Cementitious materials as promising radiative coolers for solar cells

iScience
A icle
Cemen i ious ma e ials as p omising adia i e
coole s o sola cells
Cemen i ious ma e ials
Mic o-s uc u e Molecula simula ions
Elec omagne ic
p ope ies
Radia i e cooling
o sola cells
E ec i e
medium
R
T
1
Re lec o
Cemen pas e
Sola cell
Ma eo Cagnoni,
Albe o Tibaldi,
Jo ge S. Dolado,
Fede ica
Cappellu i
[email p o ec ed]
Highligh s
A mul i-scale app oach
p edic s dielec ic
p ope ies o cemen i ious
ma e ials
Cemen i ious slabs can
emi he mal adia ion in
he a mosphe ic window
Low-cos cemen i ious
ma e ials can be e ec i e
adia i e coole s o sola
cells
Cemen -based adia i e
cooling could signi ican ly
ex end sola cells li e ime
Cagnoni e al., iScience 25,
105320
No embe 18, 2022 ª2022
The Au ho (s).
h ps://doi.o g/10.1016/
j.isci.2022.105320
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iScience
A icle
Cemen i ious ma e ials as p omising
adia i e coole s o sola cells
Ma eo Cagnoni,
1,5,
*Albe o Tibaldi,
1,2
Jo ge S. Dolado,
3,4
and Fede ica Cappellu i
1
SUMMARY
Nowadays, adia i e coole s a e ex ensi ely in es iga ed o he he mal man-
agemen o sola cells wi h he aim o imp o ing hei pe o mance and li e ime.
Cu en solu ions ely on me a-ma e ials wi h sca ce elemen s o complex ab ica-
ion p ocesses, o o ganic polyme s possibly a ec ed by UV deg ada ion. He e,
he po en ial o inno a i e cemen -based solu ions as a mo e sus ainable and
cos -e ec i e al e na i e is epo ed. By combining chemical kine ics, molecula
mechanics and elec omagne ic simula ions, i is shown ha he mos common ce-
men s, i.e., Po land cemen s, can be equipped wi h excellen adia i e cooling
p ope ies, which migh enable a educ ion o he ope a ing empe a u e o sola
cells by up o 20 K, wi h ou s anding e iciency and li e ime gains. This s udy ep-
esen s a i s s ep owa d he ealiza ion o a no el class o ene gy-e icien ,
economically iable and obus adia i e coole s, based on cheap and a ailable
cemen i ious ma e ials.
INTRODUCTION
Reducing he ope a ing empe a u e is a key challenge in sola cells echnology. A lowe empe a u e no
only inc eases he powe con e sion e iciency, by abou 0:5%=K in silicon-based de ices (Skoplaki and
Paly os, 2009), bu also ex ends he sys em li e ime, by oughly 23=10 K (Dup e
´e al., 2017).
Mo i a ed by he possibili y o achie ing signi ican gains in pe o mance, esea che s ha e p oposed
se e alcoolingsolu ionso e heyea swhicha ebasedondi e seconcep s(Chand aseka e al.,
2015). Among hese, adia i e cooling has been a ac ing much a en ion la ely, no only o he he mal
managemen o sola cells (Li e al., 2017,2021;Pe akis e al., 2020,2021;Sa i and Munday, 2015;Wang
e al., 2020), bu also o applica ion in buildings (Hossain and Gu, 2016;Li and Fan, 2019;Zhao e al.,
2019). This echnology s ands ou hanks o i s ema kable po en ial in e ms o ene ge ic e iciency,
economical iabili y, en i onmen al iendliness, and eliabili y, os e ed by i s comple ely passi e na u e,
e ec i eness, sys emic simplici y and absence o mo ing pa s.
Radia i ecoole sa ebodiesdesigned os onglyemi he mal adia ionwi hin hea mosphe e anspa -
ency window (AW) be ween 8 and 13 mm(seeFigu e S1)(Ca alano i e al., 1975). Radia ion ejec ed h ough
his channel dodges he bounce-back e ec o he a mosphe e and eaches ou e space wi hou e u ning
o he sende . This uncompensa ed ene gy emo al educes he empe a u e o adia i e coole s. Mo e-
o e , i s ic spec al equi emen s a e ul illed, sub-ambien empe a u e can be eached e en unde
di ec sunligh , as expe imen ally p o en only ecen ly (Raman e al., 2014).
Thanks o hese cha ac e is ics, adia i e coole s can ac as e ec i e hea sinks when he mally coupled o a
wa ming body, such as a sola cell. Indeed, he excess hea gene a ed wi hin he cell on sunligh abso p ion
is going o low owa d he colde adia i e coole . Then, he la e is going o pe manen ly emo e i om
he sys em in he o m o he mal adia ion h ough he a mosphe ic window. Rema kably, his p ocess can
educe he ope a ing empe a u e o silicon-based de ices by up o 18:5K(Zhu e al., 2014), oughly lead-
ing o a 9 % e iciency gain (Skoplaki and Paly os, 2009) and 360 % o li e ime (Dup e
´e al., 2017).
