Ce amics-Siliká y 64 (2), 180-189 (2020)
www.ce amics-silika y.cz doi: 10.13168/cs.2020.0007
180 Ce amics – Siliká y 64 (2) 180-189 (2020)
INVESTIGATION OF ELECTRIC AND THERMAL PROPERTIES OF
ALKALI-ACTIVATED ALUMINOSILICATES WITH
A CNT ADMIXTURE
#OLDRICH ZMESKAL*, LUCIE TRHLIKOVA*, JAN POSPISIL*, LUKAS FIALA**, PAVEL FLORIAN*
*Facul y o Chemis y, B no Uni e si y o Technology,
Pu kyňo a 118, 612 00 B no, Czech Republic
**Depa men o Ma e ials Enginee ing and Chemis y, Facul y o Ci il Enginee ing, Czech Technical Uni e si y in P ague,
Tháku o a 7, 166 29 P aha 6, Czech Republic
#E-mail: [email p o ec ed]
Submi ed Oc obe 15, 2019; accep ed Decembe 9, 2019
Keywo ds: Alkali-ac i a ed aluminosilica es, Ca bon nano ubes, elec ic and dielec ic p ope ies, The mal p ope ies
The pape is ocused on measu emen s o elec ic and he mal p ope ies o alkali-ac i a ed aluminosilica es (AAAs) wi h
a ca bon nano ube (CNT) admix u e. Such composi es, ab ica ed om blas - u nace slag, qua z sand, wa e glass as an
alkali ac i a o , a small amoun o elec ically conduc i e CNT admix u e and wa e exhibi be e elec ic and he mal
p ope ies han he e e ence ma e ial wi hou he CNT. Such an enhancemen opens new p ac ical applica ions, such as
designing snow-mel ing, de-icing o sel -sensing sys ems ha do no need any ex e nal senso s o de ec he cu en condi ion
o he building’s ma e ials. Mo eo e , he economic aspec is mo e a ou able in he case o AAA han ha o Po land
cemen -based ma e ials. The DC (di ec cu en ) elec ic p ope ies a e de e mined expe imen ally om he cu en - ol age
(I-V) cha ac e is ics, he dielec ic p ope ies by means o impedance spec oscopy. Dielec ic measu emen s allow us o
de e mine he con ibu ion o he indi idual componen s o he conduc i i y o he composi e. The elec ic and he mal
conduc i i ies in he ans e se di ec ion we e 16.16 µS∙m-1 and 0.907 W∙m-1∙K-1 o 0 % o CNT and 34.46 µS∙m-1 and
1.298 W∙m-1∙K-1 o 0.4 % o CNT, espec i ely.
INTRODUCTION
P esen ly, composi es based on a cemen ma ix
wi h elec ically conduc i e admix u es a e used in a-
ious applica ions, o example: sel -sensing elemen s
[1], sel -hea ing o de-icing sys ems [1] o elec omagne-
ic shielding sys ems [2]. Va ious o ms o ca bon pa -
icles, such as ca bon black (CB), g aphi e powde (GP),
ca bon ib es (CFs) o ca bon nano ubes (CNTs) a e
commonly used admix u es o enhancing he elec ic
p ope ies [3]. The elec ically enhanced cemen -based
ma e ials we e s udied due o hei widesp ead use in
he cons uc ion indus y [4]. Howe e , alkali-ac i a ed
aluminosilica es (AAAs) wi h compa able s eng h,
good chemical esis ance and lowe p ice we e also in-
es iga ed in e ms o he mechanical, wa e anspo
and he mal p ope ies [4, 6].
In his ega d, he aim o he p esen wo k is o
s udy he in luence o he CNT admix u e amoun on he
elec ic and he mal p ope ies o he AAA composi es
( he he mal p ope ies o AAAs ha e been e iewed
[4, 7]). Speci ically, he ma e ial includes h ee basic
componen s: qua z sand as a ille , blas - u nace slag
ac i a ed by wa e glass and a small amoun o CNT.
The elec ic pa ame e s o he AAA componen s a e
known om li e a u e [8, 9]. Howe e , he p ope ies o
he composi e ma e ial in ol ing such componen s can
di e signi ican ly. The elec ic and he mal p ope ies o
silicon oxide (sand) a e summa ised in he monog aphy
[8] and s udied in he pape [9]. The p esen ed esul s
o he elec ic conduc i i y and he ela i e pe mi i i y
a e abou 0.10 S∙m-1 and abou 20 a 1 GHz and wi h a
20 % wa e concen a ion. The he mal conduc i i y o
he sand depends on he po osi y o he ma e ials and is
2.7 - 2.8 W∙m-1∙K-1 wi h po osi y o 0.4. The dielec ic
p ope ies o he aluminosilica es we e s udied in [9].
