Diffusion and migration in polymer electrolytes

Mixtures of neutral polymers and lithium salts have the potential to serve as electrolytes in next-generation rechargeable Li-ion batteries. The purpose of this review is to expose the delicate interplay between polymer-salt interactions at the segmental level and macroscopic ion transport at the battery level. Since complete characterization of this interplay has only been completed in one system: mixtures of poly(ethylene oxide) and lithium bis(trifluoromethanesulfonyl)imide (PEO/LiTFSI), we focus on data obtained from this system. We begin with a discussion of the activity coefficient, followed by a discussion of six different diffusion coefficients: the Rouse motion of polymer segments is quantified by Dseg, the self-diffusion of cations and anions is quantified by Dself,+ and Dself,−, and the build-up of concentration gradients in electrolytes under an applied potential is quantified by Stefan-Maxwell diffusion coefficients, D0+, D0-, and D+-. The Stefan-Maxwell diffusion coefficients can be used to predict the velocities of the ions at very early times after an electric field is applied across the electrolyte. The surprising result is that D0- is negative in certain concentration windows. A consequence of this finding is that at these concentrations, both cations and anions are predicted to migrate toward the positive electrode at early times. We describe the controversies that surround this result. Knowledge of the Stefan-Maxwell diffusion coefficients enable prediction of the limiting current. We argue that the limiting current is the most important characteristic of an electrolyte. Excellent agreement between theoretical and experimental limiting current is seen in PEO/LiTFSI mixtures. What sequence of monomers that, when polymerized, will lead to the highest limiting current remains an important unanswered question. It is our hope that the approach presented in this review will guide the development of such polymers

Theoretical interpretation of ion velocities in concentrated electrolytes measured by electrophoretic NMR

Electrophoretic NMR (eNMR) is emerging as a powerful technique for characterizing ion transport in electrolyte systems. We show that the standard approach for analyzing eNMR data is valid only for dilute electrolytes and provide a theoretical framework for interpreting eNMR results for all binary electrolyte systems with univalent salts. We derive relationships between the velocities of the ion species and the solvent in terms of the electrochemical Stefan-Maxwell diffusion coefficients and provide modified expressions for correctly calculating the transference number and conductivity from eNMR data in concentrated electrolytes. Our approach suggests that it is necessary to measure not just the displacement of ion species during the application of current in an eNMR experiment but also the displacement of the uncharged solvent in order to correctly calculate ion mobilities and the transference number

Effect of molecular weight and salt concentration on ion transport and the transference number in polymer electrolytes

Transport of ions in polymer electrolytes is of significant practical interest, however, differences in the transport of anions and cations have not been comprehensively addressed. We present measurements of the electrochemical transport properties of lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) in poly(ethylene oxide) (PEO) over a wide range of PEO molecular weights and salt concentrations. Individual self-diffusion coefficients of the Li+ and TFSI- ions, D+ and D-, were measured using pulsed-field gradient nuclear magnetic resonance both in the dilute limit and at high salt concentrations. Conductivities calculated from the measured D+ and D- values based on the Nernst-Einstein equation were in agreement with experimental measurements reported in the literature, indicating that the salt is fully dissociated in these PEO/LiTFSI mixtures. This enables determination of the molecular weight dependence of the cation transference number in both dilute and concentrated solutions. We introduce a new parameter, s, the number of lithium ions per polymer chain, that allows us to account for both the effect of salt concentration and molecular weight on cation and anion diffusion. Expressing cation and anion diffusion coefficients as functions of s results in a collapse of D+ and D- onto a single master curve

Theoretical interpretation of ion velocities in concentrated electrolytes measured by electrophoretic NMR

