Gypsum based composite materials with micro-encapsulated PCM: Experimental correlations for thermal properties estimation on the basis of the composition

Abstract

Composite materials containing phase change materials (PCMs) are obtained by mixing PCM microcapsules with traditional construction materials. The composite materials thermal properties, which depend on the composition, are required when dynamic simulations of building structures containing composite material with PCM are performed. In order to avoid the need of measuring density, thermal conductivity and specific heat capacity for each possible composition, in this work correlations for the estimation of these thermal properties for gypsum based composite materials with micro-encapsulated PCM are derived. The correlations, obtained on the basis of experimental measures, give the composite material thermal properties as function of gypsum, water and PCM mass and volume fractions; it is verified that the correlations for density and thermal conductivity can be applied in the whole temperature range, including both the PCM liquid and solid phases, while a correction based on the temperature is applied for the correlation for specific heat capacity to extend its validity to the phase change temperature range. The correlations fit the experimental data with an error comparable with the measurement uncertainty and, when tested on a commercial product, they are able to predict its thermal properties with good accuracy.

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227–236
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Gypsum
based
composite
materials
with
micro-encapsulated
PCM:
Experimental
correlations
for
thermal
properties
estimation
on
the
basis
of
the
composition
Tommaso
Toppi∗,
Livio
Mazzarella
Politecnico
di
Milano,
Dipartimento
di
Energia,
Via
Lambruschini,
4
(20156)
Milano,
Italy
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
19
June
2012
Received
in
revised
form
9
October
2012
Accepted
5
November
2012
Keywords:
Micro-encapsulated
phase
change
material
Composite
material
Thermal
properties
Experimental
correlation
Building
material
Gypsum
a
b
s
t
r
a
c
t
Composite
materials
containing
phase
change
materials
(PCMs)
are
obtained
by
mixing
PCM
microcap-
sules
with
traditional
construction
materials.
The
composite
materials
thermal
properties,
which
depend
on
the
composition,
are
required
when
dynamic
simulations
of
building
structures
containing
composite
material
with
PCM
are
performed.
In
order
to
avoid
the
need
of
measuring
density,
thermal
conductivity
and
specific
heat
capacity
for
each
possible
composition,
in
this
work
correlations
for
the
estimation
of
these
thermal
properties
for
gypsum
based
composite
materials
with
micro-encapsulated
PCM
are
derived.
The
correlations,
obtained
on
the
basis
of
experimental
measures,
give
the
composite
material
thermal
properties
as
function
of
gypsum,
water
and
PCM
mass
and
volume
fractions;
it
is
verified
that
the
correlations
for
density
and
thermal
conductivity
can
be
applied
in
the
whole
temperature
range,
including
both
the
PCM
liquid
and
solid
phases,
while
a
correction
based
on
the
temperature
is
applied
for
the
correlation
for
specific
heat
capacity
to
extend
its
validity
to
the
phase
change
temperature
range.
The
correlations
fit
the
experimental
data
with
an
error
comparable
with
the
measurement
uncertainty
and,
when
tested
on
a
commercial
product,
they
are
able
to
predict
its
thermal
properties
with
good
accuracy.
©
2012
Elsevier
B.V.
All
rights
reserved.
1.
Introduction
PCMs
are
widely
investigated
for
energy
storage
in
buildings,
where
they
can
be
used
to
improve
the
thermal
storages
capacity
[1,2],
or
to
increase
the
building
structures
thermal
capacity,
espe-
cially
in
lightweight
construction
[3].
The
most
common
techniques
for
the
integration
of
PCMs
in
building
structures
are
the
macro
or
micro-encapsulation
and
shape
stabilized
PCM.
With
encap-
sulation,
the
PCM
is
contained
in
a
capsule
which
can
have
the
size
of
some
centimeters,
as
for
macro-encapsulated
materials,
or
some
micrometers,
as
for
micro-encapsulated
[4,5].
Shape
stabi-
lized
materials
are
obtained
by
absorbing
the
PCM
in
a
porous
solid
matrix,
which
maintains
its
shape
without
leakages
even
when
the
PCM
is
melted.
Shape
stabilized
materials
are
obtained
by
the
incorporation
of
PCM
in
a
traditional
construction
material,
as
gyp-
sum
or
concrete,
with
a
maximum
PCM
mass
fraction
of
about
25–30%
[6,7],
or
in
materials
as
high
density
polyethylene,
where
the
PCM
mass
fraction
can
be
increased
up
to
70%
or
more
[8,9].
When
micro-encapsulation
is
used
to
integrate
a
PCM
in
a
build-
ing
structure,
the
capsule
shell
prevents
any
physical
or
chemical
∗Corresponding
author.
Tel.:
+39
02
2399
3922;
fax:
+39
02
2399
3868.
E-mail
address:
tommaso.toppi@polimi.it (T.
Toppi).
interaction
between
the
PCM
and
the
traditional
construction
material
and
avoids
leakages
when
the
PCM
is
in
the
liquid
form;
moreover
there
is
no
extra
work
at
the
building
site
to
integrate
the
PCM
products.
The
small
size
of
microcapsules
avoid
the
need
to
protect
them
against
destruction
and
gives
a
very
good
sur-
face/volume
ratio,
with
positive
effect
on
the
heat
transfer
rate
[10].
The
performances
of
PCM
in
building
structures
are
usually
investigated
via
a
dynamic
building
performance
simulation.
Many
models
have
been
developed
or
added
to
existing
software
to
sim-
ulate
PCM
in
building
structures
[11–18].
All
the
models
taken
into
consideration
need
as
input
data
the
thermal
properties
of
the
layer
with
PCM
and
the
specific
heat
capacity
or
the
enthalpy
val-
ues
within
the
typical
temperature
range
of
building
applications.
When
microcapsules
are
embedded
in
a
material,
they
modify
its
thermal
properties
(density,
thermal
conductivity
and
specific
heat
capacity),
so
the
composite
material
properties
depend
on
the
com-
ponents
mass
fractions
and
on
their
properties.
On
the
basis
of
this
consideration,
whenever
the
material
composition
has
changed,
its
thermal
properties
have
to
be
measured
in
order
to
be
used
in
the
simulation
tools.
This
work
is
part
of
a
larger
research
activity
on
the
use
of
phase
change
materials
in
building
structures.
In
order
to
avoid
the
need
of
measuring
the
thermal
properties
each
time
the
0378-7788/$
–
see
front
matter
©
2012
Elsevier
B.V.
All
rights
reserved.
http://dx.doi.org/10.1016/j.enbuild.2012.11.009

