Characterising the Ionic Transport and Thermodynamic Properties of Potassium-ion Electrolytes

Potassium-ion batteries (KIBs) are emerging as a promising complementary technology to lithium-ion batteries (LIBs) due to the availability and low cost of potassium. The lower charge density of K + compared to Li + has been suggested to result in superior ion transport in the electrolyte with KIBs potentially able to deliver superior rate capability and low-temperature performance. However, a comprehensive characterisation of the ionic transport and thermodynamic properties of nonaqueous K-ion electrolytes, critical to the development of KIBs, has not yet been reported. Here, for the ﬁrst time, we fully characterise the ionic transport and thermodynamic properties of a nonaqueous K-ion electrolyte, potassium bis(ﬂuorosulfonyl)imide (KFSI) in 1,2-dimethoxyethane (DME) and compare it with its Li-ion equivalent (LiFSI:DME) over the concentration range 0.25–2 m. This was realised by developing a K metal preparation protocol enabling suﬃcient K metal stability for electrolyte characterisation. Our results demonstrate that KFSI:DME indeed displays signiﬁcantly higher salt diﬀusion coeﬃcients and cation transference numbers than LiFSI:DME, evidencing the potential for high-power applications of KIBs. The lithium price has increased more than sevenfold since the start of 2021 (as of May 2022), reaching unprecedented price levels and demonstrating signiﬁcant challenges for the security of supply of lithium for lithium-ion batteries (LIBs). 1 With forecasts showing a potential signiﬁcant lithium supply deﬁcit by 2030,

][4][5][6][7] Potassium-ion batteries (KIBs) have a significant advantage over sodium-ion batteries (NIBs) as K + can reversibly intercalate into the graphite electrodes used in LIBs, 8,9 thus one of the primary components of KIBs is already available at commercial scale, unlike for NIBs. 2 KIBs may even have an advantage over LIBs in terms of rate and power.Early data show improved rate performance of KIBs compared to LIBs, 11 suggesting faster transport in potassium-ion (K-ion) electrolytes. 12The larger size of K + compared to Li + results in a lower charge density, and thus weaker interactions with solvent molecules and a smaller Stokes radius, 13 which is expected to facilitate faster ionic transport in the electrolyte. 2This is supported by the results from Landesfeind et al. who found improved transport properties of a nonaqueous sodium-ion (Na-ion) electrolyte compared to the lithium-ion (Li-ion) equivalent, and improved K-ion aqueous electrolyte transport compared to Li-and Na-ion. 14K + has also been found to have the lowest desolvation activation energy of the three cations. 12,15ough studies suggest improved rate performance, a comprehensive understanding of mass transport in nonaqueous K-ion electrolytes can only be obtained through full and accurate characterisation of the fundamental ionic transport and thermodynamic properties: the salt diffusion coefficient (D), the cation transference number (t 0 + ), the ionic conductivity (κ), and the thermodynamic Fig. 1 Schematic of our K preparation protocol enabling K-ion electrolyte transport and thermodynamic property characterisation.Our K metal preparation involves melting K metal chunks, skimming off impurities floating on the melt and quenching the clean metal.Clean K metal spheres are rolled, punched into discs and the surface polished using a microtoming technique adapted from a methodology developed in our group for Li. 10 Our K preparation enables characterisation of the K-ion electrolyte salt diffusion coefficient (D), the cation transference number (t 0 + ), the ionic conductivity (κ), and the thermodynamic factor (χ M ).The higher D and t 0 + of KFSI:DME compared to LiFSI:DME results in reduced concentration gradient formation, which is represented schematically.
factor (χ M ). 168][19][20][21][22][23] Spectroscopic techniques, capable of determining these properties for Li-ion electrolytes through direct visualisation of concentration gradients, have also recently been developed.These include X-ray spectroscopy, 24 Raman spectroscopy, 25 or magnetic resonance imaging (MRI). 26,27However, there is currently no study which has fully characterised the ionic transport and thermodynamic properties for nonaqueous K-ion electrolytes.Given these properties are challenging and time-consuming to obtain for Li-ion electrolytes, the added complication of the extreme reactivity of K metal provides significant additional challenges to K-ion electrolyte characterisation.
In this study we comprehensively characterise the critical transport and thermodynamic properties of a nonaqueous K-ion electrolyte, potassium bis(fluorosulfonyl)imide (KFSI) in 1,2-dimethoxyethane (DME), and of its Li-ion equivalent (LiFSI in DME) for comparison.We developed a K metal preparation protocol to ensure sufficient stability and data reproducibility to enable K-ion electrolyte characterisation using the most accurate electrochemical characterisation techniques.FSI -in DME is used as a model electrolyte system because of the ability of the FSI -anion to more effectively passivate the K and Li metal surface [28][29][30] and due to the stability of ethers in contact with both K and Li metal. 29,31ur K metal preparation protocol enables improved K metal stability, opening up the potential for more accurate K-ion electrode and electrolyte characterisation. 2,28By providing a comprehensive understanding of K-ion electrolyte transport, our work lays the foundation for more accurate Doyle-Fuller-Newman (DFN) modelling of KIBs and, most importantly, facilitates the development of novel, high performance K-ion electrolytes.

