Mathematical modelling of influence functions in computer-controlled polishing: Part I

Computer-controlled polishing (CCP) is commonly used to finish high-quality surfaces, such as optical lenses. Based on magnetorheological finishing (MRF), a mathematical model to calculate the polishing tool characteristic (influence function) was developed and verified experimentally. The first part of this paper introduces the model to predict the size and shape of an influence function. The second part of this paper describes the calculation of the distribution of material removal within the size of an influence function. The model supersedes the current cumbersome procedure for determining an influence function and thus results in considerably improved and more economical manufacture. Furthermore, the model enables the quality of the final surface to be enhanced when polishing complex, for example aspherical or free-form, workpiece geometries and provides the first step in the application of time-variant influence functions.     

Counterexamples to Additivity of Minimum Output p-Rényi Entropy for p Close to 0

Complementing recent progress on the additivity conjecture of quantum information theory, showing that the minimum output p-Rényi entropies of channels are not generally additive for p > 1, we demonstrate here by a careful random selection argument that also at p = 0, and consequently for sufficiently small p, there exist counterexamples. An explicit construction of two channels from 4 to 3 dimensions is given, which have non-multiplicative minimum output rank; for this pair of channels, numerics strongly suggest that the p-Rényi entropy is non-additive for all p ≲ 0.11. We conjecture however that violations of additivity exist for all p < 1.     

Self‐assembly of π‐conjugated bis(terpyridine) ligands with zinc(II) ions: New metallosupramolecular materials for optoelectronic applications

A series of main‐chain metallopolymers ( P1–P10 ) was prepared by the self‐assembly of rigid‐linear π‐conjugated bis(terpyridine) monomers ( 1–10 ) with Zn^II ions and was fully characterized. The polymerization was additionally confirmed by UV/vis titration experiments. A strong increase in viscosities (around 1.6 times) relative to those of the monomer solutions was found. The thermal stability of P1–P10 compared with that of 1–10 was enhanced as a result of the metallopolymerization. The electro‐optical properties of the materials were investigated in detail. Tuning of the electrochemical and photophysical properties was enabled; thus, bright purple to green photoluminescent (PL) emission (PL quantum yields of 0.12–0.81) for P1–P10 was observed in solution with the emission color strongly depending on the nature of the π‐conjugated bis(terpyridine) system. Thin homogeneous films of P6 were prepared by solution processing, that is, spin‐coating and inkjet‐printing, and exhibited intense yellow PL emission in the solid state. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 4083–4098, 2009     

Synthesis and characterization of synthetic polymer colloids colloidally stabilized by cationized starch oligomers

A method is developed for anchoring enzymatically degraded cationized starch as electrosteric stabilizers onto synthetic latices, using cerium(IV) to create free‐radical grafting sites on the starch. Direct anchoring of debranched starch onto a poly(methyl methacrylate) seed latex yields a latex stabilized by well‐defined oligosaccharides. Using α‐amylase to randomly cleave starch to form (1→4)‐α‐glucans, and a comonomer, N‐isopropyl acrylamide (NIPAM), whose corresponding polymer exhibits a lower critical solution temperature (LCST), creates a means to synthesize block (or graft) oligomers of oligosaccharide and synthetic polymer, which are water soluble at room temperature. Above 30 °C, they become amphiphilic and form self‐emulsifying nanoparticles (sometimes termed “frozen micelles”) from which a synthetic latex is grown after addition of methyl methacrylate, the collapsed NIPAM‐containing entities functioning as a type of in situ seed. This synthesis of stable synthetic latex particles is shown to have a high grafting efficiency. The starch fragments were characterized by ¹H solution‐state NMR before grafting, and ¹³C solid‐state cross‐polarization magic‐angle spinning (CP‐MAS) NMR was used to characterize the starch oligomers actually grafted on the final latex. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 1836–1852, 2009