The esul s o he impedance analysis o he Po land
cemen pas e ob ained in he equency egion om
100 kHz o 15 MHz a e summa ised in he pape [9].
Two p ocesses we e ecognised, one ela ed o he solid
ma ix and he o he o he liquid phase illing he po es.
F om he measu emen p esen ed in [10], a signi ican
impac on he composi ion o he dielec ic p ope ies
is e iden . The spec a show one pola dielec ic peak
con ained only alkali-ac i a ed slag, sand, wa e glass
and wa e a low equencies o he sample. This peek
is shi ed by he addi ion o a ca bon admix u e o he
lowe equencies.
The speci ic hea o he slag in he wide in e al
o empe a u es is p esen ed in [12]. I a ies om
700 J∙kg-1∙K-1 a oom empe a u e o 1100 J∙kg-1∙K-1 a
600 °C. The p esen ed he mal conduc i i ies depend
on he ype o he alkali elemen (Li, Na, K) and di e in
he in e al (0.1 - 0.6) W∙m-1∙K-1.
In es iga ion o elec ic and he mal p ope ies o alkali-ac i a ed aluminosilica es wi h a CNT admix u e
Ce amics – Siliká y 64 (2) 180-189 (2020) 181
MATERIALS AND SAMPLES
The se o AAA samples wi h di e en concen -
a ions o he CNT admix u e was p epa ed oge he
wi h he e e ence AAA sample. All he s udied ma e-
ials (i.e., he e e ence AAA sample and he AAA
samples wi h he di e en concen a ions o he CNT
admix u e) we e p epa ed om slag SMŠ 380 p oduced
in Ko ouč Š ambe k s. .o, om wa e glass SUSIL MP
2.0 (an alkali-ac i a o ), om wa e and om a di e en
amoun o mul i-walled CNT G aphis eng h CW 2-45
in mix u e wi h ca boxyme hylcellulose (a homogeni-
sed 1 % CNT suspension). The samples o dimensions
equal o 30 × 30 × 10 mm3 we e p epa ed by using no -
malised PG1 qua z sand, which ul ils he unc ion (in
his mix u e) o he ille . The ab ica ed samples we e
imme sed in wa e o he nex 28 days. The composi ions
o he used slag is desc ibed in Table 1, he s a ing
mix u es o hese samples a e desc ibed in Table 2.
The samples o he elec ic, dielec ic and he -
mal measu emen s a e p esen ed in Figu e 1a, b. The
sample sizes (diame e s and hicknesses) oge he wi h
he basic pa ame e s o he ma e ials a e desc ibed
in Table 3. All he samples we e con ac ed by he SPI
Supplies conduc i e ca bon pain , colloidal g aphi e
in isop opanol. The measu emen s we e ealised in he
ans e se (abou 10 mm in hickness) and longi udinal
(abou 30 mm in hickness) di ec ion. The elec ic con-
ac a ea was, in bo h cases, he same 10 × 30 mm2. The
a angemen o he expe imen is demons a ed in Figu-
e 1c.
The measu emen s o he cu en - ol age cha ac-
e is ics we e ca ied ou by using a Kei hley 6517B
elec ome e and a Kei hley 2410 sou ce me e wi h in-
eg a ed ol age sou ces. The equency dependences
we e pe o med on a Sola on SI 1260 Impedance/Gain-
Phase Analyze wi h a Sola on Dielec ic In e ace
1296 de ice. The he mal measu emen s we e ca ied ou
on he 30 × 30 mm2 side o he samples in he ans e se
di ec ion. The good he mal con ac was ensu ed by a hea
sink compound (Dow Co ning 340). The a angemen o
he empe a u e measu emen appa a us is p esen ed in
Figu e 1d.
Hea ing he samples we e ealised by an Agilen
6622A Powe Supply and he empe a u es we e mea-
su ed by an Agilen 34420A nano ol me e .
Table 2. The composi ion o he ab ica ed AAA composi es.
Componen CNT concen a ion (%)
0.00 0.05 0.10 0.2 0.30 0.40
slag (g) 140 140 140 140 140 140
sand (g) 140 140 140 140 140 140
wa e glass (g) 28 28 28 28 28 28
wa e (g) 57 57 57 57 57 57
CNT (mg) 0 70 140 280 420 560
Table 1. The composi ion o he used slag.
Componen SiO2 Fe2O3 Al2O3 CaO MgO SO3 Na2O K2O MnO Cl
Amoun [%] 39.66 0.47 6.45 40.12 9.50 0.72 0.33 0.55 0.65 0.05
Table 3. The speci ica ions o he s udied samples.