K Metal Electrode Preparation
State-of-the-art electrochemical techniques used to characterise electrolyte transport and thermodynamic properties rely on metallic electrodes that are chemically and electrochemically stable in the electrolyte under investigation.The reactivity of metallic K is one of the reasons why a thorough characterisation of a nonaqueous K-ion electrolyte has not yet been reported.
In this study, we developed a K electrode preparation protocol to ensure sufficient K metal stability and data reproducibility.The first step involves melting K metal chunks in an argon glovebox, skimming off impurities floating on the melt and quenching the clean metal.Right before cell assembly, a clean K metal sphere is rolled into a metal sheet (thickness ∼0.6 mm), punched into discs and the surface polished using a microtoming technique adapted from a methodology developed in our group for metallic lithium (Fig. 1). 10 It has been shown that standard K metal preparation results in high open-circuit voltages (OCVs) in symmetric K cells, > 100 mV, indicating K metal instability and inhomogeneous distribution of impurities. 28,32Figure 2a shows the exceptionally low OCVs and superior reproducibility for K symmetric cells prepared using our K electrode preparation protocol compared to the standard preparation procedure commonly employed in literature, 28,33 demonstrating significantly improved surface stability and homogeneity. 32This is also supported by the considerably reduced total impedance of cells prepared using our preparation compared to the standard method (Fig. 2b).Crucially, our preparation protocol enables sufficient K stability for electrolyte transport property characterisation (Supplementary Discussion 1).Whereas the standard preparation cannot be used to determine certain critical properties, such as D (Supplementary Fig. 5).
X-ray photoelectron spectroscopy (XPS) with Ar + depth-profiling was utilised to examine the surfaces of K metal prepared using both the standard literature method and our preparation protocol to understand our improved stability.The O 1s spectra from the standard preparation in Fig. 2c exhibits a broad peak at 533.6 eV as a result of Na KLL Auger electron emission 34 and Na is the main species identified throughout the majority of the examined depth (Supplementary Discussion 2).However, Na is a minor impurity element in the electrode prepared with our method, as evidenced by the small Na KLL peak in Fig. 2d.Inhomogeneous distributions of impurity elements like Na could alter the activity of the K metal electrodes, leading to the non-zero OCV evident in Fig. 2a. 32dditionally, the oxide peak at 527.0 eV 35 in Fig. 2c is the most prevalent oxygen species at the surface of the standard sample, and its proportion increases with increasing Na content, suggesting the electrode surface is Na 2 O-rich.Such an oxide-rich surface layer could impede the transport of K + across the interface and be responsible for the large initial impedance observed (Fig. 2b).In contrast, the O 1s spectra from the electrode prepared with our preparation method are dominated by the KOH peak at 529.3 eV 34 in Fig. 2d.Due to the high reactivity of K metal this KOH likely forms within the XPS as fresh K metal is exposed, suggesting the surface is rich in metallic K.
The K 2p XPS spectra from the standard K electrode in Fig. 2c show a decreasing K 2p doublet peak area with sputtering depth, while the K 2p doublet from our method remains intense during sputtering in Fig. 2d. 35These results therefore demonstrate that our K electrode preparation process produces K-rich electrode surfaces with greater uniformity and reduced levels of impurity elements, allowing K metal electrodes to be prepared with greater reproducibility.
K metal electrodes prepared with our protocol enable us to apply and adapt the most accurate electrochemical characterisation methods to measure the K-ion electrolyte t 0 + , κ, χ M and D.

