Most slurry reactors peak between 0.3 and 1.5 g/L. At a specific extinction near 2.5 L g−1 cm−1, 1 g/L of TiO2 P25 absorbs 92 % of 365 nm light within the first 10 mm, while 0.5 g/L absorbs 71 %. Past about 1 g/L you add scattering and mixing load faster than you add absorbed photons.
A slurry is a Beer–Lambert absorber with a scattering complication. To a first approximation the absorbance per centimetre is ε·C, so the 1/e penetration depth is Leff = 1/(ε·C). Doubling the loading halves the depth of the active zone; it does not double the usable photons, because they were already being absorbed, just deeper in the liquid.
That is why the useful variable is not grams but the fraction of incident light absorbed inside the irradiated volume. For a cell with a 10 mm optical path, the absorbed fraction is 1−exp(−ε·C·1 cm), and the rate per gram of catalyst is proportional to that fraction divided by C.
| Loading | ε·C | Penetration depth | Light absorbed over 10 mm | Photons absorbed per gram (relative) | Practical note |
|---|---|---|---|---|---|
| 0.1 g/L | 0.25 cm−1 | 40 mm | 22 % | 1.56 | Light escapes the cell; most catalyst sits in the dark |
| 0.25 g/L | 0.63 cm−1 | 16 mm | 46 % | 1.31 | Only viable with a thin cell or a long path |
| 0.5 g/L | 1.25 cm−1 | 8 mm | 71 % | 1.00 | Common starting point for 100–300 mL |
| 1.0 g/L | 2.50 cm−1 | 4 mm | 92 % | 0.65 | Near-saturated absorption; best volumetric rate |
| 2.0 g/L | 5.00 cm−1 | 2 mm | 99 % | 0.35 | Half the reactor volume is optically dead |
| 4.0 g/L | 10.0 cm−1 | 1 mm | >99 % | 0.18 | Aggregation and wall deposits dominate |
Conditions: TiO2 P25 in water, 365 nm, ε = 2.5 L g−1 cm−1, 10 mm path. Real suspensions scatter strongly below 400 nm, so treat ε as a value fitted from your own dilution series.
Between 0.5 and 1.0 g/L the absorbed fraction rises from 71 % to 92 %, a 30 % relative gain in available photons. Measured hydrogen rates usually gain 10–20 % over that interval, because the extra particles also backscatter light out through the front window, shadow each other, and thicken the suspension. Beyond 2 g/L the volumetric rate is flat or falling.
The per-gram metric falls monotonically and is the honest one for comparing catalysts: at 4 g/L each gram sees about 18 % of the photons that a gram at 0.5 g/L sees, so single-loading figures reported per gram are not comparable between papers.
Loading also changes hydrodynamics. Primary 25 nm particles settle at about 1.6 µm/s and stay suspended under gentle stirring, but aggregates above roughly 20 µm settle at millimetres per second and form a sediment layer on the illuminated window within minutes. A sediment layer behaves like a fixed film: light is absorbed in the first few micrometres and the measured rate becomes a mass transfer artefact.
To separate the two effects, run the loading series at fixed stirring, then repeat the best point at two higher speeds. If the rate changes by more than 5 %, external mass transfer or suspension quality is limiting and the apparent optimum is a mixing artefact. Record stirrer type and speed: 600 rpm on a 20 mm bar in 100 mL is not 300 rpm on an impeller in 500 mL.
Because the optimum is set by the optical path, a loading figure without a path length is not a specification. A 0.5 g/L suspension in a 10 mm flat cell and in a 50 mm immersion-well reactor differ fivefold in areal loading: the second behaves optically like 2.5 g/L in the first. The normalisation that travels between labs is mass per irradiated area, so 0.5 g/L in 100 mL over 20 cm2 of window is 2.5 mg/cm2. Quote loading, path, area and volume together.
A well-behaved series rises, plateaus and then declines; the plateau marks saturated absorption. If the rate keeps climbing to 4 g/L, either the cell is much thinner than assumed or the window geometry limits light delivery, and extra catalyst is compensating for a badly illuminated reactor.
For a 10–50 mm optical path, 0.5–1.0 g/L covers most reported optima, with 1 g/L absorbing over 90 % of 365 nm light in the first 10 mm. Thin flat cells below 5 mm shift the optimum to 1.5–3 g/L, and thick immersion wells below 0.5 g/L.
No. Above the point where absorption saturates, additional particles only add scattering and shadowing, and the rate per litre stays flat or falls. Loadings above 2 g/L also promote aggregation and window deposits, which reduce the rate further.
Increase stirring speed at fixed loading. A rate change above 5 % means external mass transfer or incomplete suspension is limiting; a change below 5 % with a flat response to further loading increases means the optical path, not the catalyst amount, sets the ceiling.
Both. g/L is what you weigh, mg/cm2 is what the photons see. Reporting only g/L makes the result unusable in a reactor with a different optical path, which is the main reason literature optima appear to contradict each other.
