NMR Analysis of Battery Electrolytes: Measuring Ionic Diffusion Across Temperature

Abstract

Battery electrolyte performance is influenced by the mobility of solvents and charge-carrying ions, which varies with the molecular identity and is highly dependent on the temperature. This Application Note demonstrates the capabilities of the Oxford Instruments X-Pulse 90 benchtop NMR spectrometer and pulsed-field-gradient NMR methods to determine diffusion coefficients for carbonate solvents, [PF₆]⁻ anions and Li⁺ cations in a lithium-ion battery. Measurements across ¹H, ¹⁹F, ³¹P and ⁷Li nuclei distinguish the transport behaviour of individual electrolyte components. Variable-temperature NMR measurements quantify the relationship between temperature and diffusion coefficients, providing insight into electrolyte transport properties under different operating conditions. Together, these measurements enable component-specific mobility analysis for electrolyte development and battery performance studies.

Introduction

Lithium-ion (Li-ion) batteries have become ubiquitous in daily life, providing power for a diverse range of applications, ranging from mobile phones, computers, power tools, and medical devices to the green technologies including electric cars and solar energy storage. As our usage of lithium-ion batteries has grown, so has the need to optimise their performance and to ensure reliability over a long lifetime. At the same time new technologies including sodium-ion (Na-ion) batteries are in development.

Electrolytes play a crucial role in the performance and reliability of Li-ion batteries, providing the medium that allows anions and cations to carry charge between the electrodes, as shown in Figure 3.1. In the current generation of commercial batteries, the electrolyte is typically made up of organic small-molecule liquid solvents, commonly a mixture of alkyl carbonates, combined with a lithium salt. Additionally, various additives are used to ensure specific chemical and electrochemical properties.

Figure 3.1 Diagram of a lithium-ion battery, showing major components including the anode, cathode, separator, and electrolyte.

While lithium-ion batteries have played a major role in transforming our daily lives, benchtop NMR spectroscopy has similarly begun to revolutionise quality assurance and quality control (QA/QC) processes by making a powerful technique easier and more accessible for routine analysis in any laboratory. Benchtop NMR has many potential lithium-ion battery QA/QC applications, as the well-resolved spectra of the small organic molecules and ions are ideally suited for quick, convenient analysis.

The Oxford Instruments X-Pulse broadband benchtop NMR spectrometer (available with a 60 MHz or 90 MHz permanent magnet) provides significant advantages for the development and analysis of battery electrolytes. Since the X-Pulse comes with ≥50 G/cm pulsed-field gradients as standard, the X-Pulse can be used to measure diffusion constants on all its supported nuclei, and hence for all the components of a Li-ion (or Na-ion) battery electrolyte. Accurate measurements of diffusion constants, particularly for the charge carrying Li-ions and fluorinated anions, are essential to accurately model the electrochemistry of the cell and hence understand the performance of the battery.

Measuring Diffusion by NMR

Diffusion can be measured by NMR using pulsed-field gradient experiments, most commonly Pulsed field Gradient Spin Echo (PGSE) (Figure 3.2) or Pulsed Field Gradient STimulated Echo (PFGSTE) (Figure 3.3) pulse sequences. These encode the position of nuclear spins with a magnetic-field gradient and then attempt to refocus that magnetisation after a defined diffusion time. Molecules that remain effectively stationary during this interval are refocused efficiently, whereas molecules that move by translational diffusion experience incomplete refocusing and therefore show reduced signal intensity.

A diffusion experiment records a series of spectra, usually systematically increasing the gradient strength (G), while keeping the gradient duration (δ) and diffusion time (Δ) constant. Therefore, each signal is attenuated according to how rapidly the corresponding molecular species diffuses. The resulting signal attenuation is fitted using the Stejskal–Tanner equation [1] to obtain the self-diffusion coefficient, D, which can then be related to properties including molecular size, viscosity, temperature. In battery electrolytes, it can be related to the mobility of solvent molecules, anions and cations, all of which are important to understand the electrochemical performance of the battery.

Figure 3.2 Graphical representation of the Pulsed field Gradient Spin Echo (PGSE) pulse sequence

Figure 3.3 Pulsed Field Gradient STimulated Echo (PFGSTE) pulse sequence diagram

The Stejskal–Tanner equation is shown as Equation 3.1:

Equation 3.1 The Stejskal-Tanner equation

where:

• l_g is the signal intensity at the applied gradient strength
• l_o is the signal intensity with zero applied gradient
• γ is the gyromagnetic ratio
• G is the applied gradient strength
• δ is the gradient duration
• Δ is the diffusion time

Since γ, δ, Δ and D are constants, when plotting the applied gradient strength, G, against the signal intensity (or integral), I_g, the data points can be fitted to the function

The diffusion constant can be calculated from

Example Diffusion Measurements of Battery Electrolyte Components

A sample of Li-ion battery electrolyte, Li[PF₆] in EC/DMC/DEC, is used to demonstrate the range of diffusion measurements possible on a X-Pulse 90 broadband benchtop NMR spectrometer. For these measurements, either the Pulsed field Gradient Spin Echo (PGSE) or Pulsed Field Gradient STimulated Echo (PFGSTE) pulse sequence was used, with the gradient strengths varied from 0 up to 58 G/cm.

All these measurements can also be performed on an X-Pulse 60.