Di e en kinds o adia i e coole s we e disco e ed in he las ew yea s (Hossain and Gu, 2016). The mos com-
mon ones a e me a-ma e ials made o e ically s acked hin ilms (Li e al., 2017;Raman e al., 2014;Kecebas
e al., 2017), o hick laye s wi h a mic o-pa e ned su ace (Pe akis e al., 2021;Zhu e al., 2014;Hossain e al.,
2015;Kong e al., 2019).Ye ,i isunclea whe he hese echnologiesa eadap able o la ge-scale manu ac u ing,
1
Depa men o Elec onics
and Telecommunica ions,
Poli ecnico di To ino, Co so
Duca degli Ab uzzi 24, To ino
10129, I aly
2
Is i u o di Ele onica e di
Ingegne ia dell’In o mazione
e delle Telecomunicazioni,
Consiglio Nazionale delle
Rice che c/o Poli ecnico di
To ino, Co so Duca degli
Ab uzzi 24, To ino 10129, I aly
3
Cen o de Fı
´sica de
Ma e iales, CSIC-UPV/EHU,
Paseo Manuel de La dizabal
5, San Sebas ia
´n 20018, Spain
4
Donos ia In e na ional
Physics Cen e , Paseo
Manuel de La dizabal 4, San
Sebas ia
´n 20018, Spain
5
Lead con ac
*Co espondence:
[email p o ec ed]
h ps://doi.o g/10.1016/j.isci.
2022.105320
iScience 25, 105320, No embe 18, 2022 ª2022 The Au ho (s).
This is an open access a icle unde he CC BY license (h p://c ea i ecommons.o g/licenses/by/4.0/).
1
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because o hei eliance on sca ce ma e ials such as Ag o H (EuChemS, 2021), o complex deposi ion and
pa e ning me hods. To o e come hese issues, o ganic ma e ials such as hie a chical po ous polyme s ha e
been p oposed as a low cos al e na i e (Ca losena e al., 2021;Wang e al., 2021b,a;Li e al., 2019;Mandal
e al., 2018), bu hei use migh be jeopa dized by UV deg ada ion (Zhao e al., 2019). This impasse is o cing
esea che s in o a ade-o be ween pe o mance, cos , and eliabili y, and calls o p omp ac ion o iden i y
al e na i e classes o adia i e coole s capable o ul illing all hese equi emen s simul aneously.
Faced wi h his challenge, we ha e conside ed se e al op ions and iden i ied (me a-)conc e es as a e y
p omising class o cheap and scalable (me a-)ma e ials. Con en ional conc e e is made by gluing oge he
agg ega es such as sand o g a el wi h a cemen pas e (binde ) (Allen and Iano, 2019). These agg ega es
canbe eplacedwi hmo e‘‘exo ic’’inclusions o o mme a-conc e e, a conc e e-like me a-ma e ial ha
canbeequippedwi huncon en ionalp ope ies(Mi chell e al., 2014). A i s hin a he possible applica-
ion o hese ma e ials as adia i e coole s is p o ided by hei mul i-scale po ous s uc u e (Dolado and
Van B eugel, 2011), which s ongly esembles he one o he a o emen ioned hie a chical po ous polyme s.
Fu he mo e, he e exis many ecipes o he cemen pas e and many possible choices o he agg ega es,
which lead o conc e es wi h e y di e en chemis y and mic o-s uc u e (Aı
¨ cin, 2000;Bens ed and Ba nes,
2002;Bohne and Ullmann, 2003). As a ma e o ac , hese ma e ials o m an ex emely b oad class, which
can be used no only in buildings (Gagg, 2014),bu alsoinclinicalapplica ionssuchasbonep os heses
(Kenny and Buggy, 2003) and oo h es o a ion (Chadwick and E ans, 2007). This cha ac e is ic p o ides e-
sea che s wi h many knobs o une p ope ies. Finally, conc e es a e al eady being in es iga ed in he
con ex o buildings as a s uc u al ma e ial equipped wi h adia i e cooling capaci ies (Eu opean Commis-
sion, 2021), wi h ecen expe imen s con i ming hei s ong he mal emissi i y in he a mosphe ic window
(Lu e al., 2021) and high e lec ance a sunligh wa eleng hs (Le inson and Akba i, 2002).
Encou aged by hese obse a ions, we ha e ans e ed o he i s ime wi h his wo k he idea o cemen -
and conc e e-based adia i e coole s om buildings o sola cells. In pa icula , we ha e in es iga ed he
sui abili y o o dina y Po land cemen s (OPC) (Taylo , 2004),whicha e hemos commonlyused ypeo
binde , o hei he mal managemen . Rema kably, we ha e disco e ed ha hey can be equipped wi h
dielec ic p ope ies sui able o he he mal managemen o sola cells and po en ially capable o
p o iding ou s anding gains in pe o mance. These indings may ep esen a majo b eak h ough in adi-
a i e cooling esea ch, because he main elemen s ound in hese cemen s, such as Ca, Si, O, and H, a e
among he cheapes and mos a ailable on Ea h (EuChemS, 2021). A he same ime, he s abili y and eli-
abili y o cemen - and conc e e-based solu ions is some hing ha we expe ience e e y day. Wi h his
a icle, we demons a e ha cemen s and conc e es can also be equipped wi h he p ope ies needed
o he e ec i e adia i e cooling o sola cells and can become he ul ima e adia i e coole s, capable
o ul illing pe o mance, cos and eliabili y equi emen s a he same ime. These indings call o u he
esea ch aimed a ealizing an ul ima e pho o ol aic sys em design and ab ica ion p o ocol.
To each hese conclusions, we ha e de ined a mul i-scale in e disciplina y simula ion wo k low ha calcu-
la es he cemen pas e elec omagne ic p ope ies om sc a ch and uses hem in a powe balance model
o es ima e he sola cell empe a u e educ ion d i en by i s coupling o he cemen -based adia i e
coole . The essen ials o he wo k low a e depic ed in Figu e 1.
