Determination of specific heat capacity
The specific heat capacity (cp) is an important, temperature-dependent material property and is often specified in material data sheets. It can be conveniently and reliably measured by DSC. The specific heat capacity is a key property for improving technical processes such as injection molding, spray drying or crystallization as well as for the safety analysis of chemical processes and the design of chemical reactors.
In this Webinar, we will discuss six different methods for determining the specific heat capacity and present some interesting applications.
The Webinar covers the following topics:
- Definition of Specific Heat Capacity, cp
- Importance of cp
- Direct method
- Sapphire method
- IsoStep® DSC
- Steady State ADSC
DSC is a measurement technique commonly used for the determination of specific heat capacity because of its ease of use, short measurement times and because it provides adequate accuracy.
The specific heat capacity is used to specify materials and is quoted in data sheets. It is important for improving technical processes such as injection molding, spray drying, and crystallization, and is an important property for the safety analysis of chemical processes and reactor construction.
Heat capacity vs specific heat capacity
The measured heat capacity depends on the sample size and does not characterize the material.
For DSC measurements, the heat capacity is essentially the ratio of the heat flow and the heating rate. The unit of the heat capacity, Cp, is Joules per Kelvin.
A more meaningful material property is the determination of specific heat capacity, cp. This is the heat capacity divided by the sample mass. The unit is Joules per gram Kelvin.
cp measurement methods
This webinar presents six different methods included in METTLER TOLEDO's thermal analysis STARe software. The so-called Direct and Sapphire methods are performed using a conventional DSC instrument and a linear temperature program. The specific heat capacity can be also measured using different temperature-modulated DSC techniques, namely IsoStep DSC, Steady State ADSC, ADSC, and TOPEM.
Specific heat capacity
Ladies and Gentlemen,
Welcome to the METTLER TOLEDO webinar on the specific heat capacitydetermination by DSC.
The determination of accurate values of the specific heat capacity of materials and substances has always been very important. Differential scanning calorimetry, or DSC as it is called, is a measurement technique commonly used to determine heat capacity because of its ease of use, short measurement times and because it provides adequate accuracy.
During this webinar, I want to discuss the different methods for determining specific heat capacity by DSC.
Slide 1: Contents
First, I would like to define what we mean by the specific heat capacity and then briefly discuss the technical importance of this property.
In practice, several different methods can be used to determine the specific heat capacity from the DSC heat flow. The METTLER TOLEDO STARe software supports the six main methods. I will explain each method in detail during the course of the seminar.
Finally, I want to discuss the advantages of heat capacity measurements using a number of practical applications.
Slide 2: Definition of Heat Capacity
The heat capacity of a sample is a property that can be measured under different experimental conditions, normally either at constant pressure or at constant volume.
The heat capacity of solids and liquids is usually performed at constant pressure. The symbol for this is Cp, that is, a capital C with the subscript p.
Cp is a physical quantity that characterizes the amount of heat, delta Q, that is required to change the sample temperatureby delta T. Consequently, Cp is the ratio of the exchanged heat and the temperature change of the sample.
The larger the heat capacity, the greater the quantity of heat required to increase the sample temperature by one Kelvin.
Slide 3: Definition of Specific Heat Capacity
The heat capacity consists of two components: the sensible heat capacity and the latent heat capacity.
The latent heat capacity is related to physical or chemical transitions such as melting, crystallization or chemical reactions. Thermal events like this are observed in a DSC curve as endothermic or exothermic peaks. Consequently, the latent heat capacity is positive for endothermic events and negative for exothermic events.
The sensible heat capacity is related to the amount of heat absorbed due to rearrangements and movement of the molecules as a whole. This component is positive. The DSC curve in the diagram shows that the sensible heat capacity is directly related to the measured heat flow if no thermal events occur. In many transitions, the sensible heat capacity defines the baseline of the related peak.
For DSC measurements, the heat capacity is essentially the ratio of the heat flow and the heating rate. The unit of the heat capacity, Cp, is Joules per Kelvin. The heat capacity depends on the sample size and does not characterize the material.
