The discussion of the results is focused on the control and improvement of the mechanical and dielectric properties of SEBS by the incorporation of G and by grafting with MA. However, in order to better explain the structure–property relation regarding the mechanical and dielectric properties, as well as the correlation between these properties, we start this section with the presentation of the results, giving first the information on the structure of SEBS, SEBS-MA, and their composites.
3.3. FTIR Spectroscopy
FTIR spectra of the SEBS and SEBS-MA composites are shown in
Figure 4a,b. SEBS has the main peaks at 3083/3061/3026 cm
−1 (triple bands—C-H aromatic stretching), 2918/2848 cm
−1 (C-H aliphatic stretching), 1603/1493/1454 cm
−1 (C=C aromatic stretching), 1379 cm
−1 (CH
3 bending [
23]), and 756/698/540 cm
−1 (C−H out-of-plane bending), similar to other observations [
24,
25]. Moreover, new peaks appear at 1267 and 1728 cm
−1, with a shoulder at 1720 cm
−1 and a hump at 1656 cm
−1, typical for C-O and C=O group stretching [
23]. Similarly, a broad absorption rising between 3100 and 3500 cm
−1 due to bonded OH stretching was detected [
23]. The presence of carbonyl/carboxyl and hydroxyl groups on the SEBS surface suggests some degradation processes that might have occurred during the melt processing steps (melt compounding and compression molding), which take place at high temperatures (175–185 °C) or during synthesis or prior processing of the original material. All these groups, detected by ATR FTIR on the surface of SEBS, significantly influence dielectric behavior, as discussed in the next section.
Interestingly, the band at 1728–1720 cm
−1 changes the shape in the case of composites by broadening and by the evidence of an obvious shoulder at about 1743 cm
−1, characteristic of the ester bond (
Figure 4c, marked with a red circle). This shift from a lower wavenumber to a higher one in the range 1720–1743 cm
−1 shows the transformation of aldehyde or acid groups in ester groups. This is probably due to the reaction of -CHO or -COOH groups from SEBS with some OH groups from the surface of G. In a similar manner, the decrease in the intensity of the peak at 1267 cm
−1 in composites compared to the matrix (
Figure 4c, marked with a red circle) supports the involvement of C-O and C=O groups from SEBS in reactions with hydroxyl groups on the G surface [
26].
The FTIR spectrum of SEBS-MA shows the bands characteristic to aliphatic and aromatic C-H bonds and aromatic C=C, similar to SEBS. In SEBS-MA, maleic anhydride can be in a ring form or in a hydrolyzed form, showing dicarboxylic acid groups; the ring form shows the peaks characteristic to the vibrational coupling of the two C=O groups at 1856, 1780, and 1720 cm
−1 [
27,
28] and maleic acid shows signals at 1707 cm
−1, characteristic to the intramolecular H-bonded C=O stretch, at 1733 cm
−1, characteristic to C=O stretch, and at 1262 cm
−1, due to C–O–C stretching vibrations [
29].
One can observe from
Figure 4d that no important peak appears between 1870 and 1750 cm
−1, and only a double peak is observed at 1726/1717 cm
−1. A medium-intensity peak is observed at 1265 cm
−1. Therefore, it can be concluded that the MA ring in SEBS-MA was most frequently in the open state, with carboxylic groups. Interestingly, the band at 1726–1717 cm
−1 changed significantly in both shape and intensity in the case of composites, regardless of the G concentration: it became broader, and its intensity was smaller. This means that carbonyl or carboxyl groups were consumed, and probably an esterification reaction occurred between the (hydrolyzed) maleic anhydride groups (-CHO or -COOH) from SEBS-MA and the hydroxyl groups on the surface of G [
26,
30,
31]. As expected, the peak at 1265 cm
−1 showed the same behavior.