CNT conc. Mass Thickness Size/Diame e Volume Bulk densi y
(%) (g) (m) (m) (cm3) (kg∙m-3)
PMMA 3.53 0.0041 0.0303 2.98 1185
0.00 17.61 0.0105 0.0300 9.45 1863
0.05 19.11 0.0110 0.0300 9.90 1930
AAA-CNT 0.10 19.39 0.0110 0.0310 10.57 1834
composi e 0.20 19.09 0.0110 0.0310 10.57 1805
0.30 18.92 0.0115 0.0300 10.35 1828
0.40 18.72 0.0110 0.0310 10.57 1770
b)a)
Figu e 1. The con igu a ion o he measu ed samples o : a) he elec ic and dielec ic measu emen s, b) he he mal measu emen s.
Zmeskal O., T hliko a L., Pospisil J., Fiala L., Flo ian P.
182 Ce amics – Siliká y 64 (2) 180-189 (2020)
ELECTRIC PROPERTIES
Expe imen al
The DC cu en - ol age cha ac e is ics we e
measu ed in he ans e se di ec ion by using a Kei hley
6517B elec ome e and in he longi udinal di ec ion
by a Kei hley 2410 sou ce me e . Embedded ol age
sou ces o he equipmen (± 1000 V) we e used o
sample powe . This me hod o wi ing de ices allows
one o measu e he cu en - ol age cha ac e is ics in
he ans e se di ec ion IT = (VT) o he di e en
longi udinal ol ages (VL = cons .), see Figu e 1c.
The cu en - ol age cha ac e is ics o he h ee ypes o
samples a e gi en in Figu e 2. Fo be e dis inc ion o
he I-V cha ac e is ics o he di e en longi udinal ol-
ages VL, he cha ac e is ics we e shi ed in he ho izon al
Figu e 1. The measu emen p inciple o : c) he cu en - ol age and impedance cha ac e is ics, d) he empe a u e ansien s.
Figu e 2. The dependence o he ans e se cu en IT on he sum o he ans e se and he longi udinal ol ages (VT + VL) o he
selec ed samples o he di e en concen a ion o he CNT: a) 0.00 %, b) 0.10 %. The longi udinal ol age (VL) is he pa ame e
o dependence. (Con inue on nex page)
Kei hley 6517B
I, V
Kei hley 2410
I, V
Sola on 1296
Z,
φ
Sola on 1296
Z,
φ
longi udinal
di ec ion
ans e se
di ec ion
−2000 −1000 0 1000
2000
Vol age (V)
Cu en (A)
1000 V
750 V
500 V
250 V
0 V
−250 V
−500 V
−750 V
−1000 V
−0.0004
−0.0003
−0.0002
−0.0001
0
0.0001
0.0002
0.0003
–
Agilen 34420 A
T
0
∆U
h
+
Agilen 6622 A
I, V
sample
–
+
–
+
−2000 −1000 0 1000
2000
Vol age (V)
Cu en (A)
1000 V
750 V
500 V
250 V
0 V
−250 V
−500 V
−750 V
−1000 V
−0.000015
−0.000010
−0.000005
0
0.000005
0.000010
0.000015
d)
b)
c)
a)
In es iga ion o elec ic and he mal p ope ies o alkali-ac i a ed aluminosilica es wi h a CNT admix u e
Ce amics – Siliká y 64 (2) 180-189 (2020) 183
di ec ion ( he sum o he ans e se and longi udinal
ol ages, VT + VL). I is e iden ha he cu en - ol age
cha ac e is ics exhibi an ohmic (linea ) cha ac e o
a concen a ion o 0.10 % o he CNT (see Figu e 2b)
and he cu en is app oxima ely one o de less han o
a smalle and la ge concen a ion o he CNT (see Fi-
gu es 2b, c). Mo eo e , o hese cases, he cha ac e is ics
ha e a nonlinea cha ac e .
Resul s
The ans e se and he longi udinal DC elec ic
conduc i i y o he s udied samples a e p esen ed in
Table 4, and in Figu e 3, espec i ely. I is e iden ha he
sample wi h 0.1 % o CNT exhibi ed he smalles elec ic
conduc i i y, which ag ees wi h he cu en - ol age
cha ac e is ics p esen ed in Figu e 2. In he case o he
0.1 % CNT concen a ion, he dependences a e linea ,
because he pola isa ion o he dipoles is compensa ed
o . The nonlinea cha ac e is ics ( o smalle and la ge
concen a ions o he CNT) a e caused by dipoles o he
molecules o he alkali-ac i a ed slag and sand ha a e
no compensa ed. The di e ences be ween he cu en -
ol age cha ac e is ics o he di e en VL a e caused
by he inhomogenei ies o he samples ( o he di e en
VL, he e is a di e en pe pendicula elec ic ield and
a di e en pa h o elec ic cu en ). Mo e de ailed
in o ma ion can be ob ained by using he Sola on SI
1260 impedance analyse .
