page_title: Dielectric spectroscopy
section_title: Double layer capacitance
hierarchical_section_title: Dielectric spectroscopy / Principles / Dynamic behavior / Double layer capacitance
caption_attribution_description: English: Equivalent circuit for redox reaction without mas-transfer limitation Français&#160;: Circuit équivalent de la réaction redox en l'absence de limitation par le transport de matière
context_page_description: Dielectric spectroscopy measures the dielectric properties of a medium as a function of frequency. It is based on the interaction of an external field with the electric dipole moment of the sample, often expressed by permittivity.
  It is also an experimental method of characterizing electrochemical systems. This technique measures the impedance of a system over a range of frequencies, and therefore the frequency response of the system, including the energy storage and dissipation properties, is revealed. Often, data obtained by electrochemical impedance spectroscopy is expressed graphically in a Bode plot or a Nyquist plot.
  Impedance is the opposition to the flow of alternating current in a complex system. A passive complex electrical system comprises both energy dissipater and energy storage elements. If the system is purely resistive, then the opposition to AC or direct current is simply resistance. Materials or systems exhibiting multiple phases commonly show a universal dielectric response, whereby dielectric spectroscopy reveals a power law relationship between the impedance and the frequency, ω, of the applied AC field.
context_section_description: An electrode  electrolyte interface behaves like a capacitance called electrochemical double-layer capacitance . The equivalent circuit for the redox reaction in Fig. 2 includes the double-layer capacitance as well as the charge transfer resistance. Another analog circuit commonly used to model the electrochemical double-layer is called a constant phase element.
  The electrical impedance of this circuit is easily obtained remembering the impedance of a capacitance which is given by:
  where  is the angular frequency of a sinusoidal signal (rad/s), and .
  It is obtained:
  Nyquist diagram of the impedance of the circuit shown in Fig. 3 is a semicircle with a diameter  and an angular frequency at the apex equal to  (Fig. 3). Other representations, Bode plots, or Black plans can be used.
caption: Fig. 2: Equivalent circuit for a redoxin reaction without mass-transfer limitation
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