Self-Organization of Electroactive Suspensions in Discharging Slurry

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Self-organization of Electroactive Suspensions in Discharging Slurry Batteries: A Mesoscale Modeling Investigation Garima Shukla, Diego Del Olmo Diaz, Vigneshwaran Thangavel, and Alejandro A. Franco ACS Appl. Mater. Interfaces, Just Accepted Manuscript • Publication Date (Web): 11 May 2017 Downloaded from http://pubs.acs.org on May 11, 2017

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ACS Applied Materials & Interfaces

Self-organization of Electroactive Suspensions in Discharging Slurry Batteries: A Mesoscale Modeling Investigation Garima Shuklaa,b, Diego del Olmo Diaz a,b, Vigneshwaran Thangavela,b, and Alejandro A. Franco a,b,c,d,*

a

Laboratoire de Réactivité et Chimie des Solides (LRCS), CNRS UMR 7314, Université de Picardie Jules Verne, 33 rue Saint Leu, 80039 Amiens Cedex, France. b

Réseau sur le Stockage Electrochimique de l’Energie (RS2E), FR CNRS 3459, France c

ALISTORE-ERI, European Research Institute, FR CNRS 3104, France d

Institut Universitaire de France, 75005 Paris, France

KEYWORDS: redox flow batteries, slurry electrodes, electroactive suspensions, silicon, carbon, mesoscale, computational modeling, kinetic Monte Carlo.

ABSTRACT: We report a comprehensive modeling-based study of electroactive suspensions in slurry redox flow batteries undergoing discharge. A three-dimensional kinetic Monte Carlo model based on the variable step size method is used to describe the electrochemical discharge of a silicon/carbon slurry electrode in static mode (i.e. no fluid flow conditions). The model

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accounts for Brownian motion of particles, volume expansion of silicon upon lithium insertion, and formation and destruction of conducting carbon networks. Coupled to an electrochemical model, this study explores the impact of carbon fraction in the slurry and applied c-rate on the specific capacity. The trends obtained are analyzed by following the behavior of parameters such as number of contacts between electroactive particles and the percentage of electroactive silicon particles. Furthermore, instead of studying the bulk behavior of the slurry, here the focus is given to the slurry/current collector interface in order to illustrate its importance. Hereby, it is demonstrated how this modeling tool can lead to deeper understanding and optimization of electroactive particle suspensions in redox flow batteries.

INTRODUCTION Developing energy storage devices for smart grids is critical to meet both consumer and industrial electricity demands, and to inhibit further ecological damage by providing sustainable means to incorporate renewable energy sources. Electrochemical energy storage systems offer a wealth of redox couples that can be tailored to satisfy requirements of a large variety of scales. Furthermore, out of all the stationary technologies, Redox Flow Batteries (RFBs) provide the highest technical flexibility by decoupling energy and power. Although vanadium-based RFBs have dominated stationary applications for decades,1 the concept of Slurry Redox Flow Batteries (SRFBs) introduced by Chiang et al.,2 offers a new approach for incorporation of a variety of families of materials that were previously only studied in the context of solid state electrodes for nomad applications. SRFBs are fueled by semi-solid suspensions of high energy density lithium storage compounds that are electrically wired by dilute percolating networks of nanoscale conductor particles. Furthermore, a slurry electrode system can help overcome disadvantages of higher energy density materials that are cheap but fail as solid state electrodes. Recent efforts