The dependence o he elec ic conduc i i y (in
he longi udinal and ans e se di ec ion) on he con-
cen a ion o he CNT a ze o ol age in a pe pendicula
di ec ion ( ans e se, longi udinal) is p esen ed in
Figu e 3.
DIELECTRIC PROPERTIES
Theo y
The dielec ic p ope ies can be exp essed by he
impedance Z, which is desc ibed by he esis ance R and
he capaci i e eac ance XC as ollows
Z = R + jXC = |Z| exp(jφ), (1)
whe e j = √–1 is he imagina y uni , |Z| = √R2 + XC
2
is
he impedance modulus and φ = a c g(XC/R) is he phase
shi be ween he eal and imagina y pa .
Figu e 2. The dependence o he ans e se cu en IT on he
sum o he ans e se and he longi udinal ol ages (VT + VL)
o he selec ed samples o he di e en concen a ion o he
CNT: c) 0.30 %. The longi udinal ol age (VL) is he pa ame e
o dependence.
−2000 −1000 0 1000
2000
Vol age (V)
Cu en (A)
1000 V
750 V
500 V
250 V
0 V
−250 V
−500 V
−750 V
−1000 V
−0.0008
−0.0006
−0.0004
−0.0002
0
0.0002
0.0004
c)
Table 4. The speci ica ions o he s udied samples.
T ans e se di ec ion Longi udinal di ec ion
CNT conc. esis ance conduc i i y esis ance conduc i i y
(%) (MΩ) (μS∙m-1) (MΩ) (μS∙m-1)
0.00 2.17 16.16 12.25 7.77
0.05 3.10 11.81 36.05 2.52
AAA-CNT 0.10 14.46 2.37 136.37 0.67
composi e 0.20 1.09 31.64 10.51 8.65
0.30 2.25 17.00 5.47 15.91
0.40 1.00 34.46 6.69 13.59
0.1
00
.3 0.
40.5
0.2
CNT concen a ion (%)
Conduc i i y (µS m-1)
0.1
100
1
10
ans e se
longi udinal
Figu e 3. The dependence o he elec ic conduc i i y on he
concen a ion o he CNT in he alkali-ac i a ed blas - u nace
slag composi e measu ed in he ans e se and longi udinal
di ec ion.
Zmeskal O., T hliko a L., Pospisil J., Fiala L., Flo ian P.
184 Ce amics – Siliká y 64 (2) 180-189 (2020)
In hese equa ions, R = ρ*∙l/S = l/(σ∙S) and
XC = −1/(ω∙C) = −l/(ω∙ε∙S), whe e ρ* is he elec ic
esis i i y, l is he hickness, S is he con ac a ea, σ is he
elec ic conduc i i y, ω is he angula equency and ε is
he elec ic pe mi i i y. In he case o he dispe sion o
he elec ic cha ge ca ie s du ing anspo h ough he
ma e ial, he cons an phase elemen (CPE), desc ibed by
Equa ion 2, needs o be aken in o conside a ion:
. (2)
The capaci ance XC = −1/(ω∙Y0) = −1/(ω∙C), ( o
n = 1), esis ance R = 1/Y0 = 1/G, ( o n = 0) o induc ance
XL = ω/Y0 = ω∙L, ( o n = –1) a e special cases o his e m.
This means ha he Y0 pa ame e , he e o e, depends on
he ype o componen s ( esis o R, capaci o C, induc o
L, o , gene ally, he cons an phase elemen CPE).
Expe imen al sec ion
Measu emen s o he AC (al e na ing cu en ) cha-
ac e is ics we e ca ied ou ( o he ans e se and
longi udinal di ec ion o he samples) on a Sola on
SI 1260 impedance analyse wi h a Sola on 1296 di-
elec ic in e ace in he equency ange o 0.01 Hz o
1 MHz. The ob ained esul s a e p esen ed in Figu e 4.
I is e iden ha he ans e se impedance in low
equencies (see Figu es 4a, c) is abou one o de o mag-
ni ude lowe han o he longi udinal di ec ion – he
dis ance o he con ac s in he ans e se di ec ion is
app oxima ely h ee imes lowe han in he longi udinal
di ec ion. The phase shi (see Figu es 4b, d) is nea ing
he ze o alue o he low equencies, which indica es
he esis i e cha ac e o he beha iou . The esul s a e in
a good ag eemen wi h he DC measu emen esul s (see
Table 4). F om Figu e 4b, d, i is also e iden ha he
impedance phase shi (dependence on he equency)
is mo e complica ed o he longi udinal han o he
ans e se a angemen o he con ac s. I can be due
o he inhomogenei y and aniso opy o he samples
and due o he highe dispe sion o he cha ge ca ie s
o e he longe dis ance. The elec ic p ope ies o he
com-posi es (see Figu e 1 and Table 2) and he cha ge
anspo can also be a ec ed by he elec ic p ope ies
o each componen , which can bind a dopan ep esen ed
by he CNT conduc i e componen .
