Thermal and mechanical properties of a dendritic hydroxyl‐functional hyperbranched polymer and tetrafunctional epoxy resin blends

Blends of a tetrafunctional epoxy resin, tetraglycidyl‐4,4′‐diaminodiphenylmethane (TGDDM), and a hydroxyl‐functionalized hyperbranched polymer (HBP), aliphatic hyperbranched polyester Boltorn H40, were prepared using 3,3′‐diaminodiphenyl sulfone (DDS) as curing agent. The phase behavior and morphology of the DDS‐cured epoxy/HBP blends with HBP content up to 30 phr were investigated by differential scanning calorimetry (DSC), dynamic mechanical analysis (DMA), and scanning electron microscopy (SEM). The phase behavior and morphology of the DDS‐cured epoxy/HBP blends were observed to be dependent on the blend composition. Blends with HBP content from 10 to 30 phr, show a particulate morphology where discrete HBP‐rich particles are dispersed in the continuous cured epoxy‐rich matrix. The cured blends with 15 and 20 phr exhibit a bimodal particle size distribution whereas the cured blend with 30 phr HBP demonstrates a monomodal particle size distribution. Mechanical measurements show that at a concentration range of 0–30 phr addition, the HBP is able to almost double the fracture toughness of the unmodified TGDDM epoxy resin. FTIR displays the formation of hydrogen bonding between the epoxy network and the HBP modifier. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 417–424, 2010     

Identifying the primitive path mesh in entangled polymer liquids

Similar to entangled ropes, polymer chains cannot slide through each other. These topological constraints, the so-called entanglements, dominate the viscoelastic behavior of high-molecular-weight polymeric liquids. Tube models of polymer dynamics and rheology are based on the idea that entanglements confine a chain to small fluctuations around a primitive path which follows the coarse-grained chain contour. To establish the microscopic foundation for these highly successful phenomenological models, we have recently introduced a method for identifying the primitive path mesh that characterizes the microscopic topological state of computer-generated conformations of long-chain polymer melts and solutions. Here we give a more detailed account of the algorithm and discuss several key aspects of the analysis that are pertinent for its successful use in analyzing the topology of the polymer configurations. We also present a slight modification of the algorithm that preserves the previously neglected self-entanglements and allows us to distinguish between local self-knots and entanglements between distant sections of the same chain. Our results indicate that the latter make a negligible contribution to the tube and that the contour length between local self-knots, N_lk is significantly larger than the entanglement length N_e. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 917–933, 2005     

-symmetry for (r,s)-hypergeometric series

Contiguous operators for a two-parameter analogue of hypergeometric series are constructed. These represent a two-parameter quantum enveloping algebra introduced by Takeuchi.     

Polyisophthalamides with heteroaromatic pendent rings: Synthesis,physical properties,and water uptake

A set of novel aromatic polyamides containing pyridine pendent groups was prepared from aromatic diamines and new monomers that are 5‐substituted derivatives of isophthalic acid bearing nicotinamide, isonicotinamide, or picolinamide groups. The polymers were obtained in high yield and high molecular weight by the phosphorylation method of polycondensation. They were characterized by spectroscopic and chromatographic methods and several of their properties were investigated. All of the polymers were soluble in polar aprotic solvents and gave films of good mechanical properties. Glass transition temperatures were higher than that of the reference polymer, poly(m‐phenyleneisophthalamide) (IP‐MPD), while the thermal resistance, defined by the initial decomposition temperature observed by thermogravimetry, was in the range 370–420 °C, lower by 30–70 °C than that of IP‐MPD. The presence of a pendent pyridine group and an additional amide side group per repeat unit made the polymers essentially amorphous and greatly improved their abilities to absorb water in comparison with nonsubstituted polyamides. Water uptake values up to 15% were observed at 65% relative humidity. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5300–5311, 2005     

A congruence for the Fourier coefficients of a modular form and its application to quadratic forms

Let F(z)=∑ _n=1^∞ A(n)q ⁿ denote the unique weight 6 normalized cuspidal eigenform on Γ₀(4). We prove that A(p)≡0,2,−1(mod 11) when p≠11 is a prime. We then use this congruence to give an application to the number of representations of an integer by quadratic form of level 4.      

Weierstrass points on X 0(p ℓ) and arithmetic properties of Fourier coefficients of cusp forms

Generally it is unknown, whether or not ∞ is a Weierstrass point on the modular curve X ₀(N) if N is squarefree. A classical result of Atkin and Ogg states that ∞ is not a Weierstrass point on X ₀(N), if N=pM with p prime, p ∤ M and the genus of X ₀(M) zero. We use results of Kohnen and Weissauer to show that there is a connection between this question and the p-adic valuation of cusp forms under the Atkin–Lehner involution. This gives, in a sense, a generalization of Ogg’s Theorem in some cases.      

Isomer‐dependent properties of poly(vinyl pyridine)‐based films grown on copper surfaces

The effect of poly(2‐vinyl pyridine) (P2VP) and poly(4‐vinyl pyridine) (P4VP) isomers on the growth of surface films on copper substrates was studied by electrochemical, spectroscopic, thermogravimentric, and microscopic methods. In acid environment (3% v/v acetic acid) and in the presence of KSCN, electrochemically generated copper cations reacted rapidly with SCN^? and P2VP or P4VP, yielding coordination compounds, which deposited onto copper surfaces as films. The characteristics of such polymer–metal complexes (films) were markedly isomer‐dependent. Cu(I)/P2VP/SCN^? complexes with monovalent cations and sulfur‐coordinated thiocyanate were obtained in the presence of P2VP, whereas the formation of Cu(II)/P4VP/SCN^? complexes with divalent cations and nitrogen‐coordinated thiocyanate was observed in the presence of P4VP. Interestingly, similar physical–chemical properties (electronic structure, stoichiometry, and thermal behavior) were observed for materials synthesized by electrochemical and chemical methods. These results suggest, therefore, that control over the surface properties of copper substrates can be achieved using electrosynthesized films based on different PVP isomers. Besides acting as effective protective barriers against aggressive media and thus reducing the metal dissolution (corrosion) kinetics, these materials are potentially attractive for other applications in which surface properties are paramount, such as in catalysis. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 215–225, 2009     

A new matrix inverse

We compute the inverse of a specific infinite-dimensional matrix, thus unifying a number of previous matrix inversions. Our inversion theorem is applied to derive a number of summation formulas of hypergeometric type.

     

Fluorinated comblike homopolymers: The effect of spacer lengths on surface properties

A series of polyacrylate monomers with F‐alkylalkyl [F(CF₂)_n(CH₂)_n′] side groups were prepared by free‐radical polymerization. The effect of the chemical structure on the surface properties of poly(ethylene terephthalate)s was evaluated by variations in the relative length of the fluorocarbon and hydrocarbon units in the side group. The resulting polymers were quite surface‐active in the solid state. The surface and bulk organization was investigated by X‐ray photoelectron spectroscopy analysis. A strong correlation between the bulk organization and surface properties of the polymers was established. The outmost layer, formed from trifluoromethyl groups and some ester functions, suggests that the side chain is arranged irregularly in the polymer–air interface. The length of the lateral chain governs this organization: long fluorinated chains and short hydrocarbon spacers are essential elements of the molecular design for such low‐surface‐energy materials. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3737–3747, 2005