Design and verify: a new scheme for generating cutting-planes

A cutting-plane procedure for integer programming (IP) problems usually involves invoking a black-box procedure (such as the Gomory–Chvátal procedure) to compute a cutting-plane. In this paper, we describe an alternative paradigm of using the same cutting-plane black-box. This involves two steps. In the first step, we design an inequality $cx \le d$ where $c$ and $d$ are integral, independent of the cutting-plane black-box. In the second step, we verify that the designed inequality is a valid inequality by verifying that the set $P \cap \{x\in \mathbb R ^n \mid cx \ge d + 1\} \cap \mathbb Z ^n$ is empty using cutting-planes from the black-box. Here $P$ is the feasible region of the linear-programming relaxation of the IP. We refer to the closure of all cutting-planes that can be verified to be valid using a specific cutting-plane black-box as the verification closure of the considered cutting-plane black-box. This paper undertakes a systematic study of properties of verification closures of various cutting-plane black-box procedures.     

Monte Carlo simulation of osmotic equilibria

We present a Metropolis Monte Carlo simulation algorithm for the Tpπ-ensemble, where T is the temperature, p is the overall external pressure, and π is the osmotic pressure across the membrane. The algorithm, which can be applied to small molecules or sorption of small molecules in polymer networks, is tested for the case of Lennard-Jones interactions.     

Tuning the electronic coupling in a low-bandgap donor-acceptor copolymer via the placement of side-chains

We present a spectroscopic and theoretical investigation of the effect of the presence and position of hexyl side-chains in the novel low-bandgap alternating donor-acceptor copolymer poly[bis-N,N-(4-octylphenyl)-bis-N,N-phenyl-1,4-phenylenediamine-alt-5,5'-4',7',-di-2-thienyl-2',1',3'-benzothiadiazole] (T8TBT). We use electronic absorption and Raman spectroscopic measurements supported by calculations of chain conformation, electronic transitions, and Raman modes. Using these tools, we find that sterically demanding side-chain configurations induce twisting in the electronic acceptor unit and reduce the electronic interaction with the donor. This leads to a blue-shifted and weakened (partial) charge-transfer absorption band together with a higher photoluminescence efficiency. On the other hand, sterically relaxed side-chain configurations promote coupling between donor and acceptor units and exhibit enhanced absorption at the expense of luminescence efficiency. The possibility of tuning the donor-acceptor character of conjugated polymers by varying the placement of side-chains has very important ramifications for light emitting diode, Laser, display, and photovoltaic device optimization.     

Properties of new ferroelectric materials

A homologous series of chiral 4-(3-methylpentyl)benzenethio-4′-n-alkoxy-benzoates has been studied. These thioesters display a ferroelectric, chiral smectic C phase in addition to cholesteric and smectic A phases. A comparison is made between the thioester series and a phenylbenzoate, having the same molecular end group. The effect of the different central linkage on the transition temperature, and on the physical and ferroelectric liquid crystal (FLC) properties has been investigated. Several mixtures, containing these thioester components, were calculated and formulated to obtain room temperature chiral smectic C phases. Spontaneous polarization P_s values and electro-optical response times are correlated with chemical structures. Although these thioesters have very low P _s values, they are useful components for FLC mixtures because of their convenient chiral smectic C temperature ranges and their low viscosities.     

Synthesis and characterization of guest-host azo dyes with broad absorption bands

Abstract

Three groups of dyes were synthesized and characterized in order to examine their solubility, absorption spectrum, and order parameter in liquid crystal hosts. Our synthesis method allowed the formation of the diazonium salts and the diazo coupling in ethyl acetate instead of an aqueous medium, permitting the formation of long and neutral azo dyes. In the liquid crystal BDH-E7, they showed order parameters in the range of 0.52 to 0.76. The two dyes with the longest molecular lengths were particularly interesting due to their very broad absorption spectra in the visible region. Each of these two compounds behave as single component black dye guest/host systems, which generally require a mixture of two or three dyes in the liquid crystal host. These dyes were also evaluated for use in polymer dispersed liquid crystal films.     

