET area does not represent a real monolayer area, so "micropore area" is a comparative number. Micropore volume is the more robust quantity.