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en:grundlagenhandbuch:materialkenngroessen:polymerblends [2026/01/26 11:00] – deppe2en:grundlagenhandbuch:materialkenngroessen:polymerblends [2026/02/05 08:49] (aktuell) – pka
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 ====== Polymerblends ====== ====== Polymerblends ======
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-  *[[en:Grundlagenhandbuch:Materialkenngrößen:Polymerblends:Grenzflächenspannung von Polymerblends]] 
- 
  
 ===== Interfacial Surface Tension of Polymer Blends ===== ===== Interfacial Surface Tension of Polymer Blends =====
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   * "Spinning Drop".   * "Spinning Drop".
  
-The "Breaking Thread"- method is based on the theoretical basis of the description of the break-up of a Newton thread in a Newtonian matrix. Indeed this method is restricted on binary systems where the melt temperature of the disperse phase is above the one of the matrix phase. In addition to this the viscosity at zero shear rate η0 of the matrix should not exceed 40kPas. The experimental setup to obtain the measurements is displayed in the figure. Through-out the test, the system is cooled by nitrogen. Before the measuring starts the system is heated for approximately 10 minutes at 220°C in order to minimise retardation effects during the melting process. After this the heating of the systems with the required temperature follows. Once the thread has been melted capillary waves appear at the interface of the matrix. The whole process is re-corded with a CCD- camera.+The ‘breaking thread’ method is based on the theoretical description of the breakup of a liquid Newtonian thread in a Newtonian matrix. However, this method is limited to multi-component systems in which the melting temperature of the dispersed phase is higher than that of the matrix. In addition, the zero viscosity $\eta_0$ (viscosity $\eta$ at $\dot{\gamma}$ towards 0) of the matrix should not exceed 40 kPas. The following image shows the schematic structure of the test rig set up for the measurements. The heating table is flushed with nitrogen throughout the entire duration of the experiment. Before the measurement begins, the system is tempered in the heating table for approximately 10 minutes at 220 °C to minimise retardation effects during melting. The system is then heated to the desired test temperature. As soon as the filament has melted, capillary waves form at its interface with the matrix. The entire process is recorded with a CCD camera.
  
 This sinus shaped capillary wave or thread constriction is analyzed and entered into a computer in intervals. This sinus shaped capillary wave or thread constriction is analyzed and entered into a computer in intervals.
  
-**Figure:** Experimental setup for the detection and analyze of disperse thread breaking processes with a heated table for the detection of the interfacial tension.+From the thread the initial diameter $D_0$, the wavelength $\lambda$ the largest and the smallest thread diameter $D_{max}$ and $D_{min}$ are measured. The figure shows the principle shape of such capillary waves with their characterizing values.
  
-From the thread the initial diameter D0, the wavelength λ the largest and the smallest thread diameter Dmax und Dmin are measured. The figure shows the principle shape of such capillary waves with their characterizing values.+{{ :en:grundlagenhandbuch:materialkenngroessen:en_sigma150_dlg_grundlagenhandbuch_materialkenngroessen_023.svg?500%nolink |}}
  
-**Figure:** Sinus shaped thread constriction with the wave length λ, the max. and the min. amplitude Dmax and Dmin, and the initial diameter D0+**Figure:** Scematic of a capillary wave with its characterizing values
  
-The interfacial tension γ12 is a function of the amplitude growth rate q, the dimensionless growth rate Ω, the matrix viscosity ηc and the outer thread diameter D0 . This is written as follows:+The interfacial tension $\gamma_{12}$  is a function of the amplitude growth rate $q$, the dimensionless growth rate $Ω$, the matrix viscosity $\eta_c$ and the outer thread diameter $D_0$ . This is written as follows:
  
 $$\gamma_{12} = \frac{q \cdot \eta_c \cdot D_0}{\Omega(p,X)} \tag{1}$$ $$\gamma_{12} = \frac{q \cdot \eta_c \cdot D_0}{\Omega(p,X)} \tag{1}$$
  
