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Register a new userA Grid-free Approach for Simulating Sweep and Cyclic Voltammetry
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We present a new computational approach to simulate linear sweep and cyclic voltammetry experiments that does not require a discretized grid in space to quantify diffusion. By using a Greens function solution coupled to a standard implicit ordinary differential equation solver, we are able to simulate current and redox species concentrations using only a small grid in time. As a result, where benchmarking is possible, we find that the current method is faster (and quantitatively identical) to established techniques. The present algorithm should help open the door to studying adsorption effects in inner sphere electrochemistry.
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Linear sweep and cyclic voltammetry techniques are important tools for electrochemists and have a variety of applications in engineering. Voltammetry has classically been treated with the Randles-Sevcik equation, which assumes an electroneutral supported electrolyte. In this paper, we provide a comprehensive mathematical theory of voltammetry in electrochemical cells with unsupported electrolytes and for other situations where diffuse charge effects play a role, and present analytical and simulated solutions of the time-dependent Poisson-Nernst-Planck (PNP) equations with generalized Frumkin-Butler-Volmer (FBV) boundary conditions for a 1:1 electrolyte and a simple reaction. Using these solutions, we construct theoretical and simulated currentvoltage curves for liquid and solid thin films, membranes with fixed background charge, and cells with blocking electrodes. The full range of dimensionless parameters is considered, including the dimensionless Debye screening length (scaled to the electrode separation), Damkohler number (ratio of characteristic diffusion and reaction times) and dimensionless sweep rate (scaled to the thermal voltage per diffusion time). The analysis focuses on the coupling of Faradaic reactions and diffuse charge dynamics, although capacitive charging of the electrical double layers (EDL) is also studied, for early time transients at reactive electrodes and for non-reactive blocking electrodes. Our work highlights cases where diffuse charge effects are important in the context of voltammetry, and illustrates which regimes can be approximated using simple analytical expressions and which require more careful consideration.
Discovery of electrocatalytic materials for high-performance energy conversion and storage applications relies on the adequate characterization of their intrinsic activity, which is currently hindered by the dearth of a protocol for consistent and precise determination of double layer capacitance (CDL). Herein, we propose a seven-step method that aims to determine CDL reliably by scan rate-dependent cyclic voltammetry. The method considers three aspects that strongly influence the outcome of the analysis: measurement settings, data collection, and data processing. To illustrate the proposed method, two systems were studied: a resistor-capacitor electric circuit and a glassy carbon disk in an electrochemical cell. With these studies it is demonstrated that when any of the mentioned aspects of the procedure are neglected, substantial deviations of the results are observed with misestimations as large as 61% in the case of the investigated electrochemical system. Moreover, we propose allometric regression as a more suitable model than linear regression for the determination of CDL for both the ideal and the non-ideal systems investigated. We stress the importance of assessing the accuracy of not only highly specialized electrochemical methods, but also of those that are well-known and commonly used as it is the case of the voltammetric methods. The methodology proposed herein is not limited to the determination of CDL, but can be effectively applied to any other voltammetry-based analysis that aims to deliver quantitative results.
We describe a simplified approach to simulating Raman spectra using ab initio molecular dynamics (AIMD) calculations. Our protocol relies on on-the-fly calculations of approximate molecular polarizabilities using a sum over orbitals (as opposed to states) method.
Approximation of a tensor network by approximating (e.g., factorizing) one or more of its constituent tensors can be improved by canceling the leading-order error due to the constituents approximation. The utility of such robust approximation is demonstrated for robust canonical polyadic (CP) approximation of a (density-fitting) factorized 2-particle Coulomb interaction tensor. The resulting algebraic (grid-free) approximation for the Coulomb tensor, closely related to the factorization appearing in pseudospectral and tensor hypercontraction approaches, is efficient and accurate, with significantly reduced rank compared to the naive (non-robust) approximation. Application of the robust approximation to the particle-particle ladder term in the coupled-cluster singles and doubles reduces the size complexity from $mathcal{O}(N^6)$ to $mathcal{O}(N^5)$ with robustness ensuring negligible errors in chemically-relevant energy differences using CP ranks approximately equal to the size of the density-fitting basis.
The next generation of High Energy Physics experiments requires a GRID approach to a distributed computing system and the associated data management: the key concept is the Virtual Organisation (VO), a group of geographycally distributed users with a common goal and the will to share their resources. A similar approach is being applied to a group of Hospitals which joined the GPCALMA project (Grid Platform for Computer Assisted Library for MAmmography), which will allow common screening programs for early diagnosis of breast and, in the future, lung cancer. HEP techniques come into play in writing the application code, which makes use of neural networks for the image analysis and shows performances similar to radiologists in the diagnosis. GRID technologies will allow remote image analysis and interactive online diagnosis, with a relevant reduction of the delays presently associated to screening programs.
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