Polymer Physics 2015 Matilda Larsson Dynamic Mechanical Analysis of Solid Polymers and Polymer Melts Polymer & Materials Chemistry
Introduction Two common instruments for dynamic mechanical thermal analysis are the dynamic mechanical analyzer (DMA) for solid state experiments and the rheometer for melt state experiments (in shear mode). Apart from the application of these instruments in research, they are also used in industry. In a simplified way you can say that the DMA can be used to test the dynamic mechanical properties of an already manufactured plastic detail, such as a car bumper or a plastic bag, while the Rheometer can be used to understand molecular structure and how these details can be processed and manufactured, i.e. the flow of polymer melts. In this lab session both the rheometer and the DMA will be used. Theory A rheometer and a DMA can be used to measure the dynamic mechanical properties and to detect thermal transitions of polymeric materials. The material is subjected to a sinusoidal strain or stress at varying frequencies and temperatures. The response of the material to the input signal varies depending on molecular mobility, the degree of crystallinity, the temperature and the frequency. According to the response of the material it can be characterized as: ELASTIC - A material that stores and releases all mechanical energy when deformed is defined as pure elastic. The material will return back to its original shape and position instantaneously. A good example is a steel spring. VISCOUS - A material that loses all mechanical energy when deformed is defined as pure viscous. The mechanical energy is dissipated as heat. It does not return back to its original shape. A typical example of a material which exhibits only viscous behavior would be a Newtonian fluid (eg water). VISCO-ELASTIC - Polymers exhibit visco-elastic behavior when deformed. They will simultaneously store and lose mechanical energy. A material that loses a high amount of energy has a high loss modulus and a good example of this is an amorphous polymer at the glass transition. A polymeric material has time dependant properties. This means that the mechanical properties depend on the frequency or rate of deformation. In some cases such as for instance car tires, which are exposed to dynamic stress it is clear that this is very important for the application. In other cases such as a plastic shelf under constant load, it is less drastic but still important in the performance during longer times. From a fundamental point of view, when working with polymer research, the time dependence is also very interesting because it can reveal information about the molecular structure of the polymer.
Technique If a sinusoidal force is applied to an elastic material the strain will be in phase with the stress. Viscous materials exhibit a 90 phase lag. A visco-elastic material exhibits a phase lag between 0 and 90. ( Rheology is used to measure dynamic mechanical properties such as modulus, damping and time dependant visco-elastic properties. The Modulus is a measure of resistance against deformation. Damping is the capacity to absorb mechanical energy. Mechanical energy is lost from conversion of mechanical energy into heat. At the glass-transition temperature the material becomes softer and this leads to a decreased elastic modulus and the damping (loss modulus) reaches a maximum. The two primary outputs of a rheological measurement are the dynamic shear modulus G d ( ) and the phase angle. The dynamic modulus is defined as the amplitude of stress divided by the amplitude of strain and the phase angle is the phase lag between the input sinusoidal strain and the sinusoidal output stress. The dynamic modulus can be split into two parts: G'( ) = G d ( ) cos ( ) G''( ) = G d ( ) sin ( ) G' is the shear storage modulus and represents the stored and recovered elastic energy of the sample during one cycle. G'' is the shear loss modulus and represents the dissipated energy of the sample per cycle. tan = G''/G' This principle is analogous to DMA where the complex tensile modulus E*(ω), also known as the elastic modulus or Young s modulus, is measured. The storage modulus E is a measure of the stiffness of the material, or the ability to store and return energy. The loss modulus E
corresponds to the materials ability to dissipate energy, and tan δ is a measure of the damping ability of the material. Linear Viscoelastic Region Using a strain at which the polymer is within its linear viscoelastic region (LVR), where the stress is linearly related to the strain, ensures that the measured properties depends on properties of the sample, such as molecular structure, and not permanent deformation of the material.
