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en:grundlagenhandbuch:materialkenngroessen:mischungsregeln_fuer_polymerblends [2026/01/27 12:43] – deppe2en:grundlagenhandbuch:materialkenngroessen:mischungsregeln_fuer_polymerblends [2026/01/27 12:53] (aktuell) – [Densities of Binary Systems] neelest
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 Both the rheological and the thermodynamical characteristic values of a binary system (e.g. solid and melting enthalpy of polymer blends) are generally deemed as being insufficiently describable over a linear average of the data from the raw components. This means for the simulation with SIGMA that before one starts a simulation, the material data of the binary systems should be determined. This would result in numerous measurements before the simulation process actually starts. If one only has the material data for the single components, the calculations for the binary systems using SIGMA will use the material data of the single components in the following ways: Both the rheological and the thermodynamical characteristic values of a binary system (e.g. solid and melting enthalpy of polymer blends) are generally deemed as being insufficiently describable over a linear average of the data from the raw components. This means for the simulation with SIGMA that before one starts a simulation, the material data of the binary systems should be determined. This would result in numerous measurements before the simulation process actually starts. If one only has the material data for the single components, the calculations for the binary systems using SIGMA will use the material data of the single components in the following ways:
  
- 
-  *[[en:Grundlagenhandbuch:Materialkenngrößen:Mischungsregeln für Polymerblends: Rheologische Kenngrößen von Mehrstoffsystemen]] 
-  *[[en:Grundlagenhandbuch:Materialkenngrößen:Mischungsregeln für Polymerblends:Thermodynamische Kenngrößen von Mehrstoffsystemen]] 
-  *[[en:Grundlagenhandbuch:Materialkenngrößen:Mischungsregeln für Polymerblends:Dichten von Mehrstoffsystemen]] 
  
 ===== Rheological Characteristic Values of Binary Systems ===== ===== Rheological Characteristic Values of Binary Systems =====
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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:
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 $$\rho_{sat} = \rho_1 + (1 - \rho_{\infty}) \cdot (1 - e) \cdot \rho_2 \tag{7}$$ $$\rho_{sat} = \rho_1 + (1 - \rho_{\infty}) \cdot (1 - e) \cdot \rho_2 \tag{7}$$
  
-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**