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Acta Materialia 67 (2014) 81–94

Calcium silicate hydrate from dry to saturated state:Structure, dynamics and mechanical properties

Hou Dongshuai a,⇑, Ma Hongyan a,⇑, Yu Zhu b, Li Zongjin a,⇑

a Department of Civil and Environmental Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kongb Department of Civil Engineering Henan Polytechnic University, Henan, China

Received 14 July 2013; received in revised form 12 November 2013; accepted 11 December 2013Available online 24 January 2014

Abstract

Calcium silicate hydrate (C-S-H) is the most important hydration product of cement-based materials. In the nanostructure of C-S-H,structural water molecules are distributed in the interlayer region and determine the mechanical performance of C-S-H gel. In this study,C-S-H gels with different water contents expressed as the water/Ca ratio are characterized in the light of molecular dynamics. In order tostudy the influence of the water molecules, the structures of 12 C-S-H gel samples with water/Ca ratios from 0 to 0.95 are investigated. Itis found that the penetration of water molecules transforms the C-S-H gel from an amorphous to a layered structure by silicate depo-lymerization as the water content gradually increases. The structures are then tested for mechanical properties by simulated uniaxial ten-sion and compression. The mechanical tests associated with structural analysis reveal that the structural water molecules can greatlyweaken the stiffness and the cohesive force by replacing the ionic–covalent bond with unstable H-bond connections. By studying the ten-sile failure mechanism of C-S-H gels at different humidity levels, the disconnecting role of the structural water molecules is comprehen-sively interpreted. Because the interlayer water molecules prevent reconstruction of the bonds between the Caw and the silicate chains, theplasticity of the C-S-H gels is reduced significantly in the change from a dry state to a saturated state. In addition, the compressivestrength of a C-S-H gel in the saturated state is much larger than the tensile strength. This provides molecular evidence for the tensileweakness of cement paste.� 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Calcium silicate hydrate (C-S-H); Water/Ca ratio; Molecular dynamics; Uniaxial tension/compression test

1. Introduction

When Portland cement reacts with water, cementhydrates are produced. Calcium silicate hydrate (C-S-H)gel is the dominant cement hydrate, and hence it deter-mines the binding force of the cement paste. For the wholeservice life of a cement paste/concrete, the interactionbetween water and C-S-H gel determines the mechanicalproperties and durability of cement-based materials. Onthe one hand, the initial water content of the cement paste,or water-to-cement ratio, influences the microstructure of

1359-6454/$36.00 � 2013 Acta Materialia Inc. Published by Elsevier Ltd. All

http://dx.doi.org/10.1016/j.actamat.2013.12.016

⇑ Corresponding authors.E-mail addresses: dhou@ust.hk (D. Hou), cehy@ust.hk (H. Ma),

zongjin@ust.hk (Z. Li).

the cement hydrates [1]; on the other hand, the water mol-ecules, as essential elements of C-S-H gel, are sensitive tothe surrounding environment and humidity [2]. For exam-ple, when immersed in water, C-S-H gel is very likely toreach a saturated state, while the structural water of theC-S-H may be missing in the case of a fire.

In order to understand the role of water in C-S-H gel, itis necessary to investigate the intrinsic structure andmechanical performance of the gel at different humiditylevels. The molecular structure of C-S-H has been studiedfor more than half a century, particularly using a varietyof experimental techniques, including nuclear magneticresonance (NMR) imaging [3], X-ray diffraction [4] andsmall-angle neutron scattering (SANS) [5], and C-S-H isnow widely believed to be the analogue of the layered

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Fig. 1. Initial dry C-S-H structure for water adsorption simulation.Simulation box size: a = 21.3, b = 21.2, c = 21.9; a = 90�, b = 90�,c = 90�. Yellow and red bonds represents the silicate chain (Si–Os); thegray and green balls correspond to the interlayer calcium atoms (Caw) andthe layered calcium atoms (Cas), respectively. (For interpretation of thereferences to color in this figure legend, the reader is referred to the webversion of this article.)

82 D. Hou et al. / Acta Materialia 67 (2014) 81–94

minerals tobermorite [6,7] and jennite [8]. Based on exper-imental data, Pellenq et al. [9] employed the moleculardynamics method to construct a C-S-H model that candescribe well the structural, dynamical and mechanicalproperties of cement at the nanoscale. Because the modelis based on previous experimental results, it has beenwidely accepted in the nanoscale simulation field and isdefined as a “realistic model”. The “CSHFF force field”

[10] was developed to describe the interaction betweenatoms in cement systems, and this force field demonstratedgood transferability in simulating cement-based materials.

