Determination of Lorenz number of composite films based on copper chloride(II) in polyvinyl alcohol matrix

Abstract

The electrical and thermal conductivities as well as Lorenz number of polyvinyl alcohol (PVA) composites have been investigated at different concentrations of the copper chloride II (0, 1, 3, 5, 7 and 12 wt-%). The powder of copper chloride II (CuCl₂) was casted with the PVA polymer1. The electrical conductivity was measured by using the impedance technique, and it was studied as functions of the CuCl₂ concentrations, applied frequency range of 100–7000 kHz, and temperature range of 30–100 °C. The activation energy (E_a) was also determined for all the studied samples at applied frequency of 1000 kHz. It was found that the E_a decreased with increasing the CuCl₂ concentration. Moreover, the thermal conductivity of the samples was studied as functions of the CuCl₂ concentration and temperature. It was found that the thermal conductivity increased with increasing the CuCl₂ concentrations and temperature. Using the measured values of the thermal and electrical conductivities of the studied samples, the relationship between the Lorenz number (L) of the PVA and CuCl₂ concentrations with constant temperature was also studied based on the Wiedemann–Franz law. The results showed that the L number increased with CuCl₂ concentrations increase at constant temperature.

Introduction

Generally, polymers are inactive electrical insulators; the existence of impurities enables them to be electric conductors because of the free movement of the ions of impurities through them. In the recent years, studies of the electrical and thermal properties of polymers have attracted much attention in view of their applications in electronic and thermal devices. ¹ However, the electrical conduction in polymers has been studied, in order to understand the nature of the charge transport prevalent in these materials while the thermal properties are aimed at achieving better thermal conductivity and thermal diffusion.

One of the important classes of polymer electrolytes is the polar polymer such as polyethylene oxide (PEO), polypropylene oxide (PPO) and polyvinyl alcohol (PVA). The PVA is a polymer that has been studied intensively due to its several interesting physical properties such as high dielectric strength, good charge storage capacity and damping dependent electrical properties in both forms pure and composite. The PVA has been widely used as a solid polymer electrolyte (SPE) as a stabiliser for producing conducting polymer dispersions. It is observed that doping a polymer with metal salts has significant effect on their structural, optical, thermal, and electrical properties.^2,3 These effects on the physical properties of the polymers depend on the chemical nature of the dopant materials and on the way in which they interact with the host polymer. As a result, inorganic additives such as CuCl₂ have considerable effect on the structural, electrical, and thermal properties when it is doped with a polymer. ⁴

The thermal conduction in the solid polymers is produced by phonon, ions transport (as major contributors), electrons and impurities existing in their bulk structure. Measurements of the thermal conductivity of polymeric materials is difficult since its value is relatively small which is in the range of 0.1–0.4 W·m⁻¹·K⁻¹. In addition to, the thermal conductivity is so sensitive to the measuring conditions, physical, and chemical structure of the polymer composite. Thus, the growing needs for materials to be used in thermal applications leads to the design of a new composite material with the appropriate combination of selected polymeric matrices and suitable fillers. ⁵

In this paper, we used the PVA as a host polymer because the PVA is a semi-crystalline polymer, and it has very important applications due to the role of OH group and hydrogen bonds. ⁶ The present study could be contributed to understand the effect of different concentrations of copper chloride II (0, 1, 3, 5, 7 and 12 wt-%) on the electrical and thermal properties of the PVA films such as AC conductivity (σ_AC), thermal conductivity (κ) as well as on the Lorenz number (L).

Experimental work

Sample preparation

The polyvinyl alcohol composite doped with copper chloride (PVA/CuCl₂) films were prepared at room temperature by solution casting method. The PVA composite was dissolved in distilled water and heated gently in water bath to prevent thermal decomposition of polymer. The PVA was stirred by magnetic stirrer for completely dissolved. Whereas the copper chloride with different concentrations (0, 1, 3, 5, 7 and 12 wt-%) were dissolved in distilled water and added to the polymer solution, they were heated until they were completely dissolved. Then the solution poured onto a glass plate and left to dry for 24 h to remove any residual solvent. By using the electronic micrometer, the thickness range of the PVA/CuCl₂ films was found to be 60–70 μm.

