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Schematic view of carbon black processing in a furnace reactor. Primary aggregates are built by two simultaneous growth processes: (i) surface growth (SG) and (ii) aggregate growth (AG)
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![Table 1 Estimated fraction [%] of the four different types of energetic...](profile/Manfred-Klueppel/publication/225778871/figure/tbl1/AS:668679280812039@1536436972142/Estimated-fraction-of-the-four-different-types-of-energetic-sites-I-IV-for-ad_Q320.jpg)
The chapter considers the disordered nature of filler networks on different length scales and relates it to the specific reinforcing properties of active fillers in elastomer composites. On nanoscopic length scales, the surface structure and primary aggregate morphology of carbon blacks, the most widely used filler in technical rubber goods, are an...
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Context 1
... inter- action strength confirm this finding [64, 65, 106, 107]. The combination of two types of disorder, given by the pronounced morphological roughness ( d s =2.6) and the inhomogeneous energetic surface structure of carbon blacks, enhances the polymer filler coupling, significantly. It represents an important reinforcing mechanism on atomic length scales associated with the required strong phase binding in high performance elastomer composites. Carbon blacks for the rubber industry are produced in a variety of classes and types, depending on the required performance of the final product. In general they consist of a randomly ramified composition of primary particles that are bonded together by strong sinter bridges. Significant effects of the different grades of carbon blacks in elastomer composites result from variations in the specific surface and/or “structure” of the primary aggregates [26, 27]. The specific surface depends strongly on the size of the primary particles and differs from about 10 m 2 /g for the very coarse blacks up to almost 200 m 2 /g for the fine blacks. The “structure” of the primary aggregates describes the amount of void volume and is measured, e.g., by oil (DBP) absorption. It typically varies between 0.3 cm 3 /g and 1.7 cm 3 /g for furnace blacks. The characteristic shape of carbon black aggregates is illustrated in Fig. 17, where transmission electron micrographs (TEM) of three different grades of furnace blacks (N220, N330, N550) are shown. The variation in size of the primary particles, increasing from left to right, becomes apparent. It implies a decline of the specific surface from 116 m 2 /g for N220, 81 m 2 /g for N330, up to 41 m 2 /g for N550. The “structure” or amount of specific voids of the three grades is almost the same and differs between 1 cm 3 /g and 1.2 cm 3 /g, only. Since the specific weight of carbon black is almost twice that for DBP, this corresponds to a factor of 2 for the void volume as compared to the solid volume of the aggregates. It means that about 2/3 of the aggregate volume is empty space, i.e., the solid fraction F of the primary aggregates is relatively small ( F 0.33). It is shown below that F p fulfills a scaling relation which involves the size and mass fractal dimension of the primary aggregates. Due to significant deviations of the solid fraction F p from 1, the filler volume fraction F of carbon black in rubber composites has to be treated as an effective one in most applications, i.e., F = F / F (compare [22]). For a quantitative analysis of the structure of carbon blacks as shown in Fig. 17 it is useful to consider the solid volume V p or the number of primary particles N p per aggregate in dependence of aggregate size d . In the case of fractal objects one expects the scaling behavior [1, 2] V p $ N p $ d d f ð 11 Þ The exponent d f is denoted mass fractal dimension or simply fractal dimension. It characterizes the mass distribution in three dimensional space and can vary between 1< d f <3. This kind of fractal analysis of furnace blacks was performed, e.g., by Herd et al. [108] or Gerspacher et al. [109, 110]. The solid volume V p of primary aggregates is normally determined (ASTM: 3849) from the cross-section area A and the perimeter P of the single carbon black aggregates by referring to a simple Euclidean relation [108]: 8 A 2 V p 1⁄4 3 P ð 12 Þ However, it is not quite clear whether this relation can be applied for non-Euclidean, ramified structures. Simulation results of carbon black formation under ballistic conditions by Meakin et al. [14] indicate that a scaling equation is fulfilled, approximately, between the number of particles N p in a primary aggregate and the relative cross section area A / A p : N p 1⁄4 1 : 51 ð A = A p Þ 1 : 08 ð 13 Þ Here, A p is the cross section area of a single primary particle. Dependent on the application of Eqs. (12) or (13), respectively, significantly different values for the mass fractal dimension are obtained. This discrepancy is demonstrated in Fig. 18 and Fig. 19 by considering an example of a fractal analysis of primary carbon black aggregates. Figure 18 shows a TEM-micrograph of the furnace black N339 prepared from a ready mixed composite of S-SBR after removing of the unbounded polymer as ex- plained in Sect. 2.3 (in-rubber state). A double logarithmic plot of the solid volume V p and the particle number N p , estimated from Eqs. (12) and (13), vs aggregate diameter d is shown in Fig. 19a,b, respectively. The