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BatCAT project deliverable 2.1: Simulation campaign plan

BOCCARDO, GIANLUCA; Horsch, Martin Thomas; Petit, Martin; Montero-Chacón, Francisco; Seaton, Michael Andrew; Valseth, Eirik; Zausch, Jochen; Castelli, Ivano Eligio; Linhart, Andreas

Abstract

This document constitutes the first step in the activity of the multiphysics modelling and simulation workpackage (WP2) and delivers a plan of the simulations that are to be performed throughout the duration of the project. These models are the ones that have been identified to be the most important in the representation of the whole process regarding both the manufacturing step and the operation (i.e. charge/discharge) phase of the two use cases considered: Vanadium redox-flow batteries (VRFB) and Lithium (and Sodium)-ion batteries. The necessary groundwork for the preparation of this simulation campaign plan is found in the finalized deliverables D6.1 regarding the use-case requirements, and D4.1 regarding the data and infrastructure requirements. The first crucial step was to expand and detail the work which was present in a seminal form in D6.1 on the identification of the most important phases of these processes and the more important quantities to be considered: Both in terms of them being important metrics for the evaluation of the techno-economical performance of a process, or them being information and data which have been found to have the greater impact on the mentioned metrics, and as such would constitute prime candidates for parameter optimization processes. The provided schemas have been used by each unit participating in WP2 to identify the relevant physics-based models to be employed (and possibly develop) and will serve as a guide for the next step of the modelling activity in the BatCAT project, the construction of full simulation workflows. This objective (itself connected to the necessity of building parallel digital twins of the processes in WP5) will be attained by structuring a graph of the relevant process steps (and the connected physics-based model) composed by the presently presented planned models, together with the necessary mapping tools needed to relay information from one model to another in the appropriate form. As such, this work will serve as the basis for the preparation of the two workflows (for each use case) to be delivered by M27 in the finalized integrated multiphysics modelling workflows in D2.3. In the core of the present D2.1 deliverable, contained in Section 2 of this document, each identified model can be found, described first in their purposes and underlying methodology, and secondly from a more purely technical point of view for software deployment purposes. This list of scientific models, together with their implementation details, constitutes the current simulation campaign plan for BatCAT.

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101137725/BatCAT/WP2/D2.1 D2.1: Simulation Campaign Plan Grant agreement number: 101137725 Project acronym: BatCAT Project title: Battery Cell Assembly Twin Project website: http://batcat.info/ Project start date: 01.01.2024 Project duration: 42 months Call topic: HORIZON-CL5-2023-D2-01-03 Deliverable type1: Report (R) Related work package: WP2 Due date: 31.12.2024 Actual submission date: 31.12.2024 Responsible beneficiary: POLITO Dissemination level2: Public (PU) Version: D2.1 v1.0 (31.12.2024) Abstract: This deliverable outlines the simulation campaign plan for WP2, focusing on key physics-based models for manufacturing and operation processes of vanadium redox-flow and Li/Na-ion batteries. It identifies critical process steps, and the more relevant physical quantities. Process maps and technical model descriptions are provided to define interconnections and ensure eventual compatibility between connected models. These elements will guide the development of complete workflows, linking simulations of individual process steps into an integrated framework to represent manufacturing and operation phases for the two battery use cases. 1 Deliverable type: R = Report, P = Prototype, D = Demonstrator, O = Other. 2 Dissemination level: PU = Public, SEN = Sensitive. Ref. Ares(2024)9288277 - 31/12/2024 Public Version v1.0 Page 2 of 61 Author list Beneficiary Name Contact e-mail POLITO Gianluca Boccardo [email protected] NMBU Martin Thomas Horsch [email protected] IFPEN Martin Petit [email protected] LOYOLA Francisco Montero-Chacón [email protected] UKRI Michael Seaton [email protected] SIMULA Eirik Valseth [email protected] ITWM Jochen Zausch [email protected] DTU Ivano Eligio Castelli [email protected] VANEVO Andreas Linhart [email protected] Reviewers List Beneficiary Name Contact e-mail NMBU Martin Thomas Horsch [email protected] Document history Version Date Reason/comment Revised by 0.1 16.12.2024 Initial draft Gianluca Boccardo 0.2 31.12.2024 Pre-submission final draft Gianluca Boccardo (and see list of authors for contributions) 1.0 31.12.2024 Submission-ready format L. Eduardo Cordova-Lopez Disclaimer Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Climate, Infrastructure and Environment Executive Agency (CINEA). Neither the EU nor the CINEA can be held responsible for them. Abbreviations and acronyms CGA Consortial general assembly CINEA European Climate, Infrastructure and Environment Executive Agency EAB external advisory board KER key exploitable resource NDA non-disclosure agreement PMB project management board PMO project management officer TMWG technical management working group BatCAT has received funding from the European Union’s Horizon Europe research and innovation programme under grant agreement no. 101137725. Public Version v1.0 Page 3 of 61 Contents 1. Executive summary...................................................................................................................................... 4 Description of the deliverable content and objectives ................................................................................... 4 2. List of modelling tools ................................................................................................................................. 7 Li-ion electrode-scale charge-discharge simulations ............................................................................... 8 DFT simulations of SEI formation in Li/Na-ion batteries .......................................................................... 14 Continuum modelling of Li/Na-ion ............................................................................................................. 20 Electrode-scale charge-discharge simulations of Lithium-Ion cells ...................................................... 28 Lattice-particle model for multiphysical simulation of electrodes ......................................................... 35 Molecular modelling and simulation of redox-flow electrolyte properties ............................................ 41 Multiphysics Modeling of Redox Flow Batteries ....................................................................................... 45 Density Functional Theory (DFT) modelling of carbon felt electrode materials for vanadium redox flow batteries ...................................................................................................................................... 49 Redox flow battery pore-scale (mesoscopic) simulations ...................................................................... 54 3. Conclusions ................................................................................................................................................ 