Equivalence of Butson-type Hadamard matrices

Journal of Algebraic Combinatorics - Two matrices $$H_1$$ and $$H_2$$ with entries from a multiplicative group G are said to be monomially equivalent, denoted by $$H_1cong H_2$$ , if one of the...     

Enumeration of 2-(9, 3, λ) Designs and Their Resolutions

We consider 2-(9, 3, ) designs, which are known to exist for all 1, andenumerate such designs for = 5 and their resolutions for 3 5, the smallestopen cases. The number of nonisomorphic such structures obtained is 5 862 121 434, 426, 149 041, and 203 047732, respectively. The designs are obtained by an orderly algorithm, and the resolutions by two approaches:either by starting from the enumerated designs and applying a clique-finding algorithm on two levels or by anorderly algorithm.     

Synthesis of poly(styrene-graft-ethylene oxide) by ethoxylation of amide group containing styrene copolymers

Graft copolymers containing poly(ethylene oxide) side chains on a polystyrene backbone have been synthesized. Styrene copolymers synthesized by free radical mechanism and containing between 5 and 15 mol % acrylamide or methacrylamide were used as backbones. The amide groups in the copolymers were ionized by using potassium tert-butoxide or potassium naphthalene, and grafting was achieved by utilizing the amide anions as initiator sites for the polymerization of ethylene oxide in 2-ethoxyethyl ether at 65°C. The graft copolymers were characterized with respect to molecular weight and composition using elemental analysis, NMR, gel permeation chromatography, IR, and viscosity measurements. The size of the side chains were between 600 and 2000 g/mol. GPC results from a hydrolyzed graft copolymer sample suggest a narrow size distribution for the poly(ethylene oxide) grafts. Solution properties of the graft copolymers were investigated in different toluene/methanol mixtures. The intrinsic viscosities of the graft copolymers were found to depend primarily on the poly(ethylene oxide) content rather than the graft density or the poly(ethylene oxide) chain length. © 1993 John Wiley & Sons, Inc.     

Classification of resolvable balanced incomplete block designs — the unitals on 28 points

Approaches for classifying resolvable balanced incomplete block designs (RBIBDs) are surveyed. The main approaches can roughly be divided into two types: those building up a design parallel class by parallel class and those proceeding point by point. With an algorithm of the latter type — and by refining ideas dating back to 1917 and the doctoral thesis by Pieter Mulder — it is shown that the list of seven known resolutions of 2-(28, 4, 1) designs is complete; these objects are also known as the resolutions of unitals on 28 points. This research was supported in part by the Academy of Finland, Grants No. 107493, 110196, and 117499.     

Amphiphilic polymer gel electrolytes. I. preparation of gels based on poly(ethylene oxide) graft copolymers containing different ionophobic groups

Amphiphilic graft copolymers were prepared via the radical copolymerization of poly(ethylene oxide) (PEO) macromonomers with fluorocarbon or hydrocarbon acrylates in toluene with 2,2′‐azobisisobutyronitrile (AIBN) as an initiator. ¹H NMR spectroscopy confirmed that the composition of the graft copolymers corresponded well to the monomer feed. For gel electrolytes prepared from the amphiphilic copolymers, the nature of the ionophobic parts of the amphiphilic graft copolymers had a great influence on the ion conductivity. Gel electrolytes based on graft copolymers containing fluorocarbon side chains showed significantly higher ion conductivity than electrolytes based on graft copolymers containing hydrocarbon groups. The ambient‐temperature ion conductivity was about 2.6 mS/cm at 20 °C for a gel electrolyte based on an amphiphilic graft copolymer consisting of an acrylate backbone carrying PEO and fluorocarbon side chains. Corresponding gels based on graft copolymers with PEO side chains and hydrocarbon groups showed an ambient‐temperature ion conductivity of about 1.2 mS/cm. The gel electrolytes contained 30 wt % copolymer and 70 wt % 1 M LiPF₆ in an ethylene carbonate/γ‐butyrolactone (2/1 w/w) mixture. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2223–2232, 2001     

Continuous lipid bilayers derived from cell membranes for spatial molecular manipulation

Progress with respect to enrichment and separation of native membrane components in complex lipid environments, such as native cell membranes, has so far been very limited. The reason for the slow progress can be related to the lack of efficient means to generate continuous and laterally fluid supported lipid bilayers (SLBs) made from real cell membranes. We show in this work how the edge of a hydrodynamically driven SLB can be used to induce rupture of adsorbed lipid vesicles of compositions that typically prevent spontaneous SLB formation, such as vesicles made of complex lipid compositions, containing high cholesterol content or being derived from real cell membranes. In particular, upon fusion between the moving edge of a preformed SLB and adsorbed vesicles made directly from 3T3 fibroblast cell membranes, the membrane content of the vesicles was shown to be efficiently transferred to the SLB. The molecular transfer was verified using cholera toxin B subunit (CTB) binding to monosialoganglioside receptors (G(M1) and G(M3)), and the preserved lateral mobility was confirmed by spatial manipulation of the G(M1/M3)-CTB complex using a hydrodynamic flow. Two populations of CTB with markedly different drift velocity could be identified, which from dissociation kinetics data were attributed to CTB bound with different numbers of ganglioside anchors.     

On the macro- and microphase separation of compatibilizers in immiscible polymer blends

Macro- and microphase separation of compatibilizing graft copolymers in melt-mixed polystyrene/polyamide-6 blends was studied by transmission electron microscopy and thermal analysis. Three different graft copolymers with main chains of polystyrene and side chains of poly(ethylene oxide) were used as additives at various concentrations. The polyamide-6 domain sizes decreased with increasing amounts of compatibilizing graft copolymers in the blends up to a saturation concentration, after which no further reduction was noted. Macrophase separation of the graft copolymers into discrete macrodomains 20–200 nm in size occurred at concentrations equal to or slightly lower than the saturation concentration. The macrodomains of the graft copolymers were microphase separated, and the sizes and shapes of the microdomains were found to largely depend on the graft copolymer structure and composition. As a consequence of microphase separation, poly(ethylene oxide) crystallinity was noted in blends with sufficiently high macrophase contents. Observations of a graft copolymer interphase between the polystyrene matrix and the polyamide-6 domains confirmed that the graft copolymer was present at the blend interfaces in some of the compatibilized blends. © 1996 John Wiley & Sons, Inc.     

Symmetry Breaking in Chiral Ionic Liquids Evidenced by Vibrational Optical Activity

Ionic liquids (ILs) are receiving increasing interest for their use in synthetic laboratories and industry. Being composed of charged entities, they show a complex and widely unexplored dynamic behavior. Chiral ionic liquids (CILs) have a high potential as solvents for use in asymmetric synthesis. Chiroptical methods, owing to their sensitivity towards molecular conformation, offer unique possibilities to study the structure of these chiral ionic liquids. Raman optical activity proved particularly useful to study ionic liquids composed of amino acids and the achiral 1‐ethyl‐3‐methylimidazolium counterion. We could substantiate, supported by selected theoretical methods, that the achiral counterion adopts an overall chiral conformation in the presence of chiral amino acid ions. These findings suggest that in the design of chiral ionic liquids for asymmetric synthesis, the structure of the achiral counter ion also has to be carefully considered.