Morphologies of a spherical bimodal polyelectrolyte brush induced by polydispersity and solvent selectivity

It is commonly realized that polydispersity may significantly affect the surface modification properties of polymer brush systems. In light of this, we systematically study morphologies of bidisperse polyelectrolyte brush grafted onto a spherical nanocolloid in the presence of trivalent counterions using molecular dynamics simulations. Via varying polydispersity, grafting density, and solvent selectivity, the effects of electrostatic correlation and excluded volume are focused, and rich phase behaviors of binary mixed polyelectrolyte brush are predicted, including a variety of pinned-patch morphologies at low grafting density and micelle-like structures at high grafting density. To pinpoint the mechanism of surface structure formation, the shape factor of two species of polyelectrolyte chains and the pair correlation function between monomers from different polyelectrolyte ligands are analyzed carefully. Also, electrostatic correlations, manifested as the bridging through trivalent counterions, are examined by identifying four states of trivalent counterions. Our simulation results may be useful for designing smart stimuli-responsive materials based on mixed polyelectrolyte coated surfaces.     

The Quasi-Exactly Solvable Problems in Relativistic Quantum Mechanics

We study the quasi-exactly solvable problems in relativistic quantum mechanics. We consider the problems for the two-dimensional Klein-Gordon and Dirac equations with equal vector and scalar potentials, and try to find the general form of the quasi-exactly solvable potential. After obtaining the general form of the potential, we present several examples to give the specific forms. In the examples, we show for special parameters the harmonic potential plus Coulomb potential, Killingbeck potential and a quartic potential plus Cornell potential are quasi-exactly solvable potentials.     

在二带京兹堡朗道理论下MgB_2的超导参量的研究

文中通过G-L理论二带模型来研究相干长度ξ(T)、伦敦穿透深度λ(T)以及京兹堡朗道参量κ(T)=λ(T)/ξ(T)在Tc附近对温度T的依赖关系。理论计算结果与MgB2样品的实验数据符合的很好。同时与单带模型算出的结果做了对比,发现G-L理论二带模型能更精确描述MgB2的超导特性。     

具有复介电常量一维光子晶体的特性研究

利用传输矩阵法计算了一维光子晶体的能带结构和光传输特性,重点讨论了介电常量的虚部为负值时对传输特性的影响。当在介质中掺入具有增益特性的介质时,靠近光子带隙边缘就会出现较强的受激辐射放大。同时,光子晶体的长度和介电常量虚部的大小都会影响晶体的受激辐射。随着虚部数值的增加,受激增强并不是单调递增,而是存在一极值点。     

Diffusion activation energy versus the favourable energy in two-order-parameter model:A molecular dynamics study of liquid Al

In the present work, we find that both diffusion activation energy E_a(D) and E_a(S^ex) increase linearly with pressure and have the same slope (0.022±0.001 eV/GPa) for liquid Al. The temperature and pressure dependence of excess entropy is well fitted by the expression -S^ex(T,P)/k_B=a(P)+b(P)T+c(P)exp(E_f/k_BT), which together with the small ratio of E_f/k_BT leads to the relationship of excess entropy to temperature and pressure, i.e. S^ex≈-cE_f/T, where c is about 12 and E_f (=Δ E-PΔV) is the favourable energy. Therefore, there exists a simple relation between E_a(S^ex) and E_f, i.e. E_a(S^ex)≈cE_f.