Most low apparent quantum yields are radiometric or arithmetic errors, not bad catalysts. At 365 nm, 100 mW/cm2 equals 0.305 µmol photons/cm2/s, so a 20 cm2 window supplies 22 mmol photons per hour. A measured 10 µmol/h of H2 is therefore 0.09 % AQY — check the denominator before redesigning the material.
Apparent quantum yield is defined on photons arriving at the reactor, not photons absorbed by the powder: AQY = (n × moles of product) / (moles of incident photons) × 100 %, with n the number of electrons the product requires — 2 for H2 or CO, 4 for O2, 8 for CH4. Internal quantum yield uses absorbed photons instead and is always larger, often by a factor of two to five in a scattering slurry.
A 365 nm beam at 100 mW/cm2 carries 0.305 µmol photons/cm2/s; across a 20 cm2 window that is 6.1 µmol/s, or 21.9 mmol/h. Fifty micromoles of H2 in one hour is 2 × 50 / 21 960 = 0.46 %. Anything above 10 % at 365 nm on an unoptimised powder deserves a look at the denominator.
Measured at the lamp port. A reading at the source exit ignores the window, the liquid and the distance. An uncoated quartz window transmits about 92 % at 365 nm per surface, so two surfaces plus a 10 mm water path cost 15–20 % before any catalyst is involved. Measure at the inner window face, reactor filled.
Nominal power for optical power. A 300 W xenon housing draws 300 W electrically and delivers a small fraction of that as collimated flux; the two are not interchangeable in any calculation.
Meter spectral mismatch. A silicon photodiode calibrated at 633 nm and used at 365 nm without a correction factor typically reads 10–25 % away from truth, and thermal heads saturate easily in a focused beam. Check the certificate's wavelength, not just its date.
Area mismatch. If the spot is 30 mm across and the window 40 mm, the irradiated area is 7.1 cm2, not 16 cm2. Mask the beam or measure the spot, and state which area you used.
Hotspot quoted as mean. Centre-to-edge non-uniformity of 20–40 % is normal for a collimated xenon beam, and quoting the brightest point inflates the photon count by the same margin. Report the mean over the irradiated area.
Dissolved hydrogen left out of the balance. This is the largest single error in water-splitting work. Hydrogen solubility in water at 25 °C is about 0.78 mmol/L/atm, so 500 mL of slurry holds roughly 390 µmol of H2 at equilibrium — eight times what a modest sample produces in an hour. Sampling the headspace at 30 min without equilibration under-reports the rate by 30–60 %.
GC calibration built where it does not matter. A five-point curve spanning 1–100 % and then used at 20 ppm carries 10–30 % uncertainty at the low end, because the slope near the detection limit sits in a different noise regime. Bracket the working concentration with two standards, as set out in our GC calibration guide.
Back-reaction and donor depletion. Hydrogen and oxygen recombine on platinum once both accumulate, and a 1 % Pt sample can lose 5–15 % of its net H2 over six hours in a sealed cell. With 10 vol% methanol in 100 mL, the donor also runs down and the rate sags in the third hour.
| # | Cause | Signature in the data | Ten-minute test | Typical error |
|---|---|---|---|---|
| 1 | Irradiance taken at the lamp port | AQY plausible but 15–30 % low | Power meter at the inner window, reactor filled | 15–30 % |
| 2 | Dissolved H2 not equilibrated | Rate rises with longer sampling intervals | Stir 30 min sealed before the first injection | 30–60 % |
| 3 | Nominal instead of optical power | AQY off by an order of magnitude | Compare nameplate watts with measured mW/cm2 | ×3 to ×10 |
| 4 | Meter spectral mismatch | Same lamp reads differently on two meters | Cross-check two meters at the working wavelength | 10–25 % |
| 5 | Area defined by window, not spot | Small spot on a large window | Thermal paper or beam profiler at the window plane | 20–50 % |
| 6 | Hotspot quoted as mean | High AQY that nobody reproduces | Five-point scan across the window | 20–40 % |
| 7 | GC curve not bracketed near the sample | Scatter grows as concentration falls | Two standards at 0.5× and 2× the sample | 10–30 % |
| 8 | Sacrificial agent depleted | Rate falls monotonically after hour two | Refresh the donor and repeat | 40–70 % over 6 h |
| 9 | Loading too high for the cell | Absorbance > 2, rate flat with more catalyst | Loading series at 0.25, 0.5, 1 and 2 g/L | 2–5× on apparent AQY |
| 10 | Electron count wrong for the product | AQY exactly 2× or 0.5× a literature value | Recheck n for the half-reaction | ×2 or ×4 |
Platinum-loaded TiO2 under 365 nm with methanol as donor is usually reported at 0.5–5 % AQY; graphitic carbon nitride at 420 nm at 5–15 % with a sacrificial agent; CdS systems can exceed 20 % at 420 nm at the cost of photocorrosion. A value far outside these bands is a measurement question first.
Action spectra settle the argument: measure AQY at five wavelengths and overlay the result on the absorption spectrum. If the curves do not track each other, the photons you count are not the ones driving the reaction — usually stray light, a leaking filter, or a second phase absorbing in the same window. The neighbouring metrics are defined in IPCE versus EQE versus QE, and the route from peak area to yield is worked through in quantifying CO2 reduction products.
Not for a one-photon-per-electron process. A value above 100 % means the photon count is low — usually a small measured spot divided into a large assumed area — or that a chain reaction consumes fewer photons per product molecule, which must then be stated explicitly.
One wavelength is enough for a single comparison, provided you name it and the bandwidth (365 ± 10 nm, for example). For a mechanism claim, five to eight points from 300 to 500 nm are needed to show that the yield tracks absorbance.
Above about 1 g/L in a 10 mm cell the suspension absorbs 95 % of the beam within 2 mm, so extra catalyst adds only scattering and recombination. The rate plateaus while the photon count stays constant, and AQY drops — quantified in our slurry loading study.
A 10 °C rise cuts hydrogen solubility by roughly 8 % and shifts the apparent rate by a few percent either way — enough to matter when comparing two runs. Hold the cell at 25 ± 1 °C and say so.
