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Thermoanalytical techniques play an important role to characterize a polymer. There are many methods which include differential scanning calorimetry (DSC), differential thermal analysis (DMTA), dilatometry, measuring the different physical properties, such as polymerisation kinetics, glass transition temperature, melting and crystallization kinetics . The easiest way to measure the different thermal properties is called dilatometry . It is widely used to detect the length, area or volume dimensional changes as a function of temperature.
2. An overview of dilatometry
During heating and cooling, the sample which is fitted in a dilatometer changes in length (expansion and shrinkage). That is to say thermal events can be studied as the change in a dimension of a sample by dilatometry as the temperature is varied. Basically, a dilatometer consists of a furnace, a sample holder system, a control/sample thermocouple, a sample displacement measuring system which includes a pushrod and a linear variable displacement transducer (LVDT) sensor, a user-adjustable counterweighted pulley system to ensure the test sample has a constant and uniform contact load, a control board for furnace control and data acquisition and a dilatometer software .
2.1 Test procedure
2.1.1 Expansion Measurement
Firstly, the sample is put into a holder, a rod which is called the pushrod that touches the sample to detect the dimensional change. After that, when the sample is heated, the expansion causes a motion in the opposite directions to the tube and the pushrod. Then a transducer responses to this movement of the sample. It may be an ordinary dial gauge, a linear variable displacement transducer (LVDT), differential transformer or a capacitive one .
Fig. 1. Scheme of a traditional dilatometer with a pushrod and a displacement transducer 
2.1.2 Temperature Control and Measurement
In a dilatometry system, thermocouples are often used. It should be necessary to control the furnace with a uniform sample temperature. It is not good for a precise measurement to attach or embed the thermocouple into the sample, which may lead to an intervention with the free movement of the sample, it is best to keep the thermocouple between the sample and the dilatometer tube .
The expansion of the dilatometer tube should be defined exactly, because the movement of the pushrod can be regarded as the difference between the expansion of the dilatometer tube and the sample .
2.1.4 Heating Programmes
Basically, there are two types of heating, one is called ramp heating which provides a constant increasing rate, the other one is called stepwise heating. With stepwise heating, the sample is permitted to reach thermal equilibrium at pre-set temperatures .
2.2 Common configurations
2.2.1 Horizontal configuration
In the horizontal configuration, it is suitable to measure a thin sample with a position of lying in a dilatometer tube. The reason can be explained as follows. When the temperature program supplies a high heating speed, the thin shape sample will be obtained a low temperature gradient . The main weakness of this configuration is the difficulty for shrinkage or sintering work. It should be noted that a reasonable force given by the pushrod overcomes the friction between it and the tube. If the sample is softening, shrinkage or sintering, its length will decrease instead of increasing when heated. Likewise, the force cannot overcome the friction sufficiently, in addition, there is not an enough force to keep the sample pressed against the end plate. That is why a gap develops between the sample and the plate. Another circumstance that uses a dilatometer with a flat leaf spring suspended for the pushrod makes this phenomenon worse. A comparison of the horizontal system and the vertical system can show that the horizontal furnace ensures reasonable thermal uniformity. It is advisable to choose a horizontal system for long samples .
2.2.2 Vertical configuration
In the vertical configuration, the sample stands on the plate-end of the dilatometer tube . The dilatometer is fitted vertically into a furnace which is either a tube furnace or a pot furnace . A major advantage of vertical system is that it has the ability to study sintering or softening samples, because if the sample shortens when heated, it will be held on the plate by gravity. So it is suitable to measure large shrinkages.
2.3 Bahr dilatometer
This is the dilatometer to be used in this project.
2.3.1 General description and system construction
Definition of TTT, DTTT, TTA curves.
"The dilatometry type 805A/D is a quenching and deformation dilatometer. It is used for the registration of phase and structure transitions. The determined deformation parameters can then be used for the creation of TTT-, DTTT and TTA diagrams or for the calculation of flow curves ."
2.3.2 Two types of Bahr-Dilatometer
There are two types of Bahr-dilatometer, one is a quenching dilatometer which measures the phase transitions occurring in the continuous cooling process or in the isothermal holding phase. The other one is called a deformation dilatometer. It has an additional application that includes the investigation of creep and relaxation processes. The quenching dilatometer can quickly be converted into a deformation dilatometer by the assembly or disassembly of components.