3.5. Dynamic Mechanical Analysis
The storage modulus (G’) and the mechanical tan δ variations with temperature are shown in
Figure 7. A double broad peak (~85 °C; ~110 °C) was observed in the tan δ curve for the SEBS composites (
Figure 7a) with a higher amount of G, and only a weak peak at about 85 °C for SEBS and SEBS/G5. A very weak deviation was observed close to 110 °C for SEBS/G5. Considering the DSC results and previous reports [
33], the double peak could be ascribed to the glass transition of the PS blocks, the lower temperature shoulder to the “unrestricted” PS blocks, and the higher temperature peak to the PS chains close to the G surface.
It is worth remarking on the important increase in storage modulus with the increase in G content in SEBS or SEBS-MA composites. The storage modulus of SEBS-MA/G20 was higher by 125% compared to the SEBS-MA matrix and that of SEBS/G20, with 97% vs. the SEBS matrix. This shows both the reinforcing effect of graphite and the compatibilizing effect of MA, which increased the strength at the interface and reduced intermolecular slippage [
34], leading to a higher increase in storage modulus.
DMA results for 1 Hz and increasing temperature reveal the increase in mechanical stiffness with G content for both SEBS/G and SEBS-MA/G composites. This increase is important in the glassy region of PS blocks, especially between 30 and 80 °C, showing that the G presence leads to the stiffening of the polymeric chains and to the reinforcing of the SEBS structure. Even though the reinforcing mechanism is not completely understood, the immobilization of polymer chains around particles and the creation of flexible nets of polymer chains between particles are the most agreed-upon mechanisms [
33]. Hence, the modification of the molecular dynamics close to the polymer–particle interface is considered to be the main cause of the increase in the storage modulus [
35]. Thus, in the case of the SEBS/G composite, we suppose that the stiffening was mainly determined by the fixation of PS blocks on G particles by π-π interactions between the benzene quadrupoles of graphite/graphene flakes and those of PS blocks. Kocman et al. showed that the quadrupolar electric field that the carbon atoms exhibit in aromatic compounds due to electron distribution is high enough to contribute significantly to intermolecular interaction, either in the case of small flat structures, such as graphene flakes with sizes smaller than 100 Å, or when considerably large graphene flakes of sizes of some μm or more are corrugated or bent [
36]. When the graphene sheets are flat, the quadrupolar field near the surface vanishes with increasing sheet size. In our case, the SEBS/G and SEBS-MA/G composites contain graphene flakes of some tens of μm, which are bent or corrugated, as shown by SEM analysis in our previous paper [
15]. Thus, high quadrupolar intermolecular interactions are expected between graphene and graphite bends and folds and the rigid PS blocks of SEBS, with a strong impact on the dielectric behavior of the SEBS/G and SEBS-MA/G composites, as discussed in the next section. Most of these interactions are thought to be attractive since the most favorable π stacking geometries are the parallel, edge-to-face, or T-shaped displacements [
37].
The storage modulus was higher for SEBS-MA than for SEBS, which shows that the presence of MA grafts enhances the polymer chain immobilization. Moreover, the storage modulus exhibited a higher increase in the function of G content for SEBS-MA/G composites than for SEBS/G composites. This can be due to the interactions between the G and MA groups of SEBS-MA through hydrogen bonds between MA and surface carbonyl/carboxyl groups on G, which, besides the quadripolar interactions between G and SEBS, influence the molecular dynamics at the filler–polymer interface and, consequently, the reinforcing strength.
Moreover, the storage modulus variation with temperature is different for SEBS-MA and its composites compared to that for SEBS and its composites. While the storage modulus is quite constant for SEBS and SEBS/G composites up to 70 °C, it continuously decreases with temperature for SEBS-MA and SEBS-MA/G composites, suggesting a lower onset and/or a higher range of the phase transition of styrene blocks for the latter. This decrease in storage modulus at temperatures lower than 70 °C for SEBS-MA and SEBS-MA/G composites is probably due to their lower average molecular weight (Mn) and higher melt flow index (MFI) compared to the ones for SEBS and SEBS/G composites. Indeed, the MFI measured in the same conditions is 5.0 g/10 min for SEBS and 17.2 g/10 min for SEBS-MA, while Mn is 79,100 for SEBS and 58,000 for SEBS-MA, according to the producer data.