Fi s , se e al cemen mic o-s uc u es a e gene a ed by modeling he cemen pas e o ma ion wi h
me hods om chemical kine ics. A he same ime, he IR dielec ic p ope ies o he basic componen s
o he he e ogeneous cemen pas e a e calcula ed by a omis ic simula ions. Nex , hese mic o-s uc u al
and dielec ic da a a e combined in o a sui able e ec i e medium heo y o con e he space-dependen
dielec ic unc ion in o an equi alen homogeneous dielec ic unc ion. Then, his is plugged in o an elec-
omagne ic simula o o calcula e he cemen slab emissi i y. Finally, his slab is ‘‘a ached’’ o he sola cell
and he ope a ing empe a u e o he esul ing de ice is calcula ed by he de ailed balance model.
Mo e in o ma ion on each o hese me hods and he co esponding indings is p o ided in he esul s and
discussion sec ion, wi h addi ional de ails in he STAR me hods sec ion and he supplemen al in o ma ion.
RESULTS AND DISCUSSION
We s a ou discussion wi h he hypo he ical plana s uc u e depic ed in Figu e 2A, based on he ypical
model used o he pe o mance assessmen o adia i e coole s made o me a-ma e ials (Pe akis e al.,
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2020,2021;Sa i and Munday, 2015;Zhu e al., 2014;Cagnoni e al., 2022). The de ice consis s o a s ack made by
a e lec o , a cemen -based adia i e coole and a bi acial (Gue e o-Lemus e al., 2016) sola cell; he sola cell
op su ace is acing he Sun. This s uc u e could be ealized, o example, by building a hin ilm sola cell on o
a cemen -based subs a e by spu e ing, e apo a ion o solu ion deposi ion echniques. Expe imen s can be
ound in he li e a u e, whe e hin- ilm sola cells ha e been placed on o s uc u al elemen s o buildings such
as oo iles and conc e e blocks (A
´guas e al., 2011;Iencinella e al., 2009;Hosseini e al., 2013).
By design, he sola cell and he adia i e coole a e he mally coupled bu mu ually anspa en . Indeed,
he o me abso bs sunligh in he UV- isible spec al ange, whe eas he la e emi s he mal adia ion in
heIRspec al ange,whe e heAWis ound.Because abso bance and emissi i y spec a o a body a e
equal acco ding o Ki chho ’s law o he mal adia ion (Balaji, 2014) ( hey will be used in e changeably
om his poin onwa d), he sola cell and he adia i e coole do no exchange ene gy wi h each o he
IR pe mi i i y o cemen pas e componen s
Chemical kine ics (µic) A omis ic simula ions (GULP)
Cemen pas e mic os uc u e
H2O
E ec i e medium heo y (Slo ick)
Homogenized cemen pas e IR pe mi i i y
Elec omagne ic simula ions (gene alized TMM)
Cemen slab abso bance/emissi i y
De ailed-balance model
Sola cell ope a ing empe a u e s band-gap
Ideal mi o
Cemen pas e
Sola cell
Figu e 1. Wo k low o he assessmen o cemen -based adia i e coole s o he he mal managemen o sola
cells
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elec omagne ically, bu do so only wi h he Sun and he a mosphe e, sepa a ely. These obse a ions a e
cla i ied in Figu e 2B, whe e he mos signi ican spec a a e depic ed (see Figu e S1 o a mosphe e ans-
mi ance spec a).
Acco ding o he conside a ions abo e, he de ice can be modeled as a single body a empe a u e T,
whose elec omagne ic p ope ies a e he ones o he sola cell in he UV- isible ange and he ones o
he adia i e coole in he IR spec al ange (Sa i and Munday, 2015). Then, one can calcula e he ne powe
densi y (powe pe op su ace uni a ea) Pne ðTÞexi ing he de ice as unc ion o Tand de e mine he ope -
a ing empe a u e by sol ing Pne ðTÞ=0, which co esponds o he s a iona y s a e o he sys em. Pne con-
sis s o se e al e ms, as depic ed in Figu e 2A:
Pne ðTÞ=Pcell
ad T;EgPSunESun
e;l;Eg
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
UV  isible spec um
+PelecT;Eg+Pcool
ad T;Acool
U;lPa mT0;Aa m
U;l;Acool
U;l
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
IR spec um
+PconðT;T0;hcÞ(Equa ion 1)
PSun,Pcell
ad and Pelec a e he powe densi ies ha he sola cell abso bs om he Sun, emi s as adia ion
and deli e s o he end-use load a maximum powe poin (MPP), espec i ely; hey ha e been calcu-
la ed acco ding o he Shockley-Queisse model (Shockley and Queisse , 1961). On he o he hand,
Pa m and Pcool
ad a e he powe densi ies ha he adia i e coole abso bs om he a mosphe e and emi s
as he mal adia ion, espec i ely. Finally, Pcon is an empi ical e m o accoun o conduc ion and
con ec ion phenomena be ween he de ice and he en i onmen . All hese e ms a e widely
discussed in he li e a u e (Pe akis e al., 2020,2021;Sa i and Munday, 2015;Zhu e al., 2014). The e o e,
we e e he eade o he STAR me hods sec ion o hei explici o mulas and we show he e only
hei pa ame ic dependencies, o highligh which in o ma ion mus be known o ob ain Pne as a unc ion
o Tonly.