Author's personal copy
228
T.
Toppi,
L.
Mazzarella
/
Energy
and
Buildings
57
(2013)
227–236
Nomenclature
c
specific
heat
capacity
[J/(kg
K)]
f
mass
fraction
in
the
initial
mixture
for
material
preparation
m
mass
fraction
in
the
composite
material
v
volume
fraction
in
the
composite
material
Greek
symbols

density
[kg/m3]
corrected
density
[kg/m3]

thermal
conductivity
[W/(m
K)]
Subscript
c
composite
material
g
gypsum
l
total
liquid
(water
plus
liquid
part
of
the
PCM
dis-
persion)
mc
microcapsules
p
paraffin
s
microcapsules
shell
w
water
composition
changes,
experimental
correlations
are
derived
to
calculate
the
composite
material
properties
as
function
of
its
com-
position.
Such
correlations
may
also
be
used,
when
choosing
the
material
composition,
in
order
to
obtain
the
required
properties.
The
correlations
are
based
on
experimental
results
obtained
from
gypsum
based
composite
material
containing
paraffin
micro-
capsules
produced
by
the
chemical
company
BASF
and
known
with
the
commercial
name
MICRONAL.
For
this
reason,
the
results
are
directly
applicable
only
to
this
type
of
composite
material,
while
there
is
no
evidence
that
they
can
be
used
as
they
are
for
material
obtained
from
different
microcapsules
or
gypsum
matrix.
2.
Materials
and
methods
In
this
section
the
properties
and
the
features
of
the
mate-
rial
used
for
the
composite
material
preparation
are
presented,
together
with
the
approach
followed
to
derive
the
correlations.
2.1.
Gypsum
based
composite
material
preparation
and
main
features
The
data
used
to
derive
the
correlations
are
collected
through
an
experimental
activity
based
on
composite
material
obtained
by
mixing
gypsum
with
MICRONAL.
The
microcapsules
have
a
spher-
ical
shape
and
are
made
of
a
polymeric
shell
filled
with
PCM.
The
main
features
of
the
microcapsules
are:
-
average
diameter:
D
=
5
␮m;
-
shell
width:
d
=
0.1–0.2
␮m;
-
phase
change
material:
mixture
of
heptadecane,
octadecane
and
nonadecane;
-
material
of
the
shell:
poly-methil-metacrilate
(PMMA).
The
nominal
melting
temperature
of
the
PCM
varies
according
to
the
composition
of
the
mixture
of
heptadecane,
octadecane
and
nonadecane.
Three
different
kinds
of
PCM
mixtures
are
available,
with
nominal
melting
temperature
of
21 ◦C,
23 ◦C
and
26 ◦C;
for
this
work,
the
type
with
26 ◦C
as
nominal
melting
temperature
is
used.
It
is
necessary
to
refer
to
a
nominal
melting
temperature
because
the
paraffin
mixture
does
not
have
a
well
defined
phase
change
tem-
perature,
but
the
transition
between
solid
and
liquid
phase
happens
5 10 15 20 25 30 35
0
5
10
15
20
25
30
temperature (°C)
specific heat capacity (kJ kg−1 K−1)
Fig.
1.
Specific
heat
capacity
between
5◦C
and
30 ◦C
for
microcapsules
with
nominal
phase
change
temperature
of
26 ◦C.
Source:
BASF.
in
a
wide
temperature
range.
This
is
due
both
to
the
fact
that
the
microcapsules
contain
a
mixture
of
different
molecules
and
not
a
pure
substance
and
to
the
impurities
left
from
the
production
pro-
cess.
This
feature
is
well
described
in
Fig.
1,
where
the
specific
heat
capacity
values
between
5◦C
and
35 ◦C
are
reported.
Other
thermal
properties
considered
in
the
correlations
are:
-
PCM
thermal
conductivity
(liquid
phase):
p=
0.14
W/(m
K)
[19];
-
PMMA
thermal
conductivity:
PMMA =
0.19
W/(m
K)
[20];
-
microcapsules
density:
mc =
980
kg/m3;
this
value
is
not
calcu-
lated,
but
provided
directly
by
the
microcapsules
manufacturer.
Gypsum
properties
depend
on
the
composition
of
the
mixture
used
to
prepare
the
material.
From
the
chemical
point
of
view,
gypsum
is
calcium
sulfate
dihydrate,
obtained
by
adding
a
certain
amount
of
water
to
the
calcium
sulfate
hemihydrate
in
powder
form;
the
chemical
reaction
which
takes
place
is:
CaSO4·(1/2)H2O
+
(3/2)H2O
→
CaSO4·2H2O
+
heat
(1)
The
chemical
reaction
is
exothermic,
so
it
releases
energy
in
form
of
heat,
which
increases
the
temperature
of
the
mate-
rial
during
the
process.
The
stoichiometric
water–calcium
sulfate
hemihydrate
ratio
is
around
18
g
of
water
per
100
g
of
calcium
sul-
fate
hemihydrate,
but
for
practical
reason
of
well
mixing
of
the
two
substances,
a
much
larger
amount
of
water
(50–100
g)
is
used.
When
the
calcium
sulfate
hemihydrate
is
added
to
the
water,
a
liq-
uid
mixture
is
obtained.
Within
this
work,
this
mixture
is
called
water–gypsum
mixture
or
simply
initial
mixture.
Moreover,
the
calcium
sulfate
hemihydrate
in
powder
form
is
simply
called
gyp-
sum
powder,
while
the
resulting
calcium
sulfate
dihydrate,
once
it
has
solidified
and
the
not
reacted
water
has
evaporated,
is
called
gypsum.
When
PCM
microcapsules
are
included,
they
are
added
directly
to
the
initial
mixture.
Microcapsules
are
provided
by
the
manufacturer
in
form
of
a
dispersion,
where
microcapsules
repre-
sent
42%
of
the
mass
fraction,
while
the
remaining
58%
is
liquid.
When
PCM
dispersion
is
added,
it
becomes
part
of
the
initial
mix-
ture
used
for
the
material
preparation,
together
with
water
and
gypsum
powder.
After
the
solidification
of
the
mixture
and
the
evaporation
of
water,
the
composite
material
is
obtained.
The
mix-
ture
becomes
solid
within
15–20
min,
while
the
non
reacted
water
evaporates
in
a
time
which
can
range,
at
room
temperature,
from
a
couple
of
days
for
small
samples
to
some
weeks
for
bigger
items.
The
evaporation
of
the
not
reacted
water
leaves
pores
in
the
mate-
rial;
this
means
that
the
amount
of
water
in
the
initial
mixture

