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NAUKA
Nr I-IV/2014 Polska Energetyka Słoneczna 39
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:
NAUKA
40 Polska Energetyka Słoneczna Nr I-IV/2014
• 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:
NAUKA
Nr I-IV/2014 Polska Energetyka Słoneczna 41
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.
NAUKA
42 Polska Energetyka Słoneczna Nr I-IV/2014
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.
NAUKA
Nr I-IV/2014 Polska Energetyka Słoneczna 43
Fig. 2. Theoretical DSC curve for a exemplary PCM substances
NAUKA
44 Polska Energetyka Słoneczna Nr I-IV/2014
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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