In pa icula , some elec omagne ic spec a mus be supplied as a unc ion o wa eleng h land zeni h
angle q( he sys em is in a ian wi h espec o he azimu h angle). The i s one is he Sun spec al i adiance
ESun
e;lðlÞ, modeled using he global s anda d spec um AM1.5g (ASTM In e na ional, 2022). The nex one is
he a mosphe e spec al di ec ional emissi i y Aa m
U;lðl;qÞ,ob ainedacco ding o he o mulaAa m
U;lðl;qÞ=
1Ta m
0;lðlÞ1=cosðqÞ(Pe akis e al., 2020), Ta m
0;lðlÞbeing he ze o-zeni h spec al di ec ional ansmi ance
Re lec o (ideal mi o )
Radia i e coole (cemen pas e)
Sola cell (Shockley-Queisse )
A mosphe e
Ou e space
AW
AB
Figu e 2. Illus a ion o he de ailed balance model employed
(A) Plana s uc u e used o assess he sui abili y o a adia i e coole o he he mal managemen o sola cells. The
powe densi y e ms ep esen ing he channels h ough which he de ice, he en i onmen and he end-use load
exchange ene gy a e also depic ed, oge he wi h he a mosphe e adia ion shielding e ec ou side o i s anspa ency
window (AW).
(B) Compa ison be ween he main elec omagne ic spec a in ol ed in he ope a ion o a sola cell equipped wi h a
adia i e coole . ESun
e;lis he no malized Sun spec al i adiance (AM1.5g), Ea m
e;lis he no malized a mosphe e spec al
i adiance, and AW a e he a mosphe e anspa ency windows. I is shown ha sola cell and Sun a e elec omagne ically
ac i e in a spec al ange di e en om he one o adia i e coole and a mosphe e.
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calcula ed o he summe season wi h he so wa e LOWTRAN (Hi sch, 2016). The las one is he spec al
di ec ional abso bance o he cemen -based adia i e coole Acool
U;lðl;qÞ, calcula ed acco ding o he wo k-
low ou lined in he In oduc ion and depic ed in Figu e 1.
The esul s o igina ing om his wo k low a e he co e subjec o his sec ion. Howe e , be o e mo ing o
hei discussion, a ew pa ame e s o Equa ion 1 s ill need explana ion. In pa icula , Egis he band-gap o
he sola cell semiconduc o , o which we ha e conside ed alues in he ange be ween 1 and 3 eV,
whe eas T0and hca e he ambien empe a u e (se o 293:15 K) and he conduc ion/con ec ion coe icien
(se o 10:6Wm
2K1 o ep esen a e age winds (Pe akis e al., 2020)); di e en alues o hese wo do
no a ec ou indings, hence hey a e no conside ed he e.
Back o Acool
U;l, his can be eadily de e mined by he ans e -ma ix me hod (TMM) o a plana s uc u e
made o laye s wi h known homogeneous pe mi i i y (Bo n and Wol , 2019). Howe e , as al eady an ic-
ipa ed, common cemen pas es a e made o a he e ogeneous mix u e o chemical species a anged in o
a complex mul i-scale po ous s uc u e (Dolado and Van B eugel, 2011). This appa en incompa ibili y
can be li ed by eso ing o a sui able e ec i e medium heo y (Choy, 2016), which enables us o sub-
s i u e he mic oscopically inhomogeneous pe mi i i y wi h a homogeneous one ha p o ides equi a-
len elec omagne ic p ope ies a he mac o-scale. This p ocedu e equi es knowledge o he cemen
pas e mic o-s uc u e and o he complex pe mi i i y o i s homogeneous componen s, as well as a
p ope choice o he homogeniza ion (e ec i e medium) model. We a e now going o discuss hese
aspec s one by one.
Mic o-s uc u e o he cemen pas e
Common cemen pas es a e p epa ed by mixing a ine powde (clinke ) wi h wa e . This mix u e unde goes
a hyd a ion p ocess whose p oduc s o m he cemen pas e, which g adually ha dens o e ime. Fo OPCs,
hepowde ismadeo ali e,whosechemical o mulaisCa
3SiO5(C3S in cemen chemis no a ion), by up o
70 % (Taylo , 2004). Acco dingly, we ha e conside ed a cemen pas e made by hyd a ing ali e only, o
simpli y he model while cap u ing all he essen ial ea u es o OPCs.
Hyd a ion ime
A
B
CDE
Figu e 3. Simula ion o he ali e hyd a ion p ocess o an ini ial pa icle size dis ibu ion co esponding o N0=
105pa icles pe ð100 mmÞ3
(A) Ske ch o he hyd a ion p ocess o a single ali e pa icle ep esen ing he model used in his wo k.
(B) De ini ion o he adii used o quan i y he pa icles size in his wo k.
(C) Simula ion snapsho o he ini ial cemen powde .
(D) Simula ion snapsho o he pa ially hyd a ed cemen pas e.
(E) Simula ion snapsho o he ully hyd a ed cemen pas e.
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The su ace o he ali e powde pa icles, which a e ypically assumed o be sphe ical (Na i and Pigna ,
1996), dissol es on eac ion wi h wa e . The dissolu ion p oduc s o m shells o calcium silica e hyd a e,
whose chemical o mula is ðCaOÞ3ðSiO2Þ2ðH2OÞ4(CSH in cemen chemis no a ion), a ound he o iginal
pa icles, o o m new pa icles made o po landi e, whose chemical o mula is CaðOHÞ2(CH in cemen
chemis no a ion), by nuclea ion and g ow h in he in e s i ial egions. This p ocess is ske ched in Figu e 3A
and ollows he olume ic o mula (Pigna e al., 2005):
1:0VC3S+1:318 VH2O/1:57 VCSH +0:596 VCH (Equa ion 2)
The esul ing cemen pas e is made o a diso de ed ensemble o wo kinds o domains, namely he ones
wi h a co e o C3S and a shell o CSH, and he ones made o CH only, cha ac e ized by a pseudo-sphe ical
shape.