Resul s
The dependence o he eac ance X on he esis ance
R (Cole-Cole diag am, Figu e 5a) and he dependence o
he se ial capaci y C on he se ial esis ance R (o con-
duc ance, see Figu e 5b) we e calcula ed using he
o mulas ou lined in he heo e ical pa . The di e ences
Figu e 4. The impedance cha ac e is ics: dependence o he impedance magni ude (a, c) and he phase shi (b, d) on he equency
o he longi udinal (a, b) and he ans e se (c, d) di ec ions.
1E−02 0 1E+02 1E+04
1E+06
F equency, (Hz)
longi udinal
Impedance magni ude, │Z│ (Ω)
1E+03
1E+04
1E+05
1E+06
1E+07
1E+08
1E+09
0 %
0.10 %
0.30 %
0.05 %
0.20 %
0.40 %
1E−02 0 1E+02 1E+04 1E+06
F equency, (Hz)
ans e se
Impedance magni ude, │Z│ (Ω)
1E+03
1E+04
1E+05
1E+06
1E+07
1E+08
1E+09
0 %
0.10 %
0.30 %
0.05 %
0.20 %
0.40 %
1E−02 0 1E+02 1E+04 1E+06
F equency, (Hz)
longi udinal
Impedance phase shi , φ (°)
0 %
0.10 %
0.30 %
0.05 %
0.20 %
0.40 %
-80
-60
-40
-20
-70
-50
-30
-10
0
1E−02 0 1E+02 1E+04
1E+06
F equency, (Hz)
ans e se
Impedance phase shi , φ (°)
0 %
0.10 %
0.30 %
0.05 %
0.20 %
0.40 %
-80
-60
-40
-20
-70
-50
-30
-10
0
d)
b)
c)
a)
Z = exp
(
− n
)
1
Y0 ωn
j
2

In es iga ion o elec ic and he mal p ope ies o alkali-ac i a ed aluminosilica es wi h a CNT admix u e
Ce amics – Siliká y 64 (2) 180-189 (2020) 185
be ween he esponses o he samples wi h he di e en
CNT concen a ions a e ob ious. The de ailed analysis
showed ha a p edic ed equi alen ci cui consis s o
pa allel esis o s and a capaci i e CPE co esponding o
he indi idual componen s (qua z sand, alkali-ac i a ed
slag – aluminosilica e, po e solu ion and CNT) connec-
ed in se ies (see he scheme in Table 5).
The elec ic pa ame e s o he componen s ( esis-
ance, capaci ance and di usion CPE pa ame e ) o
he longi udinal di ec ion a e summa ised in Table 5.
The calcula ed alues ela i ized o he sample size a e
hen gi en in Figu e 6.
The esul s p esen ed in Figu e 6 e ealed ha
highe CNT concen a ions lead o an inc ease he
Figu e 5. The dependence o : a) he eac ance X on he esis ance R (i.e., Cole-Cole diag am) and b) he capaci ance C on he
esis ance R.
Figu e 6. The elec ic (a), dielec ic (b) and CPE (c) pa ame e s in he longi udinal measu emen s. (Con inue on nex page)
05E+06
1E+07
Resis ance, R (Ω)
longi udinal
Reac ance, X (Ω)
0
1E+06
2E+06
3E+06
4E+06
5E+06
0 %
0.10 %
0.30 %
0.05 %
0.20 %
0.40 %
00
.20
CNT concen a ion (%)
0.30 0.400.05 0.10
Conduc i i y, σ (µS m-1)
Sand
Aluminosilica e
Solu ion in po es
CNT
1
103
10
104
102
1E+03 1E+04 1E+05 1E+06 1E+07 1E+08
1E+09
Resis ance, R (Ω)
longi udinal
Capaci ance, C (F)
1E−12
1E−11
1E−10
1E−09
1E−08
1E−07
1E−06
1E−05
0 %
0.10 %
0.30 %
0.05 %
0.20 %
0.40 %
00
.20
CNT concen a ion (%)
0.30 0.400.05 0.10
1
103
10
104
105
106
102
Pe mi i i y, ε (µS m-1)
Sand
Aluminosilica e
Solu ion in po es
CNT
b)
b)
a)
a)
Table 5. The speci ica ions o he s udied samples.
