Effect of phase change materials on the hydration reaction and kinetic of PCM-mortars

Effect of phase change materials on the hydration reactionand kinetic of PCM-mortars

Anissa Eddhahak • Sarra Drissi • Johan Colin •

Sabine Care • Jamel Neji

Received: 28 January 2014 / Accepted: 29 April 2014

� Akademiai Kiado, Budapest, Hungary 2014

Abstract The phase change materials are considered an

attractive way to reduce energy consumption thanks to

their heat storage capacity. Their incorporation in the

construction materials allows the energy to be an integral

part of the building structure. Even though PCMs have

shown their reliability from a thermal point of view, some

drawbacks linked to their use were emphasized such as the

loss of the compressive strength of the PCM-material. This

paper attempts to provide an explanation by the investi-

gation of the hydration kinetic of PCM-mortars. The semi-

adiabatic Langavant test was adapted to this case. The

numerical diffuse element method was used for the com-

putation of the heat flux, which is a compulsory step for the

determination of the hydration degree. The results showed

a lower heat released by the PCM mortars compared to a

control mortar as well as a delay in the hydration progress

with the addition of PCMs.

Keywords Phase change materials (PCMs) � Langavant �DEM � Hydration degree � Damage

Introduction

Much attention is still paid on phase change materials

(PCMs) thanks to their latent heat storage capacity. Since the

energy crisis of 1970s and given the restrictive challenges

which have been agreed by the Kyoto protocol aiming at the

reduction of the energy consumption and the emission of

greenhouse gases, the thermal energy storage (TES) systems

have been considered also important as the new and

renewable energy sources [1, 2]. In order to get advantage of

their storage capacity, professionals of building sector are

more and more interested by the integration of PCMs into

the building structure for the improvement of its thermal

inertia and thereby the occupants thermal comfort.

Numerous research studies have recently focused on

PCMs, their elaboration and the measurement of their

thermal properties [3–5]. For instance, in order to allow the

specific heat measurement of PCM-wallboards in macro

scale, the research of Eddhahak et al. [6] described an

innovative experimental exchanger bench test adapted to

this specific case. Other researches [7–10] have been

reported in the literature for the investigation of the

mechanical and thermal properties of construction materi-

als (concrete, gypsum) incorporating PCMs, in the fol-

lowing denoted ‘‘PCM-materials.’’ Most of them

highlighted the enhancement of the specific capacity of the

PCM-material and the loss of the compressive strength

with the addition of PCMs.

A. Eddhahak (&) � S. Drissi � J. Colin

Universite Paris-Est - Institut de recherche en constructibilite,

ESTP, 28 Avenue du President Wilson, 94234 Cachan Cedex,

France

e-mail: [email protected]

S. Drissi


J. Colin


S. Drissi � S. Care

Laboratoire Navier (UMR 8205), CNRS, ENPC, IFSTTAR,

Universite Paris-Est, 6-8 Av. Blaise Pascal,

77455 Marne La Vallee, France


S. Drissi � J. Neji

LAMOED- Ecole Nationale d’Ingenieurs de Tunis, Universite

Tunis El Manar- Laboratoire de Materiaux, d’Optimisation et

d’Energie pour la Durabilite, BP 37, 1002 Le belvedere, Tunisia


123

J Therm Anal Calorim

DOI 10.1007/s10973-014-3844-x

Although the extensive literature references in PCMs

field, several scientific locks remain still questionable. In

fact, the PCMs characteristics themselves are not suffi-

ciently well controlled notably due to the lack of specific

standards for the PCMs testing and data exploitation [11].

Also, many questions have been raised regarding the

damage of PCMs, which could be occurred during the

manufacture of the PCM-material (by mixing for example

[10] ), and its impact on the apparent thermo-mechanical

properties of the PCM-material on the one hand and the

long term behavior on the other hand. Apart from these

discussion points, the problem of the mechanical resistance

loss of the PCM-material needs to be clarified. Questions

are raised about the reasons for which the PCMs addition

affects the compressive strength of the material. The loss of

the mechanical strength may be explained by the volume

content of PCMs particles which may be considered as

porosity. However, it appears necessary to consider the

possible modification of the cement hydration kinetic

leading to a decrease of the mechanical strength. Scientific

explanations are obviously needed to improve our knowl-

edge and understanding of the PCMs effects from a

mechanical point of view. Besides, by this way, one can

find optimized solutions to account for this problem and

establish the required balance between the thermal effi-

ciency and the structural performance.

