Thermal Analysis by hcj

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									Thermal analysis

Thermal analysis


Thermal analysis embraces all methods in which measurements are made of a physical property that changes as the temperature is varied. A number of the techniques can be also complemented by the addition of time or oscillatory variation to enhance the information that can be obtained from these measurements. The experiments can usually be divided into isothermal in which continuous measurements as a function of time and/or frequency are performed at a constant temperature and programmed temperature measurements where the temperature is varied in a well defined manner. Techniques such as differential scanning calorimetry, DSC, or differential thermal analysis, DTA, primarily measure the thermal properties of the material and allow calculation of the enthalpy (ΔH) or entropy (ΔS) changes that occur when transformations such as crystal melting occur. Measurements of the variation in physical properties such as the modulus in dynamic mechanical thermal analysis, DMTA, and electrical permittivity in dielectric thermal analysis, DETA, are both useful methods for characterizing polymers and can also provide valuable information on the molecular dynamics. Modulus and electrical data are often valuable design data and can be used directly. By making measurements at different frequencies the methods can be used for the estimation of activation energies or analysed using the time-temperature relationships based on free volume exemplified in the Williams-Landel-Ferry (WLF) equation.

12.2 DIFFERENTIAL THERMAL ANALYSIS (DTA) AND DIFFERENTIAL SCANNING CALORIMETRY (DSC) The DTA and DSC techniques are very similar and may be discussed together. The essential features of the DTA apparatus are shown in Fig.12.1. The sample is placed in a cell S, located in a block which can be heated (or cooled) at a programmed rate. A reference sample in an identical cell R is located close to the sample cell in the uniform temperature block; its temperature is represented by Tr. The reference sample may either have a precise transition in the region of observation (e.g. naphthalene with a melting point of ~ 80℃) or have a fairly constant heat capacity (e.g. an aluminium disc or powder). The purpose of the reference is to provide a direct comparator for temperature measurement for the sample, assisting minimization of inaccuracies due to thermal lag in the equipment. When the sample passes through a transitional state its temperature (Ts) departs from that of its surroundings. If the programme is set for heating, at an endothermic transition such as a crystal melting transition, Ts falls below the programme temperature and the reference temperature and ΔT (=TsTr) is negative. the size of ΔT depends on the thermal properties of the equipment, particularly the thermal capacity of the cell, as well as the mass of sample and, for finite samples, the thermal conductivity.


Thermal analysis

For this reason it is difficult to extract quantitative measurements of the thermal properties of the sample using DTA, though the temperatures at which transitions occur can be located fairly accurately.

Fig.12.1 Schematic of a DTA apparatus; r is reference; s is specimen. W r and Ws are constant instrument factors that depend on the thermal characteristics of equipment. Careful consideration must be given to the handling of the data, for it is easy to use erroneous criteria for locating a specific temperature of interest, e.g. the glass transition temperature (see Section 12.2.2). More direct measurement of thermal properties is possible using DSC and it is generally preferred for quantitative analysis. In this method the sample and reference are provided with independent heaters, Fig. 12.2. Background heating of the block is usually provided separately so that the microheaters are sensitive to the requirements of the sample and reference cell at the programme temperature (Tp(t)). The temperature of each cell is measured continuously and compared with the instantaneous value of Tp(t). It is arranged that the power delivered to the sample and reference cells via the individual heaters is a function of the departure from the programme temperature, i.e. Ws(TsTp) and Wr(TrTp) respectively. The differential power requirement { Ws(TsTp)  Wr(TrTp)} is the quantity plotted and can be presented as a function of Tp, Tr or Ts. With this arrangement Tp, Tr or Ts should be very close together even near a transition and therefore much closer than Ts and Tr, in the DTA method whenever thermal changes are taking place.


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12.2.1 QUANTITATIVE ANALY5B OF DTA AND DSC To analyse the DTA or DSC experiments one must firstly consider the heat flow between the block and the sample. Assume that the block temperature is Tp and that of the sample Ts and let the total resistance to heat flow between cell and block be 'R', Fig. 12.3. When heat flows into the sample from the surroundings

Fig. 12.2 Schematic of a DSC apparatus: r is reference; s is specimen. W r and W s are constant instrument factors that depend on the thermal characteristics of the equipment.

Fig. 12.3 Heat transfer in a DSC cell: R represents the thermal resistance to heat flow between cell and the block.


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(at a rate dQs/dt) the energy balance gives:

dQs dT dH s  Cs s  dt dt dt


where Hs is the enthalpy of the sample and Cs is the heat capacity of the sample plus the cell. The rate of heat now can alternatively be given as

dQs (T p  Ts )  dt R


dH s dT (T p  Ts )  Cs s  dt dt R


If a suitable internal reference sample has been selected, the equivalent expression for the reference cell can be written as

dH r dT (T p  Tr )  0  Cr r  dt dt R


where subscript r stands for the reference cell and R is assumed equal for the (identical) sample and reference cells:


dH s d (Ts  Tr ) dT  (Ts  Tr )  R(Cs  Cr ) r  RCs dt dt dt dT dH dT  T  R(C s  Cr ) r  RCs dt dt dt


where ΔT (=TsTr) and the subscript s is dropped from H since it is redundant when changes in enthalpy occur only in the sample. Remembering that the DTA method produces a plot of ΔT versus T (or t) then, in principle, equation (12.5) can be used for quantitative analysis. In practice it is neither convenient nor accurate to do this, for it requires a knowledge of R, the thermal resistance, which depends on several things including the conductivity of both sample and reference. These values not only alter with temperature, but show marked changes on either side of a transition. For DSC we can take equation (12.1) and the equivalent equation for the reference cell and find

d (Qs  Qr ) dT dT dH dQ  C s s  Cr r   dt dt dt dt dt
where ΔQ is the difference in heat supplied to the two cells, i.e.



Thermal analysis

d (Ts  Tr ) dT dH dQ   (Cs  Cr ) r  Cs dt dt dt dt
Now from equation (12.2) we have


dQs (T p  Ts ) dQr (T p  Ts )   and dt R dt R
so that

d (Qs  Qr ) dQ Tr  Ts   dt dt R
Substitution of (Tr-Ts) from equation (12.8) into equation (12.7) gives


dT dH dQ d 2 Q   (C s  C r ) r  RC s dt dt dt dt 2


If R is made sufficiently small then the final term in equation (12.9) can be made negligible; this can be achieved without affecting the sensitivity of the method, whereas inspection of equation (12.6) shows that with DTA the sensitivity depends on R (i.e. ΔT ∝ R). Using DSC, if ΔC is the difference in heat capacity between the sample and reference cell then the measured heat flow (Q1) when both pans are empty will be Q1 = KΔC (12.10)

where K is a constant for the apparatus. If the same measurement procedure is now used with the sample in position the difference in heat capacity between the two cells becomes (ΔC + msCp,s), where ms is the mass of the sample and Cp,s is the specific heat capacity of the sample and the corresponding measurement is Q2 = K(ΔC + msCp,s) (12.11)

If now the sample is replaced by a calibrant (c) (e.g. alumina) and the procedure is repeated the measurement becomes Q3 = K(ΔC + mcCp,c) From equations (12.10), (12.11) and (12.12) it follows that (12.12)

C p ,s 

(Q2  Q1 )mc C p ,c (Q3  Q1 )ms 



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Thus Cp,s versus temperature curves can be obtained. These can be integrated to give enthalpy changes (see Section 12.2.2(a)).

12.2.2 MODULATED DSC (MDSC) In equation (12.13) the heat capacity of the sample is determined with the assumption that the heating or cooling is a linear ramp. For a simple first order thermodynamic transition the form of the curve, its magnitude and location are the same for both cooling and heating cycles. The system is therefore thermodynamically reversible. However, for a number of processes such as the glass transition and polymerization of a thermoset resin the heat capacity can be thermodynamically irreversible. The glass transition is normally considered to be a uniquely defined temperature however in practice the precise value does reflect the effects of disorder which may be frozen as a consequence of rapid cooling of the sample. The effect of irreversible processes on the measured DSC trace is that the first measured curve is often different from the second and subsequent traces obtained by cooling and re-heating the sample. This fact can be used to determine the extent of residual monomer in a fabricated sample and also the frozen-in entropy in a supercooled glassy material. The modulated technique has been devised to allow separation of reversible and irreversible components to the total measured heat capacity. Superposition of an oscillatory heating and cooling cycle on the linear ramp allows separation of these components. The sample is heated to a temperature T1' that is above the linear ramp value T1 and then cooled to T1" which is below the linear ramp value. The temperature seen by the sample will therefore have the form shown below (Fig. 12.4).

