In Situ Characterization of Size, Spatial Distribution, Chemical Composition, and Electroanalytical Response of Hybrid Nanocomposite Materials

Abstract

Life in the twenty-first century is dependent on an unlimited variety of advanced hybrid materials – among them, nanomaterials (NMs). The design of these NMs mostly depends on the current necessities of the society, the availability of resources, and the investment required for an appropriate scale-up production. Thus, regarding the preparation of novel NMs, it is mandatory for the evaluation of their properties in order to satisfy the desired applications with high performance. In this chapter, we discuss different techniques that offer the possibility of the in situ characterization of NMs and nanocomposite materials (NCs), in terms of their chemical composition, spatial distribution, and optical and electrochemical features, without modifying the material itself.

Annexe

1.1 Basics of Electrochemical Techniques for the Characterization and Optimization of Nanocomposite Sensing Materials

Electrochemical methods are interesting tools, which provide very useful information in order to characterize (bio)nanocomposites [66]. Electrochemical impedance spectroscopy (EIS) and cyclic voltammetry (CV) are the most common.

1.2 Electrochemical Impedance Spectroscopy

EIS is one of the most powerful and reliable methods to extract information about electrochemical characteristics of electrochemical systems [77, 78], thus it is extensively applied in several fields, e.g., corrosion [79, 80], electrode kinetics [81, 82], coatings, membranes [83], batteries [84, 85] and fuel cells [86, 87], interfaces, biochemistry, and solid-state electrochemistry [88].

Basically, it is based on applying an AC potential to an electrochemical cell and measuring the current through the cell. When a process occurs in an electrochemical cell, it can be modeled using combination of electrical components using the principle of the equivalent circuits. This principle consists on obtaining values of electrical parameters such as resistance, capacitance, etc., when an experimental spectrum is fitted with a theoretical curve corresponding to the selected circuit model.

Two different types of impedance measurements can be performed: Faradaic and non-Faradaic measurements. In the first case, redox species are added to the bulk solution in order to test the electrical properties at the interface solution-electrode. In the second one, no additional reagents are required and the measured current is due to the charging of the double layer at the interface electrolyte-electrode [95]. Faradaic or non-Faradaic measurements are used depending on the application. This part of the chapter is focused on the first method.

If it is applied a sinusoidal potential excitation E _t :

$$ {E}_t={E}_o\bullet \sin \left(\omega \bullet t\right) $$

(8.9)

Where E _t is the potential at time t, E _o is the amplitude of the signal, and ω = 2πf is the angular frequency (f is the frequency expressed in Hertz (Hz)).

An AC current signal with a current intensity I _t is obtained in response to this potential applied. I _t also depending on t with the same frequency but with an amplitude I _o and a phase angle φ depending on the impedance of the system.

$$ {I}_t={I}_o\bullet \sin \left(\omega \bullet t+\varphi \right) $$

(8.10)

To calculate the impedance of the system, an expression analogous to Ohm’s law is used:

$$ \mathrm{Z}=\frac{E_t}{I_t}=\frac{E_o\bullet \sin \left(\omega \bullet t\right)}{I_o\bullet \sin \left(\omega \bullet t+\varphi \right)}={Z}_o\bullet \frac{\sin \left(\omega \bullet t\right)}{\sin \left(\omega \bullet t+\varphi \right)} $$

(8.11)

According to Euler’s expression:

$$ \exp\ \left( j\varphi \right)=\cos \varphi +j\sin \varphi $$

(8.12)

A common way to represent the impedance vector model is to use complex notation:

$$ E(t)={E}_o\bullet \exp \left( j\omega \bullet t\right) $$

(8.13)

$$ I\ (t)={I}_o\bullet \exp \left( j\omega \bullet t- j\varphi \right) $$

(8.14)

Therefore, impedance is represented as:

$$ Z=\frac{E}{I} = {Z}_o\exp \left( j\varphi \right)={Z}_o\left(\cos \varphi +j\sin\ \varphi \right)={Z}_r+j{Z}_i $$

(8.15)

where Z _r is the real part of the impedance and Z _i the imaginary part.

In order to acquire an impedimetric spectrum, an AC excitation signal is setting to the system within a selected frequency range, reaching to obtain an AC current response for each analyzed frequency value.

