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DOE OSTI2025

Toward Establishing Uniqueness of Experimentally Determined Transference Numbers

The passage of current through a battery results in the development of concentration gradients in the electrolytic phase. For a fully characterized binary electrolyte, where the conductivity, salt diffusion coefficient, cation transference number, and the thermodynamic factor are known, concentration and potential gradients in the electrolytic phase can be modeled using Newman’s concentrated solution theory. We report two methods for measuring the transference number: the standard method based on electrochemical measurements ( t + , echem 0 ) and electrophoretic NMR ( t + , eNMR 0 ). The electrochemical approach requires combining measurements from multiple experiments; the equations used to determine the cation transference number and the thermodynamic factor are coupled, nonlinear algebraic equations. In the electrophoretic-NMR-based approach, however, the equations used to determine the cation transference number and the thermodynamic factor are decoupled. We find for a liquid electrolyte comprised of a lithium salt dissolved in tetraglyme, the values of the transference numbers obtained by these two methods are distinct. For example, at 30 °C, t + , echem 0 = −1.02 ± 1.11 and t + , eNMR 0 = 0.25 ± 0.04. The corresponding thermodynamic factors are also different. While the magnitude of the predicted concentration gradients based on the two sets of parameters are different, the predicted current-voltage relationships are similar.

Hickson, Darby T. (ORCID:0000000251339755)↗

DOE OSTI2023

Polymer Architecture-Induced Trade-off between Conductivities and Transference Numbers in Salt-Doped Polymeric Ionic Liquids

Recent experiments have demonstrated that polymeric ionic liquids that share the same cation and anion but possess different architectures can exhibit markedly different conductivity and transference number characteristics when doped with lithium salt. In this study, we used atomistic molecular simulations on polymer chemistries inspired by the experiments to probe the mechanistic origins underlying the competition between conductivity and transference numbers. Our results indicate that the architecture of the polycationic ionic liquid plays a subtle but crucial role in modulating the anion–cation interactions, especially their dynamical coordination characteristics. Chemistries leading to longer-lived anion–cation coordinations relative to lithium–anion coordinations lead to lower conductivities and higher transference numbers. Furthermore, our results suggest that higher conductivities are accompanied by lower transference numbers and vice versa, revealing that alternative approaches may need to be considered to break this trade-off in salt-doped polyILs.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2022

The Transference Number

The performance of rechargeable batteries and other electrochemical systems depends on the rate at which the working ion (often a cation) is transported from one electrode to the other. The cation transference number is an important transport parameter that affects this rate. The purpose of this perspective is to distinguish between approximate and rigorous methods used in the literature to measure the transference number. We emphasize the fact that this parameter is dependent on the reference frame used in the analysis; care must be taken when comparing values obtained from different sources to account for differences in reference frames. We present data obtained from a well‐characterized electrolyte. We compare rigorously determined transference numbers in two reference frames with values obtained by an approximate method. We conclude with a qualitative discussion of the relationship between the transference number and salt concentration gradients that are obtained when current is drawn through a battery.

Gao, Kevin W.↗

DOE OSTI2023

Conductivity and Transference Numbers in Lithium Salt-Doped Block Copolymeric Ionic Liquid Electrolytes

We present multiscale molecular dynamics simulation results comparing the conductivity and transference numbers in lithium salt-doped polymeric ionic liquids (PolyILs) and the lamellar phases of block copolymeric ionic liquids (coPolyILs). In both systems, the anion mobilities decreased with salt loading. Lithium ions exhibited negative mobilities in both systems, but the magnitudes decreased with an increase in salt concentrations. More interestingly, the anion mobilities were lower in the lamellar systems compared to homopolymers in magnitude, but the lithium ion mobilities and transference numbers were less negative in such systems. We examine the anion–cation and lithium–anion interactions in terms of radial distribution functions, coordination characteristics, and ion-pair relaxation timescales. Based on such analyses, we rationalize the salt concentration dependencies as a result of the interfacial interactions in lamellar systems and the competition between anion–cation and lithium–anion interactions in both PolyILs and coPolyILs. Altogether, the findings presented in this study demonstrate that the modified anion–cation and lithium–anion interactions in the microphase-separated coPolyILs may provide a strategy for realizing higher lithium ion transference numbers relative to the homopolymeric counterparts.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Elucidating the Molecular Origins of the Transference Number in Battery Electrolytes Using Computer Simulations

