Aggregation of Calcium Silicate Hydrate ... - ACS Publications

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Aggregation of Calcium Silicate Hydrate Nanoplatelets Maxime Delhorme,†,‡ Christophe Labbez,*,† Martin Turesson,† Eric Lesniewska,† Cliff E. Woodward,§ and Bo Jönsson‡ †

ICB, UMR 6303 CNRS, Univ. Bourgogne Franche-Comté, FR-21000 Dijon, France Theoretical Chemistry, Chemical Center, POB 124, S-221 00 Lund, Sweden § PEMS, University of New South Wales, Canberra 260x ACT, Australia ‡

S Supporting Information *

ABSTRACT: We study the aggregation of calcium silicate hydrate nanoplatelets on a surface by means of Monte Carlo and molecular dynamics simulations at thermodynamic equilibrium. Calcium silicate hydrate (C-S-H) is the main component formed in cement and is responsible for the strength of the material. The hydrate is formed in early cement paste and grows to form platelets on the nanoscale, which aggregate either on dissolving cement particles or on auxiliary particles. The general result is that the experimentally observed variations in these dynamic processes generically called growth can be rationalized from interaction free energies, that is, from pure thermodynamic arguments. We further show that the surface charge density of the particles determines the aggregate structures formed by C-S-H and thus their growth modes.

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5 nm.6,7,11 The platelets are highly charged due to titrating silanol groups,12 and the dissolution of C3S and precipitation of C-S-H take place at high pH (≈13 or higher).13 Thus, the surface charge densities of both C-S-H and C3S are pH dependent, and it is only at pH ≳ 13 that they are fully ionized. The ionization is of course also facilitated by increased salt concentration. The growth of charged aggregates in colloidal solution is often controlled by electrostatic interactions and limited due to internal electrostatic repulsion. For example, in protein solution it has been observed that the aggregation process halts once a certain aggregate size is reached. This has been explained in terms of internal Coulombic repulsion.14−17 The C-S-H platelets in cement paste, however, have an extremely high surface charge density and are typically neutralized by divalent calcium ions. Under such conditions ionic correlations play a significant role, and electrostatic interactions do not inhibit the growth. On the contrary, in some extreme conditions it facilitates it. Thus, the limited size of C-S-H platelets is a nonequilibrium phenomenon, and by combining simulated free energies for the crystalline (platelet) growth with experimental data, we have been able to show that the limited platelet size (crystalline growth) has a kinetic origin.18 At early age of cement hydration, C-S-H platelets are formed on or close to the surface of C3S,19 and due to the highly charged surfaces with Ca2+ counterions, there will be a net attractive interaction between the platelets and the C3S grains

INTRODUCTION Cement is a widely used material which has a strong impact on the environment due to its high energy consumption and large CO2 emission. Thus, there is a considerable interest in making cement use more efficient.1−5 One way to achieve this is by obtaining a better understanding of the setting and hydration (involving the simulateneous dissolution of anhydrates and the nucleation/growth of hydrates) of cement on a microscopic scale. In addition, cement can serve as an important model system as to how material forms at the nanoscale. Modern Portland cement is a polyphasic material including calcium silicates (Ca3SiO5 = C3S and Ca2SiO4 = C2S), calcium aluminate, and aluminoferrite. The composition can vary significantly, and a number of additives are used in order to obtain a cement with desired properties. One interesting aspect of this complex mixture is that the properties of the final concrete are reasonably constant. That is the chemical composition can vary within generous limits, but the final product still has the desired strength. This indicates that the forces operating on the microscopic scale are generic and likely of electrostatic origin. When C3S comes into contact with water, a dissolution process begins and the grains start to dissolve. The solution soon contains a variety of anions and cations, and the ionic strength is high. The solution rapidly becomes supersaturated with respect to calcium silicate hydrate (C-S-H), which precipitates and constitutes at least 60% of the fully hydrated cement paste. C-S-H are nanocrystalline particles6−10 and have a phyllosilicate type molecular structure. The growth of C-S-H particles is both directional and limiteda typical C-S-H particle is a platelet with approximate dimensions of 50 × 30 × © 2016 American Chemical Society