-The amplitude growth rate q can be determined by the slope S of the relative amplitude $\log \left(2 \cdot \frac{a_s}{D_0}\right)$ over the time (see figure):+The amplitude growth rate $q$ can be determined by the slope $S$ of the relative amplitude $\log \left(2 \cdot \frac{a_s}{D_0}\right)$ over the time (see figure):
  
 $$q = S \cdot \ln 10 \tag{2}$$ $$q = S \cdot \ln 10 \tag{2}$$
 +
 +{{ :en:grundlagenhandbuch:materialkenngroessen:en_sigma150_dlg_grundlagenhandbuch_materialkenngroessen_024.svg?500%nolink |}}
  
 **Figure:** Profile of the relative amplitude over the time for a PPT/B4 –and a PPH/B3 -blend at 260 °C **Figure:** Profile of the relative amplitude over the time for a PPT/B4 –and a PPH/B3 -blend at 260 °C
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 $$a_s = \frac{D_{max} - D_{min}}{4} \tag{3}$$ $$a_s = \frac{D_{max} - D_{min}}{4} \tag{3}$$
  
-To calculate the interfacial tension λ12 , the dimensionless growth rate $\Omega(p,X)$ is used. The following rules are applied for the viscosity ratio:+To calculate the interfacial tension $\gamma_{12}$ , the dimensionless growth rate $\Omega(p,X)$ is used. The following rules are applied for the viscosity ratio:
  
 $$p = \frac{\eta_d}{\eta_c} \tag{4}$$ $$p = \frac{\eta_d}{\eta_c} \tag{4}$$
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 $$X = \frac{\pi \cdot D_0}{\lambda} \tag{5}$$ $$X = \frac{\pi \cdot D_0}{\lambda} \tag{5}$$
  
-The figure shows the profile of the dimensionless growth rate Ω independent from viscosity p and the wave number X. The solid line represents the maxi-mum value of the dimensionless growth rate Ωm.+The figure shows the profile of the dimensionless growth rate $Ω$ independent from viscosity $p$ and the wave number $X$. The solid line represents the maximum value of the dimensionless growth rate $Ω_m$.
  
-If one plots the determined λ12-values for the different temperatures T, the pair of values above the crystalline melt temperature TK for partially crystalline polymer pairs, the glass transition temperature TG for amorphous polymer pairs, are approximated through a linear approximation function in the following way:+If one plots the determined $\gamma_{12}$-values for the different temperatures $T$, the pair of values above the crystalline melt temperature $T_K$ for partially crystalline polymer pairs, the glass transition temperature $T_G$ for amorphous polymer pairs, are approximated through a linear approximation function in the following way:
  
 $$\gamma_{12}(T) = \gamma_{12,0} - \gamma_{12,m} \cdot T \tag{6}$$ $$\gamma_{12}(T) = \gamma_{12,0} - \gamma_{12,m} \cdot T \tag{6}$$
  
-**Figure:** Dimensionless growth rate Ω as a function of the wave number X and the viscosity ratio p. 
  
 The value γ12,0 is the point of intersection of the approximation function with the co-ordinate axis while γ12,m is common with the slope of this function. In the figure one can see the principle profile of the interfacial tension γ12, as a function of temperature T, for a polypropylene (PP) / polyamide (PA6)- blend. The value γ12,0 is the point of intersection of the approximation function with the co-ordinate axis while γ12,m is common with the slope of this function. In the figure one can see the principle profile of the interfacial tension γ12, as a function of temperature T, for a polypropylene (PP) / polyamide (PA6)- blend.
 +
 +{{ :en:grundlagenhandbuch:materialkenngroessen:en_sigma150_dlg_grundlagenhandbuch_materialkenngroessen_025.svg?500%nolink |}}
  
 **Figure:** Profile of the interfacial tension γ12 as a function of temperature T for a partially crystalline polypropylene (PP) / polyamide (PA6) – blend. **Figure:** Profile of the interfacial tension γ12 as a function of temperature T for a partially crystalline polypropylene (PP) / polyamide (PA6) – blend.
  
