In this book, we provide a comprehensive introduction to the most recentadvances in the application of machinelearning methods in quantum sciences. Wecover the use of deep learning and kernel methods in supervised, u...
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We consider learning of fundamental properties of communities in large noisy networks, in the prototypical situation where the nodes or users are split into two classes according to a binary property, e.g., according ...
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The potential of conjugated polymers to compete with inorganic materials in the field of semiconductor is conditional on fine-tuning of the charge carriers mobility. The latter is closely related to the material morph...
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The potential of conjugated polymers to compete with inorganic materials in the field of semiconductor is conditional on fine-tuning of the charge carriers mobility. The latter is closely related to the material morphology, and various studies have shown that the bottleneck for charge transport is the connectivity between well-ordered crystallites, with a high degree of π−π stacking, dispersed into a disordered matrix. However, at this time there is a lack of theoretical descriptions accounting for this link between morphology and mobility, hindering the development of systematic material designs. Here we propose a computational model to predict charge carriers mobility in conducting polymer PEDOT depending on the physicochemical properties of the system. We start by calculating the morphology using molecular dynamics simulations. Based on the calculated morphology we perform quantum mechanical calculation of the transfer integrals between states in polymer chains and calculate corresponding hopping rates using the Miller-Abrahams formalism. We then construct a transport resistive network, calculate the mobility using a mean-field approach, and analyze the calculated mobility in terms of transfer integrals distributions and percolation thresholds. Our results provide theoretical support for the recent study [Noriega et al., Nat. Mater. 12, 1038 (2013)] explaining why the mobility in polymers rapidly increases as the chain length is increased and then saturates for sufficiently long chains. Our study also provides the answer to the long-standing question whether the enhancement of the crystallinity is the key to designing high-mobility polymers. We demonstrate, that it is the effective π−π stacking, not the long-range order that is essential for the material design for the enhanced electrical performance. This generic model can compare the mobility of a polymer thin film with different solvent contents, solvent additives, dopant species or polymer characteristics, pr
For a binomial random variable ξ with parameters n and b/n, it is well known that the median equals b when b is an integer. In 1968, Jogdeo and Samuels studied the behaviour of the relative difference between P(ξ = ...
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