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Updated: Jun 21, 2026
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Evaluating the Electrochemical Properties of Supercapacitors using the Three-Electrode System
Published on: January 7, 2022
"Squishy capacitor" model for electrical double layers and the stability of charged interfaces
Michael B Partenskii1, Peter C Jordan
1Department of Chemistry, Brandeis University, P.O. Box 549110, MS-015, Waltham, Massachusetts 02454-9110, USA. partensky@gmail.com
Summary
Negative capacitance (NC) is theoretically possible in parts of the electrical double layer (EDL) but prohibited for the whole system. NC predictions under specific conditions signal potential instabilities in electrochemical cells.
Area of Science:
- Physical Chemistry
- Electrochemistry
- Condensed Matter Physics
Background:
- Negative capacitance (NC) is a theoretical prediction arising from electrical double layer (EDL) models.
- NC is physically permissible for individual EDL components (compact or diffuse layers) but not the entire EDL or a two-electrode system.
- Previous work analyzed NC under applied voltage (phi control); this study focuses on total surface charge (q control).
Purpose of the Study:
- To critically review the concept of negative capacitance (NC) in electrical double layers (EDLs).
- To analyze the conditions under which NC can manifest or be prohibited in electrochemical systems.
- To investigate critical behavior and stability of EDLs under total surface charge (q) control.
Main Methods:
- Theoretical review of EDL theories predicting negative capacitance.
- Analysis of artificial 'sigma control' conditions versus physically realizable 'phi control' and 'q control'.
- Utilizing an exactly solvable 'squishy capacitor' model to analyze critical behavior under q control.
Main Results:
- Negative capacitance is strictly prohibited for the entire EDL or electrochemical cell under physically controllable conditions (phi or q control).
- NC predictions under 'sigma control' indicate potential instabilities and phase transitions.
- Under q control, applied voltage (phi) can exhibit discontinuous changes, signaling lateral transitions.
- The EDL's critical point originates from serial contributions of compact and diffuse layers.
Conclusions:
- The apparent contradiction regarding NC arises from the difference between artificial 'sigma control' and realistic 'phi' or 'q control'.
- NC in theoretical models often signifies underlying instabilities or phase transitions in the physical system.
- Stability conditions for electrochemical cells are specified, and the origin of EDL critical points is clarified.
- Future theoretical studies should move beyond 'sigma control' to address more physically relevant scenarios.
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