Miscibility of polycarbonates with copolymers containing cyclohexylmethacrylate

We prepared various copolymers containing styrene and methacrylates to examine their miscibility with polycarbonates such as bisphenol A polycarbonate (PC), dimethylpolycarbonate (DMPC), and tetramethylpolycarbonate (TMPC). Among the various copolymers examined, poly(methyl methacrylate‐co‐cyclohexylmethacrylate) [P(MMA–CHMA)] copolymers containing proper amounts of cyclohexylmethacrylate (CHMA) formed miscible blends with PC and DMPC, whereas TMPC did not form a miscible blend with P(MMA–CHMA). However, TMPC was miscible with poly(styrene‐co‐cyclohexylmethacrylate) [P(S–CHMA)] copolymers containing less than about 40 wt % CHMA, whereas PC and DMPC were always immiscible with P(S–CHMA). Miscible blends exhibited lower critical solution temperature (LCST)‐type phase behavior. Binary interaction energies were calculated from the observed phase boundaries with lattice–fluid theory combined with a binary interaction model. The quantitative interaction energy of each binary pair indicated that the phenyl ring substitution of polycarbonate with methyl groups did not lead to interactions that were favorable for miscibility with methyl methacrylate (MMA) and CHMA, but it did lead to favorable interactions with styrene. The addition of CHMA to MMA initially increased the LCST but ultimately led to immiscibility with PC and DMPC; however, addition of CHMA to styrene always decreased the LCST with TMPC. The increased LCST of PC or DMPC blends stemmed from intramolecular repulsion between MMA and CHMA, whereas the decreased LCST of TMPC/P(S–CHMA) blends with CHMA content came from negative interaction energy between styrene and CHMA. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1948–1955, 2001     

Non-steady state solidification of the Nd-123 superconducting oxides

Crystal growth of the melt-textured bulk Nd_1+xBa_2−xCu₃O_6+d (Nd123) superconducting oxides was investigated by employing isothermal undercooling solidification with hot-seeding in air. From the relationship between growth length and holding time, the Nd123 crystal was found to have almost stopped growing after a certain growth period, while the growth length increased proportionally to the holding time at an early stage of the crystal growth. As a result of quantitative analysis for the Nd123 crystal of which solidification was terminated, the distribution of the Nd/Ba substitution was observed to decrease in the Nd123 single crystal matrix from the seed crystal to the edge of the Nd123 crystals. Also, the substitution content at the edge of the Nd123 crystal, which corresponds to that at the final stage of the crystal growth, was found to be in good agreement with the minimum substitution of the Nd123 solid solution phase in the equilibrium phase diagram at this process temperature. These compositional changes could be explained using the equilibrium phase diagram as associated with the solid solution formation, which is responsible for the non-steady state solidification of the Nd123 crystals even for the isothermal undercooling processing.     

Non-existence of stationary two-black-hole configurations

We resume former discussions of the question, whether the spin–spin repulsion and the gravitational attraction of two aligned black holes can balance each other. To answer the question we formulate a boundary value problem for two separate (Killing-) horizons and apply the inverse (scattering) method to solve it. Making use of results of Manko, Ruiz and Sanabria-Gómez and a novel black hole criterion, we prove the non-existence of the equilibrium situation in question.     

Effect of aromatic substitution on phase behavior of blends of halogenated polystyrene and conventional polystyrene

Miscibility phase behavior in blends of poly(bromostyrene) with polystyrene (PS) has been investigated by means of time‐resolved light scattering, optical microscopy, and DSC. Cloud point phase diagrams of blends of conventional PS with poly‐(2‐bromostyrene) (P2BrS), poly‐(3‐bromostyrene), and poly‐(4‐bromostyrene) of comparable molecular weights were established by light scattering. Of particular interest is the fact that ortho, meta, and para substitutions in the styrenic aromatic rings of poly(bromostyrene) show profound effects on the composition–temperature phase diagrams of their blends with PS, exhibiting a lower critical‐solution temperature (LCST), an upper critical solution temperature (UCST), and combined LCST/UCST diagrams, respectively. Poly‐(2‐chlorostyrene) exhibits an LCST behavior very close to that of the P2BrS blend, suggesting that these types of halogen atoms may be inconsequential to phase behavior. A similar study has been extended to a PS blend containing commercial brominated PS (66 mol % bromine substitution) to determine what location of bromine substitution is crucial for miscibility enhancement in the flame‐retardant brominated PS blends. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1605–1615, 2001     

