THIXOTROPIC FLOCCULATION EFFECTS IN CARBON BLACK–REINFORCED RUBBER: KINETICS AND THERMAL ACTIVATION

Particle-reinforced, uncrosslinked (green) rubber compounds display complex rheology, including pronounced thixotropy.¹  The thixotropic response of green compounds to transient shear and temperature profiles experienced during mixing, processing, and forming of rubber compounds can strongly affect the subsequent viscoelastic properties of crosslinked rubber products.

The physical basis for the thixotropic behavior of green rubbers is thought to be a time-, temperature-, and shear-dependent networking of particles within the rubber. This transient network formation is substantially arrested by crosslinking, giving rise to the well-documented and critically important Payne effect.^2,3  Progressive particle networking behavior prior to crosslinking is commonly referred to in the rubber literature as flocculation, and numerous experimental and theoretical studies have reported on this phenomenon.^4–18  It has been established that particle networking/flocculation in green rubbers is (1) promoted at higher temperatures,^1,4  such as those employed during vulcanization; (2) promoted in lower-molecular-weight polymers^4,13; (3) is strongly dependent on processing temperatures, shears, and shear histories^1,4,9,14 ; and (4) depends on the nature of polymer–filler interaction(s).^8,14–16 

Particle networking/flocculation in green compounds occurs over a wide range of time scales. For example, after the cessation of large shear strains, a very rapid initial recovery of modulus/viscosity is observed, followed by a slower recovery toward an apparent equilibrium value. Various efforts to model these features of particle network structural recovery using chemical kinetic^4,18  and, more recently, structural relaxation principles^9,10  have been reported in the literature. Excessive networking/flocculation is typically detrimental to the final performance of rubber goods where low hysteresis, elastic behavior is required (e.g., for energy-efficient tires). Practical efforts to suppress flocculation using various particle–rubber interface chemistries (coupling agents) and functionalized rubber/co-agent strategies have been well documented.^5–7,19,20 

Given the viscosity of common rubbers at typical processing temperatures, any diffusive particle motion must be very limited. SE calculations presented by Böhm and Nguyen⁴  indicated that at typical vulcanization temperatures, carbon black (CB) aggregates could be expected to diffuse only a fraction of their equivalent diameters during an annealing period of ∼10 min. Brochard Wyart and de Gennes²³  and, later, Cai et al.²⁴  addressed the mobility of nanoparticles in entangled polymer melts from a theoretical perspective. Their work highlighted the importance of the size of the particle relative to the size of the topological features of the polymer matrix in defining particle mobility. For entangled rubbers, topological features of note include the entanglement mesh size/Edwards tube diameter (typically ∼5 nm) and the coil radius (typically ∼20 nm).^23,25,26  By contrast, the smallest CB aggregate size encountered in rubber applications is ∼60 nm in mean equivalent diameter, which is significantly larger than chain topologies. In this case, the diffusion coefficient of the particle at long time scales is determined by the bulk viscosity of the polymer,^23,24  although at short time scales (relative to entanglement relaxation), motion may be more complicated.²⁴  Significant complications with the simple SE picture of CB aggregate mobility include (1) CB aggregates have very strong interactions with the surrounding rubber chains, likely resulting in physically or chemically bound and entangled rubber at the surface of the aggregate with the potential for a single polymer chain to bridge between two or more aggregates; (2) CBs have nonspherical aggregate structures (cf. Eq. 1); and (3) for commercially relevant reinforced rubbers, CB aggregates are typically highly packed and interpenetrated. A clear consensus on the diffusion/motion of CB aggregates in rubber has yet to be reached.²⁷ 

A further question is the extent to which the thixotropic behavior of green rubbers is controlled purely by particle networking mechanisms or by polymer-centric mechanisms. These include labile strain and temperature-dependent entanglements of chains at or near the particle-polymer interface^28–31  and the strain- and temperature-dependent stiffening of rubber because of restrictions to local segmental motion of chains constrained between adjacent aggregates.¹⁸  Evidence from studies contrasting the rheology of CBs dispersed in Newtonian liquids versus rubbers has demonstrated that networking of particles must play a key role in controlling the thixotropic phenomenology in green and crosslinked rubbers.³² 