Impedance measurements

The AC electrical measurements were measured in the frequency range of 100–7000 kHz at different temperatures. The AC measurements were performed using an LF impedance analyser (IA) manufactured by HP model 4192. The IA was a fully automatic, high-performance test instrument designed to measure a wide range of impedance related parameters, such as phase angle, real and imaginary components of the impedance, admittance, conductance and capacitance. ⁷ The LFIA gave the impedance and phase angle of the specimen by varying the applied frequency which was necessary to measure the electrical conductivity (σ_AC).

Thermal conductivity measurements

Measurements of the thermal conductivity (κ) of the PVA/CuCl₂ films were measured using the heat pulsed method, which is based on sending an electrical pulse to transmit across double test specimens separated by a current coil placed in a sample holder connected to thermocouples for temperature measurements. The cell assembly surrounded by insulating jacket to minimise the heat loss was placed in an oven. Temperature readings were taken every half hour to reach the steady state of thermal equilibrium. The quasi-steady-state temperature difference (ΔT) was found to be identical for the thermocouple pairs on one side, and to those on the other side. This gives support to the assumption of symmetry on both sides of the heat flux.

Results and discussion

The measurements of the AC conductivity of the PVA/CuCl₂ films were calculated by using the equation: ⁸

$${\sigma }_{\mathrm{AC}}=2\pi f{\epsilon }_0{\epsilon }^{\mathrm{″}}$$

(1)

Where f is the natural frequency, ε₀ is permittivity of free space and εʺ is the dielectric loss. By using equation (1), the AC conductivity versus frequency at 30 °C for different CuCl₂ concentrations is shown in Figure 1. It can be observed that the σ_AC for the pure PVA composite increases slightly within the increasing frequency in the range of 0.0017 × 10⁻⁷ to 0.0602 × 10⁻⁷ (Ω m)⁻¹. Whereas for the other composite samples with concentrations 1, 3, 5, 7 and 12 wt-%, the σ_AC show noticeable increasing over a wild range with the increasing frequency. Additionally, at high frequencies (6000 Hz) the σ_AC increases rapidly with the increase of frequency, these results comply with agree with the well-known fact that the bulk AC conductivity is induced at high frequency range. ⁹ In addition, the results could be attributed to the fact that at high frequencies, the dielectric loss (εʺ) is dominated by ionic conductivity produced from the increased electronic and ionic mobility of the existing impurities and more ions and charges are moved. ¹⁰ The observed induced conductivity at high frequencies locates the given composite in the semiconducting level of the electronic material.

Figure 1.

The AC conductivity of PVA/CuCl₂ films as a function of frequency.

Figure 2 shows the electrical conductivity (σ_AC) of the PVA/CuCl₂ films as a function of the CuCl₂ concentration at 30 °C. As shown in the figure the values of the σ_AC increase as a function of filler content at different frequencies (200, 400, 600, 800 and 1000 kHz). Also, the figure shows that the electrical conductivity slightly increases with the increasing of the concentration of CuCl₂ up to 5 wt-%. Whereas the increasing of concentration more than that, the electrical conductivity increases to the large value up to 0.42 × 10⁻⁷ (Ω m)⁻¹ at the concentration of 12 wt-% of CuCl₂ at 1000 kHz. The increasing of the electrical conductivity of the films with the increasing of the CuCl₂ concentration is caused by the increasing of the charge carriers ions in which they increased with increasing filler content. Thus, at higher concentrations of the CuCl₂, the network of the PVA/CuCl₂ films are connected to each other and hence they produce the overlapping paths to allow the charge carriers to pass through, where the charge carriers with routes through which the electrical resistance is less. ¹¹

Figure 2.

Variation of AC conductivity of the PVA/CuCl₂ films with CuCl₂ concentrations.