aggregate average diameter d is estimated as the mean value from 16 measurements on a single aggregate with a 15% variation in the angle of rotation. The obtained fractal dimensions differ significantly for the two evaluation procedures. From the slope of the two regression lines one finds d f =2.45 and d f =1.94, respectively. In view of a discussion of this discrepancy, we consider the conditions of primary aggregate growth during carbon black processing in some detail. Figure 20 shows a schematic representation of carbon black formation in a furnace reactor, where a jet of gas and oil is combusted and quenched, after- wards. Beside the aggregate growth, resulting from the collision of neighboring aggregates, surface growth due to the deposition of carbon nuclei on the aggregates takes place during the formation of primary carbon black aggregates. The surface growth leads to the universal surface roughness, analyzed by gas adsorption technique in Sect. 3.1.1 and investigated from a theoretical point of view in [18]. Obviously, the surface growth is also responsible for the strength of the primary aggregates, since it proceeds in the contact range of the collided aggregates implying a strong bonding by sinter bridges (Fig. 20). Due to the high temperature in the reactor, aggregate as well as surface growth take place under ballistic conditions, i.e., the mean free path length of both growth mechanisms is large compared to the characteristic size of the resulting structures [14–16]. Then the trajectories of colliding aggregates (or nuclei) can considered to be linear. Numerical simulations of ballistic cluster-cluster aggregation yield a mass fractal dimension d f % 1.9–1.95 [11, 12, 17]. This compares to the above TEM-result d f % 1.94 evaluated with Eq. (13). It means that the assumption of ballistic cluster-cluster aggregation during carbon black processing, used already in the derivation of Eq. (13), is confirmed by the TEM-data of the relatively fine black N339. For the more coarse blacks, with a typically small primary particle number, finite size effects can lead to a more compact morphology that differs from the scaling prediction of ballistic cluster aggregation. A further deviation can result from electrostatic repulsion effects due to the application of processing agents (alkali metal ions) for designing the coarse blacks (compare [22]). Note that a similar relation as Eq. (13) was derived in the 1960s by Medalia and Heckman [111, 112]. The value d f =1.94 also agrees fairly well with other estimates obtained, e.g., by electric force microscopy [113], TEM [114], or SAXS [95, 96]. Therefore, it appears likely that the approach considering the solid volume of primary aggregates, as evaluated from the two-dimensional cross- section area by Eq. (12), leads to an overestimation of the mass fractal dimension. A more realistic estimate is obtained with Eq. (13). By referring to Eq. (12), the data obtained by Herd et al. [108] show a successively increasing value of the mass fractal dimension from d f % 2.3 to d f % 2.8 with increasing grade number (or particle size) of the furnace blacks. As expected, they fit quite well to the above estimate d f % 2.45 for the black N339. A summary of these data and a discussion including other fractal parameters is found in [22]. It is well established that the specific properties of carbon black filled elastomers, e.g., viscoelasticity or electrical conductivity, are strongly affected by the disordered, ramified structure of the primary aggregates [26, 27]. On the one hand, this structure is characterized by the mass fractal dimension considered above. On the other hand, it is determined by a lower and upper cut-off length, i.e., primary particle size and aggregate size, respectively. In the following we will focus on the upper cut-off length or, more precisely, on the size distribution of primary aggregates in ready mixed composites. We will see that this quantity depends on the conditions of sample preparation, since aggregate rupture can take place if high shear stresses are applied during the mixing procedure. In the literature it has been found that during mixing aggregate breakdown occurs for a number of carbon blacks in highly viscous rubbers [115– 118]. Recently, the aggregate breakdown was also attributed to classes of specific shapes of individual carbon blacks [108]. The opinion about the mechanical consequences of this process is quite different. On the one side, no obvious relationship to reinforcement is conjectured [116]. On the other side, improvements of the mechanical performance, due to the creation of new, active carbon surface, is assumed, which participates in formation of a strong filler-rubber coupling [118]. Figure 21 shows results obtained from TEM-analysis of primary aggregate size distribution of E-SBR/N330-samples at various mixing levels. With increasing mixing time, a shift in aggregate size distribution to smaller values is observed. The maximum of the distribution of aggregate cross section area shifts from about 0.03 m 2 to about 0.02 m 2 . The shift of the maximum can be related to a breakdown of aggregates into smaller pieces as mixing time increases. It can also be referred to an improved micro-dispersion with specific influences on the mechanical property spectrum [85]. A characteristic effect of increasing mixing time on aggregate size is the reduction in the shoulder, occurring in the case of ...
