---
title: "Electric Double-Layer Charging Interactive Lab | Sandbox Physics"
description: "Why does the current fade when ions cannot cross an electrode? A voltage first drives ions through the liquid."
canonical_url: "https://sandboxphysics.com/labs/double-layer-charging/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/double-layer-charging/"
---

Electrochemistry · Charge gathers at an interface

# Electric Double-Layer Charging

**Why does the current fade when ions cannot cross an electrode?** A voltage first drives ions through the liquid. They accumulate beside the blocking electrodes and screen the field in the interior, so the charging current fades. Charge is stored at the interfaces even though no ions cross the plates.

Apply a voltage to a thin electrolyte cell and watch opposite ions gather at its plates. Follow the concentration profiles, screened potential and charging current through the same simulated voltage step.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

One-dimensional Poisson–Nernst–Planck transport describes an ideal dilute monovalent electrolyte at room temperature, with equal diffusivities and blocking flat plates. The length shown is a full gap of two micrometres; ion sizes, Stern capacitance, electrode reactions and fluid flow are omitted. Particle positions illustrate the computed density and are not individual molecular trajectories. Layer thickness and particle size are enlarged for viewing.

Simulated transport record

## Follow the ions and the current together

### Ion concentration across the cell

### Potential across the cell

### Current after the voltage step

Cations Anions Potential / total current Dashed current: thin-layer linear reference

Ions stop at both plates. The external current is the rate of electrode charging; the interior total current adds ionic and displacement contributions.

Equations and primary sources

$$
J_\pm=-\partial_xc_\pm\mp c_\pm\partial_x\phi,\quad -2\delta^2\partial_x^2\phi=c_+-c_-,\quad j_{\rm tot}=J_+-J_-+2\delta^2\partial_tE
$$

[Bazant, Thornton and Ajdari (2004), blocking-cell charge dynamics](https://arxiv.org/abs/cond-mat/0401118v1)

[Learn how diffusion, charge and flow connect](https://sandboxphysics.com/stories/electrochemistry/)

Physics tutorial

## Electric Double-Layer Charging

**Background** A blocking electrode prevents ions from leaving the liquid. It still attracts counterions and repels ions of its own sign. The resulting charge cloud changes the electric field that moved the ions in the first place.

**Why it matters** The current pulse is a way to watch interfacial charge storage. The liquid must carry charge across the gap before the interfacial clouds can screen the applied field.

Start with the essentials

- **Focus question**: Why does the current fade when ions cannot cross an electrode?
- **One-sentence intuition**: The same ion distribution determines both the screened potential and the electrode charge. Their time evolution determines the external charging current.

### Core mathematical model

#### Diffusion and electrical drift

$$
J_\pm=-\partial_xc_\pm\mp c_\pm\partial_x\phi,\qquad \partial_tc_\pm=-\partial_xJ_\pm
$$

Distance is scaled with the full gap, concentration with the reservoir concentration, potential with the thermal voltage, and time with gap squared divided by diffusivity. Positive flux points from left to right. Both ions have the same diffusion coefficient.

#### Charge changes the potential

$$
-2\delta^2\partial_x^2\phi=c_+-c_-,\qquad \delta=\lambda_{\rm D}/L
$$

The concentration difference is the net charge in these units. A small screening ratio lets appreciable charge collect in narrow layers. The numerical mesh resolves these layers, with its convergence checked separately.

#### A thin layer charges through a long liquid resistor

$$
\tau_{\rm RC}=\frac{\lambda_{\rm D}L}{2D},\qquad j_{\rm tot}=J_+-J_-+2\delta^2\partial_tE
$$

Here the full plate spacing is the length. The two diffuse capacitances are in series, giving the factor of two in the small-voltage thin-layer charging time. Ionic current plus displacement current is spatially uniform. The instantaneous voltage-switch impulse is outside the sampled record.

### Common difficulties

#### Blocking still permits charging

**Typical misconception** If ions cannot cross the plates, there can be no external current.

**Better mental model** The external wire charges the metal surfaces as ions rearrange inside the liquid. The displacement-current term accounts for the changing electric field at a blocking boundary.

### Run the experiment

1. 01

   #### Watch the field disappear from the middle

   Choose The current fades. Before the animation advances, predict where positive ions will gather. Pause and drag the time marker through the charging process.

   **What to observe:** Positive ions accumulate beside the negative plate. Opposite charge gathers at the positive plate, the interior field shrinks and the external current decreases.

2. 02

   #### Reverse the voltage

   Choose Reverse the polarity. Predict which density cloud and electrode charge will change sign, and compare the final profiles with The current fades.

   **What to observe:** The positive and negative ion profiles exchange places. Symmetric ions in a symmetric cell give the same charging speed for equal and opposite voltages.

3. 03

   #### Make the screening layers wider

   Choose Charge clouds overlap. Compare the potential in the middle with A gentle voltage step, and save the trajectory to inspect ion-number conservation.

   **What to observe:** Broad screening layers leave less neutral interior. Each ion species stays inside the blocking cell; the file includes its total amount at every saved time.

Physical conclusion

Interfacial charge storage and liquid transport together set the charging time.

## Related experiments and articles

Electrochemistry and ion transport · Reading path

### From ion diffusion to charge, flow and impedance

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Which way do ions move in salt water?**](https://sandboxphysics.com/stories/electrochemistry/chemical-potential-flux/)
2. [Article **How ions reshape the field that moves them**](https://sandboxphysics.com/stories/electrochemistry/pnp-boundaries/)
3. [Article **Why a blocking electrode can still charge**](https://sandboxphysics.com/stories/electrochemistry/blocking-double-layer/)

Fields & matter · Starter path

## From a field to an electron microscope

Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface.

[Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

1. [1 Make an Electric Field Visible](https://sandboxphysics.com/labs/electric-field/)
2. [2 A Charge Bending through Fields](https://sandboxphysics.com/labs/charged-particle/)
3. [3 Electron Wavelength & Voltage](https://sandboxphysics.com/labs/electron-wavelength/)
4. [4 Electron Diffraction & Reciprocal Space](https://sandboxphysics.com/labs/electron-diffraction/)
5. [5 TEM Bright Field, Dark Field & SAED](https://sandboxphysics.com/labs/tem-mode-selector/)
6. [6 SEM Secondary-Electron Topography](https://sandboxphysics.com/labs/sem-topography/)

[View the full path →](https://sandboxphysics.com/topics/fields-and-matter/#starter-path)