≪ View Page

Unterschiede

Hier werden die Unterschiede zwischen zwei Versionen angezeigt.

Link zu dieser Vergleichsansicht

Beide Seiten der vorigen RevisionVorhergehende Überarbeitung
Nächste Überarbeitung		Vorhergehende Überarbeitung
en:ermittlung_der_materialdaten [2026/05/10 23:35] – deppe2en:ermittlung_der_materialdaten [2026/05/27 23:33] (aktuell) – [Filled polymers] deppe2
Zeile 460: Zeile 460:
 Here, $\rho_{Mix}$ is obtained by linear averaging of **Calculation Types I and II**. Here, $\rho_{Mix}$ is obtained by linear averaging of **Calculation Types I and II**.
  
-======Polymer blends======+=====Polymer blends=====
  
 To describe the material behavior of polymer blends, the same material properties must be investigated and characterized as for neat polymers. To describe the material behavior of polymer blends, the same material properties must be investigated and characterized as for neat polymers.
Zeile 478: Zeile 478:
  
 These sinusoidal capillary waves or filament neckings are captured at large time intervals and evaluated by computer analysis. These sinusoidal capillary waves or filament neckings are captured at large time intervals and evaluated by computer analysis.
- 
-FIXME PLATZHALTER ABBILDUNG 111: Versuchsaufbau zur Erfassung und Auswertung von dispersen Fadenzerfallsprozessen mit einem Heiztisch zur Bestimmung der Grenzflächenspannung 
  
 For the filament, the initial diameter $D_0$, the wavelength $λ$, as well as the maximum and minimum filament diameters $D_{max}$ and $D_{min}$ are measured. The following figure shows the characteristic form of such a capillary wave with its relevant dimensions for theoretical consideration. For the filament, the initial diameter $D_0$, the wavelength $λ$, as well as the maximum and minimum filament diameters $D_{max}$ and $D_{min}$ are measured. The following figure shows the characteristic form of such a capillary wave with its relevant dimensions for theoretical consideration.
Zeile 512: Zeile 510:
  
 $$γ_{12} (T) = γ_{12.0} - γ_{12.m} \cdot T$$ $$γ_{12} (T) = γ_{12.0} - γ_{12.m} \cdot T$$
- 
-FIXME PLATZHALTER ABBILDUNG 114: Dimensionslose Wachstumsrate als Funktion der Wellenzahl X und des Viskositätsverhältnisses p 
  
 Here, $γ_{12.0}$ represents the intercept of the approximation function with the ordinate, while $γ_{12.m}$ corresponds to the slope of this function. The following figure illustrates the typical course of interfacial tension $γ_{12}$ as a function of temperature $T$ for a polypropylene (PP) / polyamide (PA6) blend. Here, $γ_{12.0}$ represents the intercept of the approximation function with the ordinate, while $γ_{12.m}$ corresponds to the slope of this function. The following figure illustrates the typical course of interfacial tension $γ_{12}$ as a function of temperature $T$ for a polypropylene (PP) / polyamide (PA6) blend.
Zeile 581: Zeile 577:
 ==== Tensile Strength ==== ==== Tensile Strength ====
  
-The tensile strength of agglomerates is defined as the maximum tensile force $F_N$, normalized to the cross-sectional area of an agglomerate, with the force acting perpendicular to the surface [[en:gefuellte_polymere#references|[Sch75]]].+The tensile strength of agglomerates is defined as the maximum tensile force $F_N$, normalized to the cross-sectional area of an agglomerate, with the force acting perpendicular to the surface [[en:ermittlung_der_materialdaten#references|[Sch75]]].
  
  
Zeile 588: Zeile 584:
 {{ :en:rex310_en_120.svg?nolink&700 |}} {{ :en:rex310_en_120.svg?nolink&700 |}}
  
-[[en:gefuellte_polymere#references|[Sch75]]]+[[en:ermittlung_der_materialdaten#references|[Sch75]]]
  
 The tensile strength is therefore obtained from the sum of the individual adhesive forces, normalized to the cross-sectional area of the agglomerates: The tensile strength is therefore obtained from the sum of the individual adhesive forces, normalized to the cross-sectional area of the agglomerates:
Zeile 594: Zeile 590:
 $$σ_z = \frac{F_{N,max}}{A} = \frac {1}{A} Σ_{i=1} F_{Np,i} (Δl)$$ $$σ_z = \frac{F_{N,max}}{A} = \frac {1}{A} Σ_{i=1} F_{Np,i} (Δl)$$
  
-Since the force–strain behavior of agglomerates is largely unknown, this relationship has little practical relevance. Schubert [[en:gefuellte_polymere#references|[Sch75]]] compiled various approaches for describing the tensile strength of agglomerates. Among these, an approach by Rumpf [[en:gefuellte_polymere#references|[Rum61]]] for statistically packed, monodisperse particles is presented:+Since the force–strain behavior of agglomerates is largely unknown, this relationship has little practical relevance. Schubert [[en:ermittlung_der_materialdaten#references|[Sch75]]] compiled various approaches for describing the tensile strength of agglomerates. Among these, an approach by Rumpf [[en:ermittlung_der_materialdaten#references|[Rum61]]] for statistically packed, monodisperse particles is presented:
  
 $$σ_z = (1-ε) \cdot k \cdot \frac{F_H}{A_p} = \frac {(1-ε)}{ε} \cdot \frac {F_H}{{d_p}^2}$$ $$σ_z = (1-ε) \cdot k \cdot \frac{F_H}{A_p} = \frac {(1-ε)}{ε} \cdot \frac {F_H}{{d_p}^2}$$
Zeile 610: Zeile 606:
 {{ :en:rex310_en_120.svg?nolink&700 |}} {{ :en:rex310_en_120.svg?nolink&700 |}}
  