Context 2
... aggregates (or nuclei) can considered to be linear. Numerical simulations of ballistic cluster-cluster aggregation yield a mass fractal dimension d f % 1.9–1.95 [11, 12, 17]. This compares to the above TEM-result d f % 1.94 evaluated with Eq. (13). It means that the assumption of ballistic cluster-cluster aggregation during carbon black processing, used already in the derivation of Eq. (13), is confirmed by the TEM-data of the relatively fine black N339. For the more coarse blacks, with a typically small primary particle number, finite size effects can lead to a more compact morphology that differs from the scaling prediction of ballistic cluster aggregation. A further deviation can result from electrostatic repulsion effects due to the application of processing agents (alkali metal ions) for designing the coarse blacks (compare [22]). Note that a similar relation as Eq. (13) was derived in the 1960s by Medalia and Heckman [111, 112]. The value d f =1.94 also agrees fairly well with other estimates obtained, e.g., by electric force microscopy [113], TEM [114], or SAXS [95, 96]. Therefore, it appears likely that the approach considering the solid volume of primary aggregates, as evaluated from the two-dimensional cross- section area by Eq. (12), leads to an overestimation of the mass fractal dimension. A more realistic estimate is obtained with Eq. (13). By referring to Eq. (12), the data obtained by Herd et al. [108] show a successively increasing value of the mass fractal dimension from d f % 2.3 to d f % 2.8 with increasing grade number (or particle size) of the furnace blacks. As expected, they fit quite well to the above estimate d f % 2.45 for the black N339. A summary of these data and a discussion including other fractal parameters is found in [22]. It is well established that the specific properties of carbon black filled elastomers, e.g., viscoelasticity or electrical conductivity, are strongly affected by the disordered, ramified structure of the primary aggregates [26, 27]. On the one hand, this structure is characterized by the mass fractal dimension considered above. On the other hand, it is determined by a lower and upper cut-off length, i.e., primary particle size and aggregate size, respectively. In the following we will focus on the upper cut-off length or, more precisely, on the size distribution of primary aggregates in ready mixed composites. We will see that this quantity depends on the conditions of sample preparation, since aggregate rupture can take place if high shear stresses are applied during the mixing procedure. In the literature it has been found that during mixing aggregate breakdown occurs for a number of carbon blacks in highly viscous rubbers [115– 118]. Recently, the aggregate breakdown was also attributed to classes of specific shapes of individual carbon blacks [108]. The opinion about the mechanical consequences of this process is quite different. On the one side, no obvious relationship to reinforcement is conjectured [116]. On the other side, improvements of the mechanical performance, due to the creation of new, active carbon surface, is assumed, which participates in formation of a strong filler-rubber coupling [118]. Figure 21 shows results obtained from TEM-analysis of primary aggregate size distribution of E-SBR/N330-samples at various mixing levels. With increasing mixing time, a shift in aggregate size distribution to smaller values is observed. The maximum of the distribution of aggregate cross section area shifts from about 0.03 m 2 to about 0.02 m 2 . The shift of the maximum can be related to a breakdown of aggregates into smaller pieces as mixing time increases. It can also be referred to an improved micro-dispersion with specific influences on the mechanical property spectrum [85]. A characteristic effect of increasing mixing time on aggregate size is the reduction in the shoulder, occurring in the case of aggregate cross section areas greater than 0.05 m 2 , in favor of smaller aggregates. This is indicative for the rupture of single aggregates into two pieces. The observed aggregate breakdown during mixing can be understood on a more fundamental level, if the above discussed two simultaneous growth mechanisms, surface- and aggregate growth, during carbon black processing are considered again (Fig. 20). Obviously, the surface growth implies a strong bonding between adjacent primary particles by rigid sinter bridges that keep the primary aggregates together. However, this process goes on during the aggregate growth leading to a hierarchy of bonding strengths. The bonds formed in the beginning of aggregate growth become stronger than the final ones, because the time for stabilization by sinter bridges decreases with increasing time in the reaction zone. The bonds formed between collided aggregates just at the end of the reaction zone, before the quenching process takes place, remain relatively weak. This also becomes apparent in the upper scheme of Fig. 20. For that reason we expect that increasing mixing severity during compounding with highly viscous polymer melts leads to aggregate breakdown and changes in aggregate size distributions. According to Fig. 22, this is also observed for an increased filler loading. As shown in Fig. 22, the maximum of the size distribution is shifted to smaller values with rising filler concentration from 40 phr N339 to 80 phr N339 in E-SBR-composites. This results from the increased viscosity, since shear forces during mixing are enhanced with rising viscosity of the composite. A comparison of the morphology of N339 in E-SBR- and S-SBR-composites with increasing carbon black concentration is summarized in Table 2. It emphasizes the successive decrease of the mean primary aggregate size with increasing filler loading for both systems. The composites with E-SBR have a slightly larger aggregate size in the range of higher filler concentrations compared to those with S-SBR. On the one hand this can be assumed to result from a lower viscosity, especially under elongation deformations, which is of high relevance for filler dispersion during mixing. On the other, it may also be related to a weaker polymer-filler coupling between the carbon black surface and the E-SBR-chains [119]. The observed effect of mixing on aggregate size distribution has a pronounced influence on the mechanical properties of the composites. This can be quantified by considering the solid fraction F p of primary aggregates that represents a measure for the “structure” of carbon blacks. It is given by the ratio between the solid volume and the overall aggregate volume. Then, with Eq. (11) one finds the following scaling relation with respect to the average diameter d of the ...