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allowed significant progress in the understanding of their electrochemical characterization with different types of materials.2–4 Silicon is one such material that offers high gravimetric capacity by forming a lithium rich alloy (Li3.75Si) at the end of discharge, at room temperature. However, the volume of Li3.75Si is about 175% larger than that of pristine Si.4 This results in significant loss of contacts between silicon and carbon particles in solid state electrodes leading to poor cyclability, thus the use of binders and polymeric additives with modified silicon surfaces have been studied to retain capacity over cycling.4,5 An elegant alternative approach to overcome this challenge consists in using silicon in the form of a slurry electrode, without the use of any additive or binder, as demonstrated by Hamelet et al.4 In this case, the stable suspension of silicon and carbon in an electrolyte offers a surprisingly appealing electrochemical performance on cycling in non-fluid flow conditions referred hereinafter to as the static mode. The growth of SEI on silicon due to large volume fraction of electrolyte is more than in solid state electrodes, however the experiments show that 80% of the theoretical capacity can be achieved with very low polarization and reasonable capacity retention. This is an interesting system from a multidisciplinary modeling perspective as particle suspension dynamics, particle growth dynamics and electrochemistry can be studied simultaneously. Despite the promise and progress achieved experimentally, a holistic picture of parameters and operation principles that influence the electrochemical behavior of SRFBs is yet to be explored.2,6–12 Indeed, very few theoretical studies have been attempted so far on SRFBs.13,14 Computational SRFB models available in the literature consider the slurry as a continuum medium in which the impact of dynamic mesostructural self-organization properties of suspended particles on the overall electrochemical response has been overlooked. Additionally, carbon and silicon/carbon suspensions in bulk have been modeled with discrete coarse-grained particles using three-dimensional Boltzmann Dynamics approaches.15–18 The latter works reported the



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effects of temperature and mass ratios of carbon and silicon particles on the number of contacts between them within the percolation networks. However, since the aforementioned studies do no simulate electrochemical reactions in the slurry, they address only a part of the challenge in understanding SRFBs. Valuable insights can come from a model that couples particle suspension dynamics with electrochemical mechanisms. Therefore, the primary objective of this paper is to report an innovative model designed to capture the mesoscopic self-organization of suspensions in an anodic slurry, comprising silicon and carbon particles in an organic electrolyte, when simulating a galvanostatic discharge versus metallic lithium in static mode (Figure 1). We focus here on the interface between the current collector and the suspension, within the experimental setup configuration of Hamelet et al.4 In the following section, we present the theoretical background of our model. Then, we illustrate its capabilities by reporting simulated sensitivity analysis of electrochemical performance vs. carbon fraction and c-rate. Finally, we conclude and indicate further directions of this work.

Figure 1. (a) Experimental set-up of the static cell in our lab; (b) schematic representation of the cell assembly containing the silicon-carbon slurry in the electrolyte; (c) mesoscopic representation of the interface between the silicon (blue) – carbon (red) slurry and the current


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collector (yellow) simulated by the model (here the empty space in slurry represents the electrolyte).

COMPUTATIONAL MODEL Kinetic Monte Carlo (kMC) models based on the variable step size method (VSSM) have been conventionally used for atomistic-type modeling.19 Recently, they have been adapted by us to simulate, with three-dimensional resolution, mesoscopic transport and electrochemical mechanisms taking place in energy devices such as fuel cells and lithium-O2 batteries.20–23 In this work, we adopt this approach to simulate the behavior of the silicon-carbon particle suspensions upon the slurry electrochemical discharge.



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Figure 2. Simulation workflow describing the three main modules: (a) Channel initialization setting up the three dimensional slurry based on size and composition requirements (module only used once at the beginning of the simulation); (b) Module to simulate the Brownian motion using VSSM under the kMC framework; (c) Electrochemical phenomena of silicon discharge. Modules (b) and (c) are implemented till the potential calculated in (c) reaches a cut-off potential.

