Determination of the heterogeneous association constants of metal ions to ω-mercaptoalkanoic acids by using double-layer capacity measurements

The binding of metal ions to ligands in homogeneous solutions and that to the same ligands anchored to metallic surfaces through self-assembled monolayers (SAMs) are expected to differ primarily due to the difference in the degree of freedom of the ligands and the surface potential. We studied the heterogeneous binding of Cd^II ions to ω-mercaptoalkanoic-acid SAMs on Au. This was accomplished by adding metal ions at a constant pH and following the changes in the double-layer capacity. A mathematical treatment, which is based on calcutating the electrochemical-potential differences at the double layer-solution interface, has been developed. Our approach follows that proposed by White et al. and Kakiuchi, who used the acid-base equilibrium at the monolayer-electrolyte interface as a means of calculating the pK of ionizable SAMs. Experimentally, SAMs of ω-mercaptoalkanoic adds, HS(CH ₂)_nCO₂H, with different chain lengths (i.e., n = 2, 5, and 10) in 0.1 M sodium perchlorate were assembled on Au surfaces and studied. The capacity was measured first in the absence of Cd^II of different pH values, and then at a constant pH while increasing the concentration of Cd^II in the solution. We found that the interfacial capacity decreased as the concentration (of either protons or Cd^II) increased. The results matched the model fairly well, which allowed the extraction of the thermodynamic equilibrium constant that is established at the monolayer-electrolyte interface. The suggested mathematical treatment of this model system is simple and yet very useful for estimating the heterogeneous association constants of metal ions by SAMs.