-In this setup, the agglomerates under investigation are placed into the circular specimen holder, compressed, and then twisted. Twisting refers to the rotation of the compression piston in the specimen holder, as known from the Jenike shear cell, allowing rearrangement and reorientation processes to take place. After the specimen holder is filled, its two halves are pulled apart, and the force required to separate them is measured. The tensile strength can then be calculated from the ratio of the breaking force to the cross-sectional area of the device. This and other testing methods are described in detail in [[en:gefuellte_polymere#references|[Sch75]]], [[en:gefuellte_polymere#references|[PC97]]], [[en:gefuellte_polymere#references|[Wic91]]].+In this setup, the agglomerates under investigation are placed into the circular specimen holder, compressed, and then twisted. Twisting refers to the rotation of the compression piston in the specimen holder, as known from the Jenike shear cell, allowing rearrangement and reorientation processes to take place. After the specimen holder is filled, its two halves are pulled apart, and the force required to separate them is measured. The tensile strength can then be calculated from the ratio of the breaking force to the cross-sectional area of the device. This and other testing methods are described in detail in [[en:ermittlung_der_materialdaten#references|[Sch75]]], [[en:ermittlung_der_materialdaten#references|[PC97]]], [[en:ermittlung_der_materialdaten#references|[Wic91]]].
  
 As an example, the tensile strength of talc is plotted as a function of porosity in the figure.  As an example, the tensile strength of talc is plotted as a function of porosity in the figure. 
Zeile 616: Zeile 612:
 {{ :en:rex310_en_118.svg?nolink&700 |}} {{ :en:rex310_en_118.svg?nolink&700 |}}
  
-The measurements were performed with an apparatus essentially similar to the one described above, which is described in detail in [[en:gefuellte_polymere#references|[Wic95]]].+The measurements were performed with an apparatus essentially similar to the one described above, which is described in detail in [[en:ermittlung_der_materialdaten#references|[Wic95]]].
  
 ==== Porosity ==== ==== Porosity ====
-Porosity is defined as the ratio of void volume to total volume [[en:gefuellte_polymere#references|[Wic95]]]:+Porosity is defined as the ratio of void volume to total volume [[en:ermittlung_der_materialdaten#references|[Wic95]]]:
  
 $$ψ = \frac{V_H}{V_{ges}} $$ $$ψ = \frac{V_H}{V_{ges}} $$
Zeile 637: Zeile 633:
 {{ :en:rex310_en_119.svg?nolink&700 |}} {{ :en:rex310_en_119.svg?nolink&700 |}}
  
-[[en:gefuellte_polymere#references|[Wic95]]]+[[en:ermittlung_der_materialdaten#references|[Wic95]]]
  
 In general, porosity measurements cannot distinguish between contributions from particle porosity $ψ_p$, agglomerate porosity $ψ_a$, and bulk porosity $ψ_b$. Instead, densities are usually measured. A porous material exhibits a lower density than the true solid density $ρ_f$. The particle density $ρ_p$ is related to porosity as follows: In general, porosity measurements cannot distinguish between contributions from particle porosity $ψ_p$, agglomerate porosity $ψ_a$, and bulk porosity $ψ_b$. Instead, densities are usually measured. A porous material exhibits a lower density than the true solid density $ρ_f$. The particle density $ρ_p$ is related to porosity as follows:
Zeile 662: Zeile 658:
  
 == Mercury Intrusion Method == == Mercury Intrusion Method ==
-The mercury intrusion method, proposed by Washburn in 1921 [[en:gefuellte_polymere#references|[Was21]]], is suitable for determining pore volume and pore size distribution. Mercury exhibits very poor wetting behavior and envelopes the agglomerates. The volume of mercury displaced by the agglomerate is measured with the mercury porosimeter illustrated in the figure. +The mercury intrusion method, proposed by Washburn in 1921 [[en:ermittlung_der_materialdaten#references|[Was21]]], is suitable for determining pore volume and pore size distribution. Mercury exhibits very poor wetting behavior and envelopes the agglomerates. The volume of mercury displaced by the agglomerate is measured with the mercury porosimeter illustrated in the figure.
- +
-FIXME PLATZHALTER ABBILDUNG 121: Quecksilber-Porosimeter [[en:gefuellte_polymere#references|[PHS79]]].+
  
-If the true solid density is known, the agglomerate density can be calculated in accordance with DIN 53193 or DIN 51057 from the displaced volume and the mass difference. Depending on the applied pressure, mercury penetrates into smaller pores in accordance with the Gauss–Laplace equation FIXME**(5.75)**:+If the true solid density is known, the agglomerate density can be calculated in accordance with DIN 53193 or DIN 51057 from the displaced volume and the mass difference. Depending on the applied pressure, mercury penetrates into smaller pores in accordance with the Gauss–Laplace equation **(4.75)**:
  
-$$p = \frac {2σcos(Θ)}{r}$$+$$p = \frac {2σcos(Θ)}{r} \tag{4.75}$$
  
 with $p$ = applied pressure, $σ$ = surface tension of mercury, $Θ$ = contact angle of mercury, and $r$ = pore radius. with $p$ = applied pressure, $σ$ = surface tension of mercury, $Θ$ = contact angle of mercury, and $r$ = pore radius.
  
-Using this equation, the pore size distribution can be calculated [[en:gefuellte_polymere#references|[PHS79]]]. At higher pressures, the compressibility of mercury must also be taken into account.+Using this equation, the pore size distribution can be calculated [[en:ermittlung_der_materialdaten#references|[PHS79]]]. At higher pressures, the compressibility of mercury must also be taken into account.
  
 ===== References ===== ===== References =====