Maskless Preparation of Spatially-Resolved Plasmonic Nanoparticles on Polydimethylsiloxane via In Situ Fluoride-Assisted Synthesis

Here, a fluoride-assisted route for the controlled in-situ synthesis of metal nanoparticles (NPs) (i.e., AgNPs, AuNPs) on polydimethylsiloxane (PDMS) is reported. The size and coverage of the NPs on the PDMS surface are modulated with time and over space during the synthetic process, leveraging the improved yield (10×) and faster kinetics (100×) of NP formation in the presence of F⁻ ions, compared to fluoride-free approaches. This enables the maskless preparation of both linear and step gradients and patterns of NPs in 1D and 2D on the PDMS surface. As an application in flexible plasmonics/photonics, continuous and step-wise spatial modulations of the plasmonic features of PDMS slabs with 1D and 2D AgNP gradients on the surface are demonstrated. An excellent spatially resolved tuning of key optical parameters, namely, optical density from zero to 5 and extinction ratio up to 100 dB, is achieved with AgNP gradients prepared in AgF solution for 12 minutes; the performance are comparable to those of commercial dielectric/interference filters. When used as a rejection filter in optical fluorescence microscopy, the AgNP-PDMS slabs are able to reject the excitation laser at 405 nm and retain the green fluorescence of microbeads (100 µm) used as test cases.     

Integral Representations of the Large and Little Schröder Numbers

In the paper, the authors establish several integral representations for the generating functions of the large and little Schröder numbers and for the large and little Schröder numbers.     

Mesoscopic Modeling of Capillarity-Induced Two-Phase Transport in a Microfluidic Porous Structure

Mesoscopic modeling at the pore scale offers great promise in exploring the underlying structure transport performance of flow through porous media. The present work studies the fluid flow subjected to capillarity-induced resonance in porous media characterized by different porous structure and wettability. The effects of porosity and wettability on the displacement behavior of the fluid flow through porous media are discussed. The results are presented in the form of temporal evolution of percentage saturation and displacement of the fluid front through porous media. The present study reveals that the vibration in the form of acoustic excitation could be significant in the mobilization of fluid through the porous media. The dependence of displacement of the fluid on physicochemical parameters like wettability of the surface, frequency along with the porosity is analyzed. It was observed that the mean displacement of the fluid is more in the case of invading fluid with wetting phase where the driving force strength is not so dominant.     

Three-term polynomial progressions in subsets of finite fields

We prove that the group of diffeomorphisms of the interval [0, 1] contains surface groups whose action on (0, 1) has no global fix point and such that only countably many points of the interval (0, 1) have non-trivial stabiliser.     

Fatigue life enhancement by irradiation of 12Cr1MoV steel with a Zr<Superscript>+</Superscript> ion beam. Mesoscale deformation and fracture

The structure and properties of 12Cr1MoV steel irradiated with a zirconium ion beam were studied by optical microscopy, scanning electron microscopy, and micro- and nanoindentation. It is shown that the modification covers the entire cross-section of the irradiated specimens to a depth of 1 mm. The data on irradiation-induced structural changes are used to interpret the changes in mechanical properties of the irradiated specimens under static and cyclic loading. Particular attention is given to analysis of strain estimation by the digital image correlation method.