Water molecules, essential constituents in C-S-H gel,have been investigated since the birth of the “realistic mod-el”. Pellenq et al. [9] simulated the stress–strain relation ofC-S-H gel in resisting shear force. By comparing themechanical performance of dry and wet C-S-H gels, itwas concluded that, during the loading process, large dis-placements of water molecules in wet C-S-H gels weakenthe shear strength and result in unrecovered deformations.Youssef et al. [11] investigated the structural and dynamicfeatures of water molecules in C-S-H gels. Due to thehighly hydrophilic nature of calcium silicate sheets, H-bonds constructed between the non-bridging oxygen andwater are very strong. Therefore, water molecules con-strained in the gel demonstrate a glassy nature: the tetrahe-dral spatial structure is distorted and the diffusion rate issignificantly reduced. Ji et al. [12] utilized five classic watermodels, SPC, TIP3P, TIP4P, TIP4P05 and TIP5P, to sim-ulate calcium silicate hydrate. They concluded that SPCand TIP5P accurately describe the intrinsic properties ofC-S-H gel, with SPC (flexible) being more computationallyefficient. Recently, Bonnaud et al. [13] interpreted the cohe-sive force of C-S-H gel by analyzing the fluid pressure ofthe water molecules and the counter-ions in the interlayerregion. Under different humidity conditions, they foundthat the cohesive force mainly results from negative pres-sure caused by the interaction between interlayer calciumatoms and the calcium silicate sheets. Even though thiswork took the amount of water in the C-S-H gel into con-sideration, the molecular structure of the calcium silicatesheet was assumed to remain unchanged under differenthumidity conditions. This assumption, ignoring the struc-tural evolution due to the water effect, needs to be furtherinvestigated.

Previous research on C-S-H gels can be categorized intotwo classes: molecular structure analysis and thermody-namics investigation. Few efforts have been made to inves-tigate the evolution of mechanical properties with watercontent variation. In particular, the tensile strength of C-S-H gels at the nanoscale, considered as the most essentialproperty of construction material, has not been studied sofar. The aim of this paper is to bridge the relationshipbetween the morphology and the mechanical performanceof C-S-H gels in different humidity conditions. On theone hand, the structural feature evolution can be character-ized by analyzing the silicate chain morphology andchemical bonds in different water contents. On the other

hand, the mechanical properties, including the stiffnessand cohesive force, can be achieved directly from uniaxialtension/compression simulation. Combining the structuraland mechanical evolution, the water molecules’ role inloading resistance can be determined and assessed.

2. Simulation method

The CSHFF force field [10], developed for cement-basedmaterials, is utilized to simulate C-S-H gels at differenthumidity states. The force field approach has been widelyused in C-S-H simulations and has been proven to be ableto describe the structure, energy and mechanical propertiesof various calcium silicate phases satisfactorily [9,11–14].The force field parameters of Ca, Si, O and H can beobtained from the literature [15].

2.1. Dry and saturated model

The C-S-H model in the present study is constructedbased on the procedures proposed by Pellenq et al. [9].Firstly, the layered analogue mineral of C-S-H, tobermor-ite 11 A without water, was taken as the initial configura-tion for the C-S-H model [16,17]. Silicate chains werethen broken to match the Q species distribution obtainedfrom NMR testing [18]. The dry disordered structure isplotted in Fig. 1. Secondly, Grand Canonical Monte Carlosimulation of the water adsorption is operated on the drydisordered C-S-H structure at 300 K. The adsorptionis conducted from 0 to 100 million steps to obtain 12

19

20

21

22

23

Spac

e in

z d

irect

ion

Water/Ca ratio0.0 0.2 0.4 0.6 0.8 1.0

Fig. 2. Evolution of space in the z direction with water/Ca ratio.

D. Hou et al. / Acta Materialia 67 (2014) 81–94 83

C-S-H gel samples with water/Ca contents from 0 toaround 0.95, respectively. The 0 step simulation gives adry C-S-H sample, and when the number of adsorptionsteps exceeds 100 million, the C-S-H gel reaches a saturatedstate [13]. The chemical formula of the saturated C-S-Hstructure in the current simulation is (CaO)1.69(SiO2)-�1.66H2O, which is quite close to the (CaO)1.7(SiO2)�1.8H2-

O obtained by the SANS test [5]. The molecular dynamicssimulations under constant pressure and temperature(NPT) for 300 ps give the structures of C-S-H gel in equi-librium states. For each case, a further 1000 ps NPT runis employed to achieve the equilibrium configuration forstructural and dynamic analysis.

2.2. Mechanical properties calculation

After 12 samples from the dry state to the saturatedstate had been obtained in previous simulations, describedin Section 2.1, their mechanical properties were calculated.Young’s modulus and the tensile strength in the z direction,describing the stiffness and the interlayer cohesive force,respectively, are obtained by uniaxial tension testing.

In order to elucidate the stress–strain relation, the C-S-H samples were subjected to uniaxial tensile or compressiveloading through gradual elongation or shortening at a con-stant strain rate at 0.08 ps�1. NPT ensembles were used forthe system throughout the whole simulation process. Takethe tension process as an example. Firstly, the simulationbox is relaxed at 300 K and coupled to zero external pres-sure in the x, y and z dimensions for 100 ps. Then, after thepressures in the three directions have reached equilibrium,the C-S-H structure is elongated in the z direction. Mean-while, the pressures in the x and y directions are kept atzero. The pressure evolution in the z direction is taken asthe internal stress rzz. The non-pressure setting in direc-tions perpendicular to the tension direction, also consider-ing Poisson’s ratio, can eliminate the artificial constrain forthe deformation and allow the free development of tensionwithout any restriction. In the simulated tension process,10,000 configurations are recorded for structural analysis.

3. Results and discussion

3.1. Molecular structures of C-S-H gel samples

3.1.1. Molecular structure transformationAfter the model construction procedures, 12 C-S-H

samples were determined with water/Ca ratios of 0, 0.13,0.3, 0.40, 0.50, 0.59, 0.66, 0.72, 0.80, 0.84, 0.86 and 0.95.As shown in Fig. 2, with increasing water content, in theequilibrium state, space in the z direction enlarges from18.9 to 22.6 A. In the saturated state, the interlayer dis-tance in the z direction reaches 11.3 A, which is consistentwith that of tobermorite [7] and the “realistic model” [9].The differences between the gel samples in the dry stateand in water-carrying states mainly result from the swellingof C-S-H structures due to water penetration.