In this context, this paper is a contribution to better

understand the PCMs effect when incorporated in the

mortar by the investigation of the heat hydration track. The

objective is to know whether PCMs may impact the cement

hydration reaction and kinetic when added in the mortar.

For this purpose, the semi-adiabatic method based on the

conventional Langavant-type experiment (NF 196-9

substituting the previous NF P 15-436) was adapted for the

PCM-mortar case. The suggested method in this paper

takes into account the non-constant specific heat capacity

of PCMs previously determined by Differential Scanning

Calorimetry measurements for an accurate estimation of

the heat released during hydration and the modification of

the cement hydration kinetic due to the presence of PCMs.

Materials and methods

PCMs and PCM-mortars

In this study, organic PCMs named Micronal DS 5038 X

(from Basf) are used. Micronal PCMs are composed of

48 % of organic paraffin wax microencapsulated in a

polymethyl methacrylate shell with a peak melting point of

25 �C and a total thermal storage heat of 142 kJ kg-1. The

choice of PCMs type (organic, inorganic, eutectic) is

determinant in the building industry. In fact, organic PCMs

are widely used in construction materials because of their

numerous advantages such as their availability in a large

temperature range, their compatibility with the cement-

based material [12], their chemical stability, the absence of

the supercooling phenomenon, etc. The observations of the

microencapsulated PCMs by means of scanning electron

microscopy (SEM) revealed the presence of bigger cap-

sules of spherical shape ranging between 100 and 300 lm

and composed of an agglomeration of many thousands of

PCMs micro-capsules. It was also observed some broken

capsules of PCMs at their initial state as shown in Fig. 1a.

In order to study the effect of PCMs on the hydration heat

reaction of mortars, PCM-mortars are manufactured using

450 kg m-3 of a Portland cement CEM II 32.5R,

930 kg m-3 of lime–sand (0/4 mm of fraction), and a water-

to-cement ratio W/C equal to 0.55. The proportions used

here were obtained by a design optimization step performed

in the framework of a current PhD research [13, 14]. During

this work, it was noticed a decrease of the compressive

strength of the PCM-concrete with the addition of PCMs

(Fig. 2) [15]. The PCMs are incorporated into the mortars by

simple addition at the last stage of the mixing process in

order to avoid their damage. Three volume proportions were

considered for mortar mixes: 1, 3, and 5 % with regards to

concrete total volume initially designed by the authors. The

PCM-mortars will be denoted ‘‘PCM-mix1, PCM-mix3, and

PCM-mix5,’’ respectively, for 1, 3, and 5 % of PCM con-

tents. A reference mortar ‘‘Ref’’ without PCMs was also

manufactured for control. Only the PCM proportion is dif-

ferent for all mixes so that one can study the only effect of

PCMs on the cement hydration reaction.

In addition, as mentioned earlier, the PCMs can be

subjected to deterioration due to the intensified shear loads

occurring during the manufacture of the PCM-material and

especially the mixing process. Accordingly, it is of interest

to know the effect of damaged PCMs on the heat hydration

reaction. This information can provide solutions for the

PCM-material implementation and help us to assess spe-

cific experimental protocols for the elaboration and man-

ufacture of the PCM-material. For this reason, some PCMs

capsules were placed between two glass slides and then

sheared manually by moving the slides in order to crash

them. Figure 1b shows the morphology of damaged PCMs

after their manual deterioration. The damaged PCMs were

then incorporated into mortars at the first step of the

manufacture using the same volume proportions (1, 3 and

5 %) and they were subjected to an intensified mixing to

further promote their damage.