Received: October 16, 2015 Revised: February 8, 2016 Published: February 9, 2016 2058

DOI: 10.1021/acs.langmuir.5b03846 Langmuir 2016, 32, 2058−2066

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single crystals in a concentrated metasilicate solution at pH ∼ 14, obtained by addition of NaOH. This caused dissolution of the substrate and subsequent germination/growth of C-S-H. The samples were maintained in the metasilicate solution for a week in order to create sufficient coverage of the calcite by C-S-H (see Figure 1).

as well as between the platelets themselves.20−22 As a consequence of the limited growth of individual C-S-H platelets, the (macroscopic) growth of C-S-H proceeds under a secondary nucleation process. That is, after C-S-H platelets initially adsorb to the C3S surface, new platelets grow either upon those platelets or adjacent to them on a free surface. Eventually, this process leads to a hydration percolated network of C-S-H nanoplatelets which extends out into the solution.7,23 In the early stages, the aggregation of the platelets onto a C3S surface is strongly oriented and depends on solution conditions, from which the notion of the concept of C-S-H growth modes is introduced. Typically, low pH and low calcium concentration promotes a lateral aggregation of platelets (i.e., next to each other) and high pH and high calcium concentration promotes an axial aggregation of the platelets (i.e., on top of each other). These are the two main heterogeneous growth modes of C-SH.23,24 To date, there have been only few attempts to simulate the formation of C-S-H at the mesoscale.25−27 They were restricted to the case of homogeneous nucleation and aggregation of C-SH using a rather simple one-component model made of nanospheres interacting via an effective pair potential. Below we will consider the heterogeneous aggregation of charged platelets (C-S-H) on like-charged surfaces (C3S) from the standpoint of equilibrium thermodynamics and computer simulations. We investigate the role played by thermodynamics, e.g., the effect of changing pH and calcium concentration on the morphology of the C-S-H structure formed via cement hydration. Simulations are performed at the level of the primitive model, thus accounting explicitly for the ions and many-body interactions. Our aim is to answer three main questions: (i) Are the heterogeneous growth modes of C-S-H thermodynamically or kinetically controlled? In other words, do the calculated equilibrium structures of charged platelets on charged surfaces resemble those formed during cement hydration? (ii) How can changes in the heterogeneous growth modes of C-S-H (C-S-H structures on surfaces) be explained? (iii) What is the main physical parameter that governs C-S-H growth modes? To this end, free energies of interaction between charged platelets in bulk and close to a charge surface are computed with Monte Carlo simulations, with varying equilibrium conditions, in order to understand the equilibrium C-S-H structures on C3S under those conditions. Equilibrium simulations of many platelets close to a surface are then performed by molecular dynamics to validate those conclusions. Finally, the simulation results at equilibrium are discussed and compared with experimental observations of hydrated cement pastes, obtained both close to and far from equilibrium conditions. Specifically those experimental data are atomic force microscopy observations of the C-S-H structure grown on calcite at close to equilibrium conditions and C-S-H growth modes obtained from the modeling of calorimetric curves of cement hydration at an early age7,24 in controlled and far from equilibrium conditions.

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Figure 1. AFM image of C-S-H nanoplatelets grown on a calcite single crystal after 1 week in a concentrated metasilicate solution.

Finally, the prepared samples were removed from the metasilicate solution and equilibrated in Ca(OH) 2 solutions at various concentrations for a month. The morphologies of the C-S-H were studied at eight different Ca(OH)2 concentrations averaged over five samples. Atomic Force Microscopy. The imaging of samples was performed with a multimode AFM (Nanoscope IIIa; Veeco Co.) in contact mode. The AFM apparatus was placed in a glovebox to prevent carbonation. The measurements were performed at 25 oC in the equilibrium solutions using a commercial fluid cell. A V-shaped silicon cantilever was used with spring constants ranging between 10 and 4000 mN/m and a Young’s modulus of approximately 440 GPa.