Measuring Solvent Diffusion using ¹H NMR

To measure diffusion constants of the various compounds in the solvent, a series of ¹H PFGSTE spectra were obtained (Figure 3.4) and the diffusion constants determined (Table 3.1).

Figure 3.4 ¹H PFGSTE spectra of Li-ion battery electrolyte

Table 3.1 Diffusion constants determined from ¹H PFGSTE spectra of Li-ion battery electrolyte

These measurements demonstrate an important fact about diffusion. Since diffusion is a molecular

property, it doesn’t matter which signal from a specific molecule is used to determine the diffusion constant. The result will be the same, as shown by the fact that both the DEC signals have effectively identical diffusion constants. This fact can also be used to distinguish signals from different compounds in a mixture by determining the diffusion constant for each signal and matching them up for each molecule. However, this only works if the signals are clearly distinguished and the molecules reasonably different is size, ensuring a sufficient difference in their diffusion constants.

Diffusion data can be displayed in various different ways, in addition to stacking the individual one-dimensional spectra that make up the pseudo -two-dimensional data set (as in Figure 3.4). A common method in to display it as a two-dimensional DOSY plot, with the chemical shift plotted on the x -axis and the diffusion constant plotted on the y-axis, as shown in Figure 3.5. The DOSY plot makes it easy to identify different components in a mixture, but accurately determining the diffusion constants relies on correctly accounting for the various experimental parameters.

Figure 3.5 ¹H PFGSTE spectra of Li-ion battery electrolyte, displayed as a two-dimensional DOSY plot

Measuring [PF₆]⁻ Anion Diffusion using ¹⁹F & ³¹P NMR

To determine the diffusion constant of the [PF₆]⁻ anion in a Li-ion battery electrolyte, three data sets were acquired:

• ¹⁹F PGSE spectra (Figure 3.6)
• ³¹P PGSE spectra, without ¹⁹F decoupling (Figure 3.7)
• ³¹P PGSE spectra, with ¹⁹F decoupling (Figure 3.8)

The diffusion constant was determined from each data set.

Figure 3.6 ¹⁹F PGSE spectra of Li-ion battery electrolyte

Figure 3.7 ³¹P PGSE spectra of Li-ion battery electrolyte

Figure 3.8 ³¹P{¹⁹F} PGSE spectra of Li-ion battery electrolyte

In all three cases, we’d expect to measure the same diffusion constant from each data set, since diffusion is a molecular property. The measured diffusion constants are shown in Table 3.2. While the measured values for ¹⁹F and ³¹P{¹⁹F} are comparable, the value obtained from ³¹P differs further.

Table 3.2 Diffusion constants determined for [PF₆]⁻ using different nuclei

The significantly higher signal-to-noise ratio (SNR) of the peaks in the 19F spectra compared to those in the ³¹P spectra, and hence the improved fit of the data to the Stejskal-Tanner equation, show that the value acquired from the ¹⁹F PGSE data set is the most accurate.

Another important point to note is the total duration of these measurements. Since diffusion data should be acquired with quantitative parameters, measurement time can range from a couple of hours for ¹⁹F to significantly longer for ³¹P. Therefore, measuring the diffusion constant of [PF₆]⁻ with ¹⁹F NMR, is not only more accurate but also quicker.

Measuring Lithium Cation Diffusion using ⁷Li NMR

The most important diffusion constant to determine for a Li-ion battery is that of the charge-carrying lithium cation itself. This can readily be acquired on the X-Pulse using a ⁷Li PGSE pulse sequence (Figure 3.9). In this case the diffusion constant, D, was measured as 8.29×10^-10 m²/s.

Figure 3.9 ⁷Li PGSE spectra of Li-ion battery electrolyte

Measuring Diffusion at Variable Temperatures

Since diffusion constants vary with temperature, it’s important for Li-ion batteries to determine the diffusion constants and the related electrochemical properties across the full range of operating temperatures.

The X-Pulse 90 can use a gas variable temperature (VT) system, which can regulate the sample temperature over a minimum range of 0°C to 60°C. By acquiring ⁷Li PGSE data sets at different temperatures (Figure 3.10) and determining the diffusion constants, we can demonstrate how diffusion is affected by temperature.

Figure 3.10 ⁷Li PGSE spectra of Li⁺, at various temperatures

The diffusion constants of Li+ over a range of different temperatures are shown in Table 3.3. The lower diffusion constants, and hence slower diffusion, at lower temperatures demonstrate one of the reasons why battery performance is generally poorer in a cold environment.

Table 3.3 Diffusion constants determined for Li⁺ at different temperatures

Summary

The X-Pulse 90 and X-Pulse 60 broadband benchtop NMR spectrometers are ideal tools for measuring diffusion constants in lithium-ion battery electrolyte. The X-Pulse family of broadband benchtop NMR spectrometers comes with pulsed-field gradients as standard, allowing for diffusion constants to be determined for a range of different species, particularly the charge carriers in Li-ion battery electrolytes.

The X-Pulse can operate in a variable-temperature configuration, therefore the relationship between temperature and the diffusion constants can be determined. Accurately determined diffusion constants are essential for the complete understanding of battery electrochemistry.

Literature

[1] E. O. Stejskal and J. E. Tanner, J. Chem. Phys., 1965, 42, 288–292, DOI: 10.1063/1.1695690.