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Heterogeneous Surface Growth and Gelation of CementHydrates

Abhay Goyal Katerina Ioannidou Christopher Tiede Pierre Levitz RolandJ-M Pellenq Emanuela del Gado

To cite this versionAbhay Goyal Katerina Ioannidou Christopher Tiede Pierre Levitz Roland J-M Pellenq et alHeterogeneous Surface Growth and Gelation of Cement Hydrates Journal of Physical ChemistryC American Chemical Society 2020 124 (28) pp15500-15510 101021acsjpcc0c02944 hal-02902372

Heterogeneous Surface Growth and Gelation of Cement HydratesAbhay Goyal Katerina Ioannidou Christopher Tiede Pierre Levitz Roland J-M Pellenq

ABSTRACT During cement hydration CminusSminusH nanoparticles precip-itate and form a porous and heterogeneous gel that glues together thehardened product CminusSminusH nucleation and growth are driven bydissolution of the cement grains posing the question of how cementgrain surfaces induce spatial heterogeneities in the formation of CminusSminusHand affect the overall microstructure of the final gel We develop a modelto examine the link between these spatial gradients in CminusSminusH density andthe time-evolving effective interactions between the nanoparticles Using acombination of molecular dynamics and Monte Carlo simulations wegenerate the 3D microstructure of the CminusSminusH gel The gel network isanalyzed in terms of percolation internal stresses and anisotropy and wefind that all of these are affected by the heterogeneous CminusSminusH growthFurther analysis of the pore structure encompassed by the CminusSminusHnetworks shows that the pore size distributions and the tortuosity of thepore space show spatial gradients and anisotropy induced by the cement grain surfaces Specific features in the effective interactionsthat emerge during hydration are however observed to limit the anisotropies in the structure Finally the scattering intensity andspecific surface area are computed from the simulations in order to connect to the experimental methods of probing the cementmicrostructure

INTRODUCTION

It is well known that soft materials such as gels are formedunder nonequilibrium conditions and these conditions canhave drastic effects on the final mechanical and morphologicalproperties of the material This is certainly the case for CminusSminusH (calciumminussilicateminushydrate) gels formed during cementhydration While cement is usually not thought of in thecontext of soft matter its mechanical properties depend on thisCminusSminusH ldquogluerdquo which binds together the other hydrationproducts1minus3 During the setting process CminusSminusH precipitatesand aggregates into a gel which becomes denser and stiffer overtime It forms a complex pore structure and developssignificant spatial heterogeneities45 These morphologicalfeatures span from nano to microscales making cement atruly multiscale material that is challenging to fully character-izeUnderstanding the physical and chemical processes under-

lying cement hydration is of immense practical importanceConcrete is the most widely used synthetic constructionmaterial and cement is its main binding agent The productionof cement accounts for about 8 of global anthropogeniccarbon dioxide emissions6 The intelligent design of newgreener cements is a pathway to greatly reduce thoseemissions but this goal is hindered by an incompleteunderstanding of what makes the existing cement work as itdoes7 The complex hydration kinetics makes it challenging to

fully understand the mechanisms that cause cement to set andhow the final mechanical properties develop8minus10 Despite thechallenges many recent studies have made inroads intodeveloping such an understandingRheology and specific surface area measurements tell us

about the development of mechanical strength and porosityduring setting41112 This is driven by the formation of CminusSminusH which precipitates as nanoparticles of size asymp5 nm113 andadvances in nano-indentation techniques have enabled newinsights into this nanoscale origin of the macroscopicmechanical properties1415 However several aspects of howthe larger-scale morphology and mechanics of the materialemerge from its nanoscale components need furtherinvestigationThe combination of reaction kinetics driving the nucleation

and growth of CminusSminusH particles1617 with changing effectiveinteractions1819 drives the nonequilibrium formation of theCminusSminusH gel This pathway has a clear effect on themicrostructure which shows strong spatial gradients and

anisotropy and it is in this context that the we need tounderstand the development of CminusSminusH morphology duringhydration To do so one important question to answer is howexactly the way CminusSminusH forms affects its final propertiesAnother is how the changing interactions couple to thenonuniform CminusSminusH precipitationWe use a mesoscale model to answer these questions

expanding on work which has had success in understanding therole of the changing interaction20 and their effects on thehardened paste21 Specifically we implement a spatial gradientin the CminusSminusH precipitation corresponding to the nucleationof CminusSminusH at cement grain surfaces Using a wide range ofcomputational analysis tools we then characterize the CminusSminusHnetwork pore structure internal stresses and more This givesinsight into the effect of heterogeneous CminusSminusH growthmechanisms on the overall microstructure but it alsodemonstrates how this effect is enhanced or limited by thefeatures of the interaction potential In particular noncontactrepulsion which is present in the early stages of hydration canlimit the density gradients and anisotropy of the CminusSminusH gelforming a percolated porous network at low volume fractionsThese results explain the surprising robustness of the CminusSminusHgel against phase separation induced by density gradients andagainst the formation of a dense CminusSminusH layer at the cementgrain surface that blocks further reaction Understanding therole of the interaction during the heterogeneous formation ofthe CminusSminusH gel is an important step toward designing newcementitious materials

