In this paper, we have proposed to apply a combinatorial approach to investigate the Schottky diode based on electrochemically polymerized conjugated polymer. The concept of combinatorial approach was emerged in the biochemical field and lately used in the materials science to screen a number of experimental conditions efficiently. Some tips for designing the polymerization bath suitable for our purpose, such as the way to suppress the interference of polymerization currents, have been described. In the case of Schottky diodes based on poly (3-methylthiophene), the system chosen to test our idea, the effects of polymer thickness and the supporting salt on the device characteristics have been surveyed clearly and rapidly. The map or library of the relationship between the polymerization condition and device characteristic may be useful to tune the device characteristics as desired. Our preliminary result has shown that the combinatorial approach proposed here can be a powerful tool to investigate the conjugated polymer devices by electrochemical polymerization such as electrochromic devices.

The classical game of peg solitaire has uncertain origins, but was certainly popular by the time of Louis XIV, and was described by Leibniz in 1710. One of the classical problems concerning peg solitaire is the feasibility issue. An early tool used to show the infeasibility of various peg games is the rule-of-three [Suremain de Missery 1841]. In the 1960s the description of the solitaire cone [Boardman and Conway] provides necessary conditions: valid inequalities over this cone, known as pagoda functions, were used to show the infeasibility of various peg games. In this paper, we recall these necessary conditions and present new developments: the lattice criterion, which generalizes the rule-of-three; and results on the strongest pagoda functions, the facets of the solitaire cone.