A more meaningful material property is the specificheat capacity, cp, that is, a small c with the subscript p. This is the heat capacity divided by the sample mass. The unit is Joules per gram Kelvin.
If we divide the heat capacity by the mole number, we get the molar heat capacity in units of Joules per mole Kelvin.
Slide 4: Importance of cp
This slide lists several practical applications of the specific heat capacity, cp.
The specific heat capacity is used to specify materials and is quoted in data sheets. It is important for improving technical processes such as injection molding, spray drying, and crystallization, and is an important property for the safety analysis of chemical processes and reactor construction.
To understand material behavior and reactions, it is important to have detailed knowledge of thermodynamic functions such as enthalpy, entropy, and Gibbs free energy. These functions can be directly determined from the specific heat capacity.
It is also an important quantity for the advanced evaluation and interpretation of DSC curves.
Slide 5: Typical values
The table in the upper part of the slide lists values of the specific heat capacity, cp, for five substances at twenty-five degrees Celsius (25 °C). Polymers, for example, typically have cp values between 1 and 2 Joules per gram Kelvin (J/gK). The value for water is about 4 Joules per gram Kelvin (J/gK).
The specific heat capacity is a function of temperature. This is illustrated in the two diagrams shown below. The diagram on the left shows the behavior of sapphire. The specific heat capacity increases with increasing temperature. This behavior is typical for most substances.
The diagram on the right shows the abnormal behavior of water with a minimum at thirty-five degrees (35 °C).
The temperature dependence of the specific or molar heat capacity of many materials is listed in different databases. The ATHAS Data Bank includes data for a large number of polymers.
Slide 6: cp Measurement Methods
I now want to discuss several different methods used to measure the specific heat capacity based on DSC.
The slide summarizes the six different methods included in the METTLER TOLEDO STARe software.
The so-called Direct and Sapphire methods are performed using a conventional DSC instrument and a linear temperature program.
The specific heat capacity can be also measured using different temperature-modulated DSC techniques, namely IsoStep DSC, Steady State ADSC, ADSC, and TOPEM.
In the following slides, I will describe the different methods using polystyrene as an example. The measurements were performed between ten (10) and forty degrees Celsius (40 °C) using a fifteen-milligram (15-mg) sample in a forty-microliter (40-mL) aluminum crucible.
The specific heat capacity data of this particular material is certified by NIST, the National Institute of Standards and Technology of the USA. The relative deviation between the true data and the measured values is the accuracy. Sometimes the much smaller precision or the repeatability is wrongly used instead of the accuracy. For example, if the measured data of sapphire is used for accuracy determinations, the result is in fact the precision if the calculation is performed with respect to measured sapphire data.
Slide 7: Direct method
The simplest method to determine the specific heat capacity is the Direct method.
The upper diagram shows the temperature program and the lower diagram the measured heat-flow curves plotted against time.
The measurements were performed at ten Kelvin per minute (10 K/min). The red curve shows the measured sample heat flow. The curve of the empty crucible is shown in black and is called the blank curve.
To determine the specific heat capacity, the STARe software divides the blank-subtracted heat-flow curve by the heating rate and the sample mass.
This approach can be also used without blank subtraction and without an initial isothermal segment, but results in reduced accuracy.
Slide 8: Direct method
This slide displays the result of the Direct method.
The upper diagram shows the blank-corrected heat flow curve. This curve is used to determine the specific heat capacity curve and is shown in the lower diagram.
The first part of the measured cp curve does not represent the sample because it is influenced by the initial start-up transient of the DSC. The data is valid about one minute after starting the measurement.
This method requires accurate calibration of the heat flow in the relevant temperature range.
The accuracy of the Direct method is not better than 5%. The advantage is the short measurement compared with other methods. The results are useful for quickly characterizing the relative change of the heat capacity.
Slide 9: Sapphire Method
The next two slides describe the so-called SapphireMethod.
The method is described in different standard procedures. An important feature of this method is that a sapphire sample is used for calibration and that possible drift can be corrected.
