Fig. 3.

Reversible-binding scenario. (A) In the reversible-binding scenario (if ${\delta }_2\ll {\delta }_1$), the cluster evolution typically proceeds via stable intermediate states (in which all constituents form two or more bonds), whereas unstable intermediates are short lived. Hence, nucleation is disfavored relative to growth because nucleation proceeds via two unstable intermediate states whereas attachment proceeds only via one. (B) Assembly time to achieve 50% yield (T₅₀) and 90% yield (T₉₀) plotted against the binding energy E_B for two-dimensional target structures of size S = 100 (with preexponential factor $A={10}^{18}C\nu$). To achieve high yield with maximal time efficiency, E_B must be fine-tuned to a narrow range (here $\approx 1.4\%$) around its optimal value. In Inset, the optimal detachment rate ${\delta }_1^{\text{opt}}$ exhibits a power-law dependence on the structure size with exponent characterized by the dimensionality of the structure. The control parameter exponents ${\varphi }_{\text{sim}}$ together with their theoretic estimates ${\varphi }_{\text{th}}$ are summarized in the table.