Three simulated C-S-H gel samples in the dry (water/Ca = 0), partially saturated (water/Ca = 0.50) and satu-rated states (water/Ca = 0.95) are shown in Fig. 3. Corre-spondingly, the intensity profiles of different atoms in thethree states are plotted in Fig. 4 vs. the distance in the zdirection. The combined information in Figs. 3 and 4 cangive a good understanding of the molecular structures ofthe C-S-H gel samples. In the dry state, as shown inFig. 4a, the distributions of Cas (calcium sheet), Si andCaw (interlayer calcium atom) overlap to a great extentalong the z direction and no obvious boundary existsbetween the interlayer region and the calcium sheet, indi-cating a loss of the layered feature. As demonstrated inFig. 3a, the silicate chains are distributed across the z direc-tion in a disorderly manner, which slows the amorphousnature of the structure in the form of silicate glass [19].In the half saturated state (water/Ca = 0.5), along the zdirection, the alternative maxima of Cas, Si, Caw and Ow

(oxygen atoms in water molecules) in the density profiles,as shown in Fig. 4b, imply that C-S-H gel has a sand-wich-like structure. It can be clearly observed in Fig. 3bthat Cas and Os (oxygen atoms in the silicate structure)form Cas–Os octahedrals, thereby constructing a Cas sheet.Defective silicate chains are grafted on both sides of the Cas

sheets, and the Caw and the water molecules are distributedbetween the neighboring calcium silicate sheets. In the sat-urated state (water/Ca = 0.95), as compared to the half sat-urated state, sharper density distributions of Cas and Si(Fig. 4c) indicate a much more ordered arrangement ofthe calcium silicate sheets. The intensity of Ow is distrib-uted across the z direction, which means that water mole-cules are not only present in the interlayer regions butalso diffuse into the defective region of calcium silicatesheet, as shown in Fig. 3c. Furthermore, the silicate chainsalso grow along the y direction with good organization, aswidely found in the mineral analogues tobermorite and jen-nite [8]. From the above analysis, it can be seen that watermolecules penetrate into the structure of the C-S-H gel andtransform the amorphous glassy structure to a layeredstructure as a water/Ca ratio increases from 0 to 0.95.

Fig. 3. Snapshots of the molecular structures of C-S-H gel samples from the dry state to the saturated state: (a) water/Ca = 0; (b) water/Ca = 0.5; (c)water/Ca = 0.95. The red and white sticks corresponding to water molecules. (For interpretation of the references to color in this figure legend, the readeris referred to the web version of this article.)

Fig. 4. Density profiles of Cas, Si, Ow, Caw atoms: (a) water/Ca = 0; (b) water/Ca = 0.5; (c) water/Ca = 0.95.

84 D. Hou et al. / Acta Materialia 67 (2014) 81–94

3.1.2. Silicate chains morphology

Silicate chain morphologies demonstrate discrepanciesin the dry and saturated samples. In the silicate glass struc-ture, Qn (n = 0, 1, 2, 3, 4) is an important parameter todescribe the silicate connections, where n is defined as thenumber of connected neighboring silicate tetrahedrons.Q0 is the monomer; Q1 represents a dimer structure (twoconnected silicate tetrahedrons); Q2 is a long chain; Q3 isa branch structure; and Q4 is a network structure [20]. Inthe saturated samples, as shown in Fig. 5c, Q1 is the dom-inant phase and dimer structures develop in an orderlyfashion along the y direction. The presence of watermolecules prevents neighboring silicate chains fromapproaching. However, when the water/Ca ratio is low, apolymerization reaction can result in short silicate chainconnections and thereby change the morphology of the sil-icate chains. On the one hand, in the dry state (shown inFig. 5a), bridging silicate tetrahedrons can link with thesurrounding monomers and connect with three neighbor-ing tetrahedrons. The sol–gel reaction produces Q3 species,which are widely distributed in the amorphous silicate glasstogether with cation atoms [19]. The Q3 species, i.e. thebranch structures, indicate the glassy nature of the dry C-S-H gel. It should be noted that the Q3 species can bridgeboth the intra- and interlayer silicate chains. Unlike the sil-icate chain growth along the y direction in the saturatedsamples, the silicate chain in the dry sample transforms

into the branch structure and develops along two dimen-sions (y and z directions). Similarly, the Q3 species has alsobeen detected experimentally in the mineral analogue of C-S-H gel, i.e. tobermorite 9 A [21], which contains no watermolecules. On the other hand, as shown in Fig. 5b, whenthe water/Ca ratio reaches 0.3, two dimers and one mono-mer can grow together to develop a long silicate chainacross the interlayer region. Even though the Q3 speciesdisappears due to the increasing water content, silicatechains can still grow in two dimensions. The polymeriza-tion process is the evolution from short silicate chains(Q0, Q1) to long chains (Q2).