The temperature program is shown in the upper diagram. It contains an isothermal segment at the beginning and at the end of the measurement with the heating ramp segment in between. The length of the isothermal segment is typically five minutes and the heating rate is usually ten Kelvin per minute (10 K/min).
It can be seen in the lower diagram, that this method requires three measurements, namely the sample, the blank and the sapphire.
The software calculates the specific heat capacity with respect to the specific heat capacity of the sapphire standard.
Slide 10: Sapphire Method
The slide summarizes the results obtained using the Sapphire Method.
The upper diagram displays the blank-subtracted heat flow curves of the sapphire standard and the sample. The resulting specific heat capacity (cp) curve is plotted in the lower diagram. The data at the beginning of the curve is not valid because of the initial start-up transient. The method gives an accuracy of about 2%.
The Sapphire Method is a standard procedure. The results are accurate and heat-flow calibration is not necessary. However, the method requires three measurements performed under the same experimental conditions.
Slide 11: IsoStep DSC
I now want to discuss the different techniques of temperature-modulated DSC. One of the advantages of these techniques is that they allow the sensible and the latent heat capacity to be separated. The quality of the separation depends on the particular technique used.
The first temperature-modulated technique is IsoStep DSC.
The temperature program consists of alternate heating and isothermal segments. The length of each segment should be at least one minute and the temperature step in the scanning segment should be less than five Kelvin.
The diagrams show the typical temperature program and the measured curves of the sample, sapphire standard and blank
The heat capacity signal is calculated from the heating segments in a similar way to in the sapphire method, but the temperature range in each heating segment is much smaller. This makes the technique more robust.
Slide 12: IsoStep DSC
The upper diagram shows the blank-subtracted heat-flow curves of the sample and the sapphire standard. The lower diagram shows the specific heat capacity curve determined by the STARe software. The accuracy of the IsoStep technique is about 2%.
The advantages of this technique are the high accuracy; that the measurement can be performed over a wide temperature range; and that the evaluation allows the latent and sensible specific heat capacity to be separated. This in turn allows overlapping effects to be separated.
The method requires three relatively long measurements performed under the same experimental conditions.
Slide 13: Steady State ADSC
The next temperature-modulated technique is known as Steady-State ADSC.
ADSC is short for alternating DSC. The technique uses a saw-tooth temperature modulation. This means that each period consists of a heating and a cooling segment as shown in the upper diagram.
The heat flow should reach near-steady-state conditions during each segment. This means that each segment should last at least one minute. In the steady-state ADSC temperature program, the average temperature changes at a typical underlying heating rate of one Kelvin per minute (1 K/min).
The evaluation of the specific heat capacity using steady-state ADSC requires the sample and blank measurements to be performed with the same temperature program.
Slide 14: Steady State ADSC
This slide shows the evaluation of the steady-state ADSC technique.
The blank-subtracted heat-flow curve of the sample is shown in the upper diagram and the resulting specific heat capacity curve (cp) curve below. The evaluation procedure calculates one point per segment. The technique achieves an accuracy of about 4%.
Steady-state ADSC requires relatively long measurement times and accurate heat-flow adjustment in the relevant temperature range.
In contrast to the techniques I have already discussed, it allows measurements under quasi-isothermal conditions, that is, at an underlying heating rate of zero.
The next two techniques, ADSC and TOPEM, are the same in this respect.
Slide 15: ADSC
Now let me explain ADSC, or alternating DSC, the conventional temperature-modulated DSC technique that uses a sinusoidal modulation function.
The temperature program is shown in the upper diagram and is defined by the underlying heating rate, the amplitude, and the period. For the measurements presented here, we chose one Kelvin/min; one Kelvin; and one minute; respectively.
ADSC achieves the best heat capacity accuracy by using measurements of sample, blank and a reference material, in this case aluminum.
Slide 16: ADSC
The upper diagram shows the measured heat-flow curves and the lower diagram the resulting specific heat capacity. The accuracy of ADSC using the selected parameters is about 3%.