Longi udinal R1 C1 nC1
R2 nR2
C2 R3 C3 nC3
R4 C4 nC4
di ec ion (MΩ) (nF) (MΩ) (nF) (MΩ) (nF) (MΩ) (nF)
0.00 % 8 200 0.66 7.0 0.38 3.0 3.4 0.7 0.67 0.10 0.020 1.00
0.05 % 45 30 0.70 25.0 0.33 6.0 20.0 0.4 0.68 0.10 0.050 1.00
0.10 % 18 0.2 0.75 4.5 0.20 10.0 2.0 0.8 0.84 6.00 0.019 1.00
0.20 % 5 70 0.64 3.5 0.42 7.0 5.0 1.8 0.65 0.13 0.018 0.98
0.30 % 3 2000 0.60 1.6 0.35 0.9 0.9 2.5 0.65 0.35 0.015 0.91
0.40 % 3 7000 1.00 1.2 0.21 0.1 0.8 1.8 0.70 0.20 0.040 0.90
R
1
C1
sand
R
2
C2
aluminosilica e
R
3
C3
po e solu ion
R
4
C4
CNT
Zmeskal O., T hliko a L., Pospisil J., Fiala L., Flo ian P.
186 Ce amics – Siliká y 64 (2) 180-189 (2020)
elec ic conduc i i y o he composi e signi ican ly
mo e han he o he componen s. The capaci y is, in he
case o he CNT, o se e al o de s o magni ude lowe
(in compa ison wi h o he componen s) and has almos
wi h no dispe sion, ( he CPE pa ame e is app oxima ely
equal o one). On he o he hand, he elec ic conduc i i y
o he sand (which is in he same amoun as he alkali-
ac i a ed slag) is e y small – con e sely, he capaci y
( he e ec i e pe mi i i y) is se e al o de s o magni ude
highe . I is also caused by he dispe sion in he AC ield
( he CPE pa ame e o capaci y is abou 0.6). The alkali-
ac i a ed slag has highe elec ic conduc i i y han he
sand and se e al o de s o magni ude lowe elec ic
capaci y – he dispe si e na u e o he ee elec ic
cha ge con ibu es o he elec ic conduc i i y ( he alue
o i s di use (CPE) pa ame e a ies om 0.2 o 0.42
depending on he CNT concen a ion, see Figu e 6c).
The las componen is a po e solu ion – i s conduc i i y
and pe mi i i y (dielec ic cons an ) is compa able o he
alkali-ac i a ed blas u nace slag, and i s CPE pa ame e
n is compa able o sand.
THERMAL PROPERTIES
Theo y
The he mal p ope ies o he ma e ials we e cal-
cula ed using he Ca slaw Jaege ma hema ical model
[14, 15]. The empe a u e esponse o he hea ing is de-
sc ibed as ollows:
, esp.
, (3)
whe e A is he coe icien o he he mal abso p ion, h is
he dis ance o he he mal senso and he hea sou ce,
a is he he mal di usi i y, R is he hea loss pa ame e
(mus be highe han he hea sou ce diame e ), ΔT0 =
= A D
α
is he empe a u e di e ence in a s eady s a e,
D = h2/4a is he di usion ime, R = R2/4a is he elaxa ion
ime. The a io o he elaxa ion and he di usion ime
R/ D = R2/h2 de e mines he in luence o he measu ed
he mal esponses by he hea losses.
The hea sou ce is cha ac e ised by he alue o α =
α0 + (D – E)/2, whe e E is a dimension o he space o
sp eading he hea ( o olume i is E = 3). D is he space
dimension o he hea ing (D = 0, 1, 2, 3 sequen ially o
a poin , linea , plana and olume hea ing, espec i ely),
and α0 de ines he ype o hea ing (α0 = 0, 1, 2 sequen ially
o pulse, s ep-wise and amp-wise hea ing, espec i ely)
[16, 17].
The he mal di usi i y a, he he mal conduc i i y
λ and he speci ic hea capaci y cp can be hen de e mined
as
, , ,
(4)
whe e P is he hea powe , S is he su ace a ea, ρ is he
bulk densi y o ma e ial, and m = ρ∙h∙S is he mass o he
measu ed sample.
Expe imen al sec ion
The he mal p ope ies we e measu ed in a Dewa
bo le [18], whe e hea was supplied o he sys em
h ough a buil -in esis o in he plana me al sou ce
(se ings: he powe o he pulse gene a ed by he Agilen
6622A Powe Supply was 4.18 W; he measu emen
du a ion was 12 hou s). K- ype he mocouples we e
used o he measu emen o he empe a u e di e ence
be ween he ho and cold su ace (DTc) o he sample
as he he moelec ic ol age DU h using an Agilen
34420A nano ol me e (Channel 1) and ano he included
K- ype he mocouple was used o ob ain he empe a u e
o he hea sou ce T0 (Agilen 34420A nano ol me e ,
channel 2), see Figu e 1d. In his case, he ollowing
applies: DTc = T0 – T1, whe e T1 was calcula ed om
he empe a u e T0 and he he moelec ic ol age DU h
(using a calib a ion cu e o a K- ype he mocouple).