From the analysis in this section, it can be seen that, inthe C-S-H gel, water molecules can isolate the neighboringcalcium silicate chains and prevent further polymerizationof defective silicate structures. The depolymerization roleof the water molecules has been explained in previoussilica synthesis simulations [22]. The hydration of cement,which produces C-S-H gel, is based on the sol–gel reactionin the presence of calcium ions. Water molecules associ-ated with the non-bridging oxygen atoms in silicatechains prevent connections between isolated silicate struc-tures, and cause decay in the polymerization process. Inthe case of low water/Ca ratio, a further polymerizationprocess contributes to the formation of the amorphoussilicate morphology and weakens the layered structureof C-S-H gel.

Fig. 5. Morphology change of silicate chain: (a) polymerization in the dry sample; (b) polymerization in the sample with water/Ca = 0.3; (c) morphologyof the silicate chain in the saturated state.

D. Hou et al. / Acta Materialia 67 (2014) 81–94 85

3.1.3. Calcium sheet and interlayer calcium

Calcium atoms in C-S-H gel have complicated localstructures. According to the geometric location, calciumatoms are categorized as sheet calcium (Cas) or interlayercalcium (Caw). The nearest neighboring oxygen atoms ofthe two types of Ca are both from Ow (O in water) andfrom Os (O in silicate chains). A radial distribution func-tion (RDF) describes the local structure of Ca–O of the sat-urated sample. To better understand the structure featuresof Ca–O, the RDF (Ca–O) is further differentiated intofour pairs, as shown in Fig. 6. For bonded atoms, the rel-evant bond distances can be readily determined by the posi-tions of the peaks in the corresponding RDF. The lengthsof the four Ca–O bonds are ranked in the following order:Cas–Os < Caw–Ow < Caw–Os < Cas–Ow.

The bond length difference reflects the local environmentof Ca atoms with respect to chemical bonds. On the one

Fig. 6. RDF of Ca–O pairs.

hand, silicate chains graft onto the calcium sheet and, incomparison with Caw, Cas atoms are more likely to associ-ate with Os in the silicate chain. Hence, Cas–Os has ashorter bond length than Caw–Os. On the other hand,water molecules energetically prefer the Caw and havefewer chances to form bonds with Cas, contributing tothe shorter bond length of Caw–Ow.

The coordination number of Ca atoms is defined as thetotal neighboring O atoms that are within 3 A from thecentral Ca atom. The Ca–O bond length is defined as3 A, as used in many references using CSHFF [9,10,15].As shown in Fig. 7, the chemical bonds of both Cas–Os

and Caw–Os reduce with increasing water content. This ismore pronounced in the Caw–Os bond because, in a drysample, 6.5 Os atoms can form chemical bonds with thenearest Caw, whereas more than 35% of the neighboringOs atoms are substituted by Ow atoms in the saturated case.

0.0 0.2 0.4 0.6 0.8 1.00

2

4

6

8 Cas-Os Cas-Ow Caw-Os Caw-Ow

CN

of C

a

Water/Ca ratio

Fig. 7. Average coordination number of Ca and Caw with increasingwater content.

RD

F (O

H)

0.

0.

1.

1.

2.

00

5

0

5

0

2

Distance (Ang)4 6 8

Os-HOw-

10

wHw

Fig. 9. RDF of O–H in saturated sample.

86 D. Hou et al. / Acta Materialia 67 (2014) 81–94

Therefore, it can be observed from Fig. 7 that the numbersof Cas–Ow and Caw–Ow bonds per calcium atom increaseto around 1 and 2.5, respectively, in the saturated state.

The variations in the coordinated oxygen atoms result indifferent bridging bonds between neighboring calcium sili-cate sheets. The chemical bond evolution is illustrated sche-matically in Fig. 8. In the case of dry samples, the ionicbonds of Os–Caw–Os can connect directly to the nearby sil-icate chains. However, since the maximum Caw–O bondlength is about 3 A, it is difficult to form an Os–Caw–Os

connection, as the distance to the neighboring Os atomsexceeds 6 A. In this case, the structural water moleculescan play a role in bridging near the Caw by Caw–Ow bonds.When the water/Ca ratio further increases, multiple layersof water molecules are packed between the calcium silicatesheets. An H-bond network is developed between neigh-boring water molecules and the surrounding Os atoms.

3.1.4. H-bonds in the interlayer region

In addition to the Si–O and Ca–O bonds, the H-bond isanother important chemical connection in the C-S-H gel.Water molecules can form H-bonds both with silicatechains and with neighboring water molecules. RDFs ofOw–Hw and Os–Hw describe local structures of the twotypes of H-bond connections. As shown in Fig. 9, the firstpeak value of Os–Hw occurs at 1.64 A, which is shorterthan the 1.75 A of Ow–Hw. This implies that Os atomsare energetically preferable to the surrounding Hw atoms.

In the medium range, from 2 to 4.5 A, the differencebetween the two RDF curves is more obvious. Doublepeaks of Os–Hw occur at 3.1 and 4.0 A and a single peakof Ow–Hw with larger intensity occurs only at 3.1 A. Dou-ble peaks mainly result from the fact that water moleculesare geometrically constrained by the surrounding silicatechains, and the spatial correlation between Os and Hw

can be maintained in the medium range. Compared tothe constraint effect from the silicate chain, the restrainedinfluence from neighboring water molecules is muchweaker and the arrangement of water molecules in themedium range is not well ordered.

Fig. 8. Schematic diagrams of the interlayer connections.

