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FACULTY OF PHARMACEUTICAL SCIENCES

INSTITUTE FOR PHARMACEUTICAL TECHNOLOGY AND BIOPHARMACY

UNIVERSITY OF DUESSELDORF

Academic year 2008-2009

TOPEM, a new temperature modulated DSC technique: A critical review

Laurine PARMENTIER First Master of Pharmacy, Pharmaceutical Care

Promotor Dr. M. Thommes

Co-promotor Prof. Dr. C. Vervaet

Commissioners Prof. Dr. W. Baeyens

Dr. K. Remaut  

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“De auteur en de promotor geven de toelating deze masterproef voor consultatie beschikbaar te stellen en delen ervan te kopiëren voor persoonlijk gebruik. Elk ander gebruik valt onder de beperkingen van het auteursrecht, in het bijzonder met betrekking tot de verplichting uitdrukkelijk de bron te vermelden bij het aanhalen van de resultaten uit deze masterproef.”

28/05/2009

Promotor Auteur Prof. Dr. C. Vervaet Laurine Parmentier

 

 

 

 

 

 

 

 

 

 

 

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Word of Thanks

I would like to thank Prof Dr. C. Vervaet and Prof. Dr. P. Kleinebudde

for generally leading my master thesis.

I would like to express my warmest thanks to Dr. M. Thommes for helping me throughout this

study, especially for his patience and great help conducting me into the right direction.

I would also like to thank the whole staff of the institute for the pleasant environment

and especially Ms. K. Matthée who stood by me from the first day.

I would like to thank all the friends,

especially F. Koppers for always being ready to help.

Further, I would like to thank my parents for their eternal support.

Finally, I would like to thank the Erasmus programm,

which made this whole experience possible.

 

 

 

 

 

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LIST OF CONTENTS

WORD OF THANKS

LIST OF CONTENTS

LIST OF ABBREVIATIONS

1 INTRODUCTION ................................................................................................. 1

1.1 Thermal analysis ........................................................................................... 1

1.1.1 In general ................................................................................................ 1

1.2 Theory ........................................................................................................... 2

1.2.1 First law of thermodynamics ................................................................... 2

1.2.2 Second law of thermodynamics .............................................................. 3

1.3 Thermal analysis methods............................................................................. 4

1.3.1 Differential thermal analysis .................................................................... 4

1.3.2 Differential scanning calorimetry ............................................................. 4

1.3.2.1 General principles................................................................................ 4

1.3.2.2 Power compensation DSC................................................................... 5

1.3.2.3 Heat flux DSC...................................................................................... 6

1.3.3 Temperature modulated differential scanning calorimetry ...................... 7

1.3.3.1 General principles................................................................................ 7

1.3.3.2 Isothermal step method differential scanning calorimetry .................... 8

1.3.3.3 Alternating differential scanning calorimetry ........................................ 9

1.3.3.4 TOPEM.............................................................................................. 10

2 MATERIALS AND METHODS ........................................................................... 16

2.1 Materials...................................................................................................... 16

2.2 Methods....................................................................................................... 17

2.2.1 Differential scanning calorimetry ........................................................... 17

2.2.2 Balance................................................................................................. 17

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2.2.3 α-mannitol ............................................................................................. 17

2.2.4 Water uptake of sugars......................................................................... 17

3 OBJECTIVES..................................................................................................... 18

4 RESULTS .......................................................................................................... 19

4.1 Preliminary tests .......................................................................................... 19

4.2 Reversing and non-reversing heat flow ....................................................... 20

4.2.1 In general .............................................................................................. 20

4.2.2 Griseofulvin ........................................................................................... 20

4.2.3 Sucrose-water mixture .......................................................................... 22

4.2.4 Moist substances .................................................................................. 23

4.3 Calculation window...................................................................................... 25

4.3.1 In general .............................................................................................. 25

4.3.2 Mannitol ................................................................................................ 26

4.3.3 Calculation window parameters ............................................................ 27

4.3.4 Effect of the pulse width on the calculation window .............................. 30

4.4 Heat capacity............................................................................................... 37

4.5 Frequency ................................................................................................... 38

4.6 Resolution ................................................................................................... 41

5 CONCLUSIONS................................................................................................. 42

6 LITERATURE LIST ............................................................................................ 43

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LIST OF ABBREVIATIONS

ADSC Alternating Differential Scanning Calorimetry

Cp Heat capacity

Cp* Complex heat capacity

DMA Dynamic Mechanical Analysis

DSC Differential Scanning Calorimetry

DTA Differential Thermal Analysis

HR Heating rate

ISMDSC Isothermal Step Method Differential Scanning Calorimetry

m Sample mass

p Period

PET Polyethylene terephtalate

PH Pulse height

PVP Polyvinylpyrolidone

TGA Thermogravimetric Analysis

TMA Thermal Mechanical Analysis

TMDSC Temperature Modulated Differential Scanning Calorimetry

TOA Thermooptical Analysis

USP United States Pharmacopeia

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1 INTRODUCTION

1.1 THERMAL ANALYSIS 1.1.1 IN GENERAL

In pharmaceutical research, the development of new medicines is the main

goal. Besides that, already existing products need to be evaluated. There are several

ways to determine the characteristics of drugs during and after the development.

Information is needed about several characteristics such as purity, interactions,

solubility, molecular weight, structure and melting point. All these physicochemical

properties can be determined with a variety of methods and devices. A few examples

are chromatographic methods, spectroscopy, titration and thermal analysis.

In thermal analysis, the behavior of a substance is analyzed when a certain

temperature program is applied. Thermal analysis is a group of techniques in which a

physical property is measured as a function of temperature. Therefore the substance

is subjected to a controlled temperature program. This can be a dynamic or an

isothermal program. The obtained curve is the measured characteristic in function of

the time or the applied temperature. (Schwarz & de Buhr, 1998)

Thermal analysis includes several techniques of which the most important are:

differential scanning calorimetry (DSC), differential thermal analysis (DTA)

thermogravimetric analysis (TGA), thermal mechanical analysis (TMA), dynamic

mechanical analysis (DMA) and thermooptical analysis (TOA). TOA is the visual

perception or measurement of the permeability of light or light reflection of a sample.

In DMA, a force is supplied to the sample whereby the sample deforms and

information about the stiffness (viscosity and elasticity) can be determined. In TMA,

the deformation (change in width or length) of the sample under a load is measured.

In TGA, the mass of the sample is measured, under a defined atmosphere. DTA

measures the temperature difference between a sample and a reference. DSC

contains several techniques which will be discussed later. All the techniques for

thermal analysis are measured with an underlying temperature program. (Schwarz &

de Buhr, 1998)

It is the latest new DSC method, TOPEM, which will be the subject of the

research in this study.

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With thermal analysis methods, several characteristics can be measured:

melting point, crystallization behavior, glass transition, expansion, mass loss, thermal

stability, decomposition temperature, oxidation time, network formation, purity, visco-

elastic behavior and chemical reactions. (Schwarz & de Buhr, 1998)

1.2 THEORY 1.2.1 FIRST LAW OF THERMODYNAMICS

The first law of thermodynamics is an expression of the law of conservation of

energy. No energy can be destroyed or created, only changes in energy can take

place. The internal energy is the sum of heat and work done by the system. (Van der

Plaats, 1992)

U = Q + W (1)

Where: U: internal energy (J) Q: heat (J) W: work (J)

A calorimeter for example is a system in which mass and pressure are

normally constant. This means that the energy is only depending on temperature and

volume.