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MODEL SYSTEMS Two Platelets. C-S-H platelets were modeled as discs composed of np spherical particles (with diameter, d = 10 Å) arranged on a regular hexagonal lattice (see Figure 2). Simulations of two discs were carried out in a cylindrical box of volume Vbox. To study the effect of changing platelet size, we used the values np = 19, 37, 61, 91, and 127. The particles making up the platelets were also assigned a charge −αe, which means that the total platelet charge was −npαe. α determined the surface charge density of the platelets. The negative surface charge density was varied in the interval 0.005−0.024 e/Å2. The platelets and the mobile cations and anions were assumed embedded in a structureless dielectric continuum with a uniform relative dielectric permittivity. This is the so-called primitive model.29 The hard core diameter of the mobile ions was the same, equal to 4 Å. Thus, two charged particles, i and j, interact via a Coulomb potential qiqj U el(rij) = 4π ϵ0ϵrrij (1)

EXPERIMENTAL STUDIES

Sample Preparation. The sample preparation, setup of the atomic force microscopy (AFM), and protocol used to visualize the morphology of the C-S-H particles grown on calcite are described elsewhere28 and are only briefly repeated here. C-S-H particles were grown on the atomically smooth, [101̅4] plane of cleaved calcite single crystals. This was accomplished by immersion of freshly cleaved calcite

where qi is the charge carried by particle i and rij the particle separation. In the cases considered, we assumed divalent 2059


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Figure 2. Schematic picture of two platelets in a salt solution. The center of mass of the platelets are constrained to the cylinder axis. The sites of the platelets are shown as red spheres while the divalent counterions as blue spheres.

counterions. All particles also interact via a dispersion potential, modeled with the Lennard-Jones function ⎛⎛ ⎞12 ⎛ ⎞6 ⎞ σLJ σLJ U (rij) = 4ϵLJ⎜⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎟ ⎜⎝ r ⎠ ⎝ rij ⎠ ⎟⎠ ⎝ ij LJ

(2) Figure 3. Sketches of two platelets (in red) and one infinite surface (in blue) used to study (a) axial aggregation and (b) lateral aggregation. Counterions and co-ions are not shown.

with ϵLJ = 0.1 kBT and σLJ was set equal to the sum of the radii of the two interacting species. The exact value of ϵLJ is of course not known, but reasonable variations of this parameter have no qualitative effect on the results. Two Platelets and an Infinite Surface. A charged surface was introduced in the simulation box and positioned at one end of the cylinder. The same model for the platelets was also used to describe the charged surface; i.e., the surface was decorated with charged sites distributed on a hexagonal lattice with the same density, charge and size as those of the platelets. The interactions between sites and counterions were the same as in the two-platelet case. The aim was to investigate two different modes of aggregation of C-S-H platelets onto the “C3S surface”axial and the lateral aggregation (see Figure 3). In the first case (Figure 3a), the center of mass of one platelet was kept fixed at the free energy minimum. The center of mass of the second platelet was moved along the z-axis, i.e., the rotation axis of the cylinder. In the second case (Figure 3b), the centers of mass of the two platelets were positioned in the free energy minimum with the surface and moved along the x-axis, parallel to the surface. Note that the platelets were allowed to rotate. Monte Carlo Simulations. The systems described above, i.e., two platelets and two platelets and an inf inite surface, were solved with Monte Carlo simulations using the Metropolis algorithm. Most simulations were carried out in the grand canonical ensemble (μ,V,T) when a finite salt concentration was considered. When only counterions were present, the canonical ensemble (N,V,T) was used. Three different kinds of moves were employed; (i) single ion translations, (ii) platelet rotations, where a platelet is rotated around a random axis, and (iii) cluster displacements. The centers of mass of the platelets were kept fixed during the simulations. The cluster move