The rate at which rechargeable batteries can be charged and discharged is governed by the selective transport of the working ions through the electrolyte. Conductivity, the parameter commonly used to characterize ion transport in electrolytes, reflects the mobility of both cations and anions. The transference number, a parameter introduced over a century ago, sheds light on the relative rates of cation and anion transport. This parameter is, not surprisingly, affected by cation–cation, anion–anion, and cation–anion correlations. In addition, it is affected by correlations between the ions and neutral solvent molecules. Computer simulations have the potential to provide insights into the nature of these correlations. We review the dominant theoretical approaches used to predict the transference number from simulations by using a model univalent lithium electrolyte. In electrolytes of low concentration, one can obtain a quantitative model by assuming that the solution is made up of discrete ion-containing clusters–neutral ion pairs, negatively and positively charged triplets, neutral quadruplets, and so on. These clusters can be identified in simulations using simple algorithms, provided their lifetimes are sufficiently long. In concentrated electrolytes, more clusters are short-lived and more rigorous approaches that account for all correlations are necessary to quantify transference. Elucidating the molecular origin of the transference number in this limit remains an unmet challenge.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Transforming an Ionic Conductor into an Electronic Conductor via Crystallization: In Situ Evolution of Transference Numbers and Structure in (La,Sr)(Ga,Fe)O 3–x Perovskite Thin Films

Mixed-conducting perovskites are workhorse electrochemically active materials, but typical high-temperature processing compromises their catalytic activity and chemo-mechanical integrity. Low-temperature pulsed laser deposition of amorphous films plus mild thermal annealing is an emerging route to form homogeneous mixed conductors with exceptional catalytic activity, but little is known about the evolution of the oxide-ion transport and transference numbers during crystallization. Here the coupled evolution of ionic and electronic transport behavior and structure in room-temperature-grown amorphous (La,Sr)(Ga,Fe)O 3-x films as they crystallize is explored. In situ ac-impedance spectroscopy with and without blocking electrodes, simultaneous capturing-synchrotron-grazing-incidence X-ray diffraction, dc polarization, transmission electron microscopy, and molecular dynamics simulations to evaluate isothermal and non-isothermal crystallization effects and the role of grain boundaries on transference numbers is combined. Ionic conductivity increases by ≈2 orders of magnitude during crystallization, with even larger increases in electronic conductivity. Consequently, as crystallinity increases, LSGF transitions from a predominantly ionic conductor to a predominantly electronic conductor. The roles of evolving lattice structural order, microstructure, and defect chemistry are examined. Grain boundaries appear relatively nonblocking electronically but significantly blocking ionically. The results demonstrate that ionic transference numbers can be tailored over a wide range by tuning crystallinity and microstructure without having to change the cation composition.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Transference Number of Electrolytes from the Velocity of a Single Species Measured by Electrophoretic NMR

Accurate measurement of the cation transference number is critical for designing batteries with a given electrolyte. A promising approach for measuring this parameter is electrophoretic NMR (eNMR). In the standard approach, the average cation, anion, and solvent velocities under an applied electric field are used to estimate the cation transference number with respect to the solvent velocity, ${t}_{+}^{0}.$ Here, in this study, we show that ${t}_{+}^{0}$ can be determined from measurements of the electric-field-induced velocities of individual species. The ${t}_{+}^{0}$ values obtained from eNMR experiments on a model electrolyte (LiTFSI/tetraglyme) based on single species velocities are consistent with the standard approach. An important parameter that enters into the analysis is the velocity of the electrode–electrolyte interface which must be finite in an eNMR experiment. Agreement is only obtained after accounting for this velocity. The single-species approach is particularly valuable when one or more components of the electrolytic mixture are not easily accessible by NMR, for example zinc and magnesium cations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

High Li + Transference Number Electrolyte Enabled by Fluoride Acceptor for Low-Temperature Li-Ion Batteries