Transference Number
The cation transference number, t 0 + , is the fraction of current carried by the cation.It has been shown even increasing the transference number by 0.2 can significantly improve accessible capacity during charge and discharge. 36t 0 + is difficult to measure accurately, and is often mischaracterised as the transport number using steady-state techniques such as the Bruce-Vincent method, 37 relying on assumptions of electrolyte ideality and neglecting ionic species interaction. 16,26ere the densitometric Hittorf method was used to characterise the transference number relative to the solvent velocity. 17,26,38,39This method involves applying a polarisation to a large symmetric cell, then closing two stopcocks to form three isolated chambers before extracting the solutions and measuring their densities to determine concentration changes (Methods and Supplementary Methods 2).The transference number is then determined via Eq. 1.
The partial molar volume of salt, V e , of the K-ion and Li-ion electrolytes are used to determine t 0 + (Supplementary Discussion 3).
Where V chamber is the volume of the cathodic or anodic cell chamber, c f is the concentration of the chamber after the experiment, c is the concentration of the neutral chamber, I pulse is the current applied and t pulse is the pulse duration.
Figure 3a shows the valid transference numbers from the Hittorf measurements for KFSI and LiFSI in DME.The results show the t 0 K + is significantly higher than t 0 Li + at lower concentrations of 0.25 m (0.49 and 0.34, respectively), though the t 0 K + decreases with increasing concentration so that it is is only slightly higher than t 0 Li + from 1.5-2 m. t 0 K + and t 0 Li + appear to be trending to similar values suggesting that the lower charge density of K + delays some of the ion-ion and ion-solvent interaction effects of increasing concentration.t 0 K + decreases from around 0.49 to 0.38 over the concentration range indicating increasing ion-ion and ion-solvent interactions are acting to bind up K + more strongly than FSI -.Whereas for Li + these interactions appear to have become significant at concentrations below those measured as t 0 Li + remains constant in this concentration range.The t 0 K + results are similar to those reported for NaPF 6 :EC:DEC by Landesfeind et al., though it is important to note their study treats the cosolvent as a single entity, assuming identical velocity of the two solvents, which is an assumption that has recently been shown by Wang et al. to have an impact on transference number measurements. 39upplementary Fig. 11 shows the anodic and cathodic chamber t 0 + measurements, with t 0 K + exhibiting significant deviation between them.Only Error bars for t 0 + depict error in the mean (Supplementary Methods 6).Fits described in Supplementary Methods 7 (b) Ionic conductivity κ measured with a conductivity cell, fit with the Casteel-Amis equation (Supplementary Methods 3). the anodic t 0 Li + and t 0 K + results were used and the cathodic data was discounted for two reasons.First, the high reactivity of K results in continuous formation of SEI, shown by the increasing impedance in Supplementary Fig. 20 for KFSI:DME.It is expected that at the cathodic K electrode the freshly plated K continuously reacted with the electrolyte, continuing to form SEI and reducing the salt concentration in the cathodic chamber, resulting in a lower density cathodic solution and greater difference from the neutral chamber concentration, hence, resulting in exaggeratedly low transference numbers.Therefore, given the highly sensitive density measurements, the cathodic transference numbers are likely underestimated.Second, significant discolouration was observed in the cathodic solution for many of the Li-ion and K-ion experiments, indicating a possible side reaction or dendrite formation (Supplementary Fig. 12).The same was found in the study by Hou and Monroe and their cathodic data was also discounted. 17

Ionic Conductivity
Figure 3b shows the ionic conductivities over the concentration range.LiFSI has higher κ from low concentrations through until ∼1.5 m, after which κ decreases significantly, matching previous findings. 40FSI, however, continues increasing and appears to plateau at 2 m.It has been shown to decrease after this point. 11This indicates there is likely significant species-species interaction for the LiFSI electrolyte compared with the KFSI electrolyte above ∼1.5 m.The trend matches that found by Hosaka et al. for KPF 6 and LiPF 6 in EC:DMC where the K-ion electrolyte conductivity was lower than the Li-ion electrolyte below 1.5 m.However they also found KFSI:PC had significantly higher conductivity than LiFSI:PC at all concentrations tested. 3This shows the importance of the combination of salt and solvent for optimum ionic conductivities for K-ion electrolytes.Since the χ M for KFSI is closer to ideality than LiFSI at lower concentrations (Fig. 4b), indicating less ion-ion interaction than for Li + , it appears that the lower ionic conductivity for KFSI for the majority of the concentration range could be due to inferior KFSI salt dissociation. 3Plotting the equivalent conductance over concentration also indicates that both are weak electrolytes with their non-linear dependence of conductance on the square root of concentration 38,41 (Supplementary Fig. 13).Though KFSI:DME is more non-linear than LiFSI:DME, again indicating inferior salt dissociation for KFSI.At higher concentrations above 1.7 m, the drop in conductivity for LiFSI is likely due to the greater ion-solvent and ion-ion interaction for Li + , where it is dragging more solvent than the K + due to its higher charge density and thus stronger solvation, while the stronger coulombic interaction of the Li + also results in greater ion-ion association, forming aggregates that increase the electrolyte viscosity. 40Aggregates have been shown not to form in KFSI:DME until concentrations above this range (> 3 M). 42High ionic conductivities are reached in the DME electrolytes, 16 mS cm −1 for KFSI:DME at 2 m and 15 mS cm −1 for LiFSI:DME at 1.5 m.The κ reached here are significantly higher than that for carbonate equivalents due to the lower viscosity of DME, 43 matching previous findings. 11,44upplementary Fig. 15 shows that the activation energies of ionic conduction of KFSI and LiFSI in DME are very similar and increase with concentration as a result of increasing ion-solvent interactions. 45The activation energy for both KFSI and LiFSI appears to be limited by the bulky FSI - anion.