involves rotation of a single platelet together with surrounding ions. Maximum displacements (displacement parameters) for all moves were set so as to return an acceptance ratio between 20% and 40%. The temperature was kept constant at T = 298 K in all simulations. At a given fixed distance between the centers of mass of the platelets, the force exerted on one platelet was evaluated by summing the forces exerted by each particle that interacts with the platelet. In the case of two particles with a surface, the volume fraction was kept fixed at ϕ = npπd3/3Vbox = 0.005. Many Platelets and an Infinite Surface. Simulations with an infinite surface in contact with many platelets were also performed to test the conclusions that were inferred from the free energies of interaction, obtained with Monte Carlo simulations of two individual charged platelets in bulk solution and close to an infinite surface. Note that in the same spirit the dynamic process of growth, adsorption, and aggregation of platelets on surfaces were not simulated but the equilibrium state of these systems and, in particular, their equilibrium structure. These simulations were also conducted with the primitive model, i.e., with all ions explicitly included in a rectangular box with periodic boundary conditions applied in two dimensions and truncated in the third dimension by the two parallel walls: one charged and one neutral. The simulation box contained ≈20 mM CaX2 salt solution and 50 circular platelets with a diameter of 70 Å bearing charges, compensated by divalent Ca2+ counterions. Three systems were studied, as summarized in Table 1, corresponding to low, medium, and high negative surface charge densities. The systems were 2060


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Langmuir Table 1. Simulation Detailsa ID

Q (e)

Np

Ns

NCa2+

NX−

Nw

σ (e/Å2)

Lx/Ly/Lz (Å)

s1 s2 s3

77 154 308

50 50 50

169 169 169

3115 5840 11370

780 780 780

3600 3600 3600

0.01 0.02 0.041

400/400/200 400/400/200 400/400/200

a The columns give the simulation identifier (ID), charge per platelet (Q), number of platelets (Np), number of sites per platelet (Ns), number of calcium ions (NCa2+), number of monovalent anions (NX−), number of wall sites (Nw), surface charge density (σ), and box dimensions (Lx/Ly/Lz).

freely rotating platelets with their centers of mass at some fixed separation will possess a rotational entropy Srot. As the platelets approach, this entropy decreases, which creates a repulsive force. The qualitative behavior of the entropy loss versus platelet separation is the same for platelets of all sizes. Indeed, we expect to obtain identical behavior if the center of mass separation, R, is scaled by the average radius of the platelet, Rp.18 Thus, the rotational entropy is a function of the reduced separation between platelets, i.e., Srot(R/Rp). Furthermore, we expect that

simulated using the molecular dynamics (MD) program package GROMACS.30 The interaction potentials and model details of the platelet and surface were slightly modified to suit the MD technique used. The diameter of the platelet sites was reduced to 5 Å. All the details of the model, methods, and inputs are given in the Supporting Information.

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RESULTS Interaction of Two Platelets. Figure 4 shows the interactions between a pair of platelets that have been

Srot(R /R p) ≈ Srot(R ) − Srot(2R p)

for R < 2R p

(3)

That is, the effect of increasing Rp is to essentially decrease the entropy by a constant amount for all R. This approximation is more accurate for small R/Rp. On the other hand, the electrostatic interaction between the platelets grows as Rp2. Thus, the distance-dependent part of the rotational entropy becomes negligible for large platelets by comparison. The platelet sizes, which we are able to simulate in this work, are still in the range where the rotational entropy plays a role. In Figure 5 we consider two freely rotating interacting platelets. Here we

Figure 5. Free energy of interaction between two freely rotating platelets with σ = −0.012 e/Å2 in a 10 mM 2:1 salt solution at a volume fraction of 0.023. The interaction between two parallel plates has been added for comparison (dashed line).

Figure 4. (a) Average force between two parallel platelets with σ = −0.012 e/Å2 in a 10 mM 2:1 salt solution at a volume fraction of 0.023. The number of sites, from 19 to 61, corresponds to 50 to 90 Å in diameter; ϵLJ = 0.1 kBT. (b) The corresponding osmotic pressure, Π, that is the force has been divided by the platelet area.

