The ionic polarization due to the application of an electric field on a material induces a displacement of the positive ions relative to the negative ions. This polarization intervenes for frequencies lower than terahertz. Under an applied field, the permanent dipoles of the molecules are oriented in the direction of the field. The electronic polarization is due to the displacement of the electron cloud of the atom with respect to its nucleus. The last one, electron polarization is due to a relative displacement of the nucleus of the atom relative to all the electrons that surround it.
The orientation polarisation is prevalent because it required a longer time compared to other polarizations. Therefore, the value of dielectric constant decreases reaching a constant value at higher frequency corresponding to interfacial polarization. The increase observed in values with temperature is due to the contribution of the charge carriers to the polarization.
At low temperatures, polarization is weak due to inability of the dipoles to rotate fast enough; therefore, they oscillate behind the field. The increase in temperature results in sufficient thermal excitation energy obtained by the bound charge carriers, which enhance the polarization leading to the increase in the dielectric constant. Table 1 shows the values of dielectric constant of our copolymer compared with other values in the literature. The dielectric constant is higher than that of many other aromatic organic polymers, making it a good semiconductor material.
At the same time, these values are low compared to the results recorded in [ 26 ]. This results in a reduced response time. The imaginary part of the permittivity as a function of frequency at different temperatures calculated by using equation 1 is shown in Figure 3. The behaviour of dielectric loss is similar to the real part of the permittivity, with an anomaly exception at room temperature, which does not have a presently understood origin.
The dielectric loss obtained increases with increasing temperature and has a rapid decrease at low frequencies while being almost independent at high frequencies.
In Figure 3 , the factor loss behaviour as a function of frequency can be explained by the fact that ions migrate within the material at low frequencies. The values of dielectric loss at moderate frequencies are due to the contribution of ion jump and conduction loss of ion migration, as well the ion polarization loss. At high frequency, ion vibrations may be the only source of the dielectric loss, so is frequency-independent.
Differently, the loss factor decreases with increasing frequency and expressed as follows according to the CBH model: where is a constant and m is the frequency power factor. From the plot of vs. According to Guintini model [ 36 ], equation 9 , m decreases with increasing temperature, and it is clearly shown in the inset Figure 3 b. The losses that are attributed to the conduction presumably involve the migration of ions over large distances.
This motion is the same as that occurring under DC conditions. The ions jump over the highest barriers in the network. As the ions move, they give some of their energy to the lattice as heat, which accounts for the dissipation of electrical energy as heat. The frequency dependence of the AC conductivity is obtained by equation 2. As noted, the behaviour of that follows our copolymer increases with increasing frequency.
The increase in conductivity can confidently be attributed to the hopping mechanism that appears by applying the electrical field. This can be confirmed by studying the behaviour of the frequency exponent in equation 2. The exponent decreases with increasing temperature; therefore, among all the models discussed in the theoretical background, CBH is the appropriate model for the conduction in our material. Figure 4 b shows the variation of the AC conductivity as a function of temperature at several frequencies; it is clear that there is a linear relationship between and the inverse of temperature.
As the temperature rises, AC conductivity increases as well due to the hydrogen bond strength in the molecules, which is affected by the temperature and leads to the movements of thermally excited carriers from energy levels within the band gap. We report in Table 1 the values of AC conductivity at several temperatures and frequencies for comparison with other values reported in the literature. We defined a new parameter as a figure of merit F related to the response time, which represents the relationship between the dielectric permittivity and the AC conductivity.
The higher its value, the more suitable the material for solar cell applications:. The straight lines of with inverse of temperature follow the Arrhenius equation: where is the pre-exponential constant and is the activation energy. The values of activation energy of our sample calculated as a function of frequency from the slope of the straight lines are plotted in Figure 4 b and shown in Figure 6. Activation energy decreases with increasing frequency; this could be due to the applied field frequency that enhances the electronic jumps between the localized states.
This confirms that the hopping mechanism controls the transport mechanism. The complex dielectric modulus is obtained from equation 7 and is depicted in Figure 7 a. From the figure, we observe that M r reaches maximum values at high frequencies due to the relaxation process, and it approaches to zero at low frequencies due to the lack of electric polarization. The results showed that dielectric modulus has reverse frequency behaviour compared with dielectric constant at room temperature in inset Figure 7 a , as we can notice from the figure dielectric constant decreases with frequency, while electric modulus is increasing.
The imaginary part of modulus as a function of frequency at few selected temperatures is shown in Figure 7 b. The analysis presented here of M im suggests the appearance of a dielectric relaxation peak at low frequencies and remains constant with increasing temperature.
