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Ion-electron transducers�Table of contents

Electrode-electrolyte interface

The Randles´model
Double layer capacity
Charge transfer resistance
Diffusion impedance
Impedance frequency response at low potentials

Ion-electron transducer

Electrodes and biopotentials
Electrode-skin interface
Ideal and non-ideal electrodes
IROX coated electrodes

Dr. Carmelo José Felice

Transductores Biomédicos

Ingeniería Biomédica

FACET-UNT, Argentina

Updated 11 March 2024

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BOOKS

Madrid RE, Treo EF, Herrera MC, Martinez CC (2010). Handbook of Physics in Medicine and Biology. Ed.Robert Splinter. CRC Press 2010. chapter IV. Bioelectrical Physics: Electrodes.

Felice C.J., Madrid R.E., Valentinuzzi M.E. Signal Pick Up. Chapter 4 in Understanding the human machine: A primer for Bioengineering. Series on Bioengineering & Biomedical Engineering. By Max E. Valentinuzzi. Eds. World Scientific Co. Pte. Ltd. Singapor. 2002.

Bioimpedance and Bioelectricity Basics, Second Edition. By Orjan Martinsen, and Sverre Grimnes University of Oslo, Norway . Ed.: Academic Press. 2008.

John O’M Bockris, Amulya K. N. Reddy, Maria Gamboa-Aldeco. Electrochemistry. Second Edition. Fundamentals of Electrodics. Kluver Academic Publishers. New York, Boston, Dordrecht, London, Moscow. 2002. ISBN: 0-306-46166-8.

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Electrodes are not smooth

AFM image of stainless steel electrode (polished 1 µm)

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Geometry and size of an EEI

nanometer

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Electrochemistry is the subject that describes the making of substances by means of electricity and

the making of electricity by consuming substances*

* Bernhardt Patrick John O’Mara Bockris (1923-2013)

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Electrochemistry and EEI

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IET = Ion-Electron Transducer

Electricity is conducted by:

ions in electrolyte
electrons in metal

The transition occurs through redox reactions.

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What about the ions at the interface ?

The ions are moving to electrode by:

an external electrical field: Rm
a concentration difference (diffusion): R_W

There is a spatial charge distribution: C_w
When electrons arrive at the interface could:

give or receive electrons: R_ct
charge the double layer: C_dllec (with its half cell potential E_hc)

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Electrical model of Zi: Randles´circuit

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Ions arriving at an interface

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Double layer capacity Cdl

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Origin of double layer capacitance

When an electrode is immersed in an electrolyte solution, a defect or excess of electrons (ions) is formed by Force anisotropy.
When the surface is charged, counter-ions (opposite sign) of the bulk arrive at the interface by electrostatic atraction.
Ions and counter-ions are forming the double layer capacity (Cdc of Helmholtz)

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Why appear charge in metal?

Two options:

Electrode discharges some metallic ions into electrolytic solution

Increase in # free electrons in electrode
Increase in # positive cations (electric charge) in solution;

Ions in solution combine with metallic electrodes

Decrease in # free electrons in electrode
Decrease in # positive cations in solution.

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Force anisotropy: formation of an electrified interface

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Interface in pure water at metal electrodes

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In electrical models of electrode-electrolyte interface, the charge of Cdl is modeled as a separated dc source Ehc.

Ehc is named as the Half Cell Potential

Ehc value could not be measured*, because a second electrode was ever necessary.

A standard hydrogen electrode was used as reference, to build the Table of Standard Electrode Potentials

Cdl, Half cell potential and Potential Table

*: until now…

http://hyperphysics.phy-astr.gsu.edu/hbase/tables/electpot.html

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Where could exist double layers?

Between metal electrode and electrolyte solution.

Between a red cell membrane and the plasma of the suspension.

Between a metal electrode and the skin or body organ.

Between wall cell of a bacteria or yeast, and the suspension medium.

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Evolution of Cdl models

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It was named by Helmholtz in 1850.
There is an excess or deficiency of electrons at the electrode surface.
The charge on the electrode is exactly balanced in solution by an equal but oppositely charged amount of ions.
A rigidly held layer exists in a plane parallel to the surface of the electrode and very close to it.
The double layer behave as a parallel-plate capacitor.

Electrical double layer: Helmholtz model

It only works for high concentration

It does not depend of applied overpotential

There are discrepancies with experimental data

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Electrical double layer: Gouy-Chapman model

Ions are point charges and the solvent a dielectric continuum.
The temperature is taken into account by using Poisson-Boltzman.

