Measurement of Specific Heat Functions by Differential Scanning Calorimetry M. J. O'NEILI The Perkin-Elmer Corp., Norwalk, Conn. When a sample material is sub- jected to a linear temperature pro- gram, the heat flow rate into the sample is proportional to its instan- taneous specific heat. By recording -dH this heat flow rate as a function of dt temperature, and comparing it with the heat flow rate into a standard material under the same conditions, t the specific heat of the sample is de- II termined as a fundion of temperature. II The method is illustrated by measure- I II ments on various samples in the tem- T2---l--- ' perature range 340" to 510" K., and agreement with literature specific heat values is demonstrated. The ultimate precision of the method is 0.370 or better, which approaches the Tk=-tFigure 1. Linear temperature program precision of adiabatic calorimetry. However, measurements may be made with samples which are four orders of magnitude smaller, and program transition heat effects may be obtained two sample holders, using platinum rates two orders of magnitude larger, by comparison of heat content values resistance thermometers and heating than those typical of conventional on both sides of the transition tempera- elements embedded in the sample calorimetry. ture, but this method is unreliable when holders. A secondary temperature the difference is small. control system measures the tempera- At temperatures above 350" K., ture difference between the two sample ETERMINATION of specific heat is specific heats in the absence of sharp holders, and adjusts this difference to D accomplished in two ways, de- transitions are obtained by differentia- zero by controlling a differential com- pending on the temperature range in tion of the algebraic function of T ponent of the total heating power. which the property is to be measured. which best fits the measured heat This differential power is measured and From cryogenic temperatures to ap- content data. It is evident that this recorded. proximately 350" K., adiabatic calorim- process can lead to percentage errors eters are used, while at higher temper- in the specific heat which are con- SPECIFIC HEAT DETERMINATION atures the drop calorimeter, using the siderably greater than the errors in the method of mixtures, is preferred. Rep- original measurements. The ad- In order to measure the specific heat resentative adiabatic calorimeters and vantages of a technique which would of a sample, the sample holder tempera- drop calorimeters have been described permit the direct measurement of ture is programmed as shown in Figure in detail in the literature (I, 4, 12). specific heat and determination of heat 1. To establish a base line, the pro- A common feature of these calorim- content changes by integration of the gram is carried out with no sample eters is that in order to achieve pre- specific heat function are clear. present; however, empty aluminum cision their applicability in routine foil sample containers are placed in the laboratory analysis has been seriously sample holders. Isothermally, the base compromised. Analysis time is pro- DIFFERENTIAL SCANNING CALORIMETRY line indicates the differential losses of hibitively long, large samples are re- A new instrumental method for the the two sample holders at the initial quired, and sample geometries must be direct measurement of specific heat has temperature. When the program begins, carefully controlled. been developed. In differential scan- there may be a small offset from the A more fundamental objection to ning calorimetry (DSC), the sample isothermal base line, caused by the these techniques concerns their pre- material is subjected to a linear tempera- thermal capacity mismatch between the cision at transition temperatures in the ture program, and the heat flow rate two sample holders and their contents. sample material. In the adiabatic into the sample is continuously When the temperature program ends, calorimeter, adequate resolution of measured; this heat flow rate is pro- the isothermal base line reappears. sharp transitions is possible only at portional to the instantaneous specific This procedure is then repeated, with extremely slow scanning rates, and with heat of the sample (7, 11). a weighed sample added to the sample a resultant loss in sensitivity and Two sample holders are mounted holder. The isothermal base lines are signal-to-noise @/A') ratio. In the symmetrically inside an enclosure which unaffected, since the sample has no drop calorimeter, heat contents re- is normally held at room temperature. influence on the power dissipation of the ferred to a standard temperature A primary temperature control system sample holder. However, there is an (usually 298.15' K.) are measured; controls the avcrage temperature of the additional off set from the programming VOL. 38, NO. 10, SEPTEMBER 1966 1331 -dH dt BASELINE BASELINE LtI_ I I""I~"'l*'",l Figure 2. C, calculation by ratio method STARTf UO 400 450 SO0 LTOP T- *K Figure 3. Base line, calibration, and sample analysis base line, owing to the absorption of heat by the sample. If the sample is result. However, these two parameters are the mass and specific heat of the entirely enclosed by the sample holder, may be eliminated from the calculation standard, and K is the ordinate calibra- every elementary volume within the if a material with a known specific tion factor, in cal. inch-' sec.