see that it is only for the cases, np > 37, that the free energy shows a global minimum at short separation. Two freely rotating platelets can start to overlap as soon as the center-tocenter distance is shorter than the platelet diameter. As a result, we see a more long-ranged interaction than when they are constrained to be parallel; cf. the solid and dashed curves in Figure 5. When the divalent counterions are replaced by monovalent counterions, the force and resulting free energy become purely repulsive as a result of the large increase of the system entropy (see the Supporting Information). For this reason, calculations with monovalent ions were disregarded in the remainder of the article. It is interesting to make a comparison between swelling clays, like montmorillonite, and cement paste. Both systems consist of charged platelets although of completely different origin. The

constrained to be parallel. Note the attractive interaction, typical of highly charged surfaces in the presence of divalent counterions. The major contribution to the attraction is due to the correlations between counterions in the space between the surfaces. For the three platelet sizes in the figure, one notes that the magnitude of the attraction increases with platelet size. However, dividing the force with platelet area shows that the depth at the pressure minimum becomes more similar for the three cases and converges rapidly to the value for infinite plates. Integration of the force curves gives the free energy of interaction of two parallel platelets and is strongly negative at short separations for all cases (data not shown). In reality, platelets will generally only adopt parallel (or near parallel) orientations when they are at close separation. Two 2061


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is slightly stronger in this case than for two parallel platelets, since the correlation term is stronger, despite the fact that the rotational entropy gives a repulsive contribution. The rotational entropy plays a significant role as seen from a comparison of the parallel and freely rotating pairs of platelets (solid and dashed black lines). A curious feature in the platelet-surface force in Figure 6 is the initial weak minimum, which appears for a perpendicular arrangement. It will, however, disappear for larger particles, since the rotational entropy term is more long ranged than the attractive interaction. The attractive force acting on the second platelet (green line in Figure 6) is slightly weaker than for the first platelet due to geometric factors. Interaction of Two Platelets with a Surface. From the previous results, one can conclude that at a critical size a C-S-H platelet will aggregate onto the C3S surface. The aggregation of further platelets onto the C3S surface and on the first C-S-H particle will then be dependent on both thermodynamic and kinetics factors. In this section, we investigate the role played by thermodynamics in the different modes of C-S-H aggregation onto C3S surfaces. We study the axial aggregation of charged platelets on a charged surface of the same sign using the model in Figure 3a. Figure 6 displays the axial force acting between two platelets in a 2:1 salt solution. The same qualitative behavior as in the case of one particle and a surface is observed. Again, the force displays two minima: the first one at R ∼ 30 Å corresponds to a T-shaped configuration, while the second at R ∼ 15 Å corresponds to a stacked configuration. The minima depend only weakly on salt concentration. The attraction between two freely rotating platelets increases with size, and the same is found for two platelets at a surface. A net attraction in the stacked configuration is found for np = 37 (see Figure 6). Under the same conditions, but in the absence of a charged surface, two platelets of 37 sites do not show any attraction (cf. Figure 5). This demonstrates the importance of the charged C3S surface in the aggregation process of C-S-H during the hydration of cement. Figure 7 shows the influence of the platelet charge density (∼pH) on the free energy of interaction between the platelets. At low surface charge density (low pH), the platelets repel each other. When increasing the charge density from −0.005 to −0.012 e/Å2, the same qualitative result is observed. Upon a further increase in pH, a net attraction is obtained at a separation corresponding to a T-shaped configuration. Note that in usual conditions of a cement paste the surface charge density of C-S-H approaches −0.05 e/Å2. For this surface charge density, a net attraction should also be observed in the

surface charge density is much lower in clay than in C-S-H, but the platelets are usually much larger and as a result one can observe attractive interactions in both cases. Thus, with small platelets the surface charge density needs to be high in order to create a net attraction, while with larger platelets attraction can be found at lower surface charge density. The necessary condition in all cases is the presence of divalent or higher valency counterions. It should also be stressed that the pair interaction between charged platelets and, more generally, between charged colloids is density dependent. When electrostatic interactions are strongly coupled, that is, when ion−ion correlations dominate particle interactions, increasing the colloid concentration strengthens their attraction.31,32 On the other hand, at weak coupling, typically with monovalent counterions and relatively low charge density, increasing the colloid concentration weakens their repulsion. Interaction of One Platelet with a Surface. In the initial phase of cement hydration, the C-S-H platelets form near the C3S grain and will be attracted to its surface. In order to mimic this situation, we have also simulated a single platelet outside an infinite (large) charged surface (see Figure 6). In contact with