METHODS

In our model CminusSminusH nanoparticles are coarse-grained andtreated as spherical particles of a fixed size An effectiveinteraction potential is prescribed to these particles thatincludes the net interactions mediated using the solvent Thephysics behind these interactions is a complex problem initself It has been studied extensively via both experiments andsimulation181922minus26 The forces at play emerge from thefluctuations of the electrolyte solution confined between thehighly charged CminusSminusH surfaces While we do not include thesolvent and counterions explicitly in the model here it is thecorrelations between these species that give rise to stronglyattractive noncontact forces between CminusSminusH nanoparticles

These correlations are highly dependent on ion concentrationsand pH18 so the overall interactions change over time as thecontinued dissolution of cement alters the solution chemistryFor simplicity we consider fixed forms for the effective

interaction during precipitation but investigate two differentforms corresponding to different hydration times Strikinglythe experiments show that the repulsive barrier decreases inheight eventually disappearing altogether during hydrationPotentials with competing attraction and repulsion are knownto exhibit complex phase diagrams2728 and we focus ourinvestigation on the effects of a change in the repulsive barrierheight To do so we assume a generic model for theinteraction potential that allows independent control of thewidthheight of the attractive well and repulsive barrier

εσ σ= minus +

γ γ κminusAuml

Ccedil

AringAringAringAringAringAringAringAringAringAringikjjj

yzzz

ikjjj

yzzz

Eacute

Ouml

NtildeNtildeNtildeNtildeNtildeNtildeNtildeNtildeNtildeNtildeU r

Ar r

Ar

( ) e r

1

2

2(1)

where A1 and A2 are constants σ and ε are the length andenergy scales (discussed further in next section) respectivelyand κ is the inverse Debye screening length Considering thefact that these interactions were observed to be very short-ranged and that range did not significantly vary with pH in theexperiments18 we fix γ = 12 and κ = 05σ The ratio of A1A2sets the relative strength of attraction and repulsion and wevary these so that the depth of the attractive well is fixed andonly the repulsive barrier height changes for the twointeraction potentials considered ES and LS correspondingto early and later stages of cement hydration (Figure 1 left)The ES potential exhibits a stronger repulsive barrier with A1 =96 and A2 = 12 while the LS exhibits reduced repulsion but asimilar attractive well with A1 = 6 and A2 = 4 The depth of theattractive well (set by choosing a temperature of kBT = 015ε)is such that aggregation is energetically favored but thedynamics can be studied over a reasonable simulation timeAdditionally it sets the barrier height to be gt2kBT for the ESpotential but ltkBT for the LS With these choices themaximum force (obtained from dUdr taking the particle sizeto be σ = 5 nm and the potential well depth ε asymp 7kBT) iscomparable to the values obtained from atomic forcemicroscopy measurements for low lime concentrations18

In the physical system CminusSminusH does not exist inequilibrium conditions In fact as the reaction proceeds

Figure 1 Left We use two sets of parameters A1 A2 to consider different repulsive strengths These are labeled ES and LS corresponding to a highand low repulsive barrier present in early and late stages of the cement setting Right A schematic of the variation of μ across our system Byconsidering a simulation volume between two cement grains we introduce a spatial gradient in the hydration and the precipitation of CminusSminusHnanoparticles The cement grain surface is not included explicitly but rather through an effect on the local μ turning it into a spatially varyingquantity

more and more CminusSminusH is created from the combination ofions and water9 These species are not included explicitly inour model but we mimic this precipitation via a grandcanonical Monte Carlo (GCMC) process where particles areinserted and deleted with a probability given by the metropolisMonte Carlo scheme29

prop [ ]β μplusmn minusΔP min 1 e Uinsdel

( )exc (2)

where β =k T

1

B kB is the Boltzmann constant T is the

temperature μexc is the excess chemical potential and ΔU isthe total change in the energy upon insertingdeleting aparticle In a closed system μexc is associated with all theinteractions between particles and depends on the density andphase equilibriaDuring cement hydration the dissolution of cement grains

increases the overall concentration of ions in solution andwhen saturated they combine to form a CminusSminusH molecule9

