Differential Scanning

Calorimetry

Literature study Solid State Chemistry

Bas van Gestel

July 7, 2007 – December 18, 2007

Solid State Chemistry,

Institute for Molecules and Materials,

Radboud University Nijmegen

2

Contents

1 Introduction 5

2 Introduction to calorimetry 7

2.1 The Four Elements . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Internal Energy and Heat . . . . . . . . . . . . . . . . . . . . 8

2.3 Temperature and temperature scales . . . . . . . . . . . . . . 10

2.3.1 Physiological temperature scale . . . . . . . . . . . . . 11

2.3.2 Liquid in glass . . . . . . . . . . . . . . . . . . . . . . . 11

2.3.3 Resistance Thermometers . . . . . . . . . . . . . . . . 13

2.3.4 Thermocouples . . . . . . . . . . . . . . . . . . . . . . 15

2.3.5 Thermodynamic temperature . . . . . . . . . . . . . . 16

2.4 Phase transitions . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.5 History of calorimetry . . . . . . . . . . . . . . . . . . . . . . 18

3 Differential Scanning Calorimetry 21

3.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1.1 Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . 22

3.1.2 Melting and recrystallization . . . . . . . . . . . . . . . 23

3.1.3 Glass transition . . . . . . . . . . . . . . . . . . . . . . 24

3.1.4 Solid-solid transformations . . . . . . . . . . . . . . . . 25

3.2 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . 25

3.3 Transition points . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.3.1 Melting point . . . . . . . . . . . . . . . . . . . . . . . 25

3

3.3.2 Transition enthalpy . . . . . . . . . . . . . . . . . . . . 26

3.3.3 Glass transition temperature . . . . . . . . . . . . . . . 27

4 Other TA techniques 29

4.1 Thermometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.2 Differential Thermal Analysis (DTA) . . . . . . . . . . . . . . 29

4.3 Thermogravimetric Analysis (TGA) . . . . . . . . . . . . . . . 30

4.4 Dilatometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.5 Thermomechanical Analysis (TMA) . . . . . . . . . . . . . . . 31

4.6 Thermo-optical Analysis (TOA) . . . . . . . . . . . . . . . . . 32

4.7 Evolved Gas Analysis (EGA) . . . . . . . . . . . . . . . . . . 33

5 Instrumentation 35

5.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.2 Temperature measurement . . . . . . . . . . . . . . . . . . . . 36

5.2.1 Classical heat flow sensor . . . . . . . . . . . . . . . . . 37

5.2.2 Improved classical heat flow sensor . . . . . . . . . . . 38

5.2.3 FRS5 and HSS7 heat flow sensors . . . . . . . . . . . . 38

5.3 Radboud University, Solid State Chemistry . . . . . . . . . . . 39

6 Artifacts 41

6.1 Different heating rates . . . . . . . . . . . . . . . . . . . . . . 41

6.2 Sample weight . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

6.3 Gas production . . . . . . . . . . . . . . . . . . . . . . . . . . 42

7 Applications 45

7.1 Phase diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . 45

7.2 Polymorph detection . . . . . . . . . . . . . . . . . . . . . . . 46

7.3 Purity determination . . . . . . . . . . . . . . . . . . . . . . . 47

7.4 High temperature DSC . . . . . . . . . . . . . . . . . . . . . . 48

A Derivation formula 5.2 49

4

Chapter 1

Introduction

Differential Scanning Calorimetry (DSC) is an analytical technique in which

a sample and a reference are subjected to a temperature program and where

differences in heat capacity or heat of transitions are measured. Therefore, it

is part of the group of analytical techniques called Thermal Analysis (TA). [1]

This literature study starts with an introduction to calorimetry in chapter 2.

What properties do we measure with calorimetry? Why can we measure

these properties in this way? How do we measure temperature? What are

phase transitions? How did calorimetry start in the past?

In chapter 3 details about DSC measurement and specimen preparation will

be explained. How can we measure the heat capacity? How can we find

a melting point? What kind of additional information can we get from a

thermogram?

Other thermal analysis techniques will be explained in chapter 4. Chapter 5

is about the working of the DSC equipment that is used in scientific rereach

nowadays. In chapter 6 some common practical issues will be discussed and

in chapter 7 a few applications are mentioned.

5

6

Chapter 2

Introduction to calorimetry

In calorimetry your aim is to measure heat. Because there doesn’t exist

something like a ‘heat meter’, we have to measure the amount of heat in-

directly. This can be done in different ways: we can measure temperature

changes, look at phase transitions or use chemical, electric and mechanical

heat transfers. [2]

2.1 The Four Elements

Since 450 BC Greek philosophers divide the world into four elements: earth,

water, air and fire (see figure 2.1). Every material or force on earth is built

up from these four elements. And this classification is still used in modern

physics, but with different names. Earth, water and air are replaced by three

phases: solid, liquid and gas. Fire is replaced by heat (or energy in general),

which is the quantity we want to measure in calorimetry. [3]

7

Figure 2.1: The four elements.

2.2 Internal Energy and Heat

Before we can start measuring heat, we have to understand what ‘heat’ is.

Heat Q is an extensive property (depending on the amount of substance). It

is the amount of energy in a system as a result of a temperature difference

between the system and its surroundings. So one way to determine Q is to

cool the sample to the absolute zero of temperature (without changing it

physically or chemically) and then add energy until the original temperature

is reached. The sum of the added energy is the heat Q. [4–6]

Because this way of measuring heat is not doable practically, we try to de-

scribe heat first, in order to find easier ways in measuring it. The first step

in describing heat is to look at the internal energy of a system. The internal

energy of a system, which can only produce volume work (dW = −p dV ) is

described by the First Law of Thermodynamics as

dU = dQ + dW = dQ − pdV (2.1)

In this equation U is the internal energy of the system, Q is the amount of

energy transferred as heat to the system and W is the work done on the

8

system. p stands for pressure and V for volume. The SI-unit for the three

forms of energy (U , Q and W ) is the joule (J = m2 kg s−2). An old unit is

the calorie, which is equal to 4.184 J exactly.

