Carbon based ow-electrodes are an increasing research eld and nd potential application in water treat- ment processes as well as energy conversion and storage. Flow-electrodes usually consist of a pumpable carbon slurry made of carbon particles suspended in a liquid electrolyte solution. One application for ow- electrodes is ow-electrode capacitive deionization (FCDI), which is a membrane-based, electrically-driven desalination method using mostly activated carbon as active material. In contrast to capacitive deionization (CDI) systems based on static electrodes, the use of ow-electrodes enables a continuous operation and the treatment of high salinity solutions. However, it was observed that the performance of FCDI processes heavily relies on the activated carbon quality. The process performance results from a wide range of param- eters, including the activated carbon sample characteristics, which are usually not suciently covered and predicted by standard carbon analyses. With this article, we establish a foundation for applying electro- chemical impedance spectroscopy (EIS) as predictive characterization method for ow-electrode materials. This includes the investigation of in uencing system parameters and carbon characteristics, and the devel- opment of an equivalent circuit model. Finally, we demonstrate the possibility to predict and match the desalination performance of ow-electrodes based on di erent activated carbon types using EIS. 1. Introduction, Motivation and Objectives 1 The sustainable and reliant supply of sucient water and energy to a growing 2 population with increasing demand are major challenges humanity is facing, which 3 calls for improved and new technologies. [1{4] A growing research eld pro ting from 4 these challenges are ow-electrodes, which nd potential application in the elds of 5 Phone: +49-241-8095470, Fax: +49-241-8092252, Manuscripts.cvt@avt.rwth-aachen.de 1 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 2 water treatment and energy conversion and storage. [5] Flow-electrodes, also termed 6 slurry electrodes [6], suspension electrodes [5] or uidized bed electrodes [7], consist 7 of conductive particles suspended in an electrolyte solution. The conductive parti- 8 cles can form percolating networks, which conduct electrons upon contact with the 9 electrode or current collector and, thus, function as an electrode extension. Such 10 ow-electrodes may be applied to support faradaic reactions, as required for elec- 11 trosynthesis [8], batteries (e.g. zinc-air described in 1976 [9], lithium described in 12 2011 [10]), or for capacitive energy storage ( ow capacitors, described in 2012 [11]) 13 or capacitive salt adsorption for desalination (described in 2013 [12]). 14 Flow-electrode Capacitive Deionization. The latter, usually termed ow-electrode ca- 15 pacitive deionization (FCDI), is a promising application for ow-electrodes, which 16 enables the removal of ionic species from solutions. [12, 13] It is based on the concept 17 of capacitive deionization (CDI), which attracted increasing interest in the recent 18 years due to its energy eciency, the possibility of energy recovery and the potential 19 application in selective ion removal and recovery of various ionic species. [4, 14{18] 20 CDI uses an electrical eld, which leads to the migration of ions towards the oppo- 21 sitely charged electrodes and nally the adsorption of ions in the electrical double 22 layer (EDL) at the electrode surface. The desalination step can be compared to 23 the charging of a capacitor, which enables an energy recovery during the regenera- 24 tion. [19{21] However, due to the static electrodes applied in classical CDI systems, 25 charge-discharge cycles are required, which limits the feasible salinity range to low 26 salt concentrations. This limitation does not apply to FCDI, which enables a fully 27 continuous operation due to the use of owable electrodes recirculated through the 28 module. [7, 22, 23] In case of a fully continuous operation, a diluate and concentrate 29 stream of roughly constant concentrations are produced and the slurry electrode is 30 2 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 3 recirculated and regenerated continuously. Due to the combination of continuous 31 operation and improved mass transport within the electrode, FCDI can treat even 32 high-salinity water streams. [21] Additionally, the pumpability of the electrodes 33 enables a range of new process layouts and applications. [24{26] 34 Flowable electrodes. All technologies based on such owable (slurry-)electrodes rely 35 heavily on the quality of the conductive material used to prepare the slurries. In 36 most cases, these are carbon materials in various shapes and sizes. [5, 27] In case of 37 applications with redox-active electrodes, materials with a comparably low surface 38 area may be of advantage. Adsorption is not desired in this case, but rather a swift 39 transport of the reacting components to the ( ow-)electrode particle surface and a 40 rapid transport of the products away from the surface. [28, 29] In case of technologies 41 based on adsorption of components in the EDL, a high surface area is desirable. [14] 42 Many di erent physical and chemical processes in uence the performance of ow- 43 electrodes in these processes, whose interactions are not fully understood yet. An 44 increasing number of studies are investigating these interactions by means of mod- 45 elling, [30, 31] imaging methods [32] and electrochemical characterization methods. 