A comprehensive review of C-S-H empirical and computational models, their applications, and practical aspects

Cemen and Conc e e Resea ch 156 (2022) 106784
A ailable online 7 Ap il 2022
0008-8846/© 2022 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by-
nc-nd/4.0/).
A comp ehensi e e iew o C-S-H empi ical and compu a ional models,
hei applica ions, and p ac ical aspec s
Edua do Duque-Redondo
a
,
b
,
*
, Pa ick A. Bonnaud
c
, Hegoi Manzano
d
a
School o Enginee ing, Newcas le Uni e si y, NE1 7RU Newcas le upon Tyne, UK
b
Physical Chemis y Depa men , Uni e si y o he Basque Coun y UPV/EHU, Ap do. 664, 48080 Bilbao, Spain
c
Resea ch O ganiza ion o In o ma ion Science and Technology, Depa men o Compu a ional Science and Technology, 1-18-16 Hamama sucho, Mina o 105-0013,
Tokyo, Japan
d
Fisika Saila, Uni e si y o he Basque Coun y UPV/EHU, Ap do. 664, 48080 Bilbao, Spain
ARTICLE INFO
Keywo ds:
Calcium silica e hyd a e
Molecula models
Molecula simula ion
A omic s uc u e
Nanos uc u e
ABSTRACT
The C-S-H gel is an elusi e ma e ial. I s a iable composi ion and diso de ed na u e complica e a comple e
cha ac e iza ion o i s a omic s uc u e, and he elabo a ion o models is key o unde s anding i . This wo k aims
o e iew hose p oposed models, di iding hem in o empi ical and compu a ional models. A e a b ie
desc ip ion o ela ed c ys alline calcium silica e hyd a es, empi ical C-S-H models based on in e p e a ion o
expe imen al da a a e p esen ed. Then, we ocus on he his o ic de elopmen o a omis ic models o s udy he C-
S-H, un il he cu en s a e o he a . We desc ibe cu en compu a ional C-S-H models buil om he empi ical
models and compu e simula ions. We e iew common applica ions o hese compu a ional models: he
aluminum inco po a ion, he elas ic and mechanical p ope ies, he di usion o wa e and ions in nanopo es, and
C-S-H/o ganic composi es. Finally, we discuss some p ac ical aspec s o he compu a ional models and hei
in e p e a ion, as well as possible u u e di ec ions.
1. In oduc ion
O dina y Po land cemen is a guably he mos consumed man-made
ma e ial wo ldwide. As such, he e is a as amoun o empi ical in o -
ma ion on he ma e ial and how o con ol i s wo kabili y, du abili y, o
s eng h [1–4]. Thus, i is su p ising how much emains unknown om a
undamen al poin o iew, especially i we compa e cemen o o he
cons uc ion ma e ials like s eel, o commonly used ma e ials like sili-
con. The lack o knowledge is pa icula ly no able a he nanoscale,
whe e he complex, mul icomponen , po ous, and diso de ed s uc u e
o cemen hyd a es complica es he expe imen al cha ac e iza ion o he
ma e ial. The dominan phase a ha scale is he Calcium Silica e Hy-
d a e (C-S-H) gel, an X- ay amo phous p oduc wi h a iable chemical
composi ion and s uc u e. The C-S-H gel is he glue ha agglome a es
o he c ys alline hyd a ion p oduc s and agg ega es, gi ing cohesion o
he ma e ial, and is mainly esponsible o cemen 's mechanical p op-
e ies and du abili y.
Plausible s a egies o inc ease cemen 's pe o mance and educe i s
en i onmen al oo p in include a ine con ol o he C-S-H gel s uc u e,
p ope ies, o i s p ecipi a ion kine ics. T adi ionally an empi ical ial-
e o app oach has been used o hose ends [5–7], ye mos ecen
s udies bene i om he exis ing in o ma ion a he a omic scale o
design bo om-up syn he ic app oaches [8–12]. To ex ac aluable in-
o ma ion om he a ailable as amoun o expe imen al da a, he
obse a ions mus be condensed in o comp ehensi e models consis en
wi h as much as possible da a. Many di e en models ha e been p o-
posed so a o a ionalize he expe imen al indings and unde s and he
a omic s uc u e o he C-S-H gel. Ideally, hose models should be able
no only o explain expe imen al obse a ions bu also be p edic i e, and
help o de ise a ma e ial wi h ailo ed p ope ies.
In his pape , we aim o desc ibe b ie ly mos o he models o he C-
S-H gel s uc u e p oposed in he li e a u e. We di ided hem in o wo
ca ego ies: empi ical models and compu a ional models. The i s g oup
includes sugges ions made on he basis o expe imen al ac s collec ed
o e six decades. These empi ical models aimed o desc ibe he C-S-H gel
s uc u e by compa ison wi h ela ed c ys als like po landi e o he
obe mo i e amily and o en included s oichiome ic o mulas. The
second g oup co e s he mo e de ailed a omic-scale models de eloped
in he las decade using compu a ional simula ions. These models y o
de ine he C-S-H gel s uc u e wi h he g ea es possible de ail,
* Co esponding au ho a : School o Enginee ing, Newcas le Uni e si y, NE1 7RU Newcas le upon Tyne, UK
E-mail add esses: [email p o ec ed] (E. Duque-Redondo), [email p o ec ed] (P.A. Bonnaud), [email p o ec ed] (H. Manzano).
Con en s lis s a ailable a ScienceDi ec
Cemen and Conc e e Resea ch
jou nal homepage: www.else ie .com/loca e/cemcon es
h ps://doi.o g/10.1016/j.cemcon es.2022.106784
Recei ed 31 May 2021; Recei ed in e ised o m 15 Ma ch 2022; Accep ed 17 Ma ch 2022
Cemen and Conc e e Resea ch 156 (2022) 106784
2
speci ying he coo dina es (spa ial posi ion) o e e y a om in he ma-
e ial. Nowadays, one g oup canno be unde s ood wi hou he o he . On
he one hand, empi ical models a e “jus ” schema ic ep esen a ions ha
compile expe imen al in o ma ion, ye hey se he s uc u al condi ions
and s oichiome ic ules ha should be ul illed in he compu a ional
model cons uc ion. On he o he hand, a omic-scale compu a ional
models based on he empi ical ules go beyond a me e desc ip ion and
can be used o compu e ac ual C-S-H p ope ies, o help in he in e -
p e a ion o expe imen al da a, o e en con ibu e wi h new in o ma ion
inaccessible o expe imen s. Examples o how C-S-H modeling is used o
ge insigh s in o and deep unde s anding a e p o ided in Sec ion 5.
The emaining pape is o ganized as ollows: i s , we will in oduce
b ie ly he c ys alline phases commonly used as s a ing poin s o C-S-H
model cons uc ion. Second, we will su ey he empi ical models p o-
posed o e he yea s o desc ibe he C-S-H gel and he ecen compu-
a ional models. Due o he inc easing in e es in a omis ic simula ion,
we will e iew he main applica ions o compu a ional models such as
he s udy o he aluminum inco po a ion in o he C-S-H gel, i s elas ici y,
and mechanical p ope ies, he nanocon ined wa e wi hin he C-S-H gel
laye s, he ion di usi i y, and he o ma ion o C-S-H/o ganic hyb id
composi es. We skipped o he opics o g ea in e es like C-S-H nucle-
a ion and g ow h o C-S-H ca bona ion because much less li e a u e is
a ailable ye . Finally, we will discuss p ac ical aspec s and ou
pe spec i e on u u e di ec ions.
2. C ys alline s uc u es ela ed o C-S-H
The C-S-H gel is an X- ay amo phous ma e ial and does no p esen
long- ange o de like a c ys al. Howe e , i is possible o ind sho - ange
o de a he a omic scale. NMR, IR-spec oscopy, synch o on X- ay
di ac ion, and SANS expe imen s among o he s [13–19], e eal he C-
S-H gel simila i ies wi h c ys alline calcium silica e hyd a es [20] like
wollas oni e, jenni e, hilleb andi e, and specially obe mo i e. The e is a
gene al consensus ha he C-S-H s uc u e is simila o he obe mo i e
amily membe s [21], wi h a conside able numbe o s uc u al de ec s
and a iable s oichiome y e en a low Ca/Si a ios [22].
The obe mo i e supe g oup is he classi ica ion o a amily o min-
e als wi h a laye ed s uc u e simila o clays. The amily includes
a ious membe s o he obe mo i e g oup plus ela ed mine als like
plombi`
e i e, clino obe mo i e, and i e sidei e. They di e in he basal
spacing ( ela ed o he hyd a ion deg ee) and cell symme y. Plom-
bi`
e i e, clino obe mo i e, and i e sidei e exhibi basal spacing o 1.4,
1.1, and 0.9 nm, espec i ely, and ha e Ca/Si a ios o 5/6, wi h com-
posi ions: Ca
5
Si
6
O
16
(OH)
2
⋅7H
2
O, Ca
5
Si
6
O
17
⋅5H
2
O and Ca
5
Si
6
O
16
(OH)
2
espec i ely. The basal spacing in he obe mo i e g oup is ~1.1 nm and
he Ca/Si a io is no always 5/6. The gene al o mula o he obe mo i e
g oup is Ca
4+x
(Si
6
)O
15+2x
(OH)
2−2x
⋅5H
2
O, wi h 0 ≤x ≤1. Thus, he
endmembe composi ions co espond o obe mo i e Ca
5
Si
6
O
17
⋅5H
2
O
(x =1) and o keno obe mo i e, Ca
4
Si
6
O
15
(OH)
2
⋅5H
2
O (x =0). In
gene al, he obe mo i e supe g oup membe s a e made o laye s, each
o hem consis ing o a cen al calcium oxide shee , sha ing oxygens wi h
d eie ke en o wollas oni e-like silica e chains a each side o i . These
chains un pa allel o he b c ys allog aphic axis, and d eie ke en de-
no es an a angemen ha epea s e e y h ee silica e uni s. In obe -
mo i e, wo consecu i e uni s, deno ed as pai ing si es, a e linked o he
cen al calcium oxide laye sha ing wo ou o hei ou oxygen a oms.
The hi d silica e uni , called b idging si e, is o ien ed owa ds he
in e lamina space o s e ic easons [23]. The Ca a oms in he cen al
calcium oxide shee ollow a zig-zag a angemen , wi h poo ly sym-
me ic 7- old coo dina ion o oxygen a oms [24]. This s uc u al mod-
ule, cha ac e ized by a cen al calcium oxide shee wi h 7- old
coo dina ion sandwiched be ween d eie ke en o wollas oni e-like
chains, is known as a “complex module” [25]. In he c ys al, he cal-
cium silica e laye s lie on he xy o (001) plane, while he pe iodici y in
he z-di ec ion comes om he s acking o laye s. The in e laye space is
illed by wa e and ex a calcium ions which p o ide cohesion ia
dispe si e and elec os a ic in e ac ions espec i ely (see Fig. 1) [26]. As
men ioned be o e, he obe mo i e supe g oup comp ises se e al poly-
ypes: he main ones being obe mo i e 0.9 nm, obe mo i e 1.1 nm, and
obe mo i e 1.4 nm (see Fig. 1). These poly ypes di e mainly in he
basal spacing ( he dis ance in he z c ys allog aphic di ec ion be ween
he cen e o wo consecu i e laye s), which is wide as he hyd a ion
deg ee inc eases. Thus, om obe mo i e 1.4 nm, i is possible o ob ain
obe mo i e 1.1 nm, and obe mo i e 0.9 nm by hea ing o dehyd a ion.
Ano he impo an di e ence be ween poly ypes is he in e laye c oss-
link in obe mo i e 1.1 nm. The silica e chains om adjacen laye s can
be linked in he c c ys allog aphic di ec ion by condensa ion o he
b idging si es, o ming a double wollas oni e chain wi h “zeoli ic ca -
i ies”. The p o ona ion and Al con en o silica e chains, as well as he Ca
con en in he ca i ies, de ine he dehyd a ion beha io o he 1.1 nm
poly ype, which is so ed in o no mal and anomalous a ie ies. Thus, he
p esence o in e laye c oss-linkages in anomalous obe mo i es e-
s ains he sh inkage du ing he dehyd a ion, main aining hei cha -
ac e is ic basal spacing, while he absence o in e laye Si-O-Si linkages
in no mal obe mo i es, allows he dec ease o he basal spacing and he
ans o ma ion o obe mo i e 1.1 nm in o obe mo i e 0.9 nm [27,28].
