> ## Documentation Index
> Fetch the complete documentation index at: https://docs.ionworks.com/llms.txt
> Use this file to discover all available pages before exploring further.

# 電解質輸送特性

> The four transport properties that close a binary-electrolyte DFN model, their role 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](https://doi.org/10.1149/2.0571912jes) is one of the few studies that reports all four properties for the same electrolyte systems, using the following techniques.

<AccordionGroup>
  <Accordion title="Ionic conductivity κ" icon="bolt">
    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 $\kappa$.
  </Accordion>

  <Accordion title="Salt diffusion coefficient D_e" icon="droplet">
    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 $D_{e,\mathrm{eff}} = \ell_\mathrm{sep}^2 / (\pi^2 \tau)$.
  </Accordion>

  <Accordion title="Thermodynamic factor χ and transference number t+" icon="scale-balanced">
    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](https://doi.org/10.1149/1.2086525).
  </Accordion>
</AccordionGroup>

<Note>
  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](https://doi.org/10.1088/2516-1083/ac692c).
</Note>

## Using these properties in a model

よく使われる文献パラメータ化（定数、Nyman、Landesfeind、Arrhenius ラッパー）には、あらかじめ用意された **direct entries** が用意されており、整合性のあるパラメータセットをそのままパイプラインに投入できます。物理的背景とパラメータ化の選び方については、[Electrolyte direct entries](/ja/guide/pipelines/direct-entries/electrolyte) を、これらをプログラムで構成・送信する方法については、[Pipelines → Direct Entries](/ja/pipelines/direct-entries) を参照してください。