Author's personal copy
T.
Toppi,
L.
Mazzarella
/
Energy
and
Buildings
57
(2013)
227–236
229
Table
1
Initial
mixture
composition
and
measured
properties
of
the
samples
made
of
gypsum
without
PCM.
Sample
Gypsum
Water
Density
[kg/m3]
Thermal
conductivity
[W/(m
K)]
Spec.
heat
capacity
[J/(kg
K)]
A1
67.4%
32.6%
1323
0.512
884
A2 65.2%
34.8%
1273
0.512
855
A3
63.2%
36.8%
1193
0.485
926
A4
61.0%
39.0%
1100
0.414
837
A5
58.4%
41.6%
1070
0.387
831
A6
55.6%
44.4%
992
0.343
848
A7 55.6%
44.4%
995 0.350
856
A8 54.6%
45.4%
934
0.325
944
A9
52.1%
47.9%
809
0.282
968
A10
51.7%
48.3%
871
0.294
909
A11
50.2%
49.8%
769
0.251
887
determines
the
porosity
of
the
resulting
gypsum
or
composite
material
and,
consequently,
its
thermal
properties.
Since
temperature
may
affect
the
solidification
process,
the
tem-
perature
of
both
the
water
used
for
the
sample
preparation
and
the
room
where
the
samples
have
been
placed
to
set
and
dry
has
been
maintained
constant
for
all
the
samples;
in
particular,
the
water
temperature
was
15 ◦C,
while
the
room
temperature
was
24 ◦C.
The
evaluation
of
the
influence
of
water
and
ambient
temperature
on
the
material
micro-structure
and
properties
is
not
within
the
scope
of
this
work,
also
because
this
parameters
are
rarely
available
when
dealing
with
commercial
products
or
when
preparing
the
material
on
a
building
construction
site.
2.2.
Properties
measurement
and
correlation
derivation
Since
gypsum
properties
are
strongly
dependent
on
the
compo-
sition
of
the
initial
mixture
and,
in
particular,
by
the
gypsum/water
ratio,
in
a
first
phase,
correlations
for
the
gypsum
without
PCM
are
found.
Then,
in
the
second
phase,
taking
into
account
the
presence
of
microcapsules
in
the
gypsum
matrix,
correlation
for
the
compos-
ite
material
are
derived.
The
first
set
of
gypsum
samples
is
made
of
eleven
elements,
while
fifteen
samples
of
composite
material
are
made
for
the
second
set.
The
material
density
is
calculated
as
the
ratio
between
the
sam-
ple
mass,
measured
with
a
balance,
and
the
volume,
while
the
thermal
properties
are
measured
with
a
system
based
on
the
tran-
sient
plane
source
(TPS)
method,
described
in
[21]
and
used
and
investigated
in
[22,23].
With
this
method
it
is
possible
to
measure
at
the
same
time
thermal
conductivity
and
diffusivity.
Volumetric
heat
capacity
is
than
calculated
from
the
conductivity
and
the
dif-
fusivity,
while
from
the
volumetric
heat
capacity
and
the
density
the
specific
heat
capacity
is
obtained.
The
samples
which
have
been
made
for
the
purpose
are
cylinders
with
a
diameter
of
65
mm
and
a
height
at
least
of
20
mm,
suitable
for
the
TPS
measurement
when
a
sensor
with
a
10
mm
diameter
is
used.
The
reproducibility
of
the
measures
with
the
TPS
is
observed
to
be
around
5%
for
the
ther-
mal
conductivity
and
10%
for
the
diffusivity,
slightly
higher
than
the
values
found
in
literature,
while
for
the
density
measurement,
an
uncertainty
of
about
3%
is
estimated.
From
this
estimation,
the
combined
uncertainty
for
the
specific
heat
capacity
is
around
17%.
Gypsum
properties
have
been
measured
at
room
temperature,
around
23 ◦C,
while,
for
the
composite
material,
measurements
have
been
taken
at
different
temperatures.
In
particular,
density
and
conductivity
have
been
measured
both
at
5◦C
and
at
30 ◦C,
temperature
values
where
the
PCM
is
solid
and
completely
melted
respectively,
without
finding
significant
differences.
For
this
rea-
son,
within
this
paper,
only
the
results
obtained
from
the
data
set
at
30 ◦C,
which
is
the
most
complete,
are
presented.
On
the
contrary,
the
apparent
PCM
specific
heat
capacity
varies
significantly
with
temperature,
as
reported
in
Fig.
1.
The
correla-
tion
for
the
composite
material
specific
heat
capacity
is
based
on
the
weighted
average
between
the
gypsum
and
PCM
specific
heat
capacity,
an
approach
validated
on
the
data
measured
at
30 ◦C,
with
the
PCM
in
the
melted
phase.
Since
this
may
represent
a
strong
limitation
to
the
useful-
ness
of
the
correlation,
an
approach
to
extend
its
validity
to
the
phase
change
temperature
range
is
proposed
and
experimentally
validated.
The
validation
is
performed
through
transient
tests,
in
temperature
ranges
which
include
the
phase
change
region:
start-
ing
from
a
temperature
below
the
beginning
of
the
phase
change
region,
samples
are
heated
up
by
means
of
two
electrically
heated
plates,
whose
temperature
is
known
and
controlled.
The
temper-
ature
inside
each
sample
is
monitored
through
thermocouples
embedded
in
the
material,
and
the
temperature
history
is
com-
pared
with
the
results
obtained
by
simulating
the
same
transient
conditions
with
a
numerical
model.
Since
the
thermal
conductivity
and
the
density
of
the
samples
are
experimentally
measured,
the
accuracy
of
the
correlation
for
the
specific
heat
capacity
used
in
the
model
can
be
evaluated
by
means
of
the
comparison
between
experimental
and
numerical
results.
3.
Results
and
discussion
In
this
section
the
composition
of
the
samples
initial
mixture
and
the
measured
properties
are
presented.
On
the
basis
of
the
composition
and
properties,
correlations
are
derived:
in
the
first
part
there
are
the
data
and
the
correlation
for
gypsum
without
PCM
microcapsules,
while
in
the
second,
composite
material
with
PCM
microcapsules
is
considered.
The
correlations
regarding
the
com-
posite
material
properties
are
obtained
from
the
correlations
for
gypsum,
modified
to
take
into
account
the
microcapsules
presence.
3.1.
Gypsum
samples
without
PCM
microcapsules
Eleven
samples
of
gypsum
without
PCM
are
made.
The
com-
position
of
the
initial
mixture
used
for
the
preparation
and
the
measured
properties
are
reported
in
Table
1.
The
initial
compo-
sition
of
the
different
samples
is
chosen
so
that
they
cover
the
entire
range
of
the
possible
gypsum–water
ratio.
According
to
what
observed
when
the
samples
have
been
made,
a
higher
gypsum
content
than
in
sample
A1
makes
the
mixing
process
impossible
because
of
the
too
high
mixture
viscosity
and
the
high
solidifica-
tion
velocity;
on
the
contrary,
if
a
higher
water
content
than
in
sample
A11
is
used,
part
of
the
water
is
not
included
in
the
final
product
once
it
has
solidified,
but
remains
liquid
on
its
top.
If
the
thermal
properties
are
plotted
as
function
of
the
water
fraction
in
the
initial
mixture,
as
in
Figs.
2–4,
it
is
possible
to
see
that
as
the
water
fraction
increases,
the
density
and
the
conductivity
decrease,
and
that
the
specific
heat
capacity
slightly
increases.
The
decrease
of
the
density
can
be
explained
considering
that
the
amount
of
water
which
reacts
with
gypsum
is
constant
and
close
to
the
stoichiometric
value,
while
the
excess
of
water