46 [6, 11, 31, 33{36] 47 However, the in uencing parameters and material characteristics on the perfor- 48 mance as ow-electrode for speci c applications still need further investigation. In 49 most studies which focus on the investigation of slurry electrodes by electrochemi- 50 cal methods, such as cyclic voltammetry (CV) or electrochemical impedance spec- 51 troscopy (EIS), the ow-electrodes were investigated in a static manner. The slurries 52 were lled into cells with various designs and analyzed. [5, 37{39] In some studies 53 electrochemical methods were combined with rheological measurements performed 54 in rheometers ("electro-rheology"), [5, 40, 41] and were, thus, investigated dynam- 55 3 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 4 ically. Only very few measurements were actually performed in a ow cell at dy- 56 namic conditions ("pumped ow-electrodes"). [31, 42] However, these measurements 57 were mostly applied for qualitative comparisons and not analyzed and interpreted in 58 depth. Hoyt et al. recently developed a rst electrochemical impedance spectroscopy 59 model, which matches experimental data of capacitive ow-electrodes. [31] In this 60 study, Hoyt et al. developed a new circuit element, " ZEFC", which simulates the 61 suggested quasistatic behaviour of slurries at high frequencies. 62 Motivation and Objectives. The impact of speci c material characteristics on the 63 performance of a FCDI process is not fully understood yet. During the work with 64 FCDI systems we observed signi cant di erences in the performance of activated car- 65 bon (AC) provided by the manufacturers in di erent vessels in some cases, although 66 supposedly of the same type. The actual rheology and desalination performance of a 67 owable electrode depends on a sum of parameters, such as particle size distribution, 68 particle shape [43], particle conductivity [42], pore size distribution [44], carbon sur- 69 face chemistry [45] and redox-activity [46]. These parameters can change drastically 70 from batch to batch, depending on the carbon material. Most commercial carbons are 71 not intended for the use as owable electrodes and, thus, the standard speci cations 72 are usually not sucient. Due to the focus on speci c characteristics, most clas- 73 sical physical and chemical characterization methods have only limited signi cance 74 for the evaluation of a carbon material for application in FCDI. Additionally, many 75 of these methods, such as gas adsorption measurements, are very time-consuming. 76 Hence, for an actual application, a reliable method for the evaluation of the overall 77 performance of a carbon material as owable electrode is required, which is able to 78 produce results swiftly. 79 80 4 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 5 Electrochemical impedance spectroscopy (EIS) is an electrochemical characteriza- 81 tion method, which applies an alternating potential (or current) of di erent frequen- 82 cies to any electrochemical or material system, while the current (or voltage) response 83 is recorded. The change of amplitude and the phase shift of the measured response 84 allows to draw conclusions regarding chemical and physical processes dominating the 85 system. The hypothesis behind this work is that EIS measurements can predict the 86 desalination performance of slurries accurately when performed at dynamic condi- 87 tions. EIS measurements allow conclusions regarding the most important material 88 characteristics required for FCDI, when combined with classical physical and chemi- 89 cal characterization methods. While Hoyt et al. [31] took a rst step and developed 90 a model providing detailed physical understanding using a new circuit element, we 91 use a more application oriented approach based on standard elements used in EIS 92 models. 93 The aim of this study is to establish a foundation for an application of EIS as pre- 94 dictive characterization method for ow-electrode materials, e.g. for use as method 95 for incoming goods inspection. This study includes the investigation of (1) the in u- 96 ence of di erent system parameters on the EIS response and (2) the development of 97 a simple equivalent circuit model, which matches all obtained experimental results. 98 We then go a step further by (3) examining the main in uencing carbon charac- 99 teristics on the FCDI performance, and (4) demonstrating the possibility to predict 100 and match the desalination performance of ow-electrodes based on two completely 101 di erent activated carbon types using EIS. 102 2. Materials and Methods 103 All experiments were performed with the same FCDI cell design as described 104 in previous work. [21] The FCDI cells consist of polyethylene end plates, at gas- 105 5 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 6 kets, epoxy-impregnated graphite electrodes (M uller & R ossner GmbH & Co. KG, 106 180x180x10 mm) with ow channels for the ow-electrodes (3 mm width, 2 mm 107 depth, 200 cm overall length), a pair of cation and anion exchange membranes (Fu- 108 masep FKB-PK-130/ED-100 and Fumasep FAB-PK-130/ED-100, Fumatech BWT 109 GmbH) with an e ective surface area of 121 cm2and a 0.5 mm mesh spacer (Fu- 110 matech BWT GmbH, ED-100). A section of the cell is depicted in a cross-sectional 111 view in Figure 1. 112 Figure 1. Section of the FCDI cell applied for EIS measurements and desalination measurements in cross-sectional view. The feed water was supplied to the FCDI cells by a peristaltic pump (Ismatec 113 Reglo ICC peristaltic pump with two independent channels). The salt solutions used 114 as feed water and for the slurry preparation were prepared with puri ed water and 115 60 g/L sodium chloride (VWR Chemicals, >99.8%). The ow-electrodes were recir- 116 culated through the FCDI systems using a second peristaltic pump (Ismatec MCP 117 process drive, Master ex two-channel pump head Easy-Load II, Norprene tubing). 118 All in all, four di erent activated carbon powder samples were applied in this work: 119 6 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 7 (1) Carbopal SC11PG, (2) Carbopal CCP1400 spezial (both provided by Donau Car- 120 bon GmbH, Germany) and (3)/(4) Norit D10 (Alfa Aesar), of which two di erent 121 samples (hereafter termed " Batch 1" and "Batch 2") were analyzed, which were 122 purchased in two di erent vessels, but had the same LOT number. Table 1 gives 123 an overview of the activated carbon sample properties according to conventional 124 characterization techniques, as provided by the manufacturers. 