U = U (T, V) (2)

Where: U: internal energy (J) T: temperature (°C)

V: volume (m3)

A new state function is introduced, namely the enthalpy. State functions are

functions which always give the same result when going from point A to B,

independent from the way which is taken to get there. The change of enthalpy equals

the heat under constant pressure. Further is the work given by the pressure and

volume. The minus sign means that the work is done by the system. This means that

equation 1 can be rewritten using equations 3 and 4. (Van der Plaats, 1992)

(∆H)p = Q (3)

W = -pV (4)

(dH)p = dU + pdV (5)

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Where: U: internal energy (J) H: enthalpy (J)

p: pressure (Pa) V: volume (m3)

Q: heat (J) W: work (J)

 

Under constant pressure, the heat given to the system is the same as the

increase in enthalpy. Therefore, the heat capacity of a sample under constant

pressure is the change of enthalpy in time. (Van der Plaats, 1992)

cp = p (6)

Where: cp: heat capacity (J/K) H: enthalpy (J)

T: temperature (K) p: pressure (Pa)

1.2.2 SECOND LAW OF THERMODYNAMICS

There are different ways to determine the second law of thermodynamics:

• It’s impossible to transfer heat from a cold to a warm place, without changing

the environment

• It’s impossible to transform heat completely without changing the environment

• A new state function is introduced, namely the entropy. The entropy is heat

divided by temperature, in a reversible process. (Van der Plaats, 1992)

S = (7)

Where: S: entropy (J/K) Q: Heat (J)

T: temperature (K)

Using equation 4 and 7, equation 1 can be rewritten as follows: (Van der

Plaats, 1992)

dU = TdS – pdV (8)

Where: U: internal energy (J) T: temperature (K)

S: entropy (J/K) p: pressure (Pa)

V: volume (m3)

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Further is also the Gibbs free energy defined as G = H – TS. A system will

always try to find the lowest free energy state. According to the equation, this means

that the enthalpy has to be minimal and entropy has to be maximal to achieve this.

The Gibbs free energy is minimal when the system is at equilibrium under constant

pressure and temperature. However, pressure and temperature can be influenced in

thermal analysis. Therefore, the Gibbs free energy cannot reach the mininmum.

(Van der Plaats,1992)

G = H – TS (9)

Where: G: Gibbs energy (J) H: enthalpy (J)

T: temperature (K) S: entropy (J/K)

1.3 THERMAL ANALYSIS METHODS 1.3.1 DIFFERENTIAL THERMAL ANALYSIS

DTA is the oldest technique in thermal analysis. In DTA, a sample and

reference undergo the same temperature program. The sample and reference are

put in a pan. As a reference, mostly an empty pan is used. When a reaction occurs in

the sample, energy is needed (for an endothermal reaction) or released (for an

exothermal reaction) and therefore a temperature difference is measured. The

temperature difference is measured between the sample and the reference by two

thermal elements, one for each. When a temperature difference is measured, the

oven will compensate this, so that both sample and reference have the same

temperature. The temperature difference is used as a measured value. Any change

in temperature is detected with DTA. (Widman & Riesen, 1984)

1.3.2 DIFFERENTIAL SCANNING CALORIMETRY

1.3.2.1 General principles

As in DTA, in DSC a sample and reference, put into a pan, undergo a dynamic

or isothermal temperature program. Both sample and reference are placed on

identical measuring cells next to each other in an oven. The temperature difference is

compensated by the measurement cells and not by the oven. Because the sample

and reference have their own measuring cell, the detection of the temperature

difference goes faster and with more sensitivity as in DTA. The output value is the

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heat flow. This heat flow is actually measured as a heat power, with the unit Watt. By

integration of the heat flow in time, the enthalpy of a sample is calculated, with the

unit Joule. (Widman & Riesen, 1984)

1.3.2.2 Power compensation DSC

The sample and the reference both have their own measuring cell and oven.

Both ovens separately follow a temperature program. When there is a thermal

symmetry between both systems, the same amount of power will be needed to heat

them. When a transition (endothermal or exothermal) occurs, this will lead to a

temperature difference. A proportioning controller will be activated and puts as much

heat in the sample or cools it down as needed for the transition. That’s why the

temperature difference is kept a constant. (Widman & Riesen, 1984)

The compensated power is proportional to the measured temperature

difference.

∆P = -K1∆T (10)

Where: P: power (W) T: temperature (K)

K: calibration factor, fixed value of the controller

When a good calibration is used, the temperature difference can be used to

measure the heat flow in the sample.

ΦS = -K2∆T (11)

Where: Φ: heat flow (W) T: temperature (K)

K: calibration factor

FIGURE 1.1. CROSS-SECTION OF THE OVENS USED IN POWER COMPENSATION DSC.

(HTTP://WWW.FCHPT.STUBA.SK)

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1.3.2.3 Heat flux DSC

In heat flux DSC, the sample and reference are placed in one oven. The heat

flows from the oven, over a defined heat resistance to the sample and reference. The

driving force for the heat flow is the temperature difference over the heat resistance.

The heat flow to the sample is different to the one to the reference. (Widman &

Riesen, 1984)

When heat flows under steady state conditions, the temperature difference

between the reference and sample is proportional to the difference in heat flow from

the oven to the sample (OS) and to the reference (OR).

∆Φ = ΦOS – ΦOR = -K∆T = ΦS (12)

Where: Φ: heat flow (W) T: temperature (K)

O: oven R: reference S: sample

K: calibration factor that includes the asymmetry of the system

By measuring the temperature difference between a monster and reference, using

this equation, the heat flow ΦS can be measured.

A B

FIGURE 1.2. A) CROSS-SECTION OF THE OVEN USED IN HEAT FLUX DSC.

B) TOP-VIEW OF THE SENSOR USED IN HEAT FLUX DSC. S = SAMPLE,

R = REFERENCE (HTTP://WWW.MT.COM)

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1.3.3 TEMPERATURE MODULATED DIFFERENTIAL SCANNING CALORIMETRY

1.3.3.1 General principles

In conventional DSC, the sample undergoes a linear temperature program.

The output value is the difference in heat flow between the sample and reference. In

TMDSC however, a temperature modulation is superimposed over the linear

temperature program. This allows us to separate the heat flow into two components,

the reversing and non-reversing heat flow. The separating of these can be useful

when overlaying effects occur or thermal events cannot be clearly identified with

classical DSC. (Cao, 2007)

The reversing heat flow is the sensible heat flow component. This is

associated with processes that can be reversed. Thermodynamically seen, these are

processes that occur close to a local metastable state. When a process is reversible,

the measured curve should be reproducible after cooling the sample down and

reheating it. For such processes the heat input results in a temperature change.

