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Karibayev M, Kalybekkyzy S, Wang Y, Mentbayeva A. Molecular Modeling in Anion Exchange Membrane Research: A Brief Review of Recent Applications. Molecules 2022; 27:3574. [PMID: 35684512 PMCID: PMC9182285 DOI: 10.3390/molecules27113574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2022] [Revised: 05/24/2022] [Accepted: 05/30/2022] [Indexed: 12/04/2022] Open
Abstract
Anion Exchange Membrane (AEM) fuel cells have attracted growing interest, due to their encouraging advantages, including high power density and relatively low cost. AEM is a polymer matrix, which conducts hydroxide (OH-) ions, prevents physical contact of electrodes, and has positively charged head groups (mainly quaternary ammonium (QA) groups), covalently bound to the polymer backbone. The chemical instability of the quaternary ammonium (QA)-based head groups, at alkaline pH and elevated temperature, is a significant threshold in AEMFC technology. This review work aims to introduce recent studies on the chemical stability of various QA-based head groups and transportation of OH- ions in AEMFC, via modeling and simulation techniques, at different scales. It starts by introducing the fundamental theories behind AEM-based fuel-cell technology. In the main body of this review, we present selected computational studies that deal with the effects of various parameters on AEMs, via a variety of multi-length and multi-time-scale modeling and simulation methods. Such methods include electronic structure calculations via the quantum Density Functional Theory (DFT), ab initio, classical all-atom Molecular Dynamics (MD) simulations, and coarse-grained MD simulations. The explored processing and structural parameters include temperature, hydration levels, several QA-based head groups, various types of QA-based head groups and backbones, etc. Nowadays, many methods and software packages for molecular and materials modeling are available. Applications of such methods may help to understand the transportation mechanisms of OH- ions, the chemical stability of functional head groups, and many other relevant properties, leading to a performance-based molecular and structure design as well as, ultimately, improved AEM-based fuel cell performances. This contribution aims to introduce those molecular modeling methods and their recent applications to the AEM-based fuel cells research community.
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Affiliation(s)
- Mirat Karibayev
- Department of Chemical & Materials Engineering, School of Engineering and Digital Sciences, Nazarbayev University, Nur-Sultan 010000, Kazakhstan;
| | - Sandugash Kalybekkyzy
- Laboratory of Advanced Materials and Systems for Energy Storage, Center for Energy and Advanced Materials Science, National Laboratory Astana, Nazarbayev University, Nur-Sultan 010000, Kazakhstan;
| | - Yanwei Wang
- Department of Chemical & Materials Engineering, School of Engineering and Digital Sciences, Nazarbayev University, Nur-Sultan 010000, Kazakhstan;
- Laboratory of Computational Materials Science for Energy Applications, Center for Energy and Advanced Materials Science, National Laboratory Astana, Nur-Sultan 010000, Kazakhstan
| | - Almagul Mentbayeva
- Department of Chemical & Materials Engineering, School of Engineering and Digital Sciences, Nazarbayev University, Nur-Sultan 010000, Kazakhstan;
- Laboratory of Advanced Materials and Systems for Energy Storage, Center for Energy and Advanced Materials Science, National Laboratory Astana, Nazarbayev University, Nur-Sultan 010000, Kazakhstan;
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Villani M, Albareda G, Destefani C, Cartoixà X, Oriols X. Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with Non-Commuting Energy and Momentum Operators. ENTROPY 2021; 23:e23040408. [PMID: 33808161 PMCID: PMC8065387 DOI: 10.3390/e23040408] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/04/2021] [Revised: 03/19/2021] [Accepted: 03/24/2021] [Indexed: 11/16/2022]
Abstract
Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by non-simulated degrees of freedom on the simulated ones as a transition between single-particle pure states. First, we show that Bohmian conditional wave functions (BCWFs) allow for a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of single-particle time-dependent pure states, either under Markovian or non-Markovian conditions. Second, we discuss the practical application of the method for modeling light–matter interaction phenomena in a resonant tunneling device, where a single photon interacts with a single electron. Third, we emphasize the importance of interpreting such a scattering mechanism as a transition between initial and final single-particle BCWF with well-defined central energies (rather than with well-defined central momenta).