125 Table 1. Overview of activated carbons applied in this study. Information provided by the suppliers. Carbopal Carbopal NoritD10 NoritD10 SC11PG CCP1400 spezial - Batch 1 -Batch 2 abbreviations SC CCP N- B1 N-B2 BET surface m2/g 950 1400 600 600 particle size d90 64m 80 m 140 m 140m d50 16m - 30 m 30m pH value - 4.5 - 6.5 6 - 8 alkaline alkaline type - charcoal coconut shell - - 2.1. Sieving experiments 126 The activated carbon was sieved at low amplitude in a sieving tower assembled of 127 stackable sieves (Retsch GmbH, Germany) with mesh widths (in m) of 20, 32, 40, 128 63, 80, 112, 125, 160, 230 and 350. The vibrating unit (Retsch AS200 digit) was set 129 to 1.5 for the duration of each sieving interval. The mass of the particle fractions was 130 measured at regular time intervals, sieving was stopped when no signi cant changes 131 were observed in the mass of the particle fractions. 132 7 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 8 2.2. BET/gas sorption 133 The activated carbon samples (about 0.1 g each) were analyzed regarding their 134 surface and porosity characteristics via N 2gas adsorption/desorption measurements 135 (ASAP 2020, Micromeritics). The samples were pretreated at 90C and 10 mbar for 136 24 h and degassed for 6 to 8 hours before the adsorption/desorption analysis. 137 2.3. Rheological Measurements 138 The rheological measurements were performed with a modular compact rheometer 139 (MCR) from Anton Paar with the PP50 plate-plate measuring system at 25C. Shear 140 rates between 10 1/s and 1000 1/s were applied. 141 2.4. Electrochemical impedance spectroscopy measurements 142 The electrochemical impedance spectroscopy (EIS) measurements were perfor- 143 mend in two-electrode con guration with one FCDI cell through which two ow- 144 electrodes were continuously recirculated from small glass beakers, which were con- 145 tinuously stirred. The experimental settings are summarized in Table 2. In case of 146 the EIS measurements for the prediction of the desalination performance of a spe- 147 ci c ow-electrode, the slurry was recirculated through both the desalination and 148 concentration cells, as illustrated in Figure 2. The impedance measurements were 149 performed with the desalination cell only. The EIS measurements were performed 150 with a potentiostat with inbuilt frequency response analysis (FRA)-module (Refer- 151 ence 3000, Gamry). Frequencies between 0.009 and 10000 Hz were applied with an 152 amplitude of 10 mV, experiments were performed without potential bias. In most 153 measurements, the imaginary part was negative at high frequencies (above 1000), 154 likely due to inductive e ects of the cables. These e ects were not considered in this 155 work. 156 8 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 9 Table 2. Overview of parameter settings for EIS experiments. Slurry Feed water AC conc. NaCl conc. Flow rate NaCl conc. Flow rate Figure no. wt.% g/L mL/min g/L mL/min In uence of activated carbon concentration and slurry ow rate 3 (a) 0-10 60 150 60 13 3 (b) 10 60 0-150 60 13 Comparison of four activated carbons 10 (a) 16 60 150 60 13 Prediction of desalination performance 12 (a) 10, 15, 30, 35 60 175 60 2 12 (c) 17 60 175 60 2 2.5. Desalination experiments 157 A three-channel power supply (HM8143, HAMEG Instruments GmbH) was ap- 158 plied for the desalination measurements. The electrical conductivity (EC) of the 159 aqueous solutions was measured using conductivity sensors (LTC0,35/23; Sensortech- 160 nik Meinsberg). Additionally, product water samples were taken during steady state 161 operation. The density of each sample was analyzed to verify the salt concentration 162 of the samples. The diluate stream and the concentrate stream were each treated in 163 single-pass mode, while the ow-electrodes were recirculated at a constant ow-rate. 164 The experimental settings for the desalination experiments (Figures 12 (b) and (d)) 165 equal the settings given in Table 2 for Figures 12 (a) and (c). 166 9 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 10 Figure 2. Illustration of the FCDI system layout applied for (left) the electrochemical impedance spectroscopy measurements and (right) the desalination experiments. The EIS measurements were performed with the desalination cell only. The desalination experiments were performed with the continuous two module FCDI layout described in previous publications. [21] 3. Results: EIS with Parameter Variations 167 As mentioned before, there are not many studies published in which the results 168 of dynamic EIS measurements in an actual ow cell are described. For an initial 169 understanding of the behaviour of such systems, parameter studies were performed, 170 some results of which are plotted in Figure 3 (a) and (b). The experiments described 171 in this section were performed with the activated carbon Carbopal SC11PG. 172 3.1. In uence of the activated carbon content 173 The activated carbon content was varied between 0-16 wt.%, while all other pa- 174 rameters were kept constant (Table 2). When considering the results plotted in 175 Figure 3 (a), signi cant changes can be observed due to the addition of increasing 176 amounts of activated carbon to the ow-electrode. At 0 wt.% activated carbon only 177 10 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 11 05 1 01 50510156 , 7, 8, 9, 10 wt.%5 wt.%3 wt.%2 wt.%0.5 wt.%4 wt.%1 wt.%Carbopal SC11PG-Z'' [Ω]Z ' [Ω]0 wt.% (a) Variation of the AC content. 0.00 .51 .01 .52 .00.00.51.01.52.01 00 mL/min75 mL/min50 mL/min12 mL/min2 5 mL/min10 wt.% Carbopal SC11PG-Z'' [Ω]Z ' [Ω]0 mL/min (b) Flow-electrode ow rate variation. Figure 3. Results of EIS measurements; (a) Variation of the activated carbon (AC) content with a constant NaCl concentration of 60 g/L in both water channel and ow-electrode and a ow- electrode ow rate of 150 mL/min, and (b) Variation of the ow-electrode ow rate at a carbon loading of 16 wt.% (Carbopal SC11PG) and a 60 g/L NaCl concentration in both, water channel and ow-electrode. a small shoulder is seen in the plot at high frequencies and a more or less straight 178 line at an angle of around 80towards the low frequencies, which is in agreement 179 with the behaviour of rough electrode surfaces (non-ideal capacitance). A slightly 180 depressed semicircle develops in the lower frequency range with the addition of ac- 181 tivated carbon. With increasing activated carbon content, this semicircle becomes 182 smaller, which correlates with an increasing capacitance and a decreasing interfacial 183 resistance within the ow electrode. 