Figure 5: Co-operativity in the cation exchange of CdSe NCs with Ag⁺.

A plot of the fraction of NCs in the CdSe state (black dots) and those in the Ag₂Se state (blue) as a function of added Ag⁺ is sigmoidal, indicative of co-operative behaviour. Below a critical concentration of ∼500 Ag⁺/NC, very few NCs undergo a transition to the Ag₂Se state. A fit to the Hill plot (solid black line, R=0.973) yields a co-operativity factor of n_H=3.2. The fraction of NCs in the CdSe state was determined from the height of the CdSe excitonic peak and the fraction in the Ag₂Se state was determined from the Ag₂Se band-to-band absorption at 1.82 eV. The absorption and PL data is shown in Supplementary Fig. S5, and the procedure for analysis is described in Methods. The rise in the Ag₂Se fraction tracks well with the drop in the CdSe fraction. The defect luminescence intensity (red), integrated across its broad band, increases as Ag⁺ is added, until it reaches a maximum around the critical concentration, beyond which it decreases, until it reaches zero.