Most published experimental work in this area has focused on examining variables related to polymer–filler interactions.^6–8,14  Only a limited number of studies have directly examined the influence of the morphology and size of commercial reinforcing fillers on thixotropic behavior.^4,22,33  This article presents a systematic study to determine the effects of the surface area and structure of CB on the kinetics and thermal activation of thixotropic behavior in green rubbers.

In practice, effective aggregate diameters can be measured using automated transmission electron microscopy techniques or through centrifugation-assisted Stokes sedimentation techniques (disk centrifuge photo-sedimentometer; DCP). In the case of DCP, an effective spherical diameter value is reported. An extensive body of literature on CB morphology is available for further details.^34,35,37  Both the primary particle size and aggregate structure of CB control key aspects of rubber compound mechanics and dynamics. The aggregate structure defines the volume of rubber occluded from globally applied strains and dictates the levels of strain amplification within the rubber, thereby controlling the compound static stiffness.³⁸  By contrast, the primary particle size is the dominant factor defining the aggregate size and therefore the number of aggregates per unit volume of rubber compound. Consequently, at iso loading, the primary particle size has a dominant effect on low-strain dynamic modulus and hysteresis.

Rubber compounds were prepared using emulsion SBR-1502 (M_w = 3.5 × 10⁵ g/mol, M_n = 1.0 × 10⁵ g/mol) and CBs covering a wide range of surface area and aggregate structure combinations. The analytical properties of the CBs used in this study are presented in Table I. Surface area was determined by nitrogen gas adsorption experiments to provide (1) the total nitrogen-accessible surface area (NSA) of the CB via the Brunauer–Emmett–Teller theory and (2) the external or rubber-accessible surface area via the statistical thickness surface area (STSA) model.³⁹  The structure of the CBs was quantified by oil absorption experiments. The compressed oil absorption test (COAN) is generally preferred to the virgin oil absorption test (OAN) as a descriptor of in-rubber aggregate structure. Here, the 4× 165 MPa precompression of the CB sample before the analysis simulates the attrition of aggregates during the mixing process.^40,41  The DCP mean aggregate diameter, dagg, values reported in Table I were measured from crushed (4× 165 MPa) samples of the CBs following the same reasoning.⁴²  A plot of structure (COAN) versus surface area (STSA) for all CBs in this study is presented in Figure 2.

Masterbatch compounds containing only rubber, CB, and noncurative chemical agents (Table II) were prepared in a 1.5-L Banbury internal mixer according to the mixing procedure presented in Table III. The initial Banbury chamber temperature prior to mixing was 70 °C. The drop temperature of the compounds ranges between 120 °C and 160 °C depending on the CB type. All CBs were mixed at 50 phr loading. A limited set of CBs (N660, N330, N234) were also mixed at 40 phr and 60 phr. This work was primarily focused on the rheology of compounds measured in the absence of curative chemicals. However, where crosslinked analogues of compounds were required for additional analyses, a cure package equivalent to that described in ASTM D3191 (sulfur, 1.75 phr; TBBS, 1 phr) was incorporated on a two-roll mill, and 2 mm thick sheets were cured at 160 °C to T₉₀ +5 min. Macro dispersion of CB in all compounds was quantified by interferometric microscopy measurements of razor-cut surface roughness of crosslinked compounds per ASTM-D2663 method D. All compounds had dispersion indices >90/100, indicating that excellent macro dispersion had been achieved in the crosslinked samples and, by inference, the uncured masterbatch compounds.