184 3.2. In uence of the ow-electrode ow rate 185 Next, we investigated the transition in the impedance of static ow-electrodes to 186 pumped ow-electrodes by varying the ow-electrode ow rate between 0-100 mL/min. 187 All other parameters were kept constant (Table 2). The results are plotted in Fig- 188 11 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 12 ure 3 (b). At rst sight, the changes to the Nyquist plot when increasing the ow- 189 electrode ow rate look similar to the changes when increasing the activated carbon 190 concentration. Without pumping, only a small shoulder is seen in the plot at high 191 frequencies and a more or less straight line at an angle of around 55towards the low 192 frequencies, similar to the plot without activated carbon in the ow-electrode. In 193 both cases, 0% activated carbon and 0 mL/min, the system acts like a static capaci- 194 tor. The added activated carbon in the 0 mL/min case leads to a decrease of the line 195 angle at low frequencies, which we explain by the in uence of the activated carbon 196 porosity. With increasing ow rate a slightly depressed semicircle forms at the lower 197 frequency range, which correlates with an improved charge percolation. Our theories 198 regarding these phenomena are discussed further in the following section. 199 4. Development of an equivalent electric circuit model 200 An equivalent circuit was developed, which can be used to t and improve the 201 understanding of the EIS data. The term equivalent circuit refers to a system of 202 electric circuit elements, in this case, which imitates the impedance behaviour of 203 an electrochemical system (an FCDI cell in this case) over a wide range of frequen- 204 cies. According to Fletcher et al. [47], this represents the "electrochemist's way" of 205 speaking. 206 In most EIS measurements with FCDI systems, mainly two semicircles were vis- 207 ible in the resulting Nyquist plots, which corresponds with two dominant time con- 208 stants in the system (e.g. each one R-C element). In an FCDI system, we expect 209 the EIS spectra to be in uenced by both, di usion limitation as well as the porous 210 electrode material. In fact, the observed semicircles do not appear as perfect circles, 211 but are rather depressed, which indicates an overlapping of the above mentioned 212 12 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 13 physical e ects. In the following, the thoughts which led to the development of the 213 equivalent circuit model presented in this article are illustrated in more detail. 214 4.1. Convectional current- formation of the low frequency semicircle 215 When transfering the understanding of faradaic systems and the understanding 216 of the behaviour of classical capacitive systems (e.g. electrical double-layer superca- 217 pacitors) to capacitive ow-electrodes, the formation of the "larger", low frequency, 218 semicircle can be explained. One might assume at a rst thought that capacitive 219 ow-electrodes in a FCDI cell, as applied in this study, would behave similar to a 220 regular electrochemical double-layer capacitor (EDLC). This is the case for stagnant 221 ow-electrodes or a FCDI cell with water or salt solution pumped through the ow- 222 electrode channels. In these cases, as sketched in Figure 6, a semicircle is visible at 223 the higher frequency range, which changes into a more or less linear dependence at 224 the lower frequencies, with a slope of di erent angles, depending on the experimental 225 conditions. However, in case the ow-electrode channel contains an activated carbon 226 suspension and is pumped, a second semicircle appears in the low frequency region 227 (Figure 4, Figure 3 (a) and (b)). 228 Such low-frequency semicircles are also visible in previously published work [42] 229 and was also adressed by Hatzell et al. [5]. In the latter work, it was suggested 230 that this behaviour observed for ow-electrodes results from increased electronical 231 conductivity. Hoyt et al. [31] mentioned this as "current induced by convection". 232 We agree that this behaviour is induced by electron transfer, which also leads to a 233 "loss" of electrons in case of convective transport due to pumped ow-electrodes, as 234 illustrated in Figure 4. The formation of similar semicircles in impedance spectra 235 can be observed in case of faradaic reactions, which involve a transfer of electrons 236 and are usually modelled by a R-C element, where the resistor is usually termed 237 13 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 14 charge transfer resistance. 238 Figure 4. Illustration of (a) the e ect of an electric current induced by convection on EIS spectra of a system based on capacitive ow-electrodes, and comparison to (b) an electrochemical system with faradaic reactions. In case of capacitive ow-electrodes, when no potential bias is applied and when 239 assuming ideal circumstances, no faradaic reactions should take place. The particles 240 suspended in the salt solution are expected to be charged upon contact with the cur- 241 rent collector or other charged particles (formation of charge percolation networks), 242 which results in the adsorption of ions at the particle surface. This would usually 243 result in the exhibition of a capacitive behaviour in the impedance spectra. In case 244 14 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 15 of an activated carbon concentration of 0 % (Figure 3 (a)) this is the case, as only 245 the current collector is charged and no electrons are removed by pumping. This is 246 also the case for stagnant carbon ow-electrodes. However, once the ow-electrodes 247 are pumped, the particles are charged and some of them will leave the cell in a 248 charged state, without the ability to be discharged again directly, as illustrated in 249 Figure 4. Although the charge is stored capacitively, the measuring system, thus, 250 records an apparent electric current caused by the convective charge removal. Due 251 to the apparent electron ow, this phenomenon can be modelled using a resistor. 