Recen s udies [19,29] sugges ed clino obe mo i e as he obe mo -
i e amily membe ma ching he bes wi h he C-S-H gel a omic s uc-
u e.The di e ences be ween clino obe mo i e and obe mo i e 1.1 nm
a e sub le, and hey end o coexis [21]. Thei composi ion is e y
simila , ye he hyd oxyl g oups o he b idging e ahed a a e missing in
clino obe mo i e, esul ing in he s oichiome y Ca
5
Si
6
O
17
×5H
2
O.
Fu he mo e, he o ien a ion o he op and bo om b idging e ahed a
o a gi en laye al e na e le and igh , while in obe mo i e 1.1 nm hey
poin in he same di ec ion. This di e ence has been classi ied by
naming he complex modules (see Fig. 2) as A and B o clino obe mo i e
and obe mo i e 1.1 nm espec i ely.
Hamid's obe mo i e mus be also men ioned he e [30]. I was an
ea ly a emp o esol e he c ys alline s uc u e o obe mo i e 1.1 nm.
The basal dis ance is 1.117 nm, which is sho e han he one o he
no mal o anomalous obe mo i e 1.1 nm. The s oichiome y is
Ca
4.5
Si
6
O
15
(OH)
3
×2H
2
O. In con as o Me lino's obe mo i e 1.1 nm,
Hamid's model does no include in e laye c oss-links be ween b idging
silica es om adjacen laye s. Like in obe mo i e 0.9 nm and 1.4 nm,
he silica e chains om adjacen laye s a e shi ed in he b c ys allo-
g aphic di ec ion by b/2, so he b idging si es do no ace each o he .
The laye s a e also shi ed in he z c ys allog aphic axis by z/4, so hey
a e no loca ed in he same clea age (see Fig. 2).
Jenni e desc ip ion is also included he e because his o ically i was
conside ed as a possible model o he C-S-H gel wi h high Ca/Si a ios
[31]. Nowadays, he models based on jenni e ha e los in e es . Recen
expe imen s show ha high Ca/Si a io s uc u es can be also o med
main aining a obe mo i e-like s uc u e, and bo h expe imen al and
heo e ical wo ks indica e ha obe mo i e s uc u al inge p in s
ma ch wi h he C-S-H [32–34]. Jenni e can be ound combined wi h
obe mo i e in na u e o can be ob ained by hyd o he mal syn hesis
[35,36]. I has a s oichiome y Ca
9
Si
6
O
18
(OH)
6
×8H
2
O and a Ca/Si
a io o 1.55. The s uc u es o jenni e and obe mo i e a e ela ed, since
hey bo h ha e a laye ed s uc u e and wollas oni e-like silica e chains.
Howe e , he e a e wo al e na ed calcium oxide slabs in each laye o
jenni e, which allows he b idging silica es o be connec ed o he cal-
cium oxide laye . In addi ion, he highe calcium con en o jenni e
implies ha he calcium coo dina ion polyhed al, hexagonal in his case,
a e comple ed wi h hyd oxyl g oups.
3. Empi ical C-S-H gel models
In ecen yea s he e is a clea shi om empi ical models o
compu a ional models, so e y ew addi ions ha e been done la ely.
Ne e heless, he e a e a couple o no ewo hy wo ks ha should be
men ioned. In his sec ion, we will e isi he mos ele an empi ical
models p oposed o desc ibe he C-S-H gel s uc u e. We mus men ion
E. Duque-Redondo e al.
Cemen and Conc e e Resea ch 156 (2022) 106784
3
ha he e is an ex ensi e e iew by Richa dson in [20] discussing hese
models in g ea de ail.
Laye ed C-S-H models we e i s p oposed in 1952 by Be nal and
cowo ke s based on he X- ay di ac ion (XRD) pa e ns [37,38]. Fi s ,
hey sugges ed ha wo ypes o C-S-H we e ob ained om cemen hy-
d a ion, bo h o hem we e he esul o a po landi e modi ica ion ia
condensa ion o monome ic silica e anions [37]. Thei gene al s oichi-
ome y was Ca[SiO
2
(OH)
2
][Ca(OH)
2
]
x
, wi h an ex a amoun o wa e .
La e , o he au ho s also p oposed models based on po landi e and
monome ic silica e g oups. In 1969, Shpyno a e al. [39] pos ula ed a
Ca
3
(SiO
4
)(OH)
2
s oichiome y, as a esul o he condensa ion o he 4
hyd oxyl g oups o an o hosilicic acid molecule wi h po landi e. In
1986, G udemo e al. [40] p oposed again a po landi e-silica e mono-
me model simila o he p e ious ones. Howe e , all hese models we e
soon dep eca ed due o he inconsis ency wi h he expe imen al dis i-
bu ion o silica e g oups ound by
29
Si NMR measu emen s [41,42], in
which he chains ollow he ule 3n −1 wi h n being an in ege .
Also in 1952, Be nal, Je e y, and Taylo [38] poin ed o he i s
ime o he ela ionship be ween he a omic s uc u e o C-S-H gel and
obe mo i e. They analyzed by XRD he hyd a ion p oduc o icalcium
silica e and cemen samples, concluding ha “ou o en (samples) o
which single c ys al o o ien ed ibe da a could be ob ained, se en had
one axis o 3.65 o 2 x 3.65 Å" [38], being hose leng hs equal o he
mine al i e sidei e ( obe mo i e 0.9 nm [21]). They s essed ha he
ma ked ib ous cha ac e o he C-S-H was consis en wi h hose min-
e als, ye hey do no explain u he de ails on he di e ences be ween
obe mo i e and he C-S-H.
A ew yea s la e , in 1956, Taylo and Howison add essed he di -
e ences in composi ion be ween obe mo i e and he C-S-H, especially
he high Ca/Si a io o he la e [43]. Based on he ac ha he silica e
chains in obe mo i e ha e a d eie ke en a angemen , hey pos ula ed
ha a pa ial omission o some b idging silica e e ahed a and hei
eplacemen by calcium ions in he in e laye spaces could inc ease he
Ca/Si a io o obe mo i e om 0.83 up o 1.5. [43]. This is in p ac ice
he i s men ion o a C-S-H model based on obe mo i e wi h ini e
silica e chains, and al eady in oduced he main mo i s ha nowadays
a e s ill conside ed he sou ce o C-S-H diso de .
In he ea ly 60s, Ku czyk and Schwie e measu ed he Ca/Si a io o
he C-S-H o med in icalcium and dicalcium silica es, ob aining alues
anging om 1.80 o 1.92 [44,45]. Assuming a obe mo i e-like C-S-H
e aining i s in ini e silica e chains, hey explained he disc epancy
en isioning a C-S-H gel in which calcium ca ions and hyd oxyl anions
we e loca ed in he in e laye space o obe mo i e. A he same ime,
Kan o, B unaue , and Weiss sugges ed ha he high Ca/Si a io could be
eached due o speci ic a angemen s o sandwiched obe mo i e laye s
be ween calcium hyd oxide ones [46], while Fujii and Kondo conside ed
ha was due o a solid solu ion o obe mo i e and po landi e [47].
Howe e , all hese models conside ed in ini e silica e chains, which is
no consis en wi h expe imen al obse a ions.
In he 1980s, S ade and Wieke designed a model based on he
obe mo i e s uc u e wi h ini e silica e chains [48,49]. They p oposed
a dual model: one pu ely dime ic, and ano he one mixing dime ic and
polyme ic chains. These models assumed ull p o ona ion o he silica e
chains and we e limi ed o he composi ions s udied by he au ho s, wi h
Ca/Si a ios below 1.25. [48,49]. Glasse e al. [50] ex ended he
dime ic model assuming pa ial dep o ona ion o he silica e chains and
adding ex a Ca ions o coun e balance he cha ge, eaching Ca/Si a ios
up o 1.4.
Based on his p e ious model [43], Taylo en isaged in 1986 a C-S-H
gel model buil by a combina ion o s uc u al uni s o obe mo i e and
jenni e [17,51]. Acco ding o his wo k, he pa ial dele ion o some
silica e b idging e ahed a om he in ini e silica e chains o obe -
mo i e and jenni e's s uc u es esul s in highe Ca/Si a ios and ini e
silica e chains ha ollow he 3n −1 ule. In con as o i s p e ious
model, he in e laye calcium emains unchanged since i is assumed
ha he dele ed b idging e ahed a ha e only one hyd ogen and one o
he new ends o he ini e silica e chains is p o ona ed, main aining he
elec oneu ali y o he sys em wi hou adding ex a Ca.
Fig. 1. (a) De ail o he calcium silica e laye , he main s uc u al mo i in calcium silica e hyd a es. (b) De ail o he d eie ke en o wollas oni e-like a angemen in
he silica e chains, and he 7- old coo dina ion o Ca. (c) A omic ep esen a ion o he s uc u e o obe mo i e 0.9 nm (d) obe mo i e 1.1 nm and (e) obe mo i e 1.4
nm. The p isms o med by he dashed lines ep esen he uni cells o he poly ypes o obe mo i e. To acili a e he isualiza ion o hei laye ed s uc u e, he uni
cells ha e been eplica ed 2 imes along he b-axis in all cases and 1 along he c-axis o he obe mo i e 0.9 nm. Silica e a oms a e shown in pu ple, calcium a oms in
o ange, and oxygen a oms in ed. The in e lamina wa e molecules a e ep esen ed by a blue ball in he molecula cen e o mass, and all hyd ogen a oms a e
omi ed o a be e iew. (Fo in e p e a ion o he e e ences o colou in his igu e legend, he eade is e e ed o he web e sion o his a icle.)
E. Duque-Redondo e al.
Cemen and Conc e e Resea ch 156 (2022) 106784
4
In he 1990s, a gene al model was p oposed by Richa dson and
G o es [52–54] based on he s oichiome y o obe mo i e, jenni e, and
po landi e. This model pic u es he C-S-H gel as ini e silica e chains
ollowing he 3n −1, joined o calcium hyd oxide laye s, o o m
s uc u es ha locally can esemble obe mo i e, jenni e, o po landi e.
The C-S-H gel could be hen a mix u e o obe mo i e-like egions and
jenni e-like o po landi e egions. They also in oduced a a iable
p o ona ion o he silica e chains and conside ed he p esence o a
a iable amoun o calcium and hyd oxyl g oups in he in e laye space
o compensa e o he cha ge imbalance [52]. The o mula ion o he C-
S-H p oposed in his model includes possible subs i u ions o in-
co po a ions o gues ions [54,55]. They w o e a gene al s oichiome ic
o mula by conside ing he di e en s uc u al uni s o hei model:
[Ca2nHw(Si1−aRa)3n−1O9n−2]Ic+
a
c(3n−1)(OH)w+n(y−2)Cany
2⋅mH2O(1)
whe e he numbe o silanol g oups is gi en by w and he deg ee o
p o ona ion is de ined as w/n. The e m in b aces co esponds o he
calcium and silica e laye s, while he o he e ms a e ex a ions and
wa e . R is e e ed o i alen ions, such as aluminum, ha subs i u e
b idging silicon ions, I ep esen he mono alen o di alen ca ions ha
ensu e he elec oneu ali y a e alio alen subs i u ions and c is he
o mal cha ge o hese ca ions. This o mula is ex emely lexible and
can i ually i wi h any possible se o de ec s ha he a omic s uc u e
o a C-S-H model based on obe mo i e could ha e. Taylo in [17]
ecognized ha he model o Richa dson and G o es was mo e gene al
han his own a emp s, ye he desc ibed i as “a cons i u ional a he
han a s uc u al model; ha is, i deals wi h he na u e and ela i e
p opo ions o he ions p esen bu no in any de ail wi h how hese a e
a anged”. Ne e heless, in a se ies o ollowing wo ks Richa dson
ocused on he discussion o s uc u al aspec s o he C-S-H (and C-A-S-
H) a omic s uc u es wi hin he o iginal model s oichiome y o a wide
ange o samples and condi ions [20,53,56–59].
Fig. 2. (a) C ys alline s uc u e o he clino obe mo i e and obe mo i e. The a ows indica e he o ien a ion o he b idging silica e e ahed al. (b) Tobe mo i e 1.1
nm and Hamid's obe mo i e. The in e laye spaces a e shown o guide he eye o he di e ences be ween bo h s uc u es. The colou code is he same as in Fig. 1.
E. Duque-Redondo e al.
Cemen and Conc e e Resea ch 156 (2022) 106784
5
Many o he models and e inemen s ha e been p oposed a e he
one o Richa dson and G o es. Mos o hem i wi hin he gene al
o mula ion by Richa dson and G o es and desc ibe pa icula s uc-
u es, o s uc u al mo i s, ha ma ch wi h expe imen al obse a ions.
