32 J. G. Tramell et al. Fig. 1 Picture of cured DMA samples where the glass bead size increases from left to right and uncoated and coated beads are on the top and bottom of the image, respectively Tsagaropoulos & Eisenberg first proposed modelling and decomposing tanδ traces with an exponential background and two exponentially modified Gaussian (EMG) distributions [9]. However, their approach has since been adapted By Cerri and Bohn towards HTPB systems which models tan δ traces with three EMG distributions to quantify the peak heights, widths, and areas [10]. To fit the tanδ traces to EMG curves, the data is baseline corrected then fitted to equation (1). Variables used in equation (1) are bulleted below with their associated units used. td0 was set to zero for this work. The effect of the glass bead particle size and coating on the parameters listed in equation (1) will be assessed. Any reduction in Ai is reported by Bohn et. al. to relate to the hindrance of molecular mobility in the system [4]. Additionally, the authors of this study speculate that larger wi values correlate to a larger distribution of relaxation times and thus a larger interphase region. tan(δ)BL = td0 + NX i=1 Ai τi • 1 2 • exp"0.5• wi T0i 2 − T −Tci τi #• 1−erf − 1 √2 • T −Tci wi − wi τi (1) • T - measurement temperature (K) • tan(δ)BL - value of tanδ after baseline correction as a function of T (-) • Ai - EMG peak areas (K) • wi - half width at half height of the gaussian peak (K) • Tci – temperature at Gaussian peak maximum (K) • τi - relaxation parameter in exponential part of EMG (K) • td0 – offset in tan δ data (-) • N– number of EMG fitting functions The values for Tci at each Gaussian peak are also used to calculate the activation energy (Ea) of each relaxation process with the Arrhenius equation (shown in equation 2) where f is the applied test frequency, f0 is a pre-exponential factor, Ris the ideal gas constant, and T(f) is the temperature at a given tan δ peak at each deformation frequency (Tci in this case). Calculating the Ea will provide further insight of the interphase since higher activation energies indicate stronger particle-filler interactions [11, 12]. f = f0 •exp − Ea R∗T(f) (2)
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