Self-avoiding walks and trees in spread-out lattices

LetG _R be the graph obtained by joining all sites ofZ ^d which are separated by a distance of at mostR. Let (G _R ) denote the connective constant for counting the self-avoiding walks in this graph. Let (G _R ) denote the coprresponding constant for counting the trees embedded inG _R . Then asR, (G _R ) is asymptotic to the coordination numberk _R ofG _R , while (G _R ) is asymptotic toek _R. However, ifd is 1 or 2, then (G _R )-k _R diverges to –.Dedicated to Oliver Penrose on this occasion of his 65th birthday.     

Nonuniversality and analytical continuation in moments of directed polymers on hierarchical lattices

We prove the moments of the directed polymer partition function GZ, using an exact position space renormalization group scheme on a hierarchical lattice. After sufficient iteration the characteristic functionf(n)=lnGZⁿ of the probability (Z) converges to a stable limitf ^*(n). For smalln the limiting behavior is independent of the initial distribution, while for largen,f ^*(n) is completely determined by it and is thus nonuniversal. There is a smooth crossover between the two regimes for small effective dimensions, and the nonlinear behavior of the small moments can be used to extract information on the universal scaling properties of the distribution. For large effective dimensions there is a sharp transition between the two regimes, and analytical continuation from integer moments ton0 is not possible. Replica arguments can account for most features of the observed results.     

Through-space delocalized water-soluble paracyclophane bichromophores: new fluorescent optical reporters

Conjugated polymers and oligomers can serve as highly responsive fluorescent reporters for biosensor applications. However, their optical properties in aqueous media are highly dependent upon environmental conditions. The structure of the paracyclophane framework provides a platform for designing optical reporters that show little sensitivity to surfactants, and thus is well-suited for fluorescent assays. The permanent intramolecular delocalization through the paracyclophane core dominates intermolecular perturbations in spontaneously formed aggregates.     

Viscosity of mixtures of polymers and microemulsions — the Huggins interaction coefficient

Microemulsions used in enhanced oil recovery are usually used in conjunction with a polymer solution that provides mobility control by reducing the permeability of the formation and/or increasing the viscosity of the injected fluid. Microemulsions, which are mixtures of at least four components — water, oil, surfactant and cosurfactant (and, usually, inorganic salts) are complex even in the absence of polymer and consequently, studies of their phenomenon tend to be phenomenological. An approach found to be useful to circumvent this has been to consider the microemulsion particles dispersed in their external phase to be macromolecules which retain their integrity when diluted with external phase or when mixed with polymers. Thus the dispersed phase components are treated as a pseudocomponent. If this approach is followed, many features of the phase diagram of polymer-microemulsion mixtures can be rationalized. It is therefore of some interest to determine whether a similar approach can be used to understand or predict the viscosity of mixtures in which a simple mixing rule for viscosities can be utilized to gain further insight into the polymer-microemulsion interaction.     

Synthesis,Liquid‐Crystalline Properties,and Supramolecular Nanostructures of Dendronized Poly(isocyanide)s and Their Precursors

A series of novel dendronized π‐conjugated poly(isocyanide)s were synthesized successfully by using a Pd? Pt μ‐ethynediyl dinuclear complex ([ClPt{P(C₂H₅)₃}₂C?CPt{P(C₂H₅)₃}₂Cl]) as the initiator. The polymerizations of the dendronized monomers follow first‐order kinetics, indicating that living polymerization takes place. The obtained polymers exhibit narrow polydispersities in the range of 1.03–1.20. Thermal properties of the poly(isocyanide)s as well as their isocyanide monomers and precursors with formamido (HCONH‐) moieties as apexes were investigated by using differential scanning calorimetry (DSC), polarized optical microscopy (POM) and wide‐angle X‐ray diffraction (WAXD). Both the peripheries and the apex groups of the dendrons affect the formation of supramolecular column and/or cubic phases of the precursors and monomers. The formamido precursor forms a liquid‐crystalline phase due to intermolecular hydrogen bonding. The isocyanide monomer lacks this hydrogen‐bonding ability and does not display an organized mesophase. All of the rigid poly(isocyanide)s with the monodendrons exhibit columnar liquid‐crystalline phases. Interestingly, cylindrical structures of a poly(isocyanide) were directly visualized by using transmission electron microscopy (TEM).     

A new class of aromatic polyetheraroylhydrazides. I. Synthesis and chemical–physical characterization

A series of new aromatic polyetheraroylhydrazides incorporating 4-oxybenzoyl units has been synthesized, whose general formula was [CONHNHCO? O? O–(CH₂)_x? O? phenyl O-CONHNHCOO]_n with x values in the range of 2 to 12. The increasing number of methylene units in the backbone gave rise to polymers which melted before the hydrazidic linkage underwent thermal cyclation to oxadiazole. Moreover, many polymers showed multiple endotherms on melting. X-ray diffraction studies confirmed a crystalline organization of polyhydrazides for methylene units above 4. © 1993 John Wiley & Sons, Inc.     

Synthesis and characterization of new epoxy and cyanate ester resins

New epoxide and cyanate ester resins with an aromatic ester backbone namely 1,3-[di-(4-glycidyloxy diphenyl-2,2^′-propane)]-isophthalate (DGDPI) and 1,4-[di-(4-cyanato diphenyl-2,2^′-propane)]-terephthalate (DCDPT) were synthesized and the intermediates were characterized by IR, 1H-/¹³C-NMR spectroscopic methods. The cured products from DGDPI and DHDPI exhibited higher T_g compared with standard epoxy system. The increase in the T_g may be due to the cyanate ester and rigid aromatic backbones present in the curing system.     

Ascorbic Acid Oxidation at Nonmodified and Copper‐Modified Polyaniline and Poly‐ortho‐methoxyaniline Coated Electrodes

The electrochemical oxidation of ascorbate ions is comparatively studied at polyaniline (PANI) and poly‐ortho‐methoxyaniline (POMA) layers in absence and presence of electrodeposited copper species. In comparison to PANI, POMA layers allow decreasing the overpotential necessary for driving the ascorbate oxidation reaction. A nonlinear dependence of the ascorbate oxidation current on the polymer layer redox charge is found. Copper electrodeposited in PANI and POMA layers is electrocatalytically active for the investigated reaction. Two separate oxidation waves are observed in the case of Cu‐PANI whereas a single ascorbate oxidation wave and enhanced currents are found in the Cu‐POMA case.     

The phases of polymers as determined by NMR

Nuclear magnetic resonance (NMR) spectroscopy has been used to study the morphology and dynamics in semicrystalline polymers. Dynamics may be observed through NMR relaxation rates that are sensitive to motions in the 1–10⁸ Hz range, or through modulation of anisotropic magnetic interactions, such as the chemical shift and dipole-dipole interactions. Morphological structure may be inferred through NMR measurements of polymer dynamics or investigated directly through studies of the magnetic interactions. Here, we discuss the study of morphological structure in semicrystalline polymers using NMR, and review results on poly(ethylene terephthalate) that address the question of the number of phases in this semicrystalline polymer.This work was funded by the Office of Naval Research.