A PRIORI ESTIMATE FOR LOWER SOLUTIONS OF ACLASS QUASILINEAR ELLIPTIC EQUATIONS

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Effect of hemp surface modification on the morphological and tensile properties of linear medium density polyethylene (LMDPE) composites

This work investigates different hemp surface modifications (mercerization, maleated polyethylene (MAPE) addition in solution or in melt blending) to improve the properties of linear medium density polyethylene (LMDPE). From the composites produced, a complete morphological and tensile characterization was performed for a fixed hemp content (30% wt.). The morphological analysis showed that both the direct (melt blending) and solution modifications were able to significantly improve the composites interface quality and therefore the tensile properties (151% increase in modulus and 36% increase in strength over the neat matrix) within the range of conditions tested.     

Weighted averaged equations for modeling velocity profiles of 1D steady open channel flows

A new mathematical algorithm is proposed to address the essential details of vertical distributions of horizontal velocity for one‐dimensional steady open‐channel flow. This new algorithm comprises a system of weighted averaged equations developed from corresponding Reynolds equations by performing weighted average operations instead of conventional depth average operations. It is the system of weighted averaged equations, instead of the vertical grids, that allows for more hydraulic coefficients identifiable. It can be thought of as an extension of the St. Venant equations to address the vertical distributions of horizontal velocities, as well as the water surface profiles. To avoid the difficult expansion of governing partial differential equations in high order, an indirect scheme is proposed to solve hydraulic variables through their weighted average values. The governing partial differential equations are generated by using a variety of weight functions, and the weighted averages of relevant hydraulic variables are taken as the unknown independent variables to be solved first. Then, on the basis of the values and polynomial expansions of these weighted averaged velocities, a system of linear algebraic equations is generated and the unknown hydraulic variables or their coefficients are easily solved. Note that the new model is not proposed to compete with any three‐dimensional models in modeling accuracy or accommodation ability to all conditions. It just provides a valuable option to study the vertical structure of flow in open channels where only essential detail and reasonable accuracy of vertical distributions are required, and the data availability and other conditions limit the application of fully three‐dimensional models. The performance of the model is evaluated with experimental data of flows in two different flumes. It is shown that the model well predicted the velocity profiles of sections along the centerlines of these flumes with reasonable accuracy and essential details of vertical distributions of horizontal velocity. Copyright © 2013 John Wiley & Sons, Ltd.     

时间测度上具有时滞基于半比率的捕食者-食饵扩散系统的周期解

在时间测度上研究一类具有时滞和基于半比率且有功能性反应的两种群捕食者-食饵扩散系统,利用Mawhin重合度理论建立了这类系统的周期解存在的一个充分性判据.从而使这一类系统的连续与离散情形即相应的微分方程和差分方程的周期解存在性问题得到了统一研究.     

Vacuum condensates of QCD

We study the properties of QCD vacuum state in this paper. The values of various local quark vacuum condensates, quark-gluon mixed vacuum condensates, and the structure of non-local quark vacuum condensate are predicted by the solution of Dyson-Schwinger Equations in "rainbow" approximation with three sets of different parameters for effective gluon propagator. The light quark virtuality is also obtained in a consistent way. Our all theoretical results here are in good agreement with the empirical values used widely in literature and many other theoretical calculations.     

Fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays

The fixed-point theory is first used to consider the stability for stochastic partial differential equations with delays. Some conditions for the exponential stability in pth mean as well as in sample path of mild solutions are given. These conditions do not require the monotone decreasing behavior of the delays, which is necessary in [T. Caraballo, K. Liu, Exponential stability of mild solutions of stochastic partial differential equations with delays, Stoch. Anal. Appl. 17 (1999) 743-763; Ruhollan Jahanipur, Stability of stochastic delay evolution equations with monotone nonlinearity, Stoch. Anal. Appl. 21 (2003) 161-181]. Even in this special case, our results also improve the results in [T. Caraballo, K. Liu, Exponential stability of mild solutions of stochastic partial differential equations with delays, Stoch. Anal. Appl. 17 (1999) 743-763].