Coverage versus supply cost in facility location:physics of frustrated spin systems

A comprehensive coverage is crucial for communication, supply, and transportation networks, yet it is limited by the requirement of extensive infrastructure and heavy energy consumption. Here, we draw an analogy between spins in antiferromagnet and outlets in supply networks, and apply techniques from the studies of disordered systems to elucidate the effects of balancing the coverage and supply costs on the network behavior. A readily applicable, coverage optimization algorithm is derived. Simulation results show that magnetized and antiferromagnetic domains emerge and coexist to balance the need for coverage and energy saving. The scaling of parameters with system size agrees with the continuum approximation in two dimensions and the tree approximation in random graphs. Due to frustration caused by the competition between coverage and supply cost, a transition between easy and hard computation regimes is observed. We further suggest a local expansion approach to greatly simplify the message updates which shed light on simplifications in other problems. © 2014 American Physical Society.

Direct observation of morphological development during the spin-coating of polystyrene-poly(methyl methacrylate) polymer blends

We present results of the direct observation, in real-space, of the phase separation of high molecular weight polystyrene and poly(methyl methacrylate) from ortho-xylene using our newly developed technique of high speed stroboscopic interference microscopy. Taking a fixed concentration (3 wt % in o-xylene) at a fixed composition (1:4 by weight) and by varying the rotational rate during the spin-coating process, we are able to observe the formation of a range of phase separated bicontinuous morphologies of differing length-scales. Importantly, we are able to show that the mechanism by which the final phase separated structure is formed is through domain coarsening when rich in solvent, before vitrification occurs and fixes the phase separated structure. The ability to directly observe morphological development offers a route toward controlling the length-scale of the final morphology through process control and in situ feedback, from a single stock solution. © 2013 Wiley Periodicals, Inc.

Directed phase separation of PFO:PS blends during spin-coating using feedback controlled in situ stroboscopic fluorescence microscopy

Uniform thin-films of polymer blends can be produced through spin-coating, which is used on an industrial scale for the production of light emitting diodes, and more recently organic photovoltaic devices. Here, we present the results of the direct observation, and control, over the phase separation of polystyrene and poly(9,9′-dioctylfluorene) during spin-coating using high speed stroboscopic fluorescence microscopy. This new approach, imaging the fluorescence, from a blend of fluorescent + non-fluorescent polymers allows for intensity to be directly mapped to composition, providing a direct determination of composition fluctuations during the spin-coating process. We have studied the compositional development and corresponding structural development for a range of compositions, which produce a range of different phase separated morphologies. We initially observe domains formed by spinodal decomposition, coarsening via Ostwald Ripening until an interfacial instability causes break-up of the bicontinuous morphology. Ostwald ripening continues, and depending upon composition a bicontinuous morphology is re-established. By observing compositional and morphological development in real-time, we are able to direct and control morphological structure development through control of the spin coating parameters via in situ feedback. © 2013 The Royal Society of Chemistry.

Caesium bis­(5-bromo­salicyl­aldehyde thio­semicarbazonato-κ3O,N,S)ferrate(III): supramolecular arrangement of low-spin FeIII complex anions mediated by Cs+ cations

The synthesis and crystal structure determination (at 293 K) of the title complex, Cs[Fe(C8H6BrN3OS)2], are reported. The compound is composed of two dianionic O,N,S-tridentate 5-bromo­salicyl­aldehyde thio­semicarbazonate(2-) ligands coord­inated to an FeIII cation, displaying a distorted octa­hedral geometry. The ligands are orientated in two perpendicular planes, with the O- and S-donor atoms in cis positions and the N-donor atoms in trans positions. The complex displays inter­molecular N-H...O and N-H...Br hydrogen bonds, creating R44(18) rings, which link the FeIII units in the a and b directions. The FeIII cation is in the low-spin state at 293 K.

Insights into the influence of solvent polarity on the crystallization of poly(ethylene oxide) spin-coated thin films via in situ grazing incidence wide-angle X-ray scattering

Controlling polymer thin-film morphology and crystallinity is crucial for a wide range of applications, particularly in thin-film organic electronic devices. In this work, the crystallization behavior of a model polymer, poly(ethylene oxide) (PEO), during spin-coating is studied. PEO films were spun-cast from solvents possessing different polarities (chloroform, THF, and methanol) and probed via in situ grazing incidence wide-angle X-ray scattering. The crystallization behavior was found to follow the solvent polarity order (where chloroform < THF < methanol) rather than the solubility order (where THF > chloroform > methanol). When spun-cast from nonpolar chloroform, crystallization largely followed Avrami kinetics, resulting in the formation of morphologies comprising large spherulites. PEO solutions cast from more polar solvents (THF and methanol) do not form well-defined highly crystalline morphologies and are largely amorphous with the presence of small crystalline regions. The difference in morphological development of PEO spun-cast from polar solvents is attributed to clustering phenomena that inhibit polymer crystallization. This work highlights the importance of considering individual components of polymer solubility, rather than simple total solubility, when designing processing routes for the generation of morphologies with optimum crystallinities or morphologies.