The average number of H-bonds per water is calculatedas a function of water/Ca content. According to the litera-ture [23], the formation of an H-bond requires two condi-tions: the distance between two water neighbors DHO

should be less than 2.45 A and the angle h between theOH vector and OO vector should be less than 30�. Asshown in Fig. 10, the bond number of Os–Hw graduallydecreases from around 1.6 to 1.2, while the number ofOw–Hw increases from 0.3 to 1.18, as the water/Ca ratioincreases from 0.13 to 0.95. When the water/Ca ratio islow, Os–Hw accounts for the majority of the H-bonds.Water penetration into the C-S-H gel can significantlyreduce the Os–Hw ratio, and H-bonds are progressivelysubstituted by Ow–Hw bonds. Both Os–Hw and Ow–Hw

occupy 50% of the H-bonds in the saturated sample. Asa comparison, 1.2 and 1.18 H-bonds connected by silicatechains and neighboring water molecules, as seen inFig. 10, are consistent with the H-bond number calculatedin Ref. [11] using Kumar et al.’s method [24].

The evolution of H-bond types also influences the bridg-ing between nearby calcium silicate sheets, as schematically

H-b

onds

/wat

er

0.

0.

0.

1.

1.

2.

0

4

8

2

6

0

0.2 0.4Water/Ca

0.6 0.8

Os-Ow-

1.0

HwHw

Fig. 10. Evolution of average H-bond number with water/Ca.

Fig. 11. Schematic diagrams of the interlayer H-bond connections.

D. Hou et al. / Acta Materialia 67 (2014) 81–94 87

illustrated in Fig. 11. At a low water/Ca ratio, Os–Hw

bonds can be distributed across the interlayer region anddirectly bridge the neighboring calcium silicate sheets. Withincreasing water content, the water molecules in the inter-layer region transform from single-layer to multi-layerpacking. In the case of the single layer, water moleculescan bridge the neighboring calcium silicate sheets by H-bonds of both Hw–Os and Hw–Ow, while, in the case ofmulti-layers, the water connects indirectly to the surfacewater molecules by Hw–Ow bonds. In this way, the connec-tion between neighboring calcium silicate sheets is screenedby the increasing number of water layers.

3.1.5. Stability of chemical bonds

The previous discussion describes the molecular struc-ture of C-S-H gel in both dry and saturated states in termsof chemical bonds. As shown in the snapshots of the inter-layer region in Fig. 12, the chemical bonds of Si–Os, Cas–Os, Caw–Os, Caw–Ow, Hw–Ow and Os–Hw play roles inbridging the neighboring calcium silicate sheets. Thestrengths of the bonds depend to a large extent on the sta-bility of the chemical bonds. As in previous research study-ing H-bond strength [11], the time-correlated function

Fig. 12. Chemical bonds

(TCF) is utilized to describe dynamical properties of vari-ous chemical bonds.

The TCF, C(t), of a bond is described by Eq. (1):

CðtÞ ¼ < dbðtÞdbð0Þ >< dbð0Þdbð0Þ > ð1Þ

where db(t) = b(t) � <b>, b(t) is a binary operator thattakes a value of 1 if the pair (e.g. Ca–O) is bonded and 0if not, and <b> is the average value of b over all simulationtimes and pairs. The chemical bonds break and form astime passes, which result in the connectivity variation inC-S-H gels. If the connectivity persists unchanged, theTCF of the bonds will maintain a constant value of 1.Otherwise, the breaking of the bonds leads to lower TCFvalues, and the more frequent the bond breakage, the lowerthe TCF value. By comparing the deviations from 1 in theTCF curves, the stability of various bonds can beestimated.

Fig. 13 demonstrates the evolution of the TCFs ofSi–Os, Cas–Os, Caw–Os, Caw–Ow, Hw–Ow and Os–Hw in1000 ps. The chemical bonds can be categorized into twotypes: bonds connected with Os and bonds connected withwater. The C(t) values of Os-connected bonds, includingSi–Os, Cas–Os and Caw–Os bonds, almost maintain a con-stant value with limited fluctuations, which indicates thatthey are stable chemical connections. In contrast, C(t)values of Ow-connect bonds, like Caw–Ow, Hw–Ow andOs–Hw bonds, reduce significantly with time. For H-bondsof Hw–Ow especially, the C(t) value decreases to less than0.5, implying that the connectivity of more than half ofthe bonds changes. According to the reduction extent ofC(t), the strength of chemical bonds is ranked in the follow-ing order: Si–Os > Cas–Os > Caw–Os > Caw–Ow >Hw–Os > Hw–Ow.

The stability of the bonds can be explained by the mobil-ity of different atoms in C-S-H gel. The mean square dis-placement MSD(t) [25], a parameter used to estimate thedynamic properties of water molecules, can be defined byEq. (2):

MSDðtÞ ¼< jriðtÞ � rið0Þj2 > ð2Þ

in interlayer region.

C (t

)

0.

0.

0.

0.

0.

1.

00

2

4

6

8

0

Si-OCa-CawCawOw-Hw-

200

O-O-OwHwO

400

Time (Ps)600 800 1000

Fig. 13. TCF of various chemical bonds in C-S-H gel.

0 200 400 600 800 10000

1

2

3

4

5 Ow Caw Cas Si

MSD

(Ang

2 )

Time (Ps)

Fig. 14. MSD of Ow, Caw, Cas and Si in 1000 ps.