Thermodynamic Factor
The thermodynamic factor, χ M , measures the non-ideality of an electrolyte and accounts for deviations from Nernstian behaviour, reflecting how the salt thermodynamic activity varies with concentration.Concentration cells were used in the measurement of χ M where the open-circuit voltages were measured between 'test' and 'reference' solutions (Methods and Supplementary Methods 4).The change in the OCV across the concentration cell, V , with molar concentration, c, is related to the thermodynamic factor, χ M , and transference number, t 0 + , by Eq. 2: Where f ± is the mean molar activity coefficient, F is the Faraday constant, R is the gas constant and T is the absolute temperature.The solvent concentration, c 0 , and the partial molar volume of solvent, V 0 , can be used to map the thermodynamic factor to the molar basis from the molal basis in which it is defined. 46,47As derived in Supplementary Discussion 6, we fit χ M to the function given in Eq. 3: Where c m is the molal concentration and A 1 and A 2 are fitting constants.The fits to the OCV data are presented in Fig. 4a.
Figure 4b shows how the thermodynamic factor changes with concentration.The trends match those found for other nonaqueous electrolytes. 16,17,25,38ith increasing concentration, first coulombic ion-ion interactions decrease the salt free energy relative to the DME, reducing the salt activity coefficient and hence causing a drop in χ M .As the concentration increases further, ion-solvent interactions increase, resulting in DME being increasingly bound, decreasing solvent vapour pressure, hence increasing the salt activity coefficient and χ M . 38,48The results show the decrease in χ M at lower concentrations for KFSI is significantly less than for LiFSI.This can be attributed to the following two factors.First the larger size and thus lower charge density of K + compared with Li + , resulting in weaker K + coulombic ion-ion interactions, hence the smaller reduction in χ M .Second, from Debye-Hückel theory the gradient of the χ M decrease at lower concentrations for both LiFSI and KFSI in DME should be equal as it is determined by the dielectric constant, ε, of the solvent. 47As Debye-Hückel theory assumes fully dissociated electrolytes, the lower KFSI gradient magnitude could further suggest poorer salt dissociation, 38 which is also indicated by the lower ionic conductivity (Fig. 3b) and more non-linear equivalent conductance (Supplementary Fig. S13) at low concentrations.The low ε of DME also provides minimal electrostatic screening, thus having a limited effect on reducing ion-ion interactions. 49 higher concentrations, the increase in χ M with increasing concentration is also significantly higher for LiFSI than for KFSI.This is again due to the reduced charge density of K + resulting in weaker interactions with solvent molecules and thus a smaller solvation shell of K + compared to Li + .The weaker K + solvation results in more free DME compared to Li + at higher concentrations, and therefore, the salt activity coefficient and χ M increase with increasing salt concentration at a reduced rate for KFSI.This is the same trend identified by Landesfeind et al. comparing NaPF 6 and LiPF 6 in EC:DMC. 14Le Pham et al. found a constant solvation number for KFSI:DME from Raman characterisation across this concentration range, supporting this increased binding of solvent increasing χ M . 42A similar study also found significant ion-pairing and solvent binding in LiFSI:DME. 40 Further experiments could characterise χ M over a wider concentration range with greater accuracy using the shifting-reference concentration cell + error for χ M (Supplementary Methods 6).The fits are described in Supplementary Discussion 6.
technique developed by Wang et al.. 38 Given the narrow concentration range, this was not deemed necessary for this study.

