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en:ermittlung_der_materialdaten [2026/05/10 23:33] – deppe2en:ermittlung_der_materialdaten [2026/05/27 23:33] (aktuell) – [Filled polymers] deppe2
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 The WLF equation provides a better description than the Arrhenius approach, especially for amorphous polymers whose molten state begins at a temperature slightly above the glass transition temperature. The WLF equation provides a better description than the Arrhenius approach, especially for amorphous polymers whose molten state begins at a temperature slightly above the glass transition temperature.
-This assumes that the segment mobility of polymers near the glass transition temperature is primarily determined by the free volume, which increases approximately linearly with the distance from the glass transition temperature TG. It is assumed that the segment mobility of polymers near the glass transition temperature is predominantly determined by the free volume, which increases approximately linearly with the distance from the glass transition temperature TG [[en:ermittlung_der_materialdaten#references|[Fer80]]]. If a temperature approximately 50°C above the glass transition temperature $T_G$ is selected as the standard temperature $T_S$, the parameters $C_1$ and $C_2$ in the equation can be regarded as material-independent [[en:reine_polymere#references|[Mel95]]].+This assumes that the segment mobility of polymers near the glass transition temperature is primarily determined by the free volume, which increases approximately linearly with the distance from the glass transition temperature TG. It is assumed that the segment mobility of polymers near the glass transition temperature is predominantly determined by the free volume, which increases approximately linearly with the distance from the glass transition temperature TG [[en:ermittlung_der_materialdaten#references|[Fer80]]]. If a temperature approximately 50°C above the glass transition temperature $T_G$ is selected as the standard temperature $T_S$, the parameters $C_1$ and $C_2$ in the equation can be regarded as material-independent [[en:ermittlung_der_materialdaten#references|[Mel95]]].
  
 Alternatively, the following approach can also be used: Alternatively, the following approach can also be used:
Zeile 92: Zeile 92:
 The calculation of both the melting behavior and the temperature development in The calculation of both the melting behavior and the temperature development in
 power melts requires a comprehensive knowledge of the thermodynamic material power melts requires a comprehensive knowledge of the thermodynamic material
-behavior [[en:reine_polymere#references|[Hen89]]]. The thermodynamic properties are dependent on both pressure and+behavior [[en:ermittlung_der_materialdaten#references|[Hen89]]]. The thermodynamic properties are dependent on both pressure and
 temperature and show a different material property in the solid state and in the melt temperature and show a different material property in the solid state and in the melt
 state. state.
Zeile 149: Zeile 149:
 In this function, the index $0$ denotes the material property at $0 °C$, while the index $m$ represents the slope of the property function. In this function, the index $0$ denotes the material property at $0 °C$, while the index $m$ represents the slope of the property function.
  
-Since REX / PSI / SIGMA does not account for pressure effects, the determination of the thermodynamic material properties should always be performed at a mean pressure [[en:reine_polymere#references|[Mel95]]].+Since REX / PSI / SIGMA does not account for pressure effects, the determination of the thermodynamic material properties should always be performed at a mean pressure [[en:ermittlung_der_materialdaten#references|[Mel95]]].
  
 The specific enthalpy $∆h$ results from the integration of the specific heat capacity $c$ over the temperature range between $T_1$ and $T_2$, which can be derived from DSC analysis. In this way, the amount of heat per unit mass of the polymer that must be supplied is obtained. The following relation applies: The specific enthalpy $∆h$ results from the integration of the specific heat capacity $c$ over the temperature range between $T_1$ and $T_2$, which can be derived from DSC analysis. In this way, the amount of heat per unit mass of the polymer that must be supplied is obtained. The following relation applies:
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 ==== Thermal Conductivity ==== ==== Thermal Conductivity ====
  
-In heat conduction processes, a distinction is made between steady-state and non-steady-state temperature fields. In steady-state temperature fields, the thermal conductivity $λ$ appears as a material property. It is temperature dependent and lower for amorphous materials than for semi-crystalline ones [[en:reine_polymere#references|[Mel95]]].+In heat conduction processes, a distinction is made between steady-state and non-steady-state temperature fields. In steady-state temperature fields, the thermal conductivity $λ$ appears as a material property. It is temperature dependent and lower for amorphous materials than for semi-crystalline ones [[en:ermittlung_der_materialdaten#references|[Mel95]]].
  
 The determination of the thermal conductivity $λ$ can, for example, be carried out using a Thermoflixer device manufactured by SWO Polymertechnik. The measuring principle is illustrated in the following figure. The determination of the thermal conductivity $λ$ can, for example, be carried out using a Thermoflixer device manufactured by SWO Polymertechnik. The measuring principle is illustrated in the following figure.
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.
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 $$γ_{12} (T) = γ_{12.0} - γ_{12.m} \cdot T$$ $$γ_{12} (T) = γ_{12.0} - γ_{12.m} \cdot T$$
- 
-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.
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 ==== 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:
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 $$σ_z = \frac{F_{N,max}}{A} = \frac {1}{A} Σ_{i=1} F_{Np,i} (Δl)$$ $$σ_z = \frac{F_{N,max}}{A} = \frac {1}{A} Σ_{i=1} F_{Np,i} (Δl)$$
  
-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. 
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 {{ :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 =====