An advantage of this technique is that the specific heat capacity (cp) can be determined at very low heating rates and even under quasi-isothermal conditions. This improves the sensitivity and resolution of the measurement. In addition to the specific heat capacity, the method determines the reversing and non-reversing heat flow. This allows overlapping effects in complex thermal events to be separated.
The method is less influenced by possible instrumental drift.
Three measurements are required to achieve the best accuracy. This makes the technique rather time consuming. However, if only the relative change of the specific heat capacity is required, the ADSC evaluation can be performed using just sample and blank measurements. For a relatively fast survey, only the sample measurement needs to be evaluated. If thermal events occur, the resulting specific heat capacity may be frequency dependent.
Slide 17 TOPEM
Finally, I would like to discuss TOPEM.
TOPEM is the most advanced temperature-modulated DSC technique. In contrast to all other temperature-modulated techniques, it uses a stochastic modulation function. The method delivers a maximum of information about the sample in one single measurement. The patented evaluation procedure allows the best possible separation of sensible and latent heat capacity and facilitates a consistency check of the resulting curves. This significantly improves the quality of the results. This technique can be also used to measure the specific heat capacity.
The upper diagram shows a typical temperature program. The measured heat-flow curve is plotted below. Typical TOPEM parameters for specific heat capacity (cp) measurements are heating rates between zero point five and two Kelvin per minute (0.5 and 2 K/min), a pulse height of 1 Kelvin, and a pulse width of 15 to 30 seconds, as given in the slide.
In principle, only one measurement is necessary to determine the specific heat capacity (cp). The result can however be improved by measuring a sapphire reference standard. This can be measured at higher heating rates; for example at five Kelvin per minute (5 K/min). In contrast to the other techniques, the sapphire technique can be used for long periods and for different measurement conditions.
The TOPEM measurement determines the quasi-static frequency-independent specific heat capacity.
Slide 18 TOPEM
The upper diagram shows the heat-flow curve of the sample and part of the sapphire curve measured at a faster heating rate. The lower diagram shows the specific heat capacity curve as the result of the evaluation.
An accuracy of about 2% can be achieved using TOPEM.
In principle, the TOPEM technique offers similar advantages as the other temperature-modulated techniques. The measurement accuracy is comparable to that of the IsoStep technique. In contrast, quasi-static measurements are possible and the measurement time is shorter because only one measurement is needed.
Slide 19 Comparison: cp of Polystyrene 10 to 40 °C
The diagrams in the next two slides compare the results obtained using the techniques I have discussed so far in this seminar.
The points in this first diagram show the data for the specific heat capacity of the polystyrene given by NIST. The solid line is a fit curve and the dashed lines represent a deviation of 3%.
The measurements were performed in the temperature range ten to forty degrees Celsius (10 to 40 °C) using a fifteen milligram (15-mg) sample in a sealed forty microliter (40-mL) aluminum crucible.
Slide 20 Comparison: cp of Polystyrene 10 to 40 °C
This diagram now includes all the results measured using the different methods in addition to the data from NIST.
Only the direct method gives results that deviate by more than 5% from the literature data. The results of all the other methods are within the 3% limit.
The direct and sapphire methods show a larger deviation at lower temperature. This is due to the initial start-up transient of the conventional DSC. The curves reach a steady state about ten Kelvin (10 Kelvin) after the start temperature.
Finally, I want to point out that the direct and sapphire methods measure the sum of the latent and sensible specific heat capacities whereas the modulated methods determine the sensible specific heat capacity.
This is not important for the example I have just discussed because the latent specific heat capacity is zero. This situation changes fundamentally if a thermal event occurs.
Slide 21 Applications
Let’s now discuss the practical importance of specific heat capacity measurements.
The specific heat capacity is an important property for characterizing energy storage and insulation materials. It is also important for improving processes in production, storage and transportation. Rapid and reliable measurement of the specific heat capacity is required in many industries, for example in the chemical, pharmaceutical, and food industries.
The performance of the METTLER TOLEDO DSC is excellent for applications in these fields. High-sensitivity sensors have been developed to measure low-energy transitions.
The specific heat capacity of many inorganic materials such as metals and ceramics often has to be measured up to sixteen hundred degrees Celsius (1600 °C). This can be done using the TGA-DSC.