Temperature 🡪 tendency to make the layer diffuse
Eelectrostatic attraction 🡪 tends to keep ions close to interface.

Larger electrolyte concentration 🡪 smaller L_D
Higher temperature 🡪 large L_D

The model does not work in high electrolyte concentrations.

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It is a combination of Helmholtz and Gouy-Chapman models.

Electrical double layer: Stern model

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The double layer and real Ehc measurements

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Double layer thickness vs [electrolyte]

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Double layer in particles�zeta potential and the slipping plane

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Zeta potential and liposomes

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Surface charge of particles and its electrokinetics properties

Electrophoresis:

Charged solid particles move under external electric field

Electroosmosis:

Liquid with free charge move under external electric field where charged solid is stationary

Flow potential

Free charges of liquids move under external pressure 🡪 electrical curren 🡪 potential difference

Sedimentation Potential

Occurs when dispersed particles move under the influence of either gravity or centrifugation in a medium.

Some properties are very useful in microfluidic.

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Electrophoresis

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Electroosmosis

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Streaming current and flow potential

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Sedimentation potential

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Charge transfer resistance �Rct

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Basics of Rct*

*: Chapter 8 in Electrodics in Volume 2 Modern Electrochemistry. An Introduction to an Interdisciplinary Area. John O’M. Bockris, Amulya K. N. Reddy.

It stand for the degree of easiness of electronic transfer to and from an interface during a redox reaction.

Rct could be deduced from Butler-Volmer equation.

Butler-Volmer equation relate overpotential and current at an interface:

Both exponential terms takes into account activation energy (η) and temperature dependence (T) phenomena.

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Butler-Volmer equation and Rct

Rct could be obtained by deriving and inverting BV equation:

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Non-linear behavior of Rct with overpotential

Rct is the main contributor to non-linearities of an EEI

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The Warburg diffusion impedance Zw

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The origin of diffusion at an interface

When the ions arrive at an interface, they combine with electrons and disappear (as ions…).
A concentration difference appear between the bulk of solution and the electrode ⇒ diffusion

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The Warburg diffusion impedance

In 1897 Emil Gabriel Warburg deduce the diffusion impedance, solving the semi-infinite linear diffusion equation with oscillating concentration at the boundary.

It has a constant phase of 45° (independent of frequency)

For f🡪0, Zw🡪∞

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Infinite Warburg impedance

It is unreal the unlimited growth of Zw at low frequency.

In real world Zw does not increase indefinitely, because the space where diffusion occur is finite.

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Finite Warburg impedance

The finite diffusion equation is:

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Randles model in linear zone�overpotentials ≤ 10 mV

overpotentials ≤ 10 mV

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Randles model parameters�obtaining Cdl, Rct, Rm and Zw from measurements

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ION-ELECTRON TRANSDUCER

It is a place where the ions of solution give or take electrons: electrode-electrolyte interface
Metallic electrodes are the most used transducer of biomedical signals.
They could be applied in:

Electro (encephalography/cardiography/oculography/miography/…)
Microelectrodes (lab-on-chip/microfluidic, patch clamp)
Chemical transducers
Biosensors
Electrical stimulation and/or recording
Biomedical fuell cell

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Electrode:

It is a ion-electron transducer
Ionic current at the electrolyte, electronic current at the metal

Electrolyte:

Pure electrolyte: a solution of ions as charge carriers

e.g.: extracellular action potential recording

Live tissue: electrolytes are intra and extra-cellular

e.g.: ECG, EEG, EMG, etc.

Biopotentials measurement with metallic electrodes

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Two uses:

Recording: bioelectric phenomena measurement (e.g.: EEG)
Stimulation: current injection to live tissue (e.g.: Z tomography, Functional Electrical Stimulation)

Three type:

Ohmic contact through an electrolyte (e.g.: EEG)
Capacitive: through a dielectric (e.g.: non-contact ECG).
Coated: through a selective membrane (e.g.: PO₂ sensor)

Electrodes

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Biopotential electrode sensor

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Electrode-skin interface

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Facts about electrode-skin interface

The first RC is due to metal-humidity interface.

The second RC is due to cell suspension (mostly Stratum corneum)

E_hc are distortion sources. They could saturate amplifiers (voltage offset)

Question: where and how work gels?