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0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50
0
200
400
600
800
1000
1200
1400
water fraction in the initial mixture
density (kg/m3)
experimental data
linear interpolation
95% confidence interval
Fig.
2.
Measured
density
vs.
water
content
in
the
initial
mixture
and
linear
interpo-
lation
of
the
data
for
gypsum
without
PCM
microcapsules.
evaporates,
leaving
pores
which
increase
the
volume
of
the
sample,
without
increasing
the
mass;
with
the
same
reason
the
ther-
mal
conductivity
reduction
can
be
explained:
as
the
water
ratio
increases,
the
resulting
higher
porosity
gives
a
lower
conductivity.
Through
linear
interpolation
of
the
experimental
data,
the
cor-
relations
in
Eqs.
(2),
(3)
and
(4)
are
found
to
predict
the
gypsum
density,
thermal
conductivity
and
specific
heat
capacity
on
the
basis
of
the
water
fraction
(fw)
in
the
initial
mixture:
g=
−3118.6
·
fw+
2348.9
(2)
g=
−1.5882
·
fw+
1.0496
(3)
cg=
260.76
·
fw+
775.59
(4)
The
95%
confidence
intervals
related
to
the
three
correla-
tions,
which
amplitude
is
graphically
represented
in
Figs.
2–4,
are
±56
kg/m3,
±0.026
W/(m
K)
and
±91
J/(kg
K)
respectively.
The
correlations
can
be
used
with
the
proposed
uncertainty
within
a
water
fraction
range
comprised
between
32%
and
50%,
corresponding
to
the
range
covered
by
the
samples
used
for
the
analysis.
The
specific
heat
capacity
increase
with
the
water
fraction
is
unexpected
and
it
is
supposed
to
be
due
to
uncertainty
in
the
mea-
surement,
which,
as
anticipated,
can
be
up
to
17%,
rather
than
to
an
actual
dependance
on
the
initial
water
content.
For
this
reason,
0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50
0
0.1
0.2
0.3
0.4
0.5
0.6
water fraction in the initial mixture
thermal conductivity (W m−1 K−1)
experimental data
linear interpolation
95% confidence interval
Fig.
3.
Measured
conductivity
vs.
water
content
in
the
initial
mixture
and
linear
interpolation
of
the
data
for
gypsum
without
PCM
microcapsules.
0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50
0
200
400
600
800
1000
1200
water fraction in the initial mixture
specific heat capacity (J kg−1 K−1)
experimental data
linear interpolation
95% confidence interval
Fig.
4.
Measured
specific
heat
capacity
vs.
water
content
in
the
initial
mixture
and
linear
interpolation
of
the
data
for
gypsum
without
PCM
microcapsules.
the
average
value
of
886
J/(kg
K)
is
considered
as
reference
value
for
gypsum
in
place
of
the
correlation
in
Eq.
(4).
The
95%
confidence
interval
evaluated
on
the
average
value
is
±96
J/(kg
K),
only
slightly
higher
than
the
±91
J/(kg
K)
found
for
the
correlation.
In
Table
2
the
maximum,
the
minimum
and
the
root
mean
square
percentage
(RMSP)
difference
between
the
predicted
val-
ues
and
the
experimental
data
are
reported.
The
predicted
values
are
obtained
from
Eq.
(2)
for
the
density,
from
Eq.
(3)
for
the
ther-
mal
conductivity,
while,
as
explained,
for
the
specific
heat
capacity
the
average
value
among
the
measured
data
of
886
J/(kg
K)
is
used
for
all
the
samples.
3.2.
Composite
material
with
PCM
microcapsules
The
PCM
microcapsules
are
added
in
form
of
aqueous
dispersion,
where
microcapsules
represent
42%
of
the
mass
fraction,
while
the
remaining
58%
is
liquid.
The
liquid
in
the
dispersion
is
considered
as
it
is
water
when
designing
the
initial
mixture
for
the
sample
preparation;
under
this
assumption,
in
the
initial
mixture,
the
sum
of
water
and
liquid
part
of
the
PCM
dispersion
is
called
total
liq-
uid.
The
composition
of
the
fifteen
samples
with
PCM
used
for
the
correlation
derivation
is
reported
in
Table
3,
while
their
measured
properties
are
reported
in
Table
4.
The
final
PCM
fraction
is
the
microcapsules
mass
fraction
in
the
material
once
the
not
reacted
water
has
evaporated.
When
microcapsules
are
added,
the
mixture
workability
decreases
and
it
solidifies
in
a
shorter
time.
The
reason
of
this
behavior
is
not
investigated
in
detail,
but
some
hypothesis
are
made,
on
the
basis
of
the
effect
of
fine
particles
on
the
gypsum
or
concrete
solidification
process
[24].
The
presence
of
very
small
microcapsules
creates
Van
Der
Waals
forces
which
increase
the
gypsum
viscosity,
making
the
mixing
process
more
difficult;
on
the
other
side,
microcapsules
provide
crystallization
nuclei
which
pro-
mote
the
gypsum
solidification.
As
the
solidification
time
shortens,
the
number
of
the
bubbles
which
remain
trapped
in
the
gypsum
increases.
These
bubbles
appear
to
have
a
size
up
to
one
millime-
ter
and
normally
arise
from
the
mixing
process;
if
the
solidification
Table
2
Minimum,
maximum
and
RMSP
difference
between
predicted
and
measured
values
for
gypsum
samples.
ggcg
Minimum
difference −3.4%
−4.3%
−7.5%
Maximum
difference
5.3%
3.9%
6.0%
RMSP
difference 2.9%
3.0%
5.2%