Fig. 12.4 Schematic representation of a modulated DSC experiment.


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The period of the oscillation can be adjusted to increase the sensitivity of the experiment. Typically the frequency of oscillation is about I Hz and the amplitude of the oscillation adjusted to be about 5º.The precise values can be adjusted to a particular experimental situation. The modulation pplied to the samples is then compared with the similar variation applied to a reference and the real and imaginary components of the difference signal calculated using a Fourier transform of the output against the input signal. This separation of the signals involves analysis of the change in the amplitude that provides the real component and the phase shift that provides the imaginary component.

12.2.3 ANALYSIS OF MODULATED DIFFERENTIAL SCANNING CALORIMETRY DATA The normal response of an ideal DSC is a combination of a signal that is dependent on the rate of change of temperature and one that is dependent on the value of the temperature. The former depends on the sample heat capacity and the latter on the rate of any kinetically driven process. This can be expressed as:

dQ dT  Cp  f (t , T ) dt dt


where Q is the amount of heat evolved, Cp the thermodynamic heat capacity, T the absolute temperature, t the tifue and f(t,T) some function of time and temperature that governs the kinetic response of any physical or chemical transformation. In the simplest system, the modulation is given a sinusoidal form and the temperature programme can be expressed as follows:

T  T0  bt  B sin t


where T0 is the starting temperature, ω/2πthe frequency, b the heating rate and B the amplitude of the temperature modulation. If it is assumed that the temperature modulation is small and that over this interval the response of the rate of the kinetic process to temperature can be approximated as linear, then equation (12.14) can be written as:

dQ  C p [b  B cost ]  f1 (t , T )  C sin t dt


where f1(t,T) is the average underlying kinetic function once the effect of the sine wave modulation has been subtracted, C is the amplitude of the kinetic response to the sine wave modulation and [b + Bωcosωt] is the measured quantity dT/dt. It can be seen, therefore, that the heat flow signal will contain a cyclic component that will depend on the values of B, ω and C. The two basic measurements are dQ/dt and the phase lag that is the difference between the cosine wave generated in the dT/dt signal and cyclic component found in the dQ/dt response. There is an offset in the baseline of the phase lag due to the non-ideal behaviour of the sample and measuring system. Using a discrete Fourier transform algorithm, the cyclic component is subtracted from the heat flow and the temperature signal, thus giving the underlying heat now and temperature at any point in time. By taking the


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underlying signals the traditional DSC curves can be reconstituted and are virtually indistinguishable from those obtained conventionally. When the analysis is applied to the temperature signal it yields the underlying value and the amplitude of the cyclic component. Differentiation of these results gives the underlying heating rate and the quantity Bωcosωt. The amplitude of this cyclic component of the dT/dt signal can be compared with that from the dQ/dt signal. thus enabling a value for the cyclic heat capacity to be determined. It is important to realise that this cyclic measurement comprises a contribution from the thermodynamic heat capacity (denoted Cp) plus a contribution from any kinetic event, such as a recrystallization or cure arising from Csinωt. A kinetic contribution can only occur when there is an enthalpic process, such as an exotherm from recrystallization or cure reaction or an endotherm arising from melting or a relaxation event. 12.2.4 APPLICATION OF DTA, DSC AND MDSC TO POLYMER STUDIES The techniques are ideally suited for the location and characterization of processes in which there is a change in molecular mobility in the system or when a reaction is occurring. (a) Measurement of Tg The glass transition temperature is a very important characteristic of amorphous polymers. Tg is a non-equilibrium property and is kinetic in nature and the measurements made are sensitive to the heating rate and the method used. Thus the value of Tg obtained differs from one technique to another, over a range of several degrees, but since the transition is usually rather broad these differences are not necessarily recognised. For example, if the value of Tg is required merely to test the suitability of a polymer for operating within a certain range of service temperatures, the exact value is not critical since the safety margin allowed would generally be much larger then the range of measurements by different techniques. For a particular polymer, Tg may be a function of molar mass, thermomechanical history, tacticity, etc. Accurate measurement of Tg is therefore a useful method of characterizing a particular sample of material and deducing facts about its properties (Fig. 12.5). Richardson and Saville have outlined how measurements may be performed allowing subtle differences to be accurately defined. It is found that on either side of a transition the specific heat of a sample varies linearly with temperature, i.e. Cp.s = a + bT. Thus for the glassy region and for the liquid (or rubbery) region

H1 (T )   C p,s dT  AT  0.5bT 2  C


where a, b, A and B can be determined from DSC data. Then if equations (12.17) and (12.18) are evaluated and subtracted, a value for the integration constant (c - C) can be found. If two lines represented by equations (12.17) and (12.18) are extrapolated towards one another they meet at T = Tg and setting Hg(Tg) = Ht (Ts) allows these equations to be solved to find Tg. In this way Tg is determined from data obtained well away from the transition temperature and is thus unlikely to be influenced by experimental conditions such as heating rate and is independent of the path taken from the glassy to the liquid state.

H g (T )   C p,s dT  aT  0.5bT 2  c


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Fig. 12.5 Schematic diagram of the glass transition process To illustrate how Tg can be affected by the processing conditions, consider Fig. 12.6 which shows schematically the relationship between enthalpy (H), specific volume (V) (= 1/density) and temperature for both quenched and aged (or slowly cooled) samples of the same polymer. When the polymer is quenched from the melt state it follows the liquid line until it passes Tg´, then follows the line marked 'quenched'. If when the cooling ceases (e.g. position A) the material is allowed to reside at a temperature below Tg for an extended period, both H and V fall slowly. This process is known as physical ageing and the rate is too slow to be observed if the temperature is too low, but is normally significant at temperatures in the range(Tg-50℃) to Tg. The quenched sample will have retained entropy characteristic of a higher temperature and is usually assumed to be more disordered and has a lower TR whereas the aged sample will be of lower entropy and has a higher Tg. For the purpose of the present discussion let us assume that the sample is reheated at a constant rate as soon as the quenching is complete. It follows the 'quenched' line in reverse, and the enthalpy and specific volume both increase linearly until the molecules have sufficient freedom to move in a way characteristic of the liquid state and it then follows the liquid line. The exact path from the 'quenched' line to the liquid line depends on the heating rate for there is some overshoot followed by a catching up process as the temperature passes through the Ts (see dashed lines with arrowheads). The process of ageing (often called annealing if it takes place above room temperature) allows the sample to densify so that the specific volume and enthalpy are both closer to the thermodynamic equilibrium line, which is the liquid line extrapolated through Tg into the region T < Tg. Thus after ageing the state of the material may be described by point B, and on heating it follows the 'aged' line, parallel to the 'quenched' line. Overshoot and catching up can be expected to occur again. The accepted values of Tg read from the data presented in the manner shown in Fig. 12.6 are thus Tg,q for the quenched sample and Tg,q for the annealed sample, and it is seen that the glass transition temperature for the quenched sample is above that for the annealed one. This is the result that would be obtained if a very low heating rate were used. If, on the other hand, TR is taken to be indicated by a well-defined point on the Cp,s versus temperature plot, then, because of the overshoot effect, the value given for an annealed sample is commonly higher than that for the quenched sample at normal heating rates, reversing the order given in Figure 12.6. Therefore, unless the rigorous

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method of Richardson and Saville (described above) is used, the value obtained for Tg will depend on the heating rate and it is important to record the heating rate in the report on the results. Even then the thermal inertia characteristics of the equipment will have an influence on the measured value and detailed comparisons of samples with different preparation histories should only be attempted if they are tested in the same apparatus, using the same conditions each time.