For several filled rubber compounds, CB aggregate networking was evaluated qualitatively using transmission electron microscopy (TEM). Sections of 70 nm thickness were cut from crosslinked sheets of compound using a Leica EM FC6 cryo-microtome equipped with a diamond knife and operating at a temperature of −160 °C (well below the rubber T_g). Thin sections were mounted onto a TEM grid and imaged with a FEI Tecnai F20 TEM operating at 200 kV.

The volume resistivity of crosslinked sheets of compound was evaluated using Mitsubishi Chemical Hiresta UP (MCP-HT450) and Loresta GP (MCP-T600) equipment. For compounds with high-volume resistivity, a concentric ring electrode (URS type) was used to evaluate sample resistance over a voltage range up to 1000 V. For compounds with medium- to low-volume resistivity, a four-point electrode (ASP type) was used over a voltage range up to 100 V. Resistance values were converted to volume resistivity via geometric normalization.

Bound rubber was evaluated for masterbatch compounds prepared with 50 phr CB as sampled immediately after sheeting out on a two-roll mill following the Banbury mixing pass. Initial specimens of ∼1 g masterbatch were weighed and suspended in toluene in steel mesh cylinders for 16 hours. After the immersion period, specimens were removed from solvent and washed in fresh toluene and then dried in an oven for 2 h at 110 °C. The weight of the dried specimens was recorded. Bound rubber was calculated from the initial and dried specimen weights and defined as the weight of the rubber remaining after solvent extraction and drying, expressed as a percentage of total rubber weight in the initial specimen. The total rubber weight in the initial specimen was calculated based on the masterbatch composition (Table II). Reported values of bound rubber are the average of two repeat tests. Note that the N990 50 phr compound did not form a coherent gel during solvent extraction, and consequently, bound rubber values could not be determined for this compound.

A rubber process analyzer (RPA) from Alpha Technologies (Hudson, OH, USA) was used to characterize the rheological behavior of the masterbatch compounds. To examine and quantify the role of thermal annealing on the thixotropic process, a procedure was developed based on earlier work described by Böhm and Nguyen,⁴  Böhm et al.,⁴³  and Lin et al.^6,7  Samples of masterbatch compound (i.e., without curative) were loaded into the RPA cavity at 60 °C and immediately subjected to a 100% dynamic preshear. This ensured a substantial breakup of the filler network present in the sample. The temperature was then raised and held for 15 min to anneal the sample, during which a small dynamic strain (0.1%) was applied to monitor the thixotropic recovery of the filler network. Subsequently, the temperature was dropped back to 60 °C. Note that to a crude approximation, this procedure mimics the temperature and shear profiles encountered during the processing and vulcanization of rubber compounds in industry. The heating and cooling steps were completed in ∼1 min at the maximum rate attainable on the RPA. The sample was equilibrated at 60 °C for 10 min, after which a strain sweep was performed between 0.1% and 100% at 1 Hz to evaluate the extent of filler network recovery achieved during annealing steps (i.e., the 60 °C Payne effect in the uncrosslinked compound). This experimental process was performed a total of seven times on each individual compound, with the annealing temperature varying between 60 °C and 180 °C in 20 °C steps and using a fresh sample of masterbatch for each annealing temperature. A schematic of this procedure showing an example annealing temperature of 140 °C is given in Figure 3.

The TEM images of the microtomed thin section of crosslinked compounds (50 phr CB) are shown in Figure 4. At equal volume fraction, there are clear qualitative differences in the interaggregate spacing and packing of aggregates dependent on aggregate structure and particle size. Despite the fact that macro dispersion in these compounds was found to be excellent (via interferometric light microscopy), we can observe that the distribution of CB aggregates at the micro-dispersion length scale is not entirely homogeneous. Regions of locally higher and lower concentrations of aggregates exist in each compound.

Volume resistivity data collected at room temperature on 50 phr filled crosslinked sheets are presented in Figure 5 as a function of CB surface area. A transition is observed between 20 and 60 m²/g, indicating the onset of conductive network formation for CBs with surface areas greater than that of N772.