Diffusion Coefficient
Steady-state polarisation and long-term relaxation restricted diffusion 17,[50][51][52][53] was used to characterise D as it has been identified as being more accurate than pulse polarisation methods, being less susceptible to double layer relaxation effects. 53A custom restricted diffusion cell was designed (Supplementary Fig. 3) and galvanostatic polarisation was used to form the concentration gradient which was subsequently relaxed (Methods and Supplementary Methods 5).Contrary to many recent studies, 14,17,53 no separators were used in the restricted diffusion experiments to improve accuracy, due to the errors introduced through separator tortuosity estimation and variability. 17,38The cell was oriented vertically to suppress natural convection. 17,47Exponential relaxation occurs where the concentration gradient relates to the OCV, and the diffusion coefficient, D, can be determined from the linear time dependence of the logarithm of the open-circuit voltage via Eq. 4 (Supplementary Fig. 4).The cell geometry was designed to enable longer polarisation and relaxation times (20 h for polarisation and up to a maximum of 60 h for relaxation) to ensure less noisy relaxation and a more robust fit for both KFSI and LiFSI, similar to Wang et al.. 26 This was significantly longer than the shorter relaxation times (≤ 3 h) in many recent studies. 14,18,53 where V is the restricted diffusion cell OCV measured during relaxation, L s is the bulk electrolyte thickness, t is time and τ dif f is the characteristic decay time = Ls 2 π 2 D . Figure 5a shows D is significantly higher for KFSI than for LiFSI at all concentrations at 20 • C (Supplementary Fig. 18 shows all data).At 1 m D KFSI is over 50% higher than D LiFSI (7.6 × 10 −10 m 2 s −1 and 5.0 × 10 −10 m 2 s −1 , respectively).The difference is most significant at low concentrations where D KFSI is almost double that for D LiFSI (9.6 × 10 −10 m 2 s −1 and 5.2 × 10 −10 m 2 s −1 , respectively at 0.25 m).Supplementary Fig. 19 shows the faster relaxation profile and time of KFSI compared to LiFSI at 0.25 m.With increasing concentration the difference between D KFSI and D LiFSI becomes smaller (5.2 × 10 −10 m 2 s −1 and 4.8 × 10 −10 m 2 s −1 , respectively at 2 m).This appears again to be due to increasing ion-ion and ion-solvent interactions occurring for K + at higher concentrations having a greater relative impact compared to minimal interaction at lower concentrations, matching the same trend observed for t 0 + .Both D KFSI and D LiFSI appear to be trending to similar values with increasing concentration, again matching the trends for t 0 + and supporting the argument that the lower charge density appears to delay some + and χ M errors (Supplementary Methods 6).Fits obtained by combining all parameterised transport and thermodynamic properties (Supplementary Notes 1 and 2). of the ion-ion and ion-solvent interaction effects of increasing concentration.
The higher D KFSI also matches the trend observed by Landesfeind et al. with NaPF 6 showing higher D than LiPF 6 . 14However, the difference is much more significant for the K-ion electrolyte.D KFSI is also significantly higher than those of Li-ion and Na-ion electrolytes characterised, with 2.9 × 10 −10 m 2 s −1 found for 1 M NaPF 6 :EC:DEC at higher temperature of 25 • C, 14 and with D for the majority of LiPF 6 -based electrolytes coalescing around 2-3 × 10 −10 m 2 s −1 at 1 M at 25 • C. 16,17,38,53 The values obtained for D LiFSI here are also higher than most Li-ion carbonate electrolytes characterised and this is attributed to the significantly lower viscosity of the DME solvent used compared to carbonate solvents. 49gure 5b shows D converted into the thermodynamic diffusion coefficient, D, using χ M and Supplementary Eq. 17, reflecting the diffusion coefficient with respect to salt chemical potential gradients instead of concentration gradients.The D trend matches those in literature. 17,20,25,38The initial increase in D is due to increasing ion association due to the effective merging of two species into a single species resulting in lower resistance to the single species motion. 38D LiFSI shows a greater initial increase due to greater ion-ion interaction for Li + than for K + as indicated by χ M .At higher concentrations D KFSI is only slightly higher than D LiFSI , but shows almost the same trend, demonstrating that the most significant difference in diffusion behaviour is related to concentration gradients rather than chemical potential gradients.
The Stefan-Maxwell diffusion coefficients express the mobility of each electrolyte species relative to each other in terms of the thermodynamic forces driving diffusion, providing deeper understanding of diffusional behaviour (Supplementary Discussion 8).The Stefan-Maxwell coefficients for the KFSI and LiFSI electrolytes are shown in Fig. 5c and 5d, respectively.The coefficients are relatively similar for both KFSI and LiFSI and this is due to their similar thermodynamic diffusivities.Both of the solvent-ion coefficients, D 0+ and D 0− , for LiFSI and KFSI decrease by about an order of magnitude over the concentration range, demonstrating the drag from the DME solvent becomes stronger on both cation and anion with increasing salt concentration.D 0− is higher than D 0+ across the concentration range for LiFSI, indicating weaker interaction of the FSI - with the DME compared with the Li + interaction with DME.However, for KFSI, D 0− and D 0+ are much closer and at low concentrations are almost the same.This is due to t 0 + being ∼0.5 for K + at 0.25 m indicating K + and FSI -are carrying the same amount of current.
With increasing concentration, the difference between D 0− and D 0+ increases, matching the falling t 0 K + as ion-solvent interactions increase.The ion-ion diffusivity D +− for both LiFSI and KFSI is approximately two orders of magnitude lower than the solvent-ion diffusivities, particularly at lower concentrations demonstrating ion-ion interaction is somewhat significant for both, similar to that found for LiPF 6 :PC, 17 but not as significant as the five orders of magnitude difference found for LiPF 6 :EMC, indicating substantial ion-ion interaction. 38For both KFSI and LiFSI the maximum in D +− matches their maximum ionic conductivity, suggesting the greater cation/anion interaction is occurring due to lack of free DME at a lower concentration for Li + , corresponding to its stronger solvation interactions.