When we write dU in exact differential notation, we get

dU =

(

∂U

∂T

)

V

dT +

(

∂U

∂V

)

T

dV (2.2)

Using equations (2.1) and (2.2), we can describe the heat Q in terms of the

variables of state T and V :

dQ = dU + p dV =

(

∂U

∂T

)

V

dT +

(

∂U

∂V

)

T

dV + p dV (2.3)

The heat capacity at constant volume is defined as

Cv ≡dQ

dT=

(

∂U

∂T

)

V

(2.4)

When we keep the volume constant (dV = 0) and fill in the definition of Cv

from equation (2.4), we can write equation (2.3) as

dQ|V =

(

∂U

∂T

)

V

dT = Cv dT (2.5)

So, if we use the variable of state T and keep the volume V constant, we can

measure the heat (Q) by integrating Cv dT over T :

Q|V =

∫

dQ|V =

∫ T=T1

T=T0

Cv dT = ∆U (2.6)

In most cases (read: in DSC) it is more convenient to use T and p as variables.

A comparable derivation can be done for that situation. In this case we don’t

look at the internal energy U , but consider the enthalpy H. Enthalpy has

9

the same unit as internal energy: joule (J) and is defined as

H ≡ U + pV (2.7)

When we, again, describe a system which can only produce volume work, we

get from equations (2.7), (2.1) and some mathematics (d(pV ) = p dV +V dp)

dH = dU + d(pV ) = dQ − p dV + p dV + V dp = dQ + V dp (2.8)

The heat capacity at constant pressure is defined as

Cp ≡dQ

dT=

(

∂H

∂T

)

p

(2.9)

When we write H in exact diffential notation, use equation (2.8) by constant

pressure and the definition from equation (2.9), we get

dQ|p =

(

∂H

∂T

)

p

dT = Cp dT (2.10)

So when we work at constant pressure, we can measure the heat Q by inte-

grating Cp d T over T :

Q|p =

∫

dQ|p =

∫ T=T1

T=T0

Cp dT = ∆H (2.11)

2.3 Temperature and temperature scales

In the derivation above we used temperature, without knowing the details

about it. Temperature T is the intensive parameter (independent of the

amount of substance) of heat. The standard unit of temperature nowadays

is kelvin, K. [5]

When we want to use numbers to indicate a temperature, we have to use a

10

scale. And during the last centuries many scales have been in use.

2.3.1 Physiological temperature scale

When people are born, they already are able to recognize temperatures

around body temperature by using thermoreceptors: ‘cold’ means ‘colder

than body temperature’, ‘hot’ means ‘hotter than body temperature’. [7]

Temperatures further away from body temperature can be recognized through

the degree of pain. Colder and warmer increases the amount of pain. You get

a temperature scale from ‘ice cold’, via ‘cold’, ‘lukewarm’, ‘warm’ and ‘hot’

towards ‘red hot’. But it is difficult to use numbers to describe a temperature

measured with a thermoreceptor or an amount of pain. These scales only

give qualitative information. [2]

2.3.2 Liquid in glass

In the 17th century liquid-in-glass Florentine thermometers are developed.

This kind of thermometer is based on the difference in expansion coefficient

of a liquid and the glass. The scale can be chosen in different ways: almost

every pair of setpoints is usable. Between those setpoints a linear scale is

used. Consequently, these scales are empirical. The temperature t is linear

dependent of the length ` of the liquid column. [2]

t = a + b ` (2.12)

In the next century four scales became standards. All of them are based

on the linear expansion of a liquid in glass containers. These scales are

summarized in table 2.1. Remarkable is that the Celsius scale was first used

in a reversed way: freezing water was labeled 100 ◦C, and boiling water 0 ◦C.

But also this kind of thermometers has disadvantages. The main sources of

11

errors are time and immersion effects.

• Over years the glass of the thermometer will contract, introducing an

error of about 1–2 ◦C.

• To measure a temperature, you have to wait until the bulb containing

the liquid and the environment have come to equilibrium, but as heat

flow decreases in time when getting closer to equilibrium this can take

a considerable period of time (1–2 seconds to reach half the initial

temperature difference).

• Hysteresis effects slow down the measurements. These processes take

minutes on heating, but hours on cooling, with an error of about 1–2◦C per 100 ◦C.

• Pressure excerted on the glass bulb can also influence the reliability.

• The largest deviation is caused by partial immersion of the thermometer

(see figure 2.2), but for this error corrections are possible.

Figure 2.2: Partial immersion of a thermometer.

