Literature review on superhydrophobic self‐cleaning surfaces produced by electrospinning

Self‐cleaning surface is potentially a very useful addition for many commercial products due to economic, aesthetic, and environmental reasons. Super‐hydrophobic self‐cleaning, also called Lotus effect, utilizes right combination of surface chemistry and roughness to force water droplets to form high contact angle on a surface, easily roll off a surface and pick up dirt particles on its way. Electrospinning is a promising technique for creation of superhydrophobic self‐cleaning surfaces owing to a wide set of parameters that allow effectively controlling roughness of resulted webs. This article gives a brief introduction to the theory of super‐hydrophobic self‐cleaning and basic principles of the electrospinning process and reviews the scientific literature where electrospinning was used to create superhydrophobic surfaces. The article reviewed are categorized into several groups and their results are compared in terms of superhydrophobic properties. Several issues with current state of the art and highlights of important areas for future research are discussed in the conclusion. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Online Prediction with History-Dependent Experts: The General Case

We study the problem of prediction of binary sequences with expert advice in the online setting, which is a classic example of online machine learning. We interpret the binary sequence as the price history of a stock, and view the predictor as an investor, which converts the problem into a stock prediction problem. In this framework, an investor, who predicts the daily movements of a stock, and an adversarial market, who controls the stock, play against each other over N turns. The investor combines the predictions of $n\ge 2$ experts in order to make a decision about how much to invest at each turn, and aims to minimize their regret with respect to the best-performing expert at the end of the game. We consider the problem with history-dependent experts, in which each expert uses the previous d days of history of the market in making their predictions. We prove that the value function for this game, rescaled appropriately, converges as $N\to \mathrm{\infty }$ at a rate of $O\left(N^{-1/6}\right)$ to the viscosity solution of a nonlinear degenerate elliptic PDE, which can be understood as the Hamilton-Jacobi-Issacs equation for the two-person game. As a result, we are able to deduce asymptotically optimal strategies for the investor. Our results extend those established by the first author and R.V. Kohn [14] for $n=2$ experts and $d\le 4$ days of history. © 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.     

Pd‐Catalysed Direct Arylation Polymerisation for Synthesis of Low‐Bandgap Conjugated Polymers and Photovoltaic Performance

Low‐bandgap conjugated copolymers based on a donor–acceptor structure have been synthesised via palladium‐complex catalysed direct arylation polymerisation. Initially, we report the optimisation of the synthesis of poly(cyclopentadithiophene‐alt‐benzothiadiazole) (PCPDTBT) formed between cyclopentadithiophene and dibromobenzothiadiazole units. The polymerisation condition has been optimised, which affords high‐molecular‐weight polymers of up to M _n = 70 k using N‐methylpyrrolidone as a solvent. The polymers are used to fabricate organic photovoltaic devices and the best performing PCPDTBT device exhibits a moderate improvement over devices fabricated using the related polymer via Suzuki coupling. Similar polymerisation conditions have also been applied for other monomer units.