Dielectric Relaxation Spectroscopy in Synthetic Rubber Polymers: NitrileButadieneRubberandEthylenePropyleneDieneMonomer

*e dielectric permittivity of synthetic rubber polymers, nitrile butadiene rubber (NBR) and ethylene propylene diene monomer (EPDM), with both frequency and temperature variations, was thoroughly investigated by dielectric relaxation spectroscopy (DRS).*e spectrum versus frequency of DRS was analyzed with the semiempirical Havriliak–Negami formula and conductivity contribution by employing the newly developed “dispersion analyzer” analysis program. *e main dielectric relaxations called the αand β-processes, associated with the cooperative motion of chains in polymers, were discovered in the low-temperature region. In the high-temperature region, we found Maxwell–Wagner–Sillars (MWS) relaxation associated with polymer interfacing and normal-mode (α’) relaxation responsible for end-to-end dipole vector motion. *e activation energies of schematic molecular chains responsible for the relaxation processes were obtainedwith the information about itsmotional mode.*e glass transition temperature and dipolemoment for the side group were also determined and compared with those from previous studies. In the EPDM specimen, the peaks of αand β-relaxation merged at high temperature and were separated with decreasing temperature.*e first observations of both merging and splitting were consistent with the results on the temperature dependency of the relaxation strength. Both contour mapping and three-dimensional plots for the two rubbers provide visual information for the distribution and mapping of relaxation.


Introduction
Many prior studies have been conducted by using various microscopic techniques to investigate the molecular dynamics or chain motions of synthetic rubber polymers [1][2][3][4][5]. One of the most appropriate tools for characterizing the microscopic behavior of polymer systems is dielectric relaxation spectroscopy (DRS) [6][7][8]. DRS is very sensitive to polymer chain motion attributed to primary and secondary relaxation processes, called α-, β-, and c-relaxation, respectively. Furthermore, the Maxwell-Wagner-Sillars (MWS) relaxation phenomena, which are the signals of the interfacial polarization process of heterogeneous polymers, are only detected through DRS [9][10][11].
us, by employing DRS, we have intensively investigated the molecular dynamics and entire relaxation processes embedded in two kinds of rubber polymers: nitrile butadiene rubber (NBR) and ethylene propylene diene monomer (EPDM), which are used as sealing materials for the fuel container in vehicles and other rubber applications.
By measuring the dielectric permittivity with variations in temperature and frequency, we can obtain the following four important physical properties of a polymer: (i) e origin of the relaxation phenomenon embedded in the polymer can be determined by analyzing the dielectric spectrum versus frequency and temperature [12,13] (ii) e Arrhenius temperature dependency for the secondary relaxation rate gives the activation energy for the motion of the corresponding molecular chain [14][15][16] (iii) e glass transition temperature can be obtained by fitting the Vogel-Fulcher-Tammann-Hesse (VFTH) formula to the primary relaxation rate [14][15][16] (iv) e effective dipole moment for the side group can be obtained by the theories of Onsager and Kirkwood [14][15][16] ere are a few previous studies on relaxation in synthetic rubber polymers studied here. For instance, the study on the NBR rubber conducted by Psarras et al. [6] incorrectly designated the origin of the specific relaxation spectrum. Similarly, although Xu et al. [8] and Chailan et al. [17] conducted DRS studies on EPDM and fluoroelastomer (FKM) rubbers, their results did not include the relaxation origin, calculation of activation energy, and glass to polymer transition temperatures. In addition, previous works for NBR and EPDM were not undertaken to determine the electric dipole moment of the corresponding molecular structure in polymer chains [6][7][8][17][18][19][20].
us, the four main physical properties of DRS in these rubbers were not entirely covered and intensively investigated by other researchers.
We designated the effective dipole moment for the common molecular structure. However, due to the effect of the interaction between the dipole and other polar chains in polymer chains, there is a very complicated configuration to calculate the dipole moments for the polymer. Debye tried to calculate the dipole moment using the Boltzman distribution and the relationship between polarizability and permittivity [14][15][16]. Onsager and Kirkwood modified the Debye theory.
us, we can commonly obtain a dipole moment for polymers from dielectric measurements [14,16] with the application of modified theories.
In a polymeric rubber system, the measured spectra exhibit an obvious distribution of relaxation time and broadened, superimposed, individual dielectric relaxation spectra. Furthermore, because the relaxation processes that occur on a very long time scale are merged in some temperature regions, deconvolution for complete characterization is difficult to achieve. To analyze the measured data, we developed the analysis program "dispersion analyzer." With the help of this program, we could deconvolute the superimposed dielectric spectra, finding the origin of the entire relaxation phenomenon for a synthetic polymer for the first time. e molecular chains responsible for the relaxation processes were also obtained with information about its motional mode. e activation energy, glass transition temperature, and electric dipole moment for the corresponding molecular chain were determined. Crossover peaks for α-and β-relaxation in the two polymers were observed. e first observation was consistent with the results on the temperature dependency of the relaxation strength. For visualization, the permittivity data for various temperatures and frequencies are shown as three-dimensional (3D) and contour plots for the three polymers. us, we could distinguish the distribution and mapping for relaxation processes.