Figure 6. Comparison of the force between platelets and surface for a few situations. “p+p; nonrot” shows the force between two parallel platelets (black line), and “p+p” shows the same for two freely rotating platelets (black dashed line). “s+p” shows the force between a single freely rotating platelet and a surface (red line), and “s+p+p” shows the force between two platelets where one is positioned at its minimum close to the surface and the second is freely rotating (green line). The surface charge density is the same for all platelets and surfaces, σ = −0.012 e/Å2, np = 37, and the concentration of the 2:1 salt is 10 mM.

water, the surface of C3S is known to ionize and to behave similarly to that of C-S-H as revealed by electrokinetic measurements.33 The surface charge densities of C3S and CS-H were therefore assumed to be identical. The attractive force

Figure 7. (a) Axial free energy of interaction between two platelets in a 10 mM 2:1 salt solution at various surface charge densities, obtained with the model in Figure 3a with np = 19. (b) Same as (a) but with set charge density (σ = −0.012 e/Å2) and varying particle size. 2062


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Langmuir stacked configuration. Similarly, a net attraction in the stacked configuration is found for larger platelet size (see Figure 7b). We have also tried to calculate the lateral interaction between two platelets on a surface. For this arrangement the force oscillates around 0 kBT. No attraction or repulsion is found between the particles until the Lennard-Jones potential comes into play. The salt concentration has virtually no effect on the lateral force, and the same result is found when the platelet size or the surface charge density is varied. This suggests that there is no preferential lateral position when a C-S-H particle adsorbs or starts to grow from a C3S surface. Morphology and Growth Modes of C-S-H Islets. The 5 × 5 μm AFM images of C-S-H grown on calcite monocrystal obtained in near equilibrium conditions (weak supersaturation) at five different concentrations are given in Figure 8. One

Figure 9. Experimentally determined lateral growth mode to axial growth mode ratio (GMR) of C-S-H (on surfaces) as a function of Ca(OH)2 concentration. Filled black circles: GMR obtained from atomic force microscopy measured aspect ratio of C-S-H islets formed under near equilibrium conditions on surfaces of calcite monocrystals (see Figure 8). Filled red squares: GMR obtained from calorimetric measurements of C3S hydration kinetics in controlled conditions. Dashed red squares: GMR obtained from AFM measurements of the vertical and lateral growth rates of C-S-H islets during the early hydration of a planar C3S surface. Note that the hydration of C3S proceeds far from equilibrium conditions. The GMR is expressed either as the square root of the top surface area to the height ratio (√(S)/h) of the C-S-H islets or as the ratio of lateral to vertical growth rate; see text for more details.

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DISCUSSION AND CONCLUSION The growth of individual C-S-H particles is limited because the growth rate is much smaller than the nucleation rate.18 The word “growth mode” is used here to designate the secondary nucleation of C-S-H and the way in which it aggregates on a C3S surface. In order to rationalize the change in C-S-H growth modes during cement hydration, it is useful to analyze the interaction between the platelet and surface as well as between the platelets themselves. This is done under different equilibrium conditions to see whether or not these equilibrium states and associated changes in interaction free energies can explain the observed growth modes and structures of C-S-H obtained in under nonequilibrium conditions (cf. Figure 9). This is was carried out using simulations of charged platelets on an equally charged surface, with varying platelet charge and size. It should be noted that experimentally one can always distinguish axial from lateral growth with respect to a surface (see e.g. Figure 9). In order to compare and discuss these experimentally determined growth modes with our simulations, we associate them with a basal/basal aggregation (axial aggregation) and platelet/surface aggregation (lateral aggregation). Obviously, this is an approximation which becomes all the more true as there are few platelets covering the dissolving surface (during the early stage of hydration) and all the less true at late stage where the notion of inf inite surface disappears as well as preferential growth directions. The surface charge density of a C-S-H platelet is determined by titrating silanol groups (pKa ≈ 10) on its surface (the same is true for C3S grains). The titration of these silanol groups is strongly affected by their mutual repulsion, which means that the titration does not follow the behavior of a simple acid but presents a more extended titration curve. The presence of large amounts of divalent calcium ions, however, facilitates the dissociation.12 The number of titratable sites is estimated to be around 0.04−0.05 sites/Å2, and a completely ionized surface is