Moreover, from the DSC results in
Figure 3, it can be seen that the
Tg of the PEB regions was not affected by the G content; therefore, the G presence did not influence the molecular dynamics in PEB blocks. This confirms that G particles are connected with SEBS mainly through π-π interactions between G and PS blocks.
3.7. Dielectric Spectroscopy Analysis
The dielectric spectra of real and imaginary parts of the complex relative permittivity (εr’ and εr’’) and the dielectric loss tangent (tan δ) are shown and analyzed in this section.
This discussion starts with the analysis of the results in
Figure 10 and
Figure 11 on the frequency variation of ε
r’ at different temperatures between 27 and 77 °C during the heating and cooling procedures applied to the tested samples.
The real permittivity ε
r’ has quite a small variation with frequency in the studied range for both SEBS/G and SEBS-MA/G composites as well as for the neat polymers. This shows that the dielectric activity is not highly affected by the electric field frequency in this range, as can be seen in
Figure 10. This is because, in this frequency range, the polarization is due, on one hand, to the segmental movement from the completely amorphous PEB blocks with highly mobile chains at the tested temperatures that are higher than both T
gPEB and T
mPEB and, on the other hand, to the orientation of the lateral groups, most of them resulting from oxidation (OH, aldehydes, carboxylic acids or esters), which is present throughout the entire frequency range. The relaxation of the lateral groups is expected to occur only at frequencies over 10
6 Hz, which is outside the frequency range studied here. The ε
r’ values show a small decrease with temperature (
Figure 10) because of thermal agitation, which opposes the dipole orientation.
An increase in the ε
r’ values with G concentration is noticed in both SEBS/G composites (
Figure 10a) and SEBS-MA/G composites (
Figure 10b) over the entire range of frequencies. The increase in the ε
r’ values with G content is seen at all the tested temperatures, no matter what the sense of reaching that temperature was, by heating (
Figure 10) or cooling (
Figure 11) the samples.
Moreover, the increase in ε
r’ with G concentration follows an exponential law for both SEBS/G and SEBS-MA/G composites, as can be seen in the plots of ε
r’ vs. G level at 1 Hz (
Figure 11). This increase in ε
r’ values with filler content for all frequencies is in line with a similar behavior previously remarked on for these composites but only at room temperature [
15]. This exponential increase in ε
r’ with G content has almost the same rate at 27 °C as at 77 °C for either SEBS or SEBS-MA composites, showing that the same relaxation mechanisms are present in these composites no matter the temperature in this range. A possible explanation of the increase in ε
r’ with G content can be that the G presence inside SEBS and SEBS-MA polymers leads to the formation in PEB blocks of new side groups able to determine easier and more numerous β-relaxations than in neat polymers. These new lateral groups can be esters resulting in composites from the transformation of several carboxylic acids existing in the unfilled polymers, as noticed from the FTIR result analysis. The presence of esters in composites instead of the acids from the neat polymer (either SEBS or SEBS-MA) means that strong intermolecular forces due to hydrogen bonds, present in the case of acids, are replaced by weaker dipole–dipole interactions in the case of esters [
39]. Thus, the local electric field may orient the lateral ester dipoles in composites more easily than the acid dipoles in neat polymers, explaining the increase in ε
r’ with G in the case of composites. Moreover, even the local electric field acting in composites can be higher than in neat polymers due to the high quadrupolar intermolecular interactions between graphene and graphite bends and folds and the rigid PS blocks of SEBS, as discussed in the previous section. Furthermore, the increase in ε
r’ in composites is also the result of a higher dipole moment of esters compared with the carboxylic acids from the polymer without G. Indeed, -COOCH3 has a higher dipole moment than –COOH in both aliphatic compounds (6 × 10
−30 Cm vs. 5.7 × 10
−30 Cm) and aromatic compounds (6 × 10
−30 Cm vs. 5.3 × 10
−30 Cm) [
40].
