Thermal degradation kinetics of biodegradable poly(3‐hydroxybutyrate)/layered double hydroxide nanocomposites

The thermal degradation behaviors of biodegradable poly(3‐hydroxybutyrate) (PHB) and PHB/poly(ethylene glycol) phosphonates (PEOPAs)‐modified layered double hydroxide (PMLDH) nanocomposites have been investigated using thermogravimetric analysis. Effects of PMLDH contents on the isothermal degradation kinetics of PHB were explored. These experimental results show that the degradation kinetics of PHB/PMLDH nanocomposites is the chain‐scission process of cyclic β‐elimination reaction with the following autocatalytic reactions, which is very similar to that of pure PHB matrix. Further calculated data based on the autocatalytic model can fit very well with the experimental data. The E_a value of PHB/PMLDH nanocomposites is increased as the content of PMLDH increases. This can be attributed to the incorporation of more PMLDH loading to PHB induced a decrease in the degradation rate and an increase in the residual weight for PHB/PMLDH nanocomposites. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1207–1213, 2008     

Discovery of New Natural Products by Intact‐Cell Mass Spectrometry and LC‐SPE‐NMR: Malbranpyrroles,Novel Polyketides from Thermophilic Fungus Malbranchea sulfurea

Six photosensitive polyketides, malbranpyrroles A–F, were discovered from the thermophilic fungus Malbranchea sulfurea by using intact‐cell desorption/ionization on silicon mass (ICD‐MS) and LC‐SPE‐NMR. These two strategies facilitate the searching and structural determination of unstable natural products. The ICD‐MS indicated that only brown hyphae of M. sulfurea can produce malbranpyrroles. The biosynthetic pathway of malbranpyrroles was evidenced by ¹³C isotope precursors and amino acid feeding experiments. The cytotoxicity data revealed that the conformation of the conjugated system in malbranpyrroles does not affect cytotoxic potency against cancer cell lines. In addition, the chlorine atom was shown to be the pharmacophore for cytotoxicity.     

Crystallization kinetics and melting behavior of metallocene short‐chain branched polyethylene fractions

Metallocene polyethylene (mPE) fractions are recognized as being more homogeneous with respect to short‐chain branch (SCB) distribution as compared with unfractionated mPEs. Differential scanning calorimetry and polarized optical microscopy (POM) were used to study the influences of SCB content on the crystallization kinetics, melting behavior, and crystal morphology of four butyl‐branched mPE fractions. The parent mPE of the studied fractions was also investigated for comparative purposes. mPE fractions showed a much simpler crystallization behavior as compared with their parent mPE during the cooling experiments. The Ozawa equation was successfully used to analyze the nonisothermal crystallization kinetics of the fractions. The Ozawa exponent n decreased from about 3.5 to 2 as the temperature declined for each fraction, indicating the crystal‐growth geometry changed from three‐dimensional to two‐dimensional. For isothermal crystallization, the fraction with a lesser SCB content exhibited a higher crystallization temperature (T_c) window. The results from the Avrami equation analysis showed the exponent n values were around 3 (with minor variation), which implied that the crystal‐growth geometry is pseudo‐three‐dimensional. Both of the activation energies for nonisothermal and isothermal crystallization were determined for each fraction with Kissinger and Arrhenius‐type equations, respectively. Double melting peaks were observed for both nonisothermally or isothermally crystallized specimens. The high‐melting peak was confirmed induced via the annealing effect during heating scans. The Hoffman–Weeks plot was inapplicable in obtaining the equilibrium melting temperature (T_m°) for each fraction. The relationship between T_c and T_m for the fractions is approximately T_m = T_c (°C) + 8.3. The POM results indicated that the crystals of parent or fractions formed under cooling conditions did not exhibit the typical spherulitic morphology as a result of the high SCB content. © 2002 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 325–337, 2002     

Exact stability regions for quartic polynomials

Given an arbitrary real quartic polynomial, we find the exact region containing the coefficients of the polynomial such that all roots have absolute values less than 1.     