Electrophoretic NMR (eNMR) is emerging as a powerful technique for characterizing ion transport in electrolyte systems. We show that the standard approach for analyzing eNMR data is valid only for dilute electrolytes and provide a theoretical framework for interpreting eNMR results for all binary electrolyte systems with univalent salts. We derive relationships between the velocities of the ion species and the solvent in terms of the electrochemical Stefan-Maxwell diffusion coefficients and provide modified expressions for correctly calculating the transference number and conductivity from eNMR data in concentrated electrolytes. Our approach suggests that it is necessary to measure not just the displacement of ion species during the application of current in an eNMR experiment but also the displacement of the uncharged solvent in order to correctly calculate ion mobilities and the transference number

Ion diffusion across a disorder-to-order phase transition in a poly(ethylene oxide)-: B -poly(silsesquioxane) block copolymer electrolyte

Nanostructured block copolymer electrolytes composed of organic and inorganic moieties have the potential to enable solid-state batteries. Practical uses of these materials, however, require an understanding of the microscopic and macroscopic ion transport properties across the microphase-separated systems. The self-diffusion of salt ions across a disorder-lamellar phase transition in a nanostructured poly(ethylene oxide)-b-poly(silsesquioxane) copolymer was studied using pulsed-field gradient NMR (PFG-NMR) and changes in the morphology were studied using small-angle X-ray scattering. The diffusion of the salt is isotropic when the polymer electrolyte is disordered and locally anisotropic when the polymer is microphase separated. The difference between the diffusion coefficient parallel to the lamellae, D∥, and the diffusion coefficient perpendicular to the lamellae, D measured using PFG-NMR, increases with increasing segregation strength. The anisotropy of diffusion parallels changes in the morphology measured by small-angle X-ray scattering

Diffusion and migration in polymer electrolytes

Mixtures of neutral polymers and lithium salts have the potential to serve as electrolytes in next-generation rechargeable Li-ion batteries. The purpose of this review is to expose the delicate interplay between polymer-salt interactions at the segmental level and macroscopic ion transport at the battery level. Since complete characterization of this interplay has only been completed in one system: mixtures of poly(ethylene oxide) and lithium bis(trifluoromethanesulfonyl)imide (PEO/LiTFSI), we focus on data obtained from this system. We begin with a discussion of the activity coefficient, followed by a discussion of six different diffusion coefficients: the Rouse motion of polymer segments is quantified by Dseg, the self-diffusion of cations and anions is quantified by Dself,+ and Dself,−, and the build-up of concentration gradients in electrolytes under an applied potential is quantified by Stefan-Maxwell diffusion coefficients, D0+, D0-, and D+-. The Stefan-Maxwell diffusion coefficients can be used to predict the velocities of the ions at very early times after an electric field is applied across the electrolyte. The surprising result is that D0- is negative in certain concentration windows. A consequence of this finding is that at these concentrations, both cations and anions are predicted to migrate toward the positive electrode at early times. We describe the controversies that surround this result. Knowledge of the Stefan-Maxwell diffusion coefficients enable prediction of the limiting current. We argue that the limiting current is the most important characteristic of an electrolyte. Excellent agreement between theoretical and experimental limiting current is seen in PEO/LiTFSI mixtures. What sequence of monomers that, when polymerized, will lead to the highest limiting current remains an important unanswered question. It is our hope that the approach presented in this review will guide the development of such polymers