As we have coarse-grained out these degrees of freedom theusual equilibrium chemical potential is not sufficient todescribe this Instead we consider that the backgroundchemistry has an effect of producing a net free energy gainwith the creation of CminusSminusHWith this assumption in mind we take μexc to have two

components

μ μ μ= +exc interaction chemical (3)

The interaction term is the usual μexc29 while the chemical

term represents the free energy gain of calcium silicon oxygenand hydrogen coming together to form a CminusSminusH nano-particle While the equilibrium value of the first term can becomputed (and indeed it has eg in refs 20 and 30) thischemical term is difficult to estimate Considering thatdensification does not stop during cement hydration17

previous studies have used a value of μexc that favorsinsertion31

Here our scenario is different because we want CminusSminusHprecipitation to vary spatially There is a tendency for CminusSminusHto grow at the surface of cement grains or other nucleationsites1617 If we consider our simulation box to be part of a porebetween two cement grains (Figure 1 right) the hydration ofthe cement occurs near the edges of the box as primarily doesthe precipitation of new CminusSminusH nanoparticles To implementthis we consider μexc(z) to be a quantity that depends on theposition Near the edges a higher μexc will favor insertionwhile far from the cement grains a lower μexc will discourageinsertion unless it is close to existing particlesThis GCMC process is combined with molecular dynamics

(MD) of the CminusSminusH particles Because of this coupling thesystem exists in a non-equilibrium state where the kinetics ofthe reaction (mimiced by GCMC) affect the morphology ofthe system that evolve in time through MD The rate R whichis the ratio of GCMC exchanges to MD steps can be thoughtof as setting how fast CminusSminusH particle creation occurs When Ris very high or very low the behavior of the system would beessentially dictated by either the precipitation kinetics(GCMC) or by the dynamical aggregation (MD) Howeverwhen simR (1) we are in a situation where the CminusSminusHprecipitation and the particle dynamics interfere with eachother to determine the gel morphologySimulation Details We use m as the unit mass σ as the

unit length and ε as the unit energy which defines a unit time

τ = σε

m 2 The simulation volume is a periodic cubic box of

side length L = 492σ in which we perform MD in an NVTensemble with a NoseminusHoover thermostat29 at temperaturekBT = 015ε which is comparable to room temperature whenthe interaction strength is calibrated to a modulus of 20 MPafor a CminusSminusH gel at early hydration times20 We solve theNewtonian equations of motion using the velocity Verletalgorithm with a time step of 00025τ The GCMC and MDsimulations here are done using LAMMPS32

For GCMC exchanges the simulation box is split into threeregions along the z-axis The top and bottom slices are high μregions of thickness 5σ In the case of ES (see Figure 1) weassign μES = 6ε while for the LS case we set μLS = 15ε Themiddle region has thickness 40σ and lower values of μES = minus1εand μLS = minus15ε respectively These values have beencalibrated so that insertion is always preferred in the edgeregions and in the middle regions it can only happen nearexisting clustersIn the simulations the MD and GCMC parts are connected

through the rate parameter R This is the ratio of the numberof GCMC exchanges to the number of MD time steps andprevious studies have found that varying R over the range of R= 02minusR = 4 can change the densification31 At high R moreGCMC insertionsdeletions are attempted and this drives thesystem further from the equilibrium behavior associated withthe interaction potential We focus on a relatively high value ofR = 4where the thermodynamics of the system dictated bythe interactions matters lessin order to investigate whethereven in these conditions we could see a coupling between thespatial gradient and the specific interaction potential This ratecorresponds to 400 GCMC exchanges attempted every 100MD steps with a variable but approximately even split of 200insertionsdeletions each for every GCMC cycle As we runthe MD and GCMC particles are inserted into the initiallyempty simulation box and simulations are run until N asymp57000 corresponding to a volume fraction of ϕ = 025 Hereϕ is estimated considering spheres of diameter σ and hence

computed as ϕ = πσNL6

3

3 The whole simulations require

approximately 106 MD steps with variations that depend onthe interaction potential The MD time can be converted intoreal time (hydration time in the experiments) using theargument developed in ref 27 which indicates that texp prop logtsim

31

RESULTS AND DISCUSSION

Using the microscopic information obtained from simulationswe analyze the structural and morphological features of the CminusSminusH gel First we examine how the precipitation of CminusSminusHleads to the formation of a percolating network and thebuildup of internal stresses Next the consequences of thisstructure in terms of the size of pores and diffusion withinthem are investigated Finally we characterize the specificsurface area and scattering intensity in order to make aconnection with common experimental methods of character-izing the cement microstructure The results for thepercolation and stresses are presented in reduced units (mσ ε τ and unit pressure εσ3) For the sections on porosityspecific surface area and scattering we convert to real units bysetting σ = 5 nm to give a sense of the physical scale