The error in temperature Terror caused by partial immersion can be calculated

by

Terror = kn(t − θ) (2.13)

12

In this equation k is the differential glass-mercury expansion coefficient (ap-

prox. 1.6 · 104), n is the mercury column length outside the bath (in degrees

of scale), t is the temperature the thermometer shows and θ is the temper-

ature of the stem, i.e. the glass column outside the bath (mostly at room

temperature). Using this equation the corrected temperature Tcorrected is

Tcorrected = T + Terror = t + kn(t − θ) = (1 + kn) · t − kn · θ (2.14)

Table 2.1: Temperature scales (liquid in glass)Year Person Description Value1701 Newton freezing water 0 ◦

body temperature 12 ◦

1714 Fahrenheit NaCl-ice-water 0 ◦

body temperature 96 ◦

later Fahrenheit freezing water 32 ◦

boiling water 212 ◦

1730 Reaumur ice point water/ethanol (80:20) 0 ◦

steam point water/ethanol (80:20) 80 ◦

1742 Celsius freezing water 0 ◦Cboiling water 100 ◦C

2.3.3 Resistance Thermometers

An other way of determining temperature is by measuring the electrical re-

sistance of a metal or semiconductor. [2, 8–10] Resistance is temperature

dependent and can be used as a measure for temperature. This effect is de-

scribed in an equation found by Hugh Longbourne Callendar, and refined by

Van Dusen:

RT = R0(1 + AT + BT 2 − C(T − 100)T 3) (2.15)

13

In this equation RT is the specific electrical resistance at temperature T . R0

is the resistance at 0 ◦C. T stands for the temperature in degrees Celsius (!)

and A, B and C are the Callendar-Van Dusen constants. For temperatures

above 0 ◦C C is equal to zero and the equation can be simplified to

RT = R0(1 + AT + BT 2) (2.16)

As this equation is kwadratic in T , it can be solved to an analytical expression

for T as a function of RT :

T (RT ) =−R0A +

√

R20A

2 − 4R0B(R0 − RT )

2R0B(2.17)

The Callendar-Van Dusen constants A, B and C for a standard sensor are

stated in IEC 751 by the International Electrotechnical Commission. For dif-

ferent sensors (or higher accuracy) it is possible to determine these constants

by measuring resistances at four temperatures:

• Measure R0 at t0 = 0 ◦C (freezing point of water)

• Measure R100 at t100 = 100 ◦C (boiling point of water)

• Measure Rh at th = a high temperature (e.g. Tfus zink, 419.53 ◦C)

• Measure Rl at tl = a low temperature (e.g. Tvap oxygen, −182.96 ◦C)

From these resistances α, δ and β are calculated:

α =R100 − R0

100 · R0

(2.18)

δ =th −

Rh−R0

R0·α(

th100

− 1) (

th100

) (2.19)

β =tl −

[

Rl−R0

R0·α+ δ

(

tl100

− 1) (

tl100

)

]

(

tl100

− 1) (

tl100

)3(2.20)

14

And α, δ and β can be converted into A, B and C by

A = α +α · δ

100(2.21)

B = −α · δ

1002(2.22)

C = −α · β

1004(2.23)

2.3.4 Thermocouples

The last way of thermometry (discussed in this literature study) is by us-

ing thermocouples. [2] When two connections of different metals are placed

at different temperatures (see figure 2.3), a net thermal electromotive force

occurs. This phenomenon is called the Seebeck effect, discovered in 1821 by

Thomas Seebeck.

Figure 2.3: A thermocouple.

In this way the potential difference is a measure for the temperature differ-

ence, described by the equation

EAB(t, t0) = a + bt + ct2 (2.24)

In this equation one of the connections is placed at t0 = 0 ◦C, the ice point

of water. EAB is the potential difference and t is the temperature in degrees

Celsius. a, b and c are calibration constants, depending on the materials

used.

15

It is possible to place just one or both connections at the reference temper-

ature. In the first case, the potentiometer is placed in the wiring of metal

A or B. In the second case copper wires are used to connect the two ends of

the thermocouples with the potentiometer, as depicted in figure 2.4.

Figure 2.4: Two setups for thermocouples.

In table 2.2 several combinations of metals are listed. The electromotive

forces at different temperatures are in microvolts per degree Celsius.

Table 2.2: Electromotive forces (in µV/◦C) of several combinations of metalscombination −190◦C 0◦C 500◦C 1000◦C 1500◦CCopper-Constantan 17 38.4 – – –Iron-Constantan 26 50.1 56 – –Chromel-Alumel 23 40.0 43 39 –Pt-Pt/10%Rh – 5.5 10 12 15

Nowadays there is an alternative for placing one connection at the ice point

of water. After calibration (with one connection at the ice point of water)

it is possible to use a compensator to measure the (room) temperature and

correct for the actual temperature of the reference.

2.3.5 Thermodynamic temperature

When scientists discovered that there is a minimum energy and consequently

a minimum temperature, they used this temperature as an absolute setpoint

16

for the temperature scale: 0 K. In earlier temperature scales the two setpoints

were chosen arbitrarily. This was the first scale with one arbitrary and one

absolute setpoint. [2, 4]

The other setpoint of this scale is the triple point of water, at 273.16 K. This

number is chosen so that the units of this scale are equal in size as the units

of the scale chosen by Celsius: one Kelvin temperature difference is equal to

a temperature difference of one degree Celsius.

2.4 Phase transitions

Besides temperature, you can also look at phase transitions when performing

calorimetric experiments. A liquid sample can be made gaseous by adding

energy. Adding energy increases the temperature of the sample, until it

begins to boil. Then, the temperature remains constant. When the sample

is evaporated completely, its temperature increases again. The opposite is

also possible: by removing energy, its temperature decreases and the sample

starts freezing. These are both examples of phase transitions.

In a phase transition the chemical composition of the sample doesn’t change.

Only its phase changes by adding or removing energy. Phase changes are

possible between all the three phases and as well as between two solid phases,

as summarized in table 2.3. The temperature at which the phase transition

occurs, is called the transition temperature Ttrs, where the subscript indicates

the kind of transition. [4]

Table 2.3: Names of phase transitions (IUPAC abbreviations)� Solid Liquid Gas

Solid S-S Transformation (trs) Fusion (fus) Sublimation (sub)Liquid Freezing – Vaporization (vap)Gas Deposition Condensation –

17

2.5 History of calorimetry

The first calorimetric experiments were done in the 18th century. In 1760

J. Black placed a hot object in a cavity in a block of ice and used the amount

of molten ice as a measure for the amount of heat (see figure 2.5). [2]

Figure 2.5: First setup of heat measurement.