61 Public Version v1.0 Page 4 of 61 1. Executive summary Description of the deliverable content and objectives This document constitutes the first step in the activity of the multiphysics modelling and simulation workpackage (WP2) and delivers a plan of the simulations that are to be performed throughout the duration of the project. These models are the ones that have been identified to be the most important in the representation of the whole process regarding both the manufacturing step and the operation (i.e. charge/discharge) phase of the two use cases considered: Vanadium redox-flow batteries (VRFB) and Lithium (and Sodium)-ion batteries. The necessary groundwork for the preparation of this simulation campaign plan is found in the finalized deliverables D6.1 regarding the use-case requirements, and D4.1 regarding the data and infrastructure requirements. The first crucial step was to expand and detail the work which was present in a seminal form in D6.1 on the identification of the most important phases of these processes and the more important quantities to be considered: both in terms of them being important metrics for the evaluation of the techno-economical performance of a process, or them being information and data which have been found to have the greater impact on the mentioned metrics, and as such would constitute prime candidates for parameter optimization processes. The updated schematic overview for both these processes are found in the following two pages. The provided schemas have been used by each unit participating in WP2 to identify the relevant physics-based models to be employed (and possibly develop) and will serve as a guide for the next step of the modelling activity in the BatCAT project, the construction of full simulation workflows. This objective (itself connected to the necessity of building parallel digital twins of the processes in WP5) will be attained by structuring a graph of the relevant process steps (and the connected physics-based model) composed by the presently presented planned models, together with the necessary mapping tools needed to relay information from one model to another in the appropriate form. As such, this work will serve as the basis for the preparation of the two workflows (for each use case) to be delivered by M27 in the finalized integrated multiphysics modelling workflows in D2.3. In the core of the present D2.1 deliverable, contained in Section 2 of this document, each identified model can be found, described first in their purposes and underlying methodology, and secondly from a more purely technical point of view for software deployment purposes. This list of scientific models, together with their implementation details, constitutes the current simulation campaign plan for BatCAT. Public Version v1.0 Page 5 of 61 Schematic overview of the VRFB use case quantities relevant for modelling Public Version v1.0 Page 6 of 61 Schematic overview of the Li/Na-ion use case quantities relevant for modelling Public Version v1.0 Page 7 of 61 2. List of modelling tools This section gathers the list of the modelling tools identified by the partners in WP2 to be the most appropriate to build physics-based digital twins of the manufacturing and operation processes related to both the VRFB and Li/Na-ion use cases. Each model entry is structured to have two main sections. The first section explains, in a free form, the context of the research activity of the unit proposing the model, its scientific objectives, and the general methodology for the implementation of the computational model. If necessary, the relevant physical equations and material relations are offered, together with appropriate literature references. The second section has a more fixed structure in order to facilitate both comparison and technical analysis of the models, and also to help the implementation of the same in a way that would allow for these codes horizontal interoperability, i.e. allowing for as simple and as automated as possible operation of transferring model results between one model to the other. Even more importantly, this will also inform the activity of development of accurate digital twins as prescribed by the action plan regarding WP5. In this tabular section, the Model Technical Sheet carries information on the model seen as a computer code for means of installation/use: licensing issues vs. FOSS codes, architecture requirements statements, and runtime CPU access and memory usage are listed. The following Model Information Flow carries the information which are needed for the model to run and (inputs) and just as importantly the simulation results (outputs). These are described both as a file structure summary, again to aid in the organization of structured workflows, and as a parallel description of the information carried in those files from both a tensorial (i.e. dimensionality) perspective and scientific one in terms of units of measurement. It has to be noted that in the present document only computational codes implementing relevant physics-based models are listed: at this stage, preand post-processors are not explicitly gathered (only some are listed), as this will be done in a second stage - for which the planning of the simulation campaign and the current survey of modelling tools was needed. The full list of codes and the actual technical implementation of their connections will use this information and be built into complete workflows, to be finalized in the upcoming deliverable D2.3, containing all simulations models and workflows. Public Version v1.0 Page 8 of 61 Li-ion electrode-scale charge-discharge simulations • Methodology The scripts and software described in this document are utilized to generate a 3D model of a battery half-cell in COMSOL Multiphysics. COMSOL employs the finite element method, a numerical approach that is highly effective for solving complex geometries and multi-physics problems. This software offers a comprehensive suite of tools, including a user-friendly graphical interface that allows users to define models, apply boundary conditions, and analyze results with ease. It also supports battery-specific simulations and features an application programming interface (API) in Java, which is particularly useful for automating processes such as the generation of electrodes. The micro-scale 3D modeling of Lithium-ion batteries is centered on the local numerical resolution of the charge and mass conservation of intercalated lithium and lithium ion respectively within the electrodes and the electrolyte. It has to be noted that in this model we are not focusing on the degradation phenomena that happen in a lithiumion battery, the systems are considered ideal and therefore we are not considering side reactions like the Solid Electrolyte Inter-phase (SEI) formation. The charge conservation is implemented through a steady state Ohm’s law: ∇⋅(𝑲𝑠∇𝜙𝑠)=0 while the mass conservation is expressed through Fick’s law, which describes the diffusion behavior of the lithium ions within the solid phases: 𝜕𝑐𝑠 𝜕𝑡 =∇ ⋅ (𝑫𝑠∇𝑐𝑠) In parallel, the transport equations related to the charge and mass conservation of Lithium ions in the electrolyte are solved using concentrated solution theory as: where 𝑐ℓ is the lithium-ion concentration in the electrolyte and 𝜙ℓ is the electrolyte potential, 𝐷ℓ and 𝐾ℓ are the diffusion and the electric conductivity coefficients respectively. 