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THERMOPHYSICAL PROPERTIES OF THE PHASE CHANGE MATERIAL

MIXTURES – PRELIMINARY STUDIES ON MACROMOLECULAR

HYDROCARBONS EXAMPLE

E. KLUGMANN-RADZIEMSKA1, P. WCISŁO

1, H. DENDA

1, M. RYMS

1

1. Gdansk University of Technology, Faculty of Chemistry, Gdansk, Poland

ABSTRACT

The aim of this work is a theoretical and experimental analysis

of the macromolecular hydrocarbons mixtures composition

and the impact on thermophysical parameters of the phase

change materials (PCM) made from these mixtures. The

analysis of the current state of knowledge extended by the

author’s own studies have been presented. Thermophysical

characteristics of the hydrocarbons and their mixtures have

been specified, in such a way, that on this basis description of

the nature of the effects from individual fractions can be

obtained, and the most important parameters characterizing

the PCMs, such as the temperature peak of the phase transition

or the heat of transition, can be set down.

INTRODUCTION

One of the major tasks assigned to current

knowledge of phase change materials (PCM) are both

research for the new compounds and description of

properties of the already known substances and

mixtures. At the same time the requirements for these

materials, such as high purity, heat capacity and

durability, a narrow range of the phase transition

temperature, low price, determine the intensity of

activities in this field. Therefore there is a high demand

for a description of existing mixtures (sometimes fairly

well known) of materials that could be used as PCMs.

This is an extremely important issue, from an

economic, as well as technological and environmental

points of view.

Solid-liquid phase change materials during

isothermal phase transitions absorb, store and release

heat. The heat is stored at the time of solid to liquid

transition, and released during the phase change from

liquid to solid. This allows for the economic utilization

of the waste heat, heat from the sun, surplus heat in

passive constructions or just for efficient heat

management. Research on phase change materials have

been undertaken many times before, but still there is a

demand for both new materials and a new usage of

existing materials. Among phase change materials can

be divided into [Kenisarin M., 2011]: organic

compounds (e.g.: waxes, paraffins, fatty acids,

alcohols), inorganic compounds (hydrated salts) and

eutectic mixtures.

Based on analyzes and literature the need for a

theoretical and an experimental examination of the

mutual relationships between the various

thermophysical parameters, such as: phase transition

enthalpy or melting temperature, can be indicated, not

only for the pure PCMs, but also their mixtures as a

function of their composition. This applies in particular

to macromolecular hydrocarbon mixtures, for which

primary thermophysical properties could be well

defined but only as an encyclopedic data – very useful

form application point of view, but with rather little use

in research.

Due to their ability to absorb, during isothermal

phase transitions, store and then release heat, phase

change materials (PCMs) are very useful substances in

many applications:

• plates with PCM layer that keeps the meal warm

or cups sustaining high temperatures of the drinks, used

in food industry for a constant temperatures control,

• cardboard plates or bags filled with PCM or

directly mixed with cement, used in floors and walls as

an improvement in buildings energy efficiency

[Lewandowski W., 2014],

• storing heat during engine operation, and

recovering this energy when the engine starts,

• heat-receiving materials to prevent overheating

of the devices [Höhne G., 2003],

• inserts or containers for the thermo-sensitive

materials transport e.g.: blood, organs, drugs, groceries,

sensitive electronics, chemicals etc.,

• protection when carrying out exothermic

chemical reactions in chemistry,

• sportswear materials, vests for firefighters, suits

for astronauts protecting from them temperature

fluctuations.

Mehling and Cabeza [Cabeza L.F., 2011] have been

expanded above division with reference to PCMs

enthalpy and melting temperature levels. Dubovsky at

al. [Dubovsky V., 2011] provides PCMs tests in terms

of heat exchange. Xiao at al. [Xiao W., 2009] presents

a possible application of phase change materials in

construction utilities. Felix at al. [Felix A., 2008]

presented new PCM technological innovations such as:

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• Thermal storage of solar energy, Passive storage

in bioclimatic building/architecture,

• Cooling: use of off-peak rates and reduction of

installed power, icebank,

• Heating and sanitary hot water: using off-peak

rate and adapting unloading curves,

• Thermal protection of food: transport, hotel

trade, ice-cream, etc.,

• Thermal protection of electronic devices

(integrated in the appliance),

• Medical applications: transport of blood,

operating tables, hot and cold therapies,

• Cooling of engines (electric and combustion),

• Thermal comfort in vehicles,

• Solar power plants.

