3.2. Sorption Characteristics
The sorption curves are shown in
Figure 2. Here, the moles of the solvent sorbed per 100 g of rubber,
Qt, is plotted against the square root of time. The sorption curves generally exhibit two distinct regions, the initial steep curve and the equilibrium region. Initially, due to the large concentration gradient, the solvent uptake will be high, and an equilibrium will be reached with time. The equilibrium solvent uptake in mol% of the solvent against the graphene content in various elastomer compounds is plotted and shown in
Figure 3. The uptake of benzene is the highest in all compounds, followed by toluene, with xylene being the least. This can be related to the increase in molecular weight from benzene to xylene. The effect of the partial replacement of carbon black with graphene (SDP 500) on the sorption behavior of the three different solvents is similar, as seen in
Figure 3. Compound
0 has a higher solvent uptake than compound
1 and compound
2 for all three solvents. When 1 phr of graphene is added, the solvent uptake decreases, and, on further increase in graphene to 2.5 phr, the solvent uptake shows a further decrease. This decrease can be attributed to the better dispersion of the fillers, graphene, and carbon black in the vulcanized systems. The graphene added to the system develops a tortuous path for the organic solvents to pass through and, thereby, the solvent uptake decreases. However, when the graphene content is increased to 5 phr, the trend reverses. This can be ascribed to filler–filler agglomeration and efficient reinforcement is not generated thereby in the elastomer compound. If there is no efficient reinforcement in the compound, easy passage of the solvents will be achieved and the equilibrium solvent uptake will be more or less equal to the compound, without any partial replacement. Thus, the optimum partial replacement is at and around 2 to 3 phr of graphene in place of carbon back, while keeping the total amount of carbon materials at 55 phr. Similar results were obtained for static mechanical properties, rolling resistance, and hardness.
The diffusivity (
D), sorption coefficient (
S), and permeability (
P) of the solvents through the samples were calculated using the following equations [
51,
52] and are summarized in
Table 1:
where:
h = thickness of the specimen
θ = slope of the initial linear portion of sorption curves
Q∞ = equilibrium solvent uptake
D = diffusivity
S = solubility.
The following equation is used to understand the sorption mechanism, and data obtained from the equilibrium sorption experiments were fitted to this equation:
where
Qt is the mol percentage uptake of solvent at time
t,
Q∞ is the mol percentage uptake at equilibrium,
k is a constant indicating the interaction between the sample and the solvent, and the value of n indicates the type or mechanism of diffusion. The values of n and k are obtained from the linear portion of the plots of
Qt against the square root of time (
Figure 2) through regression analysis; the corresponding plots are shown in
Figure 4 and the values are given in
Table 2. All the n values are between 0.5 and 1, which indicates that the diffusion of benzene, toluene, and xylene through the compounds follows a non-Fickian mode of transport [
39,
53]. Compared to benzene, the values of n for toluene and xylene are lower, which may be due to the increase in molecular weight of the solvents. However, there is not much difference in the values of n for toluene and xylene [
54].
To understand the mode of transport through these filled elastomer composites, four different mathematical models were utilized. These are the first-order kinetic equation, Higuchi model, Korsemayer–Peppas model, and Peppas–Sahlin model. The first-order kinetic equation is represented by the following equation:
where
Qt is the mol percentage uptake of solvent at time
t,
Q∞ is the mol percentage uptake at equilibrium, and k is the first-order rate constant.
The Higuchi model equation given below (11) is based on a hypothesis that: (i) the diffusion is a one-dimensional process, (ii) the size of the diffusing species is extremely smaller compared with the size of the matrix through which diffusion takes place, (iii) diffusivity is considered as a constant, and (iv) the swelling of the matrix and the diffusion are also considered as constants [
55].