𝑅 is the gas constant, 𝑇 is the temperature, 𝐹 is the Faraday constant. Finally, 𝑡+ is the lithium-ion transference number, and 𝑓± is the mean molar activity. The main script driving the simulation is named Script.class, which acts as the central point of control, organizing the program into classes and their corresponding methods. Three key classes — GeometryConstruction.class, PhysicsDefinition.class, and PostProcessing.class — are called by this script to handle specific tasks. The workflow is structured into several stages to ensure that each aspect of the modeling process is handled systematically and efficiently. Public Version v1.0 Page 9 of 61 The first stage of the workflow is the variable initialization. During this step, input files are read and processed to extract essential information required for the simulation. This phase ensures that the inputs are formatted correctly and consistent with the simulation requirements. For instance, the script includes a mechanism to prevent the generation of particles outside the defined domain of interest, ensuring accurate geometrical representation. One input file at this stage is EquilibriumPotential.txt, which is formatted as a two-column float array. The first column represents the state of charge, while the second contains the corresponding equilibrium potential values. The file is read into a 2×N float array, where N is the number of rows. Other input files include Setup.txt and PhysicalProperties.txt. The Setup.txt file provides key simulation parameters such as the type of electrode, mesh refinement levels, tolerance values, and the outputs requested by the user. If any parameter is missing from this file, the script assigns default values to maintain the simulation's continuity. The PhysicalProperties.txt file contains the physico-chemical properties necessary for the half-cell battery model. These are stored in a "String-float-String" format, where each entry includes the variable name, its numerical value, and a brief description, respectively. Once initialization is complete, the process transitions to geometry construction. In this stage, methods from the GeometryConstruction class are used to define the spatial arrangement of particles based on data from Geometry.txt. This file contains M rows, one for each particle, and four columns: the X, Y, and Z coordinates of each particle’s center (in meters) and the particle radius. After generating the particle arrangement, the script extracts a central portion of the particle package to define the electrode and positions a separator on top of it. The meshing process follows next, guided by the criteria specified in Setup.txt, ensuring accurate spatial discretization. The PhysicsDefinition class is then invoked to define the governing equations and boundary conditions for each domain. This involves applying the appropriate physical laws and ensuring that the equations accurately represent the behavior of the system. Finally, the simulation is executed, and methods from the PostProcessing class are used to generate the desired outputs. These results are saved in the working directory as a Model.mph file, which can be opened in the COMSOL GUI for further analysis or manual verification. With the geometry prepared, the script uses methods from the PhysicsDefinition class to define the equations and boundary conditions for each domain of the model. Once this step is complete, the simulation is run. After the computational process, methods from the PostProcessing class are invoked to generate the specified outputs. The results are saved in the working directory as a Model.mph file, which is compatible with the COMSOL GUI and can be used for further post-processing or manual verification of the simulation setup. a) b) Figure 1. a) Cathode half-cell geometry. b) Concentration contour plot. Public Version v1.0 Page 16 of 61 • Model technical sheet Name of the code VASP Version of the code to be integrated 6.3 Partner(s) involved IFPEN Contact person(s) Manuel Corral Valero [email protected], Nature of the software program: solver, preprocessor, post-processor, homogenization tool... Solver (provides solutions for the Kohn-Sham equations of DFT), though can take part in a homogenization workflow when calculating materials properties from microscopic simulations. OS: Windows/Linux and eventually Linux distribution: any, Debian, Suze, Fedora, Ubuntu, Linux Mint, Gentoo … Windows/Linux (Typically runs on Linux distributions such as Debian, SUSE, Fedora, Ubuntu, Linux Mint, Gentoo, and others). Minimum memory requirement 8 GB of RAM (may vary depending on the size and complexity of the simulation). Major software requirement MPI (Message Passing Interface) for parallel computing, LAPACK, and BLAS libraries for linear algebra operations, and other dependencies like FFT libraries (FFTW) for fast Fourier transforms. Access mode to the code: library, executable Executable Licence (free or commercial, GPL, LGPL) Commercial Open-source or not No The specific language(s) in which the code is written :C, C++, Fortran, Python C, C++ and Fortran. What kind of API is proposed (one function, several functions) ; for each used function, give a short description VASP does not provide a traditional API but offers interfaces and integration with various tools such as Python scripts for automation and data analysis (e.g., pymatgen, ASE). Execution with singleor multiple-calls Single call for each run (though the input can be varied and multiple simulations can be run in a batch process). Execution mode : sequential, parallel, distributed Sequential and parallel (OpenMPI) Public Version v1.0 Page 17 of 61 Whether compilation is necessary for each run No addendum - Website https://www.vasp.at/ • Model information flow : inputs and outputs o File structure File name POSCAR Extension txt Short description VASP input file with the models’ atomic coordinates File structuration formats* A header, a multiplication factor for the box cell vecors (default set to 1.0), the periodic box cell vectors, a line with the atom types, the X, Y, Z coordinates of each atom Storage format* ASCII Input/Output/Code Input Name of file KPOINTS Extension txt Short description VASP input file. Number of points in each direction the reciprocal space to be considered in the DFT calculation File structuration formats* Plain text Storage format* ASCII Input/Output/Code Input File name POTCAR Extension Txt Short description VASP input file. Plane-waves basis set and core-electron pseudopotentials for each atom type in the system. File structuration formats* Concatenation of several provided by the VASP team to describe atoms’ electronic structure. Public Version v1.0 Page 18 of 61 Storage format* ASCII Input/Output/Code Input File name INCAR Extension Txt Short description VASP input file. Parameters for the DFT calculations and the DFT based geometry optimizations and NEB calculations. File structuration formats* Each line contains an entry with a tag and its specified value in the format tag = value Tags can adopt numerical, alphanumerical and Boolean values (see VASP webpage for further information). Storage format* ASCII Input/Output/Code Input File name OUTCAR Extension Txt Short description VASP output file. Evolution of the iterative procedure of the calculation and the results: atomic coordinates, total energy of the system, interatomic energies and (for frequency calculations) values of the Hessian matrix. The file also contains a recap of the input settings. File structuration formats* Plain text. Each section has self-explanatory headings. Storage format* ASCII Input/Output/Code output File name vasprun Extension xml Short description Same as the OUTCAR file (see above) but in xml format (more convenient for scripting purposes). File structuration formats* Xml formatted plain text. Public Version v1.0 Page 19 of 61 Storage format* ASCII Input/Output/Code output References: 1) Bin Jassar, M.; Michel, C.; Abada, S.; De Bruin, T.; Tant, S.; Nieto-Draghi, C.; Steinmann, S. N. A Joint DFT-kMC Study To Model Ethylene Carbonate Decomposition Reactions: SEI Formation, Growth, and Capacity Loss during Calendar Aging of Li-Metal Batteries. ACS Appl. Energy Mater. 2023, 6 (13), 6934–6945 2) Kresse, G.; Furthmller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a PlaneWave Basis Set. Phys. Rev. B 1996, 54, 11169−11186. Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Liquid Metals. Phys. Rev. B 1993, 47, 558−561. Kresse, G.; Furthmller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Open-Shell Transition Metals. Phys. Rev. B Condens. Matter 1993, 48, 13115−13118. 3) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]. Phys. Rev. Lett. 1997, 78, No. 1396. 4) Steinmann, S. N.; Corminboeuf, C. Comprehensive Benchmarking of a Density-Dependent Dispersion Correction. J. Chem. Theory Comput. 2011, 7, 3567−3577. Steinmann, S. N.; Corminboeuf, C. A GeneralizedGradient Approximation Exchange Hole Model for Dispersion Coefficients. J. Chem. Phys. 2011, 134, 044117. 5) Henkelman, G.; Uberuaga, B. P.; Jónsson, H. A Climbing Image Nudged Elastic Band Method for Finding Saddle Points and Minimum Energy Paths. J. Chem. Phys. 2000, 113, 9901−9904. Public Version v1.0 Page 20 of 61 Continuum modelling of Li/Na-ion • Objective Model the formation, performance and aging behaviour of LIB and NIB using physics based modelling. This will performed thanks to a simplified DFN [1] or SPM-e modelling approach. Consequently, the model will account for main mechanisms occurring in batteries and several aging mechanisms such as SEI formation, reversible Li or Na plating and positive electrode dissolutions will be taken into account. • Context IFPEN is developing 1D cell scale modelling using the Siemens Industry Software Simcenter Amesim software for which it codevelops a dedicated library for Electrical Storage [2]. In this library 2 simplifications of the negative/separator/positive arrangement are available as shown in Figure 2. In the DFN model (b) the cell microstructure is represented by sphere distributed between the separator and the separator in both electrodes. The more simplified SPM-e model considers only 1 mean particle in both electrodes. The 2 modelling approaches are solving the same equations and will differ mainly in computational time and validity domains. Overall P2D and SPM-e approaches represent a good balance between model computational times and accuracy. Figure 2: DFN, SPM-e simplifications [3] Public Version v1.0 Page 21 of 61 • Methodology The main equations solved in these models are indicated in the Table 1. The main purpose of this model is to compute the voltage of the cell as follows: 𝑈= 𝜙𝑠(𝐿)−𝜙𝑠(0) Several variables are necessary to obtain this desired value. First of all, solid concentrations are computed thanks to equation (1), Li+ concentration in the electrolyte is obtained from equation (3). Between these 2, Li charge transfer is governed by Butler-Volmer equation (5) evaluating the current transfer reaction kinetic between solid phase and liquid phase. Besides solid and liquid concentrations, this kinetic requires, solid and liquid potentials obtained through solid charge and liquid phase conservations (resp. (2) and (4)) and the electrode potential. This value is evaluated thanks to an expression, or a look-up table given by the user. Table 1 : Equations representing the electrochemical cell model Electrochemical phenomena Governing equations Boundary conditions Eq. Solid-phase Li-ion mass conservation 𝜕𝑐𝑠 𝜕𝑡 −1 𝑟2𝜕 𝜕𝑟(𝑟2𝐷𝑠𝜕 𝜕𝑟𝑐𝑠)=0 𝐷𝑠𝜕 𝜕𝑟𝑐𝑠|𝑟=0 =0 −𝐷𝑠𝜕 𝜕𝑟𝑐𝑠|𝑟=𝑅𝑠=𝑗𝑓 𝑎𝑠𝐹 (1) Solid-phase Li-ion charge conservation 𝜕 𝜕𝑧(𝜎𝑒𝑓𝑓𝜕𝜙𝑠 𝜕𝑧)−𝑗𝑓=0 −𝜎𝑒𝑓𝑓𝜕𝜙𝑠 𝜕𝑧|𝑧=0 =−𝜎𝑒𝑓𝑓𝜕𝜙𝑠 𝜕𝑧|𝑧=𝐿 =𝐼 𝐴𝑠𝑒𝑝 (2) Liquid-phase Liion mass conservation 𝜕𝜀𝑒𝑐𝑒 𝜕𝑡 −𝜕 𝜕𝑧(𝐷𝑒 𝑒𝑓𝑓 𝜕 𝜕𝑧𝑐𝑒)−(1−𝑡+)𝑗𝑓 𝐹 =0 𝜕𝑐𝑒 𝜕𝑧|𝑧=0 =𝜕𝑐𝑒 𝜕𝑧|𝑧=𝐿 =0 (3) Liquid-phase Li-ion charge conservation 𝜕 𝜕𝑧(𝜅𝑒𝑓𝑓𝜕𝜙𝑒 𝜕𝑧)+ 𝜕 𝜕𝑧(𝜅𝐷 𝑒𝑓𝑓 𝜕 𝜕𝑧ln𝑐𝑒)+𝑗𝑓 =0 𝜕𝜙𝑒 𝜕𝑧|𝑧=0 =𝜕𝜙𝑒 𝜕𝑧|𝑧=𝐿 =0 (4) Charge-transfer reaction kinetics 𝑗𝑓=𝑎𝑠𝑖𝑜{𝑒𝑥𝑝((1−𝛼)𝐹𝜂𝑘 𝑅𝑇 ) −𝑒𝑥𝑝(−𝛼𝐹𝜂𝑘 𝑅𝑇 )} - (5) Exchange current density 𝑖𝑜=𝑘𝑜𝑐𝑒 1−𝛼(𝑐𝑠,𝑚𝑎𝑥 −𝑐𝑠,𝑠𝑢𝑟𝑓)1−𝛼𝑐𝑠,𝑠𝑢𝑟𝑓𝛼 - (6) Solid-phase electrode potential 𝜂𝑘=𝜙𝑠−𝜙𝑒−𝑈𝑟𝑒𝑓 - (7) Equilibrium electrode potential 𝑈𝑟𝑒𝑓 =𝐸𝑟𝑒𝑓(𝑐𝑠,𝑠𝑢𝑟𝑓 𝑐𝑠,𝑚𝑎𝑥) - (8) Effective liquid phase Li+ ion diffusivity 𝐷𝑒 𝑒𝑓𝑓 =𝐷𝑒𝜀𝑒 𝐵𝑟𝑢𝑔𝑔 - (9) Public Version v1.0 Page 22 of 61 Liquid phase ionic conductivity 𝜅𝑒𝑓𝑓 =𝜅𝑒𝜀𝑒 𝐵𝑟𝑢𝑔𝑔 - (10) Liquid phase ionic diffusional conductivity 𝜅𝐷 𝑒𝑓𝑓 =2𝑅𝑇 𝐹𝜅𝑒𝑓𝑓(𝑡+−1)(1+𝑑ln𝑓± 𝑑ln𝑐𝑒) - (11) Solid-phase electronic conductivity 𝜎𝑒𝑓𝑓 =𝜖𝑠𝜎𝑠 - (12) Interfacial surface area 𝑎𝑠=3𝜖𝑠 𝑅𝑠 - (13) As this model is a lumped approach of the battery, the microstructure is not fully described. Only simple descriptors are used to account for main microstructure impact: - Mean particle radius - Electrode porosity - Electrode tortuosity through a Bruggeman correlation • Aging modelling Several modelling submodels are available or in advanced implementation into Simcenter Amesim library. In version 2410 released in October 2024, SEI formation [4] and reversible Liplating [5] were implemented accounting for loss of Li inventory in the negative electrode. In the next year release, a positive electrode dissolution model [6] has been implemented. Several further models have been investigated in MODALIS² project including mechanically induced aging and will be investigated if needed in BATCAT project. All these models plug onto the DFN model described above by using computed variables such as solid concentrations, electrolyte concentrations and potentials and in turn change the behaviour of the nominal model by adding degradation reactions currents in the charge balance and/or modifying quantities such as active material volume fractions (loss of active material) or porosity (interface growth) Parameters set As seen in Table 1, several parameters are needed to run this model. Many of them are at least temperature-dependant parameters. Such parameters are implemented into the model thanks to Simcenter Amesim user interface. Preestablished dependencies (temperature, concentration…) are already in place but can be modified by creating a fit for purpose BATCAT dedicated model. Expected output data Output variables are of 2 types. Internal variables are computed inside the model and can be accessed either thanks to Simcenter Amesim GUI or retrieved through dedicated scripts in Python or Matlab. Externa variables are linked to model ports and can be used within Simcenter Public Version v1.0 Page 23 of 61 Amesim sketch to feed other models with information (eg. Generated keat flow rate used in thermal model). External variables are also accessible via the GUI or dedicated scripts. The main outputs of Simcenter Amesim battery models are the cell voltage and its generated heat flow rates which are used for charge/discharge control and thermal modelling. Public Version v1.0 Page 24 of 61 • Model technical sheet Name of the code Simcenter Amesim Version of the code to be integrated 2410 and + Partner(s) involved IFPEN Contact person(s) Martin PETIT ([email protected]) Nature of the software program: solver, preprocessor, post-processor, homogenization tool... Pre-processor, solver, post-processor OS: Windows/Linux and eventually Linux distribution: any, Debian, Suze, Fedora, Ubuntu, Linux Mint, Gentoo … Linux: Ubuntu 22.04+; Windows: 10+ Minimum memory requirement 4 GB Major software requirement MinGW GCC 13.1.0 (supplied with Simcenter Amesim) Intel Compiler (19.0 update 6 or above) Microsoft Visual C++ (versions 2015 up to 2022) Access mode to the code: library, executable Executable Licence (free or commercial, GPL, LGPL) Commercial, FNL Open-source or not No The specific language(s) in which the code is written :C, C++, Fortran, Python C What kind of API is proposed (one function, several functions) ; for each used function, give a short description FMU Scripting (Python, Matlab VBA) Execution with singleor multiple-calls Single call. Execution mode : sequential, parallel, distributed Sequential and parallel Public Version v1.0 Page 25 of 61 Whether compilation is necessary for each run No addendum - Website https://plm.sw.siemens.com/enUS/simcenter/systems-simulation/amesim/ • Model information flow : inputs and outputs File name SimulationSketch Extension ame Short description Ame file generated from Simcenter Amesim containing all information on the simulation: • Amesim Sketch • Input parameters • Results • Coompiled code File structuration formats* Zip Storage format* NA