High-throughput preparation of complex multi-scale patterns from block copolymer/homopolymer blend films

A simple, straightforward process for fabricating multi-scale micro-and nanostructured patterns from polystyrene-block-poly(2-vinylpyridine) (PS-b-P2VP)/poly(methyl methacrylate) (PMMA) homopolymer in a preferential solvent for PS and PMMA is demonstrated. When the PS-b-P2VP/PMMA blend films were spin-coated onto a silicon wafer, PS-b-P2VP micellar arrays consisting of a PS corona and a P2VP core were formed, while the PMMA macrodomains were isolated, due to the macrophase separation caused by the incompatibility between block copolymer micelles and PMMA homopolymer during the spin-coating process. With an increase of PMMA composition, the size of PMMA macrodomains increased. Moreover, the P2VP blocks have a strong interaction with a native oxide of the surface of the silicon wafer, so that the P2VP wetting layer was first formed during spin-coating, and PS nanoclusters were observed on the PMMA macrodomains beneath. Whereas when a silicon surface was modified with a PS brush layer, the PS nanoclusters underlying PMMA domains were not formed. The multi-scale patterns prepared from copolymer micelle/homopolymer blend films are used as templates for the fabrication of gold nanoparticle arrays by incorporating the gold precursor into the P2VP chains. The combination of nanostructures prepared from block copolymer micellar arrays and macrostructures induced by incompatibility between the copolymer and the homopolymer leads to the formation of complex, multi-scale surface patterns by a simple casting process.close2

The Boltzmann fair division for distributive justice

Fair division is a significant, long-standing problem and is closely related to social and economic justice. The conventional division methods such as cut-and-choose are hardly applicable to real-world problems because of their complexity and unrealistic assumptions about human behaviors. Here we propose a fair division method from a completely different perspective, using the Boltzmann division. The mathematical model of the Boltzmann division was developed for both homogeneous and heterogeneous cake-cutting problems, and the realistic human factors (contributions, needs, and preferences) of the multiple participating players could be successfully integrated. The Boltzmann division was then optimized by maximizing the players' total utility. We show that the Boltzmann fair division is a division method favorable to the socially disadvantaged or underprivileged, and it is drastically simple yet highly versatile and can be easily fine-tuned to directly apply to a variety of social, economic, and political division problems

The Boltzmann fair division for distributive justice

Fair division is a significant, long-standing problem and is closely related to social and economic justice. The conventional division methods such as cut-and-choose are hardly applicable to real-world problems because of their complexity and unrealistic assumptions about human behaviors. Here we propose a fair division method from a completely different perspective, using the Boltzmann division. The mathematical model of the Boltzmann division was developed for both homogeneous and heterogeneous cake-cutting problems, and the realistic human factors (contributions, needs, and preferences) of the multiple participating players could be successfully integrated. The Boltzmann division was then optimized by maximizing the players' total utility. We show that the Boltzmann fair division is a division method favorable to the socially disadvantaged or underprivileged, and it is drastically simple yet highly versatile and can be easily fine-tuned to directly apply to a variety of social, economic, and political division problems

Morphology selection of nanoparticle dispersions by polymer media

A systematic theory of ultrathin polymer films as organizing media to achieve 2D nanoparticle arrangements was developed. The key physical variables to achieve nanoparticle dispersions and control morphology were determined.open727