Electrochemical Control of Charge Current Flow in Nanoporous Graphene

During the last decade, on-surface fabricated graphene nanoribbons (GNRs) have gathered enormous attention due to their semiconducting π-conjugated nature and atomically precise structure. A significant breakthrough is the recent fabrication of nanoporous graphene (NPG) as a 2D array of laterally bonded GNRs. This covalent integration of GNRs could enable complex electronic functionality at the nanoscale; however, for that, it is crucial to externally control the electronic coupling between GNRs within NPGs, which, to date, has not been possible. Using quantum chemical calculations and large-scale transport simulations, this study demonstrates that such control is enabled in a newly designed quinone-NPG (q-NPG) thanks to its GNRs inter-connections based on electroactive para-benzoquinone units. As a result, the spatial distribution of injected currents in q-NPG may be tuned, with sub-nanometer precision, via the application of external electrostatic gates and electrochemical means. These results thus provide a fundamental strategy to design organic nanodevices with built-in externally tunable electronics and spintronics, which is key for future applications such as bio-chemical nanosensing and carbon nanoelectronics.     

Imaging the Electric‐Field Distribution in Organic Devices by Confocal Electroreflectance Microscopy

Space resolved Stark spectroscopy is introduced as a non invasive optical technique for imaging electric field distribution in organic semiconductors. Stark spectroscopy relies on the electric field induced change in the absorption/reflection. It is shown that local monitoring of Stark shift with confocal spatial resolution provides quantitative information on the strength of the local field as well as charge distribution within the transport channel.     

Fabrication of gold tips by chemical etching in aqua regia

We present a method to produce sharp gold tips for applications in apertureless near-field optical microscopy and spectroscopy. Thin gold wires are tapered by chemical etching in aqua regia, covered by an isooctane protective layer. Tips with apical radii of curvature of <50 nm are obtained with a 40% yield. The tip performances have been checked by shear-force imaging of amyloid fibrils samples and compared to optical fiber probes. The analysis of the tip morphology, carried out by scanning electron microscopy, shows the existence of two different etching processes occurring in bulk and at the liquid-liquid interface. A simple analytical model is presented to describe the dynamics of the tip formation at the liquid-liquid meniscus interface that fits remarkably well the experimental results in terms of tip shape and length.     

A Decision Procedure for a Sublanguage of Set Theory Involving Monotone, Additive, and Multiplicative Functions

MLSS is a decidable sublanguage of set theory involving the predicates membership, set equality, set inclusion, and the operators union, intersection, set difference, and singleton.In this paper we extend MLSS with constructs for expressing monotonicity, additivity, and multiplicativity properties of set-to-set functions. We prove that the resulting language is decidable by reducing the problem of determining the satisfiability of its sentences to the problem of determining the satisfiability of sentences of MLSS.     

A Decision Procedure for a Sublanguage of Set Theory Involving Monotone, Additive, and Multiplicative Functions, I: The Two-Level Case

2LS is a decidable many-sorted set-theoretic language involving one sort for elements and one sort for sets of elements. In this paper we extend 2LS with constructs for expressing monotonicity, additivity, and multiplicativity properties of set-to-set functions. We call the resulting language 2LSmf. We prove that 2LSmf is decidable by reducing the problem of determining the satisfiability of its sentences to the problem of determining the satisfiability of sentences of 2LS. Furthermore, we prove that the language 2LSmf is stably infinite with respect to the sort of elements. Therefore, by using a many-sorted version of the Nelson–Oppen combination method, 2LSmf can be combined with other languages modeling the sort of elements.     

A Tableau-Based Decision Procedure for a Fragment of Set Theory with Iterated Membership

MLSS is a decidable fragment of set theory involving the predicates membership and set equality and the operators union, intersection, set difference, and singleton. In this paper we extend MLSS with the iterated membership predicate, that is, with a predicate denoting the transitive closure of the membership relation. We call the resulting language MLSS⁺. We prove that MLSS⁺ is decidable by providing a decision procedure for it based on Smullyan semantic tableaux. As an application of our results, we show how our decision procedure can be used as a black box in order to allow an interactive theorem prover to verify some basic properties of the ordinal numbers.This research was in part supported by murst grant prot. 2001017741 under the Italian project Ragionamento su aggregati e numeri a supporto della programmazione e relative verifiche.