Accurate Characterization of Ion Transport Properties in Binary Symmetric Electrolytes Using In Situ NMR Imaging and Inverse Modeling

Abstract

We used NMR imaging (MRI) combined with data analysis based on inverse modeling of the mass transport problem to determine ionic diffusion coefficients and transference numbers in electrolyte solutions of interest for Li-ion batteries. Sensitivity analyses have shown that accurate estimates of these parameters (as a function of concentration) are critical to the reliability of the predictions provided by models of porous electrodes. The inverse modeling (IM) solution was generated with an extension of the Planck-Nernst model for the transport of ionic species in electrolyte solutions. Concentration-dependent diffusion coefficients and transference numbers were derived using concentration profiles obtained from in situ (19)F MRI measurements. Material properties were reconstructed under minimal assumptions using methods of variational optimization to minimize the least-squares deviation between experimental and simulated concentration values with uncertainty of the reconstructions quantified using a Monte Carlo analysis. The diffusion coefficients obtained by pulsed field gradient NMR (PFG-NMR) fall within the 95% confidence bounds for the diffusion coefficient values obtained by the MRI+IM method. The MRI+IM method also yields the concentration dependence of the Li(+) transference number in agreement with trends obtained by electrochemical methods for similar systems and with predictions of theoretical models for concentrated electrolyte solutions, in marked contrast to the salt concentration dependence of transport numbers determined from PFG-NMR data.

Visualization of Steady-State Ionic Concentration Profiles Formed in Electrolytes during Li-Ion Battery Operation and Determination of Mass-Transport Properties by in Situ Magnetic Resonance Imaging

“…In this case, a linear fit of the data points gives values of the concentration gradient equal to −(0.92 ± 0.05) × 10 5 , −(2.01 ± 0.02) × 10 5 , and −(4.08 ± 0.04) × 10 5 mol·m −4 for J = 3, 6, and 12 A·m −2 , respectively. While these estimates are somewhat crude, since mass-transport properties (especially D) are concentration-dependent, 13,32 one can see nevertheless that there exists proportionality between ∂ ∂ c x and J, as displayed in Figure 3b and expected from eq 2d. The R 2 value of 0.9998 for the linear regression in Figure 3b indicates excellent linearity.…”

“…7, 13 The advantage of the frequency-encoding method is itsin principlemore efficient use of experimental time, because a whole line in kspace (the raw data, the Fourier transformation of which forms an actual image) 24 is collected during each scan. In contrast, only one k-space data-point can be acquired in each phaseencoded step.…”

“…13 Mass transport in an electrolyte solution in the presence of an applied electric field occurs as a combination of migration and diffusion. For example, during the discharging of a cell, the electric field (giving rise to the ohmic potential difference in the electrolyte) causes the migration of cations to the positive electrode and anions toward the negative electrode.…”

“…The mass-transport parameters obtained by inverse modeling with eqs 1 of the MRI measured concentration profiles in an electrophoretic cell under applied constant current are reasonable and agree with results obtained by electrochemical methods. 13 It is, however, challenging to achieve high quality MR images in the vicinity of the electrodes due to distortions of both the static (B 0 ) and radiofrequency magnetic fields (B 1 ), which are caused by the conductive parts of the cell (current collectors and the electrodes themselves). 14,15 This limitation can be overcome by optimization of the electrochemical cell design (i.e., choice of current collectors, electrodes, etc.)…”

Determination of Transport Parameters in Liquid Binary Lithium Ion Battery Electrolytes

“…In Castiglione et al, 7 Sethurajan et al 8 and Capiglia et al, 9 pulsedfield gradient Nuclear Magnetic Resonance (NMR) is used to determine the self-diffusion coefficients of ions in an electrolyte solution, which describes the mobility of ionic species in the absence of an electrochemical potential gradient. 10 In Castiglione et al, 7 the selfdiffusion coefficients of all ions in an electrolyte composed of LiTFSI (lithium bis(trifluoromethanesulfonyl)imide) dissolved in the ionic liquid PYR 14 TFSI (N,N-dimethyl pyrrolidinium) at a molar ratio of 1:9 were determined, whereas Capiglia et al 9 investigated LiPF 6 , LiBF 4 , and LiN(C 2 F 5 SO 2 ) 2 in ethylene carbonate (EC) ethyl-methyl carbonate (EMC) solvent mixture (EC:EMC at 2:8 v:v).…”