Percolation and Stresses The choice of using a grandcanonical ensemble allows the insertion of particles to occur at

a nonuniform rate in a way that depends on the state of thesystem As seen in Figure 2 the total volume fraction ϕ startsto increase more rapidly as particles are inserteduntil ϕsaturates because of increasing density and steric repulsionbetween particles

Figure 2 also shows local ϕ in the edge and middle regionsdefined as the 5σ thick high μ regions and the 392σ thick lowμ region respectively Because of the diffusion of particles fromthe edge the middle region actually becomes denser than theedge for a period starting around t = 105 MD steps consistentwith observations of nano CminusSminusH seeds in the solution atearly hydration times35 This reversal ends around ϕ = 15when the edge ϕ starts to increase rapidly For LS this alsocorresponds to a sudden decrease in dϕdt in the middle asthe dense structure at the edge limits diffusion For ES theincreased growth rate at the edge is correlated with anincreased growth rate in the middle This holds until ϕ asymp 22when the deletions in the low μ regions balance the diffusionfrom the edge regionWe see a morphological difference between the two regions

which becomes increasingly pronounced as more particles areinserted Figure 3 shows that particles at the edge tend to bemore clustered and densely packed In these snapshots at ϕ =25 simulations with both potentials show the formation of a

percolated system-spanning cluster During the simulation asϕ increases clusters grow and aggregate into a connectedstructure and these morphological changes also couple back tohow quickly and uniformlyor notϕ increases While theCminusSminusH clusters eventually percolate in both cases the waythat structure forms and its final morphology are quitedifferentTo begin examining this process quantitatively we group

particles into clusters by defining a bonding distance rb Weuse rb = 11σ here corresponding to a bond distance such thattwo particles are near the minimum of the interactionpotential after having confirmed that varying rb around thisvalue does not change our results It is to be noted that thesebonds and clusters are defined solely by instantaneousdistance but because of the interaction strength chosen (kBT= 015ε) they correspond to CminusSminusH particles that adhere toeach other and do not continuously break and reform overtime Cluster percolation is defined as the formation of acluster which spans the simulation box in x y and z directionsFigure 4 shows the percolation probability that is the fraction

of independently generated systems that formed in the sameconditions of precipitation rate R interaction strength ε andvolume fraction ϕ a percolating connected structure Wegathered statistics from 10 independent samples for eachpotential We see that for ES the percolation transition ismore sharply defined that is it happens over a narrow range ofϕ On the other hand with LS there is a 6 volume fractiondifference between the first occurrence of a percolating clusterand 100 percolation Interestingly the percolation seems tocorrespond with the density cross-over seen in Figure 2 at ϕ =15 (where the local ϕ at the edge starts to rapidly increaseover that in the middle) This suggests that the percolatingcluster limits particle diffusion from the edge to the middleespecially for the LS potentialIn order to understand the mechanical implications of this

percolation we looked at the buildup of internal stresses withinthe material Using the virial formulation of the stress tensorone can define a coarse-grained local stress tensor36 To focusour analysis on the stresses associated with particle interactions

Figure 2 Variation of total and local (edge middle) ϕ as thesimulations progress With LS interactions the nonuniform μ leads toa much larger local ϕ difference between the edge and middle regionsThe formation of a locally dense crystalline (see the SupportingInformation) layer near the cement grain surface is consistent withobservations of the inner product or high-density CminusSminusH3334

Figure 3 Simulation snapshots with overall volume fraction ϕ = 25showing the microstructure for the ES potential (left) and LSpotential (right) Color indicates the local density with darker purpleregions indicating many neighboring particles and we see a highdegree of anisotropy in the gel network which is dependent on theinteraction potential

Figure 4 Geometric percolation probability as a function of ϕ Theparticles are clustered according to a distance cutoff of 11σ A clusteris considered percolating if it spans the system in x y and zdirections This says nothing about the persistence or rigidity of thepercolating cluster and is a geometric definition rather than amechanical one

rather than thermal motion we neglect the kinetic term andobtain

sum sumσ = minusε

α βαβneV

F r1 1

2i V j i

ij ij

cgcg (4)

where α and β indicate the vector components while i and jare summed over individual particles Taking the trace of thisgives us a local pressure which describes the forces a particleexperiences and converges to the total pressure if we expandthe coarse-graining volume Vcg For the results presented weuse π=V rcg