To enable wide-temperature operation of lithium-ion batteries (LIBs), new electrolyte formulations have been developed to enhance the performance, particularly at low temperatures. A key challenge lies in achieving both high ionic conductivity and a high lithium-ion transference number due to their inherent trade-off. In this study, we designed an electrolyte system comprising tris(pentafluorophenyl)borane (TPFPB), a fluoride acceptor, and LiF salt in ethylene carbonate (EC)-free solvents. TPFPB, with its electron-deficient boron center, facilitates fluoride transfer reactions that promote the dissociation of otherwise insoluble LiF. When methyl acetate (MA) was used as the solvent, the electrolyte exhibited a high transference number (t Li + = 0.85) and ionic conductivity (σ = 5.0 × 10 –3 S cm –1 ). The optimized electrolyte demonstrated excellent performance at −20 °C, with no evidence of lithium plating. This work presents a new strategy for electrolyte design by leveraging cation desolvation to achieve high-performance LIBs for low-temperature and high-power applications.

anions↗

DOE OSTI2024

Simplified Universal Equations for Ionic Conductivity and Transference Number

Nernst-Einstein equation can provide a reasonable estimate of the ionic conductivity of dilute solutions. For concentrated solutions, alternate methods such as Green–Kubo relations and Einstein relations are more suitable to account for ion-ion interactions. Such computations can be expensive for multicomponent systems. Simplified mathematical expressions like the Nernst-Einstein equation do not exist for concentrated multicomponent mixtures. Newman’s treatment of multicomponent concentrated solutions yields a conductivity relation in terms of species concentration and Onsager phenomenological coefficients. However, the estimation of these phenomenological coefficients is not straightforward. Here, mathematical formulations that relate the phenomenological coefficients with the friction coefficients are developed, leading to simplified, ready-to-use expressions of conductivity and transference numbers that can be used for a wide range of ionic mixtures. This approach involves spectral decomposition of the matrix of Onsager phenomenological coefficients. The general analytical expressions for conductivity and transference number are simplified for binary electrolytes, and numerical solutions are provided for ternary and quaternary mixtures with ion dissociation.

Electrochemistry↗

DOE OSTI2022

Conductivity and Transference Number Determination Protocols for Solid Oxide Cell Materials

To standardize materials and component characterization for next generation hydrogen production and energy generation solid oxide cell (SOC) technologies, test protocols are being established to facilitate comparison across the numerous laboratories and research institutions where SOC development for application in solid oxide fuel cells (SOFCs) and solid oxide electrolyzes cells (SOEC) is conducted. This paper proposes guiding protocols for fundamental electrical properties characterization of SOC materials, including temperature- and oxygen partial pressure (pO 2 )-dependent conductivity measurements, and use of the electromotive force for determining the transference numbers, or contributions of each charge carrier (i.e., ions and electrons), to the total conductivity. The protocol for Archimedes density measurements is also provided as an integral technique to both of these methods.

25 ENERGY STORAGE↗

NASA NTRS2003

Material Properties Governing Co-Current Flame Spread: The Effect of Air Entrainment

A study on the effects of lateral air entrainment on an upward spreading flame has been conducted. The fuel is a flat PMMA plate of constant length and thickness but variable width. Video images and surface temperatures have allowed establishing the progression of the pyrolyis front and on the flame stand-off distance. These measurements have been incorporated into a theoretical formulation to establish characteristic mass transfer numbers ("B" numbers). The mass transfer number is deemed as a material related parameter that could be used to assess the potential of a material to sustain co-current flame spread. The experimental results show that the theoretical formulation fails to describe heat exchange between the flame and the surface. The discrepancies seem to be associated to lateral air entrainment that lifts the flame off the surface and leads to an over estimation of the local mass transfer number. Particle Image Velocimetry (PIV) measurements are in the process of being acquired. These measurements are intended to provide insight on the effect of air entrainment on the flame stand-off distance. A brief description of the methodology to be followed is presented here.

Coutin, Mickael↗

DOE OSTI2025

Solvation governs cation transference in glyme-based lithium battery electrolytes

The efficacy of electrochemical systems is governed by the cation transference number, which represents the fraction of current carried by the working ion. Energy is wasted when field-induced motion also drives anions and solvent molecules, decreasing the transference number to near-zero. We present a systematic study of cation transference in a series of electrolytes: tetraglyme (TG), octaglyme (OG), and poly(ethylene oxide) (PEO) mixed with lithium bis(trifluoromethanesulfonyl)imide. In all three electrolytes, starting from the dilute salt concentration limit, the experimentally measured cation transference number decreases with increasing concentration, reaching a minimum between -0.1 and -0.2, before rising back to positive values. Explicit measurements of field-induced species' velocities by electrophoretic nuclear magnetic resonance indicate that negative cation transference numbers in TG and OG electrolytes are dictated by solvation interactions with minimal contribution from anion-cation interactions. Simulation-based solvation structures indicate that OG serves as a bridge between TG and PEO. Multi-charge positive clusters, which are negligible in TG, become increasingly important at higher chain lengths (OG and PEO). As migrating cations drag their solvation shells, this solvation-induced motion is amplified in glyme electrolytes because of covalent interactions between solvating glyme molecules and free glyme molecules.