In 1781 Laplace was the first to make an apparatus for this measurement,

based on the same technique, but with much better isolation (see figure 2.6).

He placed a sample of higher temperature T1 in basket LM (at the bottom

of figure 2.6), which he inserted into the calorimeter cavity ff. He placed the

lid HG (second part from the bottom of figure 2.6) on top of the basket LM.

Afterwards he placed the lid FF (at the top of figure 2.6) on the apparatus.

The heat flow from the sample made the measuring ice in volume HGbbd

melting, until equilibrium was reached. For larger samples this might take

even 12 hours. The whole calorimeter was kept adiabatic by a second, insu-

lating layer of ice in FFaaaa. After the experiment, the molten measuring ice

(water) was drawn through the stopcock y and weighed. [2, 11] The average

heat capacity was then given by

cp =mwater ∆Hfus

msample (T1 − T0)(2.25)

18

In this equation mwater is the mass of the molten measuring ice. msample is

the mass of the sample and ∆Hfus is the heat of fusion of one unit mass of

ice (unit: J g−1). T1 is the initial temperature of the sample and T0 is the

melting temperature of the measuring ice (0◦C).

Modern adiabatic calorimetry experiments are based on the Nernst calorime-

ter. This type of calorimeter is decreased in size, automated and computer-

ized. It is still the best tool to measure heat capacities from 10 K to room

temperature. [12] The heat capacity of the sample is in this case calculated

from the heater input ∆Q, determined electrically by resistance heating, and

the temperature increase ∆T . In this formula C ′ is the heat capacity of the

empty calorimeter, its ‘water value’. [5]

cp =∆Qcorrected − C ′∆Tcorrected

∆Tcorrected msample

(2.26)

The next step in the developement of calorimetry was Differential Scanning

Calorimetry (DSC), with a larger temperature range: 200 to 1000 K. The

main advantage of the DSC is that the correction procedure (needed when

using earlier calorimeters) is simplified.

19

Figure 2.6: The first ‘calorimeter’, by Laplace.

20

Chapter 3

Differential Scanning

Calorimetry

Around 1900 it became possible to measure temperature continuously using

thermocouples. This was the start of the development of Differential Thermal

Analysis. In 1904 Kurnakov and Saladin were the first to make the classical

DTA set-up: photographic T − ∆T − t-recording, reference temperature for

thermocouples and a DTA-furnace.

3.1 Basics

In a Differential Scanning Calorimetry (DSC) experiment the aim is to keep

the sample and a reference (at constant pressure) at the same temperature

throughout a temperature programme. During the experiment the heat flow

(heat transferred to or from the sample and the reference) is measured. The

term ‘Differential’ refers to the fact that the sample data are compared to

the reference data. In such an experiment one is ‘Scanning’ through a tem-

perature programme. [4, 13, 14]

21

3.1.1 Heat Capacity

Heating the sample costs more energy than heating the reference, because

one has to increase the temperature of the sample holder and the sample

itself. From the difference heat flow dQ

dt, needed to heat a sample minus the

reference, and the heating rate dTdt

one can calculate the heat capacity at

constant pressure Cp.

Cp =

(

dQ

dT

)

p

=

(

dQ

dt

dt

dT

)

p

=

(

dQ/dt

dT/dt

)

p

=

(

heat flow

heating rate

)

p

(3.1)

When using a constant heating rate (dTdt

= a), the heat flow at constant

pressure is proportional to the Cp.

(

dQ

dT

)

p

= Cp ·

(

dT

dt

)

p

= Cp · a (3.2)

In a plot of heat flow against temperature the Cp is visible (multiplied with

the (constant) heating rate). In figure 3.1 a constant heating rate is measured.

Figure 3.1: Measuring the heat capacity.

22

3.1.2 Melting and recrystallization

When you continue heating, eventually the sample will begin to melt. But

to keep the temperature of the sample and reference the same, more heat

is needed for the sample. In a plot of heat flow against temperature an

endothermal peak (increase of heat flow) will become visible. An exothermal

peak (decrease of heat flow) will appear when solidification occurs.

Figure 3.2: Measuring an (endothermal) melting peak.

In theory the Cp of melting and solidification is infinitely large. Because it

takes time to transport the heat through the sample, the peak is not infinitely

high and small, but broadened, with the same peak area as decribed in section

3.3.2.

Metastable solids can melt twice. After the first melting a metastable liquid

is formed, which recrystallizes at higher temperatures into a different crystal

structure. In this process energy will be released and an exothermic peak can

be expected. Shortly after recrystallization, the sample will melt again, with

an endothermic peak. This phenomenon was observed for bismuth germanate

by using in-situ optical microscopy. [15]

23

Figure 3.3: Measuring a recrystallization.

3.1.3 Glass transition

Glass transitions of polymers can also be determined by DSC. Below the glass

transition temperature Tg the sample is amorphous. At higher temperatures

the molecules have enough energy to become crystalline. The Cp increases

when you go from below to above the Tg. In a plot of heat flow against

temperature (with constant heating rate) this is visible as an increase in the

baseline (see also section: 3.1.1).

Figure 3.4: Measuring a glass transition.

24

3.1.4 Solid-solid transformations

Phase transitions in the solid phase can be made visible too. The integral over

the peak indicates the enthalpy change involved with transition: endothermal

or exothermal. Many different peak shapes can occur.

