Variational Approach to the Lane-Emden Equation

By the semi-inverse method, a variational principle is obtained for the Lane-Emden equation, which gives much numerical convenience when applying finite element methods or Ritz method.

Electrochemical, spectroscopic and SPM evidence for the controlled formation of self-assembled monolayers and organised multilayers of ferrocenyl alkyl thiols on Au(111)

Organised multilayers were formed from the controlled self-assembly of ferrocene alkyl thiols on Au(111) surfaces. The control was accomplished by increasing the concentration of the thiol solutions used for the assembly. Cyclic voltammetry, ellipsometry, scanning probe microscopy (STM and AFM) and in situ FTIR spectroscopy were used to probe the differences between mono- and multilayers of the same compounds. Electrochemical desorption studies confirmed that the multilayer structure is attached to the surface via one monolayer. The electrochemical behaviour of the multilayers indicated the presence of more than one controlling factor during the oxidation step, whereas the reduction was kinetically controlled which contrasts with the behaviour of monolayers, which exhibit kinetic control for the oxidation and reduction steps. Conventional and imaging ellipsometry confirmed that multilayers with well-defined increments in thickness could be produced. However, STM indicated that at the monolayer stage, the thiols used promote the mobility of Au atoms on the surface. It is very likely that the multilayer structure is held together through hydrogen bonding. To the best of out knowledge, this is the first example of a controlled one-step growth of multilayers of ferrocenyl alkyl thiols using self-assembly techniques.

Superelastic And Spring Properties Of Si3N4 Microcoils

Silicon nitride with helical structure was prepared on a large scale by CVD. On the microscale, these coiled Si3N4 ceramics still possess superelasticity and can recover their original shapes after cyclic loadings without noticeable deformations. These results suggest helical microcoils could have potential in microdevices for MEMS, motors, electromagnets, generators, and related equipment.