Using Metaphors to Understand and Solve Arithmetic Problems: Novices and Experts Working With Negative Numbers

In this study, novices and experts used the same metaphors to understand and solve problems with negative numbers. However, they used them differently. Twenty-four participants (12 middle school children and 12 postsecondary adults) computed arithmetic expressions during the problem-solving task. During this task, children used metaphors more often than adults did to compute, detect and correct errors, and justify their answers. Metaphorical computations were more accurate but slower than other methods. The participants explained 6 arithmetic expressions during the understanding task. During this task, the adults used more metaphors (with fewer details) and used them more often than the children did. Compared to the median child, the median adult showed a more integrated understanding of arithmetic through multiple metaphors, mathematical rules, and transformations. These results suggest that the metaphors used by both the children and the adults are central to understanding arithmetic. Thus, these metaphors are likely candidates for theory-constitutive metaphors.     

The spectrophotometric study of a fluorescence‐enhanced inclusion complex threaded with β‐cyclodextrin: Synthesis and characterization

A novel achiral monomer end‐capped with a phenyl‐[1,3,4]oxadiazolyl group and threaded through β‐cyclodextrin was synthesized to investigate the host‐guest interactions in the inclusion complex. ¹H NMR studies revealed that one or two cyclodextrin molecules were threaded onto the synthesized achiral monomer, leading to the formation of a fibrous construction of self‐assembled inclusion complexes. The formation of a self‐assembled inclusion complex was identified using SEM and TEM. The highly ordered alignment of self‐assembled supramolecules was confirmed using polarized optical microscopy. We demonstrate an easy process for the fabrication of nano‐structured self‐assembled inclusion complexes in pyridine/ethanol (1 mL/10 mL) as well as the enhancement of photo‐induced fluorescence via monomers end‐capped with a phenyl‐[1,3,4]oxadiazolyl moiety threaded with β‐cyclodextrins. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3368–3374, 2010     

Synthesis and computational oxidation mechanism study of novel organosoluble aramids with high modulus by low‐temperature solution polycondensation

A series of highly organosoluble polyamides with high modulus having propeller‐shaped triarylamine were synthesized using aromatic diacid chlorides by low‐temperature solution polycondensation. The polyamide films had strong, tough, flexible, and amorphous properties. These polymers revealed electrochromic characteristics both in the visible range and near‐infrared (NIR) region, with a color change from pale yellowish at its neutral state to green and blue at its oxidized state at applied potentials ranging from 0.00 to 1.35 V. Cyclic voltammetry (CV) of the polymer films cast onto an indium tin oxide (ITO)‐coated glass substrate exhibited two reversible redox couples at potentials of 0.80–0.87 V and 1.19–1.25 V, respectively, vs. Ag/Ag⁺ in acetonitrile solution. From the combination of the experimental and computational study, we proposed an oxidation mechanism based on molecular orbital (MO) theory, which well explains the CV experimental result. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

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     

Morphology and temperature responsiveness–swelling relationship of poly(N‐isopropylamide–chitosan) copolymers and their application to drug release

Poly [N‐isopropylacrylamide (NIPAAm)–chitosan] crosslinked copolymer particles were synthesized by soapless emulsion copolymerization of NIPAAm and chitosan. An anionic initiator [ammonium persulfate (APS)] and a cationic initiator [2,2′‐azobis(2‐methylpropionamidine)dihydrochloride (AIBA)] were used to initiate the reaction of copolymerization. The chitosan–NIPAAm copolymer synthesized by using APS as the initiator showed a homogeneous morphology and exhibited the characteristic of a lower critical solution temperature (LCST). The copolymer synthesized by using AIBA as an initiator showed a core–shell morphology, and the characteristic of LCST was insignificant. The LCST of the chitosan–NIPAAm copolymer depended on the morphology of the copolymer particles. In addition, the chitosan–NIPAAm copolymer particles were processed to form copolymer disks. Then, the effect of various variables such as the chitosan/NIPAAm weight ratio, the concentration of crosslinking agent, and the pH values on the swelling ratio of chitosan–NIPAAm copolymer disks were investigated. Furthermore, caffeine was used as the model drug to study the characteristics of drug loading of the chitosan–NIPAAm copolymer disks. Variables such as the chitosan/NIPAAm weight ratio and the concentration of the crosslinking agent significantly influenced the behavior of caffeine loading. Two factors (pore size and swelling ratio) affected the behavior of caffeine release from the chitosan–NIPAAm copolymer disks. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3029–3037, 2004     

Theoretical investigations of the molecular conformation and reorganization energies in the organic diamines as hole‐transporting materials

Recently, organic diamine compounds have been widely used as hole‐transporting materials. In this work, DFT B3LYP method with the 6‐31G^* basis set was performed to investigate the influence of molecular conformation on the reorganization energy of a series of tetra(aryl)benzidine‐based hole‐transport materials. The results indicate that there are two types (i.e., ISB and BD/TPD) of geometric differences of the organic diamines with the relaxation processes. The reorganization energy of the ISB type is lower than that of the BD/TPD type. For the ISB type, the terminal phenyl moiety of the molecular framework plays an important role in determining the Marcus‐type reorganization energy and the central biphenyl moiety does not. A methyl group attached to a terminal phenyl can be used to tune the reorganization energy. According to the statistical analysis, four geometric parameters could affect the reorganization energy of the BD/TPD type. The conformation of either the central biphenyl or the terminal phenyl moiety of the BD/TPD type determines the Marcus‐type reorganization energy associated with the charge transport process at the molecular level. Presumably, this calculation can be employed to predict the electroluminescence (EL) character of the other organic diamines and to improve the design of new hole‐transporting materials in organic light‐emitting devices (OLEDs). Copyright © 2007 John Wiley & Sons, Ltd.