Fig. 12.6 Variation of enthalpy and volume for quenched and annealed glassy forming polymer samples

(b) Crystal melting behaviour Many polymers will be able to form ordered crystalline regions and hence exhibit melt transitions. As in the case of low molecular mass materials, the melting process is accompanied by dramatic changes in mechanical properties and hence is a very important transition. In polyethylene, increase in the molar mass leads to a corresponding increase in the melting temperature. The melting temperature will in general not be a discrete temperature as is found in low molar mass material but is rather a broad transition reflecting a range of crystallite sizes and crystal perfection. As a result there are a number of ways of defining the value of the melt temperature Tm. If the polymer exhibits a clearly defined endothermic peak then the maximum value is used to define the mean melting point. However, in some cases the melt process can be broad and in this case it is more convenient to determine the onset point of melting as the intersection of the baseline before the melt process occurs and the back extrapolation of the melting endotherm to this baseline. In this latter case the value of Tm is an onset value and can reflect the melting point of the lower


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molar mass components of the polymer rather than that of the bulk material. If the polymer was cooled rapidly when the sample was formed, then on reheating in the thermal analysis equipment it may show 'premelting crystallization'. This arises because when the sample is at an elevated temperature (still below the melt temperature) the kinetics of crystallization are sufficiently speeded up to allow some parts of the molecules initially trapped in a disordered state to crystallize. This is an example where it is especially valuable to conduct an initial experiment with a constant heating rate, followed by controlled cooling within the thermal analysis cell, then by a repeat run using the same heating conditions. The second run can act as a reference, and reveals clearly those features in the first run for which an explanation must be sought that takes account of the previous thermomechanical history. In this sort of experiment, the MDSC allows separation of these components during the first heating cycle, and the repeat run will allow the generation of a reference curve against which effects may be judged. This type of behaviour is illustrated schematically in Fig. 12.4. Some polymers are polymorphic and the sample may contain two or more crystal types. An example of this is polytetrafluoroethylene which undergoes well defined transitions between crystal forms at about 35℃. For those polymers that can form alternative crystal structures, the likelihood of this happening is usually greatest when the material is rapidly cooled and/or when different regions have different thermomechanical histories, as in the skin and the core of an injection moulding. In this case a number of melting signals will be obtained and once more a reference thermogram from the sample, obtained on reheating after controlled cooling in the analysis equipment, will assist interpretation. Blends of polymers rarely co-crystallize and the melting peaks of the phase-separated homopolymers are usually easily identified (Fig. 12.7).

Fig. 12.7 DTA traces obtained from blends of linear polyethylene, PE, and isotactic polypropylene. PP. with the following compositions: (a) PE homopolymer; (b) 70PE: 30PP; (c) 30PE: 70PP; (d) 70PE: 90PP; (e) PP homopolymer (see Robson, P.,Sandilands, G.J.


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and White, J.R. (1981) J. Appl. Polym. Sci. 26. 3515). The enthalpy of fusion, ΔHf can be measured using the Cp versus T curve from a calibrated DK instrument by integrating under the curve over the melting range, If the curve is fairly sharp, with the peak temperature at Tm´, then the entropy of fusion can be estimated as ΔSf =ΔHf/Tm. The melting behaviour of a polymer crystal is sensitive to the lamellar thickness because of the significance of the surface tree energy in a thin crystal, though it is not yet possible to measure lamellar thickness distributions in this way.

(c) Crystallinity If the enthalpy of fusion of a semicrystalline polymer sample is Hf then the fractional crystallinity is given by fc = Hf/Hf,c, where Hf,c is the enthalpy of fusion of a completely crystalline sample of the same polymer. This quantity can rarely be determined directly because of the difficulty of obtaining a totally crystalline sample. For polyethylene, the value obtained from crystalline dotriacontane (C32H66) has been used since the paraffin crystal structure is identical to the core of a polyethylene crystal so it is indistinguishable from a polyethylene crystal with the fold structure sliced off and replaced by a set of free ends. Apart from the problem of obtaining ΔHf,c , there are other difficulties. The heat of fusion is temperature dependent and melting can occur over a wide temperature range. Quantitative analysis may sometimes be more straightforward with Cp data, noting that the measured value can be written as

C p  C p 'c f c  C p 'a (1  f c )


where the subscripts c and a stand for crystalline and amorphous respectively. The Cp, a can be obtained by making measurements on the liquid at temperatures above Tm and extrapolating back into the melting range, and Cp,c is a function of temperature and can be determined from a series of experiments on samples of different known crystallinities. These samples will usually have been studied extensively using scattering techniques and in particular X-ray methods. (d) Glass transition of copolymers and polymer blends The glass transition temperature of a random copolymer containing two monomer species ('l' and '2') can be expected to lie between the glass transition temperatures of the corresponding homopolymers (T g,1 and Tg,2). If the weight fractions of the two components are ω1 andω2 then the glass transition temperature of the copolymer (Tg,c) is normally given by an expression of the form

Tg ,c 

a1w1Tg ,1  a2 w2Tg , 2 a1w1  a2 w2


where a1 and a2 depend on the monomer type and would both equalunity if the simple rule of mixtures applied. If the two components phase separate, as is often the case with both graft copolymers and block copolymers, then the Tg of both phases can be identified. In some cases where there is a limited degree of


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solubility of one polymer phase in the other, shifts in the observed values can be observed. If, as in the case of polyurethanes, a mixed interface is possible, then an additional feature associated with the interfacial region between the pure phases can also be detected. When phase separation occurs the observed Tg values retain the values of the component phases.

(e) Determination of reaction exotherms Determination of the extent of cure of a thermoset resin is often required in order to assess whether or not the material has fully developed its mechanical properties. For quantitative measurements it is necessary that the enthalpy of reaction for the cure process is known. The approach adopted is to perform the cure in the sealed pan of a DSC instrument in isothermal conditions, and the value of Q is determined as a function of time and the integral of the area under the curve provides the enthalpy for the reaction Δ Hreaction. The analysis is then repeated at a series of different temperature, allowing the variation of the enthalpy change for the reaction with temperature to be derived. With these data it is then possible to investigate an unknown material. The difference between the first heating trace of the partially cured and the second trace corresponding to the completely cured material provides a value for the enthalpy of reaction. The ratio of the enthalpy for the unknown to that for the complete cure reaction gives the extent of reaction. In the cure process the initial liquid material is firstly converted into a gel and finally into a vitrified state. This transition from gel to glass occurs when the value of Tg of the reacting system exceeds that used for the cure process and leads to freezing of the sample in an incompletely cured state. Heating the sample above this temperature allows further reaction to occur and the process to be completed. Observation of the onset temperature for the reaction exotherm can indicate approximately the temperature used to cure or post cure the material when it was fabricated. (f) Analysis of material modified through fabrication and ageing Thermal analysis can be used to probe the thermal - mechanical history of a sample and provide useful processing information. With thermoplastics the most common processing operations are injection moulding, extrusion, blow moulding, fibre and film production and thermoforming. These all involve melting the polymer followed by deformation in the molten state and then quenching to a solid. Rapid cooling through Tg causes the material to be frozen into a higher entropy state than if it were slowly cooled. Mechanical deformation - drawing - can cause alignment of chains and induce orientation. In polymers, such as poly(ethylene terephthalate), the extent of orientation of the polymer chains has a very significant effect on gas permeability and allows these materials to be used for soft drink bottles. In the moulding process in all but the thinnest articles the rate of cooling differs considerably at different depths, causing the state of the material to be very different from one location to another. Even in injection mouldings made from simple thermoplastics such as polystyrene, very different DSC thermograms were obtained from material cut respectively from the skin and core of identical bars (Fig. 12.8). Shown for comparison in both cases are repeat runs on the same specimen after cooling down in the DSC equipment. The rerun traces are considerably displaced from those obtained from the as-moulded material in the range (Tg - 30℃) to Tg, indicating that there is a marked effect attributable to processing. In the case of the skin sample, the Tg peak is shifted relative to that on the reference (rerun) trace. With both skin and core samples a pre-Tg peak was present in the as-moulded state but disappeared in the rerun. The


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pre-Tg peak is much more prominent with the skin sample. The rerun curves for skin and core are almost exactly superimposable. The pre-Tg peak is a reflection of the entropy frozen into the material.

Fig. 12.8. DSC thermograms for polystyrene samples cut from an injection moulded bar: (a) skin; (b) core. The re-run (reference) curves are shown as solid lines, and initial runs as broken lines (courtesy of M.J. Richardson and C.S.hindle)

12.3 THERMOMECHANICAL ANALYSIS Thermomechanical analysis (TMA) is the name given to a method capable of measuring the thermal expansion coefficient of materials in their most refined form, but which is sometimes used simply to determine the location of the glass transition temperature. Figure. 12.9(a) shows the typical layout of the


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TMA apparatus.


