Fig. 4. Rate-determining steps and scaling in serial and parallel reactions. The saturating serial process (left) consists of two steps, S1 and S2, in series where the intermediate (yellow pentagon) is bound to a catalyst which is released again upon formation of the product (blue square). The parallel process consists of two steps, P1 and P2, that both yield the same product, directly from monomer (blue circles) in the case of P1 and from a different species (red triangle) in the case of P2. The mechanisms are considered in the limits of high and low concentrations of starting material (blue circles) and the rate-determining step is highlighted in each case. The behaviour of each system over the range of monomer concentrations is summarized in the scaling plots, i.e. the double logarithmic plots of the half time versus monomer concentration (the equations used to generate these plots are given in the ESI Sections 4.1 and 4.2†). Note that for the parallel network the scaling exponent increases in magnitude with increasing concentration (i.e. the faster process dominates the reaction), whereas for the serial network the magnitude of the scaling exponent decreases with increasing concentration (i.e. the slower process limits the overall rate).