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231
Table
3
Initial
mixture
composition
of
the
composite
material
properties
and
final
PCM
mass
fraction.
Sample
ID Initial
mixture
composition Final
PCM
mass
fraction
Gypsum Microcapsules
Total
liquid
B1
57.4%
4.0%
38.6%
5.7%
B2 47.5%
12.1%
40.5%
17.9%
B3
46.7%
11.9%
41.4%
17.9%
B4
51.6%
6.5%
41.9%
9.9%
B5
52.1%
4.8%
43.1%
7.6%
B6 39.8%
16.7%
43.5%
26.3%
B7
50.1%
6.3%
43.6%
10.0%
B8 43.5%
12.8%
43.7%
20.0%
B9
49.8%
6.3%
43.9%
9.8%
B10
49.7%
6.3%
44.0%
9.9%
B11
48.3%
7.3%
44.4%
11.4%
B12
44.6%
10.2%
45.2%
16.5%
B13 44.9%
9.8%
45.3%
15.8%
B14
42.7%
10.0%
47.3%
16.8%
B15
37.4%
13.1%
49.5%
23.1%
time
is
long
enough,
the
bubbles
have
the
time
to
reach
the
surface
of
the
sample,
otherwise
they
remain
trapped
in
material
once
it
has
solidified.
A
second
important
factor
is
the
formation
of
foam
while
mixing
the
materials,
which
becomes
more
evident
when
the
PCM
dispersion
is
added
to
the
water–gypsum
mixture.
The
foam
increases
the
number
of
the
bubbles
produced
and,
together
with
the
short
solidification
time,
the
number
of
bubble
trapped.
These
phenomena,
which
result
in
a
higher
material
porosity,
can
be
limited,
but
not
completely
eliminated,
by
the
use
of
additives:
an
anti-foam
agent
reduces
the
foam
formation
during
the
mixing
process,
while
a
plasticizer
reduces
the
viscosity
of
the
mixture,
giving
to
the
bubble
some
more
time
to
leave
the
mixture
itself.
3.2.1.
Composite
material
density
As
anticipated,
when
PCM
dispersion
is
added
to
the
initial
mix-
ture,
the
resulting
composite
material
has
a
higher
porosity
than
expected
for
gypsum
without
microcapsules.
If
a
simple
weighted
average
of
gypsum
and
microcapsules
density
is
used,
where
the
gypsum
density
is
calculated
according
to
Eq.
(2),
the
composite
material
density
is
strongly
overestimated,
as
displayed
in
Fig.
5(a).
For
this
reason,
the
gypsum
density
is
corrected
to
take
into
account
Table
4
Measured
properties
of
samples
with
PCM
microcapsules.
Sample
Density
[kg/m3]
Thermal
conductivity
[W/(m
K)]
Spec.
heat
capacitya[J/(kg
K)]
B1
1107
0.396
905
B2
991
0.289
958
B3
958
0.279
1034
B4
971
0.326
924
B5
959
0.320
933
B6
826
0.356
1157
B7
913
0.296
952
B8
884
0.251
1046
B9
921
0.286
935
B10
904
0.300
1018
B11
893
0.283
1037
B12 851
0.253
1164
B13 857
0.246
1076
B14
787
0.235
964
B15 708
0.193
1243
aValid
for
a
temperature
above
the
end
of
the
phase
change
region.
the
reduction
due
to
porosity
increase
because
of
the
microcap-
sules;
the
corrected
value
(
g)
is
obtained
from
Eq.
(5),
where
mmc is
the
final
microcapsules
volume
fraction
in
the
composite
material.

g=
g−
685.98
·
mmc (5)
After
the
introduction
of
the
correction,
the
estimation
of
the
composite
material
density
(c),
given
in
Eq.
(6),
fits
the
experi-
mental
data
much
better,
as
shown
in
Fig.
5(b):
c=(1
−
vmc)·

g+
vmc ·
mc (6)
where
mc is
the
microcapsules
density,
equal
to
980
kg/m3.
The
maximum
error
between
the
measured
and
the
predicted
value
is
an
overestimation
of
3.0%,
while
the
95%
confidence
inter-
val
is
±26
kg/m3.
The
correlation
found
for
the
composite
material
density
requires,
as
input
value,
the
microcapsules
volume
fraction
(vmc).
Since
the
calculation
of
vmc requires
the
composite
material
density
itself,
an
iterative
approach
has
to
be
adopted.
Starting
from
a
first
estimation
of
vmc,
equal
to
the
mass
fraction
mmc,
Eq.
(6)
is
used
to
calculate
the
cand,
on
the
basis
of
the
obtained
value
for
c,
the
vmc for
the
following
iteration
can
be
obtained.
The
composite
material
density
may
also
be
calculated
using
a
second
correlation,
given
by
Eq.
(7),
obtained
from
a
numerical
fit
of
the
experimental
data.
c=
2192.0
−
488.1
·
fmc −
2789.0
·
fl(7)
where
fmc and
flare
respectively
the
microcapsules
and
the
total
liquid
mass
fraction
in
the
initial
mixture.
This
correlation
does
not
have
an
explicit
physical
meaning
as
Eq.
(6),
but
does
not
require
any
iteration
and
fits
the
experimental
data
slightly
better.
In
fact,
the
95%
confidence
interval
is
±23.2
kg/m3and
the
maximum
dif-
ference
with
the
experimental
data
is
an
overestimation
of
2.9%.
3.2.2.
Composite
material
conductivity
The
composite
material
thermal
conductivity
(c)
is
estimated
using
Eq.
(8)
proposed
by
Porfiri
for
multiphase
particulate
com-
posite
materials
[25]:
c=
g·1
−3vmc[(g−
s)(p+
2s)
+
(s−
p)(g+
2s)(vs/vp)]
(p+
2s)[2g+
s−
vmc(s−
g)]
+
(s−
p)[2g−
2s+
vmc(g+
2s)](vs/vp)(8)
where
sis
the
thermal
conductivity
of
the
shell;
pis
the
thermal
conductivity
of
the
PCM
microcapsules
core;
vsis
the
volume
frac-
tion
of
the
shell;
vpis
the
volume
fraction
of
the
PCM
core;
vmc is
the
volume
fraction
of
microcapsules,
given
by
the
the
sum
of
vs
and
vp.
As
for
the
density,
the
gypsum
thermal
conductivity
has
to
be
corrected
to
evaluate
the
influence
of
the
microcapsules
on
the
material
porosity.
Without
correction,
the
prediction
strongly
overestimates
the
composite
material
conductivity,
as
displayed
in
Fig.
6(a),
while,
adding
the
correction
proposed
in
Eq.
(9),
the
pre-
dicted
values
fit
much
better
the
experimental
ones,
as
in
Fig.
6(b).