Differential scanning calorimetry test

The damaged and non-damaged PCMs, used for the PCM-

mortars manufacture, were tested by the differential

A. Eddhahak et al.

123

scanning calorimeter (DSC) technique using a DSC 204 F1

Phoenix from Netzsch under a nitrogen atmosphere for the

specific heat (Cp) measurement. The thermal scan was

performed in the range temperature 0–55 �C at a scanning

rate of 0.5 K min-1 with a sample mass of 12 mg. The test

was performed at least three times using a virgin PCM

sample each time. The sapphire was used here as a standard

in order to compute the calorimeter sensibility. Then, the

ratio method enables the calculation of the heat capacity of

the testing sample. For more details regarding the proce-

dure of Cp measurement, the readers could consult a pre-

vious work of the authors [14].

Langavant semi-adiabatic test

The Langavant-type semi-adiabatic calorimeter was used

here to measure the heat released by the fresh PCM-

mortars specimens. This method is normalized according

to the European Standard NF EN 196-9. After their

manufacture, the four samples (Ref, PCM-mix1, PCM-

mix3, and PCM-mix5) are placed in four cylindrical

mortar bottles closed with an insulating stopper and then

positioned at the center of four calorimeters formed by a

high vacuum Dewar flask, made of silvered Pyrex glass.

All this housed in a rigid container used as a support. The

thermal insulation used in the calorimeter allows the

minimization of the heat losses. For every calorimeter, a

temperature sensor is placed in contact with the mortar

sample for the measurement of the temperature evolution

versus time. In addition, a reference calorimeter of the

same characteristics containing a hardened mortar control

specimen is also used.

A first series of tests using mortars with non-damaged

PCMs was performed. Then, experiments were also con-

ducted for the case of mortars with damages capsules. The

temperature measurements were recorded for 5 days

(120 h) with a step time of 5 min.

Theoretical model for the released heat calculation

for PCM-mortars

The curves of the temperature evolution versus time

obtained by the semi-adiabatic test allow the determination

of the total heat released during the cement hydration

reaction. According to the standardized Langavant method,

the total hydration heat, denoted Q is expressed as follow

Q ¼ c

mc

ht þ1

mc

Z t

0

ahtdt ¼ Aþ B ð1Þ

The first term A of Eq. (1) represents the accumulated

heat in the calorimeter whereas the second term B is rel-

ative to the total thermal losses across the calorimeter.

c denotes the total thermal capacity of the calorimeter in

J K-1 and according to:

c ¼ Cpcmc þ Cpsms þ Cpwmw þ Cpbmb þ l ð2Þ

mc, ms, mw, and mb are, respectively, the mass of

cement, sand, water and the mortar bottle in gram (g).

Cpc, Cps, Cpw, and Cpb are respectively the specific

heats of cement, sand, water and the mortar bottle taken

Fig. 1 SEM observations of:

a PCMs agglomeration,

b damaged PCMs

40

35

30

25

20

15

10

5

0Ref PCM–mix1 PCM–mix3 PCM–mix5

PCM/%

Com

pres

sive

str

engt

h/M

Pa

36

31

22

19

Fig. 2 Evolution of the compressive strength versus the addition of

PCMs

Hydration reaction and kinetic of PCM-mortars

123

respectively equal to 0.8, 0.8, 3.8, and 0.5 J g-1 K-1

according to the conventional standard NF EN 196-9.

l is the thermal capacity of the empty calorimeter in

J K-1.

ht is the temperature deviation in K computed between the

fresh mortar of temperature T(t) and the hardened one Tr(t):

ht tð Þ ¼ T tð Þ � Tr tð Þ ð3Þ

a denotes the coefficient of the total thermal conduction

losses across the calorimeter in J h-1 K-1 given by:

a ¼ aþ bht ð4Þ

where a and b are the calibration constants of the

calorimeter.

The term B of Eq. (1) can also be expressed as:

B ¼ 1

mc

Xn

i¼1

�ai�ht;iDti ð5Þ

�ai and �hi are, respectively, the average heat conduction coef-

ficient due to the thermal losses and the average temperature

elevation computed between two successive stages ti and ti-1.

Dti is the time step between two successive measure-

ments in h.