Some examples are: glass transitions, melting of polymers, temperature change

when no thermal transition occurs. (Schawe, 2005a)

The non-reversing heat flow is the latent heat flow component. It is associated

with irreversible processes. Thermodynamically seen, such processes start in a non-

equilibrium state and end in an equilibrium state. They are time dependent. The heat

input doesn’t change the temperature, because the heat is used for changes in the

sample. Such changes take all the energy of the heat and therefore no heat is left for

a temperature increase. Examples are: non-reversible chemical reactions, melting,

and crystallization. (Schawe, 2005a)

For measuring the change of heat capacity with time or temperature,

temperature changes of the sample are measured. Due to that temperature

difference, there’s a change in enthalpy, given by

∆H = m cp ∆T (13)

Where : H: enthalpy (J) m: sample mass (mg)

cp: heat capacity (J/K) T: temperature (K)

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Next to the heat flow as a result from the heat capacity, there are other energy

changes due to chemical reaction or physical transitions. Therefore we should add

the heat related to chemical reactions, related to physical transitions and the drift of

the measuring system to equation 13. With respect to time, we can also split the heat

flow in the sensible heat flow and latent heat flow. (Riesen 1994)

Φ = m cp β Φb + Φr + Φt (14)

Φs Φl

Where: Φ: heat flow (W) Φr: heat flow of chemical reaction (W)

m: sample mass (mg) Φt: heat flow of physical transition (W)

cp: heat capacity (J/K) Φb: drift of the measurement (W)

β: heating rate (K/min) Φs:sensible or reversing heat flow (W)

Φl:latent or non-reversing heat flow(W)

In conventional DSC the temperature program is given by T = T0 + ß t. In

temperature modulated DSC, a temperature modulation is applied to a programmed

underlying heating rate and therefore a time-dependent function is added to the last

equation. This function is a saw tooth (ISM DSC), a sine wave (ADSC) or a

stochastic modulation (TOPEM).

T = T0 + ß t + f(t) (15)

Where: T: temperature ß: heating rate

T0: start temperature t: time

f(t): function that describes the temperature modulation

1.3.3.2 Isothermal step method differential scanning calorimetry

In ISM DSC, the temperature program consists of alternating heating and

isothermal segments. The isothermal segment should last until the heat flow remains

constant. If the temperature steps are too small, it is possible that the sample cannot

follow. When the steps are big enough, quasi-static conditions can be achieved. This

means that the sample can follow the set oven temperature and has time to

equilibrate at the isothermal parts. When the sample can follow well, there is a good

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separation of reversing and non-reversing heat flow. If the sample doesn’t have the

time to equilibrate, this separation cannot be completed. (Schawe, 2005b)

FIGURE 1.3. TEMPERATURE PROFILE OF AN ISM DSC MEASUREMENT

(METTLER-TOLEDO 2009)

1.3.3.3 Alternating differential scanning calorimetry

The temperature program in ADSC is a periodic sinusoidal change. Several

frequencies can be chose, in a range from 0.001 to 0.1 Hz. The disadvantage

however is that for every new selected frequency, a new measurement has to be

done. When low pulse heights and low underlying heating rates are used, there is an

increase in resolution. (Schawe, 2005b; Jörimann et al. 1999)

T(t) = T0 + βt + ATsin(ωt) (16)

ω = 2π/p (17)

Where: T: temperature (K) t: time (s)

ω: angular frequency (rad/s) p: period (s)

T0: start temperature (K) β: heating rate (K/min)

AT: amplitude of temperature modulation (K)

FIGURE 1.4. SINUSOIDAL HEATING RATE OF AN ADSC MEASUREMENT

(METTLER-TOLEDO 2009)

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From the raw data, the total heat flow is calculated, by averaging the signal.

This is the same approach as in conventional DSC measurements. The measured

heat flow is also a sine wave, but has a phase shift or phase lag compared to the

applied heating rate. (Jörimann, 1999)

Φ = AΦ cos(ωt + φ) (18)

Where: Φ: heat flow (W) AΦ: amplitude of the heat flow (K)

t: time (s) ω: angular frequency (rad/s)

φ: phase (rad/s)

For a certain frequency f, the heat capacity cp(f) can be calculated from

periodic changes in heat flow. Further on, the reversing heat flow and heat capacity

can be measured. The non-reversing heat flow is the difference between the total

heat flow and reversing heat flow. (Jörimann, 1999)

Φrev = β cp (19)

cp = AΦ (20)

Φrev = β AΦ (21)

Φnon = Φtot - Φrev (22)

Where: β: heating rate (K/min) cp: heat capacity (J/K)

p: period (s) AΦ: amplitude of heat flow (K)

AT: amplitude of temperature modulation (K)

Φtot: total heat flow (W) Φrev: reversing heat flow (W)

Φnon: non-reversing heat flow (W)

1.3.3.4 TOPEM

In general

In the TOPEM method, the temperature program is a stochastically changing

pulse. This means that the pulse widths change at random between a chosen

minimum and maximum. Also the pulse height has to be chosen. Figure 1.5. shows

an example of how the pulse can look like.

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FIGURE 1.5. EXAMPLE OF POSSIBLE PULSES IN TOPEM. THE VERTICAL ARROW IS

THE PULSE HEIGHT. THE HORIZONTAL ARROWS ARE TWO POSSIBLE

PULSE WIDTHS. (METTLER-TOLEDO 2009)

The stochastic pulses contain many different frequencies. After the

measurement, the heat capacity is calculated. This curve is then used for the

frequency evaluation. For a certain frequency, out of the heat capacity curve a new

heat capacity curve is calculated, which is called the complex heat capacity. Several

frequencies can be chosen, ideal for analyzing frequency dependent effects. The

heat capacity is determined under quasi-static conditions. The calculated heat flow is

the sum of the sensible and latent heat flow. (Schawe, 2005b)

The chosen temperature program defines the input signal. The output signal is

the measured heat flow. A mathematical procedure calculates the correlation

between the input (heating rate) and output signal (heat flow). After this procedure, a

component is obtained related to the input signal and one that doesn’t. The

correlated one is the reversing heat flow, the non-correlated one is the non-reversing

heat flow. (Schawe et al., 2005e)

The temperature program is defined by the underlying heating rate, switching

time and pulse height. The heating rate cannot be too high so that enough data

points are obtained. The switching time of the pulse width is set between 15 and 30

seconds. For low frequency measurements, a high switching time is needed and vice

versa. Too low or too high switching times result in noisy results. The pulse height is

determined by the behavior of the sample. The sample has to be able to follow the

oven. A sample is able to follow a little pulse height better than a high pulse height

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because it needs less time to equilibrate. On the other hand, more information is

gained with higher pulse heights because the sample is heated for a longer period.

This means that a compromise has to be found between higher and lower pulse

heights.

FIGURE 1.6. TYPICAL TEMPERATURE PROFILE (LEFT) AND CORRESPONDING HEAT

FLOW (RIGHT) IN A TOPEM MEASUREMENT (SCHAWE, 2005B)

Advantages and disadvantages of TOPEM

The new TMDSC method has many claimed benefits:

- In one measurement, there is a simultaneous determination of sample

properties as a function of time and temperature over a wide frequency range.

- Very accurate determination of the quasi-static specific heat capacity by

calculation of this heat capacity from the pulse response.