In Dirand at al. [Dirand M., 2002] paraffins of

straight hydrocarbon chains analysis in a wide range of

carbon atoms in the molecule has been conducted. In

that paper the authors also considered two Broadhurst’s

models, describing the melting point of hydrocarbons

as a function of number of carbon atoms in the

molecule. This description allowed determining the

relationship between the melting point and enthalpy of

straight-chain alkanes in a wide range of carbon atoms

in the molecule. According to data presented in [9] and

other above papers, PCMs in the form of paraffins and

waxes may find their application as heat storage. In the

present paper, the analysis of the hydrocarbons and

their mixtures has been conducted for describing

termophisical properties of PCMs made of them.

THEORETICAL CONSIDERATIONS: DSC

DIAGRAMS COMPOSITION

Differential scanning calorimetry is a useful tool for

detecting the phase change transitions. The result of a

DSC experiment is a curve of heat flux versus

temperature level or time. This curve can be used to

calculate enthalpy of transitions ∆H by integrating the

peak corresponding to a given transition [Pungor E.,

1995] or may be obtained from the definition of

constant-pressure specific heat:

p

pT

HC

=δδ

. (1)

Mathematical models for enthalpy may be obtained by

integrating expressions of specific heat with respect to

temperature.

Resulting equation in practice is simplified into:

AkH ⋅=∆ , (2)

where: k – the so-called calorimetric constant – it can

be determined by analyzing a well-characterized

sample with known enthalpies of transition, A – the

surface area under the curve which can be determined,

for example, by graphic integration.

For a pure PCM substance, a DSC diagram would

show a single significant growth of the energy flow at

points where a phase transition occurs. In the case of

mixtures, the overall performance of the mixture is a

function of the characteristics of its components.

However, provided that the components are neutral to

each other, they will react to temperature changes

independently. The theoretical characteristic of such a

mixture containing two exemplary substances was

shown in Figure 1.

Those were chosen particulary due to relatively

distant temperature levels of their phase change,

respectively t1 and t2. It is valid for all measuring

systems which work lineary, that is to say the measured

signal for two distinct pulse-like events in the sample

must be the superposition of the two single functions

from each individual event (Fig.1) [Roduit B., 2008].

Inverting this issue, this means, that observing the

characteristic growth we may infer qualitative

composition of the mixture.

Another condition is that all measured curves of

various pulse-like events should have the same shape,

in other words all these measured functions divided by

their peak area must yield the same function, the so-

called apparatus function α(T) called Green’s function.

If these conditions are fulfilled, the following is valid:

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Fig. 1. Theoretical DSC curve for a exemplary PCM substances

( ) ( ) ( )[ ] ( ) ( )TTTdTTTcT RRm αφαφφ ⋅=′′−⋅′= ∫ (3)

where: mφ – measured signal – heat flow rate, Rφ –

heat flow rate developed in the sample,

T – temperature level, α – apparatus function, c –

constant.

This defines the so-called convolution product of

two functions in the form of integral equation. The

equation is valid for all DSCs which work in the

above-described linear manner, irrespective of whether

a certain approximate formula is explicitly known. The

seamy side of this desmearing method also called

deconvolution, is the rather ambitious mathematics

required to solve integral equation (3) for the function

of interest ( )TRφ . There are essentially two methods,

the Fourier transform and the recursion method. Both

require numerical calculations. The DSC trace shows

the value of the total energy flow needed to change the

temperature by a set value. Thermodynamically, it

depends directly on the specific heat and mass of the

individual components of the mixture. This means that

by measurement of the total heat transported in the

vicinity of specific points, the quantitative component

mixture can also be estimated.