Here,
kh is the Higuchi dissolution constant. The Higuchi model equation was applied to the linear portion of the sorption curves given in
Figure 2, while representative curves for compound
2 in benzene, toluene, and xylene are shown in
Figure 5, and the corresponding values for the kinetic constants and the correlation factor are given in
Table 3. The major factors affecting the sorption are the molecular weight of the solvents and swelling with the dissolution of the polymer matrix. Fickian diffusion is observed when the permeate mobility is overtaken by the relaxation rate. From
Table 3, the
Kh value, which is the Higuchi dissolution constant for compound
0, is 0.07265 for benzene, 0.07684 for toluene, and 0.06174 for xylene, respectively. The
Kh values increased for compound
1 and compound
2 for all three solvents and they decreased for compound
3, which indicates the good synergetic dispersion of graphene and carbon black in the rubber matrix. Similar results are also reported for other systems [
56,
57]. Moreover, the mechanical properties of the composites also showed similar behavior.
The first-order kinetic equation in its exponential form:
displays the relationship between t and the ratio
Qt/
Q∞ as asymptotic. As t increases, the ratio
Qt/
Q∞ approaches zero, whereas the experimental
Qt/
Q∞ increases with t initially and approaches saturation. The Higuchi model and the first-order kinetic equation have another common drawback, that of having just one constant k. As a result, there is a shortcoming in finding the best k that restores the ratio
Qt/
Q∞ in agreement with the experimental
Qt/
Q∞. Owing to this drawback, only the initial straight-line region in the time values is chosen for plotting.
This drawback is not found in the Korsemeyer–Peppas model and the Sahlin–Peppas model equations, as the former has two constants (k and m) and the latter has 3 constants (k1, k2, and m). As a result, the entire time values from beginning to saturation have been included in plotting for the Korsemeyer–Peppas and Sahlin–Peppas models.
The Korsemeyer–Peppas model [
58] is given by the following exponential equation:
where
k is the kinetic constant and the exponent
n indicates the mechanism of transport.
The Peppas–Sahlin equation is based on the assumption that the transport properties of solvent through a matrix have both diffusional and relaxational components, which are generally additive in nature [
59], and the model is given by Equation (14) [
60], below:
where
Mt and
M∞ are the mass of solvent uptake at time t and equilibrium, respectively. The Fickian contribution (diffusion) for the solvent transport is given by the first term on the right-hand side of Equation (14), whereas the second term indicates the relaxation contribution of polymer chains and m is the Fickian diffusion exponent. The literature shows that if
k1 >
k2, then the transport mechanism is predominantly a diffusion-controlled one, and if
k1 <
k2, then it is a matrix-controlled one, and, if
k1 =
k2, then a combination of diffusion and matrix-controlled mechanisms is responsible for the transport of solvent through the matrix [
55,
61]. The Korsemeyer–Peppas model and the Peppas–Sahlin equation are applied to the entire sorption data, and the representative curves for compound
2 are shown in
Figure 6a–c. In the Peppas–Sahlin model shown in
Figure 6, the first term in the equation will always remain positive, as k
1 tends to be positive for all t values. However, k
2 and m tend to be negative. The first term in the equation remains positive since k
1 is positive. However, the second term becomes more negative than the first term, making the whole result negative for low values of t. This is why the initial values of the Sahlin model are shown as negative values in
Figure 6. Similar behavior has been reported in the literature [
55]. The constants obtained from these two kinetic models and their respective correlation coefficients are given in
Table 3. As can be seen from the figure, the Peppas–Sahlin model fits very well with the experimental data. The model considers both Fickian and case II relaxation processes. As per the prediction, the k
1 values are higher than k
2 for all compositions, as well as for the three solvents. There are slight changes in the k
1 and k
2 values for the different compositions. The values lead to the conclusion that the transport mechanism for the different organic solvents is diffusion-controlled, which is related to the chemical potential gradient [
55]. Also, the large value of n for the Korsemeyer–Peppas model indicates that the swelling of the rubber matrix is important for the transport of the organic solvents [
57,
62].
3.3. Dynamic Mechanical Analysis (DMA)
Viscoelastic properties are valuable tools to assess the suitability of a filled elastomer compound for load-bearing applications such as tire treads. The storage modulus and loss tangent values of the compounds obtained from DMA are plotted against temperature and are shown in
Figure 7. The storage modulus shows a drastic decrease for the different elastomer compounds of around −50 °C, which can be correlated with the glass transition region for the compounds. The behaviors of the storage modulus for compounds
1 and
2 are different from those of compound
0 and compound
3. Compounds
1 and
2 show higher storage moduli than the other two compounds, indicating better filler–polymer interactions at low temperatures. The storage modulus is constant after the glass transition temperature for all compounds except for compound
2. Compound
2 exhibits different behavior compared to the other three formulations as it shows higher storage modulus values in the product utilization region. These values were reconfirmed by repeated analyses and can be attributed to better reinforcement happening due to the partial replacement of carbon black with graphene. This result also corroborates the static mechanical results.