Discussion
In this work we have, for the first time, fully characterised the ionic transport and thermodynamic properties of a K-ion electrolyte and compared them to the Li-ion equivalent.
We developed a K metal preparation protocol which enabled sufficient stability for electrolyte characterisation.
The results show the salt diffusion coefficient and cation transference number of the KFSI:DME electrolyte is significantly higher than that of the LiFSI electrolyte for all concentrations below 2 m.
Higher salt diffusion coefficients and cation transference numbers reduce ionic concentration gradient formation and the associated concentration overpotentials, thus substantiating the potential of KIBs to deliver superior rate capability and low-temperature performance.The ionic conductivities were found to be similar, with LiFSI slightly higher until ∼1.7 m, likely due to inferior KFSI salt dissociation.The thermodynamic factor behaviour with concentration appears to indicate weaker solvent and ion-ion interactions of K + compared to Li + .Overall this study proves that the increased cation size and lower charge density of K + , and thus weaker solvent and ion-ion interactions are beneficial for high power applications.Full characterisation of the K-ion electrolyte has provided a more accurate understanding of K-ion electrolyte mass transport and thermodynamics, laying the foundations for further K-ion electrolyte development and optimisation.

Electrolyte Preparation and Electrochemistry
All electrolytes were prepared and handled in an Ar-filled glovebox with O 2 and H 2 O concentrations below 0.1 ppm.The electrolyte used was a solution of potassium bis(fluorosulfonyl)imide (KFSI, 99.9% Solvionic) or lithium bis(fluorosulfonyl)imide (LiFSI, battery grade, Fluorochem) in 1,2-dimethoxyethane (DME, 99.5% anhydrous, Sigma Aldrich).KFSI was dried under a high vacuum at 100 • C for 48 hours and LiFSI at 70 • C for 48 hours.DME was dried using 3 Å molecular sieves.All equipment was dried at 70 • C under vacuum for a minimum of 24 hours before being used and brought into the glovebox.The H 2 O content of the electrolyte solutions was determined by Karl Fischer titration, also performed in an argon-filled glovebox, and recorded to be below 10 ppm of H 2 O.All restricted diffusion, Hittorf and concentration cell experiments were conducted in a Binder Oven at 20 • C (±0.3 K).
All electrochemical tests were carried out using a battery cycler (VMP3, Biologic).
Electrochemical impedance spectroscopy (EIS) measurements were performed using a frequency response analyser (VMP3, Biologic), unless otherwise stated, over the frequency range of 200 kHz-500 mHz with a voltage amplitude of 10 mV.

Electrode Preparation
For the potassium electrode preparation protocol, potassium electrodes were prepared from potassium chunks in mineral oil (98% trace metals basis, Sigma Aldrich).First the K chunks were removed and melted in a beaker on a hot plate in an argon-filled glovebox.A spatula was then used to skim off and remove the visible impurity layers until the liquid K metal appeared clean.Then the liquid K metal was quenched into clean mineral oil forming spheres of clean K.These K spheres were then cleaned with hexane.Just before use the K was rolled to ∼0.6 mm thickness and one metal surface was gently polished using a plastic blade to remove any oxide and provide a sticking surface.Electrodes were then punched into discs of required diameter.The K electrode was placed on the current collector with the polished surface down.Next, for the active and exposed K surface, first the K was initially polished with the plastic blade, then followed by a second careful polish using a microtome blade, adapting a methodology developed in our group for metallic lithium. 10The microtome blade was used to form a mirror-like finish, resulting in an improved polished K surface free of surface irregularities.The active K metal surface was polished at the very end of cell setup, just before electrolyte addition, so the polished surface was exposed to the glovebox environment for minimal time before the electrolyte was added.
For the standard preparation the same method was used from literature 28,33 where K metal was cut, washed in hexane, and rolled before punching into electrodes.Lithium (99.9% trace metal basis, Sigma Aldrich) electrodes were prepared for use by first initially brushing the Li metal surfaces, then calendaring the Li to 0.3 mm thickness, before finally punching into electrodes.

