Water-assisted mechanical testing of polymeric thin-films

Thin films with a nanometer-scale thickness are of great interest to both scientific and industrial communities due to their numerous applications and unique behaviors different from the bulk. However, the understanding of thin-film mechanics is still greatly hampered due to their intrinsic fragility and the lack of commercially available experimental instruments. In this review, we first discuss the progression of thin-film mechanical testing methods based on the supporting substrate: film-on-solid substrate method, film-on-water tensile tests, and water-assisted free-standing tensile tests. By comparing past studies on a model polymer, polystyrene, the effect of different substrates and confinement effect on the thin-film mechanics is evaluated. These techniques have generated fruitful scientific knowledge in the field of organic semiconductors for the understanding of structure–mechanical property relationships. We end this review by providing our perspective for their bright prospects in much broader applications and materials of interest.     

Controlling effective interactions and spatial dispersion of nanoparticles in multiblock copolymer melts

The microscopic Polymer Reference Interaction Site Model theory is employed to study, for the first time, the effective interactions, spatial organization, and miscibility of dilute spherical nanoparticles in non‐microphase separating, chemically heterogeneous, compositionally symmetric AB multiblock copolymer melts of varying monomer sequence or architecture. The dependence of nanoparticle wettability on copolymer sequence and chemistry results in interparticle potentials‐of‐mean force that are qualitatively different from homopolymers. An important prediction is the ability to improve nanoparticle dispersion via judicious choice of block length and monomer adsorption‐strengths which control both local surface segregation and chain connectivity induced packing constraints and frustration. The degree of dispersion also depends strongly on nanoparticle diameter relative to the block contour length. Small particles in copolymers with longer block lengths experience a more homopolymer‐like environment which renders them relatively insensitive to copolymer chemical heterogeneity and hinders dispersion. Larger particles (sufficiently larger than the monomer diameter) in copolymers of relatively short block lengths provide better dispersion than either a homopolymer or random copolymer. The theory also predicts a novel widening of the miscibility window for large particles upon increasing the overall molecular weight of copolymers composed of relatively long blocks. The influence of a positive chi‐parameter in the pure copolymer melt is briefly studied. Quantitative application to fullerenes in specific copolymers of experimental interest is performed, and miscibility predictions are made. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1098–1111     

固体力学有限元体系的结构拓扑变化理论

本文是文[1]的继续.文[1]提出了杆件系统的结构拓扑变化理论和拓扑变化法本文将这一理论和方法推进到连续体有限元体系;且在此基础上揭示出有限元体系的一个新性质,称为基本位移之梯度的正交性定理,从而给出一套设计敏度的显式表达式,可直接用于计算.     

Spontaneous magnetization of the Ising model on a 4–8 lattice

The spontaneous magnetization of the Ising model on a 4–8 lattice with six different coupling constants and two different magnetic moments is studied. A formula for the spontaneous magnetization is proposed. The result agrees with the exact low-temperature series expansions up to the 12th order.     

An Analogue of Distributivity for Ungraded Lattices

In this paper, we study lattices that posess both the properties of being extremal (in the sense of Markowsky) and of being left modular (in the sense of Blass and Sagan). We call such lattices trim and show that they posess some additional appealing properties, analogous to those of a distributive lattice. For example, trimness is preserved under taking intervals and suitable sublattices. Trim lattices satisfy a weakened form of modularity. The order complex of a trim lattice is contractible or homotopic to a sphere; the latter holds exactly if the maximum element of the lattice is a join of atoms. Any distributive lattice is trim, but trim lattices need not be graded. The main example of ungraded trim lattices are the Tamari lattices and generalizations of them. We show that the Cambrian lattices in types A and B defined by Reading are trim; we conjecture that all Cambrian lattices are trim.     

静态球对称黑洞Dirac场的统计熵

利用改进的brickwall模型,给出了一类静态球对称黑洞Dirac场的熵,结果表明,在取相同的截断因子时,Dirac场的熵均为标量场的熵的72倍 关键词： 黑洞 统计熵 brickwall模型 Dirac场     

Around Multicolour Disordered Lattice Gas

We consider a system of multicolour disordered lattice gas, following closely the (monocolour) introduced by Faggionato and Martinelli^(3,4). We study the projection on the monocolour system and we derive an estimate of the closeness between grand canonical and canonical Gibbs measures. AMS Classification: Primary: 60K35, 82C20, 82C22