88 D. Hou et al. / Acta Materialia 67 (2014) 81–94

where ri(t) represents the position of atom i at time t, ri(0) isthe original position of atom i and MSD takes into accountthree-dimensional coordinates. A large MSD value at timet indicates that the atoms diffuse rapidly and are displacedfar away from the original position. Fig. 14 exhibits thatthe diffusion rate of atoms ranks in the following order:Ow > Caw > Cas > Si. It can be seen from Fig. 14 that theMSD of Ow (water) at 1000 ps is more than four times thatof the other three atoms. The high diffusion rate of watermolecules results in the frequent change of the chemicalbonds with water. It is worth noting that the MSD ofCaw has a similar variation trend to that of water. This isattributed to the fact that Caw forms clusters with waterin the interlayer region, and the diffusion rate is thus accel-erated to some extent. In addition, in the calcium silicatesheet, the diffusion rate of Si is lower than that of Cas.The dynamic properties of the Si–O bonds and Ca–Obonds revealed match previous findings using the ab initiomethod well [26]. The findings prove that Si–O bonds in sil-icate chains have more binding energy than Ca–O bondsand are hard to break.

3.2. Mechanical properties

Previous structural and dynamics analyses provide aclear picture of chemical bonds in C-S-H gels. Due to thestrong chemical strength and low diffusion rate of Si, thesilicate chains provide the most stable backbone of C-S-H gels. Cas atoms are associated with the neighboring Os

in the silicate chains to produce high-strength calciumsilicate sheet. In different humidity states, the Caw atomsassociated with various amounts of interlayer water playan important role in connecting the neighboring calciumsilicate sheets. The mechanical properties of C-S-H gelsin different humidity states are determined by the combina-tion of these chemical bonds. In light of the method intro-duced in Section 2.2, the mechanical properties of C-S-Hgel are discussed in this section, and explained in termsof the chemical bonds.

3.2.1. Stress–strain relation

Stress–strain curves are used to assess the mechanicalperformance of C-S-H gels in the whole tensile loading pro-cess. Tensile and compressive stress–strain relations of the12 samples at different humidity states are plotted inFigs. 15 and 16, respectively. Fig. 15 shows two types offailure mode during the tensile process. When the water/Ca ratio is less than 0.6 (samples 1–5), the samples demon-strate good plasticity. During the tensile process, the stressincreases up to the failure strength at a strain of around0.1 A A�1, then reduces slowly and fluctuates in a saw-likestyle. The structure of the dry C-S-H gel (sample 1) cannotbe directly stretched to fracture even when the strainreaches 0.8 A A�1. In contrast, when a sample’s water/Caratio exceeds 0.6, it is more likely to be stretched to frac-ture. As shown in Fig. 15, in samples 6–12 the stressincreases to the maximum quickly at a strain of less than0.1 A A�1 and subsequently drops to zero. With increasingwater/Ca ratio from 0.6 to 1, the strain at fracture reducesfrom 0.8 to 0.4 A A�1. That is to say, the interlayer watermolecules make the C-S-H gel more brittle.

In case of the compressive stress–strain relation inFig. 16, two distinguished failure modes can also beobserved. When the water/Ca ratio is less than 0.5 (samples1–4), the samples demonstrate good plasticity. During thecompressive process, the stress increases to the maximum,then fluctuates at the failure strength until the strainreaches around 0.35 A A�1. In the post-failure region, thestress can maintain at a long-strain plateau value withoutobvious reduction. On the other hand, when the sample’swater/Ca ratio is larger than 0.5, the stress–strain plateaudisappears and the stress reduces quickly in the post-failurestage.

3.2.2. Young’s modulus and tensile strength

The Young’s modulus, tensile strength and compressivestrength, obtained from the stress–strain curves, are impor-tant quantitative parameters for estimating the mechanicalproperties of C-S-H gels. As shown in Fig. 17a, with a

Fig. 15. Stress–strain relations of 12 samples under uniaxial tension loading along the z direction.

D. Hou et al. / Acta Materialia 67 (2014) 81–94 89

progressively increasing water/Ca ratio from 0 to 1,Young’s modulus reduces from 67 to less than 47 GPa.The Young’s moduli obtained in the current simulationsare consistent with the results from a nanoindentation test(60 GPa) [27] and previous ab initio calculations (55–68 GPa) [9]. It should be noted that the moduli of sampleswith water/Ca ratios of <0.3 are maintained at around67 GPa, much larger than other samples. It is known fromprevious structural analyses that having less water can con-tribute to further polymerization of the silicate chains, thusthe three samples may have Q3 species or developed silicatechains in the z direction which achieve the high moduli.When the water/Ca ratio is high, the silicate chains whichact as the backbone of C-S-H are shorter, and the watermolecules themselves can also significantly weaken the stiff-ness of the C-S-H gel. In terms of chemical bonds, in dry C-S-H gel, the Caw atoms fill in the defects of the silicatechains, which contribute to the Caw–Os connection. Asmentioned above, following an increase in the water/Ca

ratio, water molecules penetrate and replace the partialCaw–Os connections with H-bonds, which can soften theC-S-H gel. Furthermore, water molecules adsorbed onthe defective silicate chains result in larger interlayer dis-tances and thus a smaller coulombic attraction betweenneighboring calcium silicate layers.