As noticed, only cement, sand, water and calorimeter

are taken into account in Eq. (2) by the consideration of

their masses and specific heat values. In the case of PCM

modified mortars, the PCMs are part of the testing sam-

ples and thereby have to be taken into account in the

computation of the total released hydration heat. In

addition, one of the constraints related to the Langavant

software is that the user has to introduce constant specific

values for the mortar components. In the case of PCMs,

the corresponding specific heat is not constant but rather

evolves with temperature especially when a phase change

phenomenon takes place. Accordingly, in the case of

PCM-mortars, Eq. (2) has to be generalized and the fol-

lowing expression is proposed for the computation of the

total thermal capacity:

c¼ 0:8 mcþ msð Þ� Cp Tð Þð ÞPCM�mPCMþ 3:8mwþ 0:5mbþl

ð6Þ

where (Cp(T))PCM and mPCM are, respectively, the specific

heat and the mass of PCMs.

It is worth noticing that the minus sign in front of the

PCMs thermal capacity is due to the fact that during

cement hydration, the mortar will release heat since the

hydration is an exothermic reaction. Moreover, the PCMs

can melt in the hydration temperature range due to the

excess of the released heat and the temperature elevation.

Accordingly, they will absorb energy and store it through

an endothermic melting reaction. As a result, the total

energy to be released by the PCM-mortars will be less than

the energy which could have been released by traditional

mortars without PCMs.

Results and discussion

DSC results: damaged and non-damaged PCMs

The heat capacity curves of both damaged and non-dam-

aged PCMs are presented in Fig. 3. It can be noticed that

the two curves exhibit a similar tendency in the tempera-

ture range 0–55 �C according to the DSC test. The peak

observed in this figure is related to the phase change phe-

nomenon of the PCMs. The differences between the two

curves are slight but significant. In addition, one can see

that the damaged PCMs exhibit a lower heat capacity than

the non-damaged ones because of the damage effect which

could have resulted in the leakage of the paraffin active

material from the capsules. In fact, the microencapsulation

solution is useful since it provides a container for the

paraffin wax and prevents its leakage when the paraffin

melting point is reached. Moreover, thanks to the micro-

encapsulation, an exchange surface is created between the

polymer shell and the surrounding material which

improves the heat transfer conditions.

In Table 1, a quantitative comparison of the specific heat

values between the two cases (damaged and non-damaged) is

summarized. Cp1 and Cp2 denote the average heat capacities,

respectively, in the temperature ranges 0–10 �C and

30–55 �C whereas DH represents the total heat storage

(latent?sensible) computed by the peak integration over the

temperature range 10–30 �C. Note that the enthalpy obtained

for the non-damaged PCMs is equal to 141 kJ kg-1 which is

very satisfactory with the PCM supplier’s technical data.

Regarding the deviation values, one can notice the non-

negligible differences in the specific heat estimations

between damaged and non-damaged PCMs.

35

30

25

20

15

10

5

00 10 20 30 40 50 60

Temperature/°C

Non–damagedDamaged

Spe

cific

hea

t/J g

–1 K

–1

Fig. 3 Specific heat evolution obtained by DSC test: comparison

damaged and non-damaged PCMs

A. Eddhahak et al.

123

Heat hydration of PCM-mortars

The curves of the different PCM-mortars obtained by the

Langavant-type semi-adiabatic test are presented in Fig. 4.

The use of Eq. (1)–(5) allows the determination of the

total heat released during the cement hydration according

to the standardized method. In the present non-conven-

tional case, Eq. (6) have replaced Eq. (2) for the heat

calculation so that the PCMs contribution is taken into

account. As can be observed in the Cp curve of Fig. 3, the

energy absorbed by PCMs at melting is more important

than the one outside the phase change range. Accordingly,

it cannot be realistic to consider an equivalent heat capacity

over the total hydration temperature range. Furthermore, by

noticing from Fig. 4 that the hydration start temperatures

for PCM-mortars lie inside the PCMs phase change tem-

perature range, the heat capacity of PCMs was computed in

two regions as follow:

CpReg1

� �PCM�mixi

¼r

T1

T0iCp dT

T1 � T0i

CpReg2

� �PCM�mixi

¼r

Tfi

T1Cp dT

Tfi � T1

8>>><>>>:

ð7Þ

where CpReg1 and CpReg2 are the specific heats computed,

respectively, in region 1 and region 2 (Fig. 5). T0i and Tfi

are, respectively, the start and the final temperatures of the

hydration reaction relative to the PCM-mix containing i %

of PCMs. T1 is the upper bound of the PCMs phase change

temperature range, taken equal to 26 �C. In Table 2, are

summarized the equivalent specific heat values relative to

the PCM-mortars according to Eq. (7).