In practice, specific heat capacity data is used to obtain detailed information about materials, for example enthalpy, degree of crystallinity, content in blends, alloys or copolymers, storage heat capacity of phase-change materials, and many others.
Slide 22 Application 1: Curing and Vitrification
I would now like to describe three application examples.
In the first application, TOPEM is used to measure the sensible specific heat capacity curve during the curing of a two-component epoxy system.
The black curve is the total heat-flow curve and is almost identical to a conventional DSC curve. This curve exhibits a glass transition at about minus twenty degrees Celsius (–20 °C). The main effect is the peak due to the curing reaction at about ninety degrees (90 °C). In contrast, the blue curve shows the change of the sensible specific heat capacity with higher resolution and sensitivity. The glass transition of the initially unreacted mixture causes the step change in the cp curve at about minus twenty degrees (–20 °C).
The peak in the total heat-flow shows that the reaction begins slowly at about twenty five degrees (25 °C). The reaction rate becomes significant from about fifty degrees onward (50 °C) and the maximum rate is reached at about ninety degrees (90 °C). The reaction rate then decreases.
In a curing reaction, the size of the molecules increases. This is accompanied by an increase in viscosity and an increase in the glass transition temperature of the partially cured mixture. At a certain time, the glass transition temperature reaches the sample temperature. As a result, the reaction mixture transforms into the glassy state, in other words, the sample vitrifies. This process is indicated by the downward step in the specific heat capacity curve at about one hundred degrees (100 °C). The reaction rate slows considerably due to this vitrification process and the mechanism of molecular network formation changes in the partially cured material. At about one hundred fifty degrees (150 °C), the glass transition temperature of the cured material is reached and the specific heat capacity curve shows the typical step. Following this so-called devitrification process, the material is in the rubbery state and final curing occurs. This is reflected in the weak exothermic peak in the total heat-flow curve at about one hundred fifty degrees (150 °C).
This detailed interpretation was obtained from one single temperature-modulated DSC measurement of the specific heat capacity.
Slide 23 Application 2: Water
The second application shows the measurement of the specific heat capacity of water.
The measurement of water and dilute aqueous solutions by conventional DSC is somewhat of a problem because of evaporation, which occurs even at temperatures far below the boiling point. Due to the relative large enthalpy of evaporation of water, the small evaporation loss between ten (10) and forty degrees Celsius (40 °C) produces a significant amount of latent heat capacity. This is the reason for significant experimental errors.
TOPEM is the best technique to use because the sensible specific heat capacity is measured with the good accuracy in one single run. The result shows the correct temperature dependence. The accuracy is in the order of 3%.
Slide 24 Application 3: PET Crystallinity X (T)
The third application example illustrates the determination of the temperature-dependent crystallinity of polymers during heating.
The sample is prepared from pellets of polyethylene terephthalate or PET for short. The red curve is the specific heat capacity curve of the first heating run of the original sample. The second heating curve after rapid cooling from the melt is colored blue. A heating rate of twenty Kelvin per minute (20 K/min) was used.
The main effect in the first heating curve is the relatively sharp melting peak at two hundred and forty-five degrees Celsius (245 °C). The second heating curve clearly indicates three thermal events. These are the glass transition at eighty degrees (80 °C), the cold crystallization process at about one hundred and seventy degrees (170 °C), and finally the broad melting process between two hundred (200) and two hundred and fifty-five degrees (255 °C).
The measured specific heat capacity (cp) curves can be used to determine the specific enthalpy curves by integration. The lower limit of integration is one hundred degrees (100 °C); that is, a temperature chosen between the glass transition and the onset of cold crystallization. The upper integration limit is two hundred and ninety degrees (290 °C), a temperature in the melt. This calculation can be easily performed with the STARe software.
The resulting curves of the measured specific enthalpy can be used to determine the crystallinity. I will explain this in the next slide.