Context 3
... different grades of carbon blacks in elastomer composites result from variations in the specific surface and/or “structure” of the primary aggregates [26, 27]. The specific surface depends strongly on the size of the primary particles and differs from about 10 m 2 /g for the very coarse blacks up to almost 200 m 2 /g for the fine blacks. The “structure” of the primary aggregates describes the amount of void volume and is measured, e.g., by oil (DBP) absorption. It typically varies between 0.3 cm 3 /g and 1.7 cm 3 /g for furnace blacks. The characteristic shape of carbon black aggregates is illustrated in Fig. 17, where transmission electron micrographs (TEM) of three different grades of furnace blacks (N220, N330, N550) are shown. The variation in size of the primary particles, increasing from left to right, becomes apparent. It implies a decline of the specific surface from 116 m 2 /g for N220, 81 m 2 /g for N330, up to 41 m 2 /g for N550. The “structure” or amount of specific voids of the three grades is almost the same and differs between 1 cm 3 /g and 1.2 cm 3 /g, only. Since the specific weight of carbon black is almost twice that for DBP, this corresponds to a factor of 2 for the void volume as compared to the solid volume of the aggregates. It means that about 2/3 of the aggregate volume is empty space, i.e., the solid fraction F of the primary aggregates is relatively small ( F 0.33). It is shown below that F p fulfills a scaling relation which involves the size and mass fractal dimension of the primary aggregates. Due to significant deviations of the solid fraction F p from 1, the filler volume fraction F of carbon black in rubber composites has to be treated as an effective one in most applications, i.e., F = F / F (compare [22]). For a quantitative analysis of the structure of carbon blacks as shown in Fig. 17 it is useful to consider the solid volume V p or the number of primary particles N p per aggregate in dependence of aggregate size d . In the case of fractal objects one expects the scaling behavior [1, 2] V p $ N p $ d d f ð 11 Þ The exponent d f is denoted mass fractal dimension or simply fractal dimension. It characterizes the mass distribution in three dimensional space and can vary between 1< d f <3. This kind of fractal analysis of furnace blacks was performed, e.g., by Herd et al. [108] or Gerspacher et al. [109, 110]. The solid volume V p of primary aggregates is normally determined (ASTM: 3849) from the cross-section area A and the perimeter P of the single carbon black aggregates by referring to a simple Euclidean relation [108]: 8 A 2 V p 1⁄4 3 P ð 12 Þ However, it is not quite clear whether this relation can be applied for non-Euclidean, ramified structures. Simulation results of carbon black formation under ballistic conditions by Meakin et al. [14] indicate that a scaling equation is fulfilled, approximately, between the number of particles N p in a primary aggregate and the relative cross section area A / A p : N p 1⁄4 1 : 51 ð A = A p Þ 1 : 08 ð 13 Þ Here, A p is the cross section area of a single primary particle. Dependent on the application of Eqs. (12) or (13), respectively, significantly different values for the mass fractal dimension are obtained. This discrepancy is demonstrated in Fig. 18 and Fig. 19 by considering an example of a fractal analysis of primary carbon black aggregates. Figure 18 shows a TEM-micrograph of the furnace black N339 prepared from a ready mixed composite of S-SBR after removing of the unbounded polymer as ex- plained in Sect. 2.3 (in-rubber state). A double logarithmic plot of the solid volume V p and the particle number N p , estimated from Eqs. (12) and (13), vs aggregate diameter d is shown in Fig. 19a,b, respectively. The aggregate average diameter d is estimated as the mean value from 16 measurements on a single aggregate with a 15% variation in the angle of rotation. The obtained fractal dimensions differ significantly for the two evaluation procedures. From the slope of the two regression lines one finds d f =2.45 and d f =1.94, respectively. In view of a discussion of this discrepancy, we consider the conditions of primary aggregate growth during carbon black processing in some detail. Figure 20 shows a schematic representation of carbon black formation in a furnace reactor, where a jet of gas and oil is combusted and quenched, after- wards. Beside the aggregate growth, resulting from the collision of neighboring aggregates, surface growth due to the deposition of carbon nuclei on the aggregates takes place during the formation of primary carbon black aggregates. The surface growth leads to the universal surface roughness, analyzed by gas adsorption technique in Sect. 3.1.1 and investigated from a theoretical point of view in [18]. Obviously, the surface growth is also responsible for the strength of the primary aggregates, since it proceeds in the contact range of the collided aggregates implying a strong bonding by sinter bridges (Fig. 20). Due to the high temperature in the reactor, aggregate as well as surface growth take place under ballistic conditions, i.e., the mean free path length of both growth mechanisms is large compared to the characteristic size of the resulting structures [14–16]. Then the trajectories of colliding aggregates (or nuclei) can considered to be linear. Numerical simulations of ballistic cluster-cluster aggregation yield a mass fractal dimension d f % 1.9–1.95 [11, 12, 17]. This compares to the above TEM-result d f % 1.94 evaluated with Eq. (13). It means that the assumption of ballistic cluster-cluster aggregation during carbon black processing, used already in the derivation of Eq. (13), is confirmed by the TEM-data of the relatively fine black N339. For the more coarse blacks, with a typically small primary particle number, finite size effects can lead to a more compact morphology that differs from the scaling prediction of ballistic cluster aggregation. A further deviation can result from electrostatic repulsion effects due to the application of processing agents (alkali metal ions) for designing the coarse blacks (compare [22]). Note that a similar relation as Eq. (13) was derived in the 1960s by Medalia and Heckman [111, 112]. The value d f =1.94 also agrees fairly well with other estimates obtained, e.g., by electric force microscopy [113], TEM [114], or SAXS [95, 96]. Therefore, it appears likely that the approach considering the solid volume of primary aggregates, as evaluated from the two-dimensional cross- section area by Eq. (12), leads to an overestimation of the mass fractal dimension. A more realistic estimate is obtained with Eq. (13). By referring to Eq. (12), the data obtained by Herd et al. [108] show a successively increasing value of the mass fractal dimension from d f % 2.3 to d f % 2.8 with increasing grade number (or particle size) of the furnace blacks. As expected, they fit quite well to the above estimate d f % 2.45 for the black N339. A summary of these data and a