Stability of Negatively Charged Platelets in Calcium-Rich Anionic

May 21, 2014 - agreement with experimental observations, small stacks of platelets (tactoids) are formed, which are greatly stabilized in the presence...
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Stability of Negatively Charged Platelets in Calcium-Rich Anionic Copolymer Solutions Martin Turesson,*,‡ André Nonat, and Christophe Labbez* ICB, UMR 6303 CNRS, Université de Bourgogne, F-21078 Dijon Cedex, France S Supporting Information *

ABSTRACT: Controlling the stability of anisotropic particles is key to the development of advanced materials. Here, we report an investigation, by means of mesoscale molecular dynamics simulations, of the stability and structural change of calcium-rich dispersions containing negatively charged nanoplatelets, neutralized by calcium counterions, in the presence of either comb copolymers composed of anionic backbones with attached neutral side chains or anionic-neutral linear block copolymers. In agreement with experimental observations, small stacks of platelets (tactoids) are formed, which are greatly stabilized in the presence of copolymers. In the absence of polymers, tactoids will grow and aggregate strongly due to large attractive Ca2+-Ca2+ correlation forces. Unlike comb copolymers which only adsorb on the external surfaces, block copolymers are found to intercalate between the platelets. The present results show that the stabilization is the result of a free energy barrier induced by the excluded volume of hydrophilic chains, while the intercalation is due to bridging forces. More generally, the results shed new light on the recent finding of the first hybrid cementitious mesocrystal.

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INTRODUCTION The stability of nanoparticles dispersed in solution and their phases1,2 has been studied for over 50 years and found to be a delicate balance of entropic and energetic contributions to the total free energy. For example, it is possible to form a stable liquid or a gel as well as a colloidal glass or crystal, with identical nanoparticles whose only difference is the charged state of their surface.3−6 More recently, the phase stability and the controlled aggregation of nanoparticles dispersed in polyelectrolyte solutions have attracted intense scrutiny7 and are challenging to predict because of the computational difficulty in accessing the relevant length and time scales. Flory theories, density functional theories, and molecular simulation methods provide essential guidance, although accurate calculations are restricted to simple systems with two or at most a few spherical nanoparticles in the relevant size regime.8,9 Despite these difficulties, a vast array of selfassembled hybrid nano-objects and nanomaterials is emerging with advanced functions and properties.10−12 Although they are widespread, one often overlooked example of nanomaterials is hydrated cement paste used in construction materials, e.g., concrete, as well as in applications such as synthetic bone or teeth repair. It is composed of nanohydrates of various shapes and nature, which germinate and grow during © 2014 American Chemical Society

the hydration of the initial cement grains (clinker) under the conditions of high pH (>12) and salt concentration (mainly Ca(OH)2). Due to this complexity, the origin of cement cohesion was only discovered 10 years ago! It was shown to be the result of strong attractive electrostatic ion correlation forces, acting between the main cement hydrates, i.e, calcium silicate nanohydrates, commonly abbreviated C−S−H.13−16 In this context, the use of anionic comb copolymers dispersants, consisting of negatively charged backbones (e.g., polyacrylic acid) with grafted neutral hydrophilic side chains (most often polyalkene oxides), has allowed the emergence of highly pumpable and self-compacting concrete with high mechanical performance, essential for construction of incredible skyscrapers.17 Recently, similar copolymers were employed to stabilize and control the gelification of C−S−H suspensions, which, when used in concrete, were shown to be excellent hardening accelerators.18−20 From the self-assembly of stabilized C−S−H suspensions with linear block copolymers, Picker et al. just obtained the first cementitious hybrid mesocrystal21 with impressive elastic Received: April 1, 2014 Revised: May 13, 2014 Published: May 21, 2014 6713

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Figure 1. Simulation snapshots (for system s10), illustrating the setup used for (left) potential of mean force calculations between two parallel platelets arranged face-to-face along the z-axis. The shaded areas show a time averaged isodensity surface for the side chain monomers (white) which are connected to the polymer backbones (red). The divalent ions (Ca2+) and monovalent anions (OH−) are shown in green and blue, respectively. The right panel is a snapshot from the corresponding many-platelet simulation (at large t), from which static and dynamic properties were extracted. For clarity, only the platelets are shown.

properties. These results constitute the initial steps toward a new revolution in the field of advanced nanomaterials for construction. In this paper, we shall present the first large scale mesoscopic simulations of an assembly of highly charged platelets dispersed in like-charged comb copolymer solutions. On the basis of these extensive molecular dynamics simulations complemented with free energy calculations, see snapshot in Figure 1, we identify the kinetic and thermodynamic mechanisms responsible for the observed stabilizing effects. We further show the self-assembly of charged platelet tactoids with intercalated copolymers, which can be viewed as the first bricks toward the self-construction of hybrid C−S−H mesocrystals.