Materials and Methods
2.1. Rubber. All rubbers were provided by "KRAIBYRG Rubber" a domestic Korean company. NBR ( Figure 1) is a butadiene-based synthetic rubber made by copolymerizing various combinations of butadiene (CH 2 CH�CHCH 2 ) and acrylonitrile (CH 2 CHCN). e compositions of the NBR rubber are represented in Table 1.
To visualize the carbon black filler, the SEM images of the filler-filled NBR rubber are shown in Figure 2. EPDM ( Figure 3) is an ethylene-based synthetic rubber made by copolymerizing various combinations of ethylene (CH 2 CH 2 ), propylene (CH 2 CHCH 3 ), and ENB monomer. e chemical composition is shown in Table 2. To visualize the filling agent, the SEM (scanning electron microscope) images of the carbon black filler-filled NBR and EPDM rubbers are shown in Figure 2. e red circles in Figure 2 indicate the aggregate form of the carbon black fillers.

Dielectric Relaxation Spectroscopy.
e measurements of dielectric permittivity were carried out using a VSP-300 (Bio Logics) [21] instrument with a temperature controller. Before starting the measurement, in order to eliminate the effects of the moisture and outgassing, the heat treatment process for all specimens must be done. e heat treatment of all specimens was performed at 85°C for 24 hours, which condition was recommended by the CSA Group [22]. e frequency range was set from 0.01 Hz to 3 MHz for each specific temperature. By applying 1000 mV AC voltage to the specimen, the current was measured, and then, the impedance was obtained. e measurements were performed automatically by a measurement program in the temperature range from −40°C to 100°C. e dielectric measurement was performed with the cylinder-shaped specimens which has a diameter of 50 mm and thickness of 2.4 mm. e weight for NBR and EPDM is 5.88 g and 5.60 g, respectively.
Both the real and imaginary permittivity from the measurements using the VSP-300 frequency response analyzer were calculated from the following relations: where impedance Z � Z ′ − jZ ″ . Z ′ and Z ″ are the real and imaginary impedances, respectively. e schematic of the dielectric spectroscopy system is shown in Figure 4.

Differential Scanning
Calorimetry. e differential scanning calorimetry (DSC) measurements of the dynamic glass transition temperature were carried out using Q-600 (TA Instruments) [23]. e measurements were performed with a heating rate of 1°C/min in the temperature range from −80°C to 80°C. e DSC measurement was conducted with the small granulated-type rubbers which weighs about 8 mg to 10 mg.