Input/Output/Code Input/Output/Code Model inputs Input Type File General parameters electrode area scalar embedded in *.ame cell capacity scalar embedded in *.ame Electrode parameters electrode thickness scalar embedded in *.ame insertion rate at soc 0% scalar embedded in *.ame electrode effective conductivity expression f(T) embedded in *.ame electrode double layer capacitance scalar embedded in *.ame electrolyte volume fraction scalar embedded in *.ame active material volume fraction scalar embedded in *.ame Public Version v1.0 Page 32 of 61 • Model information flow : inputs and outputs Purpose Geometry input Number of files 3 Short description Voxel mesh with ids indexing the different materials; voxel dimensions; id assignment to material class File structuration formats* Plain text Storage format* ASCII and xml Input/Output/Code Input Purpose Model and solver parameters Number of files 3-5 Short description Parametrization for model parameters and other solver settings File structuration formats* Plain text Storage format* Xml (optionally also cpp) Input/Output/Code Input Purpose Variable parameters Number of files Arbitrary Short description Description of concentration-dependent parameters (eg. OCV) File structuration formats* Plain text Storage format* ASCII (optionally also cpp) Input/Output/Code Input Purpose Local solution fields Number of files Arbitrary Short description Spatial fields of solution variables (concentrations, potentials) and derived quantities (eg. Current densities, overpotentials, etc). One file per output time step File structuration formats* Mixed plain text and binary Storage format* Vtk Input/Output/Code Output Public Version v1.0 Page 33 of 61 • Physical quantities: type and description Material Input quantity Unit Type Active material (anode/cathode) Li diffusivity cm²/s Scalar (possibly depending on state of lithiation) Electronic conductivity S/cm Scalar (possibly depending on state of lithiation) Open-circuit voltage V Scalar depending on state of lithiation Electrolyte Li diffusivity cm²/s Scalar (possibly depending on salt concentration) Ionc conductivity S/cm Scalar (possibly depending on salt concentration) Transference number 1 Scalar (possibly depending on salt concentration) CBD (anode/cathode) Effective electronic conductivity S/cm Scalar Effective ionic conductivity S/cm Scalar (possibly depending on salt concentration) Effective ionic diffusivity cm²/s Scalar (possibly depending on salt concentration) Porosity 1 Scalar Separator Porosity 1 Scalar MacMullin number/tortuosity 1 Scalar Intercalation reaction Exchange current density A/cm² Scalar (possibly depending on salt concentration and state of lithiation) Electrode (anode/cathode) Geometry m 3d voxel data describing material distribution in simulation domain; alternatively: image stack Public Version v1.0 Page 34 of 61 Output Unit Type Cell voltage V Time series Electrode potentials V Time series Overpotentials V Time series SOC 1 Time series Current A Time series Concentration mol/cm³ Scalar field Potentials V Scalar field Intercalation flux mol/(s cm²) Vector field Ion flux mol/(s cm²) Vector field Electronic current density A/cm² Vector field Ionic current density A/cm² Vector field Heat production W/cm³ Scalar field Local electrode Pot. vs Li (Plating condition) V Scalar field Public Version v1.0 Page 35 of 61 Lattice-particle model for multiphysical simulation of electrodes • Context The lattice-particle model is designed to simulate multiphysical phenomena in a microstructured domain, namely a representative volume element (RVE) composed by particles. This model accounts for the influence of local microstructural features, including particle geometry and distribution, on the macroscopic transport properties and mechanical behavior. The primary application is to predict ion diffusion and structural integrity in heterogeneous particle-based materials, particularly useful for understanding the electrode’s performance during operation conditions and can be also extended to manufacturing processes such as drying or calendering. The methodology of the lattice-particle model encompasses two primary components: microstructure generation and the lattice-particle formulation.The microstructure is generated using a "take-and-place" approach to produce a representative volume element (RVE) that captures the heterogeneous nature of the material. The process begins by defining the four key phases of the microstructure: active material (AM), additives (conductive), binder, and pores. Active material, typically graphite-based for anodes, is characterized by its volume fraction and sieve curve data. Additives, usually carbon-based, have specific volume fractions, sieve curve, and physical properties. The binder is described by its own volume fraction, while the pores are represented by porosity, which governs ion transport. The construction of the microstructure involves placing particles within a cubic domain (RVE) sequentially, starting with the largest to optimize packing density. Partial overlap between particles is accepted to reflect realistic microstructural features. Once the particles are placed, the microstructure undergoes voxelization and segmentation, enabling computational simulations. Each voxel is assigned to a material phase based on particle and binder placement. This methodology is suitable for both anode and cathode designs, ensuring compatibility across battery electrode architectures. Figure 1. Representative volume elements (RVEs) of graphite anode with different compositions. The lattice-particle model currently accounts for the transport and mechanical behaviour by discretizing the microstructure and incorporating particle-particle and particle-pore interactions. The microstructure is discretized into lattice points corresponding to material phases. Particle interactions, including binding and diffusivity adjustments, are defined based on established models, such as those by Yu et al. (1999), Wang et al. (2010), and Chouchane (2019). Public Version v1.0 Page 36 of 61 • Methodology The solving scheme addresses governing equations for ion diffusion and diffusive-mechanical problems, which are solved iteratively following a finite element method (FEM) discretization and an explicit integration scheme. Transport properties, such as diffusivity, are assigned to lattice points based on their material phase, and linear systems are solved to obtain ion concentration and flux distributions following Fickian diffusion: ∂𝑐 ∂𝑡+∇⋅𝐽=0 where 𝑐 is the concentration of the diffusing species, 𝑡 is time, and 𝑱 is the ion flux that is defined as: 𝐽=−𝐷(∇𝑐−Ω⋅𝑐 𝑅⋅𝑇∇σℎ) where 𝑫 is the diffusion matrix in the active material, 𝑅 is the gas constant, Ω is the ion partial molar volume, 𝑇 is the absolute temperature, 𝜎ℎ is the hydrostatic stress and 𝝈 is the stress tensor. The characterization of the electrodes involves extracting diffusivity and tortuosity factors to describe the effective transport properties of the microstructure. This methodology ensures accurate representation of the electrode’s mesoscale features, enabling predictions of ion transport dynamics under various operation conditions. The diffusive-mechanical problem is solved by means of a continuum damage formulation, which reads as: σ=(1−𝑑) 𝐷0 el:εel where 𝑫𝟎 elis the initial (undamaged) elasticity matrix. In the formulation, the elastic stiffness degradation is characterized by the degradation parameter, 𝑑. The degradation parameter can take values ranging from zero (undamaged material) to one (corresponding to total loss of strength). We assume an isotropic expansion in the definition of the diffusion-induced strain tensor, ε𝑑: ε𝑑=Ω 3(𝑐−𝑐0)𝐼 Figure 2. Effective diffusion for different RVE compositions. Public Version v1.0 Page 37 of 61 ● Model technical sheet Name of the code Pekken3D Version of the code to be