where the subscript n indicates the nucleation stage and the subscript ∞ indicates the time infinitely long relative to the nucleation period but before the growth rate changes (i.e. before the growth stage). Sugimoto notes that this is mathematically identical but physically different to the balance which is obtained at the steady-state (C ′ = 0 and nucleation has ceased) of the growth phase, since changing Q would cause G to adjust accordingly whereas these values are evaluated only during the nucleation period. Chu, Owen, and Peters more recently used (2) with fewer assumptions to derive the expression