X-ray Photoelectron Spectroscopy
X-ray photoelectron spectroscopy (XPS) was performed with an ULVAC PHI Versaprobe III XPS system generating monochromatic Al Kα X-rays (1486.6 eV, 15 kV anode voltage, 25 W beam power) under ultrahigh vacuum (UHV) conditions (∼10 −7 -10 −6 Pa).K metal samples were prepared in a glovebox and were immediately transferred into the XPS chamber using a vacuum transfer vessel (ULVAC PHI GmbH) to avoid contamination and ambient exposure.A 500 µm × 500 µm area from each sample was analysed.Survey scans were acquired at pass energies of 224 eV, and a lower pass energy of 55 eV was used for core-level spectra.In-built electron and low energy Ar + sources were utilized for charge neutralization.Depth-profiling was achieved with consecutive XPS analysis and Ar + sputtering (4 keV, 3 mm × 3 mm) for a total of 60 min.Acquired spectra were fitted with Voigt lineshapes, after application of a Shirley background, using CasaXPS software. 54All spectra were charge referenced to adventitious C 1s peak at 285 eV. 34Fitted regions were quantified and relative fractions of components were estimated using the relative sensitivity factors (RSFs) provided by CasaXPS (Supplementary Fig. 6 and 7). 54

Densitometry
For greater accuracy electrolyte concentrations were prepared gravimetrically rather than volumetrically, as using an analytical balance is more precise than a volumetric flask.In order to convert the gravimetric concentrations to volumetric (molality to molarity), high precision 5-digit density measurements were obtained using an Anton Paar DMA 4100 density meter in an argon-filled glovebox.Each measurement was temperature controlled at 20 • C. The density meter was rinsed with isopropanol (≥ 99.9%, HPLC grade, Fisher Chemical) and DME (99.5% anhydrous, Sigma Aldrich) at least three times and dried in ambient argon between measurements.It was ensured that the density meter was completely clean and returned to reading the argon density between each measurement.The density correlations for KFSI and LiFSI in DME are shown in Supplementary Fig. 1.

Hittorf Method
The sealed Hittorf cell was oriented vertically in the Binder Oven, and the current was applied so stripping occurred at the bottom electrode (anodic) and plating at the top electrode (cathodic), to prevent natural convection effects. 17,47After an intial rest of 4 h, the current polarisation was applied for duration t pulse = 20 h with the stopcocks open where the cell consists of a single cavity.Once finished, the two stopcocks were immediately closed creating three isolated chambers: anodic chamber at the bottom where stripping occurred, neutral chamber in the middle, and cathodic chamber at the top.The electrolyte solutions were then extracted through access ports.Extracted solutions from the three chambers were stirred for at least 1 h to ensure uniform concentration, after which their densities were measured using the Anton Paar DMA 4100 density meter at 20 • C. The molarity of the solutions was calculated using the density correlation (Supplementary Fig. 1).The differences in concentrations of the anodic and cathodic chambers from the neutral chamber was used to calculate t 0 + .The current used for polarisation for all K-ion Hittorf experiments was 100 µA, except at 0.25 m where 50-100 µA was used.For the Li-ion Hittorf experiments 200 µA was used except at 0.25 m where 50 µA was used.I pulse and t pulse were set such that the concentration boundary layers remained within the anodic and cathodic chambers during the experiment. 55Three measurements were taken at each concentration for KFSI and LiFSI concentrations above 0.5 m.Two measurements were taken for LiFSI at 0.25 m and 0.5 m.

Ionic Conductivity
For measurement of ionic conductivity, a commercial conductivity cell of known cell constant was used (CLR, 401-S-138C).The cell was filled with ∼0.5 mL electrolyte and tested with an impedance analyser (BioLogic MTZ-35 with ITS-e temperature chamber) at 15, 20 and 25 • C. The ionic conductivity of the electrolyte was calculated by dividing the cell constant by the series resistance extracted from a Nyquist plot.The ionic conductivities in Fig. 3b were fitted with the function proposed by Casteel and Amis (Supplementary Eq. 1). 56

Concentration Cell
For the concentration cell experiments a H-cell was designed including a Grade 5 frit to mitigate the faster diffusion from the K-ion electrolyte.A Grade 4 frit was found to be insufficient to suppress interdiffusion in the K-ion electrolyte, but gave reliable results with the Li-ion electrolyte.K and Li metal were prepared and cut into ∼5 mm × 20 mm strips.Each chamber of the H-cell was filled with 4 mL of electrolyte, with 1 m electrolyte used as the constant 'reference' concentration for both electrolyte systems.The electrodes were then lowered into the electrolyte and the cell was sealed and immediately brought into the Binder Oven.The OCV was tracked for 2 h to allow the cell to stabilise and reach the correct temperature and the OCV was then averaged over the next 10 min, as shown in Supplementary Fig. 2. At least three repeat measurements were made for each concentration.

