Periodic solutions of a second order forced sublinear differential equation with delay

In this paper, existence criteria are established for the existence of periodic solutions of a second order sublinear differential equation with delay and forcing function. Our method is based on careful a priori estimation and continuation theorems, and our sublinear condition is an improvement of the boundedness condition in some recent results.     

Preparation of well-aligned carbon nanotubes by pyrolysis of phenolic resin in anodic alumina pores

Well-aligned carbon nanotubes (CNTs) of high quality were synthesized by pyrolysis of phenolic resin at 800 °C in anodic alumina oxide (AAO) pores under argon protection. The innocuous source materials and safe operational conditions permit this method to synthesize well-aligned CNTs in large-scale and low cost. The formation mechanism of the synthesized CNTs is also proposed in this work by a series of visual sketches and is proved with obvious evidence. Firstly, phenolic resin nanotubes form in the template pores through the evaporation of solvent. Heat treatment then transfers these tubes into CNTs.     

BOUNDEDNESS OF VECTOR-VALUED CALDERN-ZYGMUND OPERATORS ON HERZ SPACES WITH NON-DOUBLING MEASURES

In the paper we obtain vector-valued inequalities for Calder6n-Zygmund operator, simply CZO on Herz space and weak Herz space. In particular.we obtain vector-valued inequalities for CZO on Lq(Rd, |x|αdμ) space, with 1< q <∞, -n <α< n(q -1), and on L1,∞(Rd,|x|αdμ) space, with -n <α< 0.     

Melt rheology of polylactide/montmorillonite nanocomposites

In this article, the linear and nonlinear shear rheological behaviors of polylactide (PLA)/clay (organophilic‐montmorillonite) nanocomposites (PLACNs) were investigated by an Advanced Rheology Expanded System rheometer. The nanocomposites were prepared by master batch method using a twin‐screw extruder with poly(ε‐caprolactone) (PCL) as a compatibilizer. The presence of org‐MMT leads to obvious pseudo‐solid‐like behaviors of nanocomposite melts. The behaviors caused by the formation of a “percolating network” derived from the reciprocity among the strong related sheet particles. Therefore, the storage moduli, loss moduli, and dynamic viscosities of PLACNs show a monotonic increase with MMT content. Nonterminal behaviors exists in PLACNs nanocomposites. Besides the PLACNs melts show a greater shear thinning tendency than pure PLA melt because of the preferential orientation of the MMT layers. Therefore, PLACNs have higher moduli but better processibility compared with pure PLA. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3189–3196, 2007     

Formation of β‐iPP in isotactic polypropylene/ethylene–propylene rubber blends: Effects of preparation method,composition, and thermal condition

The effects of preparation method, composition, and thermal condition on formation of β‐iPP in isotactic polypropylene/ethylene–propylene rubber (iPP/EPR) blends were studied using modulated differential scanning calorimeter (MDSC), wide angle X‐ray diffraction (WAXD), and phase contrast microscopy (PCM). It was found that the α‐iPP and β‐iPP can simultaneity form in the melt‐blended samples, whereas only α‐iPP exists in the solution‐blended samples. The results show that the formation of β‐iPP in the melt‐blended samples is related to the crystallization temperature and the β‐iPP generally diminishes and finally vanishes when the crystallization temperature moves far from 125 °C. The phenomena that the lower critical temperature of β‐iPP in iPP/EPR obviously increases to 114 °C and the upper critical temperature decreases to 134 °C indicate the narrowing of temperature interval, facilitating the formation of β‐iPP in iPP/EPR. Furthermore, it was found that the amount of β‐iPP in melt‐blended iPP/EPR samples is dependent on the composition and the maximum amount of β‐iPP formed when the composition of iPP/EPR blends is 85:15 in weight. The results through examining the effect of annealing for iPP/EPR samples at melt state indicate that this annealing may eliminate the susceptibility to β‐crystallization of iPP. However, only α‐iPP can be observed in solution‐blended samples subjected to annealing for different time. The PCM images demonstrate that an obvious phase‐separation happens in both melt‐blended and solution‐blended iPP/EPR samples, implying that compared with the disperse degree of EPR in iPP, the preparation method plays a dominant role in formation of β‐iPP. It is suggested that the origin of formation of β‐iPP results from the thermomechanical history of the EPR component in iPP/EPR. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1704–1712, 2007     

Competitive influence of atactic polystyrene and supercritical carbon dioxide on the conformation of syndiotactic polystyrene

The crystallization behavior of miscible syndiotactic polystyrene (sPS) and atactic polystyrene (aPS) blends with different sPS/aPS weight ratios was investigated in supercritical CO₂ by using Fourier‐transform infrared spectroscopy, differential scanning calorimetry, and wide‐angle X‐ray diffraction. Supercritical CO₂ and aPS exhibited different effects on the conformational change of sPS and competed with each other. Increasing the content of amorphous aPS in the blends made its effect on the conformational change of sPS gradually surpass that of supercritical CO₂. Supercritical CO₂ favored the formation of the helical conformation of sPS in lower temperature range and the all trans planar conformation in higher temperature range, instead of forming the latter one only in higher temperature range in ambient atmosphere. However, increasing aPS content in the blends pushed the range for forming the helical conformation to lower temperature and made the all trans planar conformation dominant in aPS/sPS 25/75 blend after treating in supercritical CO₂ above 60 °C. The all trans planar zigzag conformation was more favorable than the helical conformation after mixing aPS in sPS in supercritical CO₂. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1755–1764, 2007     

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