43 c

3 where rc is the cutoff of the potential Small

variations of Vcg do not produce any qualitative differencesFigure 5 shows the local pressure distributions for two values

of ϕ in the edge and middle regions They are plotted withGaussian fit lines and show fairly normal distributions withineach region Around the percolation transition at ϕ = 15 wesee that ES and LS have similar distributions but they areshifted because of the extra repulsion in ES In both casesthere is a sharply defined value in the middle region while theedges have a wider spread Because the local ϕ in each region isroughly the same (see Figure 2) it is interesting that there issuch a difference in the stress distributions indicating that thetwo regions arrived at ϕ = 15 through different paths whichin turn modified the local morphology and stressesAs we add particles and go to ϕ = 20 the stresses in the ES

case become more uniform across the simulation box Thecenter distribution widens and the peak of the edgedistribution shifts Once the connected structure percolatesthe stresses can be transmitted between regions and this servesas a mechanism to reduce the initial heterogeneities introducedby the chemical potential gradient In contrast the LS samplesmaintain the extreme differences in edge versus center

distributions indicating that they are not effectively connectedto allow for stress redistribution The geometric percolation ofa cluster is enough to reduce the diffusion but not necessarilyto transmit stresses which suggests that the ES interactions arecrucial to give the product an early mechanical response asexperiments have seen for cement mixtures11

In Figure 6 we show snapshots from our simulations at ϕ =20 color coded according to local pressure As one wouldexpect from the stress distributions the system snapshots showstresses that are more uniformly distributed for ES In additionthere is no pronounced morphological difference between theedge and center regions For LS there is a clear distinctionwith most stressed areas lying on the edge of the system whichalso corresponds to local structures that clearly differ from theedge to the middle (see the Supporting Information for moreon local ordering)The heterogeneities in density stresses and local packing

present with the LS potential arise because of the spatialgradient in chemical potential μ and are coupled to theanisotropy that develops in the underlying network topologyIn a quantitative sense this can be probed by considering arandom walk on the network graph constructed from thebonds in structures analyzed so far The corresponding meansquared displacement (MSDg) is plotted in Figure 7 as afunction of the number of steps taken along the graph The xand y directions are expected to be symmetric in a statisticalsense and unsurprisingly the MSDg along those directions isequal On the other hand the z directionthe direction of thespatial μ gradientis set up to be distinct from the others andwe have shown that there are clear heterogeneities along thisdirection These have a clear effect on the network graph as thez displacement differs from x and y for both ES and LSpotentials Notably like the other measured properties this

Figure 5 Distributions of local pressure at the edge (circle symbols) and center (square symbols) Gaussian fits are also plotted as dashed lines

Figure 6 Thin (5σ) slice of our system at ϕ = 20 for ES (left) and LS (right) The coloring corresponds to the local pressure with red beingpositive pressure that is parts under compressionand blue being negative pressure

difference is far more pronounced with the LS potentialdemonstrating that the anisotropy in the particle insertion hasbeen built into the network topology Just as important is theobservation that although there is some shift the zdisplacement with ES still closely mirrors x and y Thehomogenization of stresses and ordering is coupled to anerasure of the underlying anisotropyPorosity Having characterized the solid network in terms

of its percolation internal stresses and anisotropy it isimportant to understand their implications on the associatedpore network The size shape and connectedness of pores notonly directly affect the compressive strength but also the long-term stability and resistance to fracture of cement Addition-ally the permeability of the pore network is crucial to thecontinued reaction of water and cement Without this thereaction area would be completely blocked off early in thehydration and stop the reactionTo start we compute the pore size distribution (PSD) This

is generated using the method of Bhattacharya and Gubbins37

It consists of constructing a finite grid taking points in thepore space and determining the largest possible radius of asphere that can fit there without overlapping any particles This

sphere is not necessarily centered at the grid point Shorrsquos r-algorithm is used to find a local maximum for the radius of anonoverlapping sphere constrained to include the selected gridpoint From this calculation we generate the pore frequencyp(s) which indicates the fraction p of the total pore space thatcorresponds to pores of size s It is to be noted that thismethod does not provide the shape of the pores what weobtain corresponds to the smallest linear size of the poreThe left panel of Figure 8 shows the full PSD with the ES

potential (PSD for LS potential in the SupportingInformation) We see that the peak pore size is fixed afterpercolation maintaining the permeability of the network Theincreasing frequency at s = 05 nm corresponds to the packingof spherical particles in high-density regions There is no suchclear trend for the LS PSD and we must separate the edge andcenter regions to understand what is happening In the rightpanel of Figure 8 we plot the first moment of the PSD for bothpotentials separated into edge and center regions as a functionof volume fractionLooking at the ES results through this new lens we see that

there is a difference in the porosity across the system At ϕ =25 the asymp10 local difference in volume fraction between theedge and center leads to the pores at the edge being a bitsmaller However relatively speaking the density differenceand consequently the pore size difference are not very largewith the ES system On the other hand the LS system shows aremarkable transformation after percolation The edge poresrapidly close upjust as the edge ϕ shoots up dramatically(see Figure 2)while almost paradoxically the central poresizes start to increase with the increasing particle number Thisis consistent with the coarsening of the initial structure whichwould lead to two separated dense CminusSminusH layers near thesystem edges This heterogeneous pore formation hasconsequences for diffusion through the pores which can bequantified by performing a random walk in the pore spaceThis random walk can be thought of as the trajectory of a

