How this works
Scaling a recipe just multiplies every component's amount by the same factor, which keeps every ratio (monomer to initiator, catalyst to ligand, concentration) exactly the same as the original. Enter each component from your recipe below, set a scale factor directly or derive one from a current and target batch size, and copy the scaled amounts back into your notebook.
Scale factor
Components
Scaled recipe
| Component | Original amount | Scaled amount |
|---|
A worked example
A copper-mediated ATRP of methyl methacrylate targeting a degree of polymerisation of 200: 5.00 g of MMA (49.9 mmol) against 0.25 mmol each of initiator, copper and ligand, in 5 mL of anisole. Multiplying every line by 20 to reach a 100 g batch gives:
| Component | Original | ×20 | ×0.02 |
|---|---|---|---|
| Methyl methacrylate | 5.00 g | 100.0 g | 100 mg |
| Ethyl α-bromoisobutyrate | 0.0488 g | 0.975 g | 0.98 mg |
| CuBr | 0.0359 g | 0.717 g | 0.72 mg |
| PMDETA | 0.0433 g | 0.867 g | 0.87 mg |
| Anisole | 5.0 mL | 100 mL | 0.10 mL |
Every ratio is untouched, so the target degree of polymerisation is still 200 and the monomer concentration is still 50 % v/v. That is all the arithmetic does – and the reason the two outer columns are worth putting side by side is that neither is simply “the same reaction, bigger”.
Scaling down fails first, and it fails on the balance rather than in the flask. At ×0.02 the catalyst and ligand land under a milligram, which is below what an ordinary four-place balance can weigh with any accuracy – a ±0.1 mg reading error on a 0.72 mg charge is a 14 % error in copper. The fix is not a better balance but a stock solution: make up the catalyst and ligand at a known concentration in the reaction solvent, weigh nothing below about 10 mg, and deliver the small components by volume. The same logic applies to any recipe where one component is present at well under a mole percent.
What does not scale with the factor
This tool multiplies quantities. Several things that determine whether the reaction works are not quantities, and they stay where they are or move the wrong way:
- Reaction time does not scale. Kinetics depend on concentration, and concentrations are unchanged, so a reaction that reached 60 % conversion in four hours still takes four hours. Time is the one line in your notebook that should be copied across untouched.
- Heat removal scales against you. Volume grows as the cube of a vessel's linear dimension and surface area only as the square, so a batch twenty times larger has roughly seven times the heat-transfer area for twenty times the exotherm. The reaction that was self-regulating in a small flask has an internal temperature the bath no longer controls, and radical polymerisations autoaccelerate when they get hot.
- Degassing time scales with volume, not with the factor. Three freeze–pump–thaw cycles on 5 mL is not three cycles on 100 mL – freezing and thawing take far longer, and a sparge needs proportionally more time at the same gas flow. Under-degassing at scale is one of the commonest reasons a scaled-up controlled polymerisation gives a worse dispersity than the small one.
- Stirring does not scale by rpm. Geometric similarity means matching tip speed or power per unit volume, not revolutions per minute. The same setting on a larger impeller is a different mixing regime, and viscosity climbs steeply with conversion in a bulk or concentrated polymerisation.
- Trace impurities scale with the reagent, not with the target. Inhibitor, water and dissolved oxygen arrive in proportion to the monomer and solvent, so their absolute amount grows with the batch – but so does the amount of catalyst they can consume. What changes is that a longer, larger run gives them more opportunity to matter.
For the exotherm in particular, the usual answer at scale is to stop scaling the recipe and change the process instead: feed monomer or initiator semi-batch rather than charging it all at once, so the rate of heat release is set by a pump rather than by the kinetics. That is a different experiment from the one this calculator describes, and worth designing deliberately.
Before you scale up
- Heat transfer gets worse as you scale up. A larger batch has a smaller surface area to volume ratio, so exotherms (radical initiation, fast catalyst turnover) shed heat more slowly. A recipe that runs isothermally at 1 mL scale can run away at 100 mL scale.
- Mixing and degassing take longer at volume. Stir efficiency, freeze pump thaw cycle time, and sparge time scale with volume rather than staying fixed.
- Kinetics depend on concentration, not absolute amount. This tool keeps every ratio and concentration identical by design; if you also change solvent volume independently, recheck your target concentration.
- Reagent grade and purity matter more at scale. Trace inhibitor, water, or oxygen that's negligible in a small aliquot can shift results in a larger, longer running batch.