- High sensitivity and high resolution allows the measurement of low energy

transitions or effect close to another.

- Separation of sensible and latent heat flow. Heat capacities can be determined

even if the effects overlap.

- Simple interpretation of the curves. Effects depending on frequency can easily

be distinguished from those independent of frequency.

- The dynamics of the system can be analyzed over a broad range of

frequencies in one single measurement. (Schawe 2005b)

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The disadvantages of TOPEM are:

- Melting of pure substances cannot be measured. During the melting, the

sample temperature doesn’t change and the sample can therefore not follow a

temperature modulation. (Schawe 2005b)

- For the evaluation, a calculation window has to be set. The recommended

width of that calculation window by Mettler-Toledo is one third of the transition

interval. This is however not strict enough. It should be less than about one

tenth of the transition interval. (Fraga et al. 2007)

- The limit frequency for TOPEM is 4 mHz, independent on the experimental or

calculation parameters. This means it is intrinsic to the TOPEM method.

(Fraga et al. 2007)

- The measured complex specific heat capacities at a selected frequency shift

to higher temperatures for higher sample mass. (Fraga et al. 2007)

- In comparison to ADSC, the measured temperature of a transition is

significantly larger. This is because both use a different temperature

modulation. (Fraga et al. 2007)

Theory

For the measured heat flow both the reversing and non-reversing heat flow

can be calculated. The total heat flow is the sum of the reversing and non-reversing

heat flow according to the equation

Φtot = Φrev + Φnon (23)

Φrev = m ß (24)

Where: Φtot: total heat flow (W) m: sample mass (mg)

Φrev: reversing heat flow (W) : quasi-static heat capacity

Φnon: non-reversing heat flow (W) ß: heating rate (K/min)

If the temperature modulation is sufficiently small, it is assumed that the

current state of the sample is almost unaffected and that it is in equilibrium.

Therefore, in a limited temperature range the sample can be described as a linear

system. (Schawe, 2005d)

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u(t) g(t) y(t)

u(t) = T(t) linear system y(t) = Φmeasured (t)

Temperature as a function of

time

The system is defined

by the sample and

instrument

Heat flow as a function of

time.

FIGURE 1.7. GENERAL PRINCIPLE OF THE TOPEM TECHNIQUE

For a linear time dependent system with an input signal u(t) and output signal

y(t), the correlation is given as: (TOPEM – The new advanced multi-frequency

TMDSC technique)

y(t) = g(t) u(t) (25)

Where: y(t): output signal g(t): pulse response of the system

u(t): input signal t: time (s)

The pulse response is calculated with a z-transformation. Generally, a

transformation is the description of the signal with another set of basic units as was

the case before. The z-transformation is the discrete analog of the Laplace

transformation. It is used to convert differential equations which come up for time

discrete processes. The time-domain signal is converted by the z-transformation into

a complex frequency-domain representation. Equation 25 can be rewritten in the z-

plane as

y(z) = H(z)u(z) (26)

Equations of the time-domain can be described and solved more easily in the

z-plane. Several functions can be used to solve H(z), but often it can be exactly

described with a rational function.

(27)

Where B(z) and A(z) are polynomials of degree q or p in the variable z.

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By using the last equation, y(z) can be rewritten as

y(z) = u(z) (28)

or A(z)y(z) = B(z)u(z) (29)

When the last equation is converted to the time domain, the unknown

parameters for A(z) and B(z) have to be defined. These parameters are determined

using the measured input and output quantities. If these parameters are known, the

values of the pulse response g(t) for a certain frequency can easily be calculated.

Once we get the pulse response, the quasi-static heat capacity is calculated from this

pulse response. (TOPEM – The new advanced multi-frequency TMDSC technique)

(30)

Where: m: sample mass (mg) : quasi-static heat capacity

g(t): pulse response t: time (s)

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2 MATERIALS AND METHODS

2.1 MATERIALS  

TABLE 3.1. LIST OF ALL USED CHEMICALS

Products Company City Country

Griseofulvin (USP

micronized)

Hawkins

Pharmaceutical

Group

Minneapolis USA

Mannitol (Pearlitol

60) Roquette Lestrem France

Indium Mettler-Toledo Gießen Germany

PET BASF Ludwigshafen Germany

Sucrose Pfeifer & Langen Cologne Germany

Glucose Roquette Lestrem Germany

Dextrose

(monohydrate ST) Roquette Lestrem France

Lactose (granulac

200) Meggleburg Wasserburg Germany

Sodium nitrate Grüssing Filsum Germany

PVP CL BASF Ludwigshafen Germany

PVP CL-M BASF Ludwigshafen Germany

PVP 17PF BASF Ludwigshafen Germany

PVP 25 BASF Ludwigshafen Germany

PVP 90F BASF Ludwigshafen Germany

PVP IR BASF Ludwigshafen Germany

PEG PVA

copolymer VA64 BASF Ludwigshafen Germany

 

 

 

 

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2.2 METHODS 2.2.1 DIFFERENTIAL SCANNING CALORIMETRY

All experiments are done with the DSC1 from Mettler-Toledo (Gießen, Germany)

equipped with sample robot and a Haake Intra-Cooler EK/MT. Sample parameters

and data-analysis are realized with the STARe software. This software also

determines if the DSC is used as a conventional DSC, ADSC or as TOPEM. All

experiments were done using Aluminium pans without pin of 40μl (Mettler-Toledo,

Gießen, Germany). Al of the pans had pierced lids unless told else. All

measurements are done under N2 with a flow of 50ml/min. The used method will be

shown in the diagrams, when provided or else in the text. The used abbreviations are

HR for heating rate, PH for pulse height and p for period.

2.2.2 BALANCE

All samples are weighed on the balance MC210P from Sartorius AG

(Goethingen, Germany). First, sample pan holder, pan and lid are set to zero before

weighing the sample. After sealing the pan with the lid, the sample is weighed again

and this value is used.

2.2.3 α-MANNITOL

In order to make α-mannitol, ß-mannitol is heated until it is completely molten.

Then it’s poured into a mortar. When it’s completely crystallized, it is pulverized into

powder and stored at room temperature.

2.2.4 WATER UPTAKE OF SUGARS

For some measurements, moist substances were needed. Glucose, fructose,

dextrose and sucrose were heated until completely molten and poured into a petri

dish. The glassy substances were equilibrated at 23°C at 60% relative humidity for at

least 10 hours.

18 

 

3 OBJECTIVES

In thermal analysis, differential scanning calorimetry (DSC) is a commonly

used technique. Later, temperature modulated DSC techniques made their entrance,

namely isothermal step DSC and alternating DSC. Recently, TOPEM, a new

temperature modulated DSC technique has been developed. However, not much

research has been done on this technique. In addition, most available information is

linked to the company which developed TOPEM. The goal of this study is to make a

critical review about this new technique. TOPEM will be compared to regular DSC

and ADSC in order to evaluate its possible advantages and drawbacks.