3.2 Sample preparation

The standard procedure for sample preparation starts with grinding the sam-

ple using a mortar and pestle to reach homogeneity. This is essential, as

samples of well-grinded and single crystals can give very different results, as

described in [16]. Between 0.5 and 20 mg of the powder is transferred into

an aluminium sample pan. A lid is pressed onto the pan. Sometimes the lid

is pierced, to maintain constant pressure (see section 6.3). [1, 14]

Using the aluminium pans above 500 ◦C will result in destruction of the

DSC sample holder. So for temperatures above 500 ◦C (or for samples which

react with the aluminium pans), gold, graphite or glass pans are available.

During the measurement, the sample is continuously flushed with an inert

gas (mostly nitrogen, between 20 and 80 cm3 min−1), to prevent oxidation of

the sample. The reference is an empty pan of the same kind.

3.3 Transition points

3.3.1 Melting point

A first order transition is characterized by its baseline and the peak. In such

a curve there are a couple of characteristic temperatures: the beginning of

melting, the peak temperature and the return to the baseline. And none of

these is the same as the melting point. To determine the melting point, one

25

has to extrapolate the baseline and the left tangent of the temperature peak

as shown in figure 3.5. [2]

Figure 3.5: Melting point determination.

3.3.2 Transition enthalpy

Using equation (2.11) we can state that the peak area A (the area between

the peak and an interpolation of the baseline) is proportional to the amount

of energy absorbed/released by the transition ∆Htrs:

A ∝ ∆Htrs (3.3)

26

3.3.3 Glass transition temperature

An amorphous sample that is heated from below to above the glass transition

temperature will become more crystalline. This transition takes time, so in

a plot of heat flow against temperature (with constant heating rate) the

increase of the baseline is spread over a temperature range. For the glass

transition temperature the middle of the incline is chosen, as depicted in

figure 3.6. [13]

Figure 3.6: The glass transition temperature.

27

28

Chapter 4

Other TA techniques

4.1 Thermometry

Thermometry is the oldest thermal analysis technique. It involves measure-

ment of temperature, usually as a function of time. When a constant heat

input is used and temperature is measured in time, a heating curve can be

created from this data. The slope of such a curve gives information about the

sample’s heat capacity and phase transition. When the temperature stays

constant, while heating up the sample, the sample must be melting (possibly

eutectic) or vaporizing. [2]

4.2 Differential Thermal Analysis (DTA)

Differential Thermal Analysis can be done in the same setup as DSC. The

difference between these techniques is the paramater that is kept constant.

By DSC the temperatures of the sample and reference are equal, by using

different heat flows Qsample and Qreference. By DTA the amount of heat Q

supplied to sample and reference is the same. Phase transitions will cause

29

the temperature of the sample Tsample to be lower (endothermic) or higher

(exothermic) than that of the reference Treference.

Figure 4.1: Differences between reference temperature and sample tempera-ture at constant heat flow.

4.3 Thermogravimetric Analysis (TGA)

In Thermogravimetric Analysis the sample is subjected to a temperature

program, while the mass of the sample is measured by a highly sensitive

electronic balance. Usually the experiment is performed under an inert at-

mosphere (nitrogen), but an oxidative one (air or oxygen) is also possible.

To compensate for gas flow effects, a blank curve is substracted. [14]

The first part of a TGA curve provides information about volatile components

(1), such as solvents or water. At higher temperatures water of crystallization

can come free (2). Eventually the sample will evaporate or decompose (3). [1]

This technique is often used in combination with a mass spectrometer or a gas

chromatograph, to analyse the volatile compounds. See also section 4.7. [2]

30

Figure 4.2: Schematic view of a TGA curve.

4.4 Dilatometry

In Dilatometry length and/or volume of a sample is measured, while being

subjected to a temperature program. This technique gives information about

linear expansion coefficients, glass transitions, polymorphic transformations

that cause volume changes of solids and shrinkage or expansion of fibers or

films.

4.5 Thermomechanical Analysis (TMA)

The aim of Thermomechanical Analysis (TMA) is roughly the same as that

of Dilatometry. The difference is that the measurements are performed

under tension or load. So the aim of this technique is measuring dimen-

sional changes of a sample under a constant, well defined load. If a period-

31

ically changing load is applied, the technique is called dynamic load TMA

(DLTMA). In dilatometric measurements the load on the sample is low or

negligable. The TMA signal represents the change in length measured with

a high resolution displacement sensor. TMA provides information on soft-

ening temperatures, dimensional stability on heating and viscoelastic behav-

ior. [1, 2]

Figure 4.3: Schematic view of a TMA curve.

4.6 Thermo-optical Analysis (TOA)

In Thermo-optical Analysis the sample is subjected to a temperature pro-

gram, while measuring the optical transmission or reflection of the sample.

Automatic melting point and dropping point instruments use this technique.

For example, a solid sample is melted, with an increase of transmittance.

Irregularities during the melting can be caused by crystals moving through

the light beam. [1]

32

Figure 4.4: Schematic view of a TOA curve.

4.7 Evolved Gas Analysis (EGA)

The name Evolved Gas Analysis is used when volatile components of a sample

are investigated, while performing thermal analysis, for example by a mass

spectrometer or an infrared spectrometer. A common combination is TGA

with a mass spectrometer. In figure 4.5 the temperature of the sample is

measured, while a mass spectrometer measured the intensity of molecules

with mass-to-charge ratio (m/q) 18 (water) and 44 (CO2). In step 1 and 2

surface water and water of crystallization is removed. In step 3 decomposition

of the organic sample takes place, by releasing water and CO2. [1]

33

Figure 4.5: Schematic view of a EGA curve.