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Fig. 12.9 (a) Schematic of TMA: S. sample; P, probe; LVDT, linear variable displacement transducer. (b) Detail of flat-ended probe. (c) Detail of 'pip' probe. (d) Detail of the fibre/film attachment. The broken line indicates the sample tube cut away for access to the specimen.

The probe (P) is made from quartz, chosen because it has a low thermal expansion coefficient compared with that for most polymers, within the range of temperature employed for most polymer studies. In the simplest form of the apparatus, the bottom end of the probe is flat and rests on the sample, located on the platform at the bottom of the sample holder tube, also made from quartz. The upper end of the probe is attached to the core of a linear variable differential transformer (LVDT) which accurately monitors position, the signal normally being displayed on a chart recorder. Above this is a counterbalancing arrangement that can be adjusted so that the vertical (gravitational) force on the probe is any chosen value. A convenient way of doing this is to counterbalance the weight of the probe so that it just floats above the surface of the sample, then to add a weight (e. g. 500 mg or 1 g) to the platform at the top. This is sufficient to ensure that the probe remains in contact with the sample and small enough to allow the elastic


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compression strain to be neglected.

A constant temperature chamber surrounds the lower part of the apparatus where the sample is located. This may consist of a cylindrical furnace element within a vacuum flask. If liquid nitrogen is used as a coolant this arrangement is capable of providing temperature scans from -100℃ to +200℃ and higher. A temperature programmer controls the furnace, giving a pre-set rate of change, usually between 1℃/min and 10℃/min. The temperature is normally displayed on the same time plot as the LVDT signal. A direct plot of displacement versus temperature can be obtained, but In practice it is more common to use two γ-t plots. If a linear increase in temperature is obtained the LVDT signal easily converts to displacement versus temperature. If a linear increase in temperature is not obtained, individual displacement versus temperature readings must be read off and replotted for analysis. This displacement is equal to the difference in expansion between the sample and an equal length of quartz tube. Thus, the linear expansion coefficient of the sample equals the slope of the expansion measurement (expressed as a strain) versus the temperature plus the linear expansion of quartz. The linear thermal expansion coefficient of an isotropic material is equal to one third of the volumetric


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expansion coefficient. For Tg measurements the probe may be modified by replacing the flat end with a pip at the bottom. The pip concentrates the load applied to the sample and when the temperature passes through the Tg the probe starts to penetrate the softened surface. Thus the direction of motion of the probe reverses and is easily detected on the TMA trace. This probe is not recommended for thermal expansion coefficient measurements, even below Tg. The size of sample used in the TMA is fairly small (e.g. a cube of 3 to 4 mm edge length is suitable) and the expansion behaviour of samples can be examined in different directions. For example, if a sample of these dimensions is extracted from an injection moulded article the expansion coefficient can be measured parallel to the now direction, transverse to it and through the wall thickness. Significant anisotropy can often be revealed in this way. Such studies are also of interest in fibre reinforced polymers, both aligned fibre composites and those filled with short fibres, especially if the fabrication process causes preferred orientation . Sometimes the thermal expansion coefficient differs markedly from one location to another on a scale even finer than the 3 mm level used for the pip probe. For example, an injection moulding normally has a 'skin', that sets very rapidly early on in the moulding process that is different in many respects to the 'core' material that cools and solidifies much more slowly. The skin thickness is often between 0.2 and 0.4 mm, and though suitable samples of this thickness can be removed (e.g. by high speed milling) they bend too easily to permit measurements to be made using the arrangements shown in Fig. 12.9(b). An alternative method is to keep the sample under a small amount tension and a suitable modification to the equipment is shown in Fig. 12.9(d). This can also be used to test polymer fibres. End effects may sometimes hamper accurate measurement of the thermal expansion coefficients. A typical result from a TMA run is shown in Figure 12.10. One of the traces follows the millivoltage output from the thermocouple plotted in the y direction with the chart paper running at a constant speed. these values have been converted to temperature and plotted at the corresponding positions on the x axis. A small horizontal shift was made to take account of the relative positions of the two pens, which are displaced to permit them to cross over so that the whole paper width can be used for both. The results shown are for a thin strip of short glass fibre reinforced nylon-6,6 cut frt3m an injection moulded bar and tested in the thickness direction with a flat ended probe. It shows the glass transition, which is not as prominent as in a non-crystalline polymer, near to 60℃. The thermal expansion coefficients estimated from this trace are approximately 10-4/℃ below Tg and 2.3×10-4/℃ above Tg. Much smaller values were obtained in the bar axis direction (approximately 3.6 ×10-5/℃ and 3.7 ×10-5/℃) because of the constraints imposed by the fibres (33% by weight) which were aligned preferentially in this direction. Unfilled nylon-6,6 moulded and tested in a similar way showed much less anisotropy.


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Fig. 12.10 TMA for glass-fibre filled nylon-6,6 cut from an injection moulding and measured in the thickness direction. LVDT (solid line) shows the probe displacement, with the sensitivity shown by the scale bar representing 0.05 mm. T he broken line shows the thermocouple output, with the sensitivity shown by the scale bar representing 5 mV (courtesy of M.W.A. Paterson).

12.4 THERMOGRAVIMETRIC ANALYSIS In thermogravimetric analytical (TGA) measurements, the mass of the sample is recorded continuously while temperature is increased at a constant rate. Weight losses occur when volatiles absorbed by the polymer are driven off and at higher temperatures when degradation of the polymer occurs with the formation of volatile products. The equipment is designed to allow precise weight measurements to be performed in a controlled environment, avoiding the effects of convection forces arising in the heating chamber and because of the changes in the density of the gaseous environment. It is important to ensure that volatiles do not condense on the weighing apparatus. It is also necessary to control the atmosphere when this has an influence on the process of degradation. Typically studies are performed using air, nitrogen as an inert atmosphere, or oxygen as a reactive atmosphere, and significant differences can often be observed. The result of a TGA run made on a nylon-6,6 sample cut from an injection moulding grade granule that had been standing in laboratory air for several months before testing is shown in Fig. 12.11: the spikes are superimposed at five minute intervals as time markers. It is evident that the predominant feature is weight loss and that this begins to become important above 120℃. The weight loss is attributed to water and the total amount driven off by the end of the run, terminated after crystal melting, was approximately 1.1% of the original weight of the sample, a value typical of that obtained by other techniques for the water content in similar samples.


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Fig. 12.11 TGA trace for nylon-6,6 grade (courtesy of M.W.A. Paterson).

12.5 DYNAMIC MECHANICAL THERMAL ANALYSIS: In the dynamic mechanical thermal analysis (DMTA) the sample is deformed cyclically, usually under forced vibration conditions. By monitoring the stress strain relationship while changing temperature, information can be obtained about the relaxation behaviour of the test piece. A number of pieces of equipment have been developed generating specific modes of deformation, the most popular being reversed bending (e .g. the double cantilever), Fig. 12.12 (a), axial tension (usually from zero load to maximum), Fig. 12.12 (b), torsion, Fig. 12.12 (c) and shear,_Fig. 12.12(d) The simplest of all of the dynamic test arrangements is the torsion pendulum in which the sample in the form of a wire or a thin narrow strip hangs vertically and supports an inertia bar or disc which is rotated about the sample axis and is then allowed to execute free vibrations and undergoes damped oscillations. The assemblies are usually counterbalanced so that the specimen is maintained under zero tension. Although the sample can be surrouned by a temperature jacket and the experiment repeated for series of temperatures to provide ‘thermal analysis’, it does not lend itself to automated thermal analysis, and for this a forced vibration system is preferred. Although there is no fundamental reason why torsion should not be chosen, it is more popular to use arrangements based on those shown schematically in Fig. 12.12(a), (b) and (d). The vibration chosen is usually sinusoidal. If the amplitude is sufficiently small a sinusoidal load gives rise to a sinusoidal deformation, and for the purpose of interpretation it does not matter whether the test is run under load control or deformation control. There are often practical reasons for choosing one rather than the other. In either case the strain lags behind the stress and this is described by a phase angle (δ).


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Fig. 12.12 Loading options for dynamic mechanical testing: (a) double cantilever (NB single cantilever is also used); (b) reversed uniaxial tension; (c) torsion; (d) shear. In the case of shear it is essential that the specimens S are identical..