The he mal measu emen s ha we e ca ied ou o all
he samples wi h he di e en CNT concen a ions in he
ans e se di ec ion a e hen p esen ed in Figu e 7a.
I is e iden (see Figu e 7a) ha he highes change
in he empe a u e was obse ed o he sample wi h
a concen a ion o 0.40 mass. % CNT. I indica es he
lowes he mal conduc i i y o his sample.
The speci ic hea capaci y can be es ima ed om he
slope o he ansien esponse. The sample wi h 0.30 %
concen a ion o he CNT had he highes speci ic hea
capaci y ( he as es esponse o he empe a u e o
he hea ing pulse), while he e e ence sample and he
sample wi h 0.05 % CNT had he smalles .
Figu e 6. The CPE (c) pa ame e s in he longi udinal measu e-
men s.
00
.20
CNT concen a ion (%)
0.30 0.400.05 0.10
0
0.6
0.2
0.8
1.0
1.2
0.4
CPE pa ame e ,
n
Sand
Aluminosilica e – nR
Solu ion in po es
CNT
c)








−− 2
24
4
exp)(
Δ
R
a
a
h
A = T α
D
2
2
4d
dln
Δ
h
=
h
T
=
a
S
h
T
P
=
S
h
Λ=λ
Δρa
λ
=
T
m
P
=
c
d
d
p
() 













−
R
D
D0 exp/Δ)(Δ
+
T= T α
In es iga ion o elec ic and he mal p ope ies o alkali-ac i a ed aluminosilica es wi h a CNT admix u e
Ce amics – Siliká y 64 (2) 180-189 (2020) 187
The PMMA (polyme hylme hac yla e) sample had
a empe a u e esponse compa able o he esponses o
he AAA-CNT samples and, he e o e, hei he mal
pa ame e s a e compa able.
Resul s
The e alua ion o he expe imen al da a was ca ied
ou analogously o hose p esen ed in he p e ious
chap e (see Chap e 4.: Dielec ic p ope ies). Fi s ly,
he di e ence o he empe a u e limi be ween he ho
and cold side o he sample was de e mined and using
he ela ionships p esen ed in he heo e ical pa o his
chap e – he dependencies o he speci ic hea capaci y
on he he mal conduc i i y we e calcula ed. The esul s
a e gi en in Figu e 7b. The e ical angen s in hese
dependencies de e mine he he mal conduc i i y o he
samples (in he s eady s a e), he ho izon al angen s
de e mine he speci ic hea ( o sho imes, he g ea es
slope o he ansien esponse). De ia ions o he speci ic
hea om he ho izon al angen o he sho imes a e
ela ed o he dispe si e na u e o he hea ans e .
The summa y o he esul s ob ained by i ing he
ma hema ical model is gi en in Table 5. I is e iden
ha he highes alue o he speci ic hea capaci y and
he minimum alue o he he mal conduc i i y is o
he e e ence sample. The esul s o all he samples
can be compa ed wi h a se o alues o a polyme hyl-
me hac yla e (PMMA) ma e ial wi h known he mal
p ope ies ( he able alue o he he mal conduc i i y
is abou 0.17 W∙m-1∙K-1, he speci ic hea is abou
1400 J∙kg-1∙K-1). The selec ed esul s om Table 6 a e
p esen ed in ba g aphs (see Figu e 8). The esul s ag eed
wi h he conclusions made in he p e ious sec ion (see
Chap e Dielec ic p ope ies).
CONCLUSIONS
The Alkali-ac i a ed aluminosilica es a e p omising
ma e ials o hei use in hea ing and sensing sys ems
due hei elec ic, dielec ic and he mal p ope ies.
The dis ibu ion o he DC elec ic conduc i i y in
he samples was de e mined om he cu en - ol age
cha ac e is ics in he ans e se and longi udinal di ec-
ion. I was obse ed ha , in bo h di ec ions, he sample
wi h 0.10 % CNT concen a ion exhibi ed a minimal
elec ic conduc i i y ( ans e se di ec ion: 2.37 μS∙m-1,
longi udinal di ec ion: 0.67 μS∙m-1, espec i ely). The
elec ic conduc i i y o he es o he samples was
mo e han 10 imes highe . The e o e, he ma e ials wi h
a highe concen a ion o CNT a e be e o sel -hea ing
sys ems.