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DESCRIPTION OF THE MODEL SYSTEM All simulations were performed on the level of the full primitive model, including ions, platelets, and copolymers explicitly, but considering water as a structureless dielectric continuum, with a dielectric constant εr, equal to 78.4. In the primitive model, two charges, qi and qj, separated by a distance rij interact via Coulombs law: u(rij) = (qiqj)/(4πε0εrrij), where ε0 is the permittivity of vacuum. Ions (here Ca2+ and OH−) were approximated as freely moving divalent and monovalent point charges, respectively. On top of the electrostatic interactions between charges in the system, all species were subjected to a strictly repulsive truncated and shifted Lennard−Jones potential UTrS LJ ,

Figure 2. 2-D schematics of the repeating units of (a) the comb copolymer of type Pcn,x (b) the block copolymer of type Pbn,x. The rightmost picture in panel c is zoom in on the C−S−H platelet, showing the hexagonal surface pattern and the symmetry axes, C1, C2, and C3, along which pairs, ij, and triplets, ijk, define bonds and angles, respectively.

Each monomer in the backbone, not being a side chain grafting point, carries a negative unit charge. No bond angle potential was implemented, yielding a freely jointed chain. Throughout the text, comb copolymers will be notated Pcn,x, with n being the number of repeating blocks, and x being the length of the side chains; see Figure 2a. More specifically, in this work we have studied two different comb copolymers, identified as Pc7,4 (54 c monomers per polymer) and P7,10 (102 monomers per polymer). They have the same backbone linear charge and side chain grafting density but differ with respect to the side chain length. In addition to the comb copolymers, a block copolymer, notated Pb10,30, was investigated, consisting of one block of 10 charged monomers linked to another block of 30 neutral monomers; see Figure 2b. Note that the described polymers are smaller than polymers typically used for industrial

⎧ ⎡⎛ ⎞12 ⎛ σij ⎞6 ⎤ ⎪ ⎢⎜ σij ⎟ ⎪ε − 2⎜⎜ ⎟⎟ ⎥⎥ + ε LJ if rij < σij TrS (rij) = ⎨ LJ⎢⎜⎝ rij ⎟⎠ ULJ ⎝ rij ⎠ ⎦ ⎪ ⎣ ⎪ ⎩ 0 otherwise (1)

εLJ = 1kT, where T (here 298 K) and k is the temperature and Boltzmann constant, respectively. Furthermore, σij = (σi + σj)/2 and σCa2+ = σOH− = 0.4 nm. The same model for comb polyelectrolytes as used in ref 22 (sketched in Figure 2a) was employed. In brief, the hydrophilic side chains are modeled by chains of neutral monomers attached in regular intervals to a chain of backbone monomers. 6714

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Table 1. Simulation Detailsa ID s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11

Ptype Pc7,4 Pc7,10 Pb10,30

Pc7,4 Pc7,4 Pc7,10 Pb10,30

Nplate

Qplate/e

Npol

NX2+

NX−

Lx/Ly/Lz (nm)

p

−308 −308 −308 −308 −84 −168 −308 −308 −308 −308 −308

0 30 24 60 0 0 0 100 300 300 300

608 818 776 908 2100 4200 8200 8900 10 300 10 300 9700

600 600 600 600 0 0 1000 1000 1000 1000 1000

30/30/30 30/30/30 30/30/30 30/30/30 35/35/35 35/35/35 35/35/35 35/35/35 35/35/35 35/35/35 35/35/35

2 2p 2p 2p 50r 50r 50r 50r 50r 50r 50r

a The columns give the simulation identifier (ID), copolymer type (Ptype), number of platelets (Nplate), total charge per platelet (Qplate), number of copolymers (Npol), number of divalent cations (NX2+), number of monovalent anions (NX−), and box dimensions (Lx/Ly/Lz). The superscripts in the third column stand for rotating (r) or parallel (p) platelets.