particle diffusing through the pores and in Figure 9 we plotthe corresponding mean square displacement (MSD) Whensplit into x y and z components the data show that the porenetwork tortuosity is isotropic for ES but not for LS With LSthe x and y components are comparable to the porosity of ESbut the z direction displays a higher tortuosityindicatingreduced diffusivity through the pores As the cement grainsurfaces are modeled to be along this z direction the diffusionis necessary for the continuation of cement hydration The

Figure 7 MSD (in reduced units ie particle diameter squared)along x y and z directions from a random walk along the networkgraph corresponding to simulated structures from ES and LSpotentials at ϕ = 25 The black line indicates what purely Brownianmotion would be and MSDg is found to be sub-diffusive Because ofthe inherently anisotropic way in which the network is created oneexpects and finds the displacement along z to differ from x and yNotably this difference and thus the underlying anisotropy of thenetwork are enhanced for LS where MSDg prop τ07 for the z directioninstead of τ08 as in the other directions

Figure 8 Left PSD with ES potential for several volume fractions The pore frequency describes what fraction of pore space is occupied by poresof a given radius Right First moment of the PSD for both potentials as a function of ϕ The solid line represents the low μ middle region while thedashed line is for the high μ edge

premature closure of pores could prevent a sufficient degree ofhydration being reachedSpecific Surface Area Experimentally the porosity of

cement pastes can be characterized in terms of the specificsurface area Ssp which is defined as the total surface area of allpores per unit mass This is probed by scattering experimentsor by measuring the ability of the material to uptake gases suchas nitrogen or water vapor into pores From our simulations itis possible to calculate Ssp through the statistics of the pores Inparticular we first compute the pore chord length distributionthat is the distribution of lengths lp that randomly drawnchords can traverse in the pore space without intersecting aparticle Our results for ϕ = 25 (Figure 10) show that the

chord length distribution p(lp) for ES exhibits a local peak at lp= 10 nm consistent with the data in the PSD (peaked at poreradius s = 5 nm) of Figure 8 and demonstrating that there is acharacteristic size associated with the porosity for ESafeature that is less pronounced for LS The repulsive barrier inthe two potentials introduces a length scale to our system

which affects the porosity and the strength of that barriercontrols how important this length scale isFrom the mean of the chord length distribution ⟨lp⟩ we

calculate the specific surface area Ssp of our system usingaccording to refs 38 and 39

ϕ= minusρϕ⟨ ⟩

Sl

4(1 )sp

p (5)

where ρ is the density of the CminusSminusH matrix which isestimated to be 243 gcm3 from atomistic simulations23

Because of the discrete nature of numerical calculations thechord length distribution is computed with a finite cutoff lcwhich affects the value of Ssp To obtain the true surface areaone can calculate this by varying lc and extrapolating to the lc =0 limit (Figure 11 left)The specific surface area computed depends on lc differently

for the two potentials This is something that needs to beconsidered when trying to compare with experimental dataInterestingly despite the clearly different nature of the porosityfor ES and LS we actually end up with quite similar overallspecific surface area (Figure 11 right) However incomparison with experiments we must be careful of thesedifferent features and try to understand which parts of theporosity an experiment will be able to access These limitationswill apply differently to the two gel morphologies correspond-ing to ES and LSThe values reported for Ssp of hardened cement paste using

the gas sorption experiments vary in the range ofapproximately 50minus200 m2g49124041 Meanwhile mesoscalesimulations21 have reported values of Ssp = 347 m2g and Ssp =283 m2g for ϕ = 33 and ϕ = 52 respectively Our resultsare clearly significantly higher than these values plateauingaround Ssp = 600 m2g at ϕ = 25 However given that Sspdecreases with increasing ϕ that is expected at the very earlystages of hydration to which our simulations correspondexperimental measurements are challenging because of howrapidly the material changes Additionally there is a significantquantity of unreacted cement at this stage skewing possibleexperimental results in comparison to our simulations (whichdo not explicitly contain cement grains) A study by Suda et alsuggests that the specific surface area associated with CminusSminusHonly is closer to 200minus300 m2g42 Finally one should keep inmind that no matter how sensitive sorption techniques onlyaccess well-connected pores of the sufficient size If we take alarger lc such that only pores of diameter greater than 3 nm areconsidered Ssp falls to be about 300 m2g Alternatively if welook at results from more sensitive small angle X-ray scatteringexperiments the values of Ssp gt 500 m2g have beenreported443