Fo ins ance, Cong, Ki kpa ick, and cowo ke s [13,41,60] p oposed a C-
S-H model based on de ec i e obe mo i e-like s uc u e, sugges ing ha
jenni e-like ea u es a e no p esen o a e negligible a bes . Thei model
was he e o e limi ed o Ca/Si a ios below 1.5. The model p oposed by
Nona e al. [61,62] was also based only on obe mo i e, bu unlike Cong
and Ki kpa ick's model, i co e s a wide ange o Ca/Si a ios. I
s esses ha he C-S-H s uc u e a high Ca/Si a ios can be achie ed in
obe mo i e by in oducing in e lamina calcium hyd oxide and ha he
C-S-H may no be as diso de ed as p e iously sugges ed. He also clas-
si ied he C-S-H in h ee di e en ia ed p oduc s ha o m a well de ined
Ca/Si a ios:
α
-C-S-H (0.66 V Ca/Si <1), β-C-S-H (1 <Ca/Si <1.5) and
γ-C-S-H (1.5 <Ca/Si <2). Mo e ecen ly, Ga ne and Ma uyama [63]
used a s uc u al model simila o he p e ious ones, bu emphasizing
he impo ance o he in e lamina calcium ion and i s sol a ion shell on
he o ma ion and sh inkage o he C-S-H gel. Chen e al. and Kulik
[64,65] used solubili y and he modynamic da a o sugges speci ic
composi ions and s uc u es o di e en Ca/Si anges, ye compa ible
wi h he gene al Richa dson-G o es s oichiome y.
Despi e he gene al ag eemen in he communi y wi h Taylo 's model
and Richa dson's s oichiome ic o mula ion, al e na i es ha e been
also sugges ed. G u zeck p oposed in 1999 a so osilica e C-S-H model,
wi h an ini ial cuspidine-like s uc u e ha may e ol e o d eie ke en
chains by di usion-con olled phase change [66,67]. Ve y ecen ly,
some au ho s ha e p oposed independen ly a model in which
obe mo i e-like laye s and po landi e mono- o bi-laye s coexis
[19,34]. In hei s udies, hey calcula ed he pai dis ibu ion unc ion
om high-ene gy X- ay expe imen s, G angeon e al. o C-S-H samples
wi h Ca/Si a io below 1.5 [34] and Cues a e al. o samples om ali e
hyd a ion [19]. Bo h ound ha , in o de o ma ch he expe imen al pai
dis ibu ion unc ion, hey should add he signal o po landi e laye s o
ha o clino obe mo i e. G angeon e al. speci ied ha he coexis ence
mus be conside ed o Ca/Si a ios >1.23, and bo h monolaye s and
bilaye s o po landi e seem o be p esen . [34]. Cues a e al. ha he
po landi e monolaye should be s e ched o a pe ec ma ch o he
PDF. This new e idences would imply a econside a ion o he accep ed
obe mo i e-like model, b inging back he possibili y o a mixed obe -
mo i e/po landi e C-S-H. I mus be kep in mind ha Richa dson's
s oichiome ic o mula ion s ill desc ibes he obe mo i e/po landi e
s uc u es. O e all, i is clea ha he a omic s uc u e o he C-S-H is
s ill a om being se led unequi ocally.
4. Compu a ional models o C-S-H gel
This sec ion summa izes he main achie emen s and miles ones in
he de elopmen o C-S-H gel a omis ic s uc u al models. The
complexi y o he p oblem lies in he non-c ys alline a omic s uc u e.
Fo c ys alline ma e ials, he a omic posi ions can be unequi ocally
de e mined using X- ay di ac ion expe imen s. E en i c ys als o en
include poin de ec s like acancies o subs i u ions and line de ec s like
disloca ions, he ideal a omic s uc u e is a ailable as s a ing poin
[68]. Tha is no he case o C-S-H, and he de ini ion o he ini ial
s uc u e is a p oblem i sel . We di ided he models in o “ea ly” and
“cu en ” models. The o me do no ep oduce some o he C-S-H mo e
impo an cha ac e is ics o he gel-like, ye hey can be used as ideal-
ized e sions o model sys ems o speci ic pu poses. The la e a e mo e
complex models ha include mos o he C-S-H s uc u al in o ma ion.
4.1. Ea ly C-S-H compu a ional models
In 1996, Faucon e al. [69,70] ca ied ou he i s s udy o he C-S-H
s uc u e employing molecula dynamics. Thei wo k aimed o e alua e
he b eaking mechanisms o he C-S-H chains and iden i y he sou ces o
i s s uc u al ins abili y. Fo ha pu pose, hey buil wo sys ems based
on he s uc u e o obe mo i e 1.1 nm p oposed by Hamid [30] ha
di e ed in he Ca/Si a ios: 0.66 and 0.83. The Ca/Si a io o 0.83 was
achie ed by he subs i u ion o wo p o ons o he obe mo i e 1.1 nm
s uc u e by a Ca ion. A Ca/Si =0.66, no b eak in he silica e chains was
obse ed when he model was elaxed a 800 K. In con as , he sub-
s i u ion o 2H
+
by Ca
2+
o each a Ca/Si a io o 0.83 esul ed in a
pa ial up u e o he silica e chains due o he o ma ion o Si-O-Ca
bonds. In his wo k, Faucon and cowo ke s also analyzed he s abili y
o Al subs i u ion in pai ing and b idging si es, which is ea ed in Sec-
ion 5.1.
A ew yea s la e , in 2002, Kaliniche and Ki kpa ick [71] employed
molecula dynamics o s udy he adso p ion mechanisms o chlo ide
anions a he su ace o di e en mine als. In pa icula , hey used
obe mo i e 0.9 nm as a model o C-S-H gel. They used he ClayFF o ce
ield [72] o desc ibe he me al‑oxygen in e ac ions, which enables he
mobili y and lexibili y o hyd oxyl g oups om he su ace. They ound
e y low chlo ide so p ion capaci y in obe mo i e 0.9 nm and he au-
ho s sugges ed ha he chlo ide so p ion capaci y o C-S-H should be
e en lowe , since he simula ed obe mo i e model con ained a ull se o
Si-OH su ace si es, while hose si es a e mainly dep o ona ed a highe
Ca/Si a ios and pH. The ex a nega i e cha ge due o his dep o ona ion
should p o oke high epulsion o chlo ide anions. La e on, hese au-
ho s employed he same app oach o s udy in de ail he s uc u e, dy-
namics, and ene ge ics o wa e con ined in C-S-H [73]. Again, he
s uc u e o non-modi ied obe mo i e 0.9 nm was employed as a model
o C-S-H, and di e en po e sizes we e conside ed, cons i u ing he i s
molecula dynamics models o s udy C-S-H po es. The molecula dy-
namics simula ions showed high s uc u ing o wa e molecules and he
de elopmen o a hyd ogen bond ne wo k be ween he wa e molecules
and he su ace. The au ho s sugges ed ha he deg ee o depolyme -
iza ion o he silica e chains and he dep o ona ion o pai ing Si-OH in C-
S-H migh cause dis o ions on he wa e s uc u e and lead o lowe
di usion coe icien s ega ding obe mo i e due o hyd ogen bonding
wi h su ace dangling a oms.
In 2004, Gmi a e al. [74] employed empi ical po en ials and ab ini io
me hods o in es iga e he na u e o he in e a omic o ces as well as he
elas ici y in he s uc u es o obe mo i e 1.1 nm de ined by Hamid [30]
and Me lino [27]. Changing he basal dis ance o a ixed in e laye
wa e and Ca con en hey iden i ied h ee ene gy minima be ween 1.0
and 1.4 nm and showed ha he cohesion in C-S-H is essen ially due o
he elec os a ic o ces and he iono-co alen o ces caused by he Ca
ions and wa e in he in e laye .
The i s a emp o build a compu a ional C-S-H model by cu ing
he silica e chains o obe mo i e 1.4 nm and jenni e mine als was done
in 2007 by Manzano e al. [75,76]. This C-S-H model consis ed o a
mix u e o dime s, pen ame s, and oc ame s ob ained by omi ing
b idging e ahed a in he in ini e silica e chains o obe mo i e 1.4 nm
and jenni e mine als. The cha ge de ec s in oduced in he c ys alline
s uc u e o hose mine als we e compensa ed by in oducing p o ons in
he e minal oxygen a oms o he ini e silica e chains, while he wa e
and Ca con en s emained unchanged. The ob ained models a e de ec-
i e c ys als a he han diso de ed C-S-H, as pe iodici y was kep in he
uni cell, ye he au ho s showed ha hey we e easonable app oaches
o s udy he dependence o he elas ic p ope ies o C-S-H gel wi h
espec o i s composi ion and silica e chain leng h. The esul s showed
ha he mechanical p ope ies inc ease as he chain leng h g ows due o
he highe s abili y o longe silica e chains. The elas ic p ope ies o he
p oposed C-S-H models we e conside ably lowe han o he pe ec
c ys als o obe mo i e 1.4 nm and jenni e, and in good ag eemen wi h
he expe imen al nanoinden a ion measu emen s once nanopo osi y
was aken in o accoun by po omechanical models.
Also in 2007, Dolado e al. [77] published a adically di e en
app oach o model C-S-H. Ins ead o using obe mo i e as a C-S-H model,
hey pe o med molecula dynamics s udy o simula e he polyme iza-
ion o silicic acids in a Ca- ich en i onmen . They employed he Li on
E. Duque-Redondo e al.

Cemen and Conc e e Resea ch 156 (2022) 106784
6
and Ga o alini po en ial o amo phous glasses [78] a e y high em-
pe a u es (>1500K). They obse ed ha he polyme iza ion was as e
a lowe Ca/Si a ios and ha he appea ance o h ee-dimensional
s uc u es, like b anched silica e and ings, dec eases as he Ca/Si
a io inc eases. Thus, he p esence o Ca ions no only slows down he
polyme iza ion o he silica e chains, bu also en o ces he o ma ion o
linea s uc u es. Likewise, hey measu ed he silica e chain leng hs,
inding ha he highe he Ca/Si a io, he sho e he silica e chains.
Howe e , he esul ing s uc u e mus be conside ed a calcium silica e
glass a he han C-S-H, as hey did no obse e any local o de o o -
ma ion o calcium silica e laye s.
4.2. Cu en C-S-H compu a ional models
Hi he o, mos C-S-H models we e essen ially c ys alline obe mo i e
o sligh ly modi ied a ian s. They we e a easonable i s app oach, bu
some o hei basic ea u es we e no compa ible wi h he cha ac e is ics
o eal C-S-H. Fo ins ance, he densi y and Ca/Si a io a e conside ably
highe in C-S-H (
ρ
m
=2.6 g⋅cm
−3
and Ca/Si =1.7 [14]) han in obe -
mo i e (
ρ
m
=2.23 g⋅cm
−3
and Ca/Si =0.83 [79]) and jenni e (
ρ
m
=2.32
g⋅cm
−3
and Ca/Si =1.5 [80]) mine als. Fo ha eason, in 2009, Pellenq
e al. [81] employed a new app oach o de elop he i s diso de ed C-S-
H model. They ook he uni cell o d y obe mo i e 1.1 nm as a s a ing
poin o build a diso de ed C-S-H by in oducing se e al modi ica ions.
—In he i s s ep, all wa e molecules we e dele ed and he speci-
ied Ca/Si a io, 1.7, was achie ed by sho ening he silica e
chains by emo ing neu al SiO
2
g oups in o de o ob ain a
de ec i e C-S-H s uc u e ma ching he expe imen al Q
0
, Q
1
, and
Q
2
dis ibu ion gi en by expe imen al NMR analysis [60,82].
—Ca was in oduced o compensa e o he cha ge imbalance p o-
oked by he SiO
2
dele ion.
— Then, he s uc u e was elaxed, ob aining a dis o ed laye ed
s uc u e.
— To ein oduce wa e , G and Canonical Mon e Ca lo (GCMC)
simula ion was pe o med, coupling he C-S-H s uc u e o an
ex e nal wa e ese oi a he chemical po en ial o liquid wa e
a 300 K. Wa e en e ed in o he o iginal in e lamina space, bu
also in new spaces c ea ed by he omission o silica e g oups,
eaching a densi y o 2.56 g⋅cm
−3
, close o he expe imen al one
(2.6 g⋅cm
−3
) ob ained by small-angle neu on sca e ing (SANS)
measu emen s [14].