integrated 2024 Partner(s) involved Loyola Contact person(s) Francisco Montero-Chacón (fpmont[email protected]) Nature of the software program: solver, preprocessor, post-processor, homogenization tool... Pre-processor, solver, post-processor OS: Windows/Linux and eventually Linux distribution: any, Debian, Suze, Fedora, Ubuntu, Linux Mint, Gentoo … Any Minimum memory requirement 4 GB Major software requirement Matlab R2020a or later. All libraries included. Access mode to the code: library, executable library Licence (free or commercial, GPL, LGPL) FNL Open-source or not No The specific language(s) in which the code is written :C, C++, Fortran, Python Matlab What kind of API is proposed (one function, several functions) ; for each used function, give a short description None Execution with singleor multiple-calls Single call. Execution mode : sequential, parallel, distributed Sequential and parallel (OpenMPI) Whether compilation is necessary for each run No addendum - Website - Public Version v1.0 Page 38 of 61 ● Model information flow Purpose Geometry input Number of files 1 Short description Number of phases; volume fractions of the phases; particle sieve curve (size and percentage); electrode thickness; electrode geometry File structuration formats* Plain text Storage format* *.m Input/Output/Code Input Purpose Local material properties Number of files 1 Short description For every material phase defined in the Geometry Input, define: diffusivity; volumetric expansion coefficient; elastic modulus; Poisson’s ratio File structuration formats* Plain text Storage format* *.m Input/Output/Code Input Purpose Model and solver parameters Number of files 1 Short description Parametrization for model parameters and other solver settings File structuration formats* Plain text Storage format* *.m Input/Output/Code Input Purpose Local solution fields Number of files User-defined Public Version v1.0 Page 39 of 61 Short description Plots and tables of vector and scalar fields of solution variables: ion concentration; displacement; stress. Time-step is userdefined. File structuration formats* CSV Storage format* CSV; PNG Input/Output/Code Output Public Version v1.0 Page 40 of 61 ● Physical quantities: type and description Inputs Type File Volume fractions (-) Array N×1 (N: number of phases) Geometry.m Porosity (-) Scalar Geometry.m Sieve curves (μm,-) Matrix 3×M (M: number of discretizations) Geometry.m Electrode thickness (μm) Scalar Geometry.m Local diffusivities (cm2/s) Array N×1 (N: number of phases) LocalProps.m Local volumetric expansion coefficients (1/var) Array N×1 (N: number of phases) LocalProps.m Local elastic moduli (GPa) Array N×1 (N: number of phases) LocalProps.m Local Poisson’s ratio (-) Array N×1 (N: number of phases) LocalProps.m Outputs Type File RVE structure (positions of the particles, μm) Array M×3 (M: number of particles) Output.m Global diffusivity (cm2/s) in each direction Array 3×1 OutputDiff.m Global Elastic Modulus (GPa) in each direction Array 3×1 OutputMech.m Damage (-) Array M×N (M: number of elements, N: time-step) OutputMech.m Displacement field (μm) Array M×N (M: number of particles, N: time-step) OutputMech.m Public Version v1.0 Page 41 of 61 Molecular modelling and simulation of redox-flow electrolyte properties • Context The work will be conducted within T2.5 (Integrated multiphysics modelling of redox flow batteries). Due to staffing at NMBU, it will be carried out from M18 to M27 (June 2025 – March 2026). The involved team members will be Maria Bashir (NMBU) and David Fertig (NMBU), with Martin Horsch (NMBU), Kristin Tøndel (NMBU), Mathijs Janssen (NMBU) and possibly Eirik Valseth (SIMULA) and Kristian Berland (NMBU) in an advisory capacity. • Modelling objective The aim is to quantify the dependence of key thermodynamic and transport properties of the homogeneous vanadium redox flow battery (VRFB) electrolytes as a function of boundary conditions, composition (preparation) and state of charge. The macroscopic degrees of freedom (input quantities) to be considered are: • Temperature and pressure within the range of VRFB operating conditions. • Total amount of sulfate (mainly represented by hydrogen sulfate). • Total amount of vanadium ions. • State of charge (represented by the ratio between vanadium ions at the two oxidation states present in the respective electrolyte). The obtained simulation output quantities are: • Thermodynamic properties including density, heat capacity, isothermal compressibility, and speed of sound. • Linear transport properties, including shear viscosity, diffusion coefficients, thermal and electric conducitivity. The above will be determined both for the anolyte and the catolyte of the VRFB. The nonlinear transport regime, interfacial properties, the influence of the electric field on thermodynamic and transport properties, and deviations from bulk behaviour in surface-near regions remain out of scope for this line of work. Surrogate models created on this basis (T3.5, M19-M33) will be used to generate input parameters for (the simulations and the surrogate models created from) dissipative particle dynamics using DL_MESO, conducted by UKRI within T2.4 and T2.5 and aggregated within Public Version v1.0 Page 48 of 61 • Model information flow : inputs and outputs o File structure File name Input Extension txt Short description Spatial characterization of the electrode particles. File structuration formats* Four columns of float numbers separated by single space. Storage format* ASCII Input/Output/Code Input File name Mesh.XX (for example) Extension Multiple (user defined) Short description Mesh file File structuration formats* Depends on format, most available accepted or easily converted to be Storage format* Multiple Input/Output/Code Input File name Output.XX (for example) Extension Multiple (user defined) Short description Output files from simulations File structuration formats* Depends on format, most available accepted or easily converted to be Storage format* Multiple Input/Output/Code output • Physical quantities : type and description FEniCSx as a general software framework will use whichever quantities that are relevant for the model at hand. Public Version v1.0 Page 49 of 61 DFT modelling of carbon felt electrode materials for vanadium redox flow batteries • Context DTU and NMBU will collaborate to supply the required density functional theory (DFT) simulations with T2.4 and T2.5. DTU will distribute its work evenly between T2.4 and T2.5, with the bulk of it being carried out between M13 and M24 (January – December 2025); José María Castillo Robles will be involved as a team member, and Ivano Castelli in an advisory capacity. NMBU will mainly contribute to T2.5, from M21 to M27 (September 2025 – March 2026), as a consequence of an analysis of the staffing situation at NMBU; Øven Andreas Grimenes will be involved as a team member, Kristian Berland in an advisory role. • Modelling objective Two objectives have been agreed: • Develop a better understanding, suitable for quantitative modelling at a higher level, of the influence of functionalizations of the carbon felt material (carbonyl, epoxy, hydroxyl, carboxyl groups, among others) on vanadium reactivity at the surface. • Model potential degradation pathways by which the above mentioned substituents are eliminated from the surface, both in dry mode during shelf life (before use in the battery) as well as in operation in contact with the highly acidic electrolyte fluid. • Methodology One of the key research interests in batteries involves investigating the solid-electrolyte interphase (SEI). Understanding SEI formation at the atomistic scale provides valuable insights for effective battery design. The dynamics of the electrode-electrolyte interactions play a crucial role in the SEI formation mechanism. To explore these dynamics, we employ ab-initio molecular