34

Chapter 5

Instrumentation

5.1 Setup

In figure 5.1 a schematic view of a DSC is shown. [17] The main parts of the

device take care of temperature control: heater and cooler. The numbers

1 and 3 to 5 show the different parts of the furnace, the numbers 6 to 9

the parts of the cooler. Number 10 shows the cabel that conducts the raw

signal to the amplifier and number 11 and 12 show the dry and purge gas

inlets. The sample and reference are shown by number 2 and are placed on a

temperature sensor, the most important part of the device (see section 5.2).

Sometimes a sample robot can be used to change samples. When using it, a

DSC can work 24 hours a day, without assistance of a researcher. For oxygen-

sensitive or hygroscopic samples there is a possiblity to let the robot remove

a protective cap from the sampleholders immediately before measurement.

35

Figure 5.1: Schematic view of a DSC. 1) Furnace lid 2) Sample and referenceon the DSC sensor 3) Silver furnace 4) PT100 of furnace 5) Flat heaterbetween two electrically insulating disks 6) Thermal resistance for cooler 7)Cooling flange 8) Compression spring construction 9) Cooling flange PT10010) DSC raw signal for amplifier 11) Dry gas inlet 12) Purge gas inlet.

5.2 Temperature measurement

In DSC three different kinds of temperature sensors are used, as described

in [18]: the classical heat flow sensor, the improved classical heat flow sensor

(based on single T0 temperature measurement) and the FRS5 and HSS7 heat

flow sensors (based on multiple T0 temperature measurement) introduced by

the Mettler-Toledo company.

36

5.2.1 Classical heat flow sensor

Figure 5.2: Classical heat flow sensor.

The classical heat flow sensor measures the temperature of the sample and

the reference each with one thermocouple (see section 2.3.4). The effective

heat flow can be calculated with the simplified formula, mentioned in [18].

dq

dt=

1

R∆T (5.1)

In this equation R stands for the thermal resistance of the sensor and ∆T

stands for the temperature difference between the sample and the reference.dq

dtis the difference in heat flow between sample and reference and is the heat

used for warming up or transforming the specimen material.

This formula can only be used under the assumption that the thermal resis-

tances and the heat capacities on the sample and the reference sides are the

same (R = RS = RR and CR = CS) and the temperature difference between

the sample and the reference is approximately zero ( d∆Tdt

≈ 0).

The main problem with this sensor is the assumption that the sample tem-

perature is uniform.

37

5.2.2 Improved classical heat flow sensor

In the improved classical heat flow sensor the sensor temperature is addition-

ally measured at one place (single T0 measurement). With this information

the thermal resistances and the heat capacities can be measured as well.

The heat flow can be calculated using the formula mentioned in [18], with-

out derivation. A possible derivation, with some remarks about mistakes in

the equation, can be found in appendix A).

dq

dt= −

∆T

RR

+ ∆TS0

(

1

RS

+1

RR

)

+ (CR − CS)dTS

dt− CR

d∆T

dt(5.2)

In this equation ∆T stands for the temperature difference between the sample

and the reference: TS − TR. RS and RR are thermal resistances and CS and

CR are heat capacities of the sample and the reference.

Figure 5.3: Improved classical heat flow sensor.

5.2.3 FRS5 and HSS7 heat flow sensors

The FRS5 and HSS7 sensors introduced by the Mettler-Toledo company

measure heat flows seperately on the sample and reference sides, by using two

rings of thermocouples. In the inner ring the sample or reference temperature

is measured, in the outer one the temperature of the sensor. In this case the

voltage outputs of the thermocouples are added, giving

38

Figure 5.4: FRS5 and HSS7 heat flow sensor.

dq

dt=

1

R

(

N∑

i=1

(∆TS0)i −N∑

i=1

(∆TR0)i

)

(5.3)

In this equation ∆TS0 and ∆TR0 stand for the temperature differences be-

tween sample and sensor and between reference and sensor.

In the FRS5 sensor 56 thermocouples are used (N = 14). In the HSS7 sensor

120 themocouples are used (N = 30). A picture of such a sensor can be

seen in figure 5.5. The sensor temperature is measured multiple times so we

speak of multiple T0 measurement. This largely improves the accuracy of the

heat flow measurement as compared to the classical heat flow sensor. When

compared with the FRS5, the HSS7 is 5 (at −64.6 ◦C) to 10 (at 135.2 ◦C)

times more sensitive.

5.3 Radboud University, Solid State Chemistry

The department of Solid State Chemistry possesses two DSC’s, one from

Mettler Toledo, one from Setaram.

39

Figure 5.5: HSS7 temperature sensor with 120 thermocouples.

• Mettler Toledo dsc822e with the Mettler Toledo TSO 801RO Sample

Robot and Julabo FT900 cooler.

• Setaram Calvet Calorimeter C80 with control device Setaram C32.

40

Chapter 6

Artifacts

6.1 Different heating rates

When scanning through a temperature profile, a heating rate needs to be set.

Depending on the type of DSC one is using, this can be set between 0.1 and

10 ◦C min−1. At different heating rates different heating curves are obtained.

At higher heating rates the peaks will get broader and the maximum (peak

value) shifts toward higher temperature. The melting point doesn’t change

(at least not as much as the maximum does), if read out in the correct way

as described in section 3.3.1.

In figure 7.1 this is shown. Remark: the areas under the different peaks must

be equal, because that is a measure for the amount of heat needed for a phase

transition. In this figure apparently different scales have been used for the

three peaks. [1]

Higher heating rate causes peak broadening while the surface area remains

constant. Moreover, less peaks will be visible, because the sample has no

time for phase transition. So a slow heating rate gives the most details. . .

until the signal-to-noise ratio becomes such low that the signal disappears

41

in the noise. For a very low heating rate a measurement takes a long time.