-l sample must eventually arrive at the heat is used to calibrate the instrument. Dividing Equation 3 by Equation 4, program rate dT/dt prescribed by the Such a material is a-aluminum oxide, and rearranging terms: sample holder, after a transient effect, or synthetic sapphire, for which the the duration of which depends on the CP - m'y specific heat has been determined to five (5) size and thermal diffusivity of the significant figures in the temperature C,' my' sample. Therefore the heat flow rate range 0" to 1200' K. (3). into the sample is given by Figure 2 illustrates the method. Thus the calculation requires only the comparison of two ordinate deflections dT After the base line and sample programs, = mC,- a third program is run with a weighed at the same temperature. It will be at at sapphire standard. At any tempera- observed that the calculation would be ture T, the following equations apply: correct even if the ordinate calibration where dH/dt is the heat flow rate in and the program rate were temperature- calories second-', m is the sample mass dT dependent. In fact, the ordinate in grams, Cp is the specific heat in Ky = mC, - (3) calibration varies by less than 2% over calories gram-' O K.-l, and dT/dt is the dt the operating temperature range of the program rate in O K. sec.-l instrument. However, the program It follows that the area under the ld_T 5% Ky' = m'C, (4) rate may vary by as much as in a dH/dt curve between any two tempera- at 100" K. interval, owing to the inevitable tures is the change in heat content, as nonlinearities in the temperature shown by Equation 2: where y and y' are the ordinate de- calibration and in the temperature flections in inches due to the sample and control system. Thus Equation 5 the standard, respectively, m' and C,' represents the better method of calcula- This illustrates the difference between scanning calorimetry and the drop calorimeter technique, where the heat content is the measured property, and the specific heat is obtained by dif- ferentiation. Although every part of the sample is programming at exactly the same rate eP dT/dt, the true temperature of the CAL. MOLE:' DE^' sample differs slightly from the indicated temperature of the sample holder, owing to temperature gradients which appear within the sample and at the interface between the sample and the sample holder. The gradient at the interface is always much larger than the gradient within the sample, and is one of the sources of error to be discussed later. In order to use Equation 1 in a specific heat calculation, the ordinate calibration and the temperature pro- gram rate must be known with at least TEMPERATURE *K the precision required of the final Figure 4. Specific heat of graphite, 39.7 mg. 1332 ANALYTICAL CHEMISTRY 4.0 4 X lo-' cal. sec.-', which was left uncorrected. The ordinate calibration is shown for reference. For each sample, C, was calculated at intervals of lo", using the method of 3.0 Equation 5, and the data were plotted against a temperature abscissa. Figures 4 and 5 show the calculated specific CP heat functions for graphite and GAL. MOLE? DEC' diamond. These samples are unusual, in 2.0 that their specific heats are quite small and very temperature-dependent. In accordance with the suggestion of Maier and Kelley (6), the heat content and specific heat functions of such samples are usually represented by '+o+ '+o+ expressions of the form H(T) - H(T0) = 0 b 300 350 400 450 500 550 UT + 2 T2+ cT-' - d (6) TEMPERATURE OK Figure 5. Specific heat of diamond, 70.2 mg. C, = a + bT - cT-2 (7) tion. For repetitive determinations at had a weight of 129 mg. The tem- The four coefficients are chosen so that the function described by a single temperature, Equation perature scale was calibrated with 1 Equation matches the measured heat might be used with a calibration factor, melting point standards. 6 but with a considerable loss of accuracy. The ordinate data were recorded content function as closely as possible. with a Leeds and Northrup Speedomax Table I shows the comparison between G 10-mv. recorder, with a chart speed the DSC data and literature values for EXPERIMENTAL of 1 inch per minute.