— Finally, he s uc u e o he sys em was u he elaxed unde
cons an p essu e and empe a u e, which caused an expansion o
he in e lamina space and he densi y was educed up o a inal
alue o 2.45 g⋅cm
−3
.
The chemical composi ion o he inal s uc u e was (CaO)
1.65
(SiO
2
)
(H
2
O)
1.75
, e y close o he expe imen al a e age composi ion [14]
(CaO)
1.7
(SiO
2
)(H
2
O)
1.8
. I is ema kable ha he inal s uc u e had a
simila amoun o wa e o obe mo i e 1.4 nm, bu in his model, wa e
is packed andomly in he in e laye space due o he p esence o de ec s
in he silica e chains, which educes he basal dis ance. The model was
alida ed by compa ison o s uc u al and physical p ope ies wi h
expe imen al measu emen s ob ained by X- ay abso p ion ine s uc u e
(EXAFS) [83], X- ay di ac ion (XRD) [84], and in a ed spec oscopy
(IR) [13]. I mus be no iced ha he expe imen al EXAFS and XRD C-S-
H samples ha e lowe Ca/Si a ios han he model (1.4 and 1.1,
espec i ely), and he compa isons se e o p o e only quali a i ely he
diso de ed na u e o he C-S-H model. Fu he mo e, his model was used
o calcula e mechanical p ope ies, such as mechanical s i ness,
s eng h, and hyd oly ic shea esponse, ob aining esul s in good
ag eemen wi h he expe imen al nanoinden a ion alues [85,86]. The
esul s gi en by his model sugges ed ha he C-S-H ha e bo h glass-like
sho - ange o de and c ys alline ea u es om obe mo i e [81].
This model was a g ea s ep o wa d in he modeling o C-S-H gel,
al hough i was ne e be e o con o e sy due o i s inconsis encies.
Indeed, some au ho s c i icized he C-S-H model p oposed by Pellenq.
Thomas e al. [88] highligh ed ha he model densi y was in be e
ag eemen wi h expe imen s han c ys alline obe mo i e, bu s ill qui e
a om eal C-S-H gel. Richa dson [89] also c i icized i because he
Ca
–
O dis ances we e ei he sho e o longe han he measu ed Ca
–
O
dis ances in calcium silica e hyd a es and ela ed phases by X- ay
di ac ion (XRD). Mo eo e , he also poin ed ou ha mo e han hal o
he Ca a oms we e unde coo dina ed, bonded o less han six oxygen
a oms. The main poin o disag eemen was he s uc u e o he silica e
chains. The model has a Q
n
dis ibu ion (Q
0
=13%, Q
1
=67% and Q
2
=
20%), simila o ha o expe imen al samples (Q
0
~10%, Q
1
~67% and
Q
2
~23%). Howe e , he expe imen s included he Q
0
si es due o he
con ibu ion o unhyd a ed C
3
S, and no p esen in C-S-H [62,90].
Despi e he c i icism and inconsis encies o he C-S-H model de el-
oped by Pellenq and cowo ke s [81], i is possibly he bigges miles one
o he desc ip ion o he C-S-H using molecula scale modeling. I
showed ha i was possible o build mo e ealis ic models han obe -
mo i e and lead o an inc easing numbe o s udies and model im-
p o emen s. Fo ins ance, in 2012, Manzano e al. [91] e ined he
model enabling he dissocia ion o wa e molecules con ined in C-S-H
mic opo es. Fo ha pu pose, hey used a eac i e o ce ield, ReaxFF
[92,93]. They did no obse e wa e dissocia ion du ing he ene gy
minimiza ion a 0 K, bu as soon as he sys em was ans e ed o he
canonical ensemble a 300 K, he dissocia ion occu s, p oducing he
ionic pai OH
−
-H
+
. The p ocess o dissocia ion is e y as , aking place
wi hin he i s 0.2 ns o MD simula ion. The p o ons eac only wi h
nonb idging oxygen a oms o he silica e chains, while he hyd oxyl
g oups coo dina e o in e lamina Ca ions, o ming Si-OH and Ca-OH
g oups. Almos hal o he o iginal wa e con en was dissocia ed,
becoming a cons i u i e pa o he C-S-H gel. I should be poin ed ou
ha no o he eac ions ook place besides he dissocia ion o wa e
molecules, so he silica e monome s did no eac o o m longe chains.
Fo ha eason, he au ho s concluded ha he monome s apped
du ing he nuclea ion p ocess may emain s able. A e he wa e
dissocia ion, he o e all densi y o he sys em inc eases. The au ho s,
based on he analysis o he a angemen s uc u e, a ibu ed his
g ow h o he o ma ion o hyd oxyl g oups, which induces a dec ease o
he long- ange o de , leading o a con igu a ion mo e diso de ed and
a o able ene ge ically.
In 2014, Abdolhosseini Qomi e al. [87] in oduced a second
imp o emen o he C-S-H model o Pellenq e al. (see Fig. 3), which
sol ed some inaccu acies c i icized by o he au ho s. The building
scheme is simila o he o iginal one om Pellenq's model [81], ye he
amoun o Q
0
si es is ze o o low Ca/Si a ios, and kep close o ze o o
high Ca/Si a ios. They also included a molecula dynamics s ep wi h he
eac i e o ce ield ReaxFF [92,93] a 500 K, allowing he dissocia ion o
wa e molecules. Then, he sys ems a e ans e ed o a non- eac i e
en i onmen using he CSH-FF o ce ield [94] due o he high compu-
a ional cos o ReaxFF. Using his non- eac i e o ce ield, he annealing
o he sample is simula ed educing he empe a u e om 500 o 300 K
along 3 ns a ambien p essu e. In his way Abdolhosseini Qomi e al.
[87] buil abou 1500 C-S-H gel con igu a ions wi h a b oad ange o
composi ions, spanning Ca/Si a ios be ween 1.1 and 2.1. I should be
no ed ha o Ca/Si a ios highe han 1.5, pai ing silica es a e emo ed
and some monome s a e c ea ed in he C-S-H s uc u e, al hough some
o hem condensa ed du ing he MD simula ion wi h ReaxFF. The aim o
he au ho s was o build a da abase o a omic con igu a ions o C-S-H
alida ed wi h s uc u al and mechanical da a and classi y hem ac-
co ding o h ee de ec a ibu es: Ca/Si a ios and co ela ion dis ances
o medium- ange Si
–
O and Ca
–
O en i onmen s [87]. In his way, i is
possible o es ablish a s uc u e-p ope y co ela ion, enabling he
sc eening o he da abase o he desi ed p ope ies agains he de ec
a ibu e.
In 2015, Ko aˇ
ce i´
c e al. [95] p oposed h ee models o he s uc-
u e o C-S-H gel based on obe mo i e 1.1 nm. They de eloped a la ge
E. Duque-Redondo e al.
Cemen and Conc e e Resea ch 156 (2022) 106784
7
Fig. 3. The e inemen o Pellenq's de ec i e obe mo i e models by Qomi e al. (a) S uc u e o obe mo i e 1.1 nm was used as a baseline o build he C-S-H models.
(b) Componen s o obe mo i e: silica e chains (abo e), in alaye calcium (medium), and in e laye calcium (below). A omic s uc u e o C-S-H models wi h Ca/Si
a ios o (c) 1.1, (d) 1.5, and (e) 1.8. Adap ed by pe mission om Sp inge Na u e, [87], Copy igh 2014.
Fig. 4. P oposed models by Ko aˇ
ce i´
c and cowo ke s o he s uc u e o C-S-H gel wi h Ca/Si a io 1.68, co esponding o (a) model 1, (b) model 2, and (c) model 3
(see ex ). The colo ed egions show examples o which ype o si e was emo ed in each model: blue o b idging si es, o ange o dime s, and ed o pai ing si es.
Adap ed om [95], Copy igh 2021, wi h pe mission om Else ie . (Fo in e p e a ion o he e e ences o colou in his igu e legend, he eade is e e ed o he
web e sion o his a icle.)
E. Duque-Redondo e al.
Cemen and Conc e e Resea ch 156 (2022) 106784
8
numbe o con igu a ions wi h a andom dis ibu ion o a iable-size
silica oligome s o each model. As a s a ing poin , hey employed he
s uc u e o obe mo i e 1.1 nm desc ibed by Me lino e al. [27], while
Pellenq- ype models [81,87] employed Hamid's obe mo i e 1.1 nm
[30]. The h ee di e en models a ise om he s a egy ollowed o in-
c ease he Ca/Si a io up o 1.68. This can be achie ed by he addi ion o
Ca ions and/o he emo al o SiO
2
g oups. In sho , he h ee models
we e done by:
— Model 1: Remo al o b idging SiO
2
si es, con olling he leng h o
he silica e chains o ollow he 3n-1 ule and adding Ca in he
in e laye space. In his way, he C-S-H model is composed o
dime s and pen ame s, wi hou he p esence o monome s
(Fig. 4a).
— Model 2: Remo al o b idging SiO
2
si es +SiO
2
dime s and
adding Ca in he in e laye space. This combina ion obeys he 3n-
1 ule, ye leads o a eas o he calcium oxide laye exposed o he
in e lamina space (Fig. 4b).
—Model 3: Random dele ion o b idging and pai ing silica e e a-
hed ons (Fig. 4c). The e o e, he e a e monome ic silica es in he
s uc u e o C-S-H, and he 3n-1 ule is no ul illed.
Following his p ocedu e, hey gene a ed a g ea numbe o C-S-H
s uc u es, mo e han a housand s uc u es in o al, a he same Ca/Si
a io (1.68) and o H/Si a ios om 1.3 o 2.3. All hose con igu a ions
we e elaxed and hen, molecula dynamics simula ions we e pe o med
using he ReaxFF o ce ield in o de o es ima e hei bulk densi ies and
o al ene gies. The models and hei con igu a ions do no ha e he same
s oichiome y and hey also con ain di e en amoun s o wa e , inse ed
by G and Canonical Mon e Ca lo, which complica es he in e p e a ion
o he esul s. The calcula ed o al ene gies a e escaled o make hem
compa able, esul ing in signi ican ene gy di e ences be ween he
h ee models. The i s model exhibi s he lowes ene gy, sugges ing ha
i is he mos p obable one. Fu he mo e, he analysis o he bulk densi y
o he samples shows ha he i s model has he highes co ec ed
densi y (2.76 g⋅cm
−3
o H/Si a io o 1.8), e y close o he expe i-
men al alue (2.6 g⋅cm
−3
). In his way, he i s model, based on he
combina ion o he inco po a ion o Ca ions and andom dele ion o
b idging silica es ha o ms dime s and pen ame s, esul s in he mos
s able model and wi h a densi y alue ha ma ches he expe imen al
one. The building s a egy and esul ing s uc u e could be conside ed as
he same one achie ed by Pellenq- ype models [81,87], co ec ing he
p esence o silica e monome s, whose p esence is no suppo ed by
expe imen al s udies [62,90]. Despi e he clea conclusions o his wo k,
o he esea che s ha e con inued using models wi h missing pai ing
si es o explo e he e ec o he silica e chain s uc u e on he C-S-H
p ope ies [96].
The C-S-H compu a ional model p oposed by Mohamed e al. in 2018
[97] is a adically di e en app oach o C-S-H cons uc ion. I is based
on he expe imen al syn hesis and cha ac e iza ion o C-S-H samples a a
wide ange o Ca/Si a ios epo ed in [8]. F om he poin o iew o he
C-S-H a omic s uc u e and s oichiome y, he model is no ha di e en
om he p e ious ones. I s main cha ac e is ic is ha Ca ions a e
inco po a ed in well de ined posi ions as b idges o e minal silica es Q
1
o he chains, a he han andomly in he in e laye space. The au ho s
claimed ha he p esence o hose b idging Ca, oge he wi h he
hyd ogen bond ne wo k, con ibu es o he s abiliza ion o he C-S-H
s uc u e, which is pa icula ly impo an a high Ca/Si a ios. The
p ocess o e ol e om obe mo i e o a mo e ealis ic s uc u e o C-S-H
s a s wi h he dep o ona ion o he silanol g oups o he b idging sili-
ca es, which is compensa ed by he inco po a ion o Ca(OH)
+
ions.
Then, he b idging silica e e ahed ons a e dele ed and he
Fig. 5. (a) De ini ion and no a ion o mo i s employed in he b ick C-S-H model. (b) Example o a b ick buil om he mo i s in (a). In his case, he b ick ep esen s
he p imi i e uni cell o 1.4 nm obe mo i e, using he mo i s co esponding o he code <S
′<C7 >S′>. Adap ed om [97], Copy igh (2018), wi h pe mission om
Else ie . C-S-H s uc u es p oposed by Kuma e al. o he C-S-H s uc u e wi h Ca/Si a ios o (c) 1.25, (d) 1.75, and (e) 2.0 iewed along he [100] di ec ion.