The exact chemical and physical origins of bound rubber are complex and beyond the scope of this work.^46,47  Bound rubber is typically taken as a measure of polymer–filler interactions, with higher values indicating a higher physical or chemical adhesion of rubber chains to the CB surface. However, there is no clear explanation for the observed dependence of layer thickness on CB surface area from the point of view of CB surface activity alone. Why should a coarse CB such as N772 develop more bound rubber per unit surface area than a CB with a much higher surface area, such as N134? There is no evidence that coarse CBs have substantially higher surface energies/activities than very high surface area CBs.^34,45  A number of researchers including Dannenberg,⁴⁴  Wolff et al.,⁴⁵  and Meissner⁴⁶  have proposed that the larger aggregates of low-surface-area CBs are more susceptible to fracture during mixing with rubber. Such fracture gives rise to higher-energy fresh surfaces on the CB, which are capable of binding more rubber per unit surface area that the virgin CB surface. The difference between OAN and COAN values of CBs can be used to get a rough idea of the level of aggregate attrition during rubber mixing. Contrasting the OAN and COAN values for the CBs evaluated here (Table I) reveals that the attrition of aggregate structures can be just as severe for high-surface-area grades as for low-surface-areas grades.

Given these observations and the potential sensitivity of the bound rubber values to the state of aggregate networking, it would be informative to evaluate bound rubber on compounds both before and after thermal annealing using the RPA procedure introduced in this work. Bound rubber values have actually been reported to increase with thermal annealing and storage time, which would appear not to reflect the temperature-induced changes in the state of aggregate networking but rather the development of polymer–filler interactions by promoting physical and/or chemical interactions of the rubber with the surface of the CB.^47,52 

Example data sets from the RPA procedure are presented in Figure 9A–D. Figure 9A shows data for the unfilled eSBR from the shear-annealing step of the RPA procedure (see Figure 3 for reference), and Figure 9B shows the subsequent strain sweeps. During the annealing steps, the temperature dependence of the viscosity of the unfilled eSBR is clearly observed. Evidence of a slight stiffening of the rubber is observed when the sample temperature is returned to 60 °C, particularly for samples subjected to the higher annealing temperatures. This is probably because of some slight crosslinking of the rubber, even in the absence of curing chemicals.⁹  Strain sweep data show no significant nonlinearity in the region 0.1% to 10% strain, as would be expected for unfilled materials. At higher strain levels (>10%) the decay in modulus is related to flow and shear thinning of the rubber.

By contrast, Figure 9C and D show the equivalent data sets for eSBR filled with 50 phr N234. In this case, following the initial 100% preshear and an initial rapid recovery of modulus, the temperature-dependent response of the viscosity of the compound during the annealing steps (i.e., a decreasing value of modulus as the cavity temperature increases) is superposed with a slow thixotropic recovery (i.e., increase in modulus value). The marked effect of temperature on the extent of the recovery process is clearly seen when the sample temperatures are returned to 60 °C and strain sweeps are performed. A systematic increase in the Payne effect is observed, up to a doubling in magnitude versus the 60 °C samples after annealing at the highest temperature level (180 °C).

From these data sets, the kinetics of the flocculation process can be examined in two different ways. First, the modulus recovery data from experiments conducted with an annealing temperature of 60 °C can be used for direct kinetic rate analysis of the recovery process. Higher annealing temperatures cannot be analyzed in this way, as they involve a step change in sample temperature, which requires a finite time for the RPA to achieve (∼1–2 min) and results in a superposition of a temperature-dependent drop in compound viscosity on top of the thixotropic recovery process. Using the data set collected at 60 °C for kinetic rate analysis is also advantageous in that any contributions to modulus from inadvertent crosslinking and/or chain decomposition should be minimized. Second, thermal activation of the process can be analyzed by evaluating the changes in Payne effect magnitude after the various annealing steps.