Dynamic Mechanical Analyzer The sample is placed in a clamp. A drive motor applies a sinusoidal deformation to the sample. A drive shaft transfers the force. An optical sensor measures the deformation under the applied force. Different clamps are available, for example tensile-clamp and compressionclamp. The clamp is chosen depending on the sample properties and shape. Rheometer Rheometer Schematic 1 6 5 2 3 4 7 1 Lead screw 2 Draw rod 3 Optical encoder 4 Air bearing 5 Drive shaft 6 Drag cup motor 7 Measuring geometry 8 Peltier elements 9 Heat exchanger 10 Pt 100 temperature sensor 11 Durable chrome surface 12 Normal force transducer 13 Auto gap set motor and encoder 10 11 12 8 9 13
Operation procedure 1. Solid sample, clamped bending In this experiment the mechanical properties of a solid sample of ABS will be investigated over a wide temperature range. In order to do this a temperature ramp will be programmed from room temperature to 150 C. In this range, a sinusoidal strain will be applied to the sample in bending. The correct strain will be determined by first performing a strain sweep, which will define the linear viscoelastic region of the sample. a) Strain sweep Start the software for DMA. The instrument and clamp has previously been calibrated, but check that the clamp is properly tightened. Measure the dimensions of the sample and specify these in the software Mount the sample in the clamp. Choose Multi strain/strain sweep procedure. o Amplitude 1 to 100 μm o Log 5 points/decade o Temperature 25 C o Frequency 1 Hz Perform the measurement Determine the LVR in TA Universal Analysis b) Temperature ramp Choose the Multi-Frequency Strain and Temp ramp/freq sweep procedure and use a strain obtained from the linear region of the strain sweep. o Start temperature 35 C o Rate 3 C/min o Equilibrium time 2 min o % strain o Frequency 1 Hz Perform the measurement Analyze the sample in TA Universal Analysis
2. Melt state, time-temperature superposition In this experiment a polymer, PVAc, in the melt state will be analyzed over a wide time/frequency range. This is done by performing time-temperature superpositioning. Frequency sweeps at different temperatures will be shifted along the frequency axis to cover a wide range of frequencies. a) Strain sweep Use the 25 mm plate. Turn on the cooling water. Perform a zero gap. Reset normal force. Perform rotational mapping. Place the sample disk centered on the Peltier plate. Set the temperature to the correct temperature. Lower the top plate carefully using the arrows on the instruments control panel. When the distance is ca 5 mm, move to the computer lower the plate until it touches the sample. The accurate distance can be determined by observing the Normal force. It should be around 1-2. Open procedure and choose strain sweep PVAC o % strain 0.01-100 o Log mode o 5 points/decade o Temperature 85 C o Frequency 1 Hz Perform the strain sweep b) Frequency sweeps Open procedure and choose the frequency sweep procedure and use a strain obtained from the linear region of the strain sweep. o Frequency 100-0.01 Hz o % strain o Temperature 85 C Perform the measurement, firstly at 85 C, than at four additional temperatures in the interval between 80-110 C. c) Time-temperature superposition Open the frequency sweep graphs in the Rheology Advantage Data Analysis program. Plot delta vs. log frequency for all measurements in one graph. Choose begin session in the TTS menu. Choose a reference curve and shift the other curves horizontally until they fit on top of each other. Change the Y-axis to G d, choose toggle axis icon and shift the curves vertically until they all fit on top of each other, start from the reference. Compare the X-shifts plot to the WLF curve and the Arrhenius curve. Open the data in a table in order to obtain the shift factor values.
Report All the results obtained in the laboratory should be presented in columns and figures with the correct units. Give comments on the results. The report should include the plots according to Table 1. Table 1: Plots which should be included in the lab report. Experiment Solid state Melt state Results Plot E' vs. temperature Plot E'' vs. temperature Plot tan vs. temperature Plot G d vs. frequency Plot vs. frequency Plot the log shift factors vs. temperature G d vs. frequency including all measurements shifted along the frequency axis Plot your log shift factors, the WLF equation and the Arrhenius equation, all in the same plot, in the temperature range of 40-250 C. In addition to the general instruction, the report should also contain: 1. Short theory (max. 1 page). 2. Discuss how the temperature affects the rheological properties. Determine the T g of the solid sample polymer. 3. Account for the different regions of the E' vs. temperature curve. 4. Perform time-temperature superposition for the data received from the frequency sweeps. 5. Compare the shift factors obtained experimentally with those obtained from the WLF equation, how does your log shift factor vs. temperature plot look compared to WLF and Arrhenius respectively? What are the limitations of the WLF equation?