Figure 8. The 5 × 5 μm AFM images of C-S-H grown in near equilibrium conditions for one month on a calcite single crystal in contact with Ca(OH)2 aqueous solutions at different concentrations: (a) 0.82, (b) 3.15, (c) 14.69, and (d) 19.13 mM. The contrast in the images is related to the spatial variation of the tip height. The relative heights are (a) 150, (b) 300, (c) 600, and (d) 700 nm.

generally observes large islets of C-S-H (bright areas) separated by porosities (dark areas). The C-S-H islets are larger (laterally) when the Ca(OH)2 concentration is small and thicker (vertically) when the Ca(OH)2 concentration (pH) is high. This is evident from Figure 9, which reports the ratio of the square root of the surface area to the thickness of the C-S-H islets, √(S)/h, averaged over five different samples per calcium hydroxide concentration. In addition, results for C-S-H grown on a C3S surface during its early hydration at far from equilibrium conditions (high supersaturation) obtained from AFM7 and from the extrapolation/modeling of measurements of hydration kinetics24 are also given. Remarkably, the same trend is observed, that is, a drop in √(S)/h as the Ca(OH)2 concentration (pH) increases, despite the changes in substrate, supersaturation conditions, and experimental technique. This gives us some confidence in the results and also shows the generality in the heterogeneous growth/aggregation modes (mechanisms) of C-S-H. Preempting our conclusions, these experimental results also strongly suggest that the heterogeneous growth of C-S-H is primarily controlled by thermodynamics. 2063


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Langmuir reached under saturated lime conditions (≈22 mM Ca(OH)2) where the solution pH reaches 12.7. These are the usual conditions for setting cement. When the Ca(OH)2 concentration is decreased to 1 mM, the solution pH drops to approximately 11, and only half of the silanol groups are ionized. That is high Ca(OH)2 concentration means high pH and strongly negatively charged C3S surfaces and C-S-H platelets and vice versa. One counterintuitive consequence is that two C-S-H surfaces attract each other more at high pH, i.e., at high surface charge densities. This phenomenon has been observed experimentally in many different systems34−37 and is well understood from both simulation work20 and analytical studies.38−40 Interestingly, one can also observe from our results that the correlation attraction between particles and/or surfaces is more affected by a change in the charge densities than in the counterion concentration. Thus, the most important effect of an increased Ca(OH)2 concentration is an increase in solution pH. These remarks brings us to the major conclusion of this work. That is the heterogeous growth modes of C-S-H at the early stage is controlled by thermodynamics. Indeed, from the free energy of interaction between charged platelets (C-S-H) close to a charged surface (C3S), one can thus conclude that at low Ca(OH)2 concentration (i.e., low pH = low surface charge density) the small platelets will adsorb on the surface but will not aggregate between themselves, as a result of a repulsive, or too weak, free energy as shown in Figure 7. The particles would preferentially form a monolayer on which, upon further crystalline growth of particles, a second layer will eventually form, etc. Similarly to experimental observations in nonequilibrium conditions, this would result in high sqrt(S)/h and give rise to low axial growth mode. On the other hand, when the Ca(OH)2 concentration is high (i.e., high pH = high surface charge density), the axial free energy between two platelets close to a charged surface becomes attractive (see e.g. Figure 6). Although less attractive than between a platelet and a large surface, one would still expect the platelets to form stacks of platelets on the surface. Indeed, even though it is energetically more favorable to adsorb platelets as monolayers on the surface, the formation of stacks is expected to be entropically favorable due to the gain in free volume. Again, this scenario inferred from calculated equilibrium interaction free energies fits well with the experimental observations in nonequilibrium conditions and high pH for which a low sqrt(S)/h is found and the axial growth mode is favored. In order to confirm these conclusions, simulations of a charged surface in contact with a dispersion of charged platelets under similar conditions of charge and calcium salt concentrations as above were performed. Snapshots of equilibrium configurations at three different surface charge densities (i.e., pHs) are shown in Figure 10. In agreement with our conclusions above, one finds that the platelets tend to form stacks at high pH and high surface charge density. At low pH and low surface charge density the platelets tend to uniformly cover the surface. This result is in good agreement with the trend observed experimentally (see Figure 9). Obviously, the choice of the model and conditions used to interpret the aggregation and growth mode of C-S-H can be criticized; there is much scope for future investigations on cement hydration, not to mention nucleation/growth, aggregation, and mesostructure of hydrates as well as anhydrate dissolution. That is cement hydration kinetics is still far from being well understood.

