≪ View Page

Unterschiede

Hier werden die Unterschiede zwischen zwei Versionen angezeigt.

Link zu dieser Vergleichsansicht

Nächste Überarbeitung		Vorhergehende Überarbeitung
en:grundlagenhandbuch:materialkenngroessen:polymerblends [2025/05/13 15:55] – angelegt deppe2en:grundlagenhandbuch:materialkenngroessen:polymerblends [2026/02/05 08:49] (aktuell) – pka
Zeile 1: Zeile 1:
 ====== Polymerblends ====== ====== Polymerblends ======
  
-  *[[en:Grundlagenhandbuch:Materialkenngrößen:Polymerblends:Grenzflächenspannung von Polymerblends]]+===== Interfacial Surface Tension of Polymer Blends ===== 
 + 
 +The interfacial tension can be determined experimentally using several methods, for example: 
 +  * "Breaking Thread", 
 +  * "Pendant Drop" and 
 +  * "Spinning Drop". 
 + 
 +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. 
 + 
 +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. 
 + 
 +{{ :en:grundlagenhandbuch:materialkenngroessen:en_sigma150_dlg_grundlagenhandbuch_materialkenngroessen_023.svg?500%nolink |}} 
 + 
 +**Figure:** Scematic of a capillary wave with its characterizing values 
 + 
 +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: 
 + 
 +$$\gamma_{12} = \frac{q \cdot \eta_c \cdot D_0}{\Omega(p,X)} \tag{1}$$ 
 + 
 +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): 
 + 
 +$$q = S \cdot \ln 10 \tag{2}$$ 
 + 
 +{{ :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 
 + 
 +The following equation is used to obtain a value for the vibration amplitude: 
 + 
 +$$a_s = \frac{D_{max} - D_{min}}{4} \tag{3}$$ 
 + 
 +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: 
 + 
 +$$p = \frac{\eta_d}{\eta_c} \tag{4}$$ 
 + 
 +And for the wave number, which is measured using: 
 + 
 +$$X = \frac{\pi \cdot D_0}{\lambda} \tag{5}$$ 
 + 
 +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 maximum value of the dimensionless growth rate $Ω_m$. 
 + 
 +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: 
 + 
 +$$\gamma_{12}(T) = \gamma_{12,0} - \gamma_{12,m} \cdot T \tag{6}$$ 
 + 
 + 
 +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. 
 + 
 +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: 
 + 
 +$$\gamma_{12} = g \cdot \Delta\rho \cdot d_1^2 \cdot \frac{1}{H} \tag{7}$$ 
 + 
 +{{ :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: 
 + 
 +$$S = \frac{d_2}{d_1} \tag{8}$$ 
 + 
 +Therefore d1 is the largest drop diameter and d2 the drop diameter with a distance from the apex of d1. Values of the correction factor 1/H can be determined numerically using tables with the following equations: 
 + 
 +$$\frac{1}{H} = \left(\frac{0,32720}{S^{2.56651}}\right) - 0,97553 \cdot S^2 + 0,84059 \cdot S - 0,18069 \tag{9}$$ 
 + 
 +for $0,401 \leq S \leq 0,46$, 
 + 
 +$$\frac{1}{H} = \left(\frac{0,31968}{S^{2.39725}}\right) - 0,46898 \cdot S^2 + 0,50059 \cdot S - 0,13261 \tag{10}$$ 
 + 
 +for $0,46 \leq S \leq 0,59$, 
 + 
 +$$\frac{1}{H} = \left(\frac{0,31522}{S^{2.62435}}\right) - 0,11714 \cdot S^2 + 0,15756 \cdot S - 0,05285 \tag{11}$$ 
 + 
 +for $0,59 \leq S \leq 0,68$, 
 + 
 +$$\frac{1}{H} = \left(\frac{0,31345}{S^{2.61267}}\right) - 0,09155 \cdot S^2 + 0,14701 \cdot S - 0,05877 \tag{12}$$ 
 + 
 +for $0,68 \leq S \leq 0,90$ and 
 + 
 +$$\frac{1}{H} = \left(\frac{0,30715}{S^{2.84636}}\right) - 0,69116 \cdot S^3 + 1,08315 \cdot S^2 - 0,18341 \cdot S - 0,20970 \tag{13}$$ 
 + 
 +for $0,90 \leq S \leq 1,00$. 
 + 
 +Using these equations the interfacial or surface tension can be calculated from the values of two diameters as well as the melt densities. But it must be ensured that the melt drop is in a state of equilibrium with the surrounding phase. At low viscous Newtonian fluids this is usually the case, whereas in the case of high viscoelastic media's the process can last for hours. 
 + 
 +Apart for the optical effort, this method is relatively simple to carry out as it does not require a great deal of apparatus. In practice however it requires a certain degree of deftness to build an analyzable drop. In addition some prerequisites and influences must be considered for the method to be a success. From equation (7) one can see that the melt densities are required to calculate the interfacial and surface tension. Though this data is barely mentioned in the literature. Therefore this data has to be determined using experiments, which can often lead to difficulties. When practicing this process one is confronted with many restrictions. When measuring the interfacial tension the melt drop is formed in the continuous melt phase of a secondary polymer. The conditions needed for an acceptable material combination are the incompatibility of the polymers as well as a not too high melt viscosity of the continuous phase that also has to be also transparent for the optical detection of the drop shape. Furthermore the formation of bubbles during the melt process due to exhausting gases or degradation phenomenon's of both phases can appear which leads to a variation in the shape of the drop and consequently to unrealistic values. 
 + 
 +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. 
 + 
 +The profile of the drop is based on the interfacial, the surface tension, the difference in density and the centrifugal force. As the influence of the gravity force is negligible, the interfacial tension (surface tension) is calculated using: 
 + 
 +$$\gamma_{12} = \frac{\Delta\rho \cdot \omega^2}{4 \cdot Q} \tag{14}$$ 
 + 
 +With the angular velocity Ω of the capillary and the constant Q: 
 + 
 +$$L_0 = \frac{(4/3) \cdot (Q \cdot R^2 + 1)}{(Q \cdot R^3)^{1/3}} \tag{15}$$ 
 + 
 +In this equation L0 is the balance length of the rotating drop and R is the radius of the drop. This method is especially used for measuring systems with extremely low interfacial tensions. Through the development of modern engineering control technology, measures of up to 10-5 - 10-6 m*N/m have been made possible. This principle excels as the interface is not disturbed by foreign bodies. As a result a de-mixing processes can be observed. The drawback of this method is the slow justification of the equilibrium state. When a fluid with an intermediate viscosity (300-500 Pas) was measured, equilibrium was finally reached after more than 3h at 6100 1/min.