To gene a e plausible cemen mic o-s uc u es, we ha e simula ed he ali e hyd a ion p ocess wi h he
open sou ce package mic (Bishnoi and Sc i ene , 2009a). In pa icula , we ha e applied he well-es ablished
model om Pigna e al. (2005) o a specimen illed wi h a 0.4 wa e /C3Smass a io,inlinewi hcommon
cemen ecipes, and conside ed ini ial pa icle size dis ibu ions (PSDs) o he ali e powde co esponding
o N0=102;103;104;105;106;107pa icles pe ð100 mmÞ3, o un a el he in e play be ween p ope ies and
mic o-s uc u e. The implemen a ion o his model in mic is well desc ibed in he doc o al hesis by Bishnoi
(2008); o he eade ’s con enience, we ha e epo ed a de ailed desc ip ion in he STAR me hods sec ion.
Table 1 epo s in o ma ion conce ning he inal chemical composi ion, cha ac e ized by he olume ac-
ions , and he esul ing pa icle size s a is ics, quan i ied by he expec a ion alue mand he s anda d de-
ia ion so he adii o he C3S co es, he CSH shells, and he CH pa icles; he de ini ion o he adii is shown
in Figu e 3B. Figu e 3 also shows h ee simula ion snapsho s o N0=105pa icles pe ð100 mmÞ3, co e-
sponding o he ini ial cemen powde (C), he pa ially hyd a ed cemen pas e (D) and he ully hyd a ed
cemen pas e (E). As expec ed, a la ge alue o N0leads o smalle inal sub-domains. Mo e impo an ly,
he size o hese sub-domains is compa able o he he mal adia ion wa eleng hs. The e o e, mic o-s uc-
u al size e ec s a e expec ed o impac he emissi i y p ope ies o he samples, hence p o iding a knob o
une he dielec ic esponse. Finally, i can be seen om he alues o C3S(%5 %) ha ali e is consumed
almos comple ely on ull hyd a ion and can be neglec ed in he homogeniza ion s ep.
Complex pe mi i i y o he cemen pas e componen s
To apply e ec i e medium heo y, he mic o-s uc u al in o ma ion ob ained abo e mus be combined wi h
he complex pe mi i i y o he cemen pas e homogeneous componen s, namely C3S, CSH and CH.
Because a omic ib a ions a e esponsible o he dielec ic esponse in he IR spec al ange whe e he
adia i e coole ope a es, we ha e eso ed o molecula simula ions o ob ain his in o ma ion.
We ha e pe o med hese simula ions wi h he Gene al U ili y La ice P og am (GULP) (Gale, 1997) acco d-
ing o he o ce ield me hod (Leach, 2001). Unde his a omis ic scheme, he in e ac ion be ween a oms is
desc ibed by pa ame e ized in e a omic po en ials so ha he sys em ene gy can be aced back om hei
posi ions. In pa icula , we ha e adop ed a well- es ed pola izable o ce ield, which is known o desc ibe
Table 1. Ini ial numbe o pa icles pe ð100 mmÞ3N0, olume ac ions and s a is ics (expec a ion alues mand
s anda d de ia ions s) o he pa icle adii Ro he simula ed samples a e ull hyd a ion
N0
ð100 mmÞ3
C3S
%
CSH
%
CH
%
m½RC3S
mm
m½RCSH
mm
m½RCH
mm
s½RC3S
mm
s½RCSH
mm
s½RCH
mm
1025 61 23 3.32 12.51 21.94 2.80 1.82 2.49
1035 62 24 0.71 5.20 11.33 1.34 1.89 2.00
1044 63 24 0.11 1.85 5.04 0.42 1.12 1.18
1054 63 24 0.01 0.58 2.27 0.12 0.52 0.58
1064 64 24 0.00 0.17 0.86 0.03 0.21 0.56
1072 66 25 0.00 0.10 0.36 0.01 0.09 0.28
The sum o he olume ac ions is no uni y because he emaining space consis s o emp y po es. The de ini ion o he adii is
depic ed in Figu e 3B.
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co ec ly he s uc u e and elas ic p ope ies o mos cemen i ious phases (Manzano e al., 2009). La e ,
we ha e calcula ed he complex pe mi i i y o C3S, CSH and CH by ollowing he me hod employed in
(Dolado e al., 2020) o s udying he esponse o cemen -based ma e ials in he THz egime.
The co esponding abso p ion coe icien is epo ed in Figu e 4A o all componen s. De ails abou mo-
lecula simula ions and c ys al s uc u es can be ound in he STAR me hods sec ion, whe eas Figu e S2 -
d awn wi h VESTA (Momma and Izumi, 2011)-andTable S1 epo in o ma ion on he uni cells. Rema k-
ably, he b oad abso p ion maximum o CSH, which is he componen wi h he highes olume ac ion (see
Table 1), o e laps signi ican ly wi h he AW, as desi ed. A he same ime, all he componen s exhibi sig-
ni ican abso p ion ou side he AW. This is an ad an age o sola cell applica ions, whe e he sup a-
ambien de ice ope a ing empe a u e ensu es ha he adia i e coole is going o ejec mo e ene gy
han he one ecei ed om he a mosphe e also ou side o he AW, hence enhancing he cooling pe o -
mance (Zhao e al., 2019). Finally, al hough he abso p ion coe icien (104cm1) is no as s ong as he
one o ypical hin- ilm abso be s (106cm1), he possible ealiza ion o hick geome ies s ill allows us
o achie e high abso bance, hence emo ing his appa en weakness.