Figure 6 depicts the heat hydration released by the

PCM-mortars during the semi-adiabatic test.

As expected, it can be observed that the PCM-mortars

released a lower hydration heat than the reference mortar.

In addition, the higher is the PCMs proportion in the

mortar, the lower is the total hydration heat. A deviation of

approximately 10 % is recorded in the total heat released

after 5 days by the addition of 5 % of PCMs with respect to

the Reference mortar. On the basis of this finding, it can be

observed that the addition of PCMs leads to the release of

Table 1 Specific heat values

Cp1 DH Cp2

Damaged PCMs 1.26 127 1.21

Non-damaged PCMs 1.98 141 1.84

Deviation/% 36 9.6 33

60

50

40

30

20

10

00 20 40 60 80 100 120 140

Time/h

Tem

pera

ture

/°C

RefPCM–mix1PCM–mix3PCM–mix5Tr

Fig. 4 Temperature evolution versus time given by the semi-

adiabatic test

35

30

25

20

15

10

5

00 10 20 30 40 50 60

Temperature/°C

Spe

cific

hea

t/J g

–1 K

–1

T0i T1 Tfi

Cpreg1

Cpreg2

Fig. 5 Illustration of PCMs

heat capacity calculation

method (dashed lines:

integration bounds)

Table 2 Equivalent specific heats

PCM-mix1 PCM-mix3 PCM-mix5

CpReg1/J g-1 K-1 22.24 21.69 21.69

CpReg2/J g-1 K-1 1.87 1.87 1.87


123

lower heat hydration which could affect the mortar curing

and thereby the development of the mechanical resistance

of the PCM-mortar. Nevertheless, the loss of the

mechanical strength of the PCM composite can not only

be attributed to PCMs since their addition in the mortar

results in a decrease of the volume proportion of the other

constituents and especially the cement. Besides, it can be

seen from Fig. 6b the evolution of the heat hydration

versus time for the PCM-mix1 in both damaged and non-

damaged PCMs cases. The PCM-mixes including dam-

aged PCMs exhibit a slight decrease in the hydration heat

in comparison with the mortar with non-damaged PCMs

(4 % after 5 days) despite of their lower heat capacity

revealed by DSC measurements (Fig. 3). This result may

be attributed to the leakage of paraffin wax into the

cementitious matrix which could have affected the

hydration process.

Heat flux and diffuse element method (DEM)

The exploitation of the heat release curves allows the

determination of the heat flux / by the temporal derivation

of the hydration heat with respect to time. It is worth

noticing that the heat flux determination seems to be

straightforward, however the result derived from the finite

difference derivative is not satisfactory due to the noisy

aspect linked to successive derivation. To account this

problem, we make use here of the diffuse element method

(DEM). This technique [16, 17] called also the diffuse

approximation method provides a nodal approximation to a

function simply known by a finite number of points. It

enables also the determination of the first derivatives of this

function. For the present case, the function to be considered

is the heat hydration Q(t). Starting by the estimation of the

K-th order Taylor expansion of Q:

Q tð Þ ¼XK

i¼0

pi tð Þ�a�i ðtÞ ð8Þ

where pi is the Taylor estimation of the heat hydration

function.

Then ai*(t) is chosen in such a way the following qua-

dratic expression is minimum:

It að Þ ¼XN

j¼1

x tj � t� �

QðtjÞ � pT tj � t� �

�aðtÞ� �

ð9Þ

where N denotes the total discretization points number and

x the weight function defined as:

xt

Dt

� �¼ exp �C

t2

Dt2

� ð10Þ

where C is the diffusion coefficient taken such as the

quadratic error between the function Q(t) and the numerical

300

250

200

150

100

50

00 20 40 60 80 100 120 140

Time/h

Hea

t hyd

ratio

n/J

g–1

RefPCM–mix1 Non–damaged

PCM–mix1 damaged

PCM–mix3PCM–mix5

Fig. 6 Heat release curves and comparison between damaged and

non-damaged cases

0.35

0.3

0.25

0.2

0.15

0.1

0.05

–0.05

–0.1

0

0.3

0.25

0.2

0.15

0.1

0.05

00 20 40 60 80 100 120

Time/h0 20 40 60 80 100 120

Time/h

Hea

t flu

x/J

g–1

h–1

Hea

t flu

x/J

g–1

h–1

Successive DerivationDiffuse Method

RefPCM–mix1PCM–mix3PCM–mix5

(a) (b)

