36 J. G. Tramell et al. Fig. 5 a) Example of EMG model fit resulting in multiple analytical solutions for P0080-SCb) P0280-SC with fitted with two and three EMG functions Activation energy calculations Due to the issues with the EMG fitting, Ea calculations were completed with the peak heights directly from the tan δ traces rather than the Tci. Peak temperatures are reported in table 3 below. Values are not reported when a material or test condition did not result in any identifiable peaks. 10 Hz data is also not reported for the second tan δ peak due to phase angle issues with data above Tg. Strain % increases within the LVR can be employed in the future to mitigate this issue when testing above the binder Tg [4]. The results suggest that introduction of the filler increases the Ea of the bulk polymer Tg and the Ea of the second tanδ peak when comparing neat binder to all the filled samples. Looking specifically at the Ea for theTg peak, no obvious trends exist between Ea and the filler particle size, or the Ea of coated vs uncoated beads. Data fitting for the second tan δ peak is relatively poor due to the lack of frequencies available. Including additional frequencies in future testing will allow more accurate Ea calculations. Despite the lack of data, there appears to be a difference between the Ea of coated and uncoated samples. Again, excluding P4000, P4000-SC, P0040, and P0040-SC samples, the remaining materials consistently exhibited a lower Ea in the coated glass beads vs the uncoated counterparts. The reduction in Ea indicates a weaker interaction with the binder [12]. Particle-binder interaction parameter The particle-matrix interaction parameter, A, was first proposed by Chua and adapted by Kubat et al. [17, 20]. The equation provided by Kubat et. al. is shown in equation 3 and is based on the energy loss at the interface. In equation 3, vf is the volume fraction of filler, and tan(δc) and tan(δm) are the composite tan δ and binder tan δ traces, respectively, as a function of temperature. The parameter A discussed here is different than the model parameter Ai discussed previously in equation 1. The parameter Ahas an inverse relationship with the polymer-filler interaction, meaning lower Avalues indicate a stronger particle-binder interaction. Calculations of the interaction parameter may shed light on interphase characteristics when coupled with AFM results. A= 1 1−vf • tan(δc) tan(δm) − 1 (3) The interaction parameter A is plotted vs temperature in figure 6 for the 1 Hz data sets. All samples follow a similar shape and can be generally broken down into three regimes. In the first regime, A increases slightly from -110 ◦C to -95 ◦C which indicates a weakening interaction strength as the temperature approaches Tg. Second, Adecreases from -95 ◦C to the -75 ◦C (in the Tg range at 1 Hz) and may be attributed to increased molecular mobility in the binder which increases viscosity and friction at the interface [21, 22]. Third, Agenerally increases from -75 ◦C until the end of the test where the binder particle interaction decreases as molecular mobility continues to increase [21, 22]. Some samples show a decrease in Aat warmer temperatures, with the P0280 samples showing a significant increase in the particle-binder interaction. The underlying mechanism for this decrease of Aat warmer temperatures is currently unknown. The difference in the A parameter between coated and uncoated glass beads is also apparent across all samples above their Tg. First, every coated sample shows a higher A parameter, again suggesting that the interaction strength is weaker than the uncoated counterpart. Next, looking at uncoated samples, the Aparameter does not exhibit many differences across
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