Similar evolution trends in the tensile strength can beobserved in Fig. 17b, decreasing from 7.5 GPa in the drystate to 3.8 GPa in the saturated state. The failure stressesobtained are consistent with the rupture strength (�3 GPa)by shear simulation [9] and the fluid pressure (2.75 GPa)calculation [13]. The huge difference in C-S-H gel tensilestrength between the dry and saturated states indicates dif-ferent failure mechanisms. The chemical bonds in the C-S-H gel determine the mechanical performance in differenthumidity states to a large extent. When C-S-H gel is trans-formed from a dry state to a saturated state, the stable andhigh-strength Ca–Os bonds are partially substituted byunstable Ca–Ow bonds and H-bonds, while the structure

Fig. 16. Stress–strain relations of 12 samples under uniaxial compression loading along the z direction.

90 D. Hou et al. / Acta Materialia 67 (2014) 81–94

transforms from an amorphous glass state to a layeredstructure. The variations in the chemical bonds and struc-ture that play important roles in bridging the calcium sili-cate sheets result in a weakening of the cohesive force. Inview of the fluid pressure, Bonnaud et al. proposed thatwater molecules have a disjoining effect in C-S-H grains[13]. The fluid pressure in C-S-H gel is contributed by thecohesive force from the Ca2+ counter-ions and the repul-sive force by the water molecules. From the dry state tothe saturated state, the repulsive effect of the water reducesthe cohesive force of the C-S-H gel.

As shown in Fig. 17c, the compressive strength of sam-ples with different water contents varies from 8 to 6 GPa.No pronounced reduction trend can be observed, implyingthat the water molecules have little influence on the com-pressive performance of the C-S-H gel. Furthermore, in

the saturated state, the compressive strength of the C-S-H gel is about twice as large as the tensile strength. Itshould be noted that, at the macrolevel, the cement pasteis strong in compression and weak in tension. Thediscrepancy between the compressive and tensile behaviorof C-S-H gel at the nanolevel gives molecular insight intothe tensile weakness of cement paste.

3.2.3. Structural analysis

In order to support the discussions on the relation betweenmechanical properties and chemical bonds, structural analy-sis is required. The strain-correlated function (SCF) is usedto describe the variation in chemical bonds in comparisonwith the original structure during the tensile process. TheSCF can be interpreted as a TCF in the presence of strainloading, and is defined in a similar way to TCF as

0.0 0.2 0.4 0.6 0.8 1.0

45

50

55

60

65

70

Youn

g' s

mod

ulus

in z

(GPa

)

Water/Ca ratio

4

5

6

7

Tens

ile s

tren

gth

(GPa

)

Water/Ca0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.00

3

6

9

Com

pres

sive

str

engt

h (G

Pa)

water/Ca

(a)

(b)

(c)

Fig. 17. Evolution of mechanical properties of C-S-H gel with water/Caratio: (a) Young’s modulus; (b) tensile strength; (c). compressive strength.

D. Hou et al. / Acta Materialia 67 (2014) 81–94 91

CðeÞ ¼ < dbðeÞdbð0Þ >< dbð0Þdbð0Þ > ð3Þ

where e denotes the strain. During uniaxial tensile testing,the chemical bonds can break and form frequently to resistthe loading, which results in structural transformation. Asshown in Fig. 18a, in the case of a dry C-S-H sample, the

C(e) values of Cas–Os bonds and Caw–Os bonds decreaseto 0.4, implying a large amount of breakage of these chemicalbonds. In contrast, the slight reduction in C(e) of Si–Os

bonds indicates that most of the silicate chains maintain theirintegrity. On the other hand, in the saturated state, as shownin Fig. 18b, the C(e) of Caw–Os bonds reduces more than thatof the Cas–Os bonds and the C(e) of the Si–Os bonds remainsconstant. This means that the Caw–Os bonds are more likelyto be broken in the presence of water molecules. As discussedpreviously, Cas–Os, Si–Os and Caw–Os are the main contrib-utors to the mechanical performance of C-S-H gel from thedry state to the saturated state. Silicate chains act as the back-bone of the C-S-H gel, and only at large deformation in thedry state can the Si–Os bonds be slightly damaged. Regard-ing the Cas–Os and Caw–Os bonds, their variationsdetermine the tensile strength of the C-S-H gel. With increas-ing amounts of water, the role of Caw–Os bonds becomesmore and more critical.

More information can be obtained from the molecularstructural evolution of C-S-H gel in resisting tensile loading,as shown in Fig. 19. It can be seen from Fig. 19a that, whenthe stain is small, even though the silicate chain distributionis amorphous, the locations of the Cas and Caw atoms canbe clearly distinguished in the z direction. Only a smallamount of the Q3 species distributed across the interlayerregion can be stretched. When the strain reaches a moderatelevel of 0.3 A A�1, local structures become more disorderedand small nanocracks are present where bonds breakagesoccur. When the strain level increases further, Caw atomsdiffuse into the defective regions of the calcium silicate sheetsand some debonded silicate chains grow into the interlayerregion. Meanwhile, small cracks coalescence both in the inter-layer region and in the calcium silicate sheets, which confirmsthat the Cas–Os bonds play as important a role as Caw–Os

bonds in the loading resistance, as illustrated by the C(e)shown in Fig. 18a. Caw and Cas atoms are mixed togetherand silicate chains are stretched along the z direction, withboth contributing to the plasticity of the dry C-S-H gel. Thesaw-like stress–strain relationship shown in Fig. 15 can beattributed to the merger of Caw and silicate chains. In thesaturated state, as shown in Fig. 19b, the tensile damage ofthe C-S-H gel exhibits a different failure mechanism. Duringthe tensile process, the breakage of the Caw–O bondsand the H-bonds results in the separation of neighboring cal-cium silicate sheets. As the strength of the H-bond is weak, theH-bonds between the water and the neighboring calciumsilicate sheets are formed and broken frequently. Therefore,as shown in Fig. 19b, nanocracks occur along the interlayerregion where the H-bonds are rich, and coalesce to causecomplete fracture of the layered structure. In addition, thecalcium silicate sheets maintain their original layeredmorphology, which indicates only a slight contribution ofthe Cas–Os bond in loading resistance. The failure mode ofinterlayer rupture is consistent with previous results bySCF, as shown in Fig. 18b, i.e. Caw–Os plays a major role inresisting the tensile loading and in determining the tensilestrength.

