L p -dual Quermassintegral sums

In this paper, we first introduce a concept of L _p -dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar projection Aleksandrov-Fenchel inequality for L _p -dual Quermassintegral sums. Moreover, by using Lutwak’s width-integral of index i, we establish the L _p -Brunn-Minkowski inequality for the polar mixed projection bodies. As applications, we prove some interrelated results. This work was partially supported by the National Natural Science Foundation of China (Grant No. 10271071), Zhejiang Provincial Natural Science Foundation of China (Grant No. Y605065) and Foundation of the Education Department of Zhejiang Province of China (Grant No. 20050392)     

Gas solubility of carbon dioxide in poly(lactic acid) at high pressures: Thermal treatment effect

The sorption of carbon dioxide in glassy Poly(lactic acid) (PLA) films was studied by quartz crystal microbalance (QCM) at high pressures. Two thermal treatments, melted and quenched, were performed in PLA with two different L:D contents, 80:20 and 98:2, films and compared with a third thermal protocol, annealed, and used in a previous work. The results obtained show that for pressures higher than 2 MPa, the carbon dioxide solubility is larger in PLA 80:20 than in PLA 98:2, indicating that the L:D plays a dominant role on this property. The thermal treatments only affect the gas solubility in PLA 98:2. Sorption isotherms at temperatures 303, 313, and 323 K, below the glass transition temperature of the polymer, and pressures up to 5 MPa were measured and analyzed with three different models, the dual‐mode sorption model, the Flory–Huggins equation, and a modified dual‐mode sorption model where the Henry's law term was substituted by the Flory–Huggins equation. This last model performs especially well for CO₂ in PLA 80:20, due to the convex upward curvature of the solubility isotherms for that system. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 616–625, 2007     

BF3-doped polyaniline: A novel conducting polymer

We review the unusual structural, transport and magnetic properties of highly conducting polyaniline, doped with boron trifluoride. Our studies establish the unique conducting state of this system, which is in distinct contrast with the conventional proton-doped polyaniline samples.     

Viscometric properties of dilute polystyrene/dioctyl phthalate solutions

We report viscometric data collected in a Couette rheometry on dilute, single‐solvent polystyrene (PS)/dioctyl phthalate (DOP) solutions over a variety of polymer molecular weights (5.5 × 10⁵ ≤ M_w ≤ 3.0 × 10⁶ Da) and system temperatures (288 K ≤ T ≤ 318 K). In view of the essential viscometric features, the current data may be classified into three categories: The first concerns all the investigated solutions at low shear rates, where the solution properties are found to agree excellently with the Zimm model predictions. The second includes all sample solutions, except for high‐molecular‐weight PS samples (M_w ≥ 2.0 × 10⁶ Da), where excellent time–temperature superposition is observed for the steady‐state polymer viscosity at constant polymer molecular weights. No similar superposition applies at a constant temperature but varied polymer molecular weights, however. The third appears to be characteristic of dilute high‐molecular‐weight polymer solutions, for which the effects of temperature on the viscosity curve are further complicated at high shear rates. The implications concerning the relative importance of hydrodynamic interactions, segmental interactions, and chain extensibility with increasing polymer molecular weight, system temperature, and shear rate are discussed. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 787–794, 2006     

Elastic and Thermophysical Properties of Poly(Vinyl Chloride) and Chlorinated Polyethylene Blends

The results of experimental and theoretical investigations of elastic and thermophysical properties of poly(vinyl chloride) (PVC) and chlorinated polyethylene (CPE) blends are presented. Eight types of specimens with different ratios of weight contents of PVC and CPE (PVC/CPE = 100/0, 90/10, 80/20, 60/40, 40/60, 20/80, 10/90, and 0/100) were tested. The effect of blend composition on the elastic constants (tensile and shear modulus) is discussed. The data on the thermal conductivity, thermal diffusivity, and heat capacity of the blends investigated are also presented.     