It can be observed that the height of the
tanδ peak for compound
2 is comparatively lower than for the other compounds. The restrictions on the mobilization of polymer chains due to the uniform distribution of nanophases of graphene can be ascribed to this reduction. This effective interaction between the filler and the polymer chains leads to the improved physical and chemical adsorption of polymer chain segments on the filler surfaces, leading to a reduction in the
tanδ peak height during dynamic mechanical deformations [
59]. The incorporation of a hybrid filler in a polymer matrix leads to the formation of a constrained region. It quantifies the elastomer chains immobilized by the hybrid fillers. The constrained region can be determined mathematically from the
tanδ peak values using Equations (15)–(17) [
3,
63,
64,
65].
For the linear viscoelastic region, the energy loss factor
W can be determined as:
where
tanδ is the dissipation factor. The volume of the constrained region
Cv can be determined from the dynamic viscoelastic region by using the following equation:
where
W0 is the energy loss factor and
C0 is the volume fraction of the constrained region of the base matrix. As the base matrix does not contain the hybrid filler system,
C0 can be considered to be zero. The volume of the constrained region
Cv then takes the form of Equation (17), as given below.
The calculated values for the volume of the constrained region
Cv for the hybrid composites (compounds
1,
2, and
3) are given in
Table 4. The volume of the constrained region increased from 0.0042 to 0.1829 for compound
2 when compared to compound
1. Then, it showed a decrease. Compound
3 has more graphene compared to compounds
1 and
2, which may lead to more and more filler–filler interaction, forming filler networks. This attribute may be influencing the mobility of the rubber chains more and decreasing the constrained region’s volume in compound
3. Similar results were reported recently in graphene/nano-silica hybrid-filled natural rubber composites [
63].
The degree of entanglement (
N) plays a major role in deciding the rubber-filler interaction and thereby influences the performance properties of the resulting hybrid composites. The values of
N can be mathematically calculated from the storage modulus (
E′) at the rubbery region (corresponding to 0 °C) using Equation (18) [
63,
66]:
where
R is the universal gas constant and
T is the absolute temperature (K). The calculated values of
N are given in
Table 4. The incorporation of graphene into the elastomer composites can lead to an increase in the degree of entanglements, as indicated by the higher values of
N for compounds
1,
2, and
3. Compound
2 shows the highest value of
N, and a further increase in the graphene content from 2.5 to 5 phr (in compound
3) results in a reduction in
N, probably due to the agglomeration of the nanofillers within the elastomer matrix.
The loss tangent (
tanδ) values corresponding to −20 °C, 0 °C, and +20 °C can be considered as an indication of grip and traction of tread compounds on icy, wet, and dry road surfaces, respectively [
67], where
tanδ values at +60 °C correlate to the rolling resistance of the tread compound [
68,
69]. A higher value of storage modulus (
E′) at 30 °C is related to better dry handling characteristics [
70]. The important parameters obtained from DMA are summarized in
Table 5.
The
tanδ peak and the height of the elastomer compounds are highly useful in predicting the properties of tire formulations. From
Table 5, it can be noted that the
tanδ peak slightly shifted toward the lower side for the compound
2 formulation. The other two formulations showed a negligible shift compared to compound
0. Overall, the partial replacement of carbon black with graphene does not have much effect on the loss factor of the formulations. However, the storage modulus values at 30 °C show a prominent improvement for compound
2, compared to the other three formulations. Similar results were also obtained for the static mechanical properties [
40]. Thus, it can be concluded that compound
2 exhibits the optimum loading of partial replacement of carbon black with graphene of these elastomer-blend compounds.
The
tanδ peak height is important for assigning various properties to the tire formulations. It indicates the heat build-up in elastomer compounds. Normally, the peak height of the formulations will be lower than for the reference sample (neat) in elastomer compounds. The decrease in
tanδ peak height is an indication of the hindrance that happens to the rubber chains through the filler particles.