The heat flow to the sample will be approximately equal the heat flow to

the reference, because the transitions in the sample are spread out over long

times.

6.2 Sample weight

The mass of a sample should be kept as small as possible, to achieve re-

producibility if neccesary. Bigger samples give various problems. The tem-

perature of the sample can become non-uniform, because heat needs time

to transfer through the sample. Through temperature differences chemical

reactions can occur. And small sample masses also protect the apparatus in

the event of explosion, deflagration or corrosion. [14]

6.3 Gas production

When the sample is heated, the sample can partially evaporate. If the lid

is placed on the pan, the pressure in the pan can increase, while the mea-

surement has to be performed at constant pressure by equation (2.11). To

maintain constant pressure, the lid can be pierced.

42

Figure 6.1: Melting point independence of heating rate.

43

44

Chapter 7

Applications

7.1 Phase diagrams

DSC is often used in the determination of phase diagrams, because the con-

ditions of the experiments are well-defined. Slow heating rates can be used to

approach equilibrium as good as possible. Several samples of different compo-

sition are measured. When the peaks of the curves are interpreted correctly

(endothermic peaks stand for melting temperatures), a phase diagram can

be constructed from this data.

In [19] the phase diagram for the rubidium bromide/copper(I) bromide sys-

tem is determined by DSC. In the system two intermediate compounds are

formed: RbCu2Br3 (melting at 537 K) and Rb3CuBr4 (melting at 544 K).

Two eutectic points are found at 501 K (54 mole%) CuBr and 522 K (74

mole%) CuBr.

For DSC measurements a Mettler Toledo DSC25 apparatus with TC15 TA

Controller and STARe Software 4.0 is used. The heating rates were 2 and

0.5 K min−1 for all samples. Further examples of the determination of phase

diagrams can be found in [20–30].

45

Figure 7.1: Phase diagram for the rubidium bromide/copper(I) bromide sys-tem.

7.2 Polymorph detection

DSC can also be used in polymorph research. [31] When heating curves of

different polymorphs of one compound are measured, different melting points

can show up. An example is Venlafaxine, a pharmaceutical compound that

46

acts a an antidepressivum. The melting points of the three polymorphs are

respectively 74.42, 77.72 and 78.47 ◦C. In figure 7.2 it is visible that form I

recrystallizes into form III.

Figure 7.2: Thermogram Venlafaxine: form I recrystallizes into form III.

7.3 Purity determination

The change of melting temperature induced by the presence of an impurity

in the material, is expressed in the Van ’t Hoff equation [32, 33]:

Tf = T0 −RT0Tfus

∆Hf

ln

(

1 − x1

F

)

(7.1)

47

This equation can be simplified to

Tf = T0 −RT 2

0

∆Hf

x1

F(7.2)

In these equations Tf is the melting temperature, T0 is the melting point

of the pure substance, R is the gas constant (8.314 Jmol−1K), ∆Hf is the

molar heat of fusion (calculated from the peak area), x is the mole fraction

of the impurity, Tfus is the melting point of the impure substance and F is

the fraction melted (F = Apart

Atot).

In [32] a ‘short’ method is compared with the commonly used one. For the

short method it is not needed to melt a sample completely, because ∆Hfus is

not used. This can be useful if samples start to decompose quickly after the

melting starts. The results of both methods are comparable.

7.4 High temperature DSC

In gas turbine engines nickel based superalloys are used. These compounds

have complex compositions and small changes in composition can affect the

properties a lot. Because industry is using higher and higher operating tem-

peratures, the alloys must have high melting points. Studies of these com-

pound have to take place at elevated temperatures. DSC is one of the few

techniques that can handle these temperatures.

To perform high temperature experiments some modifications are made to

the DSC setup. Stainless steel gas lines are used and a commercial gas

purification train is used to reduce the effects of oxygen, moisture and other

possible contaminants. Also a one way (Bunsen) valve prevents ingress of

oxygen from the exhaust. With this setup experiments up to 1400 degrees

Celsius are performed on nickel alloys. The melting points of the compounds

investigated are around 1300 and 1350 degrees Celsius. [34]

48

Appendix A

Derivation formula 5.2

Formula 5.2 is mentioned in [18], without derivation.

dq

dt= −

∆T

RR

+ ∆TS0

(

1

RS

+1

RR

)

+ (CR − CS)dTS

dt− CR

d∆T

dt

The formula is – probably – derived from a model that describes heat trans-

port (to the sample and to the reference) and the absorption of heat (by the

sample and the reference) as processes that can occur at the same time. But

physically the transport has to take place before the sample or the reference

can take up heat. From this point of view a serial process is expected to give

a better solution.

For the parallel model, mentioned first, the heat flow to the sample ( dqS

dt) and

to the reference (dqR

dt) are then described by

dqS

dt=

TS − T0

RS

− CS

dTS

dt(A.1)

dqR

dt=

TR − T0

RR

− CR

dTR

dt(A.2)

49

The difference between these heat flows is derived by substracting the two

equations.

d∆q

dt=

dqS

dt−

dqR

dt(A.3)

=TS − T0

RS

− CS

dTS

dt−

TR − T0

RR

+ CR

dTR

dt(A.4)

TS − T0 can be written as TS0. In the third term TR can be rewritten as

TR = TS − ∆T .

d∆q

dt=

∆TS0

RS

− CS

dTS

dt−

TS − ∆T − T0

RR

+ CR

dTR

dt(A.5)

The third term can be split in two parts.

d∆q

dt=

∆TS0

RS

− CS

dTS

dt−

TS − T0

RR

+∆T

RR

+ CR

dTR

dt(A.6)

The third term can be abbreviated to ∆TS0

RRand combined with the first term.

