Model for Adsorption of Ligands to Colloidal Quantum Dots with Concentration-Dependent Surface Structure

A study of the adsorption equilibrium of solution-phase CdS quantum dots (QDs) and acid-derivatized viologen ligands (N-[1-heptyl],N'-[3-carboxypropyl]-4,4'-bipyridinium dihexafluorophosphate, V(2+)) reveals that the structure of the surfaces of the QDs depends on their concentration. This adsorption equilibrium is monitored through quenching of the photoluminescence of the QDs by V(2+) upon photoinduced electron transfer. When modeled with a simple Langmuir isotherm, the equilibrium constant for QD-V(2+) adsorption, K(a), increases from 6.7 × 10(5) to 8.6 × 10(6) M(-1) upon decreasing the absolute concentration of the QDs from 1.4 × 10(-6) to 5.1 × 10(-8) M. The apparent increase in K(a) upon dilution results from an increase in the mean number of available adsorption sites per QD from 1.1 (for [QD] = 1.4 × 10(-6) M) to 37 (for [QD] = 5.1 × 10(-8) M) through desorption of native ligands from the surfaces of the QDs and through disaggregation of soluble QD clusters. A new model based on the Langmuir isotherm that treats both the number of adsorbed ligands per QD and the number of available binding sites per QD as binomially distributed quantities is described. This model yields a concentration-independent value for K(a) of 8.7 × 10(5) M(-1) for the QD-V(2+) system and provides a convenient means for quantitative analysis of QD-ligand adsorption in the presence of competing surface processes.