1) The document discusses an experiment that used differential scanning calorimetry to characterize various phase change materials, including fatty acid mixtures, for their potential use in thermal energy storage. 2) DSC was used to determine the specific heat capacity, melting point, and latent heat of fusion of the materials, which indicate their thermal energy storage properties. 3) A phase diagram was constructed for a mixture of lauric and stearic acids that showed a eutectic point at 75% lauric acid by weight and 42°C, which makes this mixture unsuitable for applications where people are present due to its high melting temperature.

1. Tanner Guerra
Lab Group 4
Module B
ENTROPY OF PHASE CHANGE
THERMAL ENERGY STORAGE
Keywords: thermal energy storage, Phase Change Materials, heat flow, phase
diagram, latent heat of fusion, DSC, MPCM, fatty acids, melting point, thermal
stability

2.
1
ABSTRACT
In the world today we have many problems, but one of our most substantial
problems is the global energy crisis. It won’t be solved by one solution, rather the sum
of many energy usage innovations. This experiment intended to understand an energy
saving innovation, namely, thermal energy storage (TES) via Latent Heat Storage. Phase
Change Materials (PCMs), used for Latent Heat Storage, were subjected to Differential
Scanning Calorimetry (DSC), to generate thermal profiles (Heat Flow vs. Temperature).
These PCMs were Micro-encapsulated paraffin wax, stearic acid, lauric acid, and binary
mixtures of these acids. DSC determined the PCMs physical properties that convey the
thermal energy storage capacity. Specifically, Specific Heat Capacity (Cp), Melting Point
(Tm), and Latent Heat of Fusion (∆Hm or Lf). DSC aids the assessment of thermal
stability (taking thermal cycle data), as well as enabling the procurement of the solid-
liquid phase diagrams for our acid mixture. The phase diagram, with the obtained
solidus and liquidus lines, presents us with a eutectic reaction. The results realize a
eutectic point for the acid mixture was at the mole fraction (𝛘lauric = .810 or 75 wt.%
lauric acid in stearic acid). The procured phase diagram with Melting Points and
corresponding Latent Heat of Fusion values along with thermal stability enable the
determination of the adequacy of certain mixtures in thermal energy storage
applications.

3.
2
INTRODUCTION
In thermal energy storage (TES) systems, materials are carefully selected based
on the type of system: Sensible Heat Storage, Thermochemical Storage, or Latent Heat
Storage. In sensible heat storage, energy is stored by changing the temperature of a
storage medium, where specific heat capacity is the relevant thermal property.
Thermochemical Storage involves chemical reactions, typically reactions where the
energy is stored indefinitely in the products at room temperature with no loss of heat
capacity. When the energy is required, these products are recombined in a chemical
reaction where energy is released. With Latent Heat Storage, energy is stored as latent
heat in suitable materials during a phase change. The energy that is absorbed during the
melting process is stored as latent heat of fusion and is released during the freezing
process. The thermal characteristics that are relevant here are the latent heat of
melting/fusion and the melting point of the material. The energy is absorbed/released
in a small temperature range making some of these materials attractive for smaller and
lighter storage devices with low storage losses [1]. For PCMs, the relationship between
Latent Heat of Fusion of (∆𝐻!"#,!) and melting temperature (T), for some pure solid A,
can be related via gas constant (R), mole fraction of A in B (𝜒!), and the melting
temperature of pure A (𝑇!!).
𝑙𝑛(𝜒!) = −
∆!!"#,!
!
(
!
!
−
!
!!!
) (3)
This equation also applies for a substance pure substance B in the mixture, and where
the two curves meet (are equal) is the eutectic temperature (𝑇!) and the eutectic
composition (𝜒!), which is applied in Figure 1 [3].

4.
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When selecting a material for TES, it is important to look at, not just melting
temperature, but at Latent Heat of Fusion. Although ∆𝐻!"#,!/∆𝐻! is mentioned above
as a part of the phase diagram, it does not explicitly quantify it. To obtain the value for
∆𝐻!, which aided in executing the phase diagram, the heat flow vs. temperature graph,
shown below in figure 2, from DSC is examined.
Figure 1:Solid-liquid equilibria of a two-
component system. A euctectic mixture of
Pure A and Pure B, where E is the Eutectic
Point at eutectic temperature Te and
eutectic composition 𝜒!. Furthermore, 𝑇!!
is the melting temp. of pure A and 𝑇!! is
the melting temp. of pure B. [3]
Figure adopted from Castellan, G. W.
Figure 2: A sketch of a DSC thermogram as
provided by the Lab B Handout.
Tm is the melting temperature, ∆𝐻! is the
latent heat of fusion, while Cp (s) and Cp (l)
are the heat capacity at constant pressure in
the solid and liquid phase. [1]

