Modeling the mechanical properties of highly oriented polymer films: A fiber/gel composite theory approach

Controlling the extent of orientation is of great interest in polymer processing and is effected by the choice of polymer, the fabrication technique and the processing conditions. Understanding the crystalline transitions that form highly oriented fibrils is necessary for modeling the changes in physical properties, relative to degree of orientation. A model is proposed to describe the mechanical properties of drawn semicrystalline polymer films based on structural transitions. With a minimal amount of experimental data (requiring testing on only two drawn films samples), this model can be used to predict film properties. These properties include the critical and maximum draw ratios, the moduli at the maximum draw ratio, the moduli of the fiber, the modulus of the nonfibrous gel relative to draw ratio, the volume fraction of fibers, and the rate of fibrillation. Where high degrees of uniaxial orientation are required, the polymer is typically drawn in the solid state, meaning the polymer is stretched in a single direction at temperatures below the melting point. During this process, pre‐existing crystallites are transformed into fiber‐like structures with large aspect ratios. The presence of these rigid asymmetric structures significantly enhances the moduli and break strength of the polymer. This work presents a model that describes the formation of fiber‐like structures. The volume fraction of fibers is predicted to be linear in draw ratio. The derived relationship between volume fraction of fibers and draw ratio can then be used for the prediction of the various properties of the oriented film. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 607–618, 2008     

Optimal birth control of age-dependent competitive species III. Overtaking problem

A study is made of an overtaking optimal problem for a population system consisting of two competing species, which is controlled by fertilities. The existence of optimal policy is proved and a maximum principle is carefully derived under less restrictive conditions. Weak and strong turnpike properties of optimal trajectories are established.     

DYNAMIC PROPERTIES OF ASSISTANT SOUNDER IN BLACK CICADA (C.atrata FABRICIUS)

The dynamic properties of the assistant sounders in the black cicada are given and the twitching properties of Contraction in the sounding muscle are revealed in this paper.For the operculum, tymbal cover and joint membrane, each of their vibration periods consists of three subgroup vibrations (SGV_(a,b,c)) corresponding to amplitude-modulation pulse trains (AMPT_(1,2,3)) in every syllable of synchro song. In comparison with the vibration at dorsum, the SGV_(a-c) have a subband with the function of regulating the tone. During calling song continuously, the pressure change inside the resonant cavity and the airspeed through the spiracles on both sides are about 7. 94—15.88 Paand 0.59—0.84 cm~3/s respectively, and they increase by about 7 and 2.6 times as the abdomen is moved. When the contraction motion of the sounding muscle comes up to the critical Sounding state, it further produces the twitching process, and drives the sounding membrane and the toning plate-membrane to produce AMPT_(1-3) and SGV_(a     

Hereditarily polaroid operators, SVEP and Weyl's theorem

A Banach space operator T∈B(X) is hereditarily polaroid, T∈HP, if every part of T is polaroid. HP operators have SVEP. It is proved that if T∈B(X) has SVEP and R∈B(X) is a Riesz operator which commutes with T, then T+R satisfies generalized a-Browder's theorem. If, in particular, R is a quasi-nilpotent operator Q, then both T+Q and T^∗+Q^∗ satisfy generalized a-Browder's theorem; furthermore, if Q is injective, then also T+Q satisfies Weyl's theorem. If A∈B(X) is an algebraic operator which commutes with the polynomially HP operator T, then T+N is polaroid and has SVEP, f(T+N) satisfies generalized Weyl's theorem for every function f which is analytic on a neighbourhood of σ(T+N), and f^∗(T+N) satisfies generalized a-Weyl's theorem for every function f which is analytic on, and constant on no component of, a neighbourhood of σ(T+N).     

Characterization of a Marshall-Olkin type class of distributions

Summary A class of bivariate distributions that generalize Marshall-Olkin's one is characterized through a functional equation which involves two associative operations. The obtained distributions concentrate positive mass on the linex=y when the two associative operations coincide; otherwise a positive mass is concentrated on a continuous monotone function. Work performed while the authors were members of CNR-GNAFA.     