2.3.3 Main components
Fig2. Main components of DIL805 
left 19'' inch main frame
right 19''inch main frame
quenching -and deformation measuring head respectively
vacuum unit: pre-pump
vacuum unit: turbo molecular pump and angle valve
supply of cooling water and gas
separate deformation computer responsible for the control and measuring data recording during a deformation step
Windows computer and computer peripheral with monitor
2.3.4 Deformation measuring head DIL805D
Fig. 3. Deformation measuring head DIL805D 
The located force sensor is on the left outside of the measuring chamber. Half of the displacement transducer is in the right chamber and half in the left chamber. The sample is mounted in the Al2O3 measuring system.
2.3.5 Heating ring
Fig. 4. The heater used in this project 
This extension enables the carrying out of a test with non-electroconductive samples.
3. Glass transition and relaxation transition
3.1 Glass transition
The glass transition is a phenomenon observed in linear amorphous polymers. "It is a reversible change of the polymer between rubbery and glassy states, and the temperature at which this occurs, is called the glass transition temperature (Tg) ."
3.2 Theories of the Glass Transition
3.2.1 Free volume theory
The condition for molecular motion is a hole or a place where there are vacancies and voids to exchange with molecule segments. That is to say, molecular motion can not occur without the holes which are called free volume. 
In 1950, Fox and Flory  studied the glass transition and free volume of polystyrene as a function of molecular weight and relaxation time. At about Tg, the specific volume (Vf) can be indicated as
Where K is related to the free volume at 0°K, and and represents the cubic (volume) expansion coef¬cients in the rubbery and glassy states.
Simha and Boyer  assumed that at Tg, the free volume should be expressed as
free volume theory.jpg
Fig. 5. A schematic diagram illustrating free volume as calculated by Simha and Boyer 
Substitution of the quantity
V=V0, R+ (3)
leads to the relation
Where V is the speci¬c volume, and V0, G and V0, R are the volumes extrapolated to 00K using and as the coef¬cients of expansion, respectively. Based on the data of polystyrene, Simha and Boyer concluded that
Equation (5) shows the discovery that the free volume is 11.3% at the glass transition temperature. This is one of the largest theoretical values. Some early findings give evidence of the free volume about 2% [10, 12].
3.2.2 The Kinetic Theory of the Glass Transition
3.2.3 Thermodynamic theory
3.3 Influence factor of glass transition temperature
Briefly, the following features are known to influence the glass transition temperature
The presence of flexible groups. Since they increase the energy required to rotate the molecule about primary bonds in the main polymer chain. This is especially true of side chains or branches.
Pressure. Part of the free volume can be expelled from polymers by putting on pressure. Therefore, the polymer must increase its temperature in order to get a regular free volume fraction, which equals to increasing the glass transition temperature.
Hydrogen bonds between polymer chains.
Relative molar mass, which in fluencies Tg because higher molar mass (M>Mc) polymers have entanglements which prevent the motion of the central portions of long chains than polymers of lower molar mass.
The presence of plasticisers. 
3.2 Minor transition
Besides the glass transition, amorphous polymers usually exist at least one relaxation which is called the secondary relaxation (transition).  It is significant to scan the secondary relaxation since it represents the subtler changes in polymeric materials. .relaxations are manifestations of motions that occur in the glassy state, and must result from localized motions. 
Fig. 6. Modulus values change with temperature and transitions in materials 
The motions styles are listed as follow
Chain slippage (2)Large scale chain (3) Gradual main chain
(4) Side groups (5) Bend and stretch (6) Local motions
4. Differential Scanning Calorimetry
Differential scanning calorimetry (DSC) is based upon the measurement of the difference in the amount of heat flow between the sample and an inert reference. Basically, DSC instruments can be divided into two categories, one is the heat flux DSC, the other one is the power/ compensation DSC . Although the two types use totally different routes to detect heat flow rates, they are both refered to as differential scanning calorimeters.
4.1 Types of DSC
4.1.1 Heat flux DSC
For heat flux DSC, heat is transferred to the sample and reference via only one well-defined heat conduction path. Along this path, a temperature distinction between the sample and reference can be got, which acts as a measured signal and is portional to the heat flow rate. [see Eq.(1)]
-1  (6)
Whereis the heat flow rate (W), is the thermal conductivity (Wm-1K-1), A is the cross-sectional area (m2), is the temperature difference (K), and l is the length (m).