Equation 7 was fitted to the 60 °C recovery data set for each compound using a nonlinear least squares regression solver (MS Excel). Figure 11 presents examples of the fits for a number of compounds. Fits to the model are reasonable, but at longer recovery times, there is some apparent underestimation of the modulus, especially for the more thixotropic compounds. This is likely because of an underestimate of the fitted equilibrium contribution to the modulus ⁠, which would, for highly networked compounds, take a significantly longer time to achieve than the time scales evaluated here. The various kinetic parameters determined from the fitting process can now be correlated with analytical properties of the CBs. The instantaneous recovery contribution, ⁠, was best correlated to the structure (COAN) of the CBs (Figure 12). Ignoring the unfilled compound data point, a linear correlation with R² = 0.92 is observed. Note that the unfilled compound also exhibits a slight instantaneous recovery, despite a lack of CB filler. This is due to the well-known thixotropic recovery of the shear thinning rubber following cessation of shear. The slow recovery contribution, ⁠, is found to be best described by a bivariate linear regression to structure (COAN) and surface area (STSA) of the CBs. The results of this regression gave a prediction of the 14 observations of with a multiple R² of 0.96 and with p values for COAN and STSA of 6.2 × 10⁻⁸ and 7.0 × 10⁻⁵, respectively. The iso surface result for the regression is plotted along with the experimental data points in Figure 13. Surface area has a dominant role in driving while the structure has a secondary effect. Rate constant values are plotted versus CB surface areas in Figure 14 and show a transition from the behavior of the unfilled rubber, which has a relatively high kinetic constant, to much slower kinetic recoveries for the highly networked CB-filled compounds. The transition in behavior occurs in a surface area range corresponding with the onset of electrical percolation shown in Figure 5. A reduction in rate constant of ∼40% is observed.

The increasing influence of surface area at longer recovery time scales (Figure 13) suggests a transition in the mechanism of structural recovery. It is well known that the CB aggregate structure controls the levels of occluded rubber and therefore strain amplification. It could be speculated that at short time scales, the strain amplification (hydrodynamic) stiffening magnitude rapidly increases as the viscosity of the rubber matrix recovers relatively quickly after cessation of shear. This is followed by a longer time scale contribution from progressive aggregate networking processes moving toward an equilibrium structure (e.g., progressive reductions in interaggregate distances). These interpretations are broadly consistent with the interpretation presented by Meier and Klüppel.¹⁸ 

Figure 15 plots the entire data set of 60 °C Payne effect ΔG′ (⁠–⁠) values collected for each compound at 50 phr CB loading after each annealing temperature step. Plotted on the secondary axis in Figure 15 is the small strain dynamic viscosity of the unfilled rubber at each annealing temperature.

A significant temperature dependence of the annealed Payne effect is seen for certain CB-filled compounds. For example, the N234-filled compound displays an approximately 2.5× increase in Payne effect (ΔG′) after annealing at 180 °C versus annealing at 60 °C. This is in contrast to the unfilled rubber and compounds containing less reinforcing CBs such as N990, for which very little temperature dependence is observed. Note that projection of the data sets back to lower temperatures indicates an almost complete arrest of thixotropic recovery at T < 0 °C. The viscosity of the unfilled rubber decreases inversely with increasing temperature, indicating an Arrhenius-type dependence on temperature. In the context of Eq. 1, this provides a D_SE ∝ T²at constant aggregate size. Figure 16 shows an Arrhenius plot of the eSBR viscosity data along with the 60 °C Payne effect ΔG′ data for the N234 compound. The activation energy for the temperature dependence of the viscosity of the unfilled rubber is calculated to be 13.4 kJ/mol. The apparent activation energy of networking/flocculation for N234 is 9.8 kJ/mol, which is consistent with values in the literature.^4,17  The close match between N234 flocculation and rubber viscosity E_a values is noteworthy, as it appears that the energetics of flocculation are strongly coupled to those of the terminal relaxation of the rubber.