The fourth term is placed as first.

d∆q

dt=

∆T

RR

+ ∆TS0

(

1

RS

−1

RR

)

− CS

dTS

dt+ CR

dTR

dt(A.7)

In this equation TR can be rewritten as TS −∆T . Expanding this term gives

d∆q

dt= . . . − CS

dTS

dt+ CR

dTS

dt− CR

d∆T

dt(A.8)

where . . . stands for ∆TRR

+ ∆TS0

(

1RS

− 1RR

)

.

50

The first two terms of equation (A.8) can be combined.

d∆q

dt= . . . (CR − CS)

dTS

dt− CR

d∆T

dt(A.9)

The complete equation becomes

d∆q

dt=

∆T

RR

+ ∆TS0

(

1

RS

−1

RR

)

(CR − CS)dTS

dt− CR

d∆T

dt(A.10)

The only difference with the formula from [18] is the absence of the minus

sign before ∆TRR

. This minus sign is also absent in the simplified equation

mentioned in the same article.

51

52

Bibliography

[1] Elisabeth Schwarz and Dr. Jurgen de Buhr. Pharmaceuticals. Collected

Applications Thermal Analysis.

[2] Bernhard Wunderlich. Thermal Analysis, text for an audio course.

ATHAS, Advanced THermal AnalysiS, A Laboratory for Research and

Instruction, 1981.

[3] Hub Zwart. Denkstijlen. Valkhof Pers, 2005.

[4] Peter Atkins and Julio de Paula. Atkins’ Physical Chemistry. Oxford

University Press, 2002.

[5] Bernhard Wunderlich. Learning about calorimetry. Journal of Thermal

Analysis, 49(1):7 – 16, 1997.

[6] Hugo Meekes. Studiewijzer FMM4. Radboud Universiteit Nijmegen,

2004.

[7] Z. P. Belikova. Effect of level of heat production of human skin ther-

moreceptor function. Bulletin of Experimental Biology and Medicine,

68(4):1081 – 1082, 1969.

[8] Unitek Systems Instrumentation & Controls. The callendar - van dusen

coefficients.

[9] Honeywell Sensing & Control. Platinum rtd resistance vs temperature

function.

53

[10] Peak Sensors LTD temperature measurement & control. Resistance ther-

mometers (rtds).

[11] Mr. Lavoisier. Elements of Chemistry, chapter III, pages 421 – 433.

Easton Press, 4th edition, 1965.

[12] W. Nernst. Der energieinhalt fester stoffe. Annalen der Physik, 341:395

– 439, 1911.

[13] http://pslc.ws/mactest/dsc.htm.

[14] Michael E. Brown. Introduction to Thermal Analysis. Kluwer Academic

Publishers, 2001.

[15] F. Smet W.J.P. van Enckevort. In situ microscopy of the growth of

bismuth germanate crystals from high temperature melts. Journal of

Crystal Growth, 82(4):678 – 688, 1987.

[16] H. R. Oswald and H. G. Wiedemann. Fatcors influencing thermoana-

lytical curves. Journal of Thermal Analysis, 12(2):147 – 168, 1977.

[17] Mettler Toledo. Differential Scanning Calorimetry for all Requirements

6/2000. Mettler-Toledo GmbH, Analytical.

[18] Mettler Toledo. Usercom 2/2003.

[19] A. Wojakowska1, E. Krzyzak, and A. Wojakowski. Phase diagram for

the rbbrcubr system. Journal of Thermal Analysis and Calorimetry,

65(2):491 – 495, 2001.

[20] Q. Zhang, S. Harada, H. Takahashi, M. Saito, and Shigeru Tamaki.

Phase diagram of the cscl-rbcl system. 1988, 23(8):2905 – 2907, 1988.

[21] W.H. Wallace M.J. Visser. Du Pont Thermogram, 3(2):9, 1966.

[22] T. Daniels. Thermal Analysis. Kogan Page, London, 1973.

[23] C.T. Mortimer J.L. McNaughton. Differential Scanning Calorimetry.

Perkin-Elmer Order No.L-604, 1975.

54

[24] M.I. Pope and M.D. Judd. Differential Thermal Analysis. Heyden,

London, 1980.

[25] Perkin Elmer. Instrument news 21, 1970.

[26] H.G. Wiedemann, editor. ICTA, Birkhauser Verlag, Basel, 1971.

[27] A.J. Majumdar W. Gutt. Differential Thermal Analysis. Academic,

London, 1972.

[28] J. Sestak. Thermophysical Properties of Solids. Elsevier, Amsterdam,

1984.

[29] H.G. Wiedemann, editor. ICTA, Birkhauser Verlag, Basel, 1980.

[30] W. Hemminger, editor. ICTA, Birkhauser Verlag, Basel, 1980.

[31] Elena V. Boldyreva1, V. A. Drebushchak, I. E. Paukov, Yulia A. Ko-

valevskaya, and Tatiana N. Drebushchak. Dsc and adiabatic calorimetry

study of the polymorphs of paracetamol. Journal of Thermal Analysis

and Calorimetry, 77(2):607 – 623, 2004.

[32] N. V. Avramenko and N. D. Topor. Application of dsc for the determina-

tion of purity of organic semiconductors. Journal of Thermal Analysis,

33(4):1221 – 1224, 1988.

[33] Mettler Toledo. Usercom 2/99 (dsc purity determination).

[34] L. A. Chapman. Application of high temperature dsc technique to nickel

based superalloys. Journal of Materials Science, 39(24):7229 – 7236,

2004.

55