252 The value of this resistor, which we will term as "charge percolation resistance Rcp" 253 from here onwards, decreases with increasing conductivity of the ow-electrode. An 254 increasing activated carbon content, for example, leads to an increased size of charge 255 percolation networks [32] and an overall improved conductivity, which agrees with 256 the discussion by Hatzell et al. [5]. 257 4.2. Charge transfer at current collector- formation of the high frequency semicircle 258 Charge transfer phenomena at the current collector and insucient contacting 259 often lead to the observation of semicircles in the higher frequency range in Nyquist 260 plots, for example in case of EDLCs [48, 49]. In case of FCDI, charge transfer at the 261 current collector may include the graphite plate itself, as well as activated carbon 262 particles resting at the surface, which are in direct contact with the graphite plate, 263 as illustrated in Figure 5. 264 The results of tting the equivalent circuit model to the experimental results 265 shown in Figure 3, given in Tables S1 and S2, support this hypothesis. Due to the 266 direct contact of the particles with the current collector, short ways and comparably 267 small electrically active surface area lead to a comparably low resistance and capaci- 268 tance. The magnitude of the capacitance and resistance in uences the time constant 269 15 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 16 Figure 5. Illustration of carbon particles in direct contact with the current collector in case of three di erent experimental conditions. Charged surfaces due to direct contact with the current collector are highlighted in blue. This leads to a change in the capacitance C CC, as can be seen in the values tted to experimental results (Tables S1 and S2). of a circuit element, which is in direct relation with the characteristic frequency of 270 the related phenomenon. For simple R-C-circuits the time constant is de ned as 271 given in Equation 1, with R being the ohmic resistance and C being the capacitance 272 of the correlating circuit elements. [50] 273 =RC (1) In case of a small resistance and a small capacitance, the time constant is small, 274 which leads to a high characteristic frequency. 275 4.3. Di usion and electrode porosity- curve depression 276 We assume that the combined e ect of di usion and electrode porosity in the 277 system lead to the non-ideal, depressed shape of the semicircles in the Nyquist plots 278 16 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 17 of experimental results regarding FCDI systems obtained in this work. Distinction 279 between di usion and porosity is not feasible with EIS, both cause a 45line in 280 impedance spectra in ideal cases. Due to the above discussed e ect of the charge 281 percolation resistance, this 45line results in depressed semicircles in case of FCDI, as 282 illustrated in Figure 6. While di usion is usually modelled using Warburg elements, 283 [51] electrode porosity is often modelled using di erent types of ladder networks, or 284 so-called transmission lines. [47, 52] Robert de Levie [53, 54] provided the basis for 285 modelling the behaviour of rough and porous electrodes by introducing the concept 286 of the so-called "RC transmission lines" in the 1960s. [53, 54] Such transmission 287 lines can be degenerated to models with ladder structures of di erent kinds, which 288 can also model non-uniform porosity, as it occurs in materials based on natural raw 289 materials, such as activated carbon. [47] Degenerate equivalent circuits are networks 290 of electrical circuit elements with di erent structures, but the same total impedance 291 behaviour over the investigated range of frequencies. [47] The disadvantage of such 292 ladder structures is the high number of parameters, which need to be tted. If the 293 system is not well-known, the parameters need to be guessed, which hardly conveys 294 an actual physical meaning. This, in combination with the fact that the observed 295 ow-electrodes not only exhibit porous behaviour, but also di usive behaviour, led 296 us to choose a constant phase element as simpli ed (and arti cial) circuit element 297 representing the systems porosity as well as di usion behaviour. A constant phase 298 element can, in fact, be seen as an in nite ladder network ranging over an in nite 299 range of time constants. However, in our measurements we often observed that an 300 "unrestrained" constant phase element does not model the system very well, which 301 leads to the conclusion that the system is not limited by porosity or di usion at low 302 frequency. To constrain this behaviour to a smaller frequency range we, thus, used a 303 charge percolation resistance in parallel to the constant phase element, which leads 304 17 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 18 to the behaviour illustrated in Figure 6. 305 (RCC, CCC) (RCP1, CPEAC)( RCC, CCC)F CDI cellEDLCu nlimiteddiffusion/ porosity contact r esistance-Z'' [W]Z ' [W] Figure 6. Typical Nyquist plots of supercapacitors and capacitive ow electrodes and indicated physical behavioural regimes. 4.4. The equivalent circuit model: Putting it together 306 By combining the above discussed observations, we developed the equivalent cir- 307 cuit illustrated in Figure 7. We found that this equivalent circuit can be tted to 308 represent measurements with FCDI systems in a wide range of settings regarding 309 di erent parameters such as activated carbon content and ow-electrode ow rate 310 with a minimum of tting parameters. 311 The circuit elements depicted in Figure 7 represent (1) the electron transfer at 312 the current collector (R CCand C CC), (2) the in uence of di usion and electrode 313 porosity (R cp1and CPE AC), (3) the capacitance and current induced by convection 314 (Rcp2and C dl) and (4) the combined, serial resistance of solutions, membranes etc. 315 (RS). 