# Interface Engineering Strategies for Fabricating Nanocrystal-Based Organic-Inorganic Nanocomposites
## 2 Overview of Ligand Exchange  
### Ligand Exchange  
Ligand exchange is the process of introducing desired ligands on NCs by displacing originally bound surfactants, considering the adsorption and desorption kinetics. Hence, the reaction rates are key factors determining the coverage of ligands. The reactions and rates can be described as follows [30]:  
\[\text{Ligand exchange:}\ M+L\to ML\] \[\text{The rate of adsorption :}\ (\frac{d[ML]}{dt})_{\text{ad}}=k_{ad}[M][L] \tag{1}\] \[\text{The rate of desorption :}\ (\frac{d[ML]}{dt})_{des}=-k_{des}[ML], \tag{2}\]  
where \(M\) and \(L\) are the binding sites on the NC surfaces and the free ligands, respectively. \(ML\) refers to the NC surface sites that bind the ligands. The terms \(k_{ad}\) and \(k_{des}\) refer to the adsorption and desorption reaction rate constants, respectively. The average surface ligand coverage (\(\theta\)) can be therefore expressed as \(\theta=[ML]/([M]+[ML])\). For a given system, the number of total binding sites (\([M]+[ML]\)) is constant. Equations (1) and (2) can thus be rewritten in terms of the change in the average surface ligand coverage, \(\frac{d[\theta]}{dt}\):  
\[\text{adsorption :}\ (\frac{d[\theta]}{dt})_{ad}=k_{ad}(1-\theta)[L] \tag{3}\] \[\text{Desorption :}\ (\frac{d[\theta]}{dt})_{des}=-k_{des}[\theta]. \tag{4}\]  
It should be noted that \(\theta\) depends on the concentration of ligands, \(k_{ad}\), and \(k_{des}\). The reaction rate constants are governed by the chemical nature of the ligands, such as the steric effects, mobility, and binding ability of the functional groups. The binding mode plays an especially significant role in the adsorption-desorption reaction. As illustrated in Figure 1, the binding mode of ligands with NC surfaces can be classified into three types, according to the suggested method by [PERSON] et al. : (1) L-type ligands (2) X-type ligands; and (3) Z-type ligands [31]. L-type ligands are two-electron donors (neutral Lewis bases) and bind to NCs via dative covalent bonding. X-type ligands donate one electron to NCs (cationic sites) and form covalent bonds. Z-type ligands are two-electron acceptors (Lewis acids). The nature of the ligands strongly depends on the stoichiometry of the NCs. The charge neutrality is maintained by balancing the metal cations on NC surfaces with X-type anionic ligands. Therefore, it is necessary to transfer protons to mediate the ligand exchange. Moreover, the fact that metal enrichment increases with decreasing nanocrystal size emphasizes the importance of stoichiometry [32; 33]. [PERSON] and co-workers demonstrate that the surface metal ions are labile; thus, they can reversibly bind to and dissociate from NCs by forming carboxylate complexes (M(O\({}_{2}\)CR)\({}_{2}\)) [32], NMR characterization revealed that various Lewis bases like tri-\(n\)-butylamine, tetrahydrofuran, \(N\),\(N\)-dimethyl-\(n\)-butylamine, tri-\(n\)-butylphosphine, \(N\),\(N\),\(N^{\prime}\),\(N^{\prime}\)-tetramethylbutylene-1,4-diamine, pyridine, \(N\),\(N\),\(N^{\prime}\),\(N^{\prime}\)-tetramethylethylene-1,2-diamine, \(n\)-octylamine can mediate the ligand exchange. The addition of L-type ligands (e.g., \(N\),\(N\),\(N^{\prime}\),\(N^{\prime}\)-tetramethylethylene-1,2-diamine (TMEDA)) leads to the detachment of the original capping ligands, which is oleic acid (OA, X-type). This, however, disrupts the charge neutrality due to the positive sites on NCs and the anionic ligands and strongly indicates that the detached carboxylic fragment is formed by TMEDA-bound cadmium carboxylate complexes displaced for charge neutrality. The potency of displacing Z-type ligands with L-type ligands was 35-40 \(\pm\) 5% (2.0 M) for primary amines and TMEDA and 95 \(\pm\) 10% (2.0 M) for pyridine and Bu\({}_{3}\)P.  
The electronic nature, chelation, and steric effect play important roles in determining the ligand displacement potency.