The scaling of the temperature dependence of thixotropic network development to surface area/aggregate size suggests that some feature of the filled rubber microstructure is thermally activated in these green rubber compounds. This could originate from the various interactions of rubber chains with the CB surface, a progressive aggregate–aggregate networking, or a combination of these effects. Additional insight into these critical microstructural features can be found by considering the thermal activation data in more detail. Superposition of the different CB loading data sets should be expected if they are replotted versus an appropriate microstructural/physical parameter, which strongly influences or controls the flocculation process. To explore this further, we focus on the subset of data for the CB types that were prepared at different loadings (N660, N330, and N234 each at 40, 50, and 60 phr).

Next, the interaggregate distances, δ, as calculated from Eqs. 5 and 6, are considered. This is a particularly appealing approach as the thermal activation of networking could well be underpinned by the aggregate proximity, which varies with CB aggregate size as well as CB loading.²⁰ Figure 20 shows the thermal activation data replotted versus the calculated interaggregate distances. Again, the data sets are not completely superposed.

Another approach is to consider the attractive force between adjacent aggregates. vdW forces are widely cited as the key interaction force between CB aggregates which governs their networking behavior in rubber. Furthermore, these forces underpin a number of microstructural models of filler networking in rubber, which relate the stiffness of a rubber compound to vdW potentials and forces between aggregates.^53–58  For balance, it should be noted that alternative proposals for the role of longer-range depletion interactions in driving the networking/flocculation mechanism have also been put forward in the literature.¹⁸  Calculation of net vdW forces between highly packed, complex aggregates with multiple body interactions is a difficult challenge and beyond the scope of this work. Therefore, an attempt is made here to calculate a parameter that is proportional to the vdW force between two adjacent aggregates under highly idealized conditions. The vdW force depends both on the size of the aggregates and the interaggregate separation. The CB aggregates are assumed to be effective spheres separated by a distance, δ, which can be calculated via Eqs. 5 and 6. The actual closest points of proximity between the two aggregates are individual primary particles at the extremities of the two aggregates. Therefore, the relevant particle radii values for calculation of vdW forces are the primary particle radii (a/2), which can be calculated from the CB surface area and density values using Eq. 2. The primary particles in the adjacent aggregates are assumed to have equivalent radii. This approach to modeling the interaction force between aggregates is consistent with the work of Hartley and Parfitt⁵⁹  and Horwatt et al.⁶⁰  Three models for the vdW force between adjacent particles are considered:

• The close approach approximation of Hamaker,⁶¹  which is valid for δ/a ≪ 1. This is given by Eq. 10.

• The full vdW model of Hamaker,⁶¹  which is valid over all particle sizes and separation permutations. This is given by Eq. 11, where α = δ² + 2aδ and β = α + 2δ² .

• The force model of Van den Tempel,⁶²  which is valid for the close approach and was derived using an averaging of Hamaker's force equations for spherical, platelike, and cube particle geometries in an attempt to account for irregular-shaped particles. This is given by Eq. 12.

Although these three models are mathematically different, they each describe a dependence of the interaggregate force on both primary particle size and aggregate separation. Equations 10 to 12 are solved for −F/A, where F is the vdW force and A is the Hamaker coefficient with units of energy.⁵³  It is assumed that the Hamaker coefficient does not vary significantly between different types of CB. This has been confirmed experimentally for a wide range of furnace CBs, although on packed powders as opposed to CB–rubber mixtures.⁵⁹  The thermal activation data sets for the various CBs prepared at multiple loadings are replotted in Figure 21 versus −F/A values calculated from Eqs. 10–12. The different models produce different predicted values of −F/A, which is to be expected when we consider the differing assumptions underpinning each model. Very good superposition of the different CB loading data sets is achieved for each vdW force model. A global power law fit to the data sets for each model is shown as the dark gray lines, and R² values are found to be >0.95 for each model. The thermal activation data sets are seemingly rationalized by considering the attractive force between aggregates resulting from the interaggregate distance and primary particle size, which in turn can be traced back to practical parameters such as the loading of CB in the rubber and the analytical properties of the CB (COAN and STSA). Note that interaggregate forces have been related to bond stiffness between aggregates and to macroscopic compound stiffness in a number of micromechanical models found in the literature.^55,57,58  Interestingly, it is the interaggregate force as opposed to the aggregate diffusion coefficient (∝1/d_agg, cf. Eq. 1 and Figure 18) that best rationalizes the thermal activation data. Reasonable superposition of the data is achieved despite the simplicity of Eqs. 10–12, which involve several large assumptions about the nature of the CB morphology and the filled rubber microstructure, namely:

• The assumptions implicit in the derivations of Eqs. 5 and 6, which are used to calculate δ, and have already been reviewed in the “Bound Rubber” section of this article. Improvements could potentially be made here by incorporating aggregate overlap into the packing model using a fractal object-packing approach.^36,63  Furthermore, CB aggregate sizes within a particular grade are actually polydisperse, in contrast to the monodisperse assumption underpinning Eq. 5. As such, the calculated values of δ based on the volume mean values of d_agg measured by DCP are likely an overestimate of the number mean of smaller gap distances present within the compounds; these shorter gap distances may be anticipated to play a dominant role in CB networking. Although the CBs appeared well dispersed on the macro-dispersion length scale (cf. interferometric microscopy data), the heterogeneous distribution of CB aggregates on the micro-dispersion length scale could lead to regions within the compound that are more densely packed with aggregates than Eq. 5 assumes. Additional experimental characterization of gap size distributions and micro-dispersion states using, for example, atomic force microscopy would be informative in this regard.

• Multiple body interactions on the aggregates and primary particles are ignored. Such interactions may be anticipated to play a substantial role when we consider the closely packed nature of the aggregates in the various rubber compounds.

• Equations 10–12 are valid for smooth spherical particles in a vacuum. In our situation, the aggregates are embedded within a rubber matrix, which would substantially reduce the magnitude of the interaggregate force.²⁰  In addition, CB is known to have a relatively rough surface topology.⁶⁴ 

• Equations 10 and 12 are valid only in the limit of close approach of particles (i.e., δ/a ≪1. Beyond this limit, the attractive force decays as a steeper power function of δ. Average values of δ/d_agg and δ/a for the various compounds in this work are 0.25 and 0.50, respectively, which are probably near the limit of applicability of the close approach approximation. Nevertheless, good data superposition is achieved using these models, and the full force model (Eq. 11), which is not restricted to specific δ/a conditions, also results in good data superposition.

The calculated interaggregate distances in this work lie between 9 and 60 nm (except for N990, which has δ > 150 nm), which are relatively large compared with the short range of vdW interactions. As mentioned, calculated values of δ may well be an overestimate of the real gap distances in these rubbers compounds. Dielectric investigations of CB-filled rubbers have reported substantially smaller gap distances of the order of a few nanometers.¹⁸  However, it would seem that calculated δ values are sufficiently proportional to the real gap distances to allow for superposition of the thermal activation data sets as seen in Figure 21.

Equations 10–12 consider only the attractive force between aggregates. The actual magnitudes of these calculated vdW forces are naturally very small when we consider the range of −F/A values on the abscissa of Figure 21 and that typical Hamaker coefficient values are in the range of 10⁻¹⁹ J to 10⁻²¹ J.^59,60  We should again consider that the number of mean gap distances could well be smaller than those calculated via Eq. 5, leading to somewhat larger interaggregate forces than predicted here. In addition, a single aggregate will be subject to many such interactions from surrounding closely packed neighbors, leading to larger net forces being exerted throughout the network of aggregates.