The exponential increase in ε
r’ values with G level can also be due to the cleavage of G flakes due to the shearing forces at the SEBS-G or SEBS/MA-G interface [
15]. The surface of these G fragments, resulting from cleavage, interacts with oxygen, leading to new groups, especially esters, and, hence, new lateral dipoles that contribute to the higher dielectric activity in composites. The ε
r’ variation with G in
Figure 9 is slightly more rapid in the case of SEBS-MA composites compared to SEBS ones, suggesting a slightly higher number of lateral dipoles due to side groups in the SEBS-MA composites, resulting either from the opening of MA rings or from a more intense fragmentation of G flakes in the case of SEBS-MA composites [
15]. This small increase in real permittivity in SEBS-MA composites compared to SEBS composites shows that the contribution of MA grafts to the new lateral dipoles is only marginal with respect to that of G flakes.
The exponential increase in εr’ with graphite content is very important for the technical applications of these composites, emphasizing the possibility of controlling the dielectric behavior and precisely tuning the permittivity and, hence, the electrical energy density by graphite concentration in composites.
This result is a small but important step towards tailored dielectric elastomers composites for sensing, actuation, or energy-harvesting applications. Certainly, the control of the permittivity values with the filler content should be continuously improved so as to take place at a significantly higher rate and up to much higher values of εr’.
The polymeric chains are more stiff in composites due to the G presence, especially in SEBS-MA/G composites, as seen from DMA analysis, so the movements of quasi-mobile charges and/or dipoles are less affected by the temperature variation. The results from
Figure 12 and
Figure 13 confirm this, showing that the temperature influence on the dielectric loss tangent (tan δ) variation of the SEBS-MA/G10 composite is less important than in the case of the neat polymer or in the case of the SEBS-G10 composite. This improved dielectric stability of tan δ with respect to the temperature variation increases with the G content, as can be seen from the results in
Figure 14. Indeed, the tan δ spectra for the SEBS-MA/G20 composite at all the studied temperatures (
Figure 14b) are closer to each other than in the case of the SEBS-MA/G10 composite (
Figure 13b). The results in
Figure 12 and
Figure 13 show a very small difference between the results in the heating procedure with respect to those from the cooling procedure, and this is due to the thermal inertia of the materials.
The more stable behavior of the dielectric losses with temperature, seen in the composites, is also supported by the XPS results, which show that the number of sp2 carbon atoms increases considerably with G in composites; they practically double at 20% G concentration compared to neat polymers for both SEBS/G composites (32.1 compared to 17) and SEBS-MA/G composites (29.9 compared to 16.6). On the other hand, the number of sp3 carbon atoms decreases significantly with G content with respect to the unfilled polymer for both SEBS/G20 (64.9 compared to 82.1) and SEBS-MA/G20 (69 compared to 81.9). These results suggest that the number of carbon single bonds decreases, whereas the number of carbon double bonds increases, in composites with respect to the unfilled polymer, leading to an increased number of π bonds and, hence, to strong π-π interactions between PS and G, which determines the high stability of dielectric losses with temperature variation.
The high stability of the dielectric loss tangent at temperature variations in the range between 27 and 77 °C, which increases the function of the G content, especially in SEBS-MA/G composites, shows, once again, how the dielectric properties can be controlled by using G as filler at different concentrations.
Besides the above discussion on the stability of dielectric losses with temperature variation, seen in composites with high G concentrations, the low level of dielectric losses for both SEBS/G and SEBS-MA/G composites as well as for the unfilled SEBS and SEBS-MA polymers should be noted. The tan δ values are in the range of 10−4–10−2, with a level of 10−3 for all the tested composites up to hundreds of kHz, which are the usual frequencies for energy-harvesting systems.