Diffusion and migration in polymer electrolytes

Mixtures of neutral polymers and lithium salts have the potential to serve as electrolytes in next-generation rechargeable Li-ion batteries. The purpose of this review is to expose the delicate interplay between polymer-salt interactions at the segmental level and macroscopic ion transport at the battery level. Since complete characterization of this interplay has only been completed in one system: mixtures of poly(ethylene oxide) and lithium bis(trifluoromethanesulfonyl)imide (PEO/LiTFSI), we focus on data obtained from this system. We begin with a discussion of the activity coefficient, followed by a discussion of six different diffusion coefficients: the Rouse motion of polymer segments is quantified by Dseg, the self-diffusion of cations and anions is quantified by Dself,+ and Dself,−, and the build-up of concentration gradients in electrolytes under an applied potential is quantified by Stefan-Maxwell diffusion coefficients, D0+, D0-, and D+-. The Stefan-Maxwell diffusion coefficients can be used to predict the velocities of the ions at very early times after an electric field is applied across the electrolyte. The surprising result is that D0- is negative in certain concentration windows. A consequence of this finding is that at these concentrations, both cations and anions are predicted to migrate toward the positive electrode at early times. We describe the controversies that surround this result. Knowledge of the Stefan-Maxwell diffusion coefficients enable prediction of the limiting current. We argue that the limiting current is the most important characteristic of an electrolyte. Excellent agreement between theoretical and experimental limiting current is seen in PEO/LiTFSI mixtures. What sequence of monomers that, when polymerized, will lead to the highest limiting current remains an important unanswered question. It is our hope that the approach presented in this review will guide the development of such polymers

Relationship between Conductivity, Ion Diffusion, and Transference Number in Perfluoropolyether Electrolytes

Connecting continuum-scale ion transport properties such as conductivity and cation transference number to microscopic transport properties such as ion dissociation and ion self-diffusivities is an unresolved challenge in characterizing polymer electrolytes. Better understanding of the relationship between microscopic and continuum scale transport properties would enable the rational design of improved electrolytes for applications such as lithium batteries. We present measurements of continuum and microscopic ion transport properties of nonflammable liquid electrolytes consisting of binary mixtures of lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) and perfluoropolyethers (PFPE) with different end groups: diol, dimethyl carbonate, ethoxy-diol, and ethoxy-dimethyl carbonate. The continuum properties, conductivity and cation transference number, were measured by ac impedance spectroscopy and potentiostatic polarization, respectively. The ion self-diffusivities were measured by pulsed field gradient nuclear magnetic resonance spectroscopy (PFG-NMR), and a microscopic cation transference number was calculated from these measurements. The measured ion self-diffusivities did not reflect the measured conductivities; in some cases, samples with high diffusivities exhibited low conductivity. We introduce a nondimensional parameter, β, that combines microscopic diffusivities and conductivity. We show that β is a sensitive function of end-group chemistry. In the ethoxylated electrolytes, β is close to unity, the value expected for electrolytes that obey the Nernst-Einstein equation. In these cases, the microscopic and continuum transference numbers are in reasonable agreement. PFPE electrolytes devoid of ethoxy groups exhibit values of β that are significantly lower than unity. In these cases, there is significant deviation between microscopic and continuum transference numbers. We propose that this may be due to electrostatic coupling of the cation and anion or contributions to the NMR signal from neutral ion pairs

Negative transference numbers in poly(ethylene oxide)-based electrolytes

The performance of battery electrolytes depends on three independent transport properties: ionic conductivity, diffusion coefficient, and transference number. While rigorous experimental techniques for measuring conductivity and diffusion coefficients are well-established, popular techniques for measuring the transference number rely on the assumption of ideal solutions. We employ three independent techniques for measuring transference number, t+, in mixtures of polyethylene oxide (PEO) and lithium bis(trifluoromethanesulfonyl) imide (LiTFSI) salt. Transference numbers obtained using the steady-state current method pioneered by Bruce and Vincent, t+,SS, and those obtained by pulsed-field gradient NMR, t+,NMR, are compared against a new approach detailed by Newman and coworkers, t+,Ne, for a range of salt concentrations. The latter approach is rigorous and based on concentrated solution theory, while the other two approaches only yield the true transference number in ideal solutions. Not surprisingly, we find that t+,SS and t+,NMR are positive throughout the entire salt concentration range, and decrease monotonically with increasing salt concentration. In contrast, t+,Ne has a non-monotonic dependence on salt concentration and is negative in the highly-concentrated regime. Our work implies that ion transport in PEO/LiTFSI electrolytes at high salt concentrations is dominated by the transport of ionic clusters