0.0 0.2 0.4 0.6 0.80.0

0.2

0.4

0.6

0.8

1.0

Cas-Os Si-Os Caw-Os

C (ε

)

Strain (Ang/Ang)0.0 0.2 0.4 0.6 0.8

0.0

0.2

0.4

0.6

0.8

1.0

C (ε

)

Cas-Os Si-Os Caw-Os

Strain (Ang/Ang)

(a) (b)

Fig. 18. SCFs of Ca–O, Si–O and Caw–O bonds in different states: (a) dry state; (b) saturated state.

Fig. 19. Molecular structural evolution of C-S-H gel in resisting tensile loading in different states (the strains from top to the middle and the bottom aresmall, moderate and large, respectively): (a) dry state; (b) saturated state.

92 D. Hou et al. / Acta Materialia 67 (2014) 81–94

Compressive loading additionally results in molecularstructure deformation, as shown in Fig. 20. For the dryC-S-H sample, illustrated in Fig. 20a, the compressiveloading reduces the interlayer distance so that the calciumsheet and silicate chains merge together. Meanwhile, themorphology of the silicate chain changes during the com-pressive process: some silicate chains grow across the inter-layer region and some react with neighboring silicatechains to enhance the polymerization degree. The morphol-ogy variation indicates better plasticity, which can explainthe long strain plateau in the stress–strain relation, asshown in Fig. 16. On the other hand, for the saturated

C-S-H sample, exhibited in Fig. 20b, the interlayer watermolecules prevent the silicate species from polymerizingso that the layered arrangement can be maintained evenat a high strain state. In addition, the loading shortensthe interlayer distance, reducing the diffusion rate for watermolecules. Thus the H-bond network is hard to break dueto compressive loading, which contributes to the high com-pressive strength for the C-S-H gel at saturated state.Therefore, the different tensile and compressive behaviorsof interlayer water molecules determine the large strengthdiscrepancy of C-S-H gel when under tension and whencompressed.

Fig. 20. Molecular structural evolution of C-S-H gel in resisting compressive loading in different states (he strains from top to the middle and the bottomare small, moderate and large, respectively): (a) dry state; (b) saturated state.

D. Hou et al. / Acta Materialia 67 (2014) 81–94 93

This structural analysis proves that the hydrolytic weak-ening found in the silicate composite also occurs in C-S-Hgels. In the dry sample, in the interlayer region, the coordi-nated atoms of Caw are Os and Caw–Os connections have ahigh potential energy. In addition, even though the break-age of local Caw–Os bonds occurs, Ca atoms can immedi-ately reconstruct the chemical bonds with neighboring Os.The reconstruction of the chemical bonds contributes tothe recovery of small defects in the elastic region. Neverthe-less, in the saturated sample, interlayer Ow atoms substitutepartial Os atoms and form unstable Caw–Ow bonds. Due tothe disjoining influence of the water molecules, the brokenCa–O connection cannot be reconstructed as easily as indry C-S-H gel. Therefore, saturated C-S-H gel has a morebrittle structure.

4. Conclusion

By considering the molecular dynamics, the structure,dynamics and mechanical performance of C-S-H gels atdifferent states have been investigated. The followingconclusions can be drawn from this study.

(1) Structurally, as the water content increases, the pene-tration of the water transforms the C-S-H gel from anamorphous to a layered structure. Meanwhile, thebridging bonds between the calcium silicate sheetsvary from only Caw–Os bonds to a combination ofCaw–O bonds and H-bonds. That is to say, the pres-ence of water molecules weakens the stability of thechemical bonds in the system.

(2) The morphology and chemical bond variationinduced by the water determine the mechanicalproperties evolution. Both the stiffness and thecohesive force are reduced with increasing watercontent.

(3) In the tensile loading process, the amorphous drysample, due to the stretching of the silicate branchand the breakage of the Cas–Os bonds, demonstrateshigh stiffness, high strength and plasticity in thepost-failure stage. In contrast, in the saturated state,the much weaker Caw–Os bonds and H-bonds playmajor roles in the loading resistance, which leadsto lower stiffness and strength, and makes the gelmore brittle.

94 D. Hou et al. / Acta Materialia 67 (2014) 81–94

(4) In the loading process, some broken bonds can bereconstructed. The presence of water molecules pre-vents this reconstruction to some extent, which isanother mechanism that influences the mechanicalproperties of C-S-H gel.

(5) In the compressive process, the H-bond network ishard to break so that the compressive strength ofC-S-H gel in the saturated state is much larger thanthe tensile strength at the molecular level.

Acknowledgements

Support from the China Ministry of Science and Technol-ogy under grant 2009CB623200 is gratefully acknowledged.

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