Theory and Applications of Electrical Impedance Spectroscopy (EIS): a Review

Marco GrossiDepartment of Electrical Energy and Information Engineering

University of Bologna, Italyhttp://www.researchgate.net/profile/Marco_Grossi

EIS is a powerful technique that can be used in a wide range of applications, such as:

1)Determination of microbial concentration2)Analysis of human body composition3)Quality evaluation of food products4)Analysis of corrosion of metal surfaces5)Characterization of the hardening process of cement paste6)Determination of State of Charge (SoC) and State of Health (SoH) in batteries.

The early works on EIS date back to 1894.

A conference dedicated to EIS is held every three years.

Electrical Impedance Spectroscopy (EIS)

Working principleA sine-wave voltage signal VIN(t) is applied between a couple of electrodes.

( ) ( )tfVVtV INMIN ⋅⋅+= π2sin,

The current through the sample IIN(t) is measured.

( ) ( )ϕπ +⋅⋅+= tfIItI INMIN 2sin,

The complex impedance Z(j2πf) is calculated in a wide range of frequencies.

( ) ( ) ( )fjjfjeI

VfjZ j

INM

INM πππ ϕ 2Im2Re2,

, +=⋅= −

Measurements can be carried out with different experimental setups

2-electrodes configuration

test voltage applied and current measured between working electrode (WE) and counter electrode (CE)

3-electrodes configuration

test voltage applied between WE and reference electrode (RE) , current measured at CE

4-electrodes configuration

test current applied between WE and CE, voltage measured between working sense electrode (WSE) and RE

The impedance Z is defined only in the case of linear time invariant (LTI) systems, exhibiting three conditions: (a) linearity, (b) stability, (c) causality. Since electrochemical systems are typically non-linear, they are forced to operate in a pseudo-linear region by applying a test signal of small amplitude.The LTI conformity of the measured EIS data can be tested using the Kramers-Kronig (KK) relations:

( ) ( ) ( )dx

x

ZxZZ ∫

+∞

−−=

022

ReRe2Im

ωω

πωω

Methods to estimate KK relations on a finite frequency range have been presented in literature.

( ) ( ) ( ) ( )dx

x

ZxZxZZ ∫

+∞

−⋅−⋅+∞+=

022

ImIm2ReRe

ωωω

πω

Determination of microbial concentration1. Impedance Microbiology (IM): the bacterial concentration is

estimated from the changes of the electrical parameters (due to bacterial metabolism) of the supporting electrolyte where the bacterial population grows.

2. Impedance biosensors: a bioreceptor (usually antibody) for the target bacterial strain is immobilized on the WE. When the target bacteria bind to the bioreceptors, the charge transfer with the WE is hindered.

Analysis of human body compositionHuman body is composed of Fat Mass (FM) and Fat Free Mass (FFM). FFM conducts electricity well while FM is a good insulator. Impedance measurements can give informations on the water content in the different body compartments.

Quality evaluation of food products1. Evaluation of the ripening state in fruits: during ripening there

are changes to the fruit properties that result in changes of its electrical parameters. The variations of the electrical parameters during the ripening process is different for different types of fruits. The impedance variations are stronger at low frequencies (50Hz).

2. Analysis of vegetable oils: edible oils are in fact the best insulators among the food products and their electrical conductivity at low frequency can be as low as 0.5 nS∙m-1. Properties of vegetable oils are often measured using capacitive sensors, by measuring the relative dielectric constant εr of the samples.

An alternative technique is mixing the vegetable oil with a suitable reagent to create an emulsion whose electrical properties are investigated by EIS.

3. Dairy products: EIS is used to characterize different dairy products, such as to detect adulteration in raw cow milk, to detect mastitis in cows, to characterize ice-cream and to monitor the fermentation process of yogurt.

4. Moisture measurements in different food products: the feasibility to measure moisture using EIS has been shown in different food products such as cookies, bread, oilseeds, meat.

Analysis of corrosion of metal surfacesOrganic polymers coatings are used to protect from corrosion metal surfaces in contact with low pH electrolytes. The quality and degradation of the coating can be assessed by EIS measurments.

Characterization of the hardening process of cement paste

The hardening process of cement paste is investigated by EIS using two graphite electrodes with the cement paste between them. The resistance of the proposed electrical model was found to increase with the hardening process.

Determination of State of Charge (SoC) and State of Health (SoH) in batteries

The Nyquist plot is composed of different parts: (1) inductive at high frequency; (2) and (3) reaction at the two battery electrodes; (4) mass transfer at low frequency. SoC is often estimated by measuring the high frequency resistance RHF.

The full lenght article for the review of Electrical Impedance Spectroscopy (EIS) and its applications

Grossi M., Riccò B. (2017), “Electrical Impedance Spectroscopy (EIS) for biological analysis and food characterization: a review”, Journal of Sensors and Sensor Systems, vol. 6, pp. 303-325.

can be downloaded for free at

https://www.j-sens-sens-syst.net/6/303/2017/