Existence of maximal points with respect to ordered bipreference relations

The maximality of a point with respect to an ordered pair of arbitrary preference relations is introduced. Necessary and sufficient conditions for the existence of maximal points are given.The authors are grateful for the referee's comments which led to an improved presentation of the paper.     

Three-Way Decision Models Based on Ideal Relations in Multi-Attribute Decision-Making

In recent years, research on applications of three-way decision (e.g., TWD) has attracted the attention of many scholars. In this paper, we combine TWD with multi-attribute decision-making (MADM). First, we utilize the essential idea of TOPSIS in MADM theory to propose a pair of new ideal relation models based on TWD, namely, the three-way ideal superiority model and the three-way ideal inferiority model. Second, in order to reduce errors caused by the subjectivity of decision-makers, we develop two new methods to calculate the state sets for the two proposed ideal relation models. Third, we employ aggregate relative loss functions to calculate the thresholds of each object, divide all objects into three different territories and sort all objects. Then, we use a concrete example of building appearance selection to verify the rationality and feasibility of our proposed models. Furthermore, we apply comparative analysis, Spearman’s rank correlation analysis and experiment analysis to illustrate the consistency and superiority of our methods.     

Synthesis and comparative study on polyetherimides from isomeric 4,4′-isopropylidenediphenoxy bis(phthalic anhydride)s

Two isomers of commercial 4,4′-(4,4′-isopropylidenediphenoxy) bis(phthalic anhydride) (4,4′-BPADA), that is, 3,4′-(4,4′-isopropylidenediphenoxy) bis(phthalic anhydride) (3,4′-BPADA) and 3,3′-(4,4′-isopropylidenediphenoxy) bis(phthalic anhydride) (3,3′-BPADA), were synthesized through aromatic nucleophilic substitution from nitrophthalonitrile and bisphenol A. 3,4′-BPADA was first synthesized from two intermediates, that is, 3-(4-[4-hydroxyphenylisopropylidene] phenoxy) phthalonitrile (3-BPADN) and 3,4′-(4,4′-isopropylidenediphenoxy) bis(phthalonitrile) (3,4′-BPATN). The corresponding three series of polyetherimides (PEIs) were prepared with two representative aromatic diamines (4,4′-oxydianiline and m-phenylenediamine (m-PDA)) via two-step procedure and chemical imidization. Isomeric polyimides showed T_gs from 206 to 256°C in nitrogen and T_d5%s from 488 to 511°C in argon, good mechanical properties (tensile moduli of 2.3–3.3 GPa, tensile strengths of 70–96 MPa, and elongations at break of 3.2%–5.1%), and good solubility. With the introduction of 3-substituted phthalimide unit, PEIs displayed higher T_g values, lower strengths and elongations, better solubility and larger d-spacings. The rheological properties of thermoplastic polyimide resins based on the BPADA isomers were investigated, which showed that polyetherimide PEI-3b derived from 3,3′-BPADA and m-PDA had the lowest melt viscosity among the isomers, indicating that the melt processibility had been greatly improved.     

Contiguity relations for linearisable systems of Gambier type

We introduce the Schlesinger transformations for the Gambier, linearisable, equation and by combining the former construct the contiguity relations of the solutions of the latter. We extend the approach to the discrete domain obtaining thus the Schlesinger transformations and the contiguity relations of the solutions of the Gambier mapping. In all cases the resulting contiguity relation is a linearisable equation, involving free functions, and which can be related to the generic Gambier mapping.     

Characterizing polymer macrostructures by identifying and locating microstructures along their chains with the kerr effect

In this brief report, we demonstrate that Kerr effect measurements, which determine the excess birefringence contributed by polymer solutes in dilute solutions observed under a strong electric field, are highly sensitive to and capable of determining their microstructures, as well as their locations along the macromolecular backbone. Specifically, using atactic triblock copolymers with the same overall composition of styrene (S) and p-bromostyrene (pBrS) units, but with two different block arrangements, that is, pBrS₉₀-b-S₁₂₀-b-pBrS₉₀ (I) and S₆₀-b-pBrS₁₈₀-b-S₆₀ (II), which are indistinguishable by NMR, we detected a dramatic difference in their molar Kerr constants (_mK), in agreement with those previously estimated. Although similar in magnitude, their Kerr constants differ in sign, with _mK(II) positive and _mK(I) negative. In addition, S/pBrS random and gradient copolymers synthesized by reversible addition-fragmentation chain-transfer (RAFT) polymerization exhibit a heretofore unexpected enhanced enchainment of racemic (r) pBrS-pBrS diads. Comparison of their observed and calculated _mKs suggests that the gradient S/pBrS copolymers possess an unanticipated additional gradient in stereosequence that parallels their comonomer gradient, that is, as the concentration of pBrs units decreases from one end of the copolymer chain to the other, so does the content of r diads. This conclusion could only be reached by comparison of observed and calculated Kerr effects, which access the global properties of macromolecules, and not NMR, which is only sensitive to local polymer structural environments, but not to their locations on the copolymer chains. Molar Kerr constants are characteristic of entire polymer chains and are highly sensitive to their constituent microstructures and their distribution along the chain. They may be used to both identify constituent microstructures and locate them along the polymer chain, thereby enabling, for the first time, characterization of their complete macrostructures. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