Im, Julia↗

DOE OSTI2022

Effect of Tethering Anions in Block Copolymer Electrolytes via Molecular Dynamics Simulations

Ion-containing block copolymers (BCPs) are promising solid-state electrolytes as they can combine ion conduction and mechanical robustness via multiple microphases. However, salt-doped BCPs can have low ion conduction and transference number. One strategy to increase transference number is to tether anions to the polymer backbone (creating a single-ion conductor), though this may impact cation mobility. Leveraging coarse-grained molecular dynamics simulations, we compare the effects of ion concentration and polymer dielectric constant on BCPs with and without bonding anions to the chain (without changing any other chemical properties). We find that single-ion BCPs have higher cation conductivity than analogous salt-doped BCPs, especially at moderate ion concentrations. Furthermore, we also compare several structural features of these systems; notably, tethering anions causes the ions to spread more evenly throughout the conducting phase, which is related to improved cation conduction.

25 ENERGY STORAGE↗

DOE OSTI2026

A structural and electrochemical study of perfluoropolyether-poly(ethylene oxide) solid polymer electrolytes

Solid polymer electrolytes offer attractive safety, processability, and interfacial adhesion for enabling high–energy solid-state lithium batteries, but they are often limited by narrow oxidative stability windows and low lithium-ion transference numbers. In an attempt to broaden the electrochemical stability window and increase lithium-ion transference number of poly(ethylene oxide) (PEO)-based solid polymer electrolytes, we produce an optically clear, crosslinked membrane of PEO and perfluoropolyether (PFPE) using a mixed solvent method and subsequently infuse the membrane with a lithium salt. Structural and thermal analyses reveal nanoscale phase separation between fluorocarbon and hydrocarbon domains with characteristic spacings of 7–8 nm and an elevated glass transition for the hydrocarbon phase. Consistent with this, PFPE-containing membranes exhibit substantially lower ionic conductivity than PEO analogs (dry and plasticized). The transference number and electrochemical stability are similar to pure PEO. These results demonstrate that fluorination implemented as segregated nanoscale domains does not deliver the anticipated transport or stability benefits; instead, phase separation increases tortuosity and suppresses hydrocarbon-phase dynamics. The work underscores the importance of fluorine placement and morphology control, guiding the design of partially fluorinated solid polymer electrolytes toward architectures that avoid detrimental nanoscale phase separation.

Carden, Peyton [ORNL] (ORCID:0000000162296538)↗

DOE OSTI2026

Understanding the Influence of Chain Architecture on the Transport Quantities of Polymer Electrolytes with Covalently Bonded Anions

Here, we use a combination of experiments and coarse-grained molecular dynamics simulations to elucidate the structure–property relationships in polymer electrolytes obtained by the copolymerization of poly(vinyl ethylene carbonate─lithium styrene bis(trifluoromethanesulfonyl)imide) or p(VEC-LiSTFSI). Experiments show that the conductivity reduces with increasing anion (i.e., STFSI) fraction on the chain, and the cation transference number (t + ) is found to be dependent on the anion fraction. Furthermore, a significant fraction of unpolymerized VEC monomers are observed. Since it is inherently difficult to experimentally control the chain architecture and the amount of unpolymerized VEC in these systems, we perform coarse-grained molecular dynamics simulations on model polymer systems with different chain architectures to mimic the plausible experimental systems. Specifically, we look at the differences in transference numbers arising from (i) a random copolymer of VEC and STFSI monomers; (ii) a blend of VEC-STFSI copolymer with VEC monomers; and (iii) a ternary blend of the VEC homopolymer, STFSI homopolymers, and VEC monomers. The ternary blend model demonstrates the closest resemblance with the experimental transference numbers and diffusivities. The lithium diffusivity obtained from the coarse-grained models with VEC monomers (plasticizers) is about 1.5 times that of the model without VEC monomers, showing that the plasticizing effect of VEC monomers is modest. We rationalize the experimental observations based on aggregate and cluster analyses obtained from molecular simulations. This work reveals that polymer electrolyte chain architecture and plasticizers can critically influence the transport properties, and these parameters should be considered when designing single ion conducting polymeric electrolytes.