This behaviour is similar and observed in previous works [ 37 , 38 ]. The values below the maximum peak are determined by the charge carriers that move on long-range distances, whereas the carriers are confined to potential wells being mobile on short distances determine the values above maximum peak. X-ray has been done and shows crystalline regions in our polymer. The imaginary part of dielectric constant shows similar behaviour to as a function of temperature and frequency. The AC conductivity appears to increase with increasing frequency and a decrease with arising temperature.
The appropriate model for was the correlated barrier-hopping CBH model. Activation energy decreases with increasing frequency.
Those results are promising compared with others in the literature; this could be exploited to investigate more in dielectric and electric properties of organic materials. The experimental data used to support the findings of this study will be made available upon request. The authors thank Prof.
Alex Brown, Department of Chemistry, University of Alberta, for comments that greatly improved the manuscript. This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Article of the Year Award: Outstanding research contributions of , as selected by our Chief Editors.
Read the winning articles. Journal overview. Special Issues. Academic Editor: Marinos Pitsikalis. Received 22 Oct Accepted 23 Dec Published 30 Jan Introduction Organic conductive and semiconductor materials are emerging as the key materials for future electronics. This equation can be approximated to obtain According to this CBH model, the conductivity can be expressed by [ 33 ] where N is the density of localized states at which carriers exist, is the dielectric constant of the material, and is the hopping distance and given as Dielectric relaxation mechanism can be obtained from the peak of the dielectric loss , impedance complex, and electric modulus.
This parameter can be defined as [ 34 ] 4. Results and Discussion 4. Figure 1. Figure 2. Dielectric constant vs. Coumpound Frequency kHz at R. DOI: Electromagnetics for Engineering Students starts with an introduction to vector analysis and progressive chapters provide readers with information about dielectric materials, electrostatic and magnetostatic fields, as well as wave propagation in different situations.
Each chapter is supported by many illustrative examples and solved problems which serve to explain the principles of the topics and enhance the knowledge of students.
In addition to the coverage of classical topics in electromagnetics, the book explains advanced concepts and topics such as the application of multi-pole expansion for scalar and vector potentials, an in depth treatment for the topic of the scalar potential including the boundary-value problems in cylindrical and spherical coordinates systems, metamaterials, artificial magnetic conductors and the concept of negative refractive index.
Author s : Sameir M. This chapter focuses on the conducting and dielectric materials and their properties under static fields condition. The dielectric constant of the solution to be measured was calculated from the relationship [11]:. G 1 : Conductance of the empty cell. G 2 : Conductance of the cell filled with the test solution. The solution in the conductivity cell had the desired temperature control by using a thermostatic Techne model U Changes of quality and composition of the dielectric material cause the dielectric constant to vary.
The variations may be measured through the variation of the capacitance of the capacitor. The capacitor behaves like a reactive resistance reactance in which no energy loss can occur. Where W is the heat developed per second in unit cube of the material, I is the current density and V is the voltage gradient.
If air is removed from the capacitor and a dielectric is inserted between the plates, the capacitor becomes lossy which may be considered as one with a resistor connected in series with it. The capacitor takes up energy from the circuit, the energy is transformed into heat and a dielectric heat loss is produced.
In most cases both factors are decreased by decreasing the concentration. This equation has been tested using a number of series of ligands and their complexes solutions. The dielectric constant increases mainly with increasing temperature due to the presence of hydrogen bonding which pointed to cooperative reinforcement of dipole fields [15].
NBA has a higher dielectric constant than BA due to the presence of the electron withdrawing nitro group where large orientational polarization is resulted with the existence of a chain type of association and the presence of molecular units of large dipole moments. The dielectric material usually contains traces of charges as impurities, where the activity increased by increasing the temperature.
Table 1. Table 2. Values of a. The electrical conductivity of solutions at a given frequency varies exponentially with the absolute temperature according to the Arrhenius relation [17].
The values of DE and s o for solutions of 10 -3 M-ligands and their complexes are given in Table 3. As the atomic number of the metal increases, the electrical conductivity regularly decreased and the activation energy DE of the complexes decreased in an irregular trend.
Table 3. The compounds BA, PB and TU are of weak electrolytic in nature with low molar conductance until very high dilutions, it increases suddenly. On the other hand, the NBA exhibits high values of molar conductance over the whole concentrations range which is considered to have strong electrolytic nature due to the presence of withdrawing nitro group. Figure 2. Molar conductance vs.
Table 4. Table 5. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Masoud MS Dielectric and electric conductivity studies of some pyrimidine compounds and their complexes. Home Contact Us.
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