Effects of Functional Groups and Ionization on the Structure of Alkanethiol-Coated Gold Nanoparticles

We report classical atomistic molecular dynamics simulations of alkanethiol-coated gold nanoparticles solvated in water and decane, as well as at water/vapor interfaces. The structure of the coatings is analyzed as a function of various functional end groups, including amine and carboxyl groups in various ionization states. We study both neutral and charged end groups for two different chain lengths (9 and 17 carbons). For the charged end groups, we simulated both mono- and divalent counterions. For the longer alkanes, we find significant local bundling of chains on the nanoparticle surface, which results in highly asymmetric coatings. In general, the charged end groups attenuate this effect by enhancing the water solubility of the nanoparticles. On the basis of the coating structures and density profiles, we can qualitatively infer the overall solubility of the nanoparticles. This asymmetry in the alkanethiol coatings is likely to have a significant effect on aggregation behavior. Our simulations elucidate the mechanism by which modulating the end group charge state can be used to control coating structure and therefore nanoparticle solubility and aggregation behavior

Nonsmooth optimization over the (weakly or properly) Pareto set of a linear-quadratic multi-objective control problem: Explicit optimality conditions

We present explicit optimality conditions for a nonsmooth functional dened over the (properly or weakly) Pareto set associated with a multiobjective linear-quadratic control problem. This problem is very dicult even in anite dimensional setting, i.e. when, instead of a control problem, we deal with a mathematical programming problem. Amongst various applications, our problem may be considered as a response for a decision maker when he has to choose a solution over the solution set of the grand coalition p-player cooperative differential game