Figure 3. (a) Net mean forces Fp,z(D), exerted on two charged (σs = −640 mC/m2) parallel platelets (oriented face-to-face), in the presence of the polyelectrolytes Pc7,4, Pc7,10, and Pb10,30. The inset shows the side chain induced barrier at longer range. A comparison between MC and MD force calculations for the polymer-free system (s1) is also included. (b) Density profiles (along the z-axis, see Figure 1) of the charged monomers in the block copolymer for system s4 (Pb10,30). In particular, we show the profile behavior between the platelets for a selection of platelet−platelet separations. The upper inset emphasizes the fact that adsorption occurs on all four platelet surfaces.

(ii) Static and kinetic properties (radial distribution functions, tactoid sizes, and auto rotational correlation functions) of many-platelet systems (on the same level of approximation as in (i), but with f reely rotating platelets) were analyzed; see Figure 1b. For this purpose, we again used MD simulations with a cubic box geometry and three-dimensional periodic conditions. Due to the heavily computer power demanding simulations, the multiplatelet systems were followed during a limited period of time of up to 100 ns. This corresponded to performing more than 10 M time steps. The simulations were run in parallel on 12 processors and took about 1 month to complete in real time. For more details about the description of the methods and input parameters used, see Supporting Information. All the simulated systems in this study, referred to as sj, with j being the simulation index, are summarized in Table 1.

applications in order facilitate the simulations, but keep the qualitative behavior. The C−S−H platelets were modeled as discs (7 nm in diameter) decorated by 169 sites (σsite = 0.5 nm) arranged in a hexagonal pattern; see Figure 2c. Each particle carries 308 negative charges, spread evenly over the sites. The resulting surface charge density σs amounts to roughly −640 mC/m2 in agreement with the literature.23 More details of the platelet and copolymer models are given in the Supporting Information. Simulation Conditions. To balance the negative charge of the platelets, 154 divalent counterions, i.e., Ca2+, per platelet, were added to the systems. In addition, the electrolyte solution always contained an excess of 2:1 salt, corresponding to a saturated calcium hydroxide solution (≈ 20 mM). Two sets of simulations were performed in the canonical (NVT) ensemble: (i) Pair potentials between two nonrotating parallel charged platelets with a face-to-face configuration in contact with the various copolymer solutions were measured as a function of the (center of mass) interplatelet distance, D; see Figure 1a. These simulations were carried out with molecular dynamics (MD) simulations (GROMACS version 4.5.424). An in-house software (Monte Carlo (MC) method) was also employed to confirm the validity of some of the MD free energy calculations. The MC method uses the standard metropolis algorithm25 to sample ion configurations, with platelets and ions confined in a closed cylindrical cell.

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RESULTS AND DISCUSSION

Force Calculations: Fixed Parallel Plates. In Figure 3a the calculated mean force of interaction between two parallel platelets as a function of their center of mass separation Fp,z(D) is shown for systems s1, s2, s3, and s4 (see snapshot in Figure 1a, illustrating the setup). In the simulations the platelet volume fraction was set to 1%. The bulk concentration (approximated as the concentration at the box boundary) of divalent ions, Ca2+, was roughly 19 mM. The number of copolymers was 6715