dynamics (AIMD) and DFT calculations to analyse the electrode-electrolyte interface and the presence of chemical reactions. AIMD simulations allow us to reveal reaction mechanisms, the formation of intermediate species, and the molecular dynamics at the interface. DFT complements these insights by providing equilibrium geometries of molecules at the interface, their electronic structures, reaction energies, and transition states. These results allow us better to understand the thermodynamics and kinetics of SEI formation processes. Kinetic Monte Carlo simulations can further extend the timescales of the simulations, allowing us to study longer-term processes beyond the timescales accessible by AIMD. Furthermore, structural properties of SEI components obtained through DFT, such as lattice parameters, bond lengths, and relative stability, offer insights into the crystalline or amorphous nature of the SEI. AIMD also facilitates the calculation of diffusion coefficients, providing insights into the ion mobility within the SEI layer. Public Version v1.0 Page 50 of 61 The application of external electric fields or voltages can also affect the processes present during the SEI formation, leading to charge transfer between the electrode and electrolyte, and altering the reaction mechanisms and stability of SEI components. The applied voltage potential can also modify the free energy landscape of the system, impacting the thermodynamics and kinetics of chemical reactions at the interface. Including these voltage effects in the simulations allows for the study of phenomena such as electrolyte decomposition, changes in ionic or electronic conductivity, and the SEI growth dynamics under a voltage, capturing the SEI evolution over time during cycling. Finally, by combining these theoretical insights with experimental data, a more complete picture of the SEI can be developed, linking atomic-scale processes to macroscopic battery performance. These atomistic Insights not only enhance our understanding of battery behaviour but also provide guidance for optimizing materials and operating conditions to improve efficiency and durability. Relevant publications: 1) B. H. Sjølin, W. S. Hansen, A. A. Morin-Martinez, M. H. Petersen, L. H. Rieger, T. Vegge, J. M. Garcia-Lastra, and I. E. Castelli, PerQueue: Managing Complex and Dynamic Workflows, Digital Discoveries 3, 1832 (2024). 2) X. Qin, A. Bhowmik, T. Vegge, and I. E. Castelli, Computational Investigation of LiF Formation at Graphite–Electrolyte Interfaces, ACS Appl. Mater. Interfaces 16, 29347 (2024). 3) B. H. Sjølin, P. B. Jørgensen, A. Fedrigucci, T. Vegge, A. Bhowmik, and I. E. Castelli, Accelerated Autonomous Workflow for Antiperovskite-based Solid State Electrolytes, Batteries & Supercaps 2023, e202300041 (2023). 4) I. E. Castelli, M. Zorko, T. M. Østergaard, P. Martins, P. P. Lopes, B. K. Antonopoulos, F. Maglia, N. Markovic, D. Strmcnik, and J. Rossmeisl, The Role of an Interface in Stabilizing Reaction Intermediates for Hydrogen Evolution in Aprotic Electrolytes, Chem. Sci. 11, 3914 (2020). 5) F. T. Bølle, N. R. Mathiesen, A. J. Nielsen, T. Vegge, J. M. Garcia Lastra, and I. E. Castelli, Autonomous Discovery of Materials for Intercalation Electrodes, Batteries & Supercaps 3, 488 (2020). 6) D. Strmcnik, I. E. Castelli, J. G. Connell, D. Haering, M. Zorko, P. Martins, P. P. Lopes, B. Genorio, T. Østergaard, H. Gasteiger, F. Maglia, B. K. Antonopoulos, V. R. Stamenkovic, J. Rossmeisl, and N. M. Markovic, Electrocatalytic Transformation of HF Impurity to H2 and LiF in Lithium Ion Batteries, Nature Catalysis 1, 255 (2018). Public Version v1.0 Page 51 of 61 • Description of the model This model investigates the surface reactions and adsorption of vanadium species on graphene felt electrodes, which are crucial for optimizing the performance of vanadium redox flow batteries (VRFB). The graphene felt is represented as a periodic slab structure, capturing key features such as defects, edge sites, and potential functional groups. Vanadium species are modelled explicitly, and their interactions with the surface are evaluated under varying conditions of surface coverage. The computational study aims to provide insights into the adsorption energies, reaction pathways, and energy barriers for vanadium-related processes. This supports the design of more efficient electrodes by linking microscopic surface properties to macroscopic experimental observations. The DFT simulations are conducted using VASP (Vienna ab-initio simulation package) and leverages density functional theory (DFT). Key methodologies include: 1 Kohn-Sham DFT to compute the ground-state electron density and total energy. 2 Dispersion-corrected functionals (e.g., vdW-inclusive methods such as DFT-D3 or vdW-DF) to model non-covalent interactions critical for accurately describing adsorption on graphene. 3 Nudged Elastic Band (NEB) method for determining reaction energy barriers along transition pathways. 4 Thermodynamic analysis of adsorption and reaction energetics, including the effects of temperature and surface coverage. The workflow involves: • Model Preparation: Construct periodic graphene slabs, including defects and relevant functional groups, and optimize the structures. • Adsorption Studies: Analyze binding energies and configurations for vanadium species on different sites. • Reaction Mechanism Exploration: Identify and compute energy barriers for key reactions using NEB. • Output Analysis: Evaluate charge density differences and identify active surface regions. Public Version v1.0 Page 52 of 61 • Model technical sheet Name of the code VASP Version of the code to be integrated 5 or later Partner(s) involved DTU and NMBU Contact person(s) [email protected] Nature of the software program: solver, preprocessor, post-processor, homogenization tool... Solver OS: Windows/Linux and eventually Linux distribution: any, Debian, Suze, Fedora, Ubuntu, Linux Mint, Gentoo … Linux Minimum memory requirement NA Major software requirement Fortran, C compiler (e.g. gcc) Access mode to the code: library, executable library Licence (free or commercial, GPL, LGPL) Commericla Open-source or not No The specific language(s) in which the code is written :C, C++, Fortran, Python NA What kind of API is proposed (one function, several functions) ; for each used function, give a short description NA Execution with singleor multiple-calls Single call. Execution mode : sequential, parallel, distributed Sequential,parallel (MPI)) Whether compilation is necessary for each run No addendum - Website https://www.vasp.at/ Public Version v1.0 Page 53 of 61 • Physical quantities: type and description Inputs Type Source Graphene slab structure CIF file Generated or DB Vanadium species geometries XYZ file Generated Pseudopotentials (PAW datasets) Files VASP database NEB calculation parameters Text file Input script Outputs Type File Name Adsorption energies and configurations Scalars, POSCARs AdsorptionResults. txt Reaction energy barriers Scalars ReactionBarriers.tx t Charge density differences CHGCAR files ChargeDiff.plots Public Version v1.0 Page 54 of 61 Redox flow battery pore-scale (mesoscopic) simulations • Methodology The models and software described herein are for the proposed modelling of redox flow batteries at UKRI STFC, specifically the transport of ions in liquid electrolytes towards the surface of pores in carbon felt. UKRI STFC will predominately use DL_POLY_5 [1], an open source particle dynamics code capable of modelling electrolytes and carbon surfaces at the mesoscale using Dissipative Particle Dynamics (DPD) [2]. This software is sufficiently generalpurpose to enable various scenarios to be modelled, including (1) the study of transport properties for the electrolytes (anolyte and catholyte), (2) identification of the minimum distance required from a carbon surface (measured from ion