Charged surface Induced Diblock Copolymer Micellization

Diblock copolymers with one charged block A and one hydrophobic block B are mainly single chains in solution when the concentration is lower than the critical micellization concentration (cmc. Electrostatic interaction between copolymers and a negatively charged surface decreases the non-ideal part of the micelle chemical potential and induce the micelle formation at the surface when the bulk copolymer concentration is still lower than the bulk cmc. The effects of surface charge density \textit{$\sigma $, }monomer number of charged block$ N_{A}$, monomer number of hydrophobic block$ N_{B }$ and the fraction of charged monomers in the charged block $f$, on the number of chains in micelles $p, $micelle radius \textit{Ls} and critical surface micellization concentration (csmc) are studied. When \textit{Ls} is smaller than the size of the micelle Wigner-Seitz cell $R$, $p$ is very small. When \textit{Ls} is equal to $R$, $p$ does not depend on the number of charged monomers in hydrophilic block. The size of the micelle has the same dependence on $N_{A}$ and $N_{B}$ as uncharged system. The effect of electrostatic is reflected by $R\sim (f$/\textit{$\sigma $})$^{1/8}$ and $p \quad \sim (f$/\textit{$\sigma $})$^{-3/4}$. The csmc rises with the increase of salt concentration when the copolymer layer charge density is lower than the surface charge density. However the cscm decline with the increase of salt concentration when the layer charge density is higher than the surface charge density.