Complex pe mi i i y o he cemen pas e
The ing edien s equi ed o es ima e he complex pe mi i i y o he gene a ed cemen pas es by a sui -
able e ec i e medium heo y a e now a ailable. Ca e should be aken because B uggeman’s o mula
(B uggeman, 1935), which is he mos commonly used model o he e ogeneous ma e ials, does no ac-
coun o mic o-s uc u e size e ec s. Indeed, i is de i ed in he long-wa eleng h (LW) limi , i.e.,unde
he assump ion ha he pa icles size is much smalle han he wa eleng hs o in e es . Howe e , we
ha e seen abo e ha he size o he cemen sub-domains is compa able o he wa eleng hs a ound he
AW. The e o e, a model capable o cap u ing he main e ec s o mic o-s uc u e on he dielec ic p ope -
ies is needed o p ope ly es ima e he e ec i e complex pe mi i i y o ou cemen pas es. Acco dingly,
we ha e used a ecen model p oposed by Slo ick (2017) o a diso de ed ensemble o sphe ical pa icles
wi h a space illing ma ix o in ini esimally small sphe es. This is ep esen a i e o ou cemen pas e, made
o a high-densi y diso de ed ne wo k o CSH and CH sphe es wi h a mean adius dependen on he ali e
ini ial PSD acco ding o Table 1, sepa a ed by emp y in e s ices (po es). Acco ding o Slo ick’s model,
he e ec i e complex pe mi i i y εe o his sys em can be ob ained by sol ing he equa ion:
CSH
εCSH FðkCSH RCSHÞεe
εCSH FðkCSH RCSHÞ+2εe
+ CH
εCH FðkCH RCHÞεe
εCH FðkCH RCHÞ+2εe
+ ai
1εe
1+2εe
=0 (Equa ion 3)
whe e ,εand ka e olume ac ion, complex pe mi i i y and complex wa e ec o , and FðxÞ=2ðsinx
xcosxÞ=½xcosx+ðx21Þsinx(Belyae and Tyu ne , 2018). I is wo h no ing ha Equa ion 3 becomes
A
B
Figu e 4. Abso p ion spec a o he ma e ials s udied
(A) Calcula ed abso p ion coe icien o he homogeneous componen s o cemen pas es made by hyd a ing ali e
powde .
(B) E ec i e abso p ion coe icien o he gene a ed cemen pas es as a unc ion o he mean pa icle (sub-domain) adii
ðRCSH;RCHÞ.
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B uggeman’s o mula in he LW limi becauseFðx/0Þ/1. Fu he mo e, by making no dis inc ion be ween
backg ound medium and inclusions, he o mula is alid o any olume ac ion, con a ily o Maxwell-
Ga ne o mula, which is alid only o a low olume ac ion o he inclusions (Ma kel, 2016).
Figu e 4B epo s he ob ained cemen pas e abso p ion coe icien as a unc ion o he mean pa icle (sub-
domain) adii ðRCSH;RCHÞ. The spec a exhibi inc eased abso p ion a wa eleng hs compa able o he pa -
icles size, because o he mul iple e lec ions occu ing a he pa icle bounda ies, leading o in e e ence
e ec s and enhanced abso p ion leng hs, simila ly o he case o plana laye s. As he pa icles become
smalle , he addi ional abso p ion band shi s owa d he UV- isible ange (sho e wa eleng h) and, e en-
ually, size e ec s become negligible in he IR ange, which can hen be desc ibed in he LW limi (see he
case ðRCSH;RCHÞ=ð0:1;0:4Þmm). The e en ual addi ional emissi i y in he UV- isible ange is no going o
impac he adia i e coole pe o mance, because i s adia ed spec al powe densi y is gi en by he p od-
uc o i s emissi i y spec um (%1) wi h he spec al powe densi y adia ed by a black-body (Balaji, 2014),
which is negligible in he UV- isible spec um a e es ial empe a u es.
These esul s show ha he abso p ion p ope ies o he cemen pas e can be uned by modi ying i s mic o-
s uc u e and ailo ed o he spec al equi emen s o adia i e cooling. As a ma e o ac , a simila
app oach has been applied o hie a chical po ous polyme s men ioned in he In oduc ion (Mandal
e al., 2018).
Al hough his is e y p omising, ca e should be aken. Indeed, modeling he cemen pas e mic o-s uc u e
as an ensemble o ai -embedded sphe ical inclusions is a geome ical app oxima ion because hese a e
e en ually going o ‘‘collide’’ du ing g ow h and pa ially ‘‘de o m’’. In addi ion, e ec i e medium heo ies
assume ha all pa icles a e subjec o he same mean ield. De ia ions migh occu close o he pe cola ion
h eshold. These aspec s should be in es iga ed in u u e s udies.
These esul s a e ex emely encou aging, bu no enough. Indeed, a la ge abso p ion coe icien does no
necessa ily imply a s onge abso bance because i s ems om a la ge ex inc ion coe icien ha migh
also inc ease he laye e lec ance a he same ime. The e o e, mo e adia ion could be los by e lec ion
be o e e en en e ing he cemen pas e, hence leading o a educed abso bance, as we shall see in a
momen .