Adap ed om [8] Copy igh (2018) wi h pe mission om Ame ican Chemical Socie y.
E. Duque-Redondo e al.
Cemen and Conc e e Resea ch 156 (2022) 106784
9
elec oneu ali y is main ained by adding wo p o ons, one p o on and
one Ca(OH)
+
, o one Ca
+2
ion, coo dina ed o he b idging si es. Ex a
Ca(OH)
2
g oups can be added o inc ease he Ca/Si a io i necessa y.
F om a compu a ional poin o iew, he cons uc ion me hod is
comple ely di e en om he p e ious wo ks. S a ing om obe mo -
i e, Mohamed e al. de ined a collec ion o basic building blocks co e ing
a ange o possible i educible mo i s wi hin he C-S-H (Fig. 5 a). Those
building blocks a e hen combined o o m di e en uni cells o “b icks”
(Fig. 5 b), which a e checked a e a DFT ene gy minimiza ion, e alu-
a ing he Ca
–
O dis ances, he coo dina ion numbe o Ca ions, and local
cha ge neu ali y a e elaxa ion. The b icks ha sa is y he s uc u al
checking a e hen combined o o m a a ie y o C-S-H s uc u es wi h
di e en s uc u es and/o composi ions (Fig. 5 c). A a iable amoun o
in e laye Ca(OH)
2
and wa e molecules can also be speci ied as addi-
ional b icks, bu i is no e y clea how hese mo i s a e placed. The
au ho s show how he b ick-by-b ick building scheme can ep oduce
obe mo i e and jenni e c ys als, as well as and p e ious C-S-H models. I
is lexible enough o c ea e mul iple s uc u es wi h Ca/Si a ios om
1.0 o 2.0, wi h poin de ec s, s acking aul s, di e en p o ona ion de-
g ees o he silica e chains, e c. They also p opose speci ic blocks o
ep oduce C-S-H su aces, an inno a i e app oach o s udy sys ema i-
cally C-S-H in e acial p ope ies. In a ecen pape [98] he au ho s
ex ended u he he collec ion o building blocks adding Al, expanding
he a ailable chemical space o include C-A-S-H.
Since he de elopmen o he p e ious models, mos wo ks ha e
ocused on hei applica ion o compu e nanoscale p ope ies, ye ecen
s udies ela ed o s uc u al e inemen s ha e also been done. Fo
ins ance, compa ing DFT simula ed and expe imen al XRD pa e ns o
syn he ic C-S-H wi h a Ca/Si =1, Basqui o o de Souza e al. sugges ed
ha he C-S-H s uc u e is less diso de ed han he p oposed by o he
models, and ha he s acking diso de is a key ac o o ake in o accoun
[99]. Al hough he basic pilla s o he C-S-H models a e well es ablished,
he e is s ill oom o imp o emen and e inemen .
4.3. C-S-H su aces and po e models
In Sec ion 5, we will see ha a la ge pa o he applica ions o
a omis ic C-S-H models is ela ed o in e acial p ope ies and nano-
po es. The e o e, i is ele an o e iew how C-S-H su ace models a e
buil .
The C-S-H su ace and po e models a e buil ollowing he s anda d
p ac ices in a omis ic simula ions: a wo dimensional slab is c ea ed by
“spli ing” a bulk sys em h ough a gi en c ys allog aphic plane, in o-
ducing a “ acuum laye ”. The plane mus be chosen ca e ully o a oid,
when possible, b eaking co alen bonds, main aining he highes
possible coo dina ion numbe s, and a oiding cha ged slabs (see he
Taske su ace classi ica ion o mo e de ails [100]). In he case o he C-
S-H gel, gi en he obe mo i e-like laye ed s uc u e, he esea che s
ha e adop ed he p ac ices om he clay communi y, in oduced mainly
by Kaliniche e al. [71]. Clay pa icles a e o med by he s acking o
independen laye s, wi h a iable wa e con en and ionic composi ion
in he in e laye space. The di ec ion pe pendicula o he laye s is
he e o e he mos ob ious choice o c ea e he su ace: i is he main
su ace in e ms o exposed a ea, and chemically s able due o he lack o
dangling bonds. The “ acuum laye ” can hen be sa u a ed wi h wa e ,
o ganic molecules, ionic solu ions, e c. [101–106].
Ne e heless, he e a e impo an di e ences be ween clays and he
C-S-H, due o he non-c ys alline na u e o he la e . In clays, he su -
aces a e unequi ocally de e mined by he c ys allog aphic s uc u e,
wi h no dangling bonds. In he case o he C-S-H gel, su aces will ha e a
andom composi ion and s uc u e, and will ha e dangling bonds om
he ini e silica e chains, jus like he bulk. The su ace (o in e acial)
s uc u e will a y depending on he po e solu ion chemis y and
especially wi h he pH. Howe e , he as majo i y o epo ed wo ks do
no ake in o accoun his poin , and he su aces ha e he same s uc u e
as he bulk laye s. The impac o such an app oxima ion is di icul o
e alua e, and conside ably mo e wo k will be necessa y. Among he ew
a emp s done so a , Jamil e al. compu ed using MD simula ions he
su ace and solid-wa e in e acial ene gies o di e en obe mo i e
planes. In ag eemen wi h he p e ious discussion, he (001) di ec ion
wi h he su ace coinciding wi h he obe mo i e laye s is he mos
a o able one, wi h negligible in e acial ene gy [107]. Howe e , o he
su aces also p esen e y low su ace ene gy, especially he (100),
making hem ele an . In addi ion, he au ho s explo e he hyd oxyl
g oup densi y on he su aces and he associa ed app oxima e pH. Ye
he sys em is obe mo i e and no a C-S-H model, he concep s in o-
duced o show ha o he su aces han he (001) canno be disca ded
and ha he su ace chemis y should be aken in o accoun . Ano he
in e es ing app oach has been p oposed, al hough no explo ed in de ail,
in he amewo k o he b ick model [97]. The au ho s sugges ed ha
speci ic b icks could be cons uc ed o ep oduce su ace s a es. Tha
opens he possibili y o c ea ing su ace composi ions and hyd oxyla ion
s a es independen o he bulk composi ion.
5. Applica ions o he C-S-H compu a ional models
In his sec ion, we e iew some o he mos p ominen applica ions o
he C-S-H compu a ional models. In many cases, we include pape “ea ly
models” o show he e olu ion o he ield, e en hough hey canno be
s ic ly conside ed C-S-H models, as we will discuss la e .
5.1. Al-inco po a ion in o he C-S-H gel
The de e mina ion o aluminum p e e en ial inco po a ion si es in o
he C-S-H gel has been p obably he mos success ul applica ion o
a omis ic simula ions in cemen esea ch, as a omis ic simula ion has
ep oduced he expe imen al obse a ions in mos cases. I is also an
in e es ing example o how he a omis ic models ha e e ol ed om e y
simple clus e models o he cu en complex models. B ie ly, expe i-
men al s udies using Si-NMR and Al-NMR p o ed ha e a-coo dina ed
aluminum, Al(IV), is inco po a ed in o he C-S-H gel silica e chains in
he b idging si e [108–113]. As a consequence, dime s me ge in o
pen ame s and longe aluminosilica e mean chain leng hs (MCL) a e
obse ed. Fo low Ca/(Si +Al) a ios, Al(IV) enhances in e lamina
chain c oss-links ia condensa ion o b idging si es, o ming zeoli e-like
ca i ies as in obe mo i e 1.1 nm and clino obe mo i e.
The i s a emp o in es iga e he aluminum inco po a ion in o
obe mo i e was done in 1994 by Kashiha a e al. [114]. They aimed o
s udy he obe mo i e 1.1 nm case using a clus e model and ab ini io
simula ions. Likely, some me hodological laws (like cha ge imbalance
due o he subs i u ion) and compu a ional powe limi a ions did no
allow a p ope ene gy minimiza ion, and hei simula ions p edic he
lowes subs i u ion ene gy o pai ing si es.
Manzano e al. used an e en simple model, es ing wi h Densi y
Func ional Theo y (DFT) he Si o Al subs i u ion ene gy in a 5-
membe ed silica e chain isola ed om obe mo i e 1.4 nm [115]. The
hea y a oms (Si and Al) we e ozen o main ain a d eie ke en
a angemen , while O and H we e elaxed. The calcula ed aluminosili-
ca e condensa ion ene gies, Al o Si subs i u ion ene gies, and clus e
s abili y index indica ed ha he b idging si e is p e e ed o e pai ing
and ending si es. The sugges ed eason was a be e s abiliza ion o he
elec onic s uc u e and cha ge localiza ion when Al was loca ed in he
b idging si e. The pai ing si e and ending si es we e ene ge ically less
a o able han he b idging by 4 and 21 kcal⋅mol
−1
espec i ely.
Pegado e al. also compu ed he subs i u ion ene gies wi h DFT
me hodology, ye in a mo e complex model consis ing o a single
obe mo i e laye isola ed om he c ys al 116. Some b idging si es om
he silica e chains we e emo ed, c ea ing ini e chains, and mul iple
possible Al o Si subs i u ions we e analyzed o good s a is ical anal-
ysis. Essen ially, hey each he same conclusion as [115], wi h he
b idging si e as he mos a o able om a he modynamic poin o iew,
ollowed by he pai ing and he ending si es. Howe e , he ene gy
E. Duque-Redondo e al.
Cemen and Conc e e Resea ch 156 (2022) 106784
16
[162] in es iga ed he mobili y in he in e laye o Ca
2+
, Mg
2+
, Al
3+
,
and Na
+
ions using ReaxFF. They ound esidence imes o wa e in he
hyd a ion shell o Al
3+
and Mg
2+
ions much g ea e han he ones o
Na
+
and Ca
2+
ions and di usion coe icien s ha ollow he o de :
D
Na
>D
Ca
>D
Al
>D
Mg
. Ne e heless, he esul s om his pape should be
aken wi h ca e, since he ReaxFF pa ame e s o Mg, Al, and Na in
combina ion wi h he Ca/Si/O/H se ha e no been es ed p ope ly.
5.5. C-S-H hyb ids and composi es
In pu sui o de eloping mo e sus ainable building ma e ials and
hei use in inno a i e applica ions, a wide a ie y o addi i es o
chemical admix u es ha e been used. [179–185]. The in e cala ion o
o ganic molecules o low dimensional ma e ials in o he C-S-H gel a he
nanoscale could ha e a syne gis ic e ec ha esul s in enhanced pe -
o mance o he hyb id C-S-H o composi e ma e ial [186–192]. A om-
is ic simula ions a e an excellen ool o p o ide de ailed in o ma ion
abou he nanoscale in e ac ion be ween he C-S-H gel and he di e en
addi i es. As a ma e o ac , MD simula ions ha e al eady been used o
in es iga e he o ganic-ino ganic in e ac ions in o he laye ed ma e ials,
like clays [101,102,107,193–196] and laye ed double hyd oxides [197].
In 2008, Sanchez and Zhang we e pionee s in he a omis ic modeling
o C-S-H composi es [193]. They s udied he in e acial in e ac ions
be ween C-S-H, using as a model he s uc u e o obe mo i e 0.9 nm
[198], wi h g aphi e and g aphi e unc ionalized wi h hyd oxyls,
ca boxyl, ca boxyla e, ca bonyl, and amine g oups. They ound ha he
binding a ini y o he g aphi ic s uc u es o he su ace o obe mo i e
inc eases wi h he pola i y o he unc ional g oup, enhancing he s a-
bili y o he in e phase and he o e all s eng h and du abili y o he
esul ing composi e. Subsequen MD s udies using Pellenq- ype models
con i med he signi ican imp o emen in Young's modulus and s eng h
o unc ionalized g aphene/C-S-H composi es and, o a much lesse
ex en , in non- uncionalized/C-S-H composi es ega ding pu e C-S-H
[199–201]. These s udies also epo ed ha highe Ca/Si a ios may
con ibu e o inc ease he ensile s eng h due o he o ma ion o mo e
Ca
–
O ionic bonds be ween he Ca ions o he C-S-H and oxygen a oms
om he g aphene oxides (GO) [201].
