Aminolysis reaction of calix [ 4 ] arene esters and crystal structures and conformational behaviors of calix[4]arene amides

We first make use of aminolysis of calix[4]arene esters to synthesize calix[4]arene amides. When the two ethyl esters of the calix[4]arene esters are aminolysized, the 1, 3-amide derivative is formed selectively. The crystal structures of the calix-[4]arene with two butyl amide (3b) and four butyl amide moieties (4b) were determined. The intermolecular hydrogen bonds make 4b form two-dimensional net work insolid state. The 1H NMR spectra prove that 3b is of a pinched cone conformation, while 4b and tetraheptylamide-calix[4]arene (6b) take fast interconversion between two C2v isomers in solution and appear an apparent cone conformation at room temperature. As decreasing temperature, the interconversion rate decreases gradually and, finally, the interconversion process is frozen at Tc = -10℃, which makes both conformations of 4b and 6b the pinched cone structures. The hydrogen bond improves the interconversion barrier, and the large different values of the potential barrier between 6b and 4b (or 6b) may     

压电陶瓷复合换能器固有频率的有限差分法*

为丰富换能器固有频率的研究理论,以及提供一种新的计算方法供工程人员选择,提出了计算其固有频率的有限差分法。以由径向极化的压电陶瓷圆管与金属预应力管沿径向复合而成的二元压电陶瓷复合换能器为例,建立并推导了其向振动的数学模型及其有限差分形式,给出了换能器径向振动的特征方程。利用MTALAB对计算实例的径向振动的固有频率进行编程计算,理论计算结果与已有实验结果符合很好,验证了有限差分法计算压电陶瓷复合换能器固有频率的可行性及准确性。通过仿真计算,给出了换能器径向振动固有频率与其结构尺寸的影响关系：换能器径向振动的固有频率随压电陶瓷圆管内径的增大而降低,随换能器壁厚比的增大而降低。该文所建立的换能器径向振动固有频率的有限差分法同样适用于结构形式相近的换能器及其他元器件。