Applied Polymer ARTICLE EGMRUP 150.2025 Figure 8. Arrhenius plots of the t values versus the reciprocal tempera- ture for the NFRUP and EGMRUP composites polymer, and the second one, which appeared at high tempera tures, was attributed to an ionic conduction effect. to further support these assignments, the activation energy (Ea) relative to the different relaxations was evaluated with the following Arrhe- nius relation: where t(= 1/2rfmax)is the relaxation time associated with the maximum M for a fixed temperature, to is the relaxation time 0.10.1502 at very high temperatures, Ea is the activation energy of the relaxation process, kg is the Boltzmann constant, and T is the Figure 9. Argand's plots of M of the (a) NFRUP and(b)Egmrup temperature. Figure 8 shows the evolution of log t versus 1/T composites at 150C for each one of the different observed relaxations: that is, x and conductivity for the NFRUP and EGMRUP composites. Ea and ities for the NFRUP composite (96.33 k]/mol for a and to were extracted from the slopes and the intercepts of the plots 10-15.47 s for to) and the EGMRUP composite(100 k]/mol for of log t versus 1/T. The mean values of Ea and to relative to the Ea and 10-15. s for to). These values were in agreement with a relaxation were 136.02 kJ/mol and 10 s and 123. 2 kJ/mol those reported in other research works. 62 and 10 s for the NFRUP and EGMRUP composites, respec- tively, as mentioned in Table Il. However, it can be noted that The Argand representation was used to analyze the nature of the incorporation of fibers decreased the apparent activation the relaxation. Cole-Cole plots of the NFRUP and EGMRUP the matrix determined in the previous study; this could be well established that the response of every relaxation mechanism This interaction determined the nature of the interfacial adhe- parameters at the most. Among others, this includes the fol sion region. The latter was characterized with SEM, as illus- trated in the previous section. It also determined the conducti Table IL. Activation Energies Ea and Relaxation Times to for the NFRUP 1+(ior)] and EGMRUP Composite Materials. This function was introduced by Havriliak-Negami and is widely used because of its suitability for mathematical process- Composite material E。化kJm 6 In this equation, Es and Eoo are the dielectric constants on NFRUP the low-and high-frequency sides of the relaxation, t is 13602 tral relaxation time, o is the radial frequency, and a and Bare Conduction 9633 0-15.47 fractional shape parameters describing the skewing and broad EGMRUP ening of the dielectric function, respectively. Both a and B range a Relaxation 1232 between 0 and 1. These coefficients act as the deviation from the Debye equation. In fact, when a and B are equal to 1, this Conduction 100 10-1586 equation reduces to the Debye equation. In the M formalism Www. MaterialSviewS. cOm WILEYONLINELIBRARY. COM/APP J APPL POLYM. SCL 2013, DOl: 10.1002/APP. 38499 495polymer, and the second one, which appeared at high tempera￾tures, was attributed to an ionic conduction effect. To further support these assignments, the activation energy (Ea) relative to the different relaxations was evaluated with the following Arrhe￾nius relation: s ¼ s0 exp Ea kBT
(5) where s (¼ 1/2pfmax) is the relaxation time associated with the maximum M00 for a fixed temperature, s0 is the relaxation time at very high temperatures, Ea is the activation energy of the relaxation process, kB is the Boltzmann constant, and T is the temperature. Figure 8 shows the evolution of log s versus 1/T for each one of the different observed relaxations; that is, a and conductivity for the NFRUP and EGMRUP composites. Ea and s0 were extracted from the slopes and the intercepts of the plots of log s versus 1/T. The mean values of Ea and s0 relative to the a relaxation were 136.02 kJ/mol and 1020.96 s and 123.2 kJ/mol and 1019 s for the NFRUP and EGMRUP composites, respec￾tively, as mentioned in Table II. However, it can be noted that the incorporation of fibers decreased the apparent activation energy (Ea a) for the two composites in comparison with that for the matrix determined in the previous study; this could be ascribed to the interaction between the fibers and the matrix.20 This interaction determined the nature of the interfacial adhe￾sion region. The latter was characterized with SEM, as illus￾trated in the previous section. It also determined the conductiv￾ities for the NFRUP composite (96.33 kJ/mol for Ea and 1015.47 s for s0) and the EGMRUP composite (100 kJ/mol for Ea and 1015.86 s for s0). These values were in agreement with those reported in other research works.62 The Argand representation was used to analyze the nature of the relaxation. Cole–Cole plots of the NFRUP and EGMRUP composites at 150
C are depicted in Figure 9(a,b). It has been well established that the response of every relaxation mechanism can be represented very precisely by a model function with four parameters at the most. Among others,63 this includes the fol￾lowing function: e ¼ e1 þ eS e1 ½1 þ ðixsÞ a  b (6) This function was introduced by Havriliak–Negami and is widely used because of its suitability for mathematical process￾ing.64 In this equation, eS and e1 are the dielectric constants on the low- and high-frequency sides of the relaxation, s is the cen￾tral relaxation time, x is the radial frequency, and a and b are fractional shape parameters describing the skewing and broad￾ening of the dielectric function, respectively. Both a and b range between 0 and 1. These coefficients act as the deviation from the Debye equation. In fact, when a and b are equal to 1, this equation reduces to the Debye equation. In the M* formalism, Figure 8. Arrhenius plots of the s values versus the reciprocal tempera￾ture for the NFRUP and EGMRUP composites. Table II. Activation Energies Ea and Relaxation Times s0 for the NFRUP and EGMRUP Composite Materials. Composite material Ea (kJ/mol) s0 (s) NFRUP a Relaxation 136.02 1020.96 Conduction 96.33 1015.47 EGMRUP a Relaxation 123.2 1019 Conduction 100 1015.86 Figure 9. Argand’s plots of M* of the (a) NFRUP and (b) EGMRUP composites at 150
C. WWW.MATERIALSVIEWS.COM WILEYONLINELIBRARY.COM/APP J. APPL. POLYM. SCI. 2013, DOI: 10.1002/APP.38499 495 ARTICLE