The main question is: does TOPEM has any added value for differential

scanning calorimetry? In the literature, some advantages and disadvantages can be

found (see also introduction p.13) and based on the described advantages and

disadvantages, the following points should be investigated:

- separation of reversing and non-reversing heat flow: measurements of several

examples

- calculation window: determination of a width of calculation window and the

influence of the pulse width on it

- heat capacity: comparison of several methods to calculate heat capacity and

evaluation of the shift in complex heat capacity

- frequency: comparison with ADSC, determination of its limits

- resolution

19 

 

4 RESULTS

4.1 PRELIMINARY TESTS To start with, there was a search for a substance to do the investigations on

TOPEM with, because no standard substances are described in the literature. As a

first substance, Indium was measured because it is commonly used as a standard for

regular DSC. The melting peak with high intensity was found at the same

temperature as DSC. No conclusions could be drawn from the reversing and non-

reversing heat flow curves because of the big intensity of the melting over small

temperature range. In addition, pure substances such as Indium cannot follow a

temperature modulation. (Schawe 2005b)

Next step was to take substances described in the literature and do

measurements with the same parameters. Own measurements were compared with

measurements described in literature. The goal was to work on with a certain

substance when comparable results were found. A lactose-water mixture containing

4,5% lactose was measured as described by Schawe (2005a). The article shows a

peak at -30°C of which the origin is not clear. There was no transition found, even

after several measurements. However, the described peak in the literature is small. It

is possible that the DSC used by Schawe (2005a) is able to detect smaller effects

because it is more sensitive.

Afterwards, polyethelene terephtalate was measured as described by Schawe

(2005c). Pet was crystallized for 10 min at 170°C. Compared to the article, smaller

curves are obtained and there is noise even after repeating the measurement. The

reason for this is that polymers often have a batch-to-batch variability. Therefore, the

next measured substance was a crystalline substance, namely sodium nitrate as

described by Schawe (2005a). The measurement showed comparable curves to the

literature with a step in the curves at the same temperature (see figure 4.1.).

From these tests was concluded to do no measuring of melting of pure

substances. Pure substances can be used when effects overly or are close to each

other. Because polymers often have differences between batches, it is better to take

crystalline substances. Also mixtures will be used for investigation.

20 

 

A B

FIGURE 4.1. A. TOTAL (UPPER), NON-REVERSING (MIDDLE) AND REVERSING (LOWER) HEAT

FLOW CURVES OF A TOPEM MEASUREMENT OF SODIUM NITRATE (SCHAWE,

2005C)

B. TOTAL (BLACK), REVERSING (GREEN) AND NON-REVERSING (BLUE) HEAT

FLOW CURVE OF A TOPEM MEASUREMENT OF SODIUM NITRATE

4.2 REVERSING AND NON-REVERSING HEAT FLOW 4.2.1 IN GENERAL

Separation of reversing and non-reversing heat flow is the main goal of using

temperature modulated DSC. To evaluate this, first griseofulvin was measured

because it is expected that TOPEM can give more information about the results

obtained from regular DSC. Also a 40:60 mixture of sucrose and water was

measured and compared to the literature. There were also several moist sugar

samples measured. Moist substances give in regular DSC only a peak between 30°C

and 120°C because of the evaporation of water. This peak overlies glass transitions

occurring in this range. TOPEM should be able to detect this glass transition.

4.2.2 GRISEOFULVIN

The conventional DSC curve of griseofulvin shows a small peak before the

melting peak which could be due to the sublimation of griseofulvin. The clue for that

is the description of a weight loss due to sublimation at about 200°C, measured with

thermogravimetry. (Analytical profiles of drug substances and excipient)

21 

 

Since sublimation is a process related to latent heat flow, it should be seen in

the non-reversing heat flow curve of a TOPEM measurement. As shown in figure

4.2.B the total heat flow curve also shows this second peak but the non-reversing

curve doesn’t. The reason for this could be that the gas phase escaped through the

hole in the pierced lid of the pan and therefore no effect can be measured. Another

measurement was done with a closed pan. As can be seen in figure 4.2.C the curves

are comparable to the curves of the measurement with a pierced pan. This means

that no extra information was gained using TOPEM.

The peak at about 18°C is due to melting. Griseofulvin is a pure substance so

its melting cannot be evaluated using TOPEM. Griseofulvin was investigated for the

small peak under the first part of melting peak. It was not used for the investigation of

the melting peak.

A B C

FIGURE 4.2. TOTAL HEAT FLOW CURVE OF A DSC MEASUREMENT OF GRISEOFULVIN

(A) AND TOTAL (BLACK), REVERSING (GREEN) AND NON-REVERSING

(BLUE) HEAT FLOW CURVES OF A TOPEM MEASUREMENT OF

GRISEOFULVIN WITH PIERCED (B) AND SEALED (C) AL PAN

22 

 

4.2.3 SUCROSE-WATER MIXTURE

A TOPEM measurement of a mixture of 40% sucrose and 60% water was

measured as described by Schawe (2005c). The total heat flow curves are

comparable to our measurement. However, the curve for the non-reversing heat flow

is not entirely published. In our measurement, a peak in the non-reversing heat flow

curve at about -5°C can clearly be seen. The little peak around -35°C is explained in

the article to be the melting of non-equilibrated crystals. The peak at -5°C is

explained by Schawe (2005c) to be an artifact.

It is interesting that the peak at -5°C, which is more than ten times larger than

the peak at -35°C is not reported in the article. The peak at -5° is also present at all

the measurements which were taken. Therefore we assume that it is not an artifact

but that the peak is due to crystallization.

FIGURE 4.3. TOTAL (BLACK), REVERSING (GREEN) AND NON-REVERSING (BLUE)

HEAT FLOW CURVES OF A TOPEM MEASUREMENT OF A 40:60

SUCROSE-WATER MIXTURE

23 

 

A B

FIGURE 4.4. A. TOTAL HEAT FLOW (BLACK) AND MEASURED HEAT FLOW (RED) OF A

TOPEM MEASUREMENT OF A 40:60 SUCROSE-WATER MIXTURE

(SCHAWE, 2005C)

B. TOTAL (BLACK), REVERSING (GREEN) AND NON-REVERSING (BLUE)

HEAT FLOW CURVES OF A TOPEM MEASUREMENT OF A 40:60

SUCROSE-WATER MIXTURE

(SCHAWE, 2005C)

4.2.4 MOIST SUBSTANCES

Moist substances show in regular DSC a peak between 30°C and 120°C

because of the evaporation of water. When some underlying effects occur at the

same range, such as a glass transition, this cannot be seen in the heat flow curve.

TOPEM however can separate the latent and sensible heat flow. The water peak will

still be seen in the total heat, but as a glass transition is a reversible process, it

should be seen in the reversing heat flow. To examine the effects underlying the

evaporation of water, several samples of polyvinylpyrolidone (PVP) were evaluated.

All the selected samples showed a large water peak in measurements obtained by

regular DSC in the past. All the PVP samples were measured between 0°C and

140°C with a heating rate of 1°C/min, a pulse height of 0.5°C and had a sample

weight of about 3.00 mg.

There was no underlying effect found for none of the PVP samples. Only the

reversing heat flow curve of the TOPEM measurement of PVP VA64 does show a

24 

 

glass transition at about the glass transition temperature of the DSC measurement.

At that point however, it is not overwhelmed by a peak of evaporation of water. This

means that for all the PVP samples, TOPEM cannot separate between reversing and

non-reversing heat flow.