5.
4
𝑇! is found by finding the temperature when the peak reaches its max (when there are
multiple peaks we take the T at the max of the last peak, because the last peak is the
peak for the liquidus line, therefore the 𝑇!). ∆𝐻! is calculated by finding the area under
the peak of the heat flow (seen in the figure above). Lastly, the 𝐶!’s are found before and
after a peak, the value is found via a ratio with a standardized material with known
mass and 𝐶! values (elaborated on in data analysis).
EXPERIMENTAL PROCEDURE
MATERIALS
INSTRUMENTS
Differential Scanning Calorimeter TA Instruments – Model Q100,
Microbalance, and a Hotplate.
SPECIMEN PREPARATION
Lauric and stearic acid mixtures of certain compositions were pre-made by the
following steps. Weigh the desired amounts of lauric acid and stearic acid of the desired

6.
5
composition to make 100 mg of the mixture. Transfer the mixture into a vial and heat it
on a hotplate until a homogenous solution is formed (T > 69˚C, the melting temperature
of stearic acid). Equilibrate for 10-15 minutes, turn off the hotplate, and cool the solution
to room temperature [1].
Weigh 2 – 8 mg (preferably 3 – 5 mg [Singh]) of the PCM on the microbalance
and put it in an aluminum pan and spread evenly to ensure proper thermal contact,
then crimp the pan with the lid [1].
DIFFERENTIAL SCANNING CALORIMETRY (DSC)
DSC [19] measures the temperature and the heat flow corresponding to the
thermal performance of materials, both as a function of time and temperature. TA
Instruments DSC is a system which the differential heat flux between a reference (a
sealed empty aluminum pan) and a sample (in a similar pan) is measured. The
reference and the sample pans are placed on adjacent, identical stages on a
thermoelectric sensor platform encircled by a furnace. As the temperature of the furnace
is changed (heating linearly), heat is transferred to the sample and reference through
the thermoelectric platform. The Q100 calculates the heat flow difference between the
sample and the by measuring the temperature difference between them by using
thermocouples attached to the each stage. A peak in heat flow represents a phase
transition, thermal values can then be calculated off of the graph as previously
explained [19].

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DSC MEASUREMENTS [19, 1]
Record a baseline thermal profile with empty, equal mass aluminum pans placed
on the reference and the sample stages, respectively. The aluminum pan on the
reference stage must be crimped. The pan on the sample stage is left uncrimped for later
use. The baseline scan corrects for any asymmetry in the heat flow to the 2 stages [1].
Obtain a thermal profile with a calibration standard (sapphire) using the same scan
conditions as above. Provide a calibration factor that translates the measured heat flow
units "(in mW) to heat capacity units (in J/g˚C). Place the crimped pan containing the
calibration standard (sapphire, mass = 25.74 mg) on the sample stage [1].
Obtain thermal profiles for each sample using same scan conditions, then enter the
weighed amount for each sample in units of in (mg). Clean the pans before placing on
them on the sample stage. Once done collecting the data must be subtracted by the
baseline data from the sample and sapphire data.
After the baseline, leave the pan on
the reference stage undisturbed for
the remaining measurements [lab].

8.
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ANALYSIS/RESULTS
SPECIFIC HEAT CAPACITY
The values of Cp for our PCMs were calculated in excel (& lab notebook) given
the data from DSC. The equation used is:
Where is a calibration factor
obtained from the sapphire standard values. Calculated Cp’s for specific temperatures
is in figure 3, below.
We see that Cp increases with temperature, which holds true because of the increased
degrees of freedom that are related to an increase in temperature.
PHASE DIAGRAM
Using the peak fitting software, we obtained values for temperature at different
phase transitions. The calculations and subsequent conversion to mole fraction for
composition are in Table 1 below.
0.000
0.500
1.000
1.500
2.000
2.500
3.000
0
0.2
0.4
0.6
0.8
1
Cp
(T)
[J/g*C]
Acid
Mixture
Composition
%
wt
Lauric
Cp
(T)
as
related
to
Compostion
of
Acid
Mixture
Cp(80°C)
[J/g°C]
Cp(60°C)
[J/g°C]
Cp(20°C)
[J/g°C]
Figure 3: Graph of the heat
capacity for constant
pressure as it varies with %
wt. of lauric acid and varying
temperatures.