Figure 3 shows the measurements of the AC-conductivity (σ_AC) of the PVA/CuCl₂ films as functions of temperature (30–90 °C) and CuCl₂ concentrations (0, 1, 3, 5, 7 and 12 wt-%) at 1000 kHz. The results show that the σ_AC increases with increasing the temperature. This result can be attributed to the fact that the polymeric chains and CuCl₂ concentration could act as traps for the charge carriers, which transited by hopping process. By increasing the temperature, segments of the polymer begin to move, releasing the trapped charges. The released of trapped charges is intimately associated with molecular mobility. The mobility depends on the structure and the temperature. ¹²

Figure 3.

AC-conductivity of the PVA/CuCl₂ films as a function of temperature at 1000 kHz.

To fully understand the electrical properties of the PVA/CuCl₂ films, the activation energy (E_a) of films has been investigated at different CuCl₂ concentrations. The E_a is defined as the minimum amount of thermal energy that is required to activate ions, atoms, and molecules to conduction in which they can undergo physical transport. The activation energy E_a of the conduction process is calculated by Arrhenius equation: ¹³

$${\sigma }_{\mathrm{AC}}={\sigma }_0{e}^{-E_{\mathrm{a}}/k_{\mathrm{B}}T}$$

(2)

where σ_AC is the electrical conductivity, σ₀ is the material constant conductivity, T is the temperature of the material in Kelvin and k_B is the Boltzmann constant. The values of the E_a were calculated from the slopes of the approximated straight lines obtained by plotting the natural logarithm of the conductivity (Ln σ_AC) versus (1000/T) for each sample at the frequency 1000 kHz as shown in Figure 4.

Figure 4.

Variation of the Ln (AC-conductivity) of the PVA/CuCl₂ films with (1000/T).

By using equation (2) and the data of Figure 4, the E_a values were determined and inserted in Table 1. The table shows the dependence of E_a on CuCl₂ concentrations. From the table, we can see that the activation energy values decrease with increasing the CuCl₂ concentration in a thermally activated process, the composites become more conductive as shown in Figure 2. The decreasing in the E_a values implies that the energy of the PVA/CuCl₂ films becomes narrower due to creation of localised energy states by heating which enhances the ion mobility and ability of the electron to tunnel or hop easily from the valence band to conduction band. Related results were reported by Salman et al. ¹⁴ who studied the AC conductivity of the PVA complexes with cobalt chloride. They attributed the increasing of the AC conductivity to some structural transitions from crystalline phase of the polymer to amorphous phase which increased the amorphous region in the polymer PVA and produced more active segmental motion that stimulated the electron hopping mechanism and thus the AC conductivity becomes high. In our study, the observed increasing and decreasing in the AC conductivity and the activation energy values, respectively with increasing the CuCl₂ content or temperature can be dominated by the mobility in the localised states bridged by the doped CuCl₂ molecules in the amorphous regions existing in the SPE. The low activation energy for copper ion transport is due to the completely amorphous nature of polymer electrolyte that facilitates the fast Cu⁺² ions motions in the polymer network. Also, the chloride ions complexes contribute to the ionic conduction process takes place in the solid electrolyte composite. ¹⁵

Table 1.

The activation energy of the PVA/CuCl₂ films with the CuCl₂ concentrations.

CuCl2 concentration/wt-%	Activation energy/eV
0	0.273
1	0.262
3	0.258
5	0.255
7	0.241
12	0.175

The thermal conductivity (κ) of the PVA/CuCl₂ films has been studied at temperature range of 30–90 °C. The values of the κ at each temperature can be calculated from following relation: ¹⁶

$$\kappa =q_{\mathrm{s}}\left({\displaystyle \frac{L}{\mathrm{\Delta }{T}_{\mathrm{s}}}}\right)={\displaystyle \frac{IVL}{2A\mathrm{\Delta }{T}_{\mathrm{s}}}}$$

(3)

Where q_s is the heat flux, L is the sample thickness, I is the electrical current, V is the electrical voltage and A is the area of the heating foil. Because of the using two circular disks of identical thickness, the factor 2 is inserted due to the symmetrical distribution of heat flux on both sides of the apparatus.