If it is assumed that the net vdW attractive forces between packed aggregates coupled with any other relevant attractive forces or aggregate diffusive motion are sufficient to perturb the surrounding rubber matrix, we could hypothesize a creep/flow-type displacement response from the uncrosslinked rubber as it is squeezed out of the gaps between the closest primary particles of the adjacent aggregates.¹⁸  This is a potential reason for the similarity in activation energies between the terminal relaxation/flow of the bulk rubber and thermal activation of flocculation (Figure 16). Higher annealing temperatures reduce the viscosity of the rubber and therefore accelerate the draining of the rubber from the interaggregate gaps. Ultimately, this creep/flow response can be expected to be arrested by the steric repulsion between adjacent layers of strongly absorbed rubber chains on the CB surfaces (i.e., tightly bound rubber as governed by the rubber–CB interaction) or by direct contact of the primary particles of the aggregates themselves. Such a dependence of the repulsive forces between aggregates on the tightly bound rubber layer at the CB surface would also explain variations in rates and extents of flocculation observed when the surface activity—and therefore rubber–CB interaction—is modified by, for example, thermal treatment/graphitization of CBs.^14,15,20  Crosslinking of the rubber compound would severely arrest such flow of the rubber chains, which is in agreement with experimental observations of the suppression of flocculation effects in crosslinked compounds. Note that the size of the interaggregate gaps are generally smaller than the diameters of unperturbed rubber coils. It is possible that chain confinement effects could add additional complexity to the hypothesis presented above.

As a final comment, the volume resistivity values for the varied loading data sets for N660, N330, and N234 (Figure 22) show that some of these compounds lie above, some on, and some below the electrical percolation threshold depending on the type and loading of CB. When contrasting Figure 22 with Figure 21, it is apparent that flocculation, as measured by mechanical spectroscopy, is measureable even in compounds well below their electrical percolation thresholds. Therefore, a lack of electrical percolation does not necessarily imply a lack of aggregate networking in CB-filled rubber compounds.

A rheological examination of a wide range of CB-reinforced eSBR compounds was reported. The kinetics of modulus recovery following cessation of high shear strains were correlated to various features of the CBs. Initial rapid recovery was correlated to the aggregate structure of CB, indicating that this is likely a strain amplification–related process. Longer time scale recovery of the modulus is predominantly correlated to the surface area of the CBs, indicating that this is likely an aggregate networking process. Rate constants of longer time scale modulus recovery are strongly reduced for CBs with a higher surface area (more networked).

Thermal activation of the networking/flocculation process in the compounds was found to scale with the surface area and mean aggregate size of the CBs over a range of volume fractions following power laws. Furthermore, it was found that the thermal activation behavior of a subset of compounds prepared with a range of different CBs at different loadings could be collapsed onto a single master line by rescaling the data to a calculated parameter related to the attractive force (vdW) between two aggregates under idealized conditions. This finding implies that the attractive forces between aggregates plays a key role in flocculation and filler network formation. The derived parameter is dependent on the interaggregate distances and the primary particle size of the aggregates, which can be traced back to practical aspects of rubber compound formulations: the rubber type, CB loading, structure, and surface area. The actual magnitudes of the forces calculated via this approach are naturally very small, but this should be balanced by considering that aggregates in crowded environments undergo many such interactions with their neighbors, leading to potentially higher net interaggregate forces than predicted here. Given the successful scaling of thermal activation sets to the vdW models, this area is open for further study and clarification.

The Arrhenius activation energy for flow of the unfilled rubber was found to be quite similar to apparent activation energies for flocculation effects seen in this work and in the literature. This suggests a strong coupling of flocculation energetics with the terminal relaxation of the polymer. This coupling may be the result of a creep/flow of rubber out of gaps between aggregates due to the interaggregate attractive and diffusive forces. Bound rubber measurements were shown to be sensitive to the state of aggregate networking in green compounds.

The author is grateful to Birla Carbon for granting permission to publish this work. Numerous discussions on this topic with Dr. C. G. Robertson (Endurica LLC) are gratefully acknowledged.