Some limitation of this technique can be listed. Firstly, the thermal resistance should be calibrated since there is a thermal lag between sample and sensor . Secondly, the differences between the sample and reference lead to a large amount of heat loss. Finally, the radiation and convection may result in a heat exchange with the environment . Nevertheless, it has advantages such as a low cost, a relatively simple way of manipulation to occupy a large market share.
4.1.2 Power/compensation DSC
In a power/compensation DSC, the sample and the reference are heated separately with individual heaters. The reference should be a well-characterized heat capacity material. Likewise, the heater should ensure that both the sample and the reference have an exactly same rate of temperature increase. In order to maintain T=0, the power of the heater needs to be changed. Therefore, the result of thermal changes can be obtained by detecting the difference in power supplied to the heaters. This outcome can represent the energy change (heat flow) in the sample effectively . That is to say, when a sample undergoes a physical transition, more or less energy will flow to it than the reference. The exothermic or endothermic behaviours in the process determines how the energy flows.
4.2 DSC curves
Fig. 7. A schematic DSC curve 
A DSC curve is the result of an experiment on cooling or heating. The enthalpies of transitions can be calculated from the following equation
Where H is the enthalpy of transition, K is the calorimetric constant, and A is the area under the curve.
4.3 Temperature-Modulated DSC
Now heat flux and power/compensation DSC can run in the temperature modulated way commercially . In this case two parts of heat flow rate exist, which can be categorized as "reversing" part and "non-reversing" part. The static heat flow is calculated by averaging over a period along the measured curve . It is easy to use MT-DSC to separate identical processes  and to measure the heat capacity precisely . The measured data are not only influenced by sample mass, thermal contact and scanning rate, but also influenced by the frequency and the temperature amplitude.
5. Dynamic mechanical thermal analysis
Dynamic mechanical thermal analysis (DMTA) is a method most used to obtain the viscoelastic properties of polymers and is the most sensitive method to measure the glass transition temperature [14.21]. It measures the stiffness and damping of polymers and reveals modulus and tan delta. Secondary relaxation events are readily observed by DMTA, such as the and transitions, simply cannot be detected by any other thermal technique . In this case, a frequency is used and the temperature should be varied from typically -100 to 200. So changes in molecular motion can be studied . There are two techniques of this method. One is the decay of free oscillations which applies a discontinuous force to the sample . It can be concluded that the sample has an applied force and oscillates after the force is removed. The other is forced oscillation which is the most widely used one. Under such conditions, the result is applied as a sinusoidal force. Because of the time-dependent relaxation occurring in polymeric material, the strain lags behind the given stress which has a frequency of oscillation of Hz, the stress is given by
Where t is the time and is the maximum stress.
The corresponding strain is shown as
Where is the phase angle and represents the amount by which the strain lags the stress, and is a measure of energy dissipation of a material [6.21].
Fig. 8. Lag of strain behind stress in dynamic testing
Ideal solids should follow the Hooke's law. Ideal fluids should follow Newton's law. A Ploymer is a kind of material with properties which include both the elastic properties and viscosity properties. Therefore, it has an elastic modulus (G') which is the storage modulus and a viscous modulus which is also called loss modulus (G''). The two moduli make up a complex modulus (G*) that can be shown as
The results of DMTA are commonly shown as plots of Log E' and tan as a function of temperature.
Fig. 9. Plot of storage modulus and tan vs temperature
At the glass transition temperature, a large drop of storage modulus can occurs. The loss modulus relates to the resistance to motion which can be measured by relaxation time () and the amount of chain motion which can be described as frequency (). Temperature should be the single influence factor when frequency is a constant. At low temperature (below Tg), most of chains are restricted in their motion which leads to a low energy dissipation. At high temperature, according to the time-temperature equivalence principle, the relaxation time  is short, which means it is easier for molecular motion to occur. At the glass transition temperature, with the viscosity in the system increasing, the resistant force increasing rapidly, molar unit become free to move but can not correspond to the applied stress. This phenomenon is called hysteresis which produces an internal friction peak and results in damping.
When the frequency is low, motor unit with little delay in their response to an applied stress, the internal friction is low, so E" is low, with the frequency increasing, the motor unit with some delay in their response to an applied stress completely, the internal friction begin to increase, so E" increases with frequency.