concentration profiles), and (3) the effects of surface functionalization including embedded charges and defects due to heat treatment of the felt. It should be noted that while we cannot directly consider the redox reaction itself in these simulations, the effect of the carbon surface on local ion concentrations relative to bulk electrolytes may give some indication of reaction rates. DPD is a mesoscopic variant of molecular dynamics (MD) that hinges upon determining forces acting on particles based on interaction potentials and applying those forces over small time durations (timesteps). These potentials are predominately pairwise in nature and are chosen to represent how the particles would interact based on their contents, often considered as ‘coarse grains’ (collections of atoms or molecules). DPD adds to these with additional pairwise forces for dissipation and randomized Brownian motion, providing temperature control in the form of a momentum-conserving thermostat that does not disrupt any applied flow to the particles. The electrolytes will be predominately represented as water beads interacting with an ‘𝑛DPD’ potential [3], a modified form of the interactions most commonly used in DPD calculations [2] to enable more realistic thermodynamic behaviour. Each water bead will consist of 5 molecules of water and predominately interact with an 𝑛DPD potential parameterised to give the correct liquid density, self-diffusivity and viscosity at the battery’s operating temperature [4]. The ionic species in the electrolytes – vanadium and sulphate (part of sulphuric acid) – will be treated as ion-water complexes and will interact similarly to water but with additional charges that interact electrostatically. Protons (hydrogen ions) will be modelled individually and interact with water and sulphate beads with a potential to represent proton transfer effects [5]. The carbon felt will be represented as a layer of beads interacting hydrophobically with other species [6] but frozen in place so it does not move. The typical diameter of a pore (tens of micrometres) compared with the size of bead (under a nanometre) means that flat surfaces for the felt will suffice. As the flow speed of electrolyte through the pore is much smaller than thermal particle motion for the operating temperature, ion diffusion will dominate over flow effects and the minimum required distance from the carbon surface will be the concentration boundary layer. For simulations examining the effects of surface functionalization, an additional region of frozen beads with bulk electrolyte will be included at the opposite end to the carbon surface. Public Version v1.0 Page 55 of 61 The presence of the carbon pore will also lead to variations in local permittivity for the electrolytes. This can be accounted for by adding dipoles to the water beads [7], which can be selected to provide the correct relative permittivity for pure water. Preliminary simulations indicate that this approach should provide realistic dipole moment distributions for the required coarse-graining level. To speed up calculations with polarizable water, we intend to apply the dipoles by using rigid bodies (a solver for which is supplied in DL_POLY_5) rather than attaching charges to water beads using flexible bonds. The process of carrying out simulations using DL_POLY_5 involve the creation of configurations defining the initial positions of particles, defining the interactions between particles (‘beads’ in the context of mesoscale modelling), and setting simulation controls. These involve creating input files in text-based formats that DL_POLY_5 reads in at the start of a calculation. The main input file driving the simulations is named CONTROL, which specifies system properties such as temperature, numbers and size of timesteps, implementation of electrostatic interactions etc. The FIELD file specifies the contents of the simulation box and the interactions between beads: while the former will vary between different simulations, the interactions should not drastically change and can be reused. The CONFIG file provides the initial positions of particles for each simulation. CONFIG files for simulations of bulk electrolytes will be created by selecting the box size and adding beads at random positions: no numerical issues would result if any beads are placed on top of one another due to ‘soft’ interactions. The configurations for simulations with carbon felt require positioning of carbon beads to either represent a flat surface or to include defects and/or embedded charges. Simulations of the concentration boundary layer can take configurations of bulk electrolytes from the trajectories of previous calculations and add these as frozen beads. All of these and their associated FIELD files will be created using Python scripts (yet to be written). The DL_POLY_5 simulations will generate HISTORY files consisting of configuration snapshots at user-specified time intervals as a trajectory. These can be visualised graphically using molecular plotting packages such as VMD, used as (partial) configurations for subsequent simulations or post-processed using Python scripts to obtain e.g. concentration profiles. • References 1) IT Todorov, W Smith, K Trachenko and MT Dove, DL_POLY_3: new dimensions in molecular dynamics simulations via massive parallelism, Journal of Materials Chemistry 16 (20), 1911 – 1918 (2006), DOI: 10.1039/b517931a 2) RB Groot and PB Warren, Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation, Journal of Chemical Physics 107 (11), 4423 – 4435 (1997), DOI: 10.1063/1.474784 3) VP Sokhan, MA Seaton and IT Todorov, Phase behaviour of coarse-grained fluids, Soft Matter 19 (30), 5824–5834 (2023), DOI: 10.1039/D3SM00835E 4) M Seaton, V Sokhan and I Todorov, Development of enhanced interactions for highly coarse-grained materials, IN: Proceedings for ASME 2024 7th International Conference Public Version v1.0 Page 56 of 61 on Micro/Nanoscale Heat and Mass Transfer, V001T08A010 (2024), DOI: 10.1115/MNHMT2024-132397 5) M-T Lee, A Vishnyakov and AV Neimark, Modeling proton dissociation and transfer using dissipative particle dynamics simulation, Journal of Chemical Theory and Computation 11 (9), 4395 – 4403 (2015), DOI: 10.1031/acs.jctc.5b00467 6) A Vishnyakov, R Mao, M-T Lee and AV Neimark, Coarse-grained model of nanoscale segregation, water diffusion, and proton transport in Nafion membranes, Journal of Chemical Physics 148, 024108 (2018), DOI: 10.1063/1.4997401 7) S Chiacchiera, PB Warren, AJ Masters and MA Seaton, Coarse-grained polarizable soft solvent models, with applications in dissipative particle dynamics, Journal of Chemical Physics 161, 174115 (2024), DOI: 10.1063/5.0226871 Public Version v1.0 Page 57 of 61 • Model technical sheet Name of the code DL_POLY_5 Version of the code to be integrated 5.2.0 Partner(s) involved UKRI Contact person(s) Michael SEATON ([email protected]) Nature of the software program: solver, preprocessor, post-processor, homogenization tool... Solver OS: Windows/Linux and eventually Linux distribution: any, Debian, Suze, Fedora, Ubuntu, Linux Mint, Gentoo … Any (Linux preferred) Minimum memory requirement ~160 bytes per particle (1.26MB for smallest calculation, ~5 GB for largest calculation) Major software requirement Fortran compiler, MPI (optional) Access mode to the code: library, executable Source code Licence (free or commercial, GPL, LGPL) LGPL-3 Open-source or not Yes The specific language(s) in which the code is written :C, C++, Fortran, Python Fortran What kind of API is proposed (one function, several functions) ; for each used function, give a short description None Execution with singleor multiple-calls Single call. Execution mode : sequential, parallel, distributed Sequential and parallel (MPI) Whether compilation is necessary for each run No addendum - Website https://gitlab.com/ccp5/dl-poly