12.5.1 DYNAMIC MECHANICAL PARAMETERS The stress (ζ) can therefore be described by the equation

(   m )   0 sin t


where ζ0 is the stress amplitude, ω is the cyclic frequency and t is the time. The mean stress ζm for


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reversed loading in which the tensile and compressive amplitudes are of equal magnitude is zero. For zero to tensile testing ζm =ζ0. For a viscoelastic solid the strain lags behind the stress. The corresponding strain is

(   m )   0 sin(t   )


where ε0 is the strain amplitude and εm is the mean strain, having special cases as described for stress. The dynamic mechanical properties of a polymer are described in terms of a complex dynamic modulus:

E *  ( E '2  E "2 )1 / 2  E '  iE "


where E' is called the storage modulus and is a measure of the recoverable strain energy and when loading is small it equates approximately with the Young's modulus. E" is called the loss modulus and is related to the hysteresial energy dissipation. The phase angle (δ) is given by

tan    E " /  E '


The stiffness and damping properties of a material can be described by any two of the quantities E′, E" and tanδ (the 'loss tangent'). The precise form of the modulus (tensile or shear) which is being measured will depend on the configuration used in the measurement, Fig. 12.12. It is very important to remember that change of the measurement configuration leads to measurement of a different mechanical property, and comparison of transition temperatures without a knowledge of the measurement configuration can lead to apparently conflicting results. 12.5.2 TEST DETAILS For a forced vibration test it is necessary to impose a chosen load or deformation programme and to measure load and deformation continuously. There are several commercial instruments that do this and although it is prudent to question the accuracy of the load and deformation measurements it will rarely be found that they are ultimately responsible for limiting the absolute accuracy of the derived material parameters. Usually the experiments are performed on small samples of material and it is appropriate to refer the values of the modulus obtained to static isothermal data. The nature of the deformation depends on both the material properties and the sample shape and is very sensitive to the sample clamping arrangement. In practice, the limiting factor in determination of the modulus is a combination of the sample shape and of the ability to successfully clamp the material. Because of the relatively high value of the thermal expansion coefficient of polymers, performing a thermal analysis of the sample held in a clamp will lead to very significant changes in the force produced on the sample by the clamps, often with the result that at the end of the experiment an indelible impression of the clamps will be left on the sample. If the sample is clamped at room temperature then slippage can be observed at low temperatures due to the shrinkage of the sample in the clamps. Clamping is the major problem with most of these measurements performed as a function of temperature. The shape of the sample is very important in defining what exactly


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is the form of the strain induced in the sample. For example, the nature of the deformation in the double cantilever vibration, Fig. 12.12(a), is very different from that in three point bending which it resembles in some ways. The relationship between load applied and the deflection of the centre of the beam is quite different for these two cases. In practice, it is not possible to ensure that the deformation is purely one of these because of problems associated with deformation within the clamps. Similar problems also occur in the tensile, torsion and shear alternatives. Clamping errorscan sometimes be reduced by testing samples of different lengths andextrapolating to infinite length. Temperature effects in the case of the double cantilever arrangement can cause the bar to slacken between the grips and may even lead to a toggle effect as the bar passes through the zero displacement position. A similar problem may arise in deformation - controlled tensile - mode testing in which buckling may occur in a thermally expanded bar. If tensile mode testing is conducted under load control, this problem does not arise. In bending, one way to reduce the problem of thermal expansion is to apply tension to the bar when mounting it in the clamps so that, on raising the temperature, the expansion no more than compensates for the initial elastic strain. This remedy is usually applied to remove the more serious problems, such as the toggle effect, but may introduce secondary, (often unknown) effects which are rarely allowed for, so that there may be an error in the absolute stiffness values derived from the measurements. Thus, unless a careful assessment is made of the mechanics of the deformation, the absolute values will be of doubtful accuracy and it is not expected that absolute modulus values can be routinely obtained using DMTA. It is, however, very important to appreciate that, whereas metals and ceramics exhibit mechanical properties which are virtually invariant over large changes of temperature, polymers can exhibit modulus changes of three or four orders of magnitude for changes of only ten or twenty degrees and therefore the temperature profile is critical in assessing the usefulness of a particular polymer for a specific application. Therefore absolute accuracy in terms of modulus data is secondary to a knowledge of the thermal profile for most polymers. However, with an appropriate choice of geometry for the test and with care taken to reproduce sample size and shape and the clamping procedure, reproducible results can be obtained that permit comparisons to be made between different materials. In many of the commercial instruments it is usual to use very small samples, often a few millimetres to a fraction of a millimetre thick and centimetres to a few millimetres in length. It is, in principle, possible to extract samples from the skin and core of injection moulded samples and investigate the differences in properties resulting from the processing. Such samples will often have differences in anisotropy revealed by making measurements on samples selected transverse and parallel to the now direction. In another application, differences in the state of cure can be obtained by examining surface and core samples from glass reinforced plastic composite materials used in ship construction where the composite may be between 30 and 60 mm in thickness. Although the modulus values may not be accurate, relaxation temperatures can be determined with good accuracy using DMTA. By conducting tests at different frequencies a time-temperature transformation can be performed. Data for this can be obtained in a single heating run using microprocessor controlled changes in the frequency and a number of instruments are capable of doing this. The vibration frequency can be programmed to change automatically at the same time as the temperature is ramping and results for several different frequencies can be recorded and displayed. The advantage of this apart from the obvious one of time saving is that all data are obtained from the same sample and any clamping error will be common to all sets of data at each frequency.


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12.5.3 INTERPRETATION OF DATA DMTA is most commonly used to identify the location of transitions which often have a significant effect on the modulus values. Table 12.l indicates typical values of the Young's modulus for various states of a polymer and appropriate magnitudes of changes for relaxation transitions. Table 12.1 Summary of typical values of modulus for various states of a polymer Phase / transition Rigid glass Ductile glass Glass-rubber transition Rubber to viscous liquid Viscous liquid to mobile fluid Modulus E’(Pa) 1010 – 109 ~109 ~109-106 106-105 105-103 Comment 0 k to T Above T to Tg; width 30-500 Typically 10-200 in width Typically 50-1000 in width and depends on Mw Typically 30-600 in width and depends on Mw

In Table 12.l Te is some sub-Tg transition which has associated with it sufficient molecular motion to transform the material from being brittle to ductile in failure. In testing a glassy polymer the measured value of E' shows a steep fall as the temperature is raised through Tg and depends on the heating rate and frequency used. At secondary transitions there is usually a recognisable change in the slope of the E' versus temperature plot, but the temperature of the transition is usually most clearly identified by the position of a peak in the tanδ plot. The glass transition temperature is associated with conformational changes of the molecular main chain, whereas the secondary transition involves conformational changes that do not require main chain movement. The preferred direction of such motion may be biased by stress just as happens with main chain relaxations, and under reversed loading conditions a particular group of atoms may change conformation repeatedly back and forth across an energy barrier, hence taking energy from the driving system and thermally heating the sample. This effect is a maximum at the so-called transition temperature and diminishes if the temperature is changed in either direction or, alternatively, if the frequency of the driving system is changed. The nature of the molecular process occurring needs to be deduced from other experiments [2]. There are, however, several general features of all time-dependent experiments which should be appreciated.

12.5.4 GENERAL FEATURES OF TIME/FREQUENCY-DEPENDENT EXPERIMENTS Title simplest definition of relaxation is that it is the time-dependent return to equilibrium of some system which has experienced a change in the constraints acting upon it. The constraints may be the familiar thermodynamic variables of temperature, pressure, volume, chemical composition or may involve v applied field such as mechanical stress, or a magnetic or electric field, The relaxation of the system is observed by monitoring the way some property changes in time. In this way we introduce the idea of a molecular response which takes a finite time to adjust to some perturbation. Very often the rate with which a perturbed system returns to equilibrium is proportional to the distance

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from equilibrium. This situation is termed an ideal relaxation and is familiar in a variety of physical situations. If we assign the parameter, P(t), to the difference between the value of an observed property at time, t. and the equilibrium value reached an infinite time after a step function change in constraint, Fig. 12.13, then


dP(t )  P(t ) dt


which has the simple exponential solution with a single time constant,

P(t )  P0 exp( t /  )


The constant T is called the relaxation time of the property under consideration and is the time taken for P to drop to 1/e of its original value. The exponential function (12.26) is often called the decay function of the observed property. In the experimental situation the change in constraints can be applied as a step function, but is very often applied as a sinusoidal variation. Under these circumstances the observed response lags in phase behind the applied constraints because of the finite time required by the molecules to make any necessary adjustment, Fig. 12.14. Thus the observed response of the system is mathematically cc3mplex. If the complex response in the time domain is given by the decay function

R  (t )   (t )


Fig. 12.13 Relaxation after a step change in constraints, C, monitored by observing the property P(t).