discussion including other fractal parameters is found in [22]. It is well established that the specific properties of carbon black filled elastomers, e.g., viscoelasticity or electrical conductivity, are strongly affected by the disordered, ramified structure of the primary aggregates [26, 27]. On the one hand, this structure is characterized by the mass fractal dimension considered above. On the other hand, it is determined by a lower and upper cut-off length, i.e., primary particle size and aggregate size, respectively. In the following we will focus on the upper cut-off length or, more precisely, on the size distribution of primary aggregates in ready mixed composites. We will see that this quantity depends on the conditions of sample preparation, since aggregate rupture can take place if high shear stresses are applied during the mixing procedure. In the literature it has been found that during mixing aggregate breakdown occurs for a number of carbon blacks in highly viscous rubbers [115– 118]. Recently, the aggregate breakdown was also attributed to classes of specific shapes of individual carbon blacks [108]. The opinion about the mechanical consequences of this process is quite different. On the one side, no obvious relationship to reinforcement is conjectured [116]. On the other side, improvements of the mechanical performance, due to the creation of new, active carbon surface, is assumed, which participates in formation of a strong filler-rubber coupling [118]. Figure 21 shows results obtained from TEM-analysis of primary aggregate size distribution of E-SBR/N330-samples at various mixing levels. With increasing mixing time, a shift in aggregate size distribution to smaller values is observed. The maximum of the distribution of aggregate cross section area shifts from about 0.03 m 2 to about 0.02 m 2 . The shift of the maximum can be related to a breakdown of aggregates into smaller pieces as mixing time increases. It can also be referred to an improved micro-dispersion with specific influences on the mechanical property spectrum [85]. A characteristic effect of increasing mixing time on aggregate size is the reduction in the shoulder, occurring in the case of aggregate cross section areas greater than 0.05 m 2 , in favor of smaller aggregates. This is indicative for the rupture of single aggregates into two pieces. The observed aggregate breakdown during mixing can be understood on a more fundamental level, if the above discussed two simultaneous growth mechanisms, surface- and aggregate growth, during carbon black processing are considered again (Fig. 20). Obviously, the surface growth implies a strong bonding between adjacent primary particles by rigid sinter bridges that keep the primary aggregates together. However, this process goes on during the aggregate growth leading to a hierarchy of bonding strengths. The bonds formed in the beginning of aggregate growth become stronger than the final ones, ...
Context 4
... growth leads to the universal surface roughness, analyzed by gas adsorption technique in Sect. 3.1.1 and investigated from a theoretical point of view in [18]. Obviously, the surface growth is also responsible for the strength of the primary aggregates, since it proceeds in the contact range of the collided aggregates implying a strong bonding by sinter bridges (Fig. 20). Due to the high temperature in the reactor, aggregate as well as surface growth take place under ballistic conditions, i.e., the mean free path length of both growth mechanisms is large compared to the characteristic size of the resulting structures [14–16]. Then the trajectories of colliding aggregates (or nuclei) can considered to be linear. Numerical simulations of ballistic cluster-cluster aggregation yield a mass fractal dimension d f % 1.9–1.95 [11, 12, 17]. This compares to the above TEM-result d f % 1.94 evaluated with Eq. (13). It means that the assumption of ballistic cluster-cluster aggregation during carbon black processing, used already in the derivation of Eq. (13), is confirmed by the TEM-data of the relatively fine black N339. For the more coarse blacks, with a typically small primary particle number, finite size effects can lead to a more compact morphology that differs from the scaling prediction of ballistic cluster aggregation. A further deviation can result from electrostatic repulsion effects due to the application of processing agents (alkali metal ions) for designing the coarse blacks (compare [22]). Note that a similar relation as Eq. (13) was derived in the 1960s by Medalia and Heckman [111, 112]. The value d f =1.94 also agrees fairly well with other estimates obtained, e.g., by electric force microscopy [113], TEM [114], or SAXS [95, 96]. Therefore, it appears likely that the approach considering the solid volume of primary aggregates, as evaluated from the two-dimensional cross- section area by Eq. (12), leads to an overestimation of the mass fractal dimension. A more realistic estimate is obtained with Eq. (13). By referring to Eq. (12), the data obtained by Herd et al. [108] show a successively increasing value of the mass fractal dimension from d f % 2.3 to d f % 2.8 with increasing grade number (or particle size) of the furnace blacks. As expected, they fit quite well to the above estimate d f % 2.45 for the black N339. A summary of these data and a discussion including other fractal parameters is found in [22]. It is well established that the specific properties of carbon black filled elastomers, e.g., viscoelasticity or electrical conductivity, are strongly affected by the disordered, ramified structure of the primary aggregates [26, 27]. On the one hand, this structure is characterized by the mass fractal dimension considered above. On the other hand, it is determined by a lower and upper cut-off length, i.e., primary particle size and aggregate size, respectively. In the following we will focus on the upper cut-off length or, more precisely, on the size distribution of primary aggregates in ready mixed composites. We will see that this quantity depends on the conditions of sample preparation, since aggregate rupture can take place if high shear stresses are applied during the mixing procedure. In the literature it has been found that during mixing aggregate breakdown occurs for a number of carbon blacks in highly viscous rubbers [115– 118]. Recently, the aggregate breakdown was also attributed to classes of specific shapes of individual carbon blacks [108]. The opinion about the mechanical consequences of this process is quite different. On the one side, no obvious relationship to reinforcement is conjectured [116]. On the other side, improvements of the mechanical performance, due to the creation of new, active carbon surface, is assumed, which participates in formation of a strong filler-rubber coupling [118]. Figure 21 shows results obtained from TEM-analysis of primary aggregate size distribution of E-SBR/N330-samples at various mixing levels. With increasing mixing time, a