Emissi i y o he cemen pas e
We ha e used he e ec i e complex pe mi i i y εe calcula ed abo e o de e mine he spec al di ec ional
abso bance Acool
U;lðl;qÞo laye s made o he gene a ed cemen s by he ans e -ma ix me hod. We ha e
conside ed cemen slabs wi h a hickness o 100 mm. Indeed, based on he abso p ion coe icien alues e-
po ed in Figu e 4B, nanome e -scale hicknesses, al hough expe imen ally easible (Rheinheime and Casa-
no a, 2012), a e unsui able o ob ain la ge abso bance/emissi i y because o he lack o abso p ion s eng h.
This is clea ly no an issue wi h cemen -based solu ions, o which e y hick geome ies a e usually p e e ed.
As a ma e o ac , we a e op ing o a a he hin cemen laye , which co esponds o a wo s case scena io
and makes ou assessmen s onge . Fu he mo e, his choice le us d aw conclusions also abou conc e e,
whe e agg ega es a e going o b eak he cemen pas e con inui y and make he e ec i e hickness smalle .
Finally, his hickness has been expe imen ally achie ed in he li e a u e (Zhang e al., 2016).
Implemen a ion-wise, we ha e adop ed a gene alized TMM capable o desc ibing incohe en p opaga ion
h ough laye s ha ing ough su aces wi h Gaussian diso de (Ka sidis and Siapkas, 2002;Cen u ioni, 2005).
This model is ep esen a i e o cemen slabs, ypically cha ac e ized by andomly diso de ed su aces wi h
oughness alues om a ew hund ed nanome e s o a ew mic ome e s, depending on polishing (Apedo
e al., 2015). This kind o ough su aces can p o ide an ad an age in e ms o emissi i y, because hey ha e
been shown o educe e lec ion and inc ease abso p ion o an incoming elec omagne ic wa e by andom-
izing i s di ec ion and enla ging he e ec i e abso p ion leng h (ligh - apping) (Yablono i ch, 1982;Ko-
walczewski e al., 2012;Cappellu i e al., 2018).
Ou calcula ions a e in ag eemen wi h hese s a emen s and show ha a oughe su ace sligh ly inc eases
he abso bance o ou cemen slabs. Because o hei supplemen a y na u e, hese esul s on he e ec o
su ace oughness a e shown in Figu e S3 and only he wo s case o a la su ace is conside ed in he main
ex . The STAR me hods sec ion con ains a de ailed desc ip ion o he gene alized TMM used.
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whe e LBB
e;U;lis he spec al di ec ional adiance o a black-body a empe a u e Twi h an applied ol age V
(Wu
¨ el, 1982):
LBB
e;U;lðl;T;VÞ=2hc
2
l5
1
exphc
=lqV
kT 1
JMPP and VMPP a e he sola cell elec ic cu en densi y and ou pu ol age a maximum powe poin (MPP),
espec i ely, calcula ed wi h he Shockley-Queisse model. l,U,h,c,kand qa e wa eleng h, solid angle,
Planck’s cons an , speed o ligh in acuum, Bol zmann’s cons an and elemen a y cha ge, espec i ely.
The o he symbols ha e been de ined in he main ex . The eade is e e ed o he li e a u e o mo e de-
ails conce ning he de ini ion o he adiome y quan i ies in oduced abo e (Balaji, 2014).
Ali e hyd a ion model
We ha e simula ed he ali e hyd a ion p ocess depic ed in Figu e 3 by implemen ing he model om Pigna
e al. (Pigna e al., 2005) in o he open-sou ce chemical kine ics package mic (Bishnoi and Sc i ene , 2009a),
as done by Bishnoi in his doc o al hesis (Bishnoi, 2008). We ha e conside ed a cubic specimen o 100 mm
side leng h wi h pe iodic bounda y condi ions ini ially illed wi h a con inuum o wa e and disc e e C3S
sphe ical pa icles in a wa e /C3S mass a io o 0.4 (Bishnoi and Sc i ene , 2009b), in line wi h common
cemen ecipes. We ha e conside ed di e en ini ial pa icle size dis ibu ions (PSDs), which we e p o ided
wi h he so wa e, co esponding o an ini ial numbe o ali e pa icles N0wi hin he 100 mm-side-leng h
cube equal o 102,10
3,10
4,10
5,10
6and 107, so ha we could in es iga e he ole o mic o-s uc u e in
hede e mina iono he adia i ecoolingp ope ies.The a eo hehyd a ionp ocess,whichisdesc ibed
by he olume ic o mula gi en in Equa ion 2 unde a mass densi y o 3:15 g cm3 o C3S, 2:0gcm
3 o
CSH and 2:24 g cm3 o CH, is con olled by he dec ease in size o he C3S pa icles. In u n, his is ela ed
o he o ma ion a e o CSH and CH. CSH shells o m on o he C3S pa icles su ace by he combina ion o
h ee mechanisms, namely a nuclea ion and g ow h mechanism, a phase bounda y mechanism, and a di u-
sion con olled mechanism. The co esponding equa ions a e:
dRC3S
d =3k1 2expk1 3
dRC3S
d =k2
dRC3S
d =k3
RCSH RC3S
whe e k1=1:14 3104h3,k2equals he minimum o he igh -hand-side o he i s equa ion, and k3=
0:01 mm2h1(Pigna e al., 2005;Bishnoi, 2008). A he same ime, new CH pa icles o m a an exponen-
ially dec easing nuclea ion a e in he in e s i ial egions o he hyd a ing cemen pas e acco ding o he
o mula
nð Þ=nmax1expða Þ
whe e nmax is se o one- i h o N0(Na i and Pigna , 1996)anda=0:213 h1(Jennings and Pa o , 1986).