Fig. 7 a Numerical derivation (reference mortar). b Heat fluxes of PCM-mortars

A. Eddhahak et al.

123

result is nearly zero. Dt is the time range of the hydration

reaction.

The minimum of It is reached at a* which satisfies the

following system:

A tð Þ�a tð Þ ¼ B tð Þ where

A tð Þ ¼P

x tj � t� �

p tj � t� �

�pT tj � t� �

B tð Þ ¼P

x tj � t� �

QðtjÞ�p tj � t� �

ð11Þ

The resolution of system (9) leads to the smoothing of

the heat curve and the calculations of its M successive

derivations (M = 1 to K):

A tð Þ ¼ a0 tð Þ; DM Q tð Þð Þ ¼ M!aMðtÞ ð12Þ

Only the first derivative of the hydration heat with respect

to time was numerically computed here. The results of deri-

vation by the DEM are highlighted in Fig. 7 (left) in com-

parison with the conventional derivation technique using

successive points. Note that the noise noticed by the finite

difference approximation vanishes when using the DEM and a

smooth response is obtained. Figure 7b presents the evolution

of the heat fluxes for the PCM-mortars computed according to

the DEM technique. As can be noticed, the higher is the PCM

amount in the mortar, the lower is the heat flux. This finding is

in accordance with the heat hydration results. In the next

section, we will make use of the computed heat flux for the

study of the PCM effect on the kinetic the hydration reaction.

Hydration kinetic: chemical affinity and degree

of hydration progress

One of the important purposes of the semi-adiabatic test is

the determination of the hydration degree progress of the

Table 3 Extrapolated heat hydration values for PCM-mortars

Ref PCM-mix1 PCM-mix3 PCM-mix5

Q?/J g-1 278 275 274 273

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

–0.1

0

0 20 40 60 80 100 120

Deg

ree

of h

ydra

tion

ξ ξD

egre

e of

hyd

ratio

n

Time/h0 20 40 60 80 100 120

Time/h

PCM–mix1 Non–damagedPCM–mix1 damagedRef


(a) (b)

Fig. 8 a Evolution of the degree of hydration of the PCM-mortars, b comparison damaged and non-damaged cases

400

350

300

250

200

150

100

50

00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Che

mic

al a

ffini

ty/1

/s

300

250

200

150

100

50

0

Che

mic

al a

ffini

ty/1

/s

Degree of hydration ξ0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Degree of hydration ξ


PCM–mix1

Fitting

(a) (b)

Fig. 9 a Chemical affinity of the PCM-mortars, b polynomial fitting (PCM-mix1)


123

exothermic reaction. This parameter governs the kinetic

hydration process. The well-known phenomenological

Arrhenius law [18] is often used for the description of the

rate of the hydration degree:

_n ¼ f nð Þ exp�Ea

RT

� ¼ dQðtÞ

dt

n1Q1

ð13Þ

where n is the degree of the hydration reaction. f(n) is the

chemical affinity in 1/s. Ea is the apparent activation energy

in J mol-1. R an T are, respectively, the perfect gas con-

stant (8.314 J mol-1 K-1) and the absolute temperature in

K. n? is the degree hydration at the end of the hydration

reaction. Q? is the final hydration heat released at the end

of the hydration reaction in J g-1.

The degree of hydration is comprised between 0 and an

ultimate value denoted n? reached at the end of the

hydration. n? can be defined according to a phenomeno-

logical relation approved on many cement types [19]:

n1 ¼ 1� exp �3:33W

C

� ð14Þ

In the present case, n? is the same for all the PCM-mortars

(equal to 0.84) since the water-to-cement ratio W/C is kept

constant (equal to 0.55) whereas Q? is determined by the

asymptotic extrapolation of the curves (1/t, Q) for t closed

to ?.Note that Q? can also be computed by weighting the

hydration heats of the cement constituents (phases) by their

mineralogical proportions (C3S, C2S, C3A, C4AF). The

extrapolated values of Q? are summarized in Table 3.