shift in aggregate size distribution to smaller values is observed. The maximum of the distribution of aggregate cross section area shifts from about 0.03 m 2 to about 0.02 m 2 . The shift of the maximum can be related to a breakdown of aggregates into smaller pieces as mixing time increases. It can also be referred to an improved micro-dispersion with specific influences on the mechanical property spectrum [85]. A characteristic effect of increasing mixing time on aggregate size is the reduction in the shoulder, occurring in the case of aggregate cross section areas greater than 0.05 m 2 , in favor of smaller aggregates. This is indicative for the rupture of single aggregates into two pieces. The observed aggregate breakdown during mixing can be understood on a more fundamental level, if the above discussed two simultaneous growth mechanisms, surface- and aggregate growth, during carbon black processing are considered again (Fig. 20). Obviously, the surface growth implies a strong bonding between adjacent primary particles by rigid sinter bridges that keep the primary aggregates together. However, this process goes on during the aggregate growth leading to a hierarchy of bonding strengths. The bonds formed in the beginning of aggregate growth become stronger than the final ones, because the time for stabilization by sinter bridges decreases with increasing time in the reaction zone. The bonds formed between collided aggregates just at the end of the reaction zone, before the quenching process takes place, remain relatively weak. This also becomes apparent in the upper scheme of Fig. 20. For that reason we expect that increasing mixing severity during compounding with highly viscous polymer melts leads to aggregate breakdown and changes in aggregate size distributions. According to Fig. 22, this is also observed for an increased filler loading. As shown in Fig. 22, the maximum of the size distribution is shifted to smaller values with rising filler concentration from 40 phr N339 to 80 phr N339 in E-SBR-composites. This results from the increased viscosity, since shear forces during mixing are enhanced with rising viscosity of the composite. A comparison of the morphology of N339 in E-SBR- and S-SBR-composites with increasing carbon black concentration is summarized in Table 2. It emphasizes the successive decrease of the mean primary aggregate size with increasing filler loading for both systems. The composites with E-SBR have a slightly larger aggregate size in the range of higher filler concentrations compared to those with S-SBR. On the one hand this can be assumed to result from a lower viscosity, especially under elongation deformations, which is of high relevance for filler dispersion during mixing. On the other, it may also be related to a weaker polymer-filler coupling between the carbon black surface and the E-SBR-chains [119]. The observed effect of mixing on aggregate size distribution has a pronounced influence on the mechanical properties of the composites. This can be quantified by considering the solid fraction F p of primary aggregates that represents a measure for the “structure” of carbon blacks. It is given by the ratio between the solid volume and the overall aggregate volume. Then, with Eq. (11) one finds the following scaling relation with respect to the average diameter d of the ...
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... Secondary structures are assembled of aggregates known as agglomerates. Agglomerates are linked by low-energy bonds [3] (Van der Waals, p, Hydrogen, etc.) which can be broken during the mixing process [4,5]. In this way, an agglomerate can split into several aggregates of low and/or high structure. ...
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... In analogy to carbon-black-filled polymers, tunnelling or possibly hopping of charge carriers across the gaps between filler particles dictates the conductivity above the percolation threshold [23]. Let us assume a sensor as proposed in the introduction. ...
A styrene-butadiene-styrene co-polymer matrix nanocomposite filled with graphene nanoplatelets was studied to prepare chemiresistive volatile organic compounds (VOCs) room temperature sensors with considerable response and selectivity. Nanofiller concentration was estimated from the electrical conductivity percolation behaviour of the nanocomposite. Fabricated sensors provided selective relative responses to representative VOCs differing by orders of magnitude. Maximum observed average relative responses upon exposure to saturated vapours of the tested VOCs were ca. 23% for ethanol, 1600% for acetone, and the giant values were 9 × 106% for n-heptane and 10 × 106% for toluene. The insensitivity of the sensor to the direct saturated water vapour exposure was verified. Although high humidity decreases the sensor’s response, it paradoxically enhances the resolution between hydrocarbons and polar organics. The non-trivial sensing mechanism is explained using the Hansen solubility parameters (HSP), enabling a rational design of new sensors; thus, the HSP-based class of sensors is outlined.
... These materials present a diversified chemical nature leading to specific vulcanisation processes and production costs. In this context, the most important factors affecting the reinforcement effect in rubber are the size and quantity (fraction per volumetric unit) of the particle reinforcement, as well as filler-filler and filler-matrix interactions [59]. ...
Rubber bushing elements are largely used in different industrial sectors thanks to their ability to withstand large reversible deformations and attenuate vibrations. Nonetheless, they are complex mechanical components that present several nonlinearities with respect to the excitation amplitude, frequency and operational temperature. These characteristics are the result of phenomenological features, such as nonlinear elasticity, viscoelasticity and Mullin's effects, that are challenging to be accurately represented in simulation environments. An additional level of complexity is then encountered when such components are included in system-level models. This work provides a general overview of rubber bushing properties and analyses different strategies to formulate bushing elements in Multibody frameworks that can be used as Virtual Sensors to predict physical quantities difficult or impossible to directly measure in the real systems. Constitutive lumped parameters models are reviewed and discussed with particular focus on the overlay approach.
... CB 62 161 is noted to have a dispersion index of 81.5, which is significantly lower than the other compounds. At a fixed surface area, a decrease in structure leads to an increase in attractive contacts per unit volume of CB; the force necessary to separate aggregates in a pellet, therefore, increases [35]. As a result, grades of CB with a comparatively low structure-to-surface area ratio, for example, CB 62 161 , become increasingly challenging to disperse. ...