g=
g−
0.413
·
vmc +
0.114
·
fl−
0.050 (9)
Once
the
correction
on
the
gypsum
conductivity
is
applied,
the
maximum
error
between
estimated
and
measured
data
is
a
overestimation
of
3.6%,
while
the
95%
confidence
interval
is
±0.013
W/(m
K).
3.2.3.
Composite
material
specific
heat
capacity
The
evaluation
of
the
specific
heat
capacity
is
obtained
by
the
weighted
average
on
the
mass
fraction
of
gypsum
matrix
and
PCM
microcapsules
in
the
composite
material,
as
in
Eq.
(10).
The
gypsum
matrix
specific
heat
capacity
is
886
J/(kg
K)
as
found
in
3.1,
while

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0.38 0.40 0.42 0.44 0.46 0.48 0.50
0
200
400
600
800
1000
1200
liquid fraction in the initial mixture
density (kg/m3)
measured density
linear interpolation − measured
predicted density
linear interpolation − predicted
(a)
0.38 0.40 0.42 0.44 0.46 0.48 0.50
0
200
400
600
800
1000
1200
liquid fraction in the initial mixture
density (kg/m3)
measured density
linear interpolation − measured
predicted density
linear interpolation − predicted
(b)
Fig.
5.
Comparison
between
measured
and
predicted
density
values
for
composite
material
and
linear
interpolation
of
the
data:
(a)
gypsum
matrix
density
calculated
as
Eq.
(2)
and
(b)
gypsum
matrix
density
corrected
as
in
Eq.
(5).
0.38
0.40
0.42
0.44
0.46
0.48
0.50
0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
liquid fraction in the initial mixture
thermal conductivity (W m−1 K−1)
measured conductivity
linear interpolation − measured
predicted conductivity
linear interpolation − predicted
(a)
0.38
0.40
0.42
0.44
0.46
0.48
0.50
0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
liquid fraction in the initial mixture
thermal conductivity (W m−1 K−1)
measured conductivity
linear interpolation − measured
predicted conductivity
linear interpolation − predicted
(b)
Fig.
6.
Comparison
between
measured
and
predicted
conductivity
values
for
composite
material
and
linear
interpolation
of
the
data:
(a)
gypsum
matrix
conductivity
calculated
as
Eq.
(3)
and
(b)
gypsum
matrix
conductivity
corrected
as
in
Eq.
(9).
as
microcapsules
specific
heat
capacity
(cmc)
is
used
1960
J/(kg
K),
which
is
the
value
related
to
the
liquid
phase,
as
reported
in
Fig.
1.
cc=
(1
−
mmc)
·
cg+
mmc ·
cmc (10)
Since
the
porosity
increase
does
not
affect
the
specific
heat
capacity,
no
correction
is
needed
to
modify
the
gypsum
matrix
specific
heat
capacity.
As
already
anticipated,
the
precision
on
the
measures
of
the
specific
heat
capacity
is
lower
than
the
precision
for
the
density
or
the
conductivity.
The
maximum
error
between
predicted
and
measured
specific
heat
capacity
is
12.6%,
which
is
lower
than
the
17%
estimated
as
the
maximum
experimental
measurement
uncertainty,
while
the
95%
confidence
interval
is
±156
J/(kg
K).
In
Table
5
the
minimum,
the
maximum
and
the
RMSP
difference
between
the
measured
and
the
estimated
value
are
reported
for
density,
thermal
conductivity
and
specific
heat
capacity.
The
magnitude
of
the
differences
found
for
the
composite
mate-
rial
is
not
different
from
the
one
found
for
pure
gypsum
samples.
Moreover,
the
maximum
and
minimum
differences
are
close
to
the
maximum
measurement
uncertainty
for
all
the
three
quantities,
while
the
RMSP
is
always
lower.
Eq.
(10)
is
validated
only
for
temperatures
above
the
end
of
the
phase
change
region.
Eq.
(11)
extends
it
also
to
the
phase
change
region
by
using
a
microcapsules
specific
heat
capacity
variable
with
the
temperature,
derived
from
the
data
displayed
in
Fig.
1.
The
experimental
validation
of
this
approach
is
reported
in
Section
5.
cc(T)
=
(1
−
mmc)
·
cg+
mmc ·
cmc(T) (11)
4.
Test
on
a
commercial
product
The
correlations
are
tested
on
a
commercial
gypsum
based
com-
posite
material,
manufactured
by
E2.
The
aim
of
the
test
is
to
verify
if
the
correlations
can
be
used
with
good
accuracy
for
gypsum
based
composite
material
produced
with
different
techniques
than
the
Table
5
Minimum,
maximum
and
RMSP
difference
between
predicted
and
measured
values
for
composite
material
samples.
cccc
Minimum
difference −2.4%
−2.9%
−8.8%
Maximum
difference
3.0%
3.6%
12.6%
RMSP
difference 1.3%
2.0%
6.8%

