Optically active vinyl polymers containing fluorescent groups—4: Synthesis and properties of copolymers of 9-vinylcarbazole with (−)menthyl vinyl ether

9-Vinylcarbazole (1) has been copolymerized with (?)menthyl vinyl ether (2) by a conventional cationic catalyst [Al(C₂H₅)Cl₂] in CH₂Cl₂ at ?78°. Reactivity ratios were estimated using a relatively new method valid up to high conversions. Chiroptical properties, including differential dichroic adsorption (Δε) of the various copolymers, have been studied in an attempt to investigate correlations between physico-optical properties, and the chemical compositions, distributions of monomeric units and stereoregularity of the copolymerization products.     

Infrared study of phase transitions in thermotropic liquid crystal polyesters

Three samples of semiflexible thermotropic liquid-crystalline polyesters based on mesogenic aromatic triads and a decamethylene spacer have been investigated by IR spectroscopy at various temperatures between room temperature and 290°C. The crystal-to-liquid crystal (either nematic or smectic) phase transition was accompanied by fairly strong spectral variations, whereas slight, but significant, changes in the IR profiles were detected at the liquid crystal-to-isotropic transition. By comparing the results obtained with the spectral behavior recorded for corresponding structural analogs of low molar mass, it was possible to attribute the spectral variations observed in the polymer samples to a decrease in intermolecular interactions rather than to conformational changes. The thermal transitions indicated by IR spectra were in good agreement with the analogous data obtained by calorimetric or optical microscopy techniques.     

Characterization of surface NH3+Cl- groups on poly(styrene-co-Boc-aminostyrene) microspheres obtained by controlled acidic treatment

Different samples of aminated latex of poly(styrene-co-Boc-aminostyrene) microspheres with mean diameters varying from 0.7 to 1.0 microm were prepared by dispersion copolymerization of styrene (ST) and Boc-aminostyrene (Boc-AMST). The copolymer compositions determined by nuclear magnetic resonance (1H NMR) were Boc-AMST/ST 6.9/93.1 mol/mol % (BOC7 sample) and Boc-AMST/ST 31.3/68.7 mol/mol % (BOC30 sample). The average molecular weights determined by gel permeation chromatography were 126 kDa (BOC7 sample) and 51 kDa (BOC30 sample). The latex containing NH-carbo-tert-butoxy groups (NH-Boc) were treated with 2 M HCl in isopropyl alcohol/water (1:1 vol/vol), at 50 degrees C for 3, 6, 9, 24, and 30 h, in order to control the extent of deprotection reaction of the NH-Boc. The deprotection reaction resulted in the formation of NH3+Cl- groups on the particle surfaces. The kinetic of the deprotection reaction was investigated by 1H NMR analyses and the yield varied from 20 to 40%. The resulting -NH3+Cl- groups on the microsphere surfaces were examined, in particular, by electron spectroscopy imaging (ESI) using an energy-filtered transmission electron microscope (EFTEM) that clearly demonstrated the presence of Cl on the particle surfaces. Scanning electron photomicrographs recorded for the above samples showed that the particle morphology was maintained after the acidic treatment.     

On the number of line separations of a finite set in the plane

Let S denote a set of n points in the Euclidean plane. A subset S′ of S is termed a k-set of S if it contains k points and there exists a straight line which has no point of S on it and separates S′ from S?S′. We let f_k(n) denote the maximum number of k-sets which can be realized by a set of n points. This paper studies the asymptotic behaviour of f_k(n) as this function has applications to a number of problems in computational geometry. A lower and an upper bound on f_k(n) is established. Both are nontrivial and improve bounds known before. In particular, $\text{f}{}_{\mathrm{k}}\text{(n) = f}{}_{\mathrm{n?k}}\text{(n) = Ω(n}\text{log}\text{k)}$ is shown by exhibiting special point-sets which realize that many k-sets. In addition, $\text{f}{}_{\mathrm{k}}\text{(n) = f}{}_{\mathrm{n?k}}\text{(n) = O(nk}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$ is proved by the study of a combinatorial problem which is of interest in its own right.     