Approximation of Matrices and a Family of Gander Methods for Polar Decomposition

Two matrix approximation problems are considered: approximation of a rectangular complex matrix by subunitary matrices with respect to unitarily invariant norms and a minimal rank approximation with respect to the spectral norm. A characterization of a subunitary approximant of a square matrix with respect to the Schatten norms, given by Maher, is extended to the case of rectangular matrices and arbitrary unitarily invariant norms. Iterative methods, based on the family of Gander methods and on Higham’s scaled method for polar decomposition of a matrix, are proposed for computing subunitary and minimal rank approximants. Properties of Gander methods are investigated in details. AMS subject classification (2000) 65F30, 15A18     

Chain length effect on dynamical structure of poly (vinyl pyrrolidone)-polar solvent mixtures in dilute solution of dioxane studied by microwave dielectric relaxation measurement

Dielectric relaxation study of the binary mixtures of poly(vinyl pyrrolidone) (PVP) (Mw=24000, 40000 and 360000 g mol⁻¹) with ethyl alcohol (EA) and poly(ethylene glycol)s (PEGs) (Mw=200 and 400 g mol⁻¹) in dilute solutions of dioxane were carried out at 10.1 GHz and 35°C. The relaxation time of PVP-EA mixtures was interpreted by the consideration of a wait-and-switch model in the local structure of self-associated ethyl alcohol molecules and also the PVP chain length as a geometric constraint for the reorientational motion of ethyl alcohol molecules. The formation of complexes and effect of PVP chain length on the molecular dynamics, chain flexibility and stretching of PEG molecules in PVP-PEG mixtures were explored from the comparative values of dielectric relaxation time. Further, relaxation time values in dioxane and benzene solvent confirm the viscosity independent molecular dynamics in PVP-EA mixtures but the values vary significantly with the non-polar solvent environment.     

Rheology of a mixture of liquid-crystal polymers in solution

The rheological behavior of a mixture of two liquid-crystal polymers, hydroxypropyl cellulose and ethyl cellulose, in acetone solution is studied. The total polymer concentration in the solvent is held constant (40%) as the ratio of the two polymers is varied. The mixtures are anisotropic, isotropic, or biphasic (isotropic/anisotropic), depending on the concentration. Curves of viscosity vs shear rate for all the mixtures studied show three regions of viscosity, as described by Onogi and Asada for liquid-crystal polymers. The viscosity as a function of the weight ratio of the two polymers at constant shear rate exhibits deviations from additivity of viscosities of the two components at all concentrations. In mixtures of two polymers in the melt, deviations are also observed; the negative ones are attributed to phase separation and the positive ones to homogenous mixing (comparison with the phase diagram). All the mixtures studied (anisotropic, isotropic, or biphasic), show ranges of shear rates where the first normal-stress difference is negative, as is generally observed for anisotropic liquid-crystal polymers. It is concluded that the isotropic solutions become anisotropic under shear, as they are not far from the critical concentration. © 1994 John Wiley & Sons, Inc.     

Synthesis and characterization of liquid crystalline side‐chain block copolymers containing luminescent 4,4′‐bis(biphenyl)fluorene pendants

A series of new liquid crystalline homopolymers, copolymers, and block copolymers were polymerized from styrene‐macroinitiator ( SMi ) and methacrylates with pendent 4,4′‐bis(biphenyl)fluorene ( M1 ) and biphenyl‐4‐ylfluorene ( M2 ) groups through atom transfer radical polymerization (ATRP). The number‐average molecular weights (Mn) of polymers P1 ‐ P4 were 10,007, 14,852, 6,275, and 10,463 g mol^?1 with polydispersity indices values of 1.21, 1.15, 1.31, and 1.22, respectively. All polymers exhibit the nematic phase. The thermal, mesogenic, and photoluminescent properties of all polymers were investigated. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4564–4572, 2007