In our model (Figure 2), the particle suspension is confined within a cubic grid with unit cells of edge length 100 nm (Figure 2 (a) (ii)), a parameter which can be tuned for obtaining the desired resolution. It is assumed that the top face of the grid is the surface of current collector and the rest of the faces are boundaries which contain a part of the slurry considered as the interfacial system under study. The relative impact of parameters on the calculated specific capacities represent only the simulated part of the slurry electrode, and do not correspond to that of the entire slurry electrode. The slurry itself is composed of carbon particles of 100 nm diameter, silicon particles of about 237 nm effective diameter (Figure 2(a) (i)), and organic electrolyte in the empty spaces around the particles. Initially, carbon and silicon particles are considered to occupy one unit cell and seven unit cells respectively, in order to generate a particle size difference which is computationally easy to handle while allowing experimental viability. Additionally, the volume occupied by each subunit for all theoretical considerations is taken as a cube of the matrix, however represented as spherical subunits for the purpose of visualization. The initial configuration of the slurry is generated by placing silicon and carbon particles randomly in the grid (Figure 2 (a) (v)). An ideal slurry electrode would be one that is capable of fully discharging all silicon particles by providing them with sufficient electrons and lithium ions, thus offering highest possible capacity. The role of the purely electron conducting carbon is to assemble itself as a network that wires silicon particles in the slurry. When a carbon network has



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contact with silicon particles that are not yet fully discharged, this network, as well as the corresponding silicon particles, are considered to be electroactive. Silicon particles are assumed to be electron sinks only, thus making them incapable of participating within a carbon network to conduct electrons. Once a silicon particle is fully discharged, it is no longer considered electroactive and the carbon network it was connected to, becomes inactive. Hence our model can track the durability of these carbon networks under different operating conditions and slurry compositions. While Brownian motion drives suspension stability, a single particle motion can potentially break essential carbon networks. In the model we consider only Brownian motion, while other destructive forces for carbon networks such as sedimentation and flocculation, that can induce suspension instability, are ignored. Interaction potentials such as Van der Waal and electrostatic forces were ignored in this first modeling attempt due to the incomplete fundamental understanding of how potentials arising from atomic interactions manifest at the mesoscale for particles, and how the solid-liquid interface transforms during the electrochemical cycling of particles experiencing electron flow while aggregating with other particles and being solvated from the electrolyte. In our model, kMC-VSSM is used to choose from a weighted list of all possible particle displacements occurring within Brownian motion (Figure 2 (b)). The weight attributed to any displacement is based on the diffusion rate. A particle with a high diffusion rate is most probably small or has available space around it, thus VSSM is most likely select this particle to move. All particles in this model are given a basal diffusion property arising from the macroscopic feature of viscosity of the slurry, modified by their respective sizes. For this purpose, the Stokes-Einstein equation (1) expressed the diffusion coefficient (, ) as a function of viscosity of the slurry ( )


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and particle radius ( , ),24 where subscript ‘i’ refers to particle type (Si or C) and ‘j’ refers to the identity:

, = .

.

. . ,

(1)

The viscosity of the slurry ( ) is a product of pure liquid viscosity ( ) and relative solid viscosity ( ), wherein the latter can be estimated on-the-fly based on solid volume fraction ( ) using the Thomas’s expression:25,26

= 1 + 2.5 ∙ + 10.05 ∙ 2

(2)

The diffusion rate is obtained by multiplying the diffusion coefficient with the degrees of freedom of the particle, which are evaluated in the model (Figure 2b (i)) by checking how many immediate neighboring locations can be occupied by the particle in question. Once the diffusion rates of all particles (!" + !# ) have been calculated, a weighted cumulative list of particle displacements can be obtained, upon which VSSM can be implemented (Figure 2b. (ii)). The total diffusion rate (% ) is taken as a sum of individual diffusion rates (&, ) of all particles:

+, +, % = ∑+. /(&", ) + ∑+. -(&#, )


(3)


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In order to choose a random particle for motion, a pseudo random number (0. ) is multiplied by the total rate. Then a search algorithm produces a pair of rates (&1 , &12. ) between which the randomly generated rate lies (4) (Figure 2b (iii)):

∑,+1 ,+. (&, )

≤ 0. ∙ % < ∑,+12. (&, ) ,+.

(4)

The mth particle is chosen to move within a time step that varies with the total diffusion rate calculated at that instant, modulated by another pseudo random number (05 ) (5) (Figure 2 (b) (iv))

67 =

8,(9: ) ;

Self-Organization of Electroactive Suspensions in Discharging Slurry

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