316 18 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 19 Figure 7. Equivalent circuit model applied to t experimental data. 5. Further results and discussion 317 5.1. Fit results and observations based on the equivalent circuit model 318 The equivalent circuit model shown in Figure 7 was tted to experimental results 319 by using the software ZView 2 (Version 3.5b, Scribner Associates, Inc.). The square 320 of the standard deviation of the resulting ts from experimental results was in the 321 range of 104in most cases. Tables S1 and S2 of the supplementary materials show 322 results for the t values of the di erent elements of the equivalent circuit model, 323 tted to the results shown in Figure 3 (a) and (b). 324 Variation of the activated carbon content and ow-electrode ow rate. The circuit 325 elements with the most signi cant changes due to a change in the activated carbon 326 content are C CC, Rcp1, Rcp2and C dl. The changes in C CCwere discussed in Section 4.2 327 19 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 20 and illustrated in Figure 5. The values of R cp1are mostly similar to R cp2, which means 328 the electrode porosity/di usion has an in uence over the whole frequency spectrum. 329 In case of low activated carbon concentrations as well as low ow-electrode ow 330 rate, the tted values of R cp1increase disproportionally. In this case, the constant 331 phase element dominates also at lower frequencies. To model this behaviour, R cp1 332 was excluded from the model in case of low activated carbon contents and low ow- 333 electrode ow rates. With an increasing activated carbon content the size of the 334 charge percolation networks increases [32], which leads to an improved exploitation 335 of the activated carbons maximum salt adsorption capacity as well as an improved 336 conductivity. This leads to an increase of the double layer capacitance C dland a 337 signi cant decrease of the charge percolation resistance R cp2, which matches the t 338 results well. In case of an increasing ow-electrode ow rate, however, there is a 339 sudden increase in C dlfrom 0 mL/min to 12 mL/min, while at further increasing 340 ow rate C dldecreases again. In case of the stagnant ow-electrode (0 mL/min), not 341 all particles get in contact with the current collector. Some of the particles "rest" in 342 the bulk of the ow-electrode, not in contact with the current collector. When the 343 ow-electrodes are pumped, the particles are moved and, thus, brought into contact 344 with the current collector. A larger fraction of the maximum salt adsorption capacity 345 is used. At even higher ow rates the capacitance apparently decreases, due to the 346 removal of charged particles by pumping. In this case, the increased capacitance has 347 an in uence on the current induced by convection and, thus, a decrease of R cp2. On 348 the other hand, an increased ow-electrode ow rate, and thus a reduced residence 349 time, may also lead to an incomplete charging of the pores, which may also reduce 350 the value of C dl. The overlap of these two e ects may explain the maximum of R cp2 351 at a ow rate of 50 mL/min. 352 20 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 21 Variation of the salt concentration. Additional experiments were performed to in- 353 vestigate the in uence of the electrode porosity/di usion in capacitive ow-electrode 354 systems. For this, EIS measurements were performed with varied NaCl concentra- 355 tions at constant activated carbon concentration. 356 0.20 .40 .60 .81 .01 .20.00.20.40.60.81.01.27 g/L NaCl1 6 g/L NaCl1 25 g/L NaCl317 g/L NaCl16 wt.% Carbopal SC11PG-Z'' [Ω]Z ' [Ω] Figure 8. Results of EIS measurements; Variation of the NaCl concentration at a constant activated carbon content of 16 wt.% (Carbopal SC11PG) and a ow-electrode ow rate of 150 mL/min. At a low NaCl concentration a strong semicircle depression at low frequencies as 357 well as a quasi-linear region at the higher frequencies is visible, described as "quasi- 358 steady porous electrode behaviour" by Hoyt et al. [31]. We agree that this behaviour 359 is caused by electrode porosity/di usion, which we chose to model with a constant 360 phase element and a parallel resistor ("charge percolation resistance"). This way 361 of modelling enables an in uence of the porosity/di usion limitation of the whole 362 spectrum of frequencies, which leads to a better t in the lower frequency range at 363 relatively low ow-electrode ow rates compared to the nice newly-developed model 364 by Hoyt et al. [31]. With increasing salt concentration, the low frequency semicircles 365 become rounder and shift to higher frequencies. This e ect may be explained by a 366 reduced di usion way at high salt concentrations and, thus, a faster charging, which 367 21 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 22 shifts the characteristic frequency of the low-frequency semicircle to higher frequen- 368 cies. This correlates well with the t results given in Table S4 of the supplementary 369 material, which show a decreasing trend of the t values of R cp2and additionally a 370 reduction of C dl. The latter may be explained by an increase in the charge loss due 371 to the convection-induced current at increasing salt concentrations. 372 5.2. The in uence of the particle size 373 In the following, we investigate the origin of the observed performance di erences 374 between the four activated carbon samples. A set of experiments was performed 375 comparing the results of impedance measurements to results from desalination ex- 376 periments, which were all performed with the same set of parameters. Figure 9 (a) 377 shows results of impedance measurements performed with the activated carbon Car- 378 bopal SC11PG and sieved particle size fractions of the same activated carbon. Fig- 379 ure 9 (b) shows results of the corresponding desalination experiments. While signi - 380 cantly di erent particle size fractions were chosen for the comparison, the di erence 381 in impedance as well as desalination performance is minute. The experiments per- 382 formed with the size fraction of 40-50 m show the most signi cant di erences to the 383 other measurements. The real as well as imaginary impedance are slightly increased, 384 which matches the result of the desalination experiments, in which this fraction 385 showed the lowest desalination rate. The microscopic images depicted in Figure S2 386 show signi cant di erences between the di erent particle size fractions. However, in 387 particle size fraction of 40-50 m, for example, is still a signi cant number of small 388 particles present, which may diminish the e ect of sieving to a certain extent. All 389 in all, the di erences between the samples are unexpectedly low, and cannot explain 390 the signi cant di erences observed in the performance of di erent carbon batches. 