Different experimental results for the influence of immersion angle on the resonant frequency of a quartz crystal microbalance in a liquid phase: with a comment

This paper presents different experimental results of the influence of an immersion angle (θ, the angle between the surface of a quartz crystal resonator and the horizon) on the resonant frequency of a quartz crystal microbalance (QCM) sensor exposed one side of its sensing surfaces to liquid. The experimental results show that the immersion angle is an added factor that may influence the frequency of the QCM sensor. This type of influence is caused by variation of the reflection conditions of the longitudinal wave between the QCM sensor and the walls of the detection cell. The frequency shifts, measured by varying θ, are related to the QCM sensor used. When a QCM sensor with a weak longitudinal wave is used, its resonant frequency is nearly independent of θ. But, if a QCM sensor with a strong longitudinal wave is employed, the immersion angle is a potential error source for the measurements performed on the QCM sensor. When the reflection conditions of the longitudinal wave are reduced, the influence of θ on the resonant frequency of the QCM sensor is negligible. The slope of the plot of frequency shifts (ΔF) versus (ρη)^1/2, the square root of the product of solution density (ρ) and viscosity (η), may be influenced by θ in a single experiment for the QCM sensor with a strong longitudinal wave in low viscous liquids, which can however, be effectively weakened by using the averaged values of reduplicated experiments. In solutions with a large (ρη)^1/2 region (0-55 wt% sucrose solution as an example, with ρ value from 1.00 to 1.26 g cm⁻³ and η value from 0.01 to 0.22 g cm⁻¹ s⁻¹, respectively), the slope of the plot of ΔF versus (ρη)^1/2 is independent of θ even for the QCM sensor with a strong longitudinal wave in a single experiment. The influence of θ on the resonant frequency of the QCM sensor should be taken into consideration in its applications in liquid phase.     

Synthesis of molecular motors incorporating para-phenylene-conjugated or bicyclo[2.2.2]octane-insulated electroactive groups

The insulating role of the bicyclo[2.2.2]octane fragment has been theoretically evaluated by comparing the electronic coupling parameter (V(ab)) in 1,4-bis(ferrocenyl)benzene (1) and 1,4-bis(ferrocenyl)bicyclo[2.2.2]octane (2). The geometries were optimized by DFT and an extended Hückel calculation was performed to evaluate V(ab) by the dimer splitting method. The calculations showed a 12-fold decrease of the electronic coupling from 60 meV for 1 to 5 meV for 2. The second part describes the synthesis of two potential molecular motors with one incorporating the insulating bicyclo[2.2.2]octane fragment. These molecules are based on a ruthenium complex bearing a tripodal stator functionalized to be anchored onto surfaces. The ferrocenyl electroactive groups and the cyclopentadienyl (Cp) rotor are connected through a p-phenylene spacer (5) or through a spacer incorporating an insulating bicyclo[2.2.2]octane moiety (6).     

X射线线形的解卷分析与Bragg角的精确计算

采用解析函数模拟X射线线形, 在排除实验测试误差影响的条件下, 研究仪器宽化修正过程中各种因素如Kα双线、线形宽度和原点选取等对傅里叶系数和真实线形的影响;分析了从傅里叶系数或真实线形分离晶粒尺寸和微观应变的可靠性; 提出了无任何假设的前提下, 由实测线形的解卷计算求得精确Bragg角的方法. 关键词： X射线线形 傅里叶变换 真实线形 Bragg角     

中心力场中散射角的简洁推导

本文从牛顿方程及角动量守恒定律出发 ,利用矢量函数的微积分运算技巧简捷地推导出中心力场中散射角 φ,避免了经典教科书中从轨道方程出发推导出 φ的繁琐性 ,不仅计算简洁 ,而且物理过程明确 .     

Gelation Dynamics and Mechanism(s) in Stereoregular Poly(Methyl Methacrylate)s

Chain conformation and gel structure of syndiotactic PMMA thermoreversible gels have been investigated using small angle neutron scattering (SANS). A double helix model for the chain conformation is proposed alongside a gel network model where the fibrils are formed by the proposed double helix and the junctions by the aggregation of 3 double helices. Preliminary results, also obtained by SANS, for stereocomplex gels prepared in bromobenzene are presented.     

GPC普适标定对星形支化聚苯乙烯适用性的实验验证

用GPC-连续型粘度计-小角激光光散射光度计三联用装置研究了GPC普适标定对星形支化聚苯乙烯试样的适用性问题.结果证实:支化度因子g'≥0.131时的所有星形聚苯乙烯级分,普适标定均适用;但对g'<0.131时的星形支化聚苯乙烯高支化级分,普适标定将不能适用.     

天府背斜上高角度仰冲断层的变形几何学问题讨论

本文以天府背计的地质构造特征为基础,提出了高角度仰冲断层的变形几何学问题。文中比较系统地阐述了变形几何学在分析石油地质构造中所涉及的无限小和有限小的概念,连续和均匀性的棍念,讨论了库仑—莫尔理论表达式,分析了变形椭球体理论中剪破裂角(θ)值的变化范围,从而为论证高角度仰冲断层提出了理论依据。     

铅球飞行轨迹方程的微分解及应用

本文根据运动学原理建立了铅球轨迹方程,考虑铅球落点位置,利用微积分和三角函数理论求出手角极值和最大飞进距离,得出了最佳出手角、最大飞进距离与出手点高度初速度之间简单表达式,并通过计算制成了最佳出手角、最大飞进距离表。     

含有多个配体的杂化与Pauling的成对-缺陷-求和近似<正>

本文报道了对于以前的工作所做的一般化处理,以前的结果仅限于分子ML_k有两个配体(k=2)的情况。现在推广到k>2的情况。假设分子中任意两键M—L_p和M—L_q间的夹角α都相同,我们得到了一些关于对角阵D(λ)酉阵U~T,重迭阵S_1和键强度F的一般公式,还讨论了SS~T的性质,进而由最大重迭法给出了Pauling的成对一缺陷一求和近似的一个理论证明,这表明,Pauling的近似对于键强的估算是很好的。     

On the problem of axisymmetrically loaded shells of revolution with small elastic strains and arbitrarily large axial deflections

For the problem of axisymmetrically loaded shells of revolution with small elastic strains and arbitrarily large axial deflections, this paper suggests a group of state variable: radial displacement u, axial displacement w, angular, deflection of tangent in the meridian X, radial stress resultant H and meridional bending moment M_s, and derives a System of First-order Nonlinear Differential Equations under global coordinate system with these variables. The Principle of Minimum Potential Energy for the problem is obtained by means of weighted residual method, and its Generalized Variational Principle by means of identified Lagrange multiplier method.This paper also presents a Method of Variable-characteristic Nondimensionization with a scale of load parameter, which may efficientlky raise the probability of success for nonlinearity calculation. The obtained Nondimensional System of Differential Equations and Nondimensional Principle of Minimum Potential Energy could be taken as the theoretical basis for the numerical computation of axisymmetrical shells with arbitrarily large deflections.