To analyze quantitatively the processes revealed by the dielectric spectra obtained for the SEBS and SEBS/MA composites, one should first identify the dielectric relaxations present in the spectra. As is well known, two dielectric relaxations (labeled α and β) can usually be found in the dielectric spectra of polymers in the frequency range of 10−2–106 Hz above room temperature. The α-relaxation is correlated with the main-chain movement, corresponding to a transition from the glassy state to the rubbery state, as the temperature rises above Tg, whereas the β-relaxation is related to the local motions, such as the rotation of side groups. Furthermore, as the dielectric materials tested in this study are not homogeneous, different interfaces being present either between the PEB and PS blocks in SEBS and SEBS/MA or between the G particles and copolymer matrices, another relaxation can be present in the dielectric spectrum, namely, the interfacial or Maxwell–Wagner–Sillars (MWS) relaxation, due to the charge trapping at these interfaces. Moreover, the free carriers present in copolymers and their composites are responsible for a conduction current that is usually emphasized by the increase in dielectric losses toward lower frequencies.
Thus, taking into account the above considerations, one can identify in the frequency variation of the dielectric loss tangent (tan δ), shown in
Figure 12,
Figure 13 and
Figure 14, two main peaks for both neat polymers SEBS and SEBS-MA as well as for their composites. One peak is located in the medium frequency (MF) range (10–10
2 Hz), and the other one is in the high frequency (HF) range, around 10
5–10
6 Hz. Besides these peaks, there is an increase in the values of tan δ at low frequencies, this being due to a combined effect of DC conduction and electrode polarization. It is interesting to note that this behavior at low frequencies is due to the translation movement of mobile charges, which diminishes significantly with the content of G in SEBS-MA/G composites, suggesting a reduction of the number and mobility of mobile charges in these composites.
The MF peak emphasizes an MWS interfacial polarization, also remarked on in other recent studies on the dielectric behavior of SEBS [
17,
41]. Ions (possibly oxygen) coming from impurities can accumulate at both the S-EB interface and the interface between G and different SEBS blocks. Supplementary charge accumulations can develop in SEBS-MA/G composites at the interface between G and PEB blocks, where there are hydrogen bonds through opened MA rings. Some air can enter together with the introduction of G powder in the melt polymer during the composite fabrication, thus explaining the oxygen molecules found inside composites by FTIR and XPS [
17,
41].
The HF peak seen in composites indicates a β-relaxation of oxygen-containing groups from the G surface, especially carboxylate esters produced by the transformation of the carboxylic acids from SEBS and SEBS-MA following G introduction, but also acids and aldehydes that are not transformed in esters. These dipoles can be responsible for the β-relaxation also seen in neat polymers, but here with a considerably higher number of acids and aldehydes than esters, which are expected to be only a few.
Once the dielectric activity in the tested materials was identified, we then continued with the modeling of the spectra. Since dielectric relaxations and the effect of conduction may commonly overlap in a dielectric spectrum, parametric functions are usually employed to separate them and facilitate the analysis of their temperature and frequency dependence. One of the most utilized functions to model a broad and asymmetric distribution of relaxation times is the Havriliak–Negami (HN) function; in contrast, a power-low function is usually used for a conductivity term. Considering all the above, we decided to analyze the non-Debye relaxations from our spectra and to fit the experimental data with the HN model [
16]. Thus, we used Equation (1), where the first term accounts for the contribution of the charge carriers on the molecular dynamics and the others are HN terms accounting for the two relaxations remarked on in the dielectric loss spectra obtained for our materials.
In Equation (1), σDC is DC conductivity, the exponent N is an indicator of the nature of the electrical conduction process of charge carriers, εr’(ω) and εr’’(ω) are the real and imaginary parts of the complex permittivity εr, ω = 2πf is the angular frequency, ε0 is the vacuum permittivity, k equals the number of relaxations of the dielectric response, Δεk is the relaxation strength, τHN is the HN relaxation time, and α and β are parameters that quantify the width and asymmetry of a given relaxation peak of the loss factor εr’’(ω).
An example of the use of Equation (1) to fit the experimental data is presented in
Figure 15, which shows the frequency variation of the imaginary permittivity ε
r’’ for the SEBS-MA/G10 composite at 57 °C.
The actual relaxation time τ
max was calculated as in Equation (2) [
17], and then the frequency f
max where the relaxation occurs was determined by
fmax = 1/(2πτ
max).
Arrhenius plots obtained by processing the dielectric spectra obtained during the heating procedure between 27 and 77 °C are presented in
Figure 16. These plots show the variation with temperature of MF and HF peak frequencies corresponding to MWS and β relaxations in SEBS/G and SEBS-MA/G composites.