cluster distribution↗

DOE OSTI2025

A quantitative figure of merit for battery SEI films and their use as functional solid-state electrolytes

As a key passivation film that governs battery operation, the solid electrolyte interphase (SEI) has long been credited for enabling high-performance batteries or blamed for their eventual death. However, qualitative descriptions of the SEI often found in the literature (e.g., “conductive,” “passivating”) highlight our incomplete understanding of this layer, where even the most basic properties foundational to SEI function remain difficult to measure. Here, we quantify SEI conductivities and SEI transference numbers using a separator-free Cu|SEI|Li architecture that treats the SEI as a functional solid-state electrolyte (SSE). We find that while any SEI property alone (e.g., electronic conductivity) is weakly correlated (R 2 < 0.67) with battery performance (e.g., Coulombic efficiency), a strong correlation (R 2 > 0.99) can be achieved by defining the “SEI cT number” as a product between the SEI transference number (T) and the ratio of SEI conductivities (c). Analogous to the thermoelectric figure of merit (i.e., zT ), SEI cT quantitatively benchmarks the holistic impact of SEI properties on battery performance and underscores the pitfalls of citing such properties in isolation. Perhaps most strikingly, we demonstrate that Li metal deposition and stripping at room temperature is possible in our separator-free Cu|SEI|Li cell, confirming that the SEI can function precisely as an SSE. Together, these results enrich our understanding of the SEI, not just as a passivation layer but as a functional structure that can potentially have important implications for solid-state batteries.

Science & Technology - Other Topics↗

DOE OSTI2022

Complete characterization of a lithium battery electrolyte using a combination of electrophoretic NMR and electrochemical methods

Improving transport properties of electrolytes is important for developing lithium-ion batteries for future energy storage applications. In Newman's concentrated solution theory, electrolytes are characterized by three transport parameters, conductivity, diffusion coefficient, and transference number, in addition to the thermodynamic factor. In this work, these parameters are all determined for an exemplar liquid electrolyte, lithium bis(trifluoromethanesulfonyl)imide mixed in tetraethylene glycol dimethyl ether, using electrochemical methods. The intrinsic coupling between parameters obtained by electrochemical methods results in large error bars in the transference number that obscure the transport behavior of the electrolyte. Here, we use electrophoretic NMR (eNMR) to measure the electric-field-induced ion and solvent velocities to obtain the transference number directly, which enables determination of the thermodynamic factor with greater certainty. In conclusion, our work indicates that the combination of eNMR and electrochemical methods provides a robust approach for complete characterization of battery electrolytes.

25 ENERGY STORAGE↗

DOE OSTI2022

Transport and mechanical behavior in PEO-LLZO composite electrolytes

Abstract Composite solid electrolytes (CEs), wherein ion-conducting polymer and ceramic/glass is mixed, are promising candidates for all-solid-state batteries due to their promise of acceptable ionic conductivity and mechanical properties compared to their individual constituents. While numerous studies have focused on improving the performance of CEs, it is still unclear what the material targets are that can result in improved macroscopic performance especially in light of the coupled needs for high transport and high mechanical strength in these materials. In this study, a two-dimensional (2D) mathematical model is developed to investigate electrochemical and mechanical characteristics of CEs. The model is compared to CEs consisting of poly-ethylene-oxide (PEO) polymer and lithium lanthanum zirconium oxide (LLZO) ceramic material with examination of the impact of varying LLZO volume fractions. The potential drop at the PEO-LLZO interface is evaluated using the junction potential theory. Using experimental data from the literature, the model estimates the ionic conductivity, effective transference number, and mechanical stiffness of the CEs. While the mechanical stiffness improves with increasing volume fraction of LLZO, the impact on conductivity and transference number depends on interfacial resistance at the interface. Finally, the study reports CE’s potential to enhance Li-ion transport and mechanical properties to inhibit lithium (Li) dendrite growth.

25 ENERGY STORAGE↗