Figure 5 shows the variation of the thermal conductivity with temperature, the κ increases slightly with increasing the temperature. In case of raising the temperature, phonons, ions, electron, and impurities are activated and thus enhancement in the thermal conductivity is produced. ¹⁷

Figure 5.

The variation of the thermal conductivity of the PVA/CuCl₂ films with temperature.

Figure 6 shows the variation of thermal conductivity of the PVA/CuCl₂ with CuCl₂ concentrations. It can be seen that the thermal conductivity increases with increasing the concentration of the CuCl₂ filler content. Thus, the dispersing CuCl₂ phase in the PVA matrix enhances the electrolyte thermal conductivity and reduces its thermal resistance, which may be useful to the thermal performance applications. This result may be due to compactness provided by increase in dopants concentration which increase the heat transfer through phonons diffusion. ¹⁸

Figure 6.

The variation of the thermal conductivity of the PVA/CuCl₂ with CuCl₂ concentration.

The Lorenz number is a thermoelectrical parameter characterising the effect of temperature on both the thermal and electrical conductivities of a solid material. Knowledge of the Lorenz number is important in the design of the thermoelectric materials and in the experimental determination of the lattice thermal conductivity. The Lorenz number is determined by using the Wiedemann–Franz law:^19,20

$$L={\displaystyle \frac{\kappa }{\sigma T}}$$

(4)

Where L is the Lorenz number, T is the absolute temperature, σ_AC is the electrical conductivity and κ is the thermal conductivity.

According to the data shown on the Figures 2 and 6, Table 2 shows a comparison between the electrical and thermal conductivities behaviour of the PVA/CuCl₂ films at 30 °C. Both the electrical conductivity and thermal conductivity increase with increasing the dispersed CuCl₂ phase in the PVA matrix.

Table 2.

The electrical and thermal conductivities of the PVA/CuCl₂ films.

Polymer electrolyte composites	Thermal conductivity/ W·m−1·K−1	Electrical conductivity × 10−7/ Ω−1 m−1
Pure PVA	0.110	0.098
1 wt-% CuCl2	0.140	0.104
3 wt-% CuCl2	0.178	0.114
5 wt-% CuCl2	0.250	0.151
7 wt-% CuCl2	0.350	0.203
12 wt-% CuCl2	0.740	0.421

Figure 7 shows the variation of Lorenz number of the PVA/CuCl₂ films with CuCl₂ concentration at 303 K. It is clearly observed that the Lorenz number increases with increasing CuCl₂ concentrations. This can be attributed to the difference in the rate of increasing of the σ_AC and the enhancement of the thermal conductivity (κ) with the filler content as shown in the Figures 2 and 6.

Figure 7.

Variation of Lorenz number of the PVA/CuCl₂ films with CuCl₂ concentration at 303 K.

Conclusions

The electrical, thermal conductivities, activation energy and Lorenz number of composite films based on copper chloride(II) in PVA matrix have been investigated as functions of the filler concentrations, applied frequency and temperature. The AC conductivity increased with frequency, CuCl₂ concentration and temperature. Whereas the thermal conductivity increased only with both temperature and CuCl₂ concentration in the studied films. The values of the activation energy (E_a) were decreasing for PVA/CuCl₂ films with increasing of the temperature and the CuCl₂ concentrations. The decreasing in the E_a values implied that the energy of the prepared PVA/CuCl₂ films become narrower due to creation of localised energy states by heating which enhanced the ion mobility and ability of the electron to tunnel or hop easily from the valence band to conduction band. The Lorenz number at 303 K increased with increasing CuCl₂ concentrations. This is due to the enhancement in thermal conductivity compared to electrical conductivity for the composites, which attributed to phonon propagation and electron hopping increasing.