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Nanocomposite tectons (NCTs) are nanocomposite building blocks consisting of nanoparticle cores functionalized with a polymer brush, where each polymer chain terminates in a supramolecular recognition group capable of driving particle assembly. Like other ligand-driven nanoparticle assembly schemes (for example those using DNA-hybridization or solvent evaporation), NCTs are able to make colloidal crystal structures with precise particle organization in three dimensions. However, despite the similarity of NCT assembly to other methods of engineering ordered particle arrays, the crystallographic symmetries of assembled NCTs are significantly different. In this study, we provide a detailed characterization of the dynamics of hybridizations through universal (independent of microscopic details) parameters. We perform rigorous free energy calculations and identify the persistence length of the ligand as the critical parameter accounting for the differences in the phase diagrams of NCTs and other assembly methods driven by hydrogen bond hybridizations. We also report new experiments to provide direct verification for the predictions. We conclude by discussing the role of non-equilibrium effects and illustrating how NCTs provide a unification of the two most successful strategies for nanoparticle assembly: solvent evaporation and DNA programmable assembly. 

Abstract The existence and multiplicity of similarity solutions for the steady, incompressible and fully developed laminar flows in a uniformly porous channel with two permeable walls are investigated. We shall focus on the so-called asymmetric case where the upper wall is with an amount of flow injection and the lower wall with a different amount of suction. The numerical results suggest that there exist three solutions designated as type $$I$$, type $II$ and type $III$ for the asymmetric case, type $$I$$ solution exists for all non-negative Reynolds number and types $II$ and $III$ solutions appear simultaneously at a common Reynolds number that depends on the value of asymmetric parameter $$a$$ and with the increase of $$a$$ the common Reynolds numbers are decreasing. We also theoretically show that there exist three solutions. The corresponding asymptotic solution for each of the multiple solutions is constructed by the method of boundary layer correction or matched asymptotic expansion for the most difficult high Reynolds number case. These asymptotic solutions are all verified by their corresponding numerical solutions.