As noticed, the values of Q? are close for all the mix-

tures. The slight difference can be attributed to the small

amounts of the PCMs in the mortar on the one hand and the

lower PCM heat capacity in comparison with the cement

constituents on the other hand [20].

The temporal integration of the function _n allows the

determination of the degree of hydration. Then, by dividing

the latter by n? one can determine the degree of reaction

progress expressed as follow:

a tð Þ ¼ nðtÞn1

ð15Þ

Given the aforementioned bounds of the degree of

hydration, a is then comprised between 0 and 1.

The evolutions of the hydration degrees of the PCM-mor-

tars are presented in Fig. 8. It can be noticed that the higher

degree hydration reaches a value of 80 % at 5 days (Reference

case) which means that the hydration process is not yet fin-

ished. The degrees of reaction progess exhibit also the same

evolutions given the definition of Eq. (13). As remarked, the

hydration reaction of PCM-mortars are in delay with regards

the reference one. A maximal deviation of 9 % is recorded at

120 h between the PCM-mix5 and the reference mortar. The

right part of Fig. 8 presents the degree hydration evolution in

the case of PCM-mix1 between the damaged and non-dam-

aged configurations. One can see that the mortar incorporating

broken PCMs are slightly delayed in comparison with non-

damaged PCM-mix1 (4 % maximum) which correlates very

well with the previous heat hydration results.

Given the degree hydration, the exploitation of the

Arrhenius law given in Eq. (13) allows the determination of

the chemical affinity f(n) as:

f nð Þ ¼ dQðtÞdt

n1Q1

expEa

RT

� ð16Þ

While the energy activation governs the dependence

relationship of the hydration kinetic with temperature

(thermo-activation), the chemical affinity ‘‘includes’’ the

information related to all the influences of the other

parameters on the hydration kinetic. Its determination

requires the preliminary knowledge of the energy activa-

tion. Several appropriate methods are available in the lit-

erature for the determination of this parameter [21], and

they are beyond the scope of the present work. For the sake

of simplicity, by assuming a current value Ea/R = 4,000 K,

the chemical affinity functions are computed according to

Eq. (16) for all the PCM-mixes.

Plots of Fig. 9 present the chemical affinity tendencies

for all the mixes versus the degree of hydration stemming

from the experimental results. One can clearly observe the

decrease of the affinity with the addition of PCMs. A

deviation higher than 30 % is recorded between the peaks

of the reference and PCM-mix5 curves. On the right, the

chemical affinity of PCM-mix1 was numerically fitted

using a 6th polynomial function [22]:

f nð Þ ¼ �1:2105 � n6 þ 3:1105 � n5 � 3:3105 � n4

þ 1:7105 � n3 � 4:9104 � n2 þ 6:6103 � n� 55;

R2 ¼ 0:97 ð17Þ

where R2 is the coefficient of determination.

Conclusions

The Langavant-type semi-adiabatic method adapted for the

case of PCM-mortars is presented in this paper for the

investigation of the PCM effect on the hydration kinetics.

The suggested method highlights the PCMs effect by

considering their thermal contribution, derived from DSC

measurements, for the computation of the total released

hydration heat. The numerical DEM was used here for the

determination of the heat fluxes by the knowledge of the

released heat from the different PCM mixes. It was shown

on the basis of the obtained results a decrease of the

hydration heat as well as a delay in the hydration kinetic

with the addition of PCMs. In addition, the results of

A. Eddhahak et al.

123

mortars with damaged PCMs demonstrated that hydration

kinetic is delayed in comparison with mortars with

unbroken capsules probably due to the paraffin leakage and

its possible interference with the surrounding material

which could have affected the hydration reaction. The

exploitation of Langavant results here presented can be

also useful for the prediction of the early-age mechanical

resistances of the PCM-mortar on site, for instance. This

task is one of the major economic concerns of engineers

and professionals for the optimization of their production

cycles.

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Effect of phase change materials on the hydration reaction and kinetic of PCM-mortars

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