The most common graphical representation of impedimetric data is the Nyquist diagram, in which the imaginary part of the impedance −Z _i is plotted versus the real part Z _r . In this plot, each point corresponds to a different frequency of the selected frequency range. In Figure 8.16 is represented a Nyquist diagram, where the impedance vector with magnitude |Z| (|Z| correspond to Z _o ) forms with the X-axis an angle corresponding to the phase angle φ. The high frequency data are represented on the left part of the diagram while the low frequency data are on the right one.

Fig. 8.16

Schematic representation of Nyquist diagram

Another way of representation data is bode diagram where the modulus of the impedance (Log|Z|) and the phase angle (φ) between the AC potential and the AC current are plotted as a function of the frequency (log ω). The impedance data, which are frequency independent, represent the behavior of the resistive processes (phase angles close to 0), whereas the ones that are dependent on the frequency are more related to capacitive or diffusive processes (phase angles between −90° or −45°).

The processing of data is performed by setting the data to an equivalent circuit that reproduces the spectrum of impedances during the experiment. These circuits are formed by electrical elements (such as resistors, capacitors, inductors, etc.) that combine to reproduce the behavior of real processes such as electrolyte resistance between the reference electrode and the charge of the double layer or charge transfer that takes place over a faradaic process.

Figure 8.17 shows an example of Nyquist diagram to a simple equivalent circuit formed by resistance R₁ in series with the parallel combination of a capacitance C and another R₂ (R₁(R₂C)). The impedance spectra is represented by a semicircle. Beginning in The point (a) corresponds to R₁ value and the point (b) to the equal R₁ + R₂. The value of capacitance of the capacitor C is obtained by the maximum value of imaginary impedance in the spectrum. The majority of impedance spectra corresponding to electrochemical systems can be fitted to this type of equivalent circuit. In those cases, the parameter R₁ represents the resistance of the solution (R_s), R₂ corresponds to the resistance (R_ct) to the charge transfer between the solution and the electrode surface, and C represents the capacitance of the double layer due to the interface between the electrode and the electrolytic solution.

Fig. 8.17

Nyquist diagram and its corresponding equivalent circuit

A Warburg impedance parameter must be considered when it is recorded at low frequencies. This parameter is related to the mass transfer between the solution and the electrode surface and can be modeled as a frequency dependent reactance with equal real and imaginary components.

$$ {Z}_w=\sigma \bullet {\left(\omega \right)}^{-\frac{1}{2}}\bullet \left(1-j\right) $$

(8.16)

Where ω is the angular frequency and σ is the Warburg coefficient (constant for a defined system).

The Warburg impedance appears on a Nyquist diagram as a diagonal line with a slope of 45°. In an electrochemical system or process, it represents the diffusion of electrochemical species in the solution. Figure 8.18 shows the impedimetric spectra and the most favorite model of equivalent circuit for a simple electrochemical reaction called Randles equivalent circuit.

Fig. 8.18

Nyquist diagram and its corresponding equivalent circuit called Randles circuit

In some cases, the semicircles of Nyquist diagrams present a depressed and not completely symmetric shape; this is due to the nonideal behavior of most capacitors in electrochemical systems. In order to fit better the experimental data to the theoretical curves, a constant phase element (CPE) is used instead of a capacitor [96]. The impedance of a CPE is represented by:

$$ {Z}_{\mathrm{CPE}}={\left(j\bullet \omega \right)}^{-\alpha }/\mathrm{C} $$

(8.17)

Where ω is angular frequency, C is capacitance, and α is an exponent, α(0 − 1). In a constant phase element, the exponent α is lower than 1, even though α = 1 corresponds to the ideal capacitor.

It is also important to highlight that impedimetric measurements should be interpreted according to the electrochemical system under study in order to understand and attribute the electrical elements corresponding to the electrochemical phenomena.

1.3 Cyclic Voltammetry

CV is a technique widely used within the field of electrochemistry. From a simple measurement, it is possible to extract useful information in different technical fields. It is also used in non-analytical purposes including basic studies of electrocatalytic properties [89, 90], redox processes [91, 92], reaction mechanisms, or the study of a reaction intermediate species. Concerning biocomposites, CV is also employed as a characterization technique, sometimes together with EIS in order to complement both techniques [66, 93].

