ARTICLE Applied Polymer Table Ill. Parameters Evaluated by Data Fitting According to the Havriliak-Negami Equation for the NFRUP and EGMRUP Composites Composite material T(C) Relaxation NFRUP 120 Conduction 0.991 0.947 0003 026 MWS 0.892 0.199 0.315 130 Conduction 0.99150.90 0 .295 0.901 0.88 031 140 Conduction 0.995 0002 0298 0.999 0.21 0316 150 Conduction 0.999 0.904 0.0 0033 0301 MWS 0.99 0863 0.153 03182 EGMRUP 120 Conduction 0.9957 0.889 00052 0.31 Conduction 005 140 0.999 0.819 000399 0.3269 the Havriliak-Negami equations [eqs. (7)and (8)) have the fol- values of a, B, Ms, and Mo that best smoothed the Havriliak- lowing form: Negami data were obtained by a successive approach method, in which the following expressions were minimized M=M MsA+(Moc-MS)cos BoJA/ MAZF(Moo-M,)M, cos Bo+(M-M, )2 r=∑(M-Mp)2 M=MM (M、-M) sin BoJA MEA2(Ms-Ms)M, cos Bo +(M-M(8) It has been proven that only one quadruplet value was able to tone with these conditions. Although the values of a and B obtained for the conductive effect were in harmony with a pu Debye type, the values of a and B obtained for interfacial pola (9) ton were in accordance with the Havriliak-Negami respons CONCLUSIONS Moc= (10) A comparative study between natural-fiber-matrix(NFRUP) and E-glass-matrix (EGMRUP) composites for thermal and A=1+2(o)-2sin+(ox)2(-y12 (11) dielectric properties was undertaken. The UP resin was used as a matrix for both of them. The thermal study(DSC)carried (ot)cos &3 (12) out on these samples showed a variation in Tg as fibers(natural 1+(or)si or mineral) were added in the matrix, and this revealed the interaction of the fibers with the matrix. The dielectric response Accordingly, dotted curves were produced by the best fitting ex- of these composites showed the presence of two common perimental points with the Havriliak-Negami equations [eqs. dielectric relaxations, which were attributed to the a relaxation (7)and(S). In Figure 9(b), the Cole-Cole diagram corre- of the polymer and to ionic conduction, which occurred above sponded to the conductivity effect for the EGMRUP composite, the glass transition and at low frequencies, respectively. The whereas in Figure 8(a), it is shown that it was impossible to fit dielectric analysis revealed that interfacial polarization could not the Havriliak-Negami model to all of the experimental points for be analyzed by the Argand representation in the EGMRUP com- the NFRUP composites So, two semicircles were obtained at ev- posite, as it was absent, whereas in the case of the NFRUP com- ery examined temperature. The first one for 0< M<0.3 was posite, the analysis of the MwS polarization exhibited a consis related to the conduction effect, and the second one for 0. 15< tency of this polarization with the Havriliak-Negami model. M<0.32 was linked to the MWS effect. This analysis confirmed The tensile properties of these composites evidenced a slight the presence of the MWS relaxation, which is overlapped with enhancement in the fiber-matrix adhesion in favor of the he dc conductivity effect. The parameters evaluated by the fitting NFRUP composite. As a parameter closely related to the static stress transfer at the interface, the Youngs modulus showed a teristics of the Havriliak-Negami model (a, B, Ms, and Moc), the slight enhancement in the NFRUP composite compared with experimental Mexp and Mex data were smoothed through a nu- that in the EGMRUP composite Moreover, this comparative ex merical simulation in the complex plane. The purpose of such a perimental study demonstrated that natural fibers enhanced the simulation was to find the theoretical values(M, and M, h ). The thermal insulation in the NFRUP composite according to the 496 J. APPL. POLYM.Sc.2013,D0:10.1002PP38499 WILEYONLINELIBRARY. COM/APP EWILEY NONLINE LIBRARYthe Havriliak–Negami equations [eqs. (7) and (8)] have the fol￾lowing form:64 M0 ¼ M1 ½MsAb þ ðM1 MsÞ cos buAb M2 SA2bðM1 MsÞMs cos bu þ ðM1 MsÞ 2 (7) M00 ¼ M1Ms ½ðM1 MsÞsin buAb M2 s A2bðM1 MsÞMs cos bu þ ðM1 MsÞ 2 (8) where Ms ¼ 1 es (9) M1 ¼ 1 e1 (10) A ¼ ½1 þ 2ðxsÞ 1a sin ap 2 þ ðxsÞ 2ð1aÞ  1=2 (11) u ¼ arctg½ ðxsÞ 2a cose ap 2 1 þ ðxsÞ 1a sin ap 2  (12) Accordingly, dotted curves were produced by the best fitting ex￾perimental points with the Havriliak–Negami equations [eqs. (7) and (8)]. In Figure 9(b), the Cole–Cole diagram corre￾sponded to the conductivity effect for the EGMRUP composite, whereas in Figure 8(a), it is shown that it was impossible to fit the Havriliak–Negami model to all of the experimental points for the NFRUP composites. So, two semicircles were obtained at ev￾ery examined temperature. The first one for 0 < M0 < 0.3 was related to the conduction effect, and the second one for 0.15 < M0 < 0.32 was linked to the MWS effect. This analysis confirmed the presence of the MWS relaxation, which is overlapped with the dc conductivity effect. The parameters evaluated by the fitting data are listed in Table III. To determine the parameters charac￾teristics of the Havriliak–Negami model (a, b, MS, and M1), the experimental M0 exp and M00 exp data were smoothed through a nu￾merical simulation in the complex plane. The purpose of such a simulation was to find the theoretical values (M0 th and M00 th). The values of a, b, MS, and M1 that best smoothed the Havriliak– Negami data were obtained by a successive approach method, in which the following expressions were minimized: v2 M0 ¼ X i ðM0 th M0 expÞ 2 (13) v2 M00 ¼ X i ðM00 th M00 expÞ 2 (14) It has been proven that only one quadruplet value was able to tone with these conditions. Although the values of a and b obtained for the conductive effect were in harmony with a pure Debye type, the values of a and b obtained for interfacial polar￾ization were in accordance with the Havriliak–Negami response. CONCLUSIONS A comparative study between natural-fiber–matrix (NFRUP) and E-glass–matrix (EGMRUP) composites for thermal and dielectric properties was undertaken. The UP resin was used as a matrix for both of them. The thermal study (DSC) carried out on these samples showed a variation in Tg as fibers (natural or mineral) were added in the matrix, and this revealed the interaction of the fibers with the matrix. The dielectric response of these composites showed the presence of two common dielectric relaxations, which were attributed to the a relaxation of the polymer and to ionic conduction, which occurred above the glass transition and at low frequencies, respectively. The dielectric analysis revealed that interfacial polarization could not be analyzed by the Argand representation in the EGMRUP com￾posite, as it was absent, whereas in the case of the NFRUP com￾posite, the analysis of the MWS polarization exhibited a consis￾tency of this polarization with the Havriliak–Negami model. The tensile properties of these composites evidenced a slight enhancement in the fiber–matrix adhesion in favor of the NFRUP composite. As a parameter closely related to the static stress transfer at the interface, the Young’s modulus showed a slight enhancement in the NFRUP composite compared with that in the EGMRUP composite. Moreover, this comparative ex￾perimental study demonstrated that natural fibers enhanced the thermal insulation in the NFRUP composite according to the Table III. Parameters Evaluated by Data Fitting According to the Havriliak–Negami Equation for the NFRUP and EGMRUP Composites Composite material T (
C) Relaxation a b MS M1 NFRUP 120 Conduction 0.991 0.947 0.003 0.26 MWS 0.92 0.892 0.199 0.315 130 Conduction 0.9915 0.90 0.002 0.295 MWS 0.901 0.88 0.185 0.3191 140 Conduction 0.995 0.93 0.002 0.298 MWS 0.999 0.92 0.21 0.316 150 Conduction 0.999 0.904 0.0033 0.301 MWS 0.99 0.863 0.153 0.3182 EGMRUP 120 Conduction 0.9957 0.889 0.0052 0.31 130 Conduction 0.995 0.83 0.005 0.32 140 Conduction 0.999 0.819 0.00399 0.3269 496 J. APPL. POLYM. SCI. 2013, DOI: 10.1002/APP.38499 WILEYONLINELIBRARY.COM/APP ARTICLE