Restricted Diffusion
The cell used for the restricted diffusion cells (Supplementary Fig. 3) was designed to ensure an airtight seal and the chamber is free of any geometric issues that can affect the concentration gradient.The cell was designed to be longer than typically used for Li-ion restricted diffusion experiments due to the identified faster diffusion of K-ion electrolytes to enable sufficient time to observe the relaxation and enable a more robust fit.The distance between the current collectors was 12 mm and the distance between the electrodes, Ls, was measured using digital calipers for each cell due to the slightly varying thickness of K.The thickness of the K was measured once it had been placed on the cell current collector due to K being soft and easily compressed.For example, Ls was 10.8 mm with K metal electrodes of 0.6 mm thickness.No separators were used to improve accuracy errors introduced through separator variability and tortuosity estimation. 17,38he experiment involved first a rest for 10 h where the OCV was tracked.Then a galvanostatic polarisation was applied for 20 h to induce the concentration gradient.The current was 35 µA for all Li-ion cells and for K-ion cells from 1 m and higher concentration.25 µA current was used for 0.25 and 0.5 m for K-ion.Finally, the current was switched off and the OCV recorded during relaxation.At least five cells were made for each K-ion diffusion concentration and at least three for Li-ion (Supplementary Fig. 18).The OCV values were adjusted by any V of f set from 0 V to ensure the OCV relaxed to 0 V so the linear behaviour of ln (V ) vs time could be analysed. 14,53he data was fit from the minimum time constant 0.5 τ dif f established by Newman and Thompson 57 for as long as it showed exponential relaxation behaviour, or until relaxation had completed (Supplementary Methods 5).The ln (V ) vs. time was plotted, with the gradient from the linear region used to obtain the salt diffusion coefficient.Representative relaxation profiles and the linear ln (V ) vs. time for 1 m KFSI and LiFSI in DME are shown in Supplementary Fig. 4.

Fig. 2
Fig. 2 Stability of K||K symmetric cells in 1 m KFSI:DME using our K preparation compared to standard K preparation at 20 • C (a) Averaged initial OCV profiles for 8 h.Light shaded areas depict standard error in the mean, calculated from at least 5 cells (Error analysis in Supplementary Methods 6) (b) Nyquist impedance plots after 1 h rest at 20 • C. XPS depth profiles on K metal after 5, 15 and 25 min of Ar + sputtering (c) O 1s, K 2p and C 1s spectra from the standard preparation (d) O 1s, K 2p and C 1s spectra from our preparation.

Fig. 3
Fig. 3 Transference numbers and ionic conductivities of KFSI and LiFSI in DME at 20 • C (a) Cation transference number t 0 + measured by Hittorf experiments.Error bars for t 0 + depict error in the mean (Supplementary Methods 6).Fits described in Supplementary Methods 7 (b) Ionic conductivity κ measured with a conductivity cell, fit with the Casteel-Amis equation (Supplementary Methods 3).
χ M is below unity until relatively high concentrations for both LiFSI and KFSI (∼1.4 m) indicating the point where ion-ion and ion-solvent interactions are equal.

Fig. 4
Fig. 4 Concentration cell and thermodynamic factor data for KFSI and LiFSI in DME at 20 • C (a) Concentration cell open-circuit voltage V (b) Thermodynamic factors χ M .Error bars depict the standard error in the mean for V , and the propagated t 0+ error for χ M (Supplementary Methods 6).The fits are described in Supplementary Discussion 6.

Fig. 5
Fig. 5 Diffusion coefficients of KFSI and LiFSI in DME at 20 • C measured by steady-state galvanostatic restricted diffusion (a) Salt diffusion coefficient D. Error bars depict the standard error in the mean (Supplementary Methods 6).Fits described in Supplementary Methods 7 (b) Thermodynamic diffusion coefficient D calculated using the measured thermodynamic factor (Fig. 4b).Stefan-Maxwell diffusion coefficients D ij (c) KFSI (d) LiFSI.Errors bars in D and D ij depict the propagated D, t 0+ and χ M errors (Supplementary Methods 6).Fits obtained by combining all parameterised transport and thermodynamic properties (Supplementary Notes 1 and 2).