Thei g ow h occu s andomly bu cons ained by he amoun o p oduc a ailable acco ding o he hyd a-
ion eac ion a e.
Molecula simula ions and c ys al s uc u es
To ob ain he IR dielec ic p ope ies o he cemen pas e componen s, we ha e pe o med molecula sim-
ula ions wi h he Gene al U ili y La ice P og am (GULP) (Gale, 1997) acco ding o he o ce ield me hod
(Leach, 2001), by adop ing a well- es ed pola izable o ce ield, which is known o desc ibe co ec ly he
s uc u e and elas ic p ope ies o mos cemen i ious phases (Manzano e al., 2009).
Fo he a omis ic s uc u e o he almos amo phous CSH, we ha e employed he model p oposed in (Do-
lado e al., 2020)and(Duque Redondo, 2018), which co esponds o a e y la ge sys em whose exac s oi-
chiome y is ðCaOÞ254ðSiO2Þ152ðH2OÞ306. Fo he c ys alline s uc u es o C3S and CH, we ha e elaxed he
expe imen al uni cells measu ed in (Mumme, 1995)and(Desg anges e al., 1993), espec i ely. The
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s oichiome y and he inal simula ion cell pa ame e s a e disclosed in Table S1. The uni cells d awn wi h
he so wa e VESTA (Momma and Izumi, 2011) a e depic ed in Figu e S2.
La e , we ha e calcula ed he complex pe mi i i y o C3S, CSH and CH by ollowing he me hod
employed in (Dolado e al., 2020) o s udying he esponse o cemen -based ma e ials in he THz egime.
The me hod eso s o exp essing he dielec ic enso in e ms o he oscilla o s eng hs o he ib a ional
modes as
εijðuÞ=εijð+NÞ+4p
VX
m
Um
ij
u2
mu2
whe e uis he angula equency, Vis he uni cell olume, mis hephononmode ank,anduma e he
mode-speci ic equencies. The oscilla o s eng h enso o each ib a ional mode mdepends on he
Bo n e ec i e cha ges qBand he eigen ec o eij o ha modeacco ding o
Uab = X
N
i
qB
iajeij
ffiffiffiffiffiffi
mi
p! X
N
i
qB
ibjeij
ffiffiffiffiffiffi
mi
p!
wi h mideno ing he ion masses. In he p ac ical compu a ional implemen a ion, we ha e used a small
damping e m do 10 cm1by he subs i u ion u2/uðu+idÞ. Finally, we ha e a e aged he p incipal com-
ponen s o he dielec ic enso , i.e.,weha e akenεðuÞ=P3
i=1εiðuÞ=3, in ag eemen wi h he diso de ed
mic o-s uc u al na u e o cemen s, which li s o any p e e ed o ien a ion.
Gene alized ans e -ma ix-me hod
We ha e used a gene alized o m o he ans e -ma ix me hod capable o desc ibing incohe en p opa-
ga ion and ough su aces. In pa icula , he su ace heigh a ia ion is supposed o ollow a Gaussian p ob-
abili y dis ibu ion wi h a gi en oo -mean-squa e alue (RMS) (Ka sidis and Siapkas, 2002;Cen u ioni,
2005).
The ampli ude Eo he elec ic ields p opaga ing om le o igh ( +)and igh ole ()on hele (L)
and igh (R) sides o he laye a e ela ed by he o mula:
0
@E+
L2
EL21
A=ðDLPD
RÞ0
@E+
R2
ER21
A
whe e DLand DRdesc ibe he ield p opaga ion ac oss he le and igh in e aces be ween he laye and
acuum, espec i ely, and Pac oss he laye . Thei o mulas a e
D=1
j l j21j lj2
j l j2j l lj2j l lj2
P= exp ðidÞ20
0exp ðidÞ2!
wi h
l = ð0Þ
l exp"22pRMS Nl
l2#
l = ð0Þ
l exp"1
22pRMS
l2
ðN NlÞ2#
d=2pNdcosq
l
The subsc ip s l and deno e le and igh sides o he in e ace, while l means om he le o he
igh side o he in e ace. A g aphical ep esen a ion o he quan i ies in oduced can be ound in
Figu e S5.
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ð0Þ
l and ð0Þ
l a e he F esnel e lec ion and ansmission coe icien s o a smoo h plana su ace ( o which we
ha e used he a e age be ween he sand ppola iza ion alues), Nis he complex e ac i e index, dis he
laye hickness, and qis he e ac ion angle.
The spec al di ec ional e lec ance, ansmi ance and abso bance a e eadily ob ained, espec i ely, om
he ollowing o mulas:
RU;lðl;qÞ=ðDLPD
RÞ21
ðDLPD
RÞ11
TU;lðl;qÞ=1
ðDLPD
RÞ11
AU;lðl;qÞ=1RU;lðl;qÞTU;lðl;qÞ
The (hemisphe ical) spec al e lec ance, ansmi ance and abso bance a e simply he angula a e age o
hei spec al di ec ional coun e pa s. Fo example, he spec al e lec ance is calcula ed as ollow o a
sys em wi h azimu hal in a iance such as he de ice depic ed in Figu e 2A:
RlðlÞ=2Zp=2
0
dqRU;lðl;qÞcosðqÞsinðqÞ
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