Thermal Analysis.docx

1、Thermal Analysis12Thermal analysis 12.1 INTRODUCTIONThermal 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 t

2、he 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

3、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 (H) or entropy (S) changes that occur when transformations such as crystal meltin

4、g 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 molec

5、ular 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

6、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

7、 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

8、 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 (not correct) due t

9、o thermal lag (to develop more slowly than others) 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

10、the programme temperature and the reference temperature and T (=TsTr) is negative. The size of T 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. For this reason it is d

11、ifficult 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. Wr and Ws are constant instrument factors that de

12、pend 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 p

13、roperties 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

14、 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 d

15、eparture from the programme temperature, i.e. Ws(TsTp) and Wr(TrTp) respectively. The differential power requirement Ws(TsTp) Wr(TrTp) 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 a

16、nd therefore much closer than Ts and Tr, in the DTA method whenever thermal changes are taking place.12.2.1 QUANTITATIVE ANALYSIS OF DTA AND DSCFig. 12.2 Schematic of a DSC apparatus: r is reference; s is specimen. Wr and Ws are constant instrument factors that depend on the thermal characteristics

17、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. 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

18、 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 (at a rate dQs/dt) the energy balance gives: (12.1)where Hs is the enthalpy of the sample and Cs is the heat capacity of the sample plus the cell. The ra

19、te of heat now can alternatively be given as (12.2)Hence (12.3)If a suitable internal reference sample has been selected, the equivalent expression for the reference cell can be written as (12.4)where subscript r stands for the reference cell and R is assumed equal for the (identical) sample and ref

20、erence cells: i.e. (12.5)where T (=TsTr) 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 T versus T (or t) then, in principle, equation (12.5) can be used for quantitative analysis. In p

21、ractice 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 trans

22、ition.For DSC we can take equation (12.1) and the equivalent equation for the reference cell and find (12.6)where Q is the difference in heat supplied to the two cells, i.e. (12.7)Now from equation (12.2) we have and so that (12.8)Substitution of (Tr-Ts) from equation (12.8) into equation (12.7) giv

23、es (12.9)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. T R). Using DSC, if C is the diff

24、erence in heat capacity between the sample and reference cell then the measured heat flow (Q1) when both pans are empty will be Q1 = KC (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 t

25、he two cells becomes (C + 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 isQ2 = K(C + msCp,s) (12.11)If now the sample is replaced by a calibrant (c) (e.g. alumina) and the procedure is repeated the measurement becom

26、es Q3 = K(C + mcCp,c) (12.12)From equations (12.10), (12.11) and (12.12) it follows that (12.13)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

27、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 n

28、umber 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

29、 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 deter

30、mine 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 heat

31、ing 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

32、. 12.4). Fig. 12.4 Schematic representation of a modulated DSC experiment.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 5.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 differen