Figu e 7. a) The esponses o he empe a u e changes be ween he ho and cold su ace o he sample (T0 – T1) on he ime o he
ans e se di ec ion o he measu emen ; b) The dependence o he speci ic hea capaci y on he he mal conduc i i y o he AAA
samples wi h he CNT admix u es calcula ed o he de e mina ion o he eal alues o he speci ic hea and he mal conduc i i y
by he di e en ial me hod.
1 100 10 000
Time, (s)
∆T
C
(K)
0
5
10
15
20
25
30
35
40
0 %
0.05 %
0.10 %
0.20 %
0.30 %
0.40 %
PMMA
0.1 1 00010
10 000
The mal conduc i i y, λ (W m-1 K-1)
Speci ic hea , c (J kg-1 K-1)
0 %
0.05 %
0.10 %
0.20 %
0.30 %
0.40 %
PMMA
1E+03
1E+02
1E+04
1E+05
1E+06
1E+07
1E+08
1E+09
b)a)
Table 3. The he mal p ope ies o he s udied composi es.
CNT P ρ ΔTc D a c λ
concen a ion (W) (kg∙m-3) (K) (s) (mm2∙s-1) (J∙kg-1∙K-1) (W∙m-1∙K-1)
PMMA 0.92 1 186 30.25 62 0.108 1 444 0.185
0.00 % 4.18 1 871 30.24 64 0.410 2 101 0.907
0.05 % 4.18 1 930 29.26 52 0.538 1 681 0.982
0.10 % 4.18 1 834 30.03 65 0.444 1 955 0.957
0.20 % 4.18 1 806 32.20 65 0.436 1 887 0.939
0.30 % 4.18 1 828 26.78 48 0.658 1 658 1.180
0.40 % 4.18 1 771 36.87 71 0.410 1 788 1.298
Zmeskal O., T hliko a L., Pospisil J., Fiala L., Flo ian P.
188 Ce amics – Siliká y 64 (2) 180-189 (2020)
The AC conduc i i y o he samples in he ans-
e se and longi udinal di ec ions con i med he esul s
o he DC measu emen s. Besides, he esul s o he AC
measu emen s we e used o he e alua ion o he RC
alues o he elemen s ep esen ed by he alkali-ac i a ed
blas - u nace slag, qua z sand, CNT and po e solu ion in
he po es. The measu emen s showed ha he dispe sion
in he longi udinal di ec ion is la ge ( he impedance
spec um is mo e complica ed) han in he ans e se
di ec ion.
The ma e ial wi h he lowes elec ic conduc i i y
( he sample wi h a 0.10 % CNT concen a ion) exhibi ed
he local maximum in he speci ic hea capaci y depen-
dence on he concen a ion o he CNT (1955 J∙kg-1∙K-1).
The sample wi h 0.40 % CNT concen a ion has he
highes alue o he he mal conduc i i y and he
lowes he mal di usi i y. The esul s we e compa ed
wi h he PMMA measu emen s (λ = 0.165 W∙m-1∙K-1,
c = 1 394 J∙kg-1∙K-1), which is in good ag eemen wi h
he abula ed alues. The empe a u e measu emen s
con i med he co ela ion be ween he he mal, elec ic
and dielec ic p ope ies.
The sample wi h 0.1 % o CNT had he minimal
elec ic conduc i i y due o i s low ionic conduc i i y.
I is explained by an inc ease in he c ys allini y o he
ac i a ed slag by he CNT. Fo highe CNT concen a-
ions, his e ec no isible due o he agglome a ion o
he CNT.
The elec ical p ope ies o he AAA ma e ials de-
pend on he p esence o he ionic species in he ma ix
which is ela ed o he deg ee o he alkali ac i a ed
eac ion. This me hod could help o de e mine he con-
e sion deg ee, hea e olu ion, de elopmen o com-
p essi e s eng h, e c.
Acknowledgemen s
The au ho s would like o hank he Minis y o
Educa ion, You h and Spo s o he Czech Republic o
i s suppo by he Czech Science Founda ion, unde
P ojec No. 19-11516S and o suppo by p ojec
FCH-S-19-5834.
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Figu e 8. The he mal pa ame e s o he samples o he ans-
e se measu emen : a) he mal conduc i i y, b) speci ic hea
and c) he mal di usi i y.
0PMMA 0.20
CNT concen a ion (%)
0.30 0.400.05 0.10
0
0.6
0.2
0.8
1.0
1.2
1.4
0.4
The mal conduc i i y, λ (W m-1 K-1)
0PMMA 0.20
CNT concen a ion (%)
0.30 0.400.05 0.10
0
1500
500
2000
2500
1000
Speci ic hea capaci y, c (J kg
-1
K
-1
)
0PMMA 0.20
CNT concen a ion (%)
0.30 0.400.05 0.10
0
0.3
0.1
0.4
0.5
0.6
0.7
0.2
The mal di usi i y, a (mm2 s-1)
a)
b)
c)