EXPERIMENTAL SECTION

Macromolecular hydrocarbons under

considerations

The In order to confirm (or not confirmed) a

dependency defined by the equation (3) PCMs and

their mixtures with different proportions of the

individual components has been examined. All

mixtures were analyzed by the TA Q20 DSC device

with the compressor cooling unit, which allows

operating in the wide temperature range between 90 to

450ºC. For individual mixture its theoretically

predicted DSC diagram has been calculated. Then the

curves obtained that way were compared with

experimental data collected from the DSC device.

To determine the presence (or absence) of

dependencies between the composition of PCMs and

their thermophysical parameters and to confront it with

the results obtained by a particular test, a verification

process of existing knowledge on the subject procedure

should be performed. Samples were prepared in two

steps. In the first step two selected higher hydrocarbons

(mixtures of various higher hydrocarbons with a chain

length from C19 to C45) were weighted and closing in

measuring cells. In the second one source materials

from the first step were mixture in proportions of 1:1,

1:3 and also closing in separate measuring cells. All

prepared samples were analyzed by the DSC device in

the temperature range of from about -50 to 90ºC. In

such way reference samples and their mixtures

compositions have been obtained. Outcome DSC

diagrams were recalculated according to the

composition of the sample in such way that the curves

obtained for the pure substances and their mixtures can

be compared on one graph. As an example of above

mentioned procedure analysis of the macromolecular

hydrocarbons has been taken into considerations.

Those substances have quite well known properties that

were promising in term of theoretical and experimental

comparisons. In Table 1 most significant DSC data

results for hydrocarbons and in Table 2 their mixture

samples has been presented.

According the fact, that most investigated

substances has distinct hysteresis between heating and

cooling of the samples, the overall analysis contains

this data, but as more important only heating DSC

diagrams has been investigated in subsequent analysis.

Seven PCM samples from the pure substances and their

mixtures mentioned in Table 1 have been chosen for

further analysis and comparison with theoretical

considerations.

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Table 1. DSC results of preliminary tests of various higher hydrocarbons

No.

Mass

[mg]

Heating/

Cooling

Program

[ºC]

Heating/

Cooling

Rate

[ºC/min]

Temperature Enthalpy ∆H

Melting

Area/Main

Peak [ºC]

Congealing

Area

[ºC]

Melting

[kJ/kg]

Crystalliza

-tion

[kJ/kg]

Temperature

range

[ºC]

1 2.07 -20 ÷ 90 10 30 ÷74 74 ÷ 30 160 - 9 ÷ 88

90 ÷ -20 10 49 49 - 153 85 ÷ 9.1

2 1.86 -5 ÷ 90 10 35 ÷ 55 55 ÷ 15 124 - 15.72 ÷ 64.88

90 ÷ -5 10 48.26 32.4 - 132.5 59.5 ÷ 5

3 2.56 5 ÷ 90 10 45 ÷ 60 55 ÷ 35 164.6 - 22.76 ÷ 65.06

90 ÷ 5 10 55.15 55.15 - 162.2 62.16 ÷ 18.25

4 2.88 5 ÷ 90 10 30 ÷ 60 55 ÷ 25 191 - 21.36 ÷ 65.17

90 ÷ 5 10 47.97 39.28 - 188 57.65 ÷ 16.64

5 1.57 -5 ÷ 90 10 35 ÷ 60 55 ÷ 20 136.4 - 23.67 ÷ 71.34

90 ÷ -5 10 50.4 37.71 - 134.9 61.04 ÷ 13.11

6 2.6 -5 ÷ 90 10 5 ÷ 55 55 ÷ 0 95.3 - 2.29 ÷ 60.39

90 ÷ -5 10 39.81 28.96 - 90.69 56.14 ÷ -2.35

7 11.95 -50 ÷ 90 10 0 ÷ 20 5 ÷ -10 154.6 - -11.39 ÷ 26.75

90 ÷ -50 10 10.61 2.35 - 156.4 13.86 ÷ -17.57

Table 2. DSC results of selected higher hydrocarbons and their compositions DSC

Sample

No.

