RTICLE Applied Polymer (a) ◆40°C ℃℃℃ 100000 120c 一-130c 10000 100000 1000000 Frequency(Hz) 0 是140°C 1000001000000 F Figure 7. Frequency dependence of M and M for the(a)NFRUP and(b) EGMRUP composites appearance of a relaxation peak associated with the interfacial interpret bulk relaxation properties is that the In olarization for the NFRUP composite. The same result was large values of the real part of the permittivity y and the lo observed by Okrassa et al., in which the a relaxation of the tor at low frequencies are minimized. In this way, common dif- yroxypropyl cellulose related to its glass transition was not visi- ficulties of the electrode nature and contact, space-charge-injo ble in the dielectric spectra. This behavior was connected with tion phenomena, and absorbed impurity conduction effects, he presence of strong hydrogen bonds between cellulose chains. which appear to hide the relaxation in the permittivity repre- As already shown, the dc conductivity can hide the a relaxation sentation, can be solved or even ignored.59 in dielectric spectra, so to minimize this effect, the formalism of With this M formalism adopted, Figure 7(a, b) shows the simi- the electric modulus(M) or inverse &* was introduced. This lar behavior of M as a function of frequency for the NFRUP M has recently been adapted for the investigation of dielectric and EGMRUP composites when they were heated over the tem- processes occurring in composite polymeric systems and those perature range from 40 to 150%C. The inset of each figure proposed for the description of systems with ionic conductiv- exhibits the isothermal variation of the M frequency depend ity. M is defined by Eq (4): ence. The value of M was nearly zero at low frequencies and high temperatures; this indicated that the electrode polarization M*== E+e222+e2+M+M"(4) gave a negligibly low contribution to M and could be g ignored.0,b After this initial low value, M increased steeply in the range of 10. A series of two distinct relaxations could be where M and M are the real and imaginary parts of the considered for each composite. The first one was related to the electric modulus, respectively. An advantage of using M to a relaxation associated with the glass-rubbery transition of the 494 J. APPL. POLYM.Sc.2013,D0:10.1002PP38499 WILEYONLINELIBRARY. COM/APP EWILEY NONLINE LIBRARYappearance of a relaxation peak associated with the interfacial polarization for the NFRUP composite. The same result was observed by Okrassa et al.,55 in which the a relaxation of the hyroxypropyl cellulose related to its glass transition was not visi￾ble in the dielectric spectra. This behavior was connected with the presence of strong hydrogen bonds between cellulose chains. As already shown, the dc conductivity can hide the a relaxation in dielectric spectra, so to minimize this effect, the formalism of the electric modulus (M*) or inverse e* was introduced. This M* has recently been adapted for the investigation of dielectric processes occurring in composite polymeric systems and those proposed for the description of systems with ionic conductiv￾ity.12 M* is defined by Eq. (4):58 M ¼ 1 e ¼ 1 e0 je00 ¼ e0 e02 þ e002 þ j e00 e02 þ e002 þ M0 þ jM00 (4) where M0 and M00 are the real and imaginary parts of the electric modulus, respectively. An advantage of using M* to interpret bulk relaxation properties is that the variation in the large values of the real part of the permittivity and the loss fac￾tor at low frequencies are minimized. In this way, common dif￾ficulties of the electrode nature and contact, space-charge-injec￾tion phenomena, and absorbed impurity conduction effects, which appear to hide the relaxation in the permittivity repre￾sentation, can be solved or even ignored.59 With this M* formalism adopted, Figure 7(a,b) shows the simi￾lar behavior of M00 as a function of frequency for the NFRUP and EGMRUP composites when they were heated over the tem￾perature range from 40 to 150
C. The inset of each figure exhibits the isothermal variation of the M0 frequency depend￾ence. The value of M0 was nearly zero at low frequencies and high temperatures; this indicated that the electrode polarization gave a negligibly low contribution to M0 and could be ignored.60,61 After this initial low value, M0 increased steeply in the range of 10. A series of two distinct relaxations could be considered for each composite. The first one was related to the a relaxation associated with the glass–rubbery transition of the Figure 7. Frequency dependence of M0 and M00 for the (a) NFRUP and (b) EGMRUP composites. 494 J. APPL. POLYM. SCI. 2013, DOI: 10.1002/APP.38499 WILEYONLINELIBRARY.COM/APP ARTICLE