The next measured substances were glucose, fructose, dextrose and sucrose.

All have a defined glass transition temperature and take up water fast and easily. All

samples were measured from 50°C below to 50°C above the glass transition

temperature, with a heating rate of 1°C/min, pulse height of 0.5°C and a sample

mass between 2.00 and 6.00 mg. In all curves, the water peak is visible, but no

underlying effects were detected. For all the substances there is an extra peak at

about the middle of the peak due to the desorption of water. It occurs at about 70°C

for dextrose and 90°C for glucose (see figure 4.6.). Desorption means that, in this

case, water molecules leave the surface to join the gas phase. It can be concluded

that also for the sugars, TOPEM cannot separate between reversing and non-

reversing heat flow.

FIGURE 4.5. TOTAL (BLACK), REVERSING (GREEN) AND NON-REVERSING (BLUE)

HEAT FLOW CURVES OF A TOPEM MEASUREMENT OF PVP VA64

25 

 

FIGURE 4.6. TOTAL (BLACK), REVERSING (GREEN) AND NON-REVERSING (BLUE)

HEAT FLOW CURVES OF A TOPEM MEASUREMENT OF DEXTROSE

(UPPER) AND GLUCOSE (LOWER)

4.3 CALCULATION WINDOW 4.3.1 IN GENERAL

For the evaluation of the data, several parameters have to be defined. The

width of calculation window, sample and pan weight, parameters for fitting the points

in a curve and the width of smoothing window have to be determined.

The calculation window is a set of data points which are considered for the

calculation of the heat flow curves out of the raw data. The chosen width is a time

interval which is considered for calculation for each data point. The shift of calculation

window is how far the calculation window moves each time. The width of the

calculation window is recommended by Mettler-Toledo to be one third of the

transition whereas it is said to be about one tenth by Fraga (2007). This window width

and its effect on the eventual curves will be investigated. When a narrow calculation

window is used, the calculation goes faster, but less information is obtained. Using

bigger calculation windows more information is obtained, but the calculation requires

more time. Large window widths need low heating rates. A small shift in calculation

window gives a good analysis but takes a long time.

26 

 

FIGURE 4.7. WIDTH AND SHIFT OF CALCULATION WINDOW (METTLER-TOLEDO 2008)

The sample and pan weight can be filled in to quantify measurements or to

define a heat capacity. These weights are without sample and are a blank. The

sample and instrument response parameters are the degrees of the polynomials

used to fit the data points in a curve. After the curves are calculated with the

calculation window, they still have to be smoothened. Therefore the width of

smoothing window has to be set. It has to be smaller than the calculation window

because it smoothens within this window.

4.3.2 MANNITOL

For the investigation of the calculation window, a 50:50 mixture of α-ß mannitol

was measured. Mannitol can crystallize in several forms of which two polymorphic

forms are widely described in the literature: α-mannitol and ß-mannitol. ß-mannitol is

the most stable one and the metastable α-mannitol transforms to the ß-form over

time. The orthorombic α and ß-forms have many similarities. Their physical

properties such as melting temperature, enthalpy of fusion, density and specific heat,

only differ little. They can be separated using X-ray diffraction and infrared

spectroscopy. It’s not possible to differentiate them with conventional DSC

measurements because their melting points are too close to each other: α-mannitol

melts at 166°C and ß-mannitol at 166.5°C. (Burger et al., 1999)

27 

 

When a mixture of α and ß-mannitol is being melted, the metastable α-form

will melt first. Because of the presence of ß-mannitol, the molten α-mannitol will

recrystallize into ß-mannitol. This is a non-reversible effect because ß-mannitol will

never crystallize into the less stable α-form when the more stable ß-form is present.

This means that this effect should be seen in the non-reversing heat flow.

4.3.3 CALCULATION WINDOW PARAMETERS

During the evaluation of mannitol, it was found that the width of the calculation

window influenced the curves. The correct width of calculation window is the one

which gives a good fit between the total and the measured heat flow. That is always

the case when the total heat flow is calculated from the measured heat flow, as in

ADSC for example. But in TOPEM, it is the reversing and non-reversing heat flows

which are calculated from the measured heat flow and the total heat flow is the sum

of both. Afterwards, it has to be checked if this total heat flow and the measured heat

flow do fit. If not, no conclusions can be drawn. To make these curves fit, the

evaluation parameters have to be set.

With every new calculation window a new curve is obtained. The window that

gives the best fitted total heat flow curve should be taken for interpretation of the

data. To see if there is a good fit, the measured heat flow and the total heat flow were

subtracted. The obtained curve should not have large fluctuations. These curves

were compared for several calculation windows for several mixtures of α-ß mannitol.

To analyze the fluctuations in the subtraction curves, the amplitudes at each point are

summed up. If there are large fluctuations, the sum of the amplitudes is high. The

lowest sum of amplitudes accords to the best fit for total and measured heat flow and

the corresponding width of calculation window is the best to analyze the sample.

28 

 

FIGURE 4.8. TOTAL HEAT FLOW (BLACK), MEASURED HEAT FLOW (RED) AND

SUBTRACTION OF BOTH (PURPLE) OF A TOPEM MEASUREMENT OF Α-ß

MANNITOL; CALCULATION WINDOW IS 120S (UPPER), 300S (MIDDLE)

AND 550S (LOWER)

The calculated window should correspond to the recommended calculation

window, namely one third of the transition interval. The transition interval for every

mixture is divided by three to obtain the recommended width of the calculation

window. As can be seen in table 4.1. the recommended and optimal calculation

windows are different. Only for the 80:20 mixture, one third of the transition interval is

close to the optimal width of the calculation window. For all the others, the window

should be bigger. In figure 4.9. can be seen that for all the mixtures, except the 60:40

mixture, several calculation window widths will yield acceptable results, because their

sums of amplitudes are in the same range.

From this data was concluded that it is important to determine the correct

calculation window before any conclusions are drawn. However, it is difficult to

determine the optimal calculation window width since similar results were obtained.

When the average of these was made, the calculation window width should be

around one fifth of the transition interval, but this should be evaluated for each

sample separately.

29 

 

A B

C D

E

FIGURE 4.9. SUM OF THE AMPLITUDES OF THE SUBTRACTION CURVE BETWEEN THE

TOTAL HEAT FLOW AND MEASURED HEAT FLOW FOR SEVERAL α-ß

MANNITOL MIXTURES: 20:80 (A), 40:60 (B), 50:50 (C), 60:40 (D) AND

80:20 (E) α-ß MANNITOL; THE LOWEST SUM IS MARKED (RED).

30 

 

TABLE 4.1. COMPARISON OF CALCULATED BEST AND RECOMMENDED CALCULATION

WINDOW (1/3 OF TRANSITION INTERVAL)

Mixture Transition

interval (s)

1/3 of

transition

interval (s)

Calculated best

calculation

window (s)

Part of

transition

interval

20:80 1200 400 250 1/5

40:60 1200 400 200 1/6

50:50 1200 400 250 1/5

60:40 1440 480 375 1/4

80:20 1440 480 475 1/3

4.3.4 EFFECT OF THE PULSE WIDTH ON THE CALCULATION WINDOW

As already pointed out, the width of the calculation window has a big influence

on the outcome of the final heat flow curves. The goal was to find a defined width of

calculation window. The problem is that TOPEM uses a stochastically changing pulse

width. In addition, TOPEM does not provide the raw data, there has already been a

mathematical modulation executed. In order to overcome the problem with the pulse

width and the data, a TOPEM simulation was carried out with regular DSC. The

modulation was done with a periodic step function of 60s.