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Fig. 12.14 Relaxation in the complex response, R*, to a sinusoidal variation in constraint C. then the complex response in the frequency domain is the Laplace transformation

R  ( )   (d [( (t ))] / dt )


The complex response can be resolved into two components, one in phase with and the other 90o out of phase with the constraint. The Laplace transformation of the ideal decay function yields an ideal complex response. The Laplace transformation allows translation of the time domain into the frequency domain and is discussed in detail elsewhere [12]. The result of the mathematical manipulation is a relatively simple form for the response function:

R 1  R0  R 1  i
This separate into


R' 1  R0  R 1   2 2


R ''   R0  R 1   2 2


where R' and R" are the real and imaginary responses and have been normalized by R0-R∞ where R0 and R∞ are the values of the response at frequencies much below and well above those in the relaxation region, T is the time constant defined by the decay and m is the angular frequency, The functions (12.30) and (12.31) are illustrated in Fig. 12.15.


Thermal analysis

Fig. 12.15 Frequency dependence of real R' (full line) and imaginary R" (broken) response to an alternating perturbation. For values of ωη < 1 and temperatures greater than Tc′ Fig. 12.16, the speed of thermally activated molecular change is faster than changes in the applied constraints and so a large value of the real response is obtained. Conversely, when ωη > l or at temperatures below T, the molecules cannot adjust to the changes in constraints and so exhibit low values of the real response. The resolved out-of-phase response R" is a maximum at the intermediate situation when ωη = 1. The curves presented above are for ideal processes in which it is assumed that there is only one relaxation time T. In practice, the effects of differences in local environment will mean that the constraints on the motion of the individual molecular entities are not all the same and there will be a distribution of relaxation times. This has two effects: the process will either be spread over a larger frequency range or a larger temperature interval. The overall result is that the above equations need to be modified to include the possibility of a distribution parameter. The observed curves will also be 'skewed' and the most general form of the empirical fitting equation available is that attributed to Havriliak and Negami:

R 1  R0  R (1  (i )1 ) 


where α and β are constants which describe the distribution of relaxation processes present in the system. An important point which is often overlooked in the analysis of DMTA and related data is that unless the curves correspond to those of an ideal relaxation process then the location of tanδ and the peak of R" will not be the same. The tanδ peak is shifted to higher or lower temperature (or frequency) dependent on the nature of the skew in the distribution. Although it is common to use the peak of tanδ to locate Tg this therefore has to be done with some caution. It is not possible to discuss more fully the analysis of frequency dependent data in this text and the interested reader is referred to a more specialized text for further information [3].


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Fig. 12.16 Temperature dependence of real, R', (full line) and imaginary, R", (broken) response to an alternating perturbation.

12.5.5 APPLICATIONS OF DMTA The DMTA data are used for a variety of different applications. Traces for an unknown polymer can help with identification of the Tg process since many thermoplastic homopolymers exhibit a change of modulus from ~ 109 to a value of ~106 Nm-2. The magnitude of the change makes it easily detected. However, there is always some discussion as to the precise identification of the exact value of Tg. Some authors use the peak in the tanδ to locate Tg whereas it is also possible to argue that the appropriate temperature is the onset of the drop of the real part of the modulus. The difference between these values can be about 10℃ and this can lead to some confusion as to the appropriate value to use. It must also be recognized that the location of the TR depends on the frequency used for the measurement. The higher the fiequency used for the measurement then the higher the apparent temperature of the transition. Once more there can be differences between measurements of several degrees as a consequence of the use of different frequencies; typically the transition will increase by about 10℃ for a decade increase in frequency. The precise rate of increase depends on the chemistry of the system and is a function of the activation energy for that molecular process. It is therefore very important to appreciate that unlike a melting point which is an almost uniquely defined transition, Te can shift with the method used for its observation. The design engineer will find the temperature dependence of the modulus an invaluable tool in assessing whether a particular material is suitable for a particular application. In copolymers, such as styrene-butadiene-styrene, or elastomeric polyurethanes, it is possible to observe separate Tg values associated with the separate phases. In a terpolymer such as acrylonitrile-butadiene-styrene, several transitions can be found. If samples with different thermomechanical histories are examined, it is found that they give rise to different loss peaks. Thus if a sample is tested over a wide temperature range then


Thermal analysis

cooled and retested it will often produce a different result the second time. Such information may be of direct value in warning that changes may occur in service, if exposure to similar temperatures are possible, and this may lead to property changes. Combined with microscopic examination, the DMTA results may help to indicate what kind of molecular reorganization is taking place during annealing. The compatibility of blends and the dependence of their properties on thermomechanical history can be examined in a similar way. An example of the use of DMTA to investigate the properties of injection moulded polypropylene reinforced with short glass fibers (20% by weight) is given in Fig. (12.17).

Fig. 12.17 DMAT traces for glass-fibre reinforced polypropylene specimens cut from the skin and core of an injection moulded bar and tested parallel and transverse to the bar axis. Results are presented for samples cut from the skin and the core of end gated bar mouldings and for both the now direction and transverse to it. Allowing for the possible uncertainty in the absolute values of the stiffness, there are obvious differences between these samples. The stiffness is considerably greater in the bar axis direction at all temperatures; this effect is attributed to fibre alignment. The TR for this material should be near to 0℃ and it is indicated by a change in slope in the E' plots and by a small peak in tanδ. The E' curve falls steeply as the temperature is increased through the crystal melting temperature and tanδ peaks sharply in this range. Much larger effects occur in this range with unreinforced polymers. A much more prominent Tg effect is observed with non-crystalline polymers. Fig. 12.18. The E' trace falls steeply as the temperature rises through Tg and a large tanδ peak is obtained at this position. The process of annealing will increase the value of Tg and will also sharpen the tanδ peak. The curing of thermoset resins can be examined, the modulus increasing with cure. The tanδ value usually rises at first then falls rapidly as the crosslink density becomes higher and progressively inhibits conformation changes. For investigations of this kind a properly designed experimental programme is essential to take account of the time-temperature effects in the chemical reaction.


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Fig. 12.18 DMTA spectra for PMMA showing E' and tanδ for unaged (+) and aged (×) samples measured at 1 Hz. The Tg of the unaged sample assessed using the onset of the fall of the modulus is ~98℃ and that of the aged sample is ~110℃.

12.5.6 TIME-TEMPERATURE TRANSFORMATION DIAGRAMS Gillham [2,3,4] has proposed that the cure of a thermosetting resin system may be best represented using a time-temperature transformation diagram, Fig. 12.19. This diagram describes the phase changes which occur when temperature and time are changed for a thermosetting system. Initially the components are present as unreacted species which at some temperature will exist in a solid state: the sol glass. If the time or temperature is increased then reaction can occur and a change of state is initiated. Increasing the temperature leads initially to the generation of a liquid, the viscosity decreasing as the temperature is increased. The liquid consists of reactive monomers which will convert to initiallly a gel, then forming a sol-gel rubber which, if the temperature is below the Tg of the glass, will vitrify, The extent to which reaction occurs will depend on the temperature of reaction. If the material is cured above the Tg of glass it will ultimately reach a value Tg,∞ which is that of the fully cured material. If, however, the temperature is kept above this value for too long chain scission can occur and the matrix may start crosslinking and degrade to form a char material. In processing of a polymer it is usually the gelation and vitrification curves which are of interest and the vibrating needle curometer is a useful method of observing these transitions.