The activation energy
wa (
Table 3) corresponding to MWS relaxation has very close values in SEBS and SEBS-MA neat polymers, showing that the MA presence does not significantly affect the number of mobile charges nor the charge dynamics near the S-EB interface.
As for the composites, the MWS activation energy increases with G content for both SEBS- and SEBS-MA-based composites, indicating reduced charge mobility due to the fixation of S blocks on G as well as a slowdown of the charge movement at the S–EB interface because of the electric field generated by the π-π quadrupolar interactions between the G and S rings. This field can also be the cause of a possible charge accumulation at the G-S interface.
The MWS activation energy is higher for SEBS-MA/G10 (1.05 eV) compared to SEBS/G10 (0.73 eV), which can be explained by the reduced mobility of the quasi-mobile charges due to the supplementary stiffening of the SEBS chains by hydrogen bonds between G and PEB through MA groups. It should be remarked on that the effect of MWS relaxation on the εr’ values is insignificant in both neat polymers and composites, showing that the local electric field, due to the charges accumulated on the interfaces, is considerably lower than the external field, due to the voltage applied to the electrodes.
The frequency of maximal loss (
fmax) corresponding to the HF peak is higher in SEBS/G and SEBS-MA/G composites than in the unfilled polymer at all tested temperatures, as seen in
Figure 16. Furthermore,
fmax is higher for SEBS-MA and its composites than in the case of SEBS and SEBS/G composites, showing that the β-relaxation of the side groups (carboxylic acids, esters, aldehydes) arises at higher frequencies, which means that the dipoles are able to follow faster electric field oscillations. The orientation of these dipoles is facilitated in the studied temperature range by an enhanced segmental movement of S blocks in SEBS-MA and SEBS-MA/G composites due to a lower molecular weight than in the case of SEBS and its composites. This segmental movement is also emphasized by DMA analysis, where an increase in S blocks flexibility is indicated by the decrease in storage modulus at temperatures lower than 70 °C for SEBS-MA and SEBS-MA/G composites.
However, even if the presence of MA grafts leads to more flexible S regions, determining the shifting of the HF peak towards higher frequencies, the orientation of the side dipoles requires more energy from the electric field in these materials compared to those without MA. Thus, the activation energy for the β-relaxation is higher in MA-grafted SEBS composites, e.g., 0.42 eV for SEBS-MA/G10 compared with 0.19 eV for SEBS/G10.
The analysis of the dielectric spectroscopy results shows that the temperature dependence of the relaxation frequency obeys the Arrhenius equation, i.e., the plot of log (
fmax) versus
T−1 gives a straight line (
Figure 16) for both the MWS relaxation (MF peak) and the β-relaxation (HF peak). This means that in the analyzed temperature range, none of the two ε
r’’ peaks found in the dielectric spectra correspond to molecular processes associated with the glass transition temperature
Tg as it is known that the temperature dependence of the relaxation frequency of the molecular process associated with
Tg does not conform to Arrhenius law, the plot log (
fmax) versus
T−1 being curved as if the activation energy were increasing towards lower temperatures [
40]. Indeed, none of the SEBS blocks have phase transitions in the studied temperature range, which is much higher than the
Tg of the PEB blocks (≈−57 °C, as shown by our DSC results) but lower than the
Tg of the PS blocks (90–100 °C, as reported in other studies [
17]). Thus, in the temperature range where we made the dielectric tests, the PEB blocks were very flexible because even the melting temperature
TmPEB was exceeded, which implies a strong segmental movement of PEB chains over the whole frequency range and, hence, the absence of any α-relaxation peak in our dielectric spectra.
The results presented in this paper show that the cumulative effect of grafted MA and G filler on the increase in mechanical stiffness, the exponential increase in real permittivity with filler content, and the increase in the stability of the dielectric loss tangent at the temperature variation of SEBS-MA/G composites suggests these composites for application as actuators or electrical-energy-harvesting devices.