The measured substance was a 50:50 mixture of α and ß-mannitol. The

following parameters were used: heating rate 0.05°/min, pulse height 0.02°C, period

60s and sample mass between 2.00 and 5.50 mg. We are especially interested in

this substance because the ADSC measurement shows no reversing effect while the

TOPEM measurement does show a peak in the reversing heat flow. This is shown in

figure 4.10. Figure 4.11. shows the raw data of the sample, an empty pan and the

reference pan. Not the heat flow but the temperature is taken for analysis because

the temperature is the only true measured value and the heat flow is correlated to it.

31 

 

A B

FIGURE 4.10. MEASURED (RED), TOTAL (BLACK), REVERSING (GREEN) AND NON-

REVERSING (BLUE) HEAT FLOW CURVE OF A TOPEM MEASUREMENT

(A) AND AN ADSC MEASUREMENT (B) OF A 50:50 MIXTURE OF α-ß

MANNITOL

FIGURE 4.11. RAW DATA OF THE SAMPLE, EMPTY PAN AND REFERENCE PAN OF A

PERIODIC TMDSC MEASUREMENT. CURVES ARE A FUNCTION OF TIME

AND TEMPERATURE.

32 

 

The three curves are still a function of time and of temperature. The aim is to

eliminate the factor temperature so that the slope of the curve becomes zero. In order

to do that, the average of the pan curve is calculated and subtracted of all the curves.

This average is actually the heating rate of the measurement. After this is done, the

peak of melting can be seen in the sample curve (pink curve in figure 4.12.). This

curve is considered for further analysis of the calculation window.

Since this is a periodic modulation, the period should be used as a calculation

window width. For comparison, two other widths are considered: 200s and 330s. As

transition interval the segment between 2600 and 3600 seconds is considered. The

width of 200 corresponds to about one fifth of the transition interval, which was found

to be the correct width. The width of 330s corresponds to about one third of the

transition interval, which is the recommended calculation window width. As can be

seen in figure 4.12. the width of the period gives the best fit. The width of 200s and

330s are not flat anymore.

FIGURE 4.12. RAW DATA OF THE SAMPLE OF A PERIODIC TMDSC MEASUREMENT.

AVERAGE CURVES OF THE SAMPLE ARE GIVEN FOR A PERIOD, 200S

AND 330S. CURVES ARE ONLY A FUNCTION OF TIME.

33 

 

To take a closer look at how the sample responses to the set value and in

order to compare each segment to another, the melting peak had to be eliminated.

For further calculations, figure 4.12. is considered. The sample curve (pink) and its

averages were subtracted for all three average curves. This means that a subtraction

was done for the width of the period (pink minus blue curve), the width of 200s (pink

minus green curve) and for the width of 330s (pink minus brown curve). These

subtraction curves were compared to the reference. The resulting curves are shown

in figure 4.13. The same colors are used for the same widths of calculation window.

In figure 4.13. can again be seen that different curves are created for the different

calculation windows and that the period gives the best width.

To compare the three window widths better, every period was overlapped to

see any changes in the curves. This means that all the curves in figure 4.13 were cut

every 60s and all these pieced were laid over each other. The result is shown in

figure 4.14. Only the first half of period is shown, but again the curves are different for

the three window widths. For the width of 330s, the curves even go below zero. The

sample is able to follow the oven temperature quickly.

FIGURE 4.13. BEHAVIOR OF THE SAMPLE; COMPARISON OF DIFFERENT CALCULATION WINDOWS

34 

 

FIGURE 4.14. BEHAVIOUR OF THE SAMPLE; COMPARISON OF DIFFERENT

CALCULATION WINDOWS; BLUE CURVES ARE BEFORE THE TRANSITION,

PINK ARE DURING AND YELLOW ARE AFTER

In order to understand the shape of the curves in figures 4.13. and 4.14., the

behavior of the sample should be investigated more. This is explained in figure 4.15.

There are two effects which have to be considered: the effect of melting (green) and

the effect of the diffusion of the heat through the sample (brown). Both curves result

in the sample curve (blue). In the mathematical evaluation of the data (see

introduction under 1.3.3.4), these curves are part of the equation 27. The equation

y(t) = g(t)u(t) was rewritten in the z-plane as y(z) = H(z)u(z) in which H(z) can be

described as a rational function.

y(t) = g(t) u(t)

Where: y(t): output signal g(t): pulse response of the system

u(t): input signal t: time (s)

Where B(z) and A(z) are polynomials of degree q in the variable z.

35 

 

The last equation holds the functions which describe the melting part and the

heat diffusion part of the sample. B(z) is the melting part and A(z) is the heat diffusion

of the sample. Using these equations, in the time domain, y(t) becomes the following:

y(t) = locally

y(t) = u(t) in general

The output value or sample curve y(t), the input value or set value u(t) and the

heat diffusion A(t) are known variables, so the melting B(t) can be determined.

FIGURE 4.15. BEHAVIOR OF THE SAMPLE, THE EFFECT OF MELTING AND EFFECT OF

HEAT DIFFUSION

A last step in comparison of the different calculation windows was to evaluate

the melting behavior. For the three different sample curves (blue, green and brown

curve) as shown in figure 4.13. the average is calculated. Since there was no

reversing effect found in the ADSC measurement, it is also expected not to see a

reversing effect in this measurement. This means that the calculated average curve

36 

 

should be flat. In figure 4.16. can be seen that this is almost the case for the period-

curve, but the bigger the calculation window, the more the curves deviate.

FIGURE 4.16. AVERAGE OF THE SAMPLE CURVE FOR DIFFERENT CALCULATION

WINDOWS

It was already clear that several widths of calculation window give different

heat flow curves. The curves shown in figure 4.13, 4.14. and 4.16. also prove this. In

addition, several ways proved that the period is the best width for the calculation

window. The problem with TOPEM is that, because of the stochastic pulses, there is

no fixed period. It is because of this that the calculation of the heat flow curves

becomes difficult. Therefore we would recommend using TOPEM in a periodic way to

overcome the problem with the calculation window. This means however that no

frequency evaluation can be done since a periodic modulation holds only one

frequency.

The difference with ADSC is that TOPEM uses a step function instead of a

sine wave as modulation. A sample cannot follow a sine wave well because there is

no time for equilibration. Because of the many fluctuations, a blank and calibration

curve need to be executed for every new method in ADSC. Using a step function as

in TOPEM, the sample has the time to equilibrate every step upwards and

downwards. That’s why there are no blank and calibration curves needed for TOPEM

as there is for ADSC. When TOPEM is used in a periodic way, more measurements

37 

 

will be needed to do a frequency evaluation. There is however no need for blank and

calibration curves, so a TOPEM evaluation will still be less time consuming than an

ADSC evaluation.