Ion‐Pairing of Phosphonium Salts in Solution: C?H⋅⋅⋅Halogen and C?H⋅⋅⋅π Hydrogen Bonds

The ¹H NMR chemical shifts of the C(α)? H protons of arylmethyl triphenylphosphonium ions in CD₂Cl₂ solution strongly depend on the counteranions X^?. The values for the benzhydryl derivatives Ph₂CH? PPh₃⁺ X^?, for example, range from δ_H=8.25 (X^?=Cl^?) over 6.23 (X^?=BF₄^?) to 5.72 ppm (X^?=BPh₄^?). Similar, albeit weaker, counterion‐induced shifts are observed for the ortho‐protons of all aryl groups. Concentration‐dependent NMR studies show that the large shifts result from the deshielding of the protons by the anions, which decreases in the order Cl^? > Br^? ? BF₄^? > SbF₆^?. For the less bulky derivatives PhCH₂? PPh₃⁺ X^?, we also find C? H???Ph interactions between C(α)? H and a phenyl group of the BPh₄^? anion, which result in upfield NMR chemical shifts of the C(α)? H protons. These interactions could also be observed in crystals of (p‐CF₃‐C₆H₄)CH₂? PPh₃⁺ BPh₄^?. However, the dominant effects causing the counterion‐induced shifts in the NMR spectra are the C? H???X^? hydrogen bonds between the phosphonium ion and anions, in particular Cl^? or Br^?. This observation contradicts earlier interpretations which assigned these shifts predominantly to the ring current of the BPh₄^? anions. The concentration dependence of the ¹H NMR chemical shifts allowed us to determine the dissociation constants of the phosphonium salts in CD₂Cl₂ solution. The cation–anion interactions increase with the acidity of the C(α)? H protons and the basicity of the anion. The existence of C? H???X^? hydrogen bonds between the cations and anions is confirmed by quantum chemical calculations of the ion pair structures, as well as by X‐ray analyses of the crystals. The IR spectra of the Cl^? and Br^? salts in CD₂Cl₂ solution show strong red‐shifts of the C? H stretch bands. The C? H stretch bands of the tetrafluoroborate salt PhCH₂? PPh₃⁺ BF₄^? in CD₂Cl₂, however, show a blue‐shift compared to the corresponding BPh₄^? salt.     

Assembly of Melleolide Antibiotics Involves a Polyketide Synthase with Cross-Coupling Activity

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A Kinetic Study of Free-Radical Styrene-Acrylonitrile Copolymerization by Differential Scanning Calorimeter

Abstract

The isothermal free-radical copolymerization of styrene and acrylonitrile was examined in the temperature range of 333-373 °K. Initial rate studies of styrene homopolymerization were conducted and agreed favorably with values in the literature. Initial rate studies for acrylonitrile solution polymerization in DMF were also performed. Initiator decomposition rate constants measured in the presence of AN and styrene monomer are reported for AIBN, BP, and DTBP. Rate functions for the full spectrum of comonomer compositions initiated by AIBN and benzoyl peroxide are reported. Several copolymerization kinetic models were tested and found to be inadequate. Conversion histories were found to be consistent with observed initial rates and follow a simple pseudohomopolymerization kinetic model. Autoacceleration was observed and found to increase in severity with increased AN feed compositions and decreased reaction temperatures.     

Small but Smart: Sensitive Microgel Capsules

Microgel capsules are micrometer‐sized particles that consist of a cross‐linked and swollen polymer network complexed with additives. These capsules can be actuated by external stimulation if they are formed from sensitive or supramolecular polymer networks. To make this truly useful, it is crucial to control the microgel size, shape, and loading; this can be achieved by droplet‐based microfluidic templating.