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Fig. 12.19 Time-temperature transformation (TTT) isothermal cure diagram for a solvent tree epoxy system. The diagram shows three critical temperatures Tg, ge1 Tg, Tg,∞ and the distinct states of matter, i.e. liquid. sol gel rubber. gel rubber (elastomer), gelled glass. ungelled glass (or sol), glass and char. The full cure line, i.e. Tg = Tg (∞) = Tg,∞ , divides the gelled region into two parts: sol gel glass and fully gel glass. Thermal degradation events are responsible for devitrification and the char region. The vitrification process below Tg (gel) has been constructed to be an isoviscous one. The transition region approximates the half width of the glass transition. (By kind permission of Gillham and RAPRA Technology Ltd.[2])

12.5.7 VIBRATING NEEDLE CUROMETERS (= CUREMETERS) A number of attempts have been made to simplify the definition of the cure process based on the torsional braid analysis (TBA) which uses a composite specimen made simply by impregnating a braid substrate with fluid [1]. The vibrating needle curometer (VNC) promoted by the Rubber and Plastic Research Association (RAPRA) and the vibrating paddle rheometer based on a design developed at the University of strathclyde and commercialised by Polymer Laboratories and Rheometrics [5,6] represent alternative approaches to the study of cure. Both systems have been developed to provide industry with a relatively simple and widely applicable method for quantification of the cure process. One of the prime prerequisites for such an instrument is that it should have a large dynamic range, be robust and easily used. Both


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instruments can be used with attachments which allow isothermal conditions to be achieved for the cure of the material or can have the probe elements inserted into a reaction medium, allowing the instrument to be used as a process control monitor. Both instruments use a similar approach, but for brevity the Strathclyde instrument will be described here, Fig. 12.20.

Fig. 12.20 A schematic representation of the Strathclyde curometer (by kind permission of RAPRA Technology Ltd. [7.9]).

The instrument uses the damping of the vibrating needle or blade tomonitor the change In viscosity as cure proceeds. The amplitude andphase of the motion of the bottom of the spring are directly related to the degree of damping produced by the gelling fluid. The motion of the probe is sensed by a linear variable differential transformer (LVDT). Comparison of the in-phase components of the amplitude of the motion and the phase shift can be used to calculate the rheological properties of the curing system. The dynamic range of the curometer is defined by the spring and the frequency of operation, and for the current system it is possible to explore the viscosity range 10-105 Pa s. Use of a weaker or stronger spring in principle allows a lower or higher range to be investigated. The motion of the needle can be described by:

k ( P1 (t )  P2 (t ))  CdP2 / dt  0


where k is the spring constant, P1 and P2 are the instantaneous displacements from equilibrium at points P1 and P2, respectively. η is the viscosity of the material and C is a geometric factor related to the probe/material contact area. Since P1 (t) is a sinusoidal function, the differential equation can be written in complex notation as


Thermal analysis

k ( P1  P2 )  iCP2  0


where the values of P1, P2, and η are also dependent upon the frequency ω. Equating real and imaginary components,

P1  P2'  (iC / k ) P2'  0


P2"  /(C / k ) P2'  0


where P'2 and P"2 are the real and imaginary components of P2. The motion of P1 is the reference state and so taken to be real. Solving for P'2 and P"2 gives

P2  P /[1  (C / k ) 2 ] 1



P2  P1C / k[1  (C / k ) 2 ]


The viscosity η can therefore be obtained directly from observation of the movement occurring at point P2 relative to that at point P1. In the current system, the linear motor is sufficiently strong for the amplitude of the motion at point P1 to be assumed to remain constant during the whole of the experiment. From the above data it is possible to calculateshear moduli.

12.5.8 CURE OF AN EPOXY RE51N SYSTEM To illustrate the type of data which may be obtained during the cure process, curves for the stoichiometric cure of the diglycidyl ether of bisphenol A (DGBA) and diamino diphenyl sulphone (DDS) are presented, Fig. 12.21. At low temperatures, gelation of this system and the viscosity increase proceed very slowly over a relatively long period of time. In contrast, the plots obtained at higher temperatures indicate a much more rapid increase in the viscosity, consistent with the faster rate of reaction and the lower possibility of relaxation of the matrixduring the cure process. The sensor monitoring the temperature indicates that the system exotherms dramatically at high temperatures. The point at which the damping is observed to be increased (tl in Fig. 12.21) is indicative of the pot life of the resin at 125℃. The pot life is an arbitrary parameter and it is possible to define it as a 3-5% reduction in amplitude or increase in the viscosity of the medium. Beyond this point, the resin begins to build a structure which will be incapable of further now and produces a lower quality moulding. The point at which the calculated viscosity reaches a value of 104 Pa s is normally accepted as the gelation point. Figure 12.21(b) gives the temperature dependence of the time to gelation for the system for which curometer data are shown in Fig. 12.21(a).


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Fig. 12.21 Cure data for the diglycidyl ether of bispherol A and diamino diphenyl sulphone. Key 125℃. --- 130℃, --- 142℃, -.-.-. 155℃, - - - 165℃. - - - - 174℃, -- ---- 190℃ temperature of cure [8,9].


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12.6 DIELECTRIC THERMAL ANALYSIS (DETA) When a polar polymer is placed in an electric field the permanent electric dipoles will attempt to align with the field direction. Their realignment is retarded by the neighbouring elements of the polymer. As the temperature is increased so various types of dipoles will become active and this give rise to changes in the polarizability of the material. If the polymer is below Tg realignment of the backbone is not possible and it is only the conformational changes of the side chain or short elements of the backbone which are possible. If an alternating field is applied the dipoles will be encouraged to move in opposite directions on alternate half cycles. If the temperature is too low or the frequency of the field too high it is impossible for them to follow. If the temperature is high, however, the dipoles can realign repeatedly and this causes energy to be withdrawn from the driving field and appears as heat. The polarization lags behind the energizing electric field and the angle, δ, and the corresponding tanδ values have a similar significance to that described for DMTA (Section 12.5).Analogous to the mechanical case, the properties of the material are described in terms of a complex dielectric permittivity (ε*), which contains a storage component (ε') and a loss component (ε")




1 E '  iE "  '2 E '2  iE " E  E "2


The negative sign in equation (12.39) follows from the relationship between the dielectric permittivity and the applied field (E). The electric displacement (D) which includes the contribution from the polarization (P) is given by

D  E  4P   * E


In. the above equation E denotes the driving force and D lags behind the case of the dielectric experiment. Otherwise the analysis used for the mechanical system is appropriate here and the curves which are observed resemble those for the mechanical case except that ε replaces E. Strictly speaking ε* is equivalent to l/E*; note that

1 1 E '  iE "  1  '2 E  E  iE " E  E "2


The value of tanδ can be expected to show a similar temperature dependence to the mechanical loss tangent, since both depend on the ease of molecular relaxation of the backbone, though the intensity of the relaxation depends on the strength of the coupling to the electric field, which depends on the dipole moment of the relaxing group. Dipole relaxation can be divided broadly into three types: 1. Relaxation of dipoles attached to polymer backbone. These are only constrained by the bond attaching the group to the backbone and hence reflect the motion of the side group relative to the backbone. 2. Relaxation of dipoles perpendicular to the chain backbone. The motion of these dipoles will reflect the


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motion of the backbone and is closely correlated with the Tg process. 3. Relaxation of dipoles parallel to the chain backbone. These dipolescannot be relaxed other than by rotation of the whole molecule and are usually only observed in solution or the liquid state. It is therefore important to recognize that dipoles, being a vectorial property of the molecule, provide the possibility of resolving the nature of the motion into its spatial components. In most amorphous materials all orientations are present and the vectorial nature is averaged. However, the vectorial nature of the processes can be sometimes apparent from an analysis of the observed processes. We shall not pursue this further and the interested reader is referred elsewhere [12] for a more complete discussion of the theory of dynamic dipole permittivity. By using a range of different methods to measure the dielectric properties an enormous frequency range can be covered, 10-4 -1010Hz. Much of the early data found in the literature were obtained using apparatus designed and assembled in the laboratories in which the measurements were made. However, commercially available computer controlled systems such as the Polymer Laboratories DETA equipment, operating over a frequency range from 20 Hz to 100 kHz are now well established. Typical samples are discs N30 mm diameter and 0.1-2mm thick and, as in the DMTA case, thermal scanning is often used to complement frequency-dependent data. Finally, it should be recognized that commercial plastics contain many additives, and if these are polar they may provide coupling to the electric field that can give a significant response even with a non-polar polymer. The opportunities for realignment of the polar impurities are governed by the movement of the neighbouring segments of the polymer in which it is embedded so that the tan8 peaks correspond to relaxations of the polymer.