9.
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The values in the table present the idea that this is not a binary system, because if it
were a binary system, we would only have a max of two peaks, or a Solidus and
liquidus line only. Our data is shown in Figure 4, the phase diagram below.
Fatty
Acid
Samples
T,
Solidus
T,
Intermediate,
1
T,
Intermediate,
2
T,
Liquidus
(Compositions
in
mole
fraction)
100%
Stearic
Acid
71.3
0
90%
Stearic,
10%
Lauric
Acid
34.8
38.9
68.3
0.136
80%
Stearic,
20%
Lauric
38.9
41.2
64.8
0.262
70%
Stearic,
30%
Lauric
37.8
41.9
64.4
0.378
60%
Stearic,
40%
Lauric
40
42.9
58.8
0.486
50%
Stearic,
50%
Lauric
39.5
44.3
50.2
55.4
0.587
40%
Stearic,
60%
Lauric
40.6
44.1
0.681
30%
Stearic,
70%
Lauric
40.8
44.3
0.768
25%
Stearic,
75%
Lauric
42.2
42.2
0.810
20%
Stearic,
80%
Lauric
41.5
0.850
10%
Stearic,
90%
Lauric
40.1
42.9
0.927
100%
Lauric
46.8
1
Table 1: Values to help graph the phase diagram for the fatty acid mixture, which will have
each T value as related to the composition in mole fraction.
0
10
20
30
40
50
60
70
80
0
0.2
0.4
0.6
0.8
1
Temperature
(C)
Mole
Fraction
of
Lauric
Acid
Phase
Change
Diagram
for
Fatty
Acids
T,
Liquidus
T,
Intermediate
1
T,
Intermediate
2
T,
Solidus
Figure 4: The
phase diagram of
the eutectic mixture
of Lauric Acid and
Stearic Acid.

10.
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It is clear that the Eutectic Point lies at the Mol fraction value of .810 (75% wt Lauric),
which is also evident in Table 1.
This is an unlikely mixture to be applied in household energy saving products because
it has a eutectic point at around 42*C, much too hot to be applicable anywhere where
people are at.
Below are the experimental and literature values for Lab B, I am currently running out
of time, otherwise I would explain further in detail the implications of these results.
Material
Tm
exp
[°C]
Tm
literature
Latent
Heat
(J/g)
Latent
Heat
-­‐
literature
Mass
[mg]
Mass
[g]
Qrev
[J]
DS
[J/K]
MPCM
18D
18.7
18
182.1
163-­‐173
3.8
0.0038
0.692
0.037
MPCM
28D
28.7
28
190.8
180-­‐195
3.6
0.0036
0.687
0.0239
Tempertex
27.6
19.24
3.7
0.0037
0.0712
0.00258
Unknown
55.2
206.7
3.2
0.0032
0.661
0.012
100%
Stearic
71.3
67.2
232.3
198.9
2.9
0.0029
0.674
0.00945
90%
Stearic,
10%
Lauric
68.3
67.8
214.2
5.18
0.00518
1.11
0.0163
80%
Stearic,
20%
Lauric
64.8
65.1
229.2
2.3
0.0023
0.527
0.00813
70%
Stearic,
30%
Lauric
64.4
62.4
203.6
4.74
0.00474
0.965
0.015
60%
Stearic,
40%
Lauric
58.8
59.4
203.1
4.1
0.0041
0.833
0.0142
50%
Stearic,
50%
Lauric
55.4
55.9
193.8
4.8
0.0048
0.93
0.0168
40%
Stearic,
60%
Lauric
44.1
33.8–47.6
193.2
189.8
4.4
0.0044
0.85
0.0193
30%
Stearic,
70%
Lauric
44.3
35.9–42.7
187.1
187.1
4.84
0.00484
0.906
0.0205
25%
Stearic,
75%
Lauric
42.2
36.9–37.6
177.7
183.4
4.8
0.0048
0.853
0.0202
20%
Stearic,
80%
Lauric
41.5
38.2–33.7
183.6
180.5
6.01
0.00601
1.1
0.0265
10%
Stearic,
90%
Lauric
42.9
41.7
173.8
4.6
0.0046
0.799
0.0186
100%
Lauric
46.8
42.4
210
186.4
4.4
0.0044
0.924
0.0197
Table
2:
The
red
data
is
most
likely
a
mass
error,
it
is
unusually
lighter
than
the
rest.
That
value
will
likely
need
to
be
re-­‐done.

11.
10
REFERENCES
(1) Kimerling, L.; Berera, G.P. 3.014 Module B Handout, 2013.
(2) Costa, M. C., Rolemberg, M. P., Meirelles, A. J. A., Coutinho, J. A. P., & Kraehenbuehl, M. A. (2009). The
solid-liquid phase diagrams of binary mixtures of even saturated fatty acids differing by six carbon atoms.
Thermochimica Acta, 496, 30–37. doi:10.1016/j.tca.2009.06.018
(3) Castellan, G. W. in Physical Chemistry, 3rd ed. Ch. 13 and 15, The Benjamin/Cummings Company Inc.
(1983).