Secondary Options and Post‐secondary Expectations: Standards‐based Mathematics Programs and Student Achievement on College Mathematics Placement Exams

Research on student achievement within the University of Chicago School Mathematics Project (UCSMP) and Core‐Plus Mathematics Project (CPMP) at the secondary level is beginning to accumulate, however, much less is known about how prepared these students are for post‐secondary education. Therefore this study involving students within one tracked school district used multiple linear regression to examine the role of differential experience within two secondary Standards‐based mathematics programs, gender, and prior mathematics achievement on college algebra and calculus readiness placement test scores. Results show that there are no significant differences between students who had completed three and four years of the CPMP curriculum. UCSMP students with four or five years of experience significantly outperformed CPMP students on both assessments. Prior achievement was a significant predictor of student achievement on both examinations. Male students outperformed female students on the algebra placement exam. Students who had studied from both CPMP and UCSMP significantly outperformed students who had studied from CPMP for four years on the calculus readiness examination.     

Synthesis and characterization of novel aromatic poly(imide–benzoxazole) copolymers

New poly(imide–benzoxazole) copolymers were prepared directly from a dianhydride, a diacid chloride, and a bis(o‐diaminophenol) monomer in a two‐step method. In the first step, poly(amic acid–hydroxyamide) precursors were synthesized by low‐temperature solution polymerization in an organic solvent. Subsequently, the thermal cyclodehydration of the poly(amic acid–hydroxyamide) precursors at 350 °C produced the corresponding poly(imide–benzoxazole) copolymers. The inherent viscosities of the precursor polymers were around 0.19–0.33 dL/g. The cyclized poly(imide–benzoxazole) copolymers had glass‐transition temperatures in the range of 331–377 °C. The 5% weight loss temperatures ranged from 524 to 535 °C in nitrogen and from 500 to 514 °C in air. The poly(imide–benzoxazole) copolymers were amorphous, as evidenced by the wide‐angle X‐ray diffraction measurements. The structures of the precursor copolymers and the fully cyclized copolymers were characterized by Fourier transform infrared, ¹H NMR, and elemental analysis. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 6020–6027, 2005     

Covering theorems of simplexes and systems of linear inequalities

A selection lemma for Ky Fan's coverings is first proved, and then applied together with Ky Fan's generalization of the classical Knaster-Kuratowski Mazurkiewicz theorem to obtain a new covering theorem of simplexes. As applications, results on the consistency for certain systems of linear inequalities are obtained.     

Morphology of microporous poly(vinylidene fluoride) membranes studied by gas permeation and scanning electron microscopy

Microporous poly(vinylidene fluoride) (PVDF) membranes with asymmetric pore structure were prepared by a wet phase inversion process. The polymer was precipitated from a casting solution when immersed in a cold water (gelation) bath. The casting solution was, in most cases, composed of polymer, solvent, and nonsolvent. In this solvent-nonsolvent system, the solvents used were triethylphosphate (TEP) and dimethylsulfoxide (DMSO), and the nonsolvents used were glycerol and ethanol. Mean pore sizes and effective porosity of the microporous membranes were calculated using the gas permeation method. They were studied as a function of evaporation time of wet nascent film, polymer molecular weight, concentration of polymer, and concentration of nonsolvent. The morphology of the membranes was examined by scanning electron microscopy (SEM).     

Some experiments on the effect of isolated protuberances on flow through tubes

At various locations in the arterial system, plaques, or small relatively isolated protuberances, can develop on the inner wall of the vessel and project into the lumen. A number of investigators have suggested that the development and growth of these protuberances is related to the flow in the vicinity of the protuberance. In this study, the conditions under which the flow separates from an isolated protuberance located in a cylindrical tube were investigated. The critical Reynolds number at which separation first takes place for a given protuberance was determined. A series of tests was performed for steady flow of a Newtonian fluid through a rigid tube in which protuberances of various sizes were inserted. The results of the tests show the effect of the protuberance height and shape on the separation characteristics. In general, the results indicate that separation takes place at relatively small values of the Reynolds number; values that commonly occur in the arterial system, so that this phenomenon may be important in the study of the “coupling” between blood flow and arterial lesions.