Tanδ values at 60 °C are a measure of the rolling resistance of the elastomer compounds. In the current study, compounds 1 and 3 show lower
tanδ values at 60 °C than compound
0, which means that the rolling resistance is lower (lower hysteresis) than for the base material. A decrease in rolling resistance is shown by the decrease in the
tanδ values at higher temperatures, which will enable fuel efficiency by reducing heat generation due to friction [
71]. The compounds prepared by replacing carbon black with graphene show lower rolling resistance (~10%) than the base materials, which may lead to a 1–2% fuel consumption efficiency increase for the tires developed using these formulations [
69,
72,
73]. The repeated destruction and reconstruction of the filler network owing to the replacement of carbon black with graphene is causing changes in
tanδ values at higher temperatures [
74].
The
tanδ values at lower temperatures (−20 °C, 0 °C, 25 °C) are also tabulated in
Table 5. It can be seen that the values for compound
2 are higher than that of the base material, compound
0. These higher values are an indication of the better grip properties of the tires on road surfaces, such as wet grip and grip on ice [
69,
75]. Sarkawi et al. reported that the higher
tanδ at 0 °C is due to a higher degree of rubber–filler interaction in the elastomer compounds [
76]. Similar results were obtained recently for natural rubber compounds with the rice-husk-derived nanocellulose replacement of carbon black [
32]. In the present study, the optimum interaction is happening in compound
2, as evidenced by the
tanδ values.
3.4. Thermogravimetric Analysis (TGA)
The TGA thermograms for the elastomer compounds are shown in
Figure 8. From the figure, it can be seen that the incorporation of graphene as a partial replacement for carbon black in the elastomer compounds resulted in an improvement in the thermal degradation profiles of these compounds. An important parameter that can be obtained from the thermograms is t
50, which is the temperature at which a 50% loss occurs for the weight of the samples. The t
50 values are 436 °C, 466 °C, 468 °C, and 449 °C for compound
0, compound
1, compound
2, and compound
3, respectively. This indicates that the degradation temperature (t
50) shifted to the higher side for those compounds that contain graphene as a partial replacement for carbon black, and, when its dosage reached 2.5 phr in the compound (compound
2), the t
50 value showed a maximum. This agrees very well with the other results reported in this investigation. The weight loss at each thermal region is an important parameter obtained from the thermogravimetric analysis. The first derivative of the thermogravimetric curve, known as the DTG curve, shows distinct peaks corresponding to each stage of thermal degradation, which can be correlated with the degradation of individual components present in the compound. The DTG peak values are considered to be the maximum degradation temperature of these components [
77]. The DTG curve for compound
0 that is included in
Figure 8 shows two major peaks, one at 370 °C, which corresponds to the maximum degradation temperature of NR [
78], and the other one at 447 °C, which corresponds to the maximum degradation temperature of the BR component [
79] of the compound. The degradation peak temperatures, the sample weight loss at these peak temperatures, and the percentage residue remaining at 750 °C for all the compounds are summarized in
Table 6. From the table, it can be seen that the incorporation of graphene in the compounds resulted in an overall decrease in weight loss corresponding to the degradation stages of NR and BR components in the blend, and the effect was more pronounced for compound
2. For compound
2, the first degradation peak shifted to a higher temperature (from 370 to 373.5 °C), with a reduction in weight loss from 29.38% to 12.80%, whereas, for the second degradation stage, the maximum degradation temperature remained almost the same for compounds
0,
1, and
2 (447 °C) and reduced to 443 °C for compound
3. The corresponding weight loss decreased from 53.51% (for compound
1) to 48.10% (for compound
3). The lowest weight loss was shown by compound
2. Hence, compound
2 can be considered to be more thermally stable compared with the thermal degradation characteristics of other compounds. The residue remaining at the end of the thermal degradation process gradually increased from compound
0 to compound
3, which indicates that the graphene present in the formulation succeeded in improving the filler–filler interactions in the compounds [
80]. The increase in residue content is due to the increase in crosslink formations within the carbon black structure due to these improved filler–filler interactions [
81].