Vapnik-Chervonenkis dimension and (pseudo-)hyperplane arrangements

An arrangement of oriented pseudohyperplanes in affined-space defines on its setX of pseudohyperplanes a set system (or range space) (X, ℛ), ℛ ⊑ 2 ^x of VC-dimensiond in a natural way: to every cellc in the arrangement assign the subset of pseudohyperplanes havingc on their positive side, and let ℛ be the collection of all these subsets. We investigate and characterize the range spaces corresponding tosimple arrangements of pseudohyperplanes in this way; such range spaces are calledpseudogeometric, and they have the property that the cardinality of ℛ is maximum for the given VC-dimension. In general, such range spaces are calledmaximum, and we show that the number of rangesR∈ℛ for whichX - R∈ℛ also, determines whether a maximum range space is pseudogeometric. Two other characterizations go via a simple duality concept and “small” subspaces. The correspondence to arrangements is obtained indirectly via a new characterization of uniforom oriented matroids: a range space (X, ℛ) naturally corresponds to a uniform oriented matroid of rank |X|—d if and only if its VC-dimension isd,R∈ℛ impliesX - R∈ℛ, and |ℛ| is maximum under these conditions. Part of this work was done while the first author was a member of the Graduiertenkolleg “Algorithmische Diskrete Mathematik,” supported by the Deutsche Forschungsgemeinschaft, Grant We 1265/2-1. Part of this work has been supported by the German-Israeli Foundation for Scientific Research and Development (G.I.F.).     

Oxo-biodegradable polymers - Effect of hydrolysis degree on biodegradation behaviour of poly(vinyl alcohol)

Poly(vinyl alcohol) (PVA) is considered to be one of the very few vinyl polymers soluble in water and susceptible to biodegradation in aqueous media by specific microorganisms, implying oxidation of the carbon backbone followed by a random endocleavage of the polymer chains. The overall process does not appear to be appreciably affected by either degree of polymerization (DPn) or degree of hydrolysis (HD) of PVA at least in the 100-1000 and 80-100% ranges, respectively.In order to assess the effect of HD on the biodegradation propensity of PVA, different PVA samples having similar DPn and noticeably different HD values were synthesized by controlled acetylation of commercial PVA (HD = 99%) and submitted to biodegradation tests in aqueous medium, mature compost and soil by using respirometric procedures. Re-acetylated PVA samples characterized by HD of between 25 and 75% underwent extensive mineralization when buried in solid media, whilst PVA (HD = 99%) showed recalcitrance to biodegradation under those conditions. An opposite trend was indeed observed in aqueous solution, thus suggesting that biodegradation is not an absolute attribute directly related to structural features of the substrate under investigation. Boundary conditions related to the framework under which the biodegradation assessment is undertaken have to be taken into account and specifically well defined.     

Optically active alternating copolymers of maleic acid and alkylvinylethers

Alternating copolymers of maleic acid (MAc) with optically active alkylvinylethers (RVE)[R = (S)-1-methylpropyl, (R)-1-methylbutyl, (S)-2-methylbutyl, (S)-3-methylpentyl, (S)-4-methylhexyl, (S)-1-methylheptyl and (S)-3,7-dimethyloctyl] were obtained by hydrolysis in aqueous alkaline medium of the corresponding copolymers with maleic anhydride (MAn). i.r. Absorption spectra, viscosity and potentiometric titration curves are described as well as u.v., ORD and CD spectra recorded in ethanol and water. Conductometric titrations in non-aqueous medium confirm the alternance of dicarboxylic and ethereal structural units. It is shown that the nature of alkyl substituents strongly affects the ionization process of the first carboxylic group. The u.v. bands connected with the $\text{n → π}{}^1$ electronic transitions of carboxylic chromophores are optically active and the ellipticities of the dichroic bands around 215 nm depend on the position of the asymmetric carbon atoms present in the side chain. Moreover for copolymers with ethereal structural unit containing an asymmetric carbon atom α with respect to the oxygen atom, the rotatory strength of such bands is dependent on the length of the alkyl substituents for measurements carried out in water, whilst no significant dependence is evident in measurements performed in ethanol. No ordered secondary structure is considered to account for these features which are probably due to asymmetric induction phenomena involving optically active side chains.     

Chiral liquid crystalline polymers: Recent issues and perspectives

The syntheses and structures of chiral liquid crystalline polymers (LCPs) are briefly reviewed with emphasis on the established structure-property correlations. The most recent advances and future trends in their potential applications in optics and electrooptics are also outlined, with particular reference to the ferroelectric, electroclinic, piezoelectric, and nonlinear optical properties of chiral LCPs.