Scattering In addition to measuring the specific surfacearea neutron and X-ray scattering experiments have been usedto characterize the microstructure of cement pastesand areone of the most powerful tools to do so The usual way tocompute I(q) is as the Fourier transform of the autocorrelationo f fl u c t u a t i o n s i n l o c a l d e n s i t y

intη ρ ρ ρ ρ = prime primerarr

minus primerarr

+ minus r r r r r( ) d ( ( ) )( ( ) )V21 3 of our simu-

lated microstructures (Figure 12) where ρ(r) is the localdensity and ρ the average density44 In case of an anisotropicmedium this computation is more involved because of theneed to compute η2(r) for each orientation of r prior toperforming the 3D Fourier transform

Figure 9 Diffusion through the pore space of the structurescorresponding to the two potentials at ϕ = 25 This is computedfrom a random walk in the pore space Assuming that a particlefollowing this random trajectory moves at some fixed speed one canobtain the overall displacement with time In an isotropic porenetwork this displacement would be evenly split between x y and zdirectionsas in the ES case For LS however there is a decreaseddisplacement along the z direction indicating an increased tortuosityof the pores along the z direction

Figure 10 Chord length distribution shows the length of chordsdrawn randomly in the pore space The results with ES show a morepronounced peak at intermediate sizes due to the well-controlled poresize

A second way more numerical tractable was proposed inrefs 45 and 46 This a two-step process First a projectionimage of the chosen 3D binary structure is performed eitheralong the x or y or z direction Second a 2D Fourier transformof this projection is calculated The associated spectral densitygives directly I(qx qy qz) with either qx = 0 or qy = 0 or qz = 0For example the projection along the optical axis x will allowone to get the 2D pattern I(qx = 0 qy qz) To estimate the levelof anisotropy an angular average along the principal directions

of these 2D scattering patterns is performed using an averagingangle of 15deg A comparison of the two methods is presented inref 46 showing a very good agreementBecause of the anisotropy in the structure the choice of

optical axis for the scattering naturally affects the resultsobtained Because of the symmetries in our system the x and ydirections are equivalentanisotropy is associated with the zdirection that is the μ-gradient direction If one considers anoptical direction along a non-z axis the μ and density gradientsproduce clear differences in the low q scattering intensity alongthe z direction compared to the x or y direction (Figure 13)For both ES and LS potentials the scattering along z exhibits alow q structure (instead of a plateau as along x or y direction)which is consistent with the system-spanning density gradientalong z direction The high q scattering is instead dominatedby the oscillations typical of monodispersed sphericalparticles47

One can also consider just the scattering from the centerregion of the system (green triangles in Figure 13) Limitingourselves to this region reveals an interesting differencebetween the two potentials With LS the z scattering deviatesfrom y scattering in the low μ center region as wellhighlighting that the anisotropy in the structure goes beyondthe large difference in density stresses porosity and so forthbetween the edge and center regions On the other hand forES this split leads to a suppression of scattering anisotropy andproduces a curve which matches the scattering along x This

Figure 11 Left The specific surface area as a function of the chosen chord length cutoff By fitting the calculated data points to = ++f l C( ) ABlc 1 c

we extrapolate to the lc = 0 limit and obtain the geometric surface area Ssp = A + C Right The value for the specific surface area obtained byextrapolation for different volume fraction ϕ

Figure 12 2D projection of local densities in the LS structure at ϕ =25 when looking down the y-axis The darker regions correspond tohigher density Scattering intensity I(q) can be computed from theautocorrelation of fluctuations in the local density η2(r)

Figure 13 Scattering intensity computed for both potentials for various different optical axes The intensity is split into components along differentdirections to highlight anisotropy The scattering component along z differs from the others at low q because of anisotropy in the structureSurprisingly for ES this effect is suppressed if we consider only the center regionmeaning all of the measured anisotropy is due to the densityvariation across the whole box Meanwhile for LS even the center region alone deviates from the x and y scattering The structure is anisotropiceven at scales smaller than the system-wide μ gradient The high q oscillations are consistent with having monodispersed spherical particles

suggests that the anisotropy is due entirely to the differencesbetween the high and low μ regionsThe anisotropy induced by the cement grain surfaces

manifests itself in our calculated scattering intensity For amacroscopic sample these grains would be distributedrandomly and give an overall isotropic response because ofthe statistical averaging of the results The isotropic I(q) hasbeen computed using similar mesoscale models for highvolume fractions21 and it was found to match experimentalmeasurements of scattering intensity It is difficult to makesuch a connection using our simulations because of limitationsof the system size at low q and the effects of particle sizemonodispersity at high q Nonetheless this calculation hasrevealed interesting differences in the anisotropy of ES and LSsystems Future studies can expand on this to make a directconnection to scattering experiments