Figure 10. Snapshots from MD simulations of C-S-H platelets adsorbed on a C3S surface. Ions are omitted for clarity. From top to bottom snapshots for C-S-H particles bearing a weak (s1), medium (s2), and strong (s3) negative charge density. The surface charge densities of the C-S-H platelets and of the C3S surface are set equal (see Table 1 for more details).

First of all, although the neglect of nonequilibrium conditions was a natural choice to investigate the role of thermodynamics, it does not mean that kinetics does not play any role. A good example is the shift in the magnitude of the growth mode ratio observed in Figure 9, which to a large degree can be attributed to the change in the supersaturation degree, i.e., kinetics. This is also a well-known result of colloidal science on homogeneous aggregation of spherical colloids which shows that a diffusion limited aggregation leads to more compact aggregate than a reaction limited aggregation. More recently, it was also shown that a fast homogeneous precipitation of attractive spherical colloids leads to more open aggregates whose local density and order is controlled by the underlying thermodynamics (free energy of interactions).25 We are not aware of similar studies on the heterogeneous precipitation of attractive platelets. In particular, in future works it would be interesting to investigate how the inclusion of nonequilibrium conditions could explain the nontrivial shift observed in Figure 9. Second, the size polydispersity of platelets as observed by e.g. neutron scattering9 was neglected in our model. Size polydispersity was introduced and discussed for example in refs 26 and 27 which studied the homogeneous aggregation of C-S-H modeled as polydisperse attractive spheres. More recently, its impact on the stacking of charged platelets was also discussed at some length.41 The main conclusion is that 2064


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Langmuir

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large polydispersity give rise to small platelet stacks (small number of platelets in a stack) and vice versa as a result of the poisoning of their formation by small platelets. Note that this is all the more true as the platelet charge density is small. Similarly, the platelet flexibility have been shown to have the same effect, i.e., to reduce the average size of platelet tactoids.32 In any case size polydispersity would certainly not change the qualitative trend of the heterogeneous C-S-H growth modes (and our conclusions) but could affect them quantitatively. Finally, if one wants to model the kinetics of cement hydration and of hydrate mesostructure formation, using coarse grain models, other major issues appear. For example, how does one model the nucleation/growth of C-S-H platelets? What is the importance of C-S-H prenucleation clusters and how to introduce them (see e.g. refs 42 and 43)? Recent studies tend to show that anhydrate dissolution is essential in the control of cement hydration kinetics (see e.g. ref 44). Also, the effective pair potentials between charged particles are density dependent (see e.g. refs 31 and 32). Ultimately, models of cement hydration should in principle include all these aspects, but the road toward this goal is still very long. However, we have clearly shown in this work that thermodynamics is an essential key and cannot be avoided in achieving it. To conclude, we have seen that using a simple geometric model for C-S-H and a combination of equilibrium simulations and thermodynamic arguments, it is possible to rationalize the change in the growth modes of C-S-H on cement grains as well as the change in morphologies of C-S-H aggregates. In particular, we showed that charge densities of C-S-H and C3S are key parameters in determining the free energy of interaction between platelets and surfaces which, in turn, drive the heterogeneous growth modes of C-S-H at early stages.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.5b03846. S1: details of the model, methods, and inputs used in molecular dynamic simulations; S2: average force and interaction free energy of two rotating platelet in 10 mM of a 2:1 salt and a 1:1 salt (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Ph +33 (0)380 396176; Fax +33 (0)380 396132 (C.L.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Cedric Plassard for the atomic force microscopy measurements. Financial support from the Region Bourgogne and CNRS as well as computational support from CRI, Université de Bourgogne, is gratefully acknowledged.

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REFERENCES

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