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233
Table
6
Comparison
between
measured
and
estimated
properties
for
the
commercial
product.
Measured
value
Estimated
value
Difference
Percentage
difference
Density
[kg/m3]
902
948
46
4.9%
Conductivity
[W/(m
K)] 0.281
0.302
0.021
7.1%
Spec.
heat
capacity
[J/(kg
K)] 1125
1025
100
−9.7%
ones
used
for
the
samples
produced
for
this
work.
The
commercial
composite
material
used
for
the
comparison
is
shaped
as
a
gypsum
slab
containing
MICRONAL
and
a
small
percentage
of
glass
fiber.
Because
of
the
mass
fraction
lower
than
1%,
the
presence
of
the
glass
fibers
is
neglected
when
the
thermal
properties
are
estimated.
Following
this
approach,
the
composition
of
the
mixture
used
for
the
preparation
of
the
slab
can
be
synthesized
as
follows:
- water:
30.6%;
-
gypsum
powder:
49.4%;
- PCM
dispersion:
20%
which
means
11.6%
of
liquid
and
8.4%
of
PCM
microcapsules.
Considering
together
water
and
liquid
part
of
the
PCM
disper-
sion,
the
total
liquid
is
42.2%,
while
the
microcapsules
mass
fraction
is
8.4%.
Since
it
has
been
seen
that
an
average
of
14
g
of
water
over
100
g
of
gypsum
powder
reacts
and
remains
in
the
gypsum,
the
final
product
composition
is
estimated
to
be:
-
87%
gypsum;
-
13%
PCM
microcapsules.
0
1
2
3
4
5
6
7
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(a) Thermocoupl
e
1
0
1
2
3
4
5
6
7
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(b) Thermocoupl
e
2
0
1
2
3
4
5
6
7
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(c) Thermocoupl
e
3
0
1
2
3
4
5
6
7
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(d) Thermocoupl
e
4
0
1
2
3
4
5
6
7
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(e) Thermocoupl
e
5
0
1
2
3
4
5
6
7
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(f) Thermocoupl
e
6
0
1
2
3
4
5
6
7
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(g) Thermocoupl
e
7
0
1
2
3
4
5
6
7
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(h) Thermocoupl
e
8
0
1
2
3
4
5
6
7
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(i) Thermocoupl
e
9
Fig.
7.
Temperature
history
recorded
by
the
nine
thermocouples
embedded
in
the
sample
with
10%
of
PCM
and
comparison
with
the
numerical
results.

Author's personal copy
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Energy
and
Buildings
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(2013)
227–236
0
2
4
6
810 12
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(a) Thermocoupl
e
1
0
2
4
6
810 12
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(b)
Thermocoupl
e
2
0
2
4
6
810 12
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(c) Thermocoupl
e
3
0
2
4
6
810 12
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(d)
Thermocoupl
e
4
0
2
4
6
810 12
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(e) Thermocoupl
e
5
0
2
4
6
810 12
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(f) Thermocoupl
e
6
0
2
4
6
810 12
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(g)
Thermocoupl
e
7
0
2
4
6
810 12
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(h)
Thermocoupl
e
8
0
2
4
6
810 12
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(i) Thermocoupl
e
9
Fig.
8.
Temperature
history
recorded
by
the
nine
thermocouples
embedded
in
the
sample
with
20%
of
PCM
and
comparison
with
the
numerical
results.
Applying
the
correlations
to
the
slab,
estimated
values
for
den-
sity,
conductivity
and
specific
heat
capacity
are
found.
These
values
are
compared
with
the
measured
values
in
Table
6.
The
results
in
Table
6
show
a
lower
accuracy
for
the
correlations
when
estimating
the
thermal
properties
of
the
commercial
product.
The
differences
between
the
measured
and
the
estimated
values
are
higher
than
the
RMSP
difference
for
all
the
quantities.
As
for
the
samples
used
for
deriving
the
correlations,
the
estimation
of
the
conductivity
is
the
most
accurate,
while
the
estimation
of
the
specific
heat
is
the
least
accurate.
If
a
higher
accuracy
is
needed,
a
possible
solution
is
to
evaluate
and
to
include
in
the
correlations
the
effect
of
other
parameters
on
the
thermal
properties,
like
the
presence
of
fibers
or
the
water
and
ambient
temperature.
Anyway,
since
the
prediction
error
is
lower
than
10%
for
all
the
three
quantities
and
not
significantly
different
from
the
estimated
measurement
uncertainty,
the
results
given
by
the
correlations
can
be
considered
a
good
properties
estimation
for
gypsum
based
composite
material
for
many
applications.
In
par-
ticular,
an
error
of
this
order
of
magnitude
is
usually
acceptable
in
long
term
building
performance
simulations,
where
there
are
many
other
sources
of
uncertainty
and
where
the
above
mentioned
additional
parameters
are
not
always
available.
5.
Test
of
the
correlations
in
the
phase
change
region
As
anticipated
in
Section
3,
within
this
paragraph
the
possibility
to
extend
the
validity
of
Eq.
(10)
to
the
phase
change
region
through
Eq.
(11)
is
verified
by
means
of
transient
tests
on
composite
mate-
rial
samples.
Three
samples
have
been
made
for
this
purpose,
one
without
PCM
and
two
with
PCM,
with
a
microcapsules
mass
frac-
tion
of
10%
and
20%
respectively.
The
meaning
of
a
sample
without
PCM
is
to
identify
the
presence
of
systematic
errors
introduced
by
the
experimental
set-up
or
by
the
procedure,
avoiding
to
count