The Payne Effect (also known as the Fletcher–Gent Effect) has a fundamental impact on the behavior of filled rubber composites and therefore must be considered during their design. This study investigates the influence of carbon black (CB) surface area and structure on the observed Payne Effect and builds on the existing models of Kraus and Ulmer to explain this phenomenon. Dynamic strain sweeps were carried out on natural rubber (NR) compounds containing eight different grades of CB at equivalent volume fractions. The loss and storage moduli were modeled according to the Kraus and Ulmer equations, using a curve optimization tool in SciPy. Subsequent regression analysis provided strong correlations between the fitting parameters and the CB structure and surface area. Using this regression analysis, this work provides further insight into the physical meaning behind the Kraus and Ulmer models, which are phenomenological in nature.
... This emphasizes the role of the mean gap size between the primary aggregates or clusters of CB particles embedded within the insulating polymer matrix. The tunnelling or hopping of charge carriers across the gaps between particles governs the conductivity of carbon-black-filled polymers above the percolation threshold [45]. The application of a strain to such a material may change the distance between the particles and influence the connectivity of the filler network, thus influencing the interparticle tunnelling. ...
A wearable and stretchable strain sensor with a gauge factor above 23 was prepared using a simple and effective technique. Conducting nanocomposite strands were prepared from styrene-b-(ethylene-co-butylene)-b-styrene triblock copolymer (SEBS) and carbon black (CB) through a solvent-processing method that uses a syringe pump. This novel nanocomposite preparation technique is a straightforward and cost-effective process and is reported in the literature for the first time. The work included two stages: the flexible nanocomposite preparation stage and the piezoresistive sensor stage. Depending on its molecular structure, the thermoelastic polymer SEBS is highly resilient to stress and strain. The main aim of this work is to fabricate a highly flexible and piezoresistive nanocomposite fibre/strand. Among the prepared composites, a composite corresponding to a composition just above the percolation threshold was selected to prepare the strain sensor, which exhibited good flexibility and conductivity and a large piezoresistive effect that was linearly dependent on the applied strain. The prepared nanocomposite sensor was stitched onto a sports T-shirt. Commercially available knee and elbow sleeves were also purchased, and the nanocomposite SEBS/CB strands were sewn separately on the two sleeves. The results showed a high sensitivity of the sensing element in the case of breathing activity (normal breathing, a 35% change, and deep breathing at 135%, respectively). In the case of knee and elbow movements, simultaneous measurements were performed and found that the sensor was able to detect movement cycles during walking.
... In fatigue-induced damage, the irreversible damage sustained by matrix is mainly associated to detachments/re-attachments of the physical bonds, the total number of which reduces over time (Klüppel, 2003). Gradual reduction of physical cross-links leads to increase of the average length of polymer chain and consequently decrease in the number of polymer chains , since . ...
A micro-mechanical constitutive model is presented to predict the concurrent effects of thermal aging and cyclic fatigue on the constitutive behavior of cross-linked polymers. The damage associated to each of those aging conditions is induced by mechanisms that have been extensively studied individually. Here, the main goal was to model the damage accumulated when those mechanisms work in parallel. In this respect, we modeled the effect of each aging condition separately through their corresponding aging mechanisms and then coupled them using the concept of network alteration platform. Accordingly, kinetic equations describing damage of each aging-mechanisms are coupled into the network alteration modular concept to allow consideration of mechanical and environmental damages synergies on the constitutive response of the polymer matrix. Following our recent models of thermal-oxidative aging, cyclic fatigue, and damage accumulation a model is developed based on the assumption of the full independence of mechanical and environmental damages. The model is implemented into finite element simulations. For validation, the devised model is bench-marked against a comprehensive set of experimental data. The proposed model shows promising results with reasonable precision.
... Accordingly, the effective filler volume fraction is larger than the real volume fraction, since part of the polymer, the so-called occluded rubber hidden in voids, is not deformed and acts like additional filler. Here, the effective filler volume fraction is obtained by fitting quasistatic stress-strain cycles of unaged samples to the Dynamic Flocculation Model (DFM) [25][26][27][28]. The DFM is a micro-mechanical model that relates the [28]. ...
The relation between thermo-oxidative aging and mechanical fatigue under repeated loading of cured elastomer compounds is investigated by referring to a wide variety of polymer types for special applications. Beside technical elastomers, typical tire tread compounds and special elastomers for high temperature resistant applications are studied. On one side, the lifetime for various loads is evaluated, whereby mechanical relaxation effects and the evolution of surface temperature are investigated. Furthermore, the internal temperature profile is calculated in relation to the measured surface temperature by referring to heat conduction theory in order to get information about the full heat history of the samples during thermo-mechanical aging. On the other side, the effect of thermal aging at various temperatures on mechanical and ultimate properties is investigated and compared to the lifetime characteristics of the samples without thermal aging. Significant differences between the various polymer types and the applied curing systems and filler types have been found. Thermal aging effects during mechanical aging are unlikely to affect the lifetime for most of the samples due to their insensitivity against thermal aging or due to relatively short aging times combined with small temperature increases. By means of the measured stress decrease during mechanical fatigue tests, several aspects influencing the lifetime of rubber compounds have been identified and analyzed.KeywordsCrack propagationLifetime predictionMechanical fatiguePolymer degradationThermo-oxidative aging
... The compounds CB 55 96 and CB 62 161 contain the lowest structure CBs in the colloidal experimental design and have comparatively high surface area values. At a fixed surface area, lower structure CBs are notoriously more difficult to disperse in rubber due to (i) the higher number of attractive contacts between aggregates in pelletized CB prior to mixing on a unit volume basis and (ii) the resulting lower mix viscosities versus medium-high structure CBs [42]. Despite the somewhat lower DI values for CB 55 96 and CB 62 161 , the compound dispersions are reasonable and well in line with dispersion indices observed for commercially prepared rubber compounds. ...