12.6.1 APPLICATIONS OF DETA Changes in the permittivity of a polymer sample as a function of frequency and temperature can provide information on the molecular dynamics of the systems. In this context the information obtained complements DMTA or dynamic NMR spectroscopy studies. Since the dipole can easily be identified by an inspection of the chemical structure of a polymer it is possible to use the observation of a particular feature as a good diagnostic test of the assignment of a particular relaxation process to a specific conformational change. Recently it has been possible to compare the activation energy and intensity of a process to the predictions of theoretical modelling and hence improve the certainty of the predictions. A number of texts exist describing the characteristics for particular polymers and the reader is referred for further information [12]. As an example of the typical dielectric spectrum for a polar polymer, data on PET are presented in Fig. (12.22). The relaxation observed in this temperature-frequency range is that of the ester group rotation. The peak in ε" shifts to higher frequency as the temperature is raised with a rate controlled by the activation energy for the process. All polar polymers are capable of exhibiting similar curves unless they form a very highly crystalline solid.


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Fig. 12.22 Dielectric permittivity and loss spectra for Poly(ethylene terephthalate (PET) at 75℃ (■), 80℃ (●), 85℃ (▲), 90℃ (▼), 95℃(◆) and 100℃ (×) and the Arsenics activation energy plot.


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Fig.12.23 (a): Variation in dielectric permittivity, ε' , for poly(ethylene terephthalate) aged at 70℃. ( b): Changes in ε' at 200 Hz for Poly(ethylene terephthalate) at 40℃ (■), 50℃ (●). 60℃ (▲) and 70℃ (▼).

12.6.2 PHYSICAL AGEING OF POLAR POLYMERS The physical ageing of polymers causes changes in the mechanical properties, an increase in the Tg and change in impact properties. In the case of PET the ageing process observed through dielectric relaxation


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causes the low frequency permittivity to be reduced consistent with an increase in Tg and a loss of impact properties, Fig, 12.23. The reduction of the permittivity is related to a densification of the polymer matrix and a reduction in the extent to which dipole rotation is able to occur. The reduction in the molecular mobility in the polymer matrix reduces the impact resistance of the polymer and alters its ability to transport gas. The latter is very important in understanding the physical properties of carbonated drink bottles.

52.6.3 MONITORING CURE IN THERMOSET POLYMER SYSTEMS Thermoset polymer systems are usually initially mixtures of low molecular mass multifunctional reactive monomers which form a low viscosity fluid. The dipole relaxation of the liquid will usually occur at higher frequencies than those available with the DETA instrument. As cure proceeds so the molar mass increases and the relaxation moves to lower frequencies. Often in the initial liquid there will be ionic species and these can lead to very large dielectric permittivity and loss processes, Fig. 12.24. As the viscosity is increased so the mobility of the ions is reduced with a corresponding reduction in the large loss processes present at low frequencies. This feature will often be observed to have disappeared at the point at which the gel is formed. The subsequent small drop in the permittivity and loss is associated with the vitrification of the material as the dipoles of the chain become frozen by the crosslinking of the matrix structure. It should be noted that the point at which the vitrification occurs changes with time and reflects the dynamic nature of the Tg process. The dielectric apparatus may be used to monitor the cure of a resin and has been used as such in the characterization of composite materials.

12.6.4 CHARACTERIZATION OF POLYMER MORPHOLOGY Whilst the main use of dielectric studies has been in the characterization of dipole relaxation it is possible to use the method to study the morphology of phase separated polymer systems. When a rubber modified amine epoxy resin is studied it is observed that a loss feature exists in the material after the system has been converted into a vitrified glass, Fig. 12.25. Since the process of vitrification has frozen all the dipoles associated with the epoxy resin one has to seek an explanation for the observed loss feature . In rubber modified epoxy resins, there exist small spherical rubber particles of about 0.l-l μm diameter. Within these rubber particles are ions that can be polarized by the electric field and since they are trapped by the hard epoxy surrounding interface can only move across the diameter of the sphere. However, since the sphere is typically 100-1000 times the distance of the typical valence bond the magnitude of the process will be correspondingly larger. A detailed mathematical analysis of the connection between the microstructure and the observed dielectric properties indicates that, with a knowledge of the ionic mobility, it is possible to calculate the number, size and shape of the rubbery phase particles. This approach has been applied to a number of systems and proven to be useful in the in situ study of the development of phase separation in thermoset polymer systems and also changes in microstructure on ageing. The interested reader is referred elsewhere for the detailed theory and outline of the analysis involved [10].


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Fig. 12.24 Typical curves for an epoxy amine thermoset system. (a) is the dielectric permittivity and (b) the dielectric loss plotted as a function of the frequency (10-1-105Hz) and time of cure (0-300 s).


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Fig. 12.25 Dielectric constant for DGEBAffETA/16.2 wt% CTBN cured at 30℃.

Fig. 12.26 The rise of the permittivity measured as a function of frequency and exposure time for an epoxy resin system.


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12.6.5 WATER ADSORPTION BY POLAR POLYMERS The adsorption of water by a polymer can cause plasticization and a lowering of the Tg. Water, being polar, can exhibit a distinct dielectric process when dispersed in a polymer system. In an epoxy resin there are observed two types of water water which is bound to hydroxyl groups generated as a consequence of the coupling reaction of amine with-the oxirane ring and water which is clustered in micro voids and exhibits characteristics of free water. Figure 12.26 shows the initial rise of the permittivity at low frequency associated with water diffusion into the polymer. Free water relaxes at frequencies of the order of 12 GHz at room temperature and therefore it is not possible to observe this process directly except with very special equipment. However, the changes observed at 1 Hz are the sum of the signal from the bound water which relaxes at about l kHz and the free water which relaxes at even higher frequency. It is possible in principle to separate out the proportions of bound and free water and to show that factors such as change in the stoichiometry of the reaction mixture, nature of the cure process and the temperature of cure all have a profound effect on both the rate at which water is absorbed and the equilibrium value. It is only water which is bound to the polymer that effectively produces plasticization and hence it is observed that not all of the water is active in reducing Tg. Dipole relaxation studies can provide a considerable amount of molecular information and give chemists insight which allows them to modify the structure of a material so as to achieve improved physical properties. The technique is most effectively used in conjunction with other dynamic methods [11] ' REIERENCES 1. Willoughby, B.C,. Scott, K.W. and Hands, D. (1990) Flow and Cure of Polymers-Measurement and Control, RAPRA Technology Ltd., Shrewsbury. 2. Gillham, J.K. (1990) flow and cure of Polymers - Measurements and Control, RAPRA Technology Ltd., Shrewsbury. 3. Gillham, J.K (1982). Developments in Polymer Characterisation (ed. J.v. Dawkins) Vol. 3, Applied Science Publishers. London, Ch. 5, pl59. 4. Gillham, J.K. (1990) Crosslinking and Scission in Polymers (ed. O. Gurven), Nato ASI Series, C. Kluwer, Dordrecht. 292, 171. 5. Polymer Laboratories, Thermal Sciences Division, The Technology Centre, Epinal Way, Loughborough, UK, LE 11 OQE. 6. Rheometrics Scientific Ltd., Surrey Business Park, Weston Road, Kiln Lane, Epsom, Surrey, KTI7 lJF. 7. Affrossman, S., Collins, A., Hayward, D., Trottier, E. and Pethrick, R.A. (1989) J. Oil and Colour Chemists Ass., 72, 452. 8. Hayward, D., MacKinnon, A.J., Pethrick, R.A., Baker, F.S., Ferguson, J., Carter, R.E. and Daly, J.H. (1990) Third European Rheology Conference (ed.D.R. Oliver) Elsevier Applied Science, London, p. 211. 9. Pethrick, R.A. (1993) Techniques in Rheological Measurement (ed. A.A. Collyer), Chapman & Hall, London. 10. Delides, C.G., Hayward, D., Pethrick, R.A. and Vatalis, A.S. (1992) Eur. Polym. J.28, 505-512. 11. Hayward, D., Hollins, E., Johncock, P., McEwan, I., Pethrick, R.A. and Pollock, E.A. (1997) Polymer 38, 1151-1168. 12. Bailey, R.T., North, A.M. and Pethrick, R.A. (1981) Molecular Motion in High Polymers. Clarendon Press, Oxford.


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