A omis ic modeling was used o s udy he mechanical p ope ies o
C-S-H ein o ced wi h ca bon nano ubes (CNT) inse ed along he
weakes di ec ion, pe pendicula o he C-S-H shee s [202]. The au ho s
epo ed an inc ease in he duc ili y and signi ican ly highe ensile
s eng h in he pe pendicula di ec ion o silica e laye s, while he
comp essi e beha io was no subs an i ely al e ed. Howe e , hey
ound a wo sening o he shea s eng h in all di ec ions o he C-S-H/
CNT composi es. Mo e ecen ly, he use o di e en su ac an s o
dispe se he CNTs in o he cemen ma ix was also in es iga ed [203].
Based on he in e ac ions be ween CNTs and he dispe sing agen s in
bulk wa e , he Gum A abic (GA) was iden i ied as he mos sui able
su ac an since only GA was able o in e ac wi h bo h he CNTs and he
C-S-H su ace. The mechanical cha ac e iza ion e ealed ha he
inco po a ion o he CNT along wi h GA in a d illed hole pe pendicula
o he silica e chains doubles he o e all s eng h, inc eases conside ably
he elas ic, shea , and bulk moduli, and swi ches he na u e o he ma-
e ial om b i le o duc ile.
Besides g aphene and CNTs, o he o ganic compounds ha e been
used o imp o e he mechanical pe o mance o he C-S-H gel (Fig. 9).
Hou e al. in es iga ed he in e cala ion o poly(ac ylic acid) (PAA), poly
( inyl alcohol) (PVA), and poly(e hylene glycol) (PEG) in he in e laye
space o a C-S-H model wi h a Ca/Si a io o 1.3 [204–207]. They used
di e en o ce ields wi h di e en esul s. When hey used a combina-
ion o ClayFF [72] o CSH-FF [94] wi h CVFF [208], hey obse ed an
inc ease in Young's modulus, ensile s eng h, and ailu e s ain, while
imp o ing he duc ili y. In con as , he polyme in e cala ion ba ely
a ec ed he Young's modulus and ensile s eng h when ReaxFF is used
[207]. The au ho s a ibu ed hese di e ences o he up u e o C
–
C
bonds om he polyme s o o m C-O-Si. Howe e , his un ealis ic esul
can be due o a me hodological law since he ReaxFF Ca/Si/OH se o
elemen s is incompa ible wi h o ganic pa ame e s. In any case, u he
esea ch is needed o e alua e he quali y o he di e en FFs.
The elas ic esponse o C-S-H/PEG composi es was also s udied by
Zhou and cowo ke s compa ing simula ions and expe imen s [209].
Expe imen al HP-XRD measu emen s e ealed a signi ican inc ease in
he bulk modulus o he C-S-H/PEG composi e (K =52.7 GPa) wi h
espec o a pu e C-S-H sample (K =45.6 GPa). MD simula ions ep o-
duced he pu e C-S-H alue (K =45.9 GPa), ye p edic ed a conside able
dec ease o he C-S-H/PEG composi e (K =34.7 GPa). The au ho s
sugges ed ha in he expe imen al samples, PEG is loca ed in la ge po es
wi hin C-S-H pa icles and no sandwiched in he in e laye space as was
assumed o he simula ion model. The esul poin s ou he impo ance
o a co ec model.
Con inuing wi h polyme s and o ganic molecules, a a ie y o s udies
ha e in es iga ed he adhesion o adso p ion and he in e ac ion o
o ganic moie ies wi h C-S-H subs a es. O e all, he esul s show he
same quali a i e esul s: highly-pola polyme s, wi h ca boxyl and
Fig. 9. Two examples o C-S-H o ganic in e ac ions. (a) C-S-H/PEG composi e. A PEG chain o 40 monome s is inse ed in o he C-S-H in e laye space. (b)C-S-H/
APTES hyb id. The APTES o ms co alen bonding wi h he C-S-H silica e chains.
E. Duque-Redondo e al.

Cemen and Conc e e Resea ch 156 (2022) 106784
17
amide g oups, adso b be e in C-S-H as he Ca/Si a io inc eases due o
he in e ac ion wi h Ca and o ma ion o hyd ogen bonds [210–212]. On
he con a y, low adhesion ene gies we e epo ed o polyme s like
polyp opylene, which does no ha e pola g oups on i s s uc u e.
Polyme s a e also used o imp o e he adhesion be ween he C-S-H
su ace and o he phases. Fo ins ance, Han e al. used PVA o enhance
he adhesion o ubbe hyd oca bon (RH) o he C-S-H [213]. Acco ding
o hei calcula ions, he adhesion ene gies o he PVA/C-S-H and RH/
PVA in e aces we e much highe han ha o he RH/C-S-H in e ace,
sugges ing ha PVA is a good candida e as a b idge be ween he RH and
he C-S-H. Thus, he p esence o PVA enhances hei adhesi eness and
mechanical pe o mance o ubbe ize cemen s, in ag eemen wi h he
expe imen s, which show a signi ican inc ease in he adhesi e and
comp essi e s eng h o RH/PVA/C-S-H composi es. Sul u -black ca -
bon (SBC) polyme s ha e been used o imp o e he poo adhesion o
conc e e laye s c ea ed wi h conc e e 3D p in ing echnology. Hosseini
e al. c ea ed CSH-SBC-CSH models by sandwiching SBC polyme s be-
ween C-S-H gel laye s and subjec ed he composi e o shea and ensile
s ains o analyze he mechanical pe o mance [214]. The simula ions
show ha he o ma ion o elec os a ic in e ac ions be ween he SBC
polyme s and he Ca ions om he C-S-H su ace inc ease he in e acial
shea and ensile s eng hs o 50% and 88% ega ding he p is ine C-S-H,
in he line wi h he expe imen al esul s ob ained by h ee-poin bending
loading es s. The a ini y o ce ain o ganic molecules, as glucona e, o
Ca ions was exploi ed by And oniuk, Kaliniche , e al. o enhance he
up ake o u anyl ions in C-S-H a Ca/Si a ios be ween 0.83 and 1.4
[215,216]. They ound ha glucona e is no di ec ly bound o he C-S-H,
bu i c ea es complexes wi h he Ca ions om he C-S-H su ace. In his
way, he complexa ion o glucona e wi h Ca educes he binding
s eng h o hese ca ions o he C-S-H and lea es acan so p ion si es on
he su ace ha can be occupied by u anyl, enhancing indi ec ly he
u anyl up ake.
6. Discussion and pe spec i es
In his sec ion, we will discuss se e al p ac ical aspec s o he cu en
compu a ional models, as well as u u e di ec ions.
6.1. Which a ailable C-S-H compu a ional model is he bes ?
Fi s o all, we mus s ess ha he discussed C-S-H models belong o
he same amily, which could be classi ied as “impe ec obe mo i e”
models. They ha e di e ences (missing pai ing si es, in e laye Ca po-
si ions, diso de deg ee) bu he e y basic ounda ions a e he same.
Tha said, we can classi y he C-S-H model cons uc ion in o wo main
g oups: he de ec i e- obe mo i e models and he b ick model [97]. The
i s g oup includes Pellenq- ype models [81,87] and Ko aˇ
ce i´
c's model
[95], which can be seen as a speci ic o mula ion o a Ca/Si =1.68. The
o iginal models as p esen ed by he au ho s had impo an di e ences,
bu , in p inciple, one could each he same C-S-H inal s uc u e using
ei he cons uc ion me hod. I mus be no ed ha we will discuss he
cons uc ion me hod a he han he speci ic models p esen ed in he
o iginal pape s. Fo ins ance, Pellenq's o iginal model had some s uc-
u al ea u es, such as silica e monome s, necessa y o each Ca/Si a ios
>1.5. Howe e , he 3n-1 ule can be ul illed by adding Ca(OH)
2
in he
in e laye space as p oposed la e [87,95,97] and Ca/Si up o 2 ha e
been epo ed [156].
The b ick cons uc ion me hod [97] is an elegan solu ion o build a
as numbe o andom models wi h he desi ed composi ion by mixing
he ype and posi ion o he p ede ined building blocks (see Table 3).
The s uc u e o a gi en model is easy o ack by using he b icks' codes,
which make hem ep oducible. I is possible o do a di ec compu a ion
o he C-S-H model p ope ies om hose b ick codes, like he Ca/Si
a io, MCL, o mal cha ge densi ies, p o ona ion deg ee, e c., wi h li le
e o . In addi ion, ha ing a clea alphanume ic code o de ine s uc u es
se s he g ound o machine lea ning applica ions [217–219].
Fu he mo e, i is possible o ex end he model by adding addi ional
and/o speci ic b icks o C-S-H su aces [97] o wi h Al o C-A-S-H
[98]. As limi a ions o he b ick model (as i has been p esen ed so a ),
we could men ion ha he esul ing s uc u es ha e a conside able
s uc u al o de . The in e laye species (Ca
2+
, OH
−
, and wa e ) a e
posi ioned in simila ini ial posi ions in each block, inducing some
co ela ion and o de ing in he s uc u es. This may no be an issue in
he con ex o C-S-H syn hesized unde con olled condi ions [8], bu
may no be a gene al case. To enci cle his possible p oblem a la ge
collec ion o b icks could be de ined, o he b icks could be used o build
he d ied skele on and wa e in oduced andomly wi h a packing al-
go i hm. Un o una ely, a p ac ical implemen a ion o he b ick model
needs a conside able p og amming e o , and so a i has been used
only by i s de elope s [97,98].
The de ec i e- obe mo i e model is he one gene ally used by e-
sea che s. O e all, his cons uc ion me hod is mo e gene al, as he C-S-
H model does no need o ely on p ede ined b icks. I is ela i ely simple
and as o build 1–5 di e en C-S-H samples o a pa icula s udy
wi hou coding, jus using isualiza ion so wa e like C ys alMake
[220], VESTA [221], o A ogad o [222], and build C-S-H models o
speci ic applica ions, b oadening he s udies o less common s uc u al
ea u es. Fo ins ance, obe mo i e 1.1 nm can be used o build C-A-S-H
models wi h Q
3
si es b idging adjacen laye s (no de eloped ye o he
b ick model). The cons uc ion me hod desc ibed in he o iginal e e -
ences [81,87] did no include any silanol o hyd oxyl g oups, which
we e o med la e du ing a molecula dynamics simula ion om he
dissocia ion o wa e molecules [91]. This would esul in a Si-OH +Ca-
OH pai o hyd oxyl g oups, which is no consis en wi h he expe i-
men al end [60,223]. Ne e heless, i is possible o se hei numbe
du ing he cons uc ion o a oid ha p oblem. The ob ained C-S-H gel
s uc u es a e gene ally mo e diso de ed han hose o he b ick model,
especially a high Ca/Si a ios. This is conside ed o be mo e ep esen-
a i e o C-S-H ob ained om cemen o C
3
S hyd a ion, bu in some cases
can lead o ins abili ies in he models, losing hei laye ed s uc u e.
6.2. How do I build a de ec i e obe mo i e model?
I is ela i ely simple o build a de ec i e obe mo i e model
ollowing he ecipes gi en in [81,87,157]. Tobe mo i e mine als a e
used as a bed ock o C-S-H model de elopmen . Bu hen, which
membe o he amily should be used o a ionalize he expe imen s and
build compu a ional models? In p inciple, he e is no limi a ion. Any o
hem could be a alid s a ing poin , p o ided ha he s uc u al mod-
i ica ions needed o ma ch he C-S-H expe imen al s oichiome y and
s uc u e a e in oduced co ec ly. Mo e igo ously, he he modynamic
p ope ies o a sys em in a gi en s able s a e a e independen o he pa h
ollowed o each ha s a e. As an example, we can conside a common
Table 3
Summa y o he discussed p ac ical aspec s and di e ences be ween he
de ec i e- obe mo i e and b ick-based C-S-H building me hodologies.
De ec i e
obe mo i e
B ick
model
Desc ip ion
Usabili y ✓ Easy and as o build up o 10
models wi hou coding
Mass
p oduc ion ✓ ✓ Capaci y o build hund eds o
models wi h a code
Rigu osi y ✓
Con idence in co ec chemical
coo dina ion, hyd oxyla ion
deg ee, cha ge balance...