基于模糊值Choquet积分定义集函数的S性与PGP性

针对模糊测度空间上已建立的模糊值Choquet积分,将这种积分整体看成可测空间上取值于模糊数的集函数,当模糊测度满足一般S性和PGP性时,研究了这种模糊值集函数所保持的遗传性质.     

Normal coderivative for multifunctions and implicit function theorems

In the framework of the theory of normal coderivative for multifunctions, new implicit function theorems are obtained. The main tools of the proofs are the Ekeland variational principle, a nonsmooth version of Fermat's rule, a sum rule, and the differential estimate for marginal functions established by B.S. Mordukhovich and Y. Shao [B.S. Mordukhovich, Y. Shao, Nonsmooth sequential analysis in Asplund spaces, Trans. Amer. Math. Soc. 348 (1996) 1235-1280].     

Physicomechanical studies on the langmuir‐blodgett films of polythiophene containing mesogenic side chains

Liquid crystalline materials display unique properties, which can be exploited in various optoelectronic device applications. The Langmuir‐Blodgett (LB) film characteristics of polythiophene model compounds containing phenyl rings linked with azomethine, ester, and alkoxy functional groups poly‐4‐{[(E)‐thiophen‐3‐ylmethylidene]amino}phenyl 4‐alkyloxybenzoate (PTAPAB series) and poly‐4‐alkyloxy phenyl 4‐{[(E)‐thiophen‐3‐ylmethylidene]amino}benzoate (PAPTAB Series) were explored in this study. The AM1 optimized geometries of the aforementioned compounds showed that the films have different type of orientation in space because of the change in the linking functional group. The LB film characteristics were studied by applying the concepts of the failure mechanism in tensile failure. The compression‐expansion hysteresis cycle of the LB films at predetermined area per repeat unit was used to study the viscous, elastic, and plastic nature of the films. The results showed that in PAPTAB series compounds, the LB films were more flexible and took less surface energy than its PTAPAB series homologues, which formed into LB films of rigid nature. The LB films of PAPTAB series compounds were of more viscoplastic in nature. The studies suggested that PAPTAB series structures exhibited good thin film forming nature than its PTAPAB series homologues. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 173–182, 2009     

Synthesis and characterization of a series of diverse poly(2‐oxazoline)s

This article describes the synthesis and characterization of a variety of new poly(2‐oxazoline)s. With regard to functional polymers, 2‐oxazolines represent an interesting class of monomers because of the easy variation of the substituent in 2‐position. Starting from the corresponding nitriles, different 2‐oxazolines were obtained containing a diverse set of 2‐substituents, including thioether bonds ( M11 ), trifluoromethyl groups ( M8 , M10 ), and alkyl‐ or aryl groups ( M1 – M7 ). The subsequent polymerization of the majority of these monomers proceeded in a living manner, which was demonstrated by linear first‐order kinetics, a linear increase of molar mass with conversion, and relatively narrow molar mass distributions. In addition, selected thermal and surface properties of the polymers were studied utilizing DSC and contact‐angle measurements to determine the effects of different 2‐substituents on the macroscopic properties. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 3829–3838, 2009     

Thermal behavior of aromatic polyamic acids and polyimides containing oxadiazole rings

Two aromatic polyimides and the corresponding poly(amic acid)s, with oxadiazole and para/meta phenoxyphenylene rings in the backbone, were synthesized and the structure — thermal properties correlation was followed by dynamic mechanical analysis. Concerning the poly(amic acid)s, the glass transition domain was emphasized only for the compound with meta-oriented rings because the process of imidization takes place with increasing temperature. A multiplex experiment was performed to calculate the activation energy of the transition localized under 200°C. Consecutive heating-cooling-heating cycles were accomplished. All phenomena are discussed by cross-examination of the storage modulus (E′), loss modulus (E″) and loss factor tanδ variation with temperature.