CONCLUSIONSWe used MD and GCMC simulations to investigate the effectof CminusSminusH growth in the presence of spatial gradients of CminusSminusH precipitation and of the changing effective interactionsbetween CminusSminusH nanoparticles on the overall morphology ofthe CminusSminusH gel Using GCMC to mimic precipitation ofnanoparticles we observed how the precipitation at cementgrain surfaces leads to spatial gradients in density whichdevelop over time but depend on the features of the CminusSminusHinteractions With the ES interaction we discovered apercolating cluster that forms around ϕ = 15 with reduceddensity and stress gradients as well as network anisotropyrelative to the LS interaction Calculations of pore size anddiffusion in the pores demonstrated that these differences inthe gel morphology translated into coarsening pores and anincrease in pore tortuosity along the gradient direction for theLS system Finally we computed the specific surface area andscattering intensity to make a connection to experimentalmethods of characterizing the cement microstructureThe heterogeneous growth of CminusSminusH nanoparticles clearly

has an effect on the morphology of the gel that is formed andthis effect of spatial gradients in the CminusSminusH precipitation iscontrolled by the features of the interaction potential betweenthe CminusSminusH nanoparticles The noncontact repulsion that ispresent in early stages of hydration because of electrostaticsplays a crucial role in the formation of a percolated and stress-bearing network with limited anisotropy It also helps preventthe formation of large pores because of coarsening whilemaintaining diffusivity in the pores These features arenecessary to the continuing hydration of cement grains andthe formation of a connected solid structure As theinteractions evolve over time the presence of the cementgrain surfaces can drive the formation of spatial gradients inCminusSminusH density and differences in local packing and densityconsistent with the two distinct morphological phases of CminusSminusH observed in the literature3334

Our study provides further support to the idea proposed byIoannidou et al the natural time evolution of the interactionbetween CminusSminusH nanoparticles is crucial to attaining the finalmechanical strength through complex tuning of the gelmorphology20 Under spatial gradients of CminusSminusH precip-itation the differences in gel morphology due to theinteractions are not only maintained but also enhanced Inthe context of heterogeneous CminusSminusH nucleation the featuresof the early stage interactions are required to explain howcement setting can be such a complex but robust process

These discoveries give insight into how the growth ofnanoscale components builds up the overall microstructureof cement hydrates and how it depends on the interactionsbetween the nanoparticles Such an insight is an important steptoward understanding how an alternative cementitious materialcould behave through the changes in chemistry and thus theeffective interactions

ASSOCIATED CONTENT

sı Supporting InformationThe Supporting Information is available free of charge athttpspubsacsorgdoi101021acsjpcc0c02944

Local ordering and signatures of locally crystalline orBernal spiral-like structures Full PSDs for bothpotentials (PDF)

AUTHOR INFORMATION

Corresponding AuthorEmanuela Del Gado minus Department of Physics Institute for SoftMatter Synthesis and Metrology Georgetown UniversityWashington DC 20057 United States orcidorg0000-0002-8340-0290 Email ed610georgetownedu

AuthorsAbhay Goyal minus Department of Physics Institute for Soft MatterSynthesis and Metrology Georgetown University WashingtonDC 20057 United States orcidorg0000-0002-0587-2145

Katerina Ioannidou minus Laboratoire de Mecanique et Genie CivilCNRS Universite de Montpellier Montpellier 34090 FranceMassachusetts Institute of TechnologyCNRSAix-MarseilleUniversity Joint Laboratory Cambridge Massachusetts 02139United States Department of Civil and EnvironmentalEngineering Massachusetts Institute of Technology CambridgeMassachusetts 02139 United States

Christopher Tiede minus Department of Physics Institute for SoftMatter Synthesis and Metrology Georgetown UniversityWashington DC 20057 United States

Pierre Levitz minus Physico-Chimie des Electrolytes et NanosystemesInterfaciaux PHENIX Sorbonne Universite CNRS F-75005Paris France

Roland J-M Pellenq minus Massachusetts Institute of TechnologyCNRSAix-Marseille University Joint Laboratory CambridgeMassachusetts 02139 United States Department of Civil andEnvironmental Engineering Massachusetts Institute ofTechnology Cambridge Massachusetts 02139 United StatesDepartment of Physics Institute for Soft Matter Synthesis andMetrology Georgetown University Washington DC 20057United States orcidorg0000-0001-5559-4190

NotesThe authors declare no competing financial interest

ACKNOWLEDGMENTS

AG and EDG acknowledge the NIST PREP GaithersburgProgram (70NANB18H151) and Georgetown University forsupport

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