This technique is based on the current intensity measurement when it is applied a triangular excitation signal, varying the applied potential using constant scan rate, inside a prefixed working potential, both direct or indirect direction. In case of positive potentials (anodic direction), the electrode becomes an oxidant agent. However, when the potential lies to negative values (cathodic direction) it becomes a reduction agent. So, it is possible to achieve a value where the electroactive species oxidation is favorable and the anodic current intensity increases remarkably. It is achieved a maximum value which corresponds to the condition of electrode maximum polarization, and it is generated in a characteristic oxidation peak. Since the measurements are carried out without agitation conditions, when the scan direction is reversed, the electroactive oxidized species that are present on the electrode surface starts to be reduced generating a cathodic current until a maximum value. In this point, a reduction peak is generated.

The most important parameters that could be extracted from a cyclic voltagramm are cathodic current peak (i_pc) and anodic current peak (i_pa), as well as their potential values in those points (cathodic peak potential, E_pc and anodic peak potential, E_pa). These parameters are defined as it is shown in Fig. 8.19. Under ideal reversible conditions the following conditions are met:

• (i) Separation between potential peaks is 0.059/n, where n corresponds to the number of electrons that are taking part on the reaction (ΔE = E_pa – E_pc = 0.059/n).

• (ii) Cathodic current peak value is the same that anodic current peak, in absolute value (ǀi_paǀ = ǀi_pcǀ).

• (iii) Peak potentials are independent of the scan rate (v).

• (iv) Peak current is proportional to the square root of the scan rate (v^1/2).

Fig. 8.19

Schematic representation of a cyclic voltagramm for an ideal reversible redox system

Commonly, it is used a redox system which is totally reversible (Fe²⁺/Fe³⁺, [Fe(CN)6]³⁻/[Fe(CN)₆]⁴⁻, [Ru(NH₃)₆]²⁺/[Ru(NH₃)₆]³⁺, etc.) in order to perform the viability studies of an electroanalytical device, or in order to compare the behavior of the different electrodes or electrochemical devices developed.

Another important relationship which allows evaluating the reversibility of the system is the modified Randles– Sevčik equation. This equation connects the current peak (I_p), the concentration of the electroanalytical species that is reacting, and the scan rate (Eq. 8.18) [97].

$$ {I}_{\mathrm{p}}=3.01\cdot {10}^5{n}^{3/2}{\left(\alpha\ {D}_a\ v\right)}^{1/2}A\ {C}_a $$

(8.18)

Where n is the number of electrons that are participating on the redox reaction, α corresponds to the transfer coefficient, D_a corresponds to the diffusion coefficient of the reduced or oxidized species, v represents the scan rate, A is the electroactive area, and C_a is the bulk concentration of the electroactive species. This equation is adequate for electron transfer-controlled processes. For a reversible system where the process is controlled by the diffusion it is obtained a linear relationship between I_p and v^1/2.

On the other hand, the relationship between log(I) and the potential is the Tafel diagram (Fig. 8.20). In order to obtain this diagram it is necessary that the electrochemical process is not controlled by the electron-transfer. This diagram provides information about the exchange current (i_o), which is related to the reversibility of the process. At the same time, this constant provides information about the charge-transfer resistance (R_ct) of the process by means of the following equation:

$$ {i}_{\mathrm{o}}=\mathrm{RT}/n{\mathrm{FR}}_{\mathrm{ct}} $$

(8.19)

Fig. 8.20

Tafel diagram for a reversible electrochemical species: i_o corresponds to exchange current and E_e corresponds to equilibrium potential

An estimation of the electrode reproducibility based on nanocomposites due to the handmade electrode fabrication process is necessary before its analytical applications. Cyclic voltammetry measurements, as it has been described above, allow obtaining useful electrochemical parameters such as electroactive area and charge-transfer resistance. Knowledge of the real surface area of electrodes is, therefore, needed since normally the geometric area does not correspond to the electroactive surface of the electrode [94]. Moreover, charge-transfer resistance value is inversely proportional to the electron-transfer rate. Both parameters affect the overall analytical performance of the nanocomposite sensors.