Slide 25 Application 3: PET Crystallinity X (T)
The specific enthalpy of an amorphous or liquid material is larger than that of a semicrystalline material. The contribution of the crystalline phase is the difference between the specific enthalpies of the liquid phase and the measured specific enthalpy curve. The crystallinity, X, is the ratio between this difference and the difference between the specific enthalpies of the liquid and crystalline phases. The values of the specific enthalpies of the liquid and crystalline phases are taken from the ATHAS Data Bank.
The diagram shows the resulting crystallinity curves of the original material and the rapidly cooled material. The initial crystallinity of the original material is about 50%. During melting, the crystallinity decreases to zero.
The initial crystallinity of the rapidly cooled material is less than 10%, but increases during the cold crystallization to 30%. The crystallinity decreases during melting.
The initial crystallinity and differences in the crystallinity curve during heating provide information about modifications in the molecular structure, the effectiveness of additives, and the thermal and mechanical history of materials.
Slide 26 Tips and Hints
The measurement of good quality quantitative heat capacity data is a challenging task for DSC. Nevertheless, it is a common and useful technique because of the availability of DSC instruments, simple sample preparation, relatively short measurement time, acceptable accuracy, and easy evaluation using commercial software.
The slide lists a number of tips and hints for obtaining good data:
Allow the instrument sufficient time to stabilize. This means that the gas flow is constant, that the measuring system has been switched on for some time, and that the sensor and furnace lid are properly installed and not contaminated.
Check the repeatability and reproducibility by repeating measurements.
Averaging of replicate measurements improves accuracy.
Usually the results are improved by blank curve subtraction. An exception is the TOPEM technique where a blank curve is not required.
Position the crucibles accurately on the sensor.
Use similar crucibles for the sample, blank and reference measurements and enter the crucible masses in the software.
Do not deform the bottom of the crucible during sample preparation. The safest way is to not use of the sealing press and manually place the lid on the crucible.
For organic substances, we recommend the forty microliter (40-mL) crucible and a sample mass between ten (10) and twenty milligrams (20 mg).
If sapphire is used as a standard or for calibration, use similar heat capacities for sample and sapphire.
Take care to ensure good thermal contact between sample and crucible.
If possible, compact samples of low-density foams and powders, but avoid mechanical stress in the crucible. This can cause artifacts.
Slide 27 Summary
I will now briefly summarize the important points discussed in this seminar.
First, we distinguish between:
The heat capacity: This is a characteristic property of the sample and depends on the sample size; and
The specific or molar heat capacity: These quantities are independent of the sample size.
The specific heat capacity contains two components: The sensible component, which is related to rearrangements of the molecules as a whole, and the latent component which is determined by all other thermal events.
The specific heat capacity is important for the advanced evaluation of DSC curves, detailed material analysis, and improvement of all processes in the life-cycle of products beginning from their production to their disposal, and finally the recycling of the product.
The specific heat capacity can be measured using DSC and in the high temperature range using the TGA-DSC.
The METTLER TOLEDO STARe software provides six different methods to measure the specific heat capacity (cp). These are the direct method and the sapphire method for conventional DSC, together with IsoStep, Steady-State ADSC, ADSC and TOPEM for temperature-modulated DSC. The method chosen depends on the sample, the experimental setup, the measuring time available, and the required accuracy.
For proper measurement of specific heat capacity (cp), the experimental setup should be carefully calibrated and installed. Attention should also be paid to sample preparation.
The specific heat capacity can be measured with an accuracy of about 2% by DSC. Precision and reproducibility can be more than one order of magnitude better. This depends largely on the sample.
Slide 28 For more information on cp
Finally, I would like to draw your attention to information about specific heat capacity that you can download from the Internet.
METTLER TOLEDO publishes articles on thermal analysis and applications from different fields twice a year in UserCom, the well-known METTLER TOLEDO biannual technical customer magazine. Back issues can be downloaded as PDFs from www.mt.com/usercoms.
Several UserCom articles relating to specific heat capacity are also listed on this slide.
In addition, you can download information about webinars, application handbooks or information of a more general nature from the Internet addresses given at the bottom of this slide.
Slide 29 Thank you
This concludes my presentation on specific heat capacity. Thank you for your interest and attention.