-Referring to the literature one can find the approximation value γ12,m=0,01 mN/m °C the slope of the straight line. In reality this value varies when using different polymer pairs. Only two measurements of the interfacial tension γ12, at two different temperatures T are required to determine the approximation function. When using the "Breaking Thread" method one is able to determine the interfacial tensions γ12 above the melt temperature TK with the help of the advanced approximation function with only a few experiments. The "pendant drop" method is the most versatile and reliable process for measuring the interfacial tension of polymers. On the one hand the state of equilibrium between the polymer phases adjusts rapidly in comparison to other methods and on the other hand this method has the ability to perform the measurements in an inert atmosphere. The process is based on the optical measurement of the shape of a fluid or melt drop that is embedded with the surrounding phase in a hydrostatic equilibrium (see figure). This shape is comparable with that of a theoretically predicted shape of drop. This shape can be calculated on the basis of the Gauss-Laplace equation. The interfacial- or surface tension is then described as follows:+Referring to the literature one can find the approximation value $\gamma_{12,0}$ the slope of the straight line. In reality this value varies when using different polymer pairs. Only two measurements of the interfacial tension γ12, at two different temperatures T are required to determine the approximation function. When using the "Breaking Thread" method one is able to determine the interfacial tensions γ12 above the melt temperature TK with the help of the advanced approximation function with only a few experiments. The "pendant drop" method is the most versatile and reliable process for measuring the interfacial tension of polymers. On the one hand the state of equilibrium between the polymer phases adjusts rapidly in comparison to other methods and on the other hand this method has the ability to perform the measurements in an inert atmosphere. The process is based on the optical measurement of the shape of a fluid or melt drop that is embedded with the surrounding phase in a hydrostatic equilibrium (see figure). This shape is comparable with that of a theoretically predicted shape of drop. This shape can be calculated on the basis of the Gauss-Laplace equation. The interfacial- or surface tension is then described as follows:
  
 $$\gamma_{12} = g \cdot \Delta\rho \cdot d_1^2 \cdot \frac{1}{H} \tag{7}$$ $$\gamma_{12} = g \cdot \Delta\rho \cdot d_1^2 \cdot \frac{1}{H} \tag{7}$$
  
-**Figure:** Profile of the pendant drop.+{{ :en:grundlagenhandbuch:materialkenngroessen:en_sigma150_dlg_grundlagenhandbuch_materialkenngroessen_026.svg?200%nolink |}} 
 + 
 +**Figure:** Shape of a hanging droplet
  
 Within equation (7) g is the gravitational acceleration, Δρ is the density difference of the polymer phases and 1/H is a correction factor whose value is dependent on the shape factor. This shape factor is determined using: Within equation (7) g is the gravitational acceleration, Δρ is the density difference of the polymer phases and 1/H is a correction factor whose value is dependent on the shape factor. This shape factor is determined using:
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 The measuring principle of the "spinning drop method" is also based on the measurement of the shape of a drop, which is built under the influence of the centrifugal force. If a cylindrical capillary containing a drop and a specifically heavier fluid, is rotated with a constant high velocity (2000-8000 1/min) around its longitudinal axis then the drop assumes a cylindrical shape with rounded ends due to the influence of the centrifugal force (see figure) The measuring principle of the "spinning drop method" is also based on the measurement of the shape of a drop, which is built under the influence of the centrifugal force. If a cylindrical capillary containing a drop and a specifically heavier fluid, is rotated with a constant high velocity (2000-8000 1/min) around its longitudinal axis then the drop assumes a cylindrical shape with rounded ends due to the influence of the centrifugal force (see figure)
 +
 +{{ :en:grundlagenhandbuch:materialkenngroessen:en_sigma150_dlg_grundlagenhandbuch_materialkenngroessen_027.svg?500%nolink |}}
  
 **Figure:** Principle layout for measuring the interfacial tension with the spinning drop method. The drop 1 of the low weighted phase is deformed to the shape 2. **Figure:** Principle layout for measuring the interfacial tension with the spinning drop method. The drop 1 of the low weighted phase is deformed to the shape 2.