Electrolyte transport properties

The four transport properties (κ, D_e, χ, t_+^0) that close a binary-electrolyte DFN model, the role of each in the equations, and how they are measured experimentally

A continuum (Doyle–Fuller–Newman) lithium-ion model treats the electrolyte as a binary salt in a single solvent and tracks a single salt concentration $c_e$. Closing the equations requires four transport properties as functions of $c_e$ and temperature $T$:

Property	Symbol	Units	Role in the model
Ionic conductivity	$\kappa(c_e, T)$	S m$^{-1}$	Ohmic drop in the electrolyte phase
Salt diffusion coefficient	$D_e(c_e, T)$	m$^{2}$ s$^{-1}$	Concentration polarization
Thermodynamic factor	$\chi(c_e, T)$	–	Activity-coefficient correction $\bigl(1 + \tfrac{\partial \ln f_\pm}{\partial \ln c_e}\bigr)$ to the diffusional driving force
Cation transference number	$t_+^0(c_e, T)$	–	Fraction of current carried by Li$^+$ in the electrolyte

The four functions appear together in the modified Nernst–Planck flux for a binary electrolyte and are tightly coupled — a coherent parameter set should report all of them under the same conditions, on the same chemistry, ideally from the same study.

How are these properties measured?

Landesfeind & Gasteiger 2019 is one of the few studies that reports all four properties for the same electrolyte systems, using the following techniques.

Ionic conductivity κ

Measured by AC impedance spectroscopy in a commercial two-platinum-microelectrode conductivity cell with a Peltier-controlled temperature stage. The high-frequency ($85$ kHz – $1$ kHz) impedance gives the bulk electrolyte resistance, which combined with the cell constant (calibrated against KCl standards) yields $\kappa$.

Salt diffusion coefficient D_e

Measured by galvanostatic-pulse / restricted-diffusion relaxation in Li $\mid$ separator $\mid$ Li symmetric coin cells. A 15-minute current pulse builds up a concentration gradient across the separator; after the current is interrupted, the cell potential decays exponentially over $\sim 4$ hours. Fitting the long-time decay $U(t) - U_\infty \propto e^{-t/\tau}$ gives a relaxation time $\tau$, from which $D_{e,\mathrm{eff}} = \ell_\mathrm{sep}^2 / (\pi^2 \tau)$.

Thermodynamic factor χ and transference number t+

These two are extracted together from a combination of two measurements:

• Concentration cells (pouch cells with two electrolyte compartments at different LiPF$_6$ concentrations) give the open-circuit potential $U_\mathrm{CC}$, which is sensitive to the activity coefficient and to $t_+^0$.
• The short-time potential response of the same Li $\mid$ Li pulse experiment used for $D_e$ gives a complementary combination of the two quantities.

Together they yield two transport factors $a$ and $b$, which Landesfeind invert via $t_+^0 = 1 - \sqrt{b/a}$ and $\chi = a^2 / (2b)$ — a variant of Newman’s full-cell method.

These are the techniques used in Landesfeind & Gasteiger 2019, but several other experimental approaches exist (Hittorf, NMR-based diffusion, electrophoretic NMR for $t_+^0$, polarization-relaxation variants, etc.). For a comprehensive review of available methods and a database of digitized literature parameters, see Wang et al. 2022, Review of parameterisation and a novel database (LiionDB) for continuum Li-ion battery models, Prog. Energy 4, 032004.

Using these properties in a model

ionworkspipeline ships a small set of pre-built direct entries in iwp.direct_entries (constant_electrolyte, nyman_electrolyte, landesfeind_electrolyte, arrhenius_electrolyte_*) that drop a coherent parameter set straight into a pipeline. For implementation details, see the Electrolyte direct entries page. For an end-to-end example of refitting the Landesfeind conductivity coefficients to data, see the Landesfeind electrolyte fit notebook in the Python reference.