391 22 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 23 0.20 .40 .60.00.20.4+ 40-50 µm<20 µm Mix< 20 µm40-50 µm17 wt.% Carbopal SC11PG-Z'' [Ω]Z ' [Ω] Standard( all particle sizes) (a) Particle sizes - Nyquist plot. 204060801001 7 wt.% Carbopal SC11PGC FeedNaCl conc. [g/L]S tandardM ix< 20 µm40-50 µmDiluatesConcentrates (b) Particle sizes- desalination. Figure 9. Results of EIS measurements and desalination experiments; A sample of the activated carbon Carbopal SC11PG was sieved into di erent particle size fractions. The standard sample was compared to the size fractions <20m and 40-50 m of the same activated carbon and a mixture of the two sieved fractions. The EIS response at the same weight percentage was measured and compared to the desalination performance. 5.3. Comparison of four AC samples: the origin of the performance di erences 392 To identify the activated carbon characteristics with the main in uence on the 393 desalination performance, we compared four di erent activated carbons, as listed 394 in the "Materials and Methods" section. The four samples exhibited signi cantly 395 di erent results regarding desalination performance and impedance behaviour, as 396 plotted in Figure 10 (a). 397 At the same mass percentage, the activated carbon slurry prepared with "Car- 398 bopal SC11PG" showed a lower impedance and resistance by more than a factor 399 of six, compared to the carbon sample with the highest impedance. The t results 400 for C DLand R CP2, plotted in Figure 10 (b), show an inversed correlation between 401 increasing capacitance and decreasing ohmic resistance. With decreasing resistance 402 the capacitance increases, which may partially be due to an improved use of the avail- 403 23 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 24 12 3 0123E IS measurementsequivalent circuit fitC arbopal CCP 1400 sp.N orit D10 - Batch 2C arbopal SC11PG-Z'' [Ω]Z ' [Ω]Norit D10 - Batch 1 (a) EIS results. 012345N orit D10 -Batch1Carbopal CCPNorit D10 -Batch2Carbopal S C11PGA ctivated carbon sampleRCP2CDLEquivalent circuit fit results 16 wt% AC samplesResistance [Ω∗10−3]0 5101520C apacitance [F] (b) EIS t values. 11 01 0002004006008001000C arbopal CCP1 400 spezialN orit D10 - Batch 1Carbopal SC11PGCumulative Pore Area [m2/g]P ore Width [nm]Norit D10 - Batch 2 (c) Cumulative Pore Area. 11 01 000.00.20.40.60.81.0C arbopal CCPN orit D10 - Batch 1Carbopal SC11PGCumulative Pore Volume [cm3/g]P ore Width [nm]Norit D10 - Batch 2 (d) Cumulative Pore Volume. Figure 10. Comparison of four di erent activated carbon samples, results of (a) EIS measurements with 16 wt.% activated carbon sample, (b) tted values using the equivalent circuit model, and (c)/(d) results of gas adsorption measurements to determine the pore size distribution. able electrically active surface area. The results from gas adsorption measurements, 404 plotted in Figures 10 (c) and (d), revealed the pore size distribution as cause of the 405 di erences. The pore size distribution also appears to be the main di erence between 406 the two di erent batches of the same activated carbon type. The two best perform- 407 ing carbons have a signi cant amount of mesopores. Especially the cumulative pore 408 24 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 25 volume, plotted in Figure 10 (d), correlates well with the desalination/impedance 409 performance of the carbons, while the cumulative pore area does not. Two e ects 410 (Figure 11) can explain the improved desalination performance with the presence of 411 mesopores: (1) an improved ion accessibility and transport and reduced transport 412 resistance within mesopores and (2) a signi cantly increased outer particle volume, 413 which leads to a signi cantly increased carbon volume fraction in the suspension 414 at the same mass fraction. The increased "outer particle" volume fraction leads to 415 a signi cant improvement in the charge percolation between particles, and a thus 416 improved desalination performance. The increased viscosities observed in carbon 417 slurries prepared with mesoporous carbons supports this hypothesis, as an increased 418 volume fraction will also increase inner friction in the suspension. However, both 419 e ects may play an important role in the performance boost due to the presence of 420 a signi cant amount of mesopores. 421 Figure 11. Charge and ion transport in carbon suspensions of microporous carbons and carbons with additional mesopores at equal carbon mass percentages. 25 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 26 In further works, the in uence of internal and external di usion should be in- 422 vestigated in more depth. A more detailed equivalent circuit model could help to 423 di erentiate between the mass transport limitations caused by the di usion within 424 the particle (internal di usion) and the di usion to the particle (outer di usion). 425 This would provide further scienti c insight into the transport mechanisms in porous 426 slurry electrodes and could help to further simplify the search for an optimized carbon 427 material. 