The influence of carbon black (CB) structure and surface area on key rubber properties such as monotonic stress-strain, cyclic stress–strain, and dynamic mechanical behaviors are investigated in this paper. Natural rubber compounds containing eight different CBs were examined at equivalent particulate volume fractions. The CBs varied in their surface area and structure properties according to a wide experimental design space, allowing robust correlations to the experimental data sets to be extracted. Carbon black structure plays a dominant role in defining the monotonic stress–strain properties (e.g., secant moduli) of the compounds. In line with the previous literature, this is primarily due to strain amplification and occluded rubber mechanisms. For cyclic stress–strain properties, which include the Mullins effect and cyclic softening, the observed mechanical hysteresis is strongly correlated with carbon black structure, which implies that hysteretic energy dissipation at medium to large strain values is isolated in the rubber matrix and arises due to matrix overstrain effects. Under small to medium dynamic strain conditions, classical strain dependence of viscoelastic moduli is observed (the Payne effect), the magnitude of which varies dramatically and systematically depending on the colloidal properties of the CB. At low strain amplitudes, both CB structure and surface area are positively correlated to the complex moduli. Beyond ~2% strain amplitude the effect of surface area vanishes, while structure plays an increasing and eventually dominant role in defining the complex modulus. This transition in colloidal correlations reflects the transition in stiffening mechanisms from flexing of rigid percolated particle networks at low strains to strain amplification at medium to high strains. By rescaling the dynamic mechanical data sets to peak dynamic stress and peak strain energy density, the influence of CB colloidal properties on compound hysteresis under strain, stress, and strain energy density control can be estimated. This has considerable significance for materials selection in rubber product development.
... Filled rubber is a composite material made of polymers and nanoscale fine filler particles, and their properties [1] are directly related to tire performance such as rolling resistance, abrasion resistance, and wet traction. To reveal the strong dependencies between the mechanical properties and the nanometer-scale structure such as filler morphologies, many researchers have been engaged in experimental studies which employed X-ray scattering, electronic microscopy, and atomic force microscopy techniques [1,2,3,4,5,6,7,8]. Furthermore, relations of the observed nanometer-scale structure and polymer chain dynamics have been formulated based on the statistical mechanics [1,9,10,11,12]. ...
... Fig. 1 shows the result of this investigation. The increase of the elastic modulus along with the aggregation of more filler particles is observed which is consistent with our existing knowledge [1,8]. The result included only one morphology exceeding stress 0.65. ...
A shortcut to understand microstructure-property relationship, such as relationship between filler morphology and its modulus, is sampling and analysis of microstructures that induce the desired material property. However, the morphologies that induces the desired property, e.g. extremely high modulus, are very limited and hard to be searched by simple random sampling. Particularly, in the case of filled rubber, the simulation of complex filler morphology involves hundreds of filler particles. This makes the random sampling infeasible, because the number of parameters is O3n when using coordinates of the n particles as the search objective. Recent advancement of the sampling methods reported as a part of the materials informatics remains efficient sampling of the targeted microstructure characterized by 10 parameters at most. In this paper, we propose a novel and effective three-step search method to efficiently sample the filler morphology inducing extremely high modulus in a several hundred dimensional parameter space. We demonstrated the efficiency of the proposed method through the comparison with the random sampling in 750 dimensional parameter space for obtaining the morphologies providing the extremely high modulus. Half of the sampled morphologies provided higher stresses than the top 0.1% morphologies found by the random sampling. This is the first work that developed the efficient sampling method of complex material microstructures having targeted properties in a very high dimensional parameter space.
... ε local Xε global X is therefore a strain amplification factor that quantifies the degree to which the applied global strain is amplified on average at the local scale level. Models with varying levels of sophistication can be used for calculating the strain amplification factor (Huber and Vilgis 1999;Klüppel 2003;Allegra et al., 2008;Domurath et al., 2012), with each having distinct advantages and limitations. ...
The thermo-mechanical properties of carbon black reinforced natural and styrene butadiene rubbers are investigated under rapid adiabatic conditions. Eleven carbon black grades with varying surface area and structure properties at 40 parts per hundred (phr) loading are studied and the unreinforced equivalents are included for reference. The results show a strong correlation of the modulus, mechanical hysteresis, temperature rise and calculated crystallinity of the rubbers measured in tensile extension with strain amplification factors. This highlights the influence of matrix overstraining on microstructural deformations of the rubber upon extension. The strain amplification factors are calculated via the Guth-Gold equation directly from carbon black type and loading, allowing a correlation of the fundamental morphological properties of carbon black with thermal and mechanical properties of rubbers upon extension. Analysis of the thermal measurements of the rubber compounds upon extension and retraction and contrasting between crystallizing and non-crystallizing rubbers reveals that a substantial irreversible heat generation is present upon extension of the rubber compounds. These irreversible effects most likely originate from microstructural damage mechanisms which have been proposed to account for the Mullins Effect in particle reinforced rubbers.