O de /
Diso de Diso de O de Deg ee o s uc u al o de o he
ini ially gene a ed s uc u es
T ans e abili y ✓ Possibili y o ep oduce he exac
same model by o he au ho s
Flexibili y ✓
Possibili y o c ea e models wi h a
wide ange o composi ions and
s uc u es ( o ins ance Q
3
si es)
E. Duque-Redondo e al.
Cemen and Conc e e Resea ch 156 (2022) 106784
18
s ep in he cons uc ion scheme o he C-S-H: he emo al o he in e -
laye wa e om he ini ial c ys alline s uc u e and einse ion a e
c ea ing de ec s. In he o iginal scheme om Pellenq [81], he de ec i e
s uc u e wi hou wa e was elaxed, wi h he consequen sh inkage o
he basal space, and hen wa e was in oduced a he ixed olume by
G and Canonical Mon e Ca lo. This p ocedu e esul s in he “co ec ”
wa e con en o a gi en basal dis ance. Bu i is compu a ionally
expensi e. Al e na i ely, and gi en ha we oughly know he expe i-
men al wa e con en [14,41], one could di ec ly in oduce he neces-
sa y amoun o wa e molecules using a andom packing algo i hm
[224], and hen elax he olume o he sys em. In bo h cases, he inal
he modynamic s a e should be he same, eaching he co ec wa e
densi y by di e en pa hs: ixing he olume and changing he numbe
o molecules in he i s case, o ixing he numbe o wa e molecules
and changing he olume in he second case.
As gene al bounda ies, he s uc u es mus ul ill Richa dson's s oi-
chiome y, he 3n-1 ule o he silica e chains, and o he aspec s shown
in he nex sec ion. O cou se, we assume ha he selec ed compu a-
ional me hod p o ides a ealis ic desc ip ion o he chemis y, i.e. local
coo dina ion a ound Ca and Si, wa e s uc u e, e c). Besides hose
poin s, some hin s a e gi en below:
— I high Ca/Si a ios a e desi ed, when calcium silica e laye s a e
independen , bo h obe mo i e 1.4 nm and Hamid's obe mo i e
a e good choices. Tobe mo i e 1.4 nm is mo e simila o he C-S-H
in e ms o wa e con en , ye i s densi y, 2.23 g⋅cm
−3
[79], is
conside ably lowe han he expe imen al one, 2.60 g⋅cm
−3
[14],
and he basal space oo la ge. Hamid's obe mo i e is o en
p e e ed as a s a ing poin , as he smalle basal dis ance and
lowe wa e con en imply a highe s a ing densi y, 2.39 g⋅cm
−3
[30]. Ne e heless, a e modi ica ions o each a gi en s oichi-
ome y and silica e chain s uc u e, bo h Hamid's obe mo i e
and obe mo i e 1.4 nm should ideally con e ge.
— I C-S-H wi h he p esence o Q
3
si es is desi ed (low Ca/Si o high
aluminum con ain), obe mo i e 1.1 nm o clino obe mo i e
should be used o model C-S-H gel due o [225]. The di e ences
be ween no mal o anomalous obe mo i e 1.1 nm, loca ed a he
in e laye space [28], should anish a e he necessa y modi i-
ca ions o achie e diso de . In con as , he di e ences be ween
he complex modules A and B o clino obe mo i e and obe -
mo i e 1.1 nm (see Sec ion 2) may pe sis when he de ec s a e
in oduced. In his case, he s uc u al di e ences a e sub le, and
he p e e ence o one s uc u e o e he o he is di icul o
p edic .
6.3. Model alida ion and p edic ion o C-S-H gel p ope ies
The eade may ha e no iced ha we ha e discussed he “quali y” o
he models wi hou much quan i a i e alida ion o compa ison wi h
expe imen al da a. Despi e he la ge numbe o ecen publica ions, he
lack o connec ion be ween he C-S-H a omic scale modeling and he
expe imen al p ope ies is s ill an open issue in he ield. The di icul y
a ises om he di e se ime and leng h scales in ol ed in compu a ion
and expe imen s. Mos o he expe imen al measu emen s in ol e la ge
sample olumes ha include impo an he e ogenei ies in he compo-
si ion and s uc u e o he C-S-H gel, po es illed (o no ) wi h a po e
solu ion in equilib ium wi h he C-S-H, e c. The e o e, he link be ween
he expe imen al da a abou he C-S-H gel and he compu a ional
a omis ic models is indi ec a bes . Howe e , ollowing ou cu en
knowledge, he e a e se e al cha ac e is ics based on expe imen s ha
can be conside ed as a checklis o C-S-H model alida ion. Some
e e ence alues a e gi en in Fig. 10:
— XRD. Any C-S-H model mus be X- ay amo phous, i.e. he lack o
long ange c ys alline o de is a necessa y cha ac e is ic o any C-
S-H model. The excep ion is he (002) e lec ion a small angles
co esponding o basal dis ances be ween adjacen laye s o
~10–14 Å, indica i e o he well de ined laye s. A ealis ic model
should ha e a laye ed s uc u e [16,17,60]. In addi ion, syn-
ch o on XRD expe imen s gi e access o Pai Dis ibu ion
Func ions (PDFs) which desc ibe he sho ange o de o he
s uc u e [19,34]. The PDFs a e collec ed o he whole sample,
and may include ea u es ha do no co espond o he bulk.
Ne e heless, a gene al ag eemen wi h he expe imen al PDFs is
desi able.
— NMR measu emen s. F om Si-NMR expe imen s i has been
possible o quan i y he mean silica e chain leng h as a unc ion o
he Ca/Si a io, and he s uc u e o hose chains (D eie ke en
a angemen and 3n-1 ule, see Sec ion 2). A C-S-H model should
in p inciple e lec ha s uc u e, al hough he silica e chain
s uc u e is s ill he subjec o ecen s udies [96]. Simila ly, Al-
NMR da a mus also be obse ed when Al is inco po a ed in o
he models.
— IR and Raman spec oscopy. Spec oscopic echniques ha e been
used o de e mine he ela i e concen a ion o silanol g oups,
hyd oxyl g oups linked o Ca, and wa e wi hin he C-S-H gel
[13,41,60]. As in he p e ious cases, he echnique will gi e a
global alue o he whole sample, including su ace g oups and
species dissol ed in he po e solu ion. Ne e heless, he concen-
a ion o hyd oxyl g oups ollows a signi ican end wi h he Ca/
Si a io ha should be p e e ably ollowed. The same holds o he
wa e con en wi hin bulk C-S-H as a unc ion o he Ca/Si a io:
despi e an indi ec measu emen in d ied sample, he alues we e
alida ed by es ima ions om SANS [14] o Ca/Si a ios o
~1.65, and should be aken in o accoun .
— Neu on Sca e ing. Small Angle Neu on Sca e ing (SANS) was
used o in es iga e he composi ion, densi y, and size o C-S-H
nanopa icles [14]. An impo an cha ac e is ic ha C-S-H
models mus ollow is he highe densi y compa ed o obe -
mo i e c ys als, be ween 2.5 and 2.65 g⋅cm
3
o he C-S-H gel
compa ed o he ~2.2 g⋅cm
3
o obe mo i e 14 Å [14]. This alue
was la e on co obo a ed by
1
H-NMR elaxome y [228].
The e o e, C-S-H a omis ic models would be dense han hei
Fig. 10. (a) Silica e Mean Chain Leng h as a unc ion o he Ca/Si om
[8,64,87,226,227] (b) Si-OH/Si and Ca-OH/Ca a io as a unc ion o he Ca/Si
[13,41,60,223] (c) Wa e o silicon a io as a unc ion o he Ca/Si a io [41].
E. Duque-Redondo e al.
Cemen and Conc e e Resea ch 156 (2022) 106784
19
c ys alline coun e pa s. On he o he hand, Inelas ic Neu on
Sca e ing expe imen s ha e been used o quan i y he Ca-OH/Ca
a io as a unc ion o he Ca/Si a io, being complemen a y o
spec oscopic echniques [223].
6.4. Cu en p oblems and limi a ions wi h C-S-H compu a ional models
Fi s o all, i is impo an o make a clea dis inc ion be ween wha is
a alid C-S-H a omis ic desc ip ion and wha is no . A non-negligible
numbe o publica ions name as C-S-H a ully c ys alline obe mo i e
s uc u e [229], o e en a ully diso de ed glass wi hou laye ed s uc-
u e. Those sys ems, oge he wi h clus e models, may be used as
o e simpli ied models o in es iga e e y speci ic aspec s o he C-S-H
gel, bu a e no alid desc ip ions in mos cases. To be labeled as “C-S-H
model” he a omic s uc u e should ha e ini e silica e chains, highe
Ca/Si a ios and densi y han obe mo i e mine als, and ce ain diso de
o a oid a leas he long- ange o de cha ac e is ic o c ys als.
A second conce n is ha nowadays a omis ic simula ion s udies on
he C-S-H a e essen ially i ep oducible. Usually, sca ce de ails o he
building p ocedu e a e gi en, and he absence o an ac ual ile in a
eadable o ma (like he C ys allog aphic In o ma ion File [230] o he
P o ein Da a Bank [231]) makes i i ually impossible o ep oduce an
exac model. Few wo ks include in hei S.I. ully ep oducible a omic
s uc u e [8,81,95,97,98]. The e o e, he s anda diza ion o he C-S-H
models used o simula ions is u gen . The b ick model has an in insic
ad an age in his sense. The use o p ede ined building blocks makes i
simple o iden i y a C-S-H gel s uc u e based on a unique code ha
speci ies he cons i uen blocks and hei o de . The e o e, his unique
code allows wo di e en au ho s o build exac ly he same model.
Un o una ely, he code used o combine he b icks in he o iginal pape
[97] is no a ailable o he communi y nowadays. This s anda diza ion
is mo e complex in he case o he de ec i e- obe mo i e models since
hei cons uc ion in ol es andom s eps, i.e. he emo al o silica e
g oups om he silica e chains and he inse ion o coun e balancing
ions, Ca, hyd oxyl g oups, and wa e molecules. The e o e, hey canno
be duplica ed exac ly. The bes op ion o a good esea ch ep oduc-
ibili y would be o collec hem in a “C-S-H s uc u e da abase”. Exis ing
models and new ones could be labeled wi h an ID numbe , so hey could
be used o ep oducible pu poses as well as new in es iga ions.
In addi ion, we should always be awa e o he a iable s uc u e o
he C-S-H when we compu e i s p ope ies. E en o a speci ic Ca/Si
a io, he e is a humongous numbe o possible con igu a ions, and
pa icula models could ha e la ge de ia ions om he a e age p op-
e ies. As a as example: i we aim o build a C-S-H model made by
eplica ing he uni cell o obe mo i e 3x3x2, and hen we emo e jus 4
ou o he a ailable 72 b idging si es, we ha e mo e han 24 ×10
6
possible combina ions! Mos o he 24 million con igu a ions abo e
men ioned will ha e he poin de ec s homogeneously dis ibu ed along
he silica e chains, esul ing in simila ene gies. Bu in he pa icula
case o he 4 de ec s in neighbo ing si es, o in he same silica e chain,
he s uc u e may be ene ge ically un a o able. The e o e, i is neces-
sa y o unde s and he sensi i i y o he di e en p ope ies o he
pa icula con igu a ion, ye mos publica ions epo p ope ies
collec ed o a single s uc u e. Ano he in e es ing case was discussed
by Mohamed and cowo ke s in [97]. They e isi ed he C-S-H models in
he S.I. o e e ence [95], and hey ound egions wi h conside able
cha ge excesses wi hin an o e all neu al sys em. F om a s a is ical poin
o iew, we could expec a conside able local cha ge homogenei y in he
C-S-H gel, wi h na ow de ia ions, and ha model would ep esen a
con o ma ion wi h less weigh in he inal a e age p ope ies. The e o e,
using esul s om a single C-S-H model is no co ec om he s a is ical
poin o iew, and a comp omise be ween compu a ional cos and good
con igu a ional sampling should be sough .
6.5. P ac ical compu a ional hin s
We ha e discussed he s a is ical alidi y o he esul s and he
comp omise be ween good sampling and compu a ional cos , we hink
ha i is in e es ing o gi e some p ac ical hin s. The e a e many
di e en ac o s ha may ha e in luence bo h on he compu a ional
pe o mance and on he simula ion esul s.