428 5.4. Prediction of the desalination performance with EIS 429 A nal set of experiments aimed at demonstrating the possibility to predict the 430 desalination performance of a carbon slurry by using EIS. We prepared ow-electrode 431 suspensions using two activated carbons with signi cantly di erent characteristics, 432 one being mainly microporous (Norit D10, Batch1, "Carbon A"), while the other also 433 contains a signi cant amount of mesopores (Carbopal SC11PG, "Carbon B"). We 434 adjusted the carbon content of the ow-electrodes to achieve a similar impedance 435 behaviour with the two di erent carbon types at two concentration ranges. The 436 results of this set of experiments are shown in Figure 12 (a). Finally, we demon- 437 strated the relevance of the impedance results for the desalination performance by 438 performing continuous desalination experiments with the two-module setup illus- 439 trated in Figure 2 (right side). Results of the desalination experiments are plotted 440 in Figure 12 (b). 441 We achieved a good match in the impedance behaviour of Carbon A and Carbon 442 B for the mass fractions of the sets 10 wt% A / 30 wt% B and 15 wt% A / 35 wt% B 443 (Figure 12 (a)). The carbon slurries also showed matching results in the correspond- 444 ing desalination experiments (Figure 12 (b)). In case of the higher percentage set 445 of carbon slurries, 15 wt% A / 35 wt% B, a slightly more pronounced deviation 446 26 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 27 0.20 .40 .60 .81 .01 .20.00.20.40.60.81.01 5, 10 wt.%Carbopal SC11PG-Z'' [Ω]Z ' [Ω]Norit D10 - Batch 13 5, 30 wt.% (a) Performance match - Nyquist plot. 35% N-B130% N-B115% SC10% SC20406080100C oncentratesD iluatesN orit D10 - Batch 1CFeedC arbopal SC11PGNaCl conc. [g/L] (b) Performance match - desalination. 101 001 0000.00.20.40.61 0,15 wt.%30,35 wt.%C arbopal SC11PGViscosity [Pas]S hear rate [1/s]Norit D10 - Batch 1 (c) Viscosity measurements. Figure 12. Results of EIS measurements, desalination and viscosity experiments; Suspensions based on two di erent activated carbons were matched regarding their EIS response at two di erent mass fraction values and the corresponding desalination performance tested. was observed between the desalination performances of the matched ow-electrodes. 447 The 15 wt% slurry of Carbon B reached a somewhat better desalination compared 448 to the 35 wt% slurry prepared with Carbon A. The curve representing the 15 wt% 449 slurry of Carbon B intersects the x-axis at a higher ohmic resistance than the curve 450 representing the 35 wt% slurry prepared with Carbon A, while the resistances at low 451 27 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 28 frequencies are nearly the same. This results in a small di erence in the overall real 452 impedance of around 0.034 , which may explain the small di erence in desalination 453 performance between the two carbon slurries. However, all in all the results for the 454 matched slurries matched well. 455 Figure 12 (c) shows results of a viscosity investigation performed with the above 456 described carbon slurries, which were adapted in weight percentage in a way to 457 exhibit a similar electrochemical performance. While the desalination performance 458 of the two pairs of slurries match very well, the rheological behaviour appears to 459 be signi cantly di erent. The slurries made of the Carbopal SC11PG carbon have 460 a signi cantly lower viscosity, while reaching the same desalination performance. 461 Hence, a combination of electrochemical impedance spectroscopy with rheological 462 measurements is well suited for a screening study for activated carbons with optimum 463 performance in FCDI processes. 464 6. Conclusions 465 In this article, we establish the foundation for EIS as a predicitve characterization 466 method for ow-electrode materials, especially in the context of water treatment. We 467 investigated the in uence of di erent system parameters on the EIS response and 468 developed an equivalent circuit model, which can be tted to match all results we 469 obtained experimentally. We investigated the in uence of di erent carbon charac- 470 teristics on the desalination performance and observed a signi cant in uence of the 471 pore size distribution. The carbon samples with a signi cant amount of mesopores, 472 additional to micropores, showed an overall improved performance. The activated 473 carbons with the highest cumulative pore volume showed the best desalination per- 474 formance, which we conclude is mainly due to an increased volume fraction of the 475 activated carbon. An increased carbon outer volume fraction leads to an improved 476 28 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 29 charge percolation and thus an improved desalination. On the other hand, the par- 477 ticle size distribution did not have a signi cant in uence on the desalination perfor- 478 mance. Finally, we demonstrated the possibility to use electrochemical impedance 479 spectroscopy measurements to adjust the performance of ow-electrode suspensions 480 made of di erent activated carbons. The desalination performance of the matched 481 ow-electrodes showed a very good congruence. The results of this study are valuable 482 for application as carbon characterization method for application in technologies us- 483 ing ow-electrodes. EIS may be applied for on-line process monitoring and control of 484 the ow-electrode performance in various processes. It can also serve as direct, easy 485 in-line method for the characterization of carbon suspensions in general, considering 486 the actual wetting and agglomeration conditions in-situ. 487 Acknowledgements 488 This work was supported by the German Federal Ministry of Education and 489 Research (BMBF) under the project ElektroWirbel (FKZ 13XP5008) and by the 490 European Research Council (ERC) under the European Unions Horizon 2020 re- 491 search and innovation program (694946). M.W. appreciates the funding from the 492 Alexander von Humboldt Foundation. The authors thank Fumatech BWT GmbH 493 and Donau Carbon GmbH for the provision of material samples. The authors thank 494 Andreas Augustin and Benedikt Aumeier for the support in the development of 495 the gas adsorption measurement method, and Jingyu Xie, Niklas K oller and Rachel 496 Krupp for their constructive e ort in this study. The authors thank Tomas Klicpera, 497 Dana Kaubitzsch, Faras Brumand-Poor, Uwe Schnakenberg and Oliver Blatt for the 498 valuable discussions. 499 29 A. Rommerskirchen et al. / Carbon 00 (2018) 1{38 30