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en:grundlagenhandbuch:materialkenngroessen:mischungsregeln_fuer_polymerblends [2026/01/27 12:44] – deppe2en:grundlagenhandbuch:materialkenngroessen:mischungsregeln_fuer_polymerblends [2026/01/27 12:53] (aktuell) – [Densities of Binary Systems] neelest
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 $$v_{m,MIX} = w_1 \cdot v_{m,1} + w_2 \cdot v_{m,2} \tag{4}$$ $$v_{m,MIX} = w_1 \cdot v_{m,1} + w_2 \cdot v_{m,2} \tag{4}$$
  
-To determine the bulk density ρS MIX of binary systems like polymer blends and compounds with a granule diameter d1 and d2 (where d1 < d2) of the single components respective of the viscosity polymer and the filler, one must firstly make the following considerations. In the figure one can see the bulk density ρS MIX of a filler of two different particle fractions.+To determine the bulk density $\rho_{S.MIX}$ of binary systems like polymer blends and compounds with a granule diameter $d_1$ and $d_2$ (where $d_1 < d_2$) of the single components respective of the viscosity polymer and the filler, one must firstly make the following considerations. In the figure one can see the bulk density $\rho_{S.MIX}$ of a filler of two different particle fractions.
  
 {{ :en:grundlagenhandbuch:materialkenngroessen:mischungsregeln_fuer_polymerblends:en_sigma150_dlg_grundlagenhandbuch_materialkenngroessen_022.svg?700&nolink |}} {{ :en:grundlagenhandbuch:materialkenngroessen:mischungsregeln_fuer_polymerblends:en_sigma150_dlg_grundlagenhandbuch_materialkenngroessen_022.svg?700&nolink |}}
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-**Figure:** Bulk density of a fill of two different particle fractions (polymer blend and compound d1<<d2). 
  
 One must take into account that the diameter of the smaller granule particle fraction is much smaller than the granule diameter of the larger fraction (d1 << d2). If one draws the bulk density ρS MIX of a fill of two different particle fractions as a function of the weight content of the smaller fraction w1 every profile will have a maximum in the saturation concentration w1 = wSät independent of the porosity e. The degree of saturation concentration is defined as follows: One must take into account that the diameter of the smaller granule particle fraction is much smaller than the granule diameter of the larger fraction (d1 << d2). If one draws the bulk density ρS MIX of a fill of two different particle fractions as a function of the weight content of the smaller fraction w1 every profile will have a maximum in the saturation concentration w1 = wSät independent of the porosity e. The degree of saturation concentration is defined as follows:
Zeile 182: Zeile 180:
 $$\rho_{sat} = \rho_1 + (1 - \rho_{\infty}) \cdot (1 - e) \cdot \rho_2 \tag{7}$$ $$\rho_{sat} = \rho_1 + (1 - \rho_{\infty}) \cdot (1 - e) \cdot \rho_2 \tag{7}$$
  
-If one wants to determine the bulk density ρS MIX of binary systems using polymer blends and compounds with d1 < d2 , three cases are distinguished. The strategy of the three cases is shown in the figure. The ratio of the particle fractions (d1/d2) is set to the sub division criteria for every case. Firstly one assumes two different basic approaches  ($d_1 < 0,25d_2$ bzw. $d_1 > 0,75d_2$) while the third basic approach is calculated by the linear average of the first two approaches in the transition zone ($0,25d_2 < d_1 < 0,75d_2$).+If one wants to determine the bulk density ρS MIX of binary systems using polymer blends and compounds with $d_1 < d_2$, three cases are distinguished. The strategy of the three cases is shown in the figure. The ratio of the particle fractions ($d_1/d_2$) is set to the sub division criteria for every case. Firstly one assumes two different basic approaches  ($d_1 < 0,25d_2$ resp. $d_1 > 0,75d_2$) while the third basic approach is calculated by the linear average of the first two approaches in the transition zone ($0,25d_2 < d_1 < 0,75d_2$).
  
 **Bulk density of binary Systems** **Bulk density of binary Systems**