Investigation Of Electric And Thermal Properties Of Alkali-Activated Aluminosilicates With A CNT Admixture

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. REFERENCES 1. Wen S., Chung D.D.L. (2007): Elec ical- esis ance-based damage sel -sensing in ca bon ibe ein o ced cemen , Ca bon, 45, 710–716. doi: 10.1016/j.ca bon.2006.11.029 2. Won J.P., Kim, Lee S.J., Lee J.H., Kim R.W. (2014): The mal cha ac e is ics o a conduc i e cemen -based com- posi e o a snow-mel ing hea ed pa emen sys em. Com- posi e S uc u es, 118, 106–111. doi: 10.1016/j.comps uc . 2014.07.021 3. Guan H., Liu Y., Duan C.K., Cheng J. (2006): Cemen based elec omagne ic shielding and abso bing building ma e ials Cemen and Conc e e Composi es, 28, 468–474. doi: 10.1016/j.cemconcomp.2005.12.004 4. Zuda L., Ce ny R. 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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)