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Affiliation(s)
- Matteo Villani
- Department of Electronic Engineering, Universitat Autònoma de Barcelona, Campus de la UAB, 08193 Bellaterra, Barcelona, Spain; (M.V.); (C.D.); (X.C.)
| | - Guillermo Albareda
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany;
- Institute of Theoretical and Computational Chemistry, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
| | - Carlos Destefani
- Department of Electronic Engineering, Universitat Autònoma de Barcelona, Campus de la UAB, 08193 Bellaterra, Barcelona, Spain; (M.V.); (C.D.); (X.C.)
| | - Xavier Cartoixà
- Department of Electronic Engineering, Universitat Autònoma de Barcelona, Campus de la UAB, 08193 Bellaterra, Barcelona, Spain; (M.V.); (C.D.); (X.C.)
| | - Xavier Oriols
- Department of Electronic Engineering, Universitat Autònoma de Barcelona, Campus de la UAB, 08193 Bellaterra, Barcelona, Spain; (M.V.); (C.D.); (X.C.)
- Correspondence:
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Plehn T, May V. Charge and energy migration in molecular clusters: A stochastic Schrödinger equation approach. J Chem Phys 2017; 146:034107. [PMID: 28109221 DOI: 10.1063/1.4973886] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The performance of stochastic Schrödinger equations for simulating dynamic phenomena in large scale open quantum systems is studied. Going beyond small system sizes, commonly used master equation approaches become inadequate. In this regime, wave function based methods profit from their inherent scaling benefit and present a promising tool to study, for example, exciton and charge carrier dynamics in huge and complex molecular structures. In the first part of this work, a strict analytic derivation is presented. It starts with the finite temperature reduced density operator expanded in coherent reservoir states and ends up with two linear stochastic Schrödinger equations. Both equations are valid in the weak and intermediate coupling limit and can be properly related to two existing approaches in literature. In the second part, we focus on the numerical solution of these equations. The main issue is the missing norm conservation of the wave function propagation which may lead to numerical discrepancies. To illustrate this, we simulate the exciton dynamics in the Fenna-Matthews-Olson complex in direct comparison with the data from literature. Subsequently a strategy for the proper computational handling of the linear stochastic Schrödinger equation is exposed particularly with regard to large systems. Here, we study charge carrier transfer kinetics in realistic hybrid organic/inorganic para-sexiphenyl/ZnO systems of different extension.
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Affiliation(s)
- Thomas Plehn
- Institute of Physics, Humboldt-University at Berlin, Newtonstraße 15, D-12489 Berlin, Germany
| | - Volkhard May
- Institute of Physics, Humboldt-University at Berlin, Newtonstraße 15, D-12489 Berlin, Germany
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Ke Y, Zhao Y. Hierarchy of forward-backward stochastic Schrödinger equation. J Chem Phys 2016; 145:024101. [DOI: 10.1063/1.4955107] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Affiliation(s)
- Yaling Ke
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People’s Republic of China
| | - Yi Zhao
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People’s Republic of China
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Wang L, Long R, Prezhdo OV. Time-Domain Ab Initio Modeling of Photoinduced Dynamics at Nanoscale Interfaces. Annu Rev Phys Chem 2015; 66:549-79. [DOI: 10.1146/annurev-physchem-040214-121359] [Citation(s) in RCA: 107] [Impact Index Per Article: 11.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Linjun Wang
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482;
- Department of Chemistry, University of Rochester, Rochester, New York 14627
| | - Run Long
- School of Physics and Complex & Adaptive Systems Laboratory, University College Dublin, Belfield, Dublin 4, Ireland
| | - Oleg V. Prezhdo
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482;
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Jing J, Yu T. Non-Markovian relaxation of a three-level system: quantum trajectory approach. PHYSICAL REVIEW LETTERS 2010; 105:240403. [PMID: 21231512 DOI: 10.1103/physrevlett.105.240403] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2010] [Indexed: 05/30/2023]
Abstract
The non-Markovian dynamics of a three-level quantum system coupled to a bosonic environment is a difficult problem due to the lack of an exact dynamic equation such as a master equation. We present for the first time an exact quantum trajectory approach to a dissipative three-level model. We have established a convolutionless stochastic Schrödinger equation called the time-local quantum state diffusion (QSD) equation without any approximations, in particular, without Markov approximation. Our exact time-local QSD equation opens a new avenue for exploring quantum dynamics for a higher dimensional quantum system coupled to a non-Markovian environment.
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Affiliation(s)
- Jun Jing
- Center for Controlled Quantum Systems and Department of Physics and Engineering Physics, Stevens Institute of Technology, Hoboken, New Jersey 07030, USA.