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Figure 3a, we see that the bridging force in the interval [15 < h < 20] is stronger in comparison with the comb copolymer systems, which is partly due to a higher backbone linear charge density. Moreover, the charged block of the block copolymer can enter the gap between the plates, without incorporating the neutral monomers, which is not the case for the comb copolymers. The two effects combined lead to the pronounced local free energy minimum at around 15 Å; see Figure 4. By the same reasoning, the repulsion starting at around 13 Å is also stronger for system s4. The implication of this difference will be further discussed in a later section. One can also notice an oscillating force profile for system s4. This behavior is reminiscent of the force profile obtained between two charged parallel flat surfaces in thermodynamic equilibrium with an (infinite) bulk solution containing a polyelectrolyte solution with oppositely charged homopolymers.29 A further indication of that similarity is the observation of the same type of non-monotonic behavior of the midplane density of the charged monomers with increasing; see Figure 3b. Comparisons with Force Measurements. Our finding of a long ranged repulsive barrier, corresponding to the overlap distance between adsorbed side chain layers, is in good agreement with recent experimental data by Flatt et al.30 In that study the force between a single flat C−S−H crystal and a colloidal tip covered with C−S−H crystals was studied by atomic force microscopy (AFM) measurements in saturated calcium hydroxide solutions containing various copolymers. After one has accepted that the measured force in such a geometry is equivalent to a free energy (via the Derjaguin approximation31), a remarkable agreement with the simulated repulsion range is found. Indeed, the measured value of 7.2 nm with polycarboxylates Pc27,13, see Table 2 in ref 30, compares very well with the value of 7 nm obtained with our model polycarboxylates Pc7,10, which have the same grafting density and almost the same side chain length; see Figure 4. However, given the size of our model platelets, the magnitude of the forces cannot be directly compared. It should also be mentioned that at high copolymer dosage purely repulsive curves were measured by AFM, while a short ranged attraction was always found in our simulations as discussed above; see Figure 3a. This apparent contradiction could be explained by (i) kinetically trapped copolymers (implying a nonequilibrium situation) in the gap between the surfaces in the AFM experiment and (ii) the usage of a low spring constant for the AFM-tip (0.6 N m−1), which may prevent the copolymers from being pushed out in the surrounding bulk solution at short distances. On the other hand, the short ranged attraction found in our simulations is fully compatible with the recent observation (by small angle X-ray scattering) of the formation of a gel network in diluted dispersions of C−S−H particles in aqueous comb copolymer solutions when sufficiently aged20 and with the well characterized problem of fluidity/workability loss of admixed cement paste with time.32−34 The latter is a phenomenon that cannot be fully explained by the reactivity of the system, i.e., by the gradual consumption of admixture by the hydration products. Nevertheless, our result sheds new light on the effect of comb copolymers in freshly hydrated cement paste, since contrary to the common idea, we here demonstrate that such polymers do not suppress the attractive interparticle forces at short range, at least not under the condition of full equilibrium between the bulk and the gap between the surfaces. In other words, the results presented here suggest that the colloidal

adjusted for each system to give a bulk concentration of charged monomers, equal to about 15 mM. Polymer-Free Systems. When the bulk electrolyte contains nothing but a calcium hydroxide salt in saturated conditions, a short-ranged attraction, with a pronounced minimum at about 9 Å, is found (see system s1). The attraction is due to ion−ion correlations between dense layers of adsorbed calcium ions on the platelet surfaces. This result is in agreement with previous atomic force measurements, as well as simulation calculations, and was identified to be the main cause of the strong cohesion in hydrated cement systems.15 For recent reviews on ion−ion correlations, see for example refs 14, 26−28. A comparison of system s1, solved with Monte Carlo simulations in the cylindrical cell model, is also included showing excellent agreement. Response to Copolymer Addition. When the bulk solution also contains copolymers, see systems s2, s3, and s4, the obtained force curves are qualitatively different. However, at short separations the force curves are practically identical for all four systems. This simply means that the platelet−platelet separation is physically too small to incorporate any copolymers between the platelets, with the dominating force being the correlation forces induced by the calcium surface counterions. As the separation is increased to about 13 Å, copolymers enter the gap between the surfaces, adsorbing to the high-density calcium layers outside the platelet surfaces, with a concomitant pronounced platelet−platelet repulsion. As the separation is further increased, the force drops and actually becomes attractive in the region [15 < h < 20], due to a copolymer bridging mechanism. This attractive bridging force diminishes with increasing side chain length, and, concurrently, the repulsive barrier, at h ≈ 14 Å, also becomes smaller. At even larger separations the force becomes repulsive, due to overlapping layers of adsorbed side chains on each surface. The repulsion is seen to have a maximum at around h = 30 Å (systems s2 and s3), decaying to zero at large separations (see inset). The corresponding interaction free energies (see the Supporting Information for more details) are shown in Figure 4, where the long ranged repulsive barrier, due to adsorbed side chains, is more clearly seen. Block vs Comb Copolymers. Quite different from systems s2 and s3 (branched copolymers) is system s4, containing the block copolymer composed of one block with charged monomers attached to a block of neutral monomers. From

Figure 4. Potentials of mean force Wp,z(D) for systems s1, s2, s3, and s4. The inset zooms in at longer range, revealing a substantial free energy barrier due to side chain excluded volume effects. 6716

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stability observed in such systems is mostly kinetically driven. The consequence of this finding will be further investigated in the next section, by means of simulations of many-platelets systems. Dynamics and Structure: Multiplatelet Systems. Radial Distribution Functions. We begin by analyzing the polymer-free systems (s5, s6, and s7) under saturated Ca(OH)2 conditions; see Table 1. The difference between these systems is the platelet surface charge density. In