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Energy
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(2013)
227–236
235
0
2
4
6
8
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(a) Thermocoupl
e
1
0
2
4
6
8
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(b) Thermocoupl
e
2
0
2
4
6
8
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(c) Thermocoupl
e
3
0
2
4
6
8
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(d) Thermocoupl
e
4
0
2
4
6
8
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(e) Thermocoupl
e
5
0
2
4
6
8
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(f) Thermocoupl
e
6
0
2
4
6
8
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(g) Thermocoupl
e
7
0
2
4
6
8
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(h) Thermocoupl
e
8
0
2
4
6
8
5
10
15
20
25
30
35
Time (h)
Temperature (°C)
Numerical
Experimental
(i) Thermocoupl
e
9
Fig.
9.
Temperature
history
recorded
by
the
nine
thermocouples
embedded
in
the
sample
without
PCM
and
comparison
with
the
numerical
results.
them
as
errors
due
to
an
imprecise
evaluation
of
the
specific
heat
capacity.
Nine
thermocouples
are
placed
in
each
sample,
spaced
1
cm
in
the
direction
of
the
heat
flux:
the
thermocouples
are
located
in
the
central
part
of
the
sample
in
order
to
avoid
the
border
effect
and
to
have
a
thermal
flux
as
much
perpendicular
to
the
sample
faces
as
possible.
The
comparison
between
the
numerical
and
experimental
results
is
reported
in
Figs.
7
and
8
for
the
samples
with
10%
and
20%
of
microcapsules
mass
fraction
respectively
and
in
Fig.
9
for
the
sample
without
microcapsules.
From
the
graphs,
it
is
possible
to
see
that
the
difference
between
numerical
and
experimental
results
is
small
for
both
the
sample
with
10%
and
with
20%
of
microcapsules.
More
in
detail,
the
maximum
difference
between
numerical
and
experimental
results
is
0.93 ◦C
for
the
sample
with
10%
of
micro-
capsules
and
0.72 ◦C
for
the
samples
with
20%,
while
the
maximum
difference
found
with
the
samples
without
PCM,
used
as
reference,
is
1.0 ◦C.
Considering
the
root
mean
square
difference,
the
maxi-
mum
values
are
0.47 ◦C
and
0.26 ◦C
for
the
samples
with
10%
and
20%
of
microcapsules
respectively;
this
values
have
to
be
compared
with
the
0.47 ◦C
found
for
the
samples
without
PCM.
Besides
the
maximum
values,
which
may
be
due
to
a
small
misplacement
of
the
thermocouple,
for
most
of
the
other
thermocouples
the
root
mean
square
difference
lies
in
the
range
0.2–0.3 ◦C
for
all
the
samples.
This
analysis
shows
that
the
numerical
results,
obtained
using
Eq.
(11)
for
the
calculation
of
the
specific
heat
capacity
in
the
whole
range,
have
a
good
agreement
with
the
experimental
results.
More-
over,
the
results
obtained
from
samples
containing
PCM
does
not
differ
from
the
experimental
data
more
than
the
results
obtained
from
the
sample
without
PCM.
When
performing
this
type
of
test,
it
has
to
be
considered
that
for
some
phase
change
materials,
the
specific
heat
capacity
variation
with
temperature
depends
on
the
temperature
variation
velocity.
Therefore,
when
validating
the
correlation
for
the
specific
heat
capacity,
particular
care
has
to
be
taken
for
the
time
scale
of
the
application
to
which
the
correlation
addresses.
In
the
case
of
the
transient
tests
described
in
this
section,
thanks
to
the
large
size
of
the
samples,
the
temperature
increases
quite
slowly,
especially

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227–236
if
compared
with
the
temperature
variation
typical
of
measuring
techniques
like
the
scanning
calorimetry.
This
means
that
the
time
scale
of
the
temperature
variation
and,
consequently,
of
the
phase
change,
is
much
closer
to
the
typical
time
scale
of
building
struc-
tures,
for
which
the
correlations
have
been
created.
6.
Conclusions
Correlation
for
gypsum
and
gypsum
based
composite
material
containing
paraffin
microcapsules
are
found
on
the
basis
of
exper-
imental
measures
done
on
two
sets
of
samples.
The
correlations
fit
the
experimental
data
with
good
accuracy
and
are
quite
pre-
cise
when
applied
to
a
commercial
product,
made
of
the
same
raw
materials,
but
manufactured
with
a
different
technique.
The
correlations
for
density
and
thermal
conductivity
show
that,
for
both
gypsum
and
composite
material,
these
quantities
decrease
when
the
liquid
content
in
the
initial
mixture
increases.
Moreover,
composite
material
properties
are
influenced
by
the
microcapsules
mass
fraction.
Two
different
aspects
are
taken
into
account
when
consider-
ing
the
microcapsules
effects
on
the
thermal
properties.
On
one
side,
microcapsules
have
different
properties
than
the
gypsum
matrix,
while,
on
the
other
side,
their
presence
increases
the
gyp-
sum
porosity
and,
consequently,
modifies
its
properties.
Thus,
the
correlations
contain
both
the
average
between
gypsum
and
micro-
capsules
properties
and
a
corrective
factor
which
modifies
the
gypsum
properties
according
to
the
microcapsules
content.
On
the
contrary,
since
the
liquid
content
affects
the
material
porosity
but
not
its
chemical
composition,
the
specific
heat
capacity
does
not
vary
significantly.
For
this
reason,
the
gypsum
specific
heat
capacity
is
considered
equal
to
the
average
of
the
values
related
to
the
different
samples,
while
the
composite
material
specific
heat
capacity
is
obtained
from
a
weighted
average
on
the
mass
fractions
between
the
gypsum
and
the
microcapsules
specific
heat
capacity.
The
correlations
for
the
calculation
of
the
gypsum
properties
and
the
correlations
for
composite
material
density
and
thermal
conductivity
are
independent
of
the
temperature
and
can
be
used
as
they
are
in
a
temperature
range
between
5◦C
and
35 ◦C.
The
correlation
for
the
composite
material
specific
heat
can
be
used
in
the
same
temperature
range
if
the
microcapsules
specific
heat,
dependent
on
the
temperature,
is
used
in
the
calculation.
This
work
shows
that
gypsum
and
composite
material
proper-
ties
can
be
found
through
correlations
on
the
basis
of
the
material
composition.
This
gives
benefits
when
the
material
composition
changes
or
has
to
be
chosen.
Since
the
correlations
are
designed
for
gypsum
based
composite
material
containing
MICRONAL
micro-
capsules,
composite
materials
based
on
different
microcapsules
or
solid
matrix
may
need
different
correlations.
Concerning
this
point,
the
procedure
followed
within
this
work
may
represent
a
reference
for
developing
new
correlations
for
different
composite
materials.
A
further
development
of
this
work
is
the
integration
of
the
cor-
relations
in
a
tool
for
dynamic
simulation
of
building
structures
containing
gypsum
based
composite
material.
Moreover,
other
cor-
relations
have
to
be
found
to
predict
the
thermal
properties
of
composite
material
with
a
different
solid
matrix,
like
plaster.
Acknowledgments
The
authors
thank
BASF
and
E2,
for
providing
the
material
needed
for
the
experimental
activities
and
useful
informations
about
composite
material
manufacturing,
and
Ing.
Andrea
Alongi
for
the
support
in
the
experimental
activities.
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