4.4 HEAT CAPACITY In TOPEM, the heat capacity (Cp) is calculated from the pulse response. The

heat capacity is the enthalpy divided by temperature and sample mass (see also

introduction). The enthalpy is given by integration of the heat flow. For a heat

capacity evaluation in an ADSC measurement, a blank and calibration curve need to

be executed for every new method. As been said before, those curves aren’t needed

in TOPEM. The sample and pan weight can be filled in in the calculation window and

this is used as a blank. The fact that no extra curves are needed in TOPEM leads

also to a simpler interpretation of the curves.

A 50:50 mixture of α and ß-mannitol is used for the evaluation of Cp. For the

calculation of Cp out of the raw data, data from the measurements under 4.3.4 are

used. To calculate Cp out of the heat flow for TOPEM and ADSC, the data from the

measurements under 4.3.3 (see also figure 4.10.) was used. All three curves are

shown in figure 4.17. The peak middle is for all three at the same time. This means

that it doesn’t matter if the heat capacity is calculated from the pulse response or

from the heat flow.

FIGURE 4.17. COMPARISON OF HEAT CAPACITY CALCULATED FOR TOPEM FROM THE

RAW DATA AND THE HEAT FLOW AND FOR ADSC FROM THE HEAT FLOW

38 

 

4.5 FREQUENCY The TOPEM technique promises a frequency evaluation in just one single

measurement. Frequency is the reciprocal of the period.

   

Where: f: frequency (s)

τ: period (Hz)

This frequency evaluation is actually the calculation of the complex heat

capacity out of the heat capacity for a set frequency. In TOPEM, the set value for the

stochastic pulses is 15 to 30 seconds and can go up to 500s. Theoretically, this

means that the frequency can take values from 33.3 mHz to 66.7 mHz. A 40:60

mixture of sucrose and water was used for the frequency evaluation. The upper limit

is 50 mHz. The 60 mHz curve cannot be seen because it’s covered by the 50 mHz

curve. The lower limit is 10 mHz. Also the 5 mHz curve cannot be seen because it’s

covered. The complex heat capacity curves can be considered between 10 and 50

mHz.

Fraga et al. (2007) mentioned a limit of 4 mHz for the frequency evaluation.

This accords to a period of 25 seconds. Because the period goes from 15 to 30

seconds, we assume that 4 mHz as a limit only counts for the substance used in that

article. Because the theoretical limit, the limit in our measurement and in the literature

differ, we assume that every substance has its own limit. The same article also

mentioned that the complex heat capacity shifts to higher temperatures for higher

sample masses for a selected frequency. This shift was also the case with the

sucrose-water mixture (see figure 4.18.). The complex heat capacity shifts to lower

temperatures because the measurement is a cooling, not a heating.

39 

 

FIGURE 4.18. COMPARISON OF MIDPOINT TEMPERATURES OF COMPLEX HEAT

CAPACITY FOR DIFFERENT SAMPLE MASSES OF A 40:60 MIXTURE OF

SUCROSE-WATER IN A TOPEM MEASUREMENT; COMPLEX HEAT

CAPACITY IS CALCULATED FOR 50 MHZ

The TOPEM frequency evaluation was compared to ADSC measurements

performed at periods according to frequencies of 10 to 50 mHz, as in TOPEM. The

results are shown in figure 4.19. and according values for the glass transition are

shown in table 4.2. In both techniques, the midpoint temperature moves to lower

temperatures for higher frequencies. The difference in the values for ADSC are

bigger but considered neglectable since the mean values for both techniques only

differ little. This is probably because both techniques use different temperature

modulations.

We can conclude that a frequency evaluation done by TOPEM is comparable

to ADSC. Of course, there has to be considered that also the heat capacity curve is

calculated from the raw data using a calculation window. First, as for any TOPEM

evaluation, a frequency evaluation can only be done if the total heat flow curve does

give a good fit with the measured heat flow. Second of all, we would recommend

doing a regular DSC measurement and comparing as well the total heat flow curve

40 

 

as the heat capacity before doing a frequency evaluation. Still a TOPEM

measurement will be less time consuming than an ADSC measurement.

A B

FIGURE 4.19. FREQUENCY EVALUATION OF A TOPEM MEASUREMENT (A) AND AN

ADSC MEASUREMENT (B) OF A 40:60 MIXTURE OF SUCROSE-WATER

TABLE 4.2. GLASS TRANSITION TEMPERATURES FOR THE TOPEM AND ADSC

MEASUREMENTS ACCORDING TO FIGURE 4.19.

TOPEM ADSC

Glass transition Onset (°C) Midpoint (°C) Onset (°C) Midpoint (°C)

10 mHz -34.94 -33.95 -35.36 -34.18

20 mHz -34.99 -33.55 -35.23 -34.20

30 mHz -34.60 -33.17 -33.59 -31.93

40 mHz -34.10 -32.92 -33.57 -31.93

50 mHz -34.07 -32.86 -33.27 -31.28

41 

 

4.6 RESOLUTION It is claimed that TOPEM has a good resolution. As can be seen in figure 4.20.

this is a true statement. To go in one period from the highest to the lowest point,

more than one hundred data points are in between. In order to have a good

resolution between the pulses, at least fifty data points are needed. It is also claimed

that TOPEM has a good sensitivity, but because the raw data cannot be obtained,

this could not be investigated.

FIGURE 4.20. MEASURED HEAT FLOW CURVE OF A TOPEM MEASUREMENT OF A

50:50 MIXTURE OF α AND ß-MANNITOL. USED PARAMETERS: HR

0.05°C/MIN, PH 0.02°C. SAMPLE MASS = 4.98 MG.

42 

 

5 CONCLUSIONS

In this study, the temperature modulated DSC technique TOPEM was

investigated. During the investigation of the separation of reversing and non-

reversing heat flow was noticed that often no extra information is gained using

TOPEM. For measurements where it is suspected that separating reversing and non-

reversing heat flow is useful, we would recommend to do a quick run with regular

DSC for comparison.

The biggest problem seems to be setting the evaluation parameters, more

specifically the width of calculation window. In order to calculate the heat flow curves,

this calculation window has to be set. Because there is no fixed period as in ADSC, it

is not easy to define this window. Different articles recommend different calculation

windows. We’ve proven that the shape of the curves is very dependent on this

calculation window. Different windows can create different curves and therefore also

false curves.

It was however found, that the frequency evaluation and heat capacity were

comparable to ADSC and that there is a good resolution. The frequency evaluation

still has a limit for every substance despite the theoretical limits and the measured

complex heat capacity has a shift in temperature for higher sample masses. Further,

it can be concluded that the pulse response can be used to define the heat capacity.

For as well the heat flow as the frequency evaluation there is still the problem of the

calculation window. The correct width of this calculation window should be checked in

advance before doing any further evaluations.

When everything is put together, we would recommend using TOPEM not in a

stochastic way but by using a fixed period. This should solve the problem with the

calculation window. This means however that there is no frequency evaluation

possible. However, there is no need to do blank and calibration curves as in ADSC,

so it will still be less time consuming as an ADSC measurement. We also

recommend doing a regular DSC measurement in advance for comparison.

43 

 

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