Improving charge transport in poly(3‐hexylthiophene) transistors via blending with an alkyl‐substituted phenylene–thiophene–thiophene–phenylene molecule

A prototypical semiconducting bicomponent system consisting of a conjugated polymer, that is, poly(3‐hexylthiophene) (P3HT), blended with a small thiophene containing conjugated molecule, that is, an alkyl‐substituted bisphenyl‐bithiophene [phenylene–thiophene–thiophene–phenylene (PTTP)], has been used as an electroactive active layer in field‐effect transistors (FETs). The self‐assembly of this bicomponent system at surfaces has been studied at different length scales, from the nanoscale to the macroscale, and compared with the behavior of monocomponent films of PTTP and P3HT. The correlation between morphology and electric properties of the semiconducting material is explored by fabricating prototypes of FETs varying the relative concentrations of the two‐component blend. The maximum charge carrier mobility value, achieved with a few percent of PTTP component, is not simply due to a uniform dispersion of the molecules in the polymer matrix, but rather to the generation of very long percolation paths, whose composition and electrical properties can be tuned with the PTTP concentration. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Methylol‐functional benzoxazines as precursors for high‐performance thermoset polymers: Unique simultaneous addition and condensation polymerization behavior

A new class of high‐performance resins of combined molecular structure of both traditional phenolics and benzoxazines has been developed. The monomers termed as methylol‐functional benzoxazines were synthesized through Mannich condensation reaction of methylol‐functional phenols and aromatic amines, including methylenedianiline (4,4′‐diaminodiphenylmethane) and oxydianiline (4,4′‐diaminodiphenyl ether), in the presence of paraformaldehyde. For comparison, other series of benzoxazine monomers were prepared from phenol, corresponding aromatic amines, and paraformaldehyde. The as‐synthesized monomers are characterized by their high purity as judged from ¹H NMR and Fourier transform infrared spectra. Differential scanning calorimetric thermograms of the novel monomers show two exothermic peaks associated with condensation reaction of methylol groups and ring‐opening polymerization of benzoxazines. The position of methylol group relative to benzoxazine structure plays a significant role in accelerating polymerization. Viscoelastic and thermogravimetric analyses of the crosslinked polymers reveal high T_g (274–343 °C) and excellent thermal stability when compared with the traditional polybenzoxazines. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Dependence of dielectric,ferroelectric, and piezoelectric properties on crystalline properties of p(VDF‐co‐TrFE) copolymers

Thermal processing at various temperatures has been used to fabricate poly(vinylidene fluoride‐co‐trifluoroethylene) [P(VDF‐co‐TrFE)] films with varied crystalline properties in an attempt to improve their piezoelectric properties. Although the dielectric constant of the films annealed at higher temperature is smaller than that of cooled and quenched ones, it has been shown that the annealed films possess larger crystallinity and stacked lamellar crystal grain size. The ferroelectric domains deriving from crystal region in all the samples are effectively improved by hot polarization. As a result, the remnant polarizations (P_r) and coercive electric field (E_c) of the corresponding films are improved at a low frequency due to the response of dipoles in crystal phase, and the largest piezoelectric constant in the longitudinal thickness mode (d₃₃=?25 pC/N) is obtained in an annealed copolymer film. The results illustrate improving the crystal structure of P(VDF‐co‐TrFE) is an effective way to realize high electromechanical properties, which provides broadly applied scenery for this kind of copolymer in piezoelectric components. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

On modifying properties of polymeric melts by nanoscopic particles

We study geometric and energetic factors that partake in modifying properties of polymeric melts via inserting well‐dispersed nanoscopic particles (NP). Model systems are cis‐1,4‐polybutadiene melts including a single atomic clusters of size varied in the range 10–150 atoms (3–7 Å in radius; 0.1–1.5% v/v). We modify the interactions between the chains and the particle by tuning attractive van der Waals interactions. Using molecular dynamics, we study equilibrium fluctuations and dynamical properties at the interface. The NPs move in the polymer matrix in two different regimes corresponding to trapped and free diffusion, depending on the NP size. Furthermore, degree of crowding around the NP by the polymer chains is quantified. Effect of NP size and interaction strength both on volume and volumetric fluctuations is manifested in mechanical properties, quantified here by bulk modulus, K. Tuning NP size and nonbonded interactions results in ～15% enhancement in K by addition of a maximum of 1.5% v/v NP. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012