Abstract: The original motivation to study Generalized Möbius-Listing GML surfaces and bodies was the observation that the solution of boundary value problems greatly depends on the domains. Since around 2010 GML’s were merged with (continuous) Gielis Transformations, which provide a unifying description of geometrical shapes, as a generalization of the Pythagorean Theorem. The resulting geometrical objects can be used for modeling a wide range of natural shapes and phenomena. The cutting of GML bodies and surfaces, with the Möbius strip as one special case, is related to the field of knots and links, and classifications were obtained for GML with cross sectional symmetry of 2, 3, 4, 5 and 6. The general case of cutting GML bodies and surfaces, in particular the number of ways of cutting, could be solved by reducing the 3D problem to planar geometry. This also unveiled a range of connections with topology, combinatorics, elasticity theory and theoretical physics.

Abstract: Films of close-packed Au nanoparticles are coupled electrodynamically through their collective plasmon resonances. This collective optical response results in enhanced light–matter interactions, which can be exploited in various applications. Here, we demonstrate their application in sensing volatile organic compounds, using methanol as a test case. Ordered films over several cm2 were obtained by interfacial self-assembly of colloidal Au nanoparticles (∼10 nm diameter) through controlled evaporation of the solvent. Even though isolated nanoparticles of this size are inherently nonscattering, when arranged in a close-packed film the plasmonic coupling results in a strong reflectance and absorbance. The in situ tracking of vapor phase methanol concentration through UV–vis transmission measurements of the nanoparticle film is first demonstrated. Next, in situ ellipsometry of the self-assembled films in the Kretschmann (also known as ATR) configuration is shown to yield enhanced sensitivity, especially with phase difference measurements, Δ. Our study shows the excellent agreement between theoretical models of the spectral response of self-assembled films with experimental in situ sensing experiments. At the same time, the theoretical framework provides the basis for the interpretation of the various observed experimental trends. Combining periodic nanoparticle films with ellipsometry in the Kretschmann configuration is a promising strategy toward highly sensitive and selective plasmonic thin-film devices based on colloidal fabrication methods for volatile organic compound (VOC) sensing applications.