Due o he ypical numbe o a oms in C-S-H models, abo e a hou-
sand in he bes case scena io, he use o ab ini io me hods is usually
p ohibi ed. The applica ion o hese me hods is limi ed o compu e
p ope ies inaccessible o empi ical po en ials in small model sys ems,
such as NMR shi s [98,234], o o benchma king pu poses
[116,234,235]. Rega ding empi ical po en ials, he e a e se e al
implemen a ions a ailable o he a omis ic simula ion o C-S-H gel,
being he mos common ones ClayFF [72], CSH-FF [94], Cemen FF
[233], he In e ace FF [232], and ReaxFF [236]. Despi e an exis ing
e iew o hei capabili ies and limi a ions [237], we lack a eal
exhaus i e benchma k o he impac o he o ce ield choice when C-S-H
p ope ies a e compu ed. In addi ion, he e is a conside able numbe o
pape s ha epo doub ul o ce ield choices. Fo ins ance, ReaxFF
[91,236,238] is a e y lexible po en ial capable o s udying bo h
diso de ed and o de ed phases and is he only o ce ield ha can
ep oduce chemical eac ions in C-S-H. Bu i also has some limi a ions,
such as i s high compu a ional cos , e en 40 imes slowe han o he FF
(see Table 4). Mo e impo an ly, i has no been speci ically pa ame-
ized o he in e ac ion o common elemen s in cemen like Cl, Mg, Zn,
e c. wi h C-S-H, and, in i s cu en o m, he C-S-H po en ials a e
incompa ible wi h o ganic compounds. In con as , IFF [232] has been
speci ically pa ame ized o be compa ible wi h common po en ials o
o ganic compounds and should be he na u al choice o hyb id sys ems.
ClayFF [72] is also a e y common choice o modeling C-S-H,
compa ible wi h o ganic o ce ields and a wide a ie y o aqueous ions.
Howe e , i has limi a ions o ep oduce some o he C-S-H p ope ies
like elas ici y, as i was ini ially de eloped o clay and clay- ela ed
ma e ials. The CSH-FF [94] po en ial was a epa ame iza ion o
ClayFF which makes i , in heo y, mo e sui able o ep oduce C-S-H
sys ems. On he bad side, he IFF, ClayFF, and CSH-FF use pa ial
cha ges on he a oms ha we e de eloped o pa icula cases, usually
obe mo i e, and hey need o be modi ied om he epo ed alues o
each elec oneu ali y in each C-S-H model, in oducing new un-
ce ain ies in he esul s. The Cemen FF sol es he issue using o mal
cha ges on a oms. Despi e o mal cha ges being a less ealis ic ep e-
sen a ion han pa ial cha ges, hey can be used consis en ly o e a wide
ange o s uc u es. In addi ion, he Cemen FF uses a co e-shell o D ude
pola iza ion scheme which p o es o be necessa y o ep oduce accu-
a ely ce ain p ope ies [239]. The cos o be paid is compu a ional
Table 4
Summa y o he mos employed o ce ields and hei main cha ac e is ics.
Fo ce
ield
Speed Cha ge
scheme
imes ep
( s)
Key aspec s Re
ClayFF e Pa ial,
ixed, non-
pola izable
1 De eloped o clays
aqueous ions
compa ible wi h C-
S-H
[72]
CSH-FF x1 Pa ial,
ixed, non-
pola izable
1 ClayFF
epa ame ized o
C-S-H
[94]
IFF x1 Pa ial,
ixed, non-
pola izable
1 Special ocus on
compa ibili y wi h
o ganic FFs
[232]
ERICAFF x0.25 Fo mal,
ixed,
pola izable
0.2 C-S-H speci ic and
pola izable
[233]
ReaxFF x0.025 Pa ial,
a iable,
pola izable
0.1 Reac i e FF [91]
E. Duque-Redondo e al.
Cemen and Conc e e Resea ch 156 (2022) 106784
20
pe o mance, due o he inc ease in he numbe o pa icles and dec ease
o he in eg a ion ime s ep. Machine lea ning Po en ials (MLP) may be
an in e es ing al e na i e in a close u u e. Some ini ial e o s ha e been
s a ed in he ield [240,241], ye s ill ocused on obe mo i e and wi h a
high compu a ional cos .
The compu a ional esou ces is ano he pa ame e o be conside ed.
Some es s o illus a ion a e gi en in Table 4. The simula ion ime
s ongly depends on he o ce ield, numbe o a oms, numbe o p o-
cesso s, and ha dwa e a chi ec u e. The es s we e made wi h a C-S-H
model wi h a Ca/Si a io o 1.65 and w/Si a io o 1.6. The ini ial sys em
had 749 a oms, and subsequen sizes we e buil by eplica ing he
simula ion box, up o 13,482 a oms. The simula ions we e done in he
supe compu e o he UPV/EHU, using Xeon 2680 4 co es a 2.8 GHz. In
Fig. 11 i can be seen he di e en pe o mance o he FFs, and he ex-
pec ed simula ion imes wi h he sys em size using 8 co es. Conside ing
a simula ion box o ~4.5x3x5 nm wi h ~6500 a oms, we can simula e
pe day nea ly 5 ns wi h ClayFF, CSHFF, and IFF, 1.25 ns wi h ERICAFF,
and 0.125 ns wi h ReaxFF. Longe imes can be achie ed by using a
la ge numbe o p ocesso s, as shown in 11. The speed up wi h he
numbe o co es is no linea , and depends on he FF used. Fo he
p e ious example, an inc ease om 8 o 32 co es will ansla e in o ~ 12
ns/day wi h ClayFF, CSHFF, and IFF, 3.75 ns/day wi h ERICAFF, and
jus 0.2 ns/day wi h ReaxFF. Those numbe s a e jus a guidance, as he
speed up depends also on he sys em size and on o he compu a ional
de ails. Bu he o de s o magni ude a e clea , and hey a e impo an o
he s udy o some p ope ies. The e is no such a hing as an “ideal
simula ion ime”, ye he expe ience ad ises us ha simula ions below
ns migh no be p ope ly equilib a ed and a e o dubious quali y.
Fu he mo e, longe simula ions could be necessa y o some p ope ies.
Fo ins ance, anspo p ope ies like di usi i y o iscosi y, a e e y
sensi i e o he sys em size and o he simula ion ime [242], and e en
hund eds o ns could be necessa y. Simila ly, when mechanical p op-
e ies a e compu ed, he e ec o he s ain a e mus be ca e ully
checked o a oid un ealis ic esponses om he ma e ial.
6.6. Wha is nex ? Do we need mo e/new/be e C-S-H (compu a ional)
models?
I we accep he consensus on Taylo 's model, wi h a C-S-H gel made
o obe mo i e-like laye s wi h de ec i e silica e chains and addi ional
calcium ions in he in e laye space, cu en compu a ional models a e
enough o co e all he possible s uc u es and s oichiome ies i hey
a e buil wi h ca e. Thus, we conside ha mo e/be e models o
desc ibe obe mo i e-like C-S-H a e no necessa y. I on he con a y, we
do no assume ha Taylo 's model desc ibes he C-S-H gel, o a leas no
all he possible a ie ies o he gel, we would need o build and es new
models.
Fo ins ance, he C-S-H s uc u e o low Ca/Si a ios can be easily
desc ibed using Taylo 's model, bu high Ca/Si a ios a e clea ly a
p oblem. By emo ing all he b idging silica e g oups and compensa ing
all he dangling siloxane g oups wi h Ca, he maximum possible Ca/Si
a io is 1.5. In ac , ecen s udies based on pai dis ibu ion unc ions
om high-ene gy X- ay expe imen s ha e p oposed ha
clino obe mo i e-like laye s and po landi e mono- o bi-laye s should
coexis in he C-S-H gel [19,34], se ing he Ca/Si h eshold o 1.23 [34].
Howe e , Kuma and cowo ke s [8] used a e y ine- uned syn he ic
me hod o ob ain C-S-H wi h Ca/Si a ios up o 2 wi hou de ec ing he
p esence o po landi e. The di e ence be ween hose s uc u es has
g ea implica ions on he C-S-H p ope ies, especially o long- e m
du abili y, decalci ica ion, e c. [243–245]. Compu a ional models
could be a g ea ool o u he in es iga e di e ences be ween sug-
ges ed C-S-H models and de e mine hei s abili y [246].
Ano he in e es ing poin ha could be explo ed wi h compu a ional
models is he s acking aul s and o ien a ion o he C-S-H laye s and
silica e chains. In obe mo i e, bo h he laye s and he chains a e
pe ec ly aligned. A key aspec o he s abili y o a diso de ed ma e ial
is he maximiza ion o i s en opy, o in o he wo ds, he numbe o
possible con igu a ions o a gi en he modynamic s a e, and hose de-
ec s would inc ease d ama ically he en opy o he sys em and hence
i s (me a)s abili y. In ac , i has been al eady sugges ed ha s acking
aul s could be necessa y o ep oduce he C-S-H XRD pa e ns.
Fu he mo e, a omis ic simula ion is an app op ia e ool o explo e he
con igu a ional space, looking o new o exo ic s uc u es, like C-S-H
nano ubes [247], C-S-H nanopa icles, and clus e s based on di e en
c ys alline phases like xono li e, e c.
The nex on ie in he C-S-H gel a omic s uc u e de e mina ion
mus be linked o in es iga ions o i s nuclea ion and g ow h mecha-
nism. I we unde s and how he solid C-S-H “pa icles” a e o med, we
would implici ly ob ain e y de ailed in o ma ion o hei s uc u e.
F om an expe imen al poin o iew, ecen pape s ha e explo ed in
g ea de ail he s uc u e de elopmen du ing he he e ogeneous
nuclea ion o C-S-H and po landi e [248–250]. A omis ic simula ions
could be used as a complemen a y echnique o unde s and he p ocess.
Despi e un a eling nuclea ion and g ow h mechanisms o c ys als and
nanopa icles is a complex p oblem o a omis ic simula ions, ecen
ad ances in he ield a e opening new possibili ies [251–254].
7. Conclusions
A e decades o esea ch, he C-S-H gel con inues o be a ho n in he
lesh in he ield o cemen science. I s s uc u e, composi ion, nucle-
a ion and g ow h, and du abili y a e ecu en esea ch opics, and
di e en models a e used o a ionalize he esul s. In his e iew, we
ha e made a ou o he mos ele an empi ical and compu a ional C-S-
H models p oposed o e he yea s.
Taylo 's obe mo i e-like s uc u e and Richa dson's s oichiome y
a e he accep ed empi ical C-S-H desc ip ions by he communi y.
Howe e , many impo an de ails emain unse led, as he p esence o
Fig. 11. (a) Simula ed ime (ns) in 1 h o eal ime using 8 co es as a unc ion o he sys em size o di e en FFs. The ClayFF and CSHFF imes o e lap and a e shown
oge he . (b) Speed up as a unc ion o he numbe o p ocesso s used o he simula ion o he selec ed FFs.
E. Duque-Redondo e al.
Cemen and Conc e e Resea ch 156 (2022) 106784
21
nanopo landi e a high Ca/Si a ios. Compu a ional C-S-H models and
a omis ic simula ions ha e bu s on o in he las yea s, aiming o b ing
some ligh o hese unce ain ies, and explo e nanoscale p ope ies
ha dly accessible o expe imen s. We ha e e iewed he his o ic de el-
opmen o C-S-H compu a ional models, om he ea ly a emp s wi h
simple models o he cu en ealis ic diso de ed obe mo i e-like
s uc u es. Then, we ha e inspec ed he main applica ion o hese C-S-
H models o in es iga e Aluminum inco po a ion o he silica e chains,
C-S-H elas ici y and mechanics, wa e and ion mobili y wi hin he C-S-H
nanopo es, and ecen s udies o C-S-H/o ganic sys ems. Finally, we
discussed p ac ical aspec s o he main compu a ional models, as well as
gi e some hin s on possible u u e di ec ions.
O e all, we hope ha his pape will se e as a good e e ence guide
o esea che s in he ield, gi ing a global ision o he empi ical and
compu a ional C-S-H models and hei common applica ions.
CRediT au ho ship con ibu ion s a emen
Edua do Duque-Redondo: Concep ualiza ion, In es iga ion,
W i ing – o iginal d a , W i ing – e iew & edi ing, Supe ision. Pa -
ick A. Bonnaud: In es iga ion, W i ing – o iginal d a , W i ing – e-
iew & edi ing. Hegoi Manzano: Concep ualiza ion, In es iga ion,
W i ing – o iginal d a , W i ing – e iew & edi ing, Supe ision, P ojec
adminis a ion.
Decla a ion o compe ing in e es
The au ho s decla e ha hey ha e no known compe ing inancial
in e es s o pe sonal ela ionships ha could ha e appea ed o in luence
he wo k epo ed in his pape .
Acknowledgmen s
The au ho s would like o acknowledge unding om “Depa amen o
de Educaci´
on, Polí ica Lingüís ica y Cul u a del Gobie no Vasco” (G an
No. IT912-16 and IT1639-22) and he echnical and human suppo
p o ided by he Scien i ic Compu ing Se ice o SGIke (UPV/EHU/
ERDF, EU). E.D.-R. also acknowledges he pos doc o al ellowship om
“P og ama Posdoc o al de Pe eccionamien o de Pe sonal In es igado
Doc o ” o he Basque Go e nmen .
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