Figure 2: Sigmoidal nature of the cation exchange titration. | Nature Communications

Figure 2: Sigmoidal nature of the cation exchange titration.

From: Co-operativity in a nanocrystalline solid-state transition

Figure 2

Experimental plot (a) of the fraction of NCs in the CdSe state (black) and those in the Cu2Se state (blue) as a function of added Cu+ is strikingly sigmoidal, representative of a strongly co-operative process. Below a critical concentration of 500 Cu+ ions per NC, very few NCs undergo a transition to the Cu2Se state. A fit to the Hill plot (solid black line, R=0.996) yields a co-operativity factor of nH=7.1. Note we use total Cu+ concentration, although the Hill equation is strictly valid for free concentrations. The fraction of NCs in the CdSe state was determined from the height of the CdSe excitonic peak from Fig. 1a and the fraction in the Cu2Se state was determined from the Cu2Se band-to-band absorption at 1.82 eV. The procedure for analysis is described in Methods. The rise in the Cu2Se fraction tracks well with the drop in the CdSe fraction, further confirming two-state behaviour. The defect luminescence intensity (red), integrated across the broad band shown in Fig. 1b increased as Cu+ was added, until it reached a maximum around the critical concentration, beyond which it decreased, until it reached zero. A theoretical simulation (b) of a 20-site NC reproduced the observed nature of the cation exchange transformation. Sequential binding was used to model the positive co-operative behaviour. The simulated fraction of Cu2Se NCs in solution as a function of the total Cu+ concentration, plotted as the number of ions per NC, follows a strongly sigmoidal curve (blue). The fraction of all NCs in the CdSe state, either pure or doped, is also shown (black). The simulated concentration of Cu+ dopants and associated Cd2+ vacancies (red) reproduces the observed evolution of the defect luminescence. The defect concentration reaches a maximum around the critical Cu+ concentration, beyond which it gradually decreases to zero.

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