Mass

[mg]

Temperature Enthalpy ∆H

Melting

Area/Main

Peak [ºC]

Congealing

Area

[ºC]

Melting

[kJ/kg]

Crystallization

[kJ/kg]

Temperature

range

[ºC]

9 3.35 20 ÷ 80 70 ÷ 20 137.2 - 15.46 ÷ 81.06

47.51 45.84 - 132.4 69.97 ÷ 8.07

10 3.56 10 ÷ 80 75 ÷ 15 154.9 - 11.59 ÷ 84.6

46.56 47.31 - 150.9 85.67 ÷ 8.59

11 4.31 20 ÷ 70 70 ÷ 20 162.4 - 16 ÷ 79.34

54.64 49.89 - 161.4 69.78 ÷ 8.27

12 2.33 20 ÷ 75 70 ÷ 20 158 - 5.14 ÷ 82.45

53.55 50.4 - 158.5 77.19 ÷ 8.8

13 1.96 25 ÷ 75 70 ÷ 20 172.8 - 12.99 ÷ 84.39

54.11 50.35 - 166 82.33 ÷ 8.74

14 3.53 25 ÷ 75 20 ÷ 70 165.2 - 11.16 ÷ 84.39

52.59 49.66 - 156.6 11.49 ÷ 75.9

15 2.93 25 ÷ 70 70 ÷ 20 176.5 - 14.81 ÷ 80.95

54.6 50.54 - 169.8 11.06 ÷ 73.22

16 3.36 25 ÷ 75 75 ÷ 20 163.5 - 14.06 ÷ 83.31

53.09 49.95 - 157.2 74.62 ÷ 12.02

17 3.37 10 ÷ 80 70 ÷ 10 121.8 - 10.09 ÷ 82.24

38.73 40 - 107.4 72.9 ÷ 7.3

18 3.17 10 ÷ 80 75 ÷ 10 140.2 - 10.63 ÷ 85

46.03 42.86 - 127.8 76.98 ÷ 7.51

19 5.64 -35 ÷ 80 70 ÷ -40 164.1 - -33.55 ÷ 82.4

8.98 3.41 - 153.6 74.13 ÷ -38.3

20 2.56 -35 ÷ 85 70 ÷ -40 166.6 - -34.7 ÷ 83.85

8.09 2.78 - 162 77.1 ÷ -38.35

RESULTS

DSC diagrams obtained during measurements have

been compared with theoretically calculated functions

representing superposition of the basic component

mixtures form Table 1. Calculations has been

conducted with specially designed computer software,

according to theoretical considerations, and will be the

subject of separate article.

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Fig. 2. Theoretical DSC curve for a exemplary PCM substances

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Fig. 3. Theoretical DSC curve for a exemplary PCM substances

In Figure 2 and 3 all experimental and

theoretical data for chosen examples of differently

composition mixtures has been presented. Samples 9

and 10 are a mixture of test samples 1 and 2 in 1:1 and

1:3 ratio respectively. Sample 11 and 12 are a mixture

of test samples 1 and 3 in 1:1 and 1:3 ratio

respectively. Sample 13 and 14 are a mixture of test

samples 1 and 4 in 1:1 and 1:3 ratio respectively.

Sample 15 and 16 is a mixture of test samples 1 and 5

in a 1:1 and 1: 3 ratio respectively. Sample 17 and 18 is

a mixture of test samples 1 and 6 in a 1:1 and 1: 3 ratio

respectively. Sample 19 and 20 is a mixture of test

samples 1 and 6 in a 1:1 and 1: 3 ratio respectively.

As shown in the Figure 2 the correlation

between the resulting from the measurement and the

designated theoretical overlap of 80% (the standard

differential individual values in the range of the graph

is equal about 20%, hence known that the curves are

consistent at about 80%).

CONCLUSIONS

Nearly 100 different samples with different

compositions have been examined. DSC diagrams

analysis confirmed a dependency in signals from not

only the pure substances and their mixtures, but also

between mixtures and their mixtures compositions.

However, the correlation of those diagrams, with

theoretical superposition functions, reaches only about

80%.

Therefore it is necessary to continue this future

analysis to determine the relevant correlating functions,

which allows better matching between theoretical and

experimental DSC diagrams.

The analysis of the graphs shows that it is possible

to predict with fairly good accuracy the theoretical

shape of DSC diagrams of the mixtures made from

substances with well known DSC diagrams and thus to

evaluate the usefulness of the potential PCM mixtures,

taking into account the probable properties of such

product.

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