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Alonso D, de Vega I. Multiple-time correlation functions for non-markovian interaction: beyond the quantum regression theorem. PHYSICAL REVIEW LETTERS 2005; 94:200403. [PMID: 16090229 DOI: 10.1103/physrevlett.94.200403] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2004] [Indexed: 05/03/2023]
Abstract
We derive the dynamical equation of the reduced propagator, an object that evolves state vectors of the system conditioned to the dynamics of its environment, which is not necessarily in the vacuum state at the initial time. Such a reduced propagator is essential to obtain multiple-time correlation functions (MTCFs). We also study the evolution of MTCFs within the weak-coupling limit and show that the quantum regression theorem is, in general, not satisfied. We illustrate the theory in two different cases: first, solving an exact model, and, second, presenting the results of the numerical integration for a system coupled with a thermal environment through a nondiagonal interaction.
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Affiliation(s)
- Daniel Alonso
- Departamento de Física Fundamental y Experimental, Electrónica y Sistemas, Universidad de La Laguna, La Laguna 38203, Tenerife, Spain
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de Vega I, Alonso D, Gaspard P, Strunz WT. Non-Markovian stochastic Schrödinger equations in different temperature regimes: A study of the spin-boson model. J Chem Phys 2005; 122:124106. [PMID: 15836368 DOI: 10.1063/1.1867377] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Stochastic Schrodinger equations are used to describe the dynamics of a quantum open system in contact with a large environment, as an alternative to the commonly used master equations. We present a study of the two main types of non-Markovian stochastic Schrodinger equations, linear and nonlinear ones. We compare them both analytically and numerically, the latter for the case of a spin-boson model. We show in this paper that two linear stochastic Schrodinger equations, derived from different perspectives by Diosi, Gisin, and Strunz [Phys. Rev. A 58, 1699 (1998)], and Gaspard and Nagaoka [J. Chem. Phys. 13, 5676 (1999)], respectively, are equivalent in the relevant order of perturbation theory. Nonlinear stochastic Schrodinger equations are in principle more efficient than linear ones, as they determine solutions with a higher weight in the ensemble average which recovers the reduced density matrix of the quantum open system. However, it will be shown in this paper that for the case of a spin-boson system and weak coupling, this improvement does only occur in the case of a bath at high temperature. For low temperatures, the sampling of realizations of the nonlinear equation is practically equivalent to the sampling of the linear ones. We study further this result by analyzing, for both temperature regimes, the driving noise of the linear equations in comparison to that of the nonlinear equations.
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Affiliation(s)
- Inés de Vega
- Departamento de Física Fundamental II, Universidad de La Laguna, La Laguna 38203, Tenerife, Spain
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Käb G. Statistical Mechanics of Mean Field Ehrenfest Quantum/Classical Molecular Dynamics: The Damped Harmonic Oscillator. J Phys Chem A 2004. [DOI: 10.1021/jp048891a] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Günter Käb
- Max-Planck-Institut für Biophysikalische Chemie, Am Fassberg 11, D-37077 Göttingen, Germany
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Esposito M, Gaspard P. Quantum master equation for a system influencing its environment. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:066112. [PMID: 14754274 DOI: 10.1103/physreve.68.066112] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2003] [Indexed: 05/24/2023]
Abstract
A perturbative quantum master equation is derived for a system interacting with its environment, which is more general than the ones derived before. Our master equation takes into account the effect of the energy exchanges between the system and the environment and the conservation of energy in the finite total system. This master equation describes relaxation mechanisms in isolated nanoscopic quantum systems. In its most general form, this equation is non-Markovian and a Markovian version of it rules the long-time relaxation. We show that our equation reduces to the Redfield equation in the limit where the energy of the system does not affect the density of state of its environment. This master equation and the Redfield one are applied to a spin-environment model defined in terms of random matrices and compared with the solutions of the exact von Neumann equation. The comparison proves the necessity to allow energy exchange between the subsystem and the environment in order to correctly describe the relaxation in an isolated nanoscopic total system.
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Affiliation(s)
- Massimiliano Esposito
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium
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Kondov I, Kleinekathöfer U, Schreiber M. Stochastic unraveling of Redfield master equations and its application to electron transfer problems. J Chem Phys 2003. [DOI: 10.1063/1.1605095] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
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