Formula for Analyzing Complex Dielectric Permittivity and Relaxation Processes
To understand the dynamics of the relaxation process in polymers, the experimental complex dielectric permittivity ε * (ω) data could be fitted to the Havriliak-Negami (HN) function. e HN functional formalism can be phenomenologically described as a combination of the conductivity term with the HN functional form [24][25][26][27] as follows: where the first term σ dc /ε 0 ω s accounts for the DC conductivity of the samples and electrode polarization effect; its contribution is dominant at the highest temperature and the lowest frequency considered in the study; σ dc is the DC conductivity; ε 0 is the vacuum permittivity of 8.854 × 10 −12 F/m; s is the included ionic charge carrier which causes electrode or Maxwell-Wagner Polarization effects; in practice, often ε ″ ∼ ω −s with s < 1; the summation symbol in the last term indicates the occurrence of more than one relaxation process; τ HNk is the characteristic average relaxation time of process k; the exponents a k and b k ((0 ≤ a k ≤ 1, b k ≤ 1)are the HN-shape parameters describing the distribution of the relaxation times; the values of α k and β k are related to the linewidth and asymmetry relaxation loss peak, respectively; the dielectric relaxation strength ε s -ε ∞ is represented as Δε k .
To deconvolute the complex dielectric spectra, we employed the "dispersion analyzer" which was developed by us.
A secondary relaxation due to isolated molecules or impurities may also be present, showing comparably higher relaxation rates [23]. e activation energies of secondary relaxations for α'-, β-, and c-relaxations were determined by assuming the Arrhenius temperature dependence: where f p,β is the position of the center peak for the secondary relaxation rate, f ∞,β is the pre-exponential factor, and E a is the activation energy. e activation energy E a , related to the slope of log f p,β versus 1/T, depends on both the internal rotation barriers and the environment of a moving unit. e position (f pα ) of the peak center in the relaxation rate for the α-process allows the non-Arrhenius temperature dependence described by the VFTH temperature dependence model: where f p∞ and A are constants and T 0 is the so-called ideal glass transition or the Vogel temperature [14][15][16].

NBR.
e 3D frequency and temperature dependence for imaginary parts of permittivity in NBR are shown in Figure 5. e entire five relaxation values, called conductivity, α', α, β, and c, by simulation could be assigned by employing the "dispersion analyzer." e arrows in Figure 5 indicate the evolution of the relaxation peak versus temperature variation.
After deconvolution, the simulation results of the relaxation processes by the dispersion analyzer for five   representative temperatures (−40°C, −25°C, 20°C, 50°C, and 100°C) in the frequency domain are shown in Figure 6. Also, the fitting parameters of each relaxation process are summarized in Table 3. e α'-and α-relaxation spectra were well fitted by HN of equation (2). e β-and c-relaxation spectra were fitted by the Cole-Cole equation when β � 1 in the HN function because the secondary relaxation has a symmetrical shape [15]. e entire loss spectra for the relaxation process visibly shifted toward lower frequency with decreasing temperature. e α'-process is called normal mode relaxation, which is a signal of the fluctuational motion of the end-to-end dipole vector for the polymer chain and only observed in a Stockmayer type A polymer with a dipole moment vector parallel to the backbone chain [28][29][30][31]. Since the EPDM has a nonparallel dipole vector with the backbone chain, the α'-process was only detected in NBR, which has a parallel dipole vector with the backbone chain. Additionally, the α-relaxation is responsible for backbone chain motion [32][33][34][35], which was also detected in EPDM. e origins of the β-and c-relaxations are the orientational motion of the vinyl groups [-C 2 H 3 ] and cyano groups [-CN], respectively. e c-relaxation, of even smaller molecular parts (cyano groups [-CN]), can often be found at higher frequencies or temperatures below β-relaxation in isochronal scans [15,[36][37][38].
e origins of the corresponding dielectric relaxation for NBR are represented with a schematic molecular chain structure and its motional mode in Figure 7.
e position (f 0 ) of the center peak for the relaxation rate versus the reciprocal temperature for NBR is shown in Figure 8. As shown in the inset of Figure 8, Δε for α-relaxation increases with decreasing temperature. e entire relaxation peaks shifted to the lower frequency with decreasing temperature, which was the same as that seen in Figure 6. e temperature behavior of Δε is a general trend for α-relaxation. is temperature dependence of Δε can be predicted and explained by the dipole theory of Kremer and Schönhals [14]. e activation energy for the α'-, β-, and c-processes was calculated by the Arrhenius temperature dependence of equation (3) Figure 3: Molecular structure of EPDM.   e results are summarized in Table 4. e activation energies of the β-and c-relaxations, which are related to the orientational motion of the vinyl and cyano groups, respectively, were compared with prior results [39]. e E a values are consistent with each other within A-type measurement uncertainty. e glass transition temperature T g for DRS can be obtained from the temperature dependence of f 0 for an α-relaxation process measured at different frequencies. e T g at DRS is defined as the temperature at which f 0 of the α-relaxation process reaches 1.6 mHz, which was empirically defined in many other prior studies, by extrapolating the fitting of equation (4) in Figure 9(a) [15,[40][41][42][43]. T g for DRS was determined to be 242.1 K (±3.2), as shown in Figure 9(a), which was compared with the T g determined by DSC measurements (Figure 9(b)), where T g for DSC is usually defined as the half-height of the heat capacity increase ((1/2)ΔC p , also called the "temperature of half-unfreezing") [15]. T g (DSC) obtained was 242.2 K. Compared with two other experimental results, the T g values are consistent with each other. e dipole moment for each monomer in NBR can be calculated from the dielectric measurement data. We used the Onsager and Kirkwood dipole theory.
e Onsager theory was considered as the enhancement of the permanent dipole moment of a molecule μ by the polarization of the environment. e relaxation strength (Δε) in the Onsager formula is given by where μ is the permanent molecular electric dipole moment, k B is the Boltzmann constant, N and V are the number of dipoles in the system and system volume, respectively, and the F value corresponds to the error introduced by neglecting the reaction field. Kirkwood theory considered the effect of dipole-dipole interactions. e Kirkwood formula was given by where g KF is the Kirkwood factor considering the effect of dipole-dipole interactions. However, the calculation of g KF for an isolated polymeric chain is more complicated than that for molecules with low mass because carbon atoms with numbers from 10 4 to 10 6 are covalently bound for the isolated polymeric chain [14]. In our case, the two specimens have a complicated constitution and a large bond scale. us, Kirkwood theory through the calculation of g KF was not applied. Since our dipole moment calculation was performed on the polymeric system to which various monomers were combined, it was carried out with macroscopic calculation of the dipole chain corresponding to the respective dielectric relaxation process. e calculation results contain some effects on other dipole chains.
In case of the NBR rubber, because β-and c-peaks were observed at approximately −40°C, the calculations for the dipole moment were carried out at this temperature. By applying the epsilon parameters (Δε, ε s . and ε ∞ ) obtained through the fitting simulations to equation (2), the dipole moments were determined as shown in Table 5 μ Ons indicates the dipole moment calculated by equation (5). e calculation results were comparable with prior results [44]. e α-and α'-relaxations were mapped with 2D contours of imaginary permittivity for the relaxation rate versus reciprocal temperature. e mapping results are shown in Figure 10. e α'-relaxation has a symmetrical spectrum. However, the morphologies of the α-relaxation spectra have asymmetric shapes in the frequency domain, as indicated by arrows.

EPDM.
e 3D frequency and temperature dependence for imaginary parts of permittivity for EPDM are shown in Figure 11. e four relaxations called conductivity, MWS, α, and β were observed. e arrows in Figure 11 indicate the evolution of the relaxation peak versus temperature variation.
e simulation results for five representative temperatures (−40°C, −20°C, 20°C, 60°C, and 100°C) in the frequency domain are shown in Figure 12. After deconvolution, four relaxation spectra observed at five temperatures were defined as a corresponding relaxation process. e fitting parameters of each relaxation process are also summarized in Table 6. e α-relaxation spectrum was fitted by the HN equation. As the temperature increased, the two separate α-and β-peaks merged above 290 K. us, the loss spectrum above 290 K was fitted using the superposition of the Cole-Cole and HN equations. When the temperature decreases, the positions of the relaxation peaks of MWS and α shifted significantly toward the low frequency. However, the β-relaxation peak was less shifted visibly than the other relaxation spectra in the same polymer and in different rubber polymers. is behavior for the β-process was explained by the relationship between the molecular size and activation energy [15]. e α-relaxation originates from the rotation of the segmental chain, and the β-relaxation originates from the orientation of the methyl group [-CH 3 ], which is the side group in the propylene monomer [-C 3 H 6 ]. e MWS relaxation (also called the interfacial relaxation) originates from the polarized process in the interfacial surface of heterogeneous polymers [9,45,46]. However, the origin of the unknown peak observed at −40°C is still unclear. e origins of the corresponding dielectric relaxation for EPDM are represented with a schematic molecular chain structure and its motional mode in Figure 13.
e position (f 0 ) of the center peak for the relaxation rate plot versus the reciprocal temperature for EPDM is shown in Figure 14. e entire loss spectra for the relaxation process were visibly shifted toward lower frequencies with decreasing temperature. Δε for α-relaxation increased with decreasing temperature, whereas Δε for β-relaxation            decreased. e temperature behaviors of Δε are a general trend for α-and β-relaxations. As the temperature increased from 233 K, the two α-and β-peaks separated in the temperature range from 233 K to 290 K and merged from 290 K to 373 K, as shown in Figure 14. e two arrows in Figure 14 indicate the temperature at which the merge occurred. e intersection at 290 K in Δε and f 0 comes from the coexistence of two α-and β-processes with the same relaxation time. is is the first observation in polymers. Additionally, because the EPDM contains the flexibly attached dipolar side groups (methyl group [-CH 3 ]), the value of Δε of the β-relaxation was smaller than that of α-relaxation at low temperature [47,48]. e activation energies for β and MWS dielectric relaxation phenomena were also determined by the Arrhenius temperature dependence of equation (3). e activation energies of β and MWS were 17.7 and 113 kJ/mol, respectively. e fitting results are summarized in Table 7. e activation energy of β-relaxation related to the orientational motion of the methyl group was compared with prior results [39]. e relaxation rate of α-relaxation with the non-Arrhenius temperature dependence could be described by the VFTH temperature dependence model of equation (4). T g could also be obtained from the temperature dependence of the imaginary permittivity measured at different frequencies.

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e determined T g is shown in Figure 15. is was compared with T g (DSC) determined by the DSC measurement (Figure 15(b)). e T g (DRS) for the dielectric measurement result was found to be 227.3 K (±4.3). T g (DSC) determined by DSC measurements was found to be 221.0 K. e difference in T g between the two methods is relatively large, which may be related to the heating rate of the two methods. e reason for the inconsistency is under investigation.
Similar to NBR, the dipole moment for each monomer in EPDM could be calculated from the dielectric measurement data. e dipole moment calculated according to the theory of Onsager is shown in Table 8, together with that obtained from prior results [49]. e large difference between the two calculations may be due to the merging process at 298 K, which could cause an increase in the uncertainty in the deconvolution of the dielectric spectrum. And, in the reference data, Work et al. [49] has approached a traditional calculation of the electrical dipole moment of a microscopic system. However, our calculation was applied to macroscopically explain the local electric field effect in an isotropic dipolar system. us, the above critical reason may cause the difference between two calculations.
For legible visualization of the relaxation rate of every dielectric relaxation spectrum, the positions of the relaxation   peak versus reciprocal temperature are mapped in Figure 16. e 2D contour mapping of imaginary permittivity can be verified by the relaxation morphology. e width for the dielectric relaxation peak of β and MWS is symmetric on the basis of the top for the relaxation peak in the frequency domain. However, the width of the dielectric relaxation peak of α is asymmetric.

Conclusion
e dielectric spectra are mainly dependent on relaxation times for primary and secondary relaxation processes with conductivity contribution. In addition, they are broadened by a wider distribution or superimposed relaxation processes. us, it is not easy to determine the corresponding relaxation processes embedded in a polymer and elucidate the origin of the mechanism. To overcome this problem, we have developed a computer simulation program "dispersion analyzer" by employing a modified numerical method of nonlinear optimization.
With the help of the developed simulation program, we could perform a molecular dynamics study of synthetic rubber polymers. e authentication, i.e., the monomers in synthetic polymers, could be defined by the dielectric relaxation response. e results were plainly designated using a monomer schematic. We calculated the activation energy of each monomer for the synthetic polymer using the Arrhenius temperature dependence model, and the glass transition temperature was calculated by the VFTH temperature dependence model; these results were similar to the DSC measurement results. Finally, we defined the electronic-permanent dipole moment for each side group in the polymer, and there has been no prior DRS study about these polymers.
In future research, we will supplement the additional functions in the program simulation, such as the constraint  of the temperature dependency behavior of relaxations and the three-dimensional contour plot. e study of molecular dynamics for conductivity mechanisms at high temperatures and for secondary relaxation processes at low temperatures is in progress.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Disclosure
Young Il Moon's present address is Department of Electronic and Electrical Engineering, Pohang University of Science and Technology (POSTECH), 77 Cheongam-ro, Pohang 790-784, Republic of Korea.

Conflicts of Interest
e authors have no conflicts of interest to declare.