Microcantilever arrays functionalised with spiropyran photoactive moieties as systems to measure photo-induced surface stress changes

[EN] Herein we investigate the feasibility of detecting photo-induced surface stress changes using the deflection response of cantilevers. For this purpose, silicon microcantilevers have been functionalised with spiropyran photochromic molecules, using both a monolayer and a polymeric brushes approach. Uponultraviolet light irradiation, the spiropyran unit is converted to the merocyanine form due to the photo-induced cleavage of the Cspiro-O bond. The two forms of the molecule have dramatically different charge,polarity and molecular conformations. This makes spiropyrans an ideal system to study the correlation between photo-induced molecular changes and corresponding changes in surface stress. Our investigations include monitoring the changes in static cantilever deflection, and consequently, surface stress of the spiropyran functionalised cantilevers on exposure to ultraviolet light. Cantilever deflection data reveals that ultraviolet induced conformational changes in the spiropyran moiety cause a change incompressive surface stress and this varies with the type of functionalisation method implemented. The change in surface stress response from the spiropyran polymer brushes functionalised cantilevers gives an average surface stress change of 98 Nm−1(n = 24) while the spiropyran monolayer coated cantilevers have an average surface stress change of about 446 Nm−1(n = 8) upon irradiation with UV light.

Search of symmetric composition methods of symmetric integrators

Composition methods are useful when solving Ordinary Differential Equations (ODEs) as they increase the order of accuracy of a given basic numerical integration scheme. We will focus on sy-mmetric composition methods involving some basic second order symmetric integrator with different step sizes [17]. The introduction of symmetries into these methods simplifies the order conditions and reduces the number of unknowns. Several authors have worked in the search of the coefficients of these type of methods: the best method of order 8 has 17 stages [24], methods of order 8 and 15 stages were given in [29, 39, 40], 10-order methods of 31, 33 and 35 stages have been also found [24, 34]. In this work some techniques that we have built to obtain 10-order symmetric composition methods of symmetric integrators of s = 31 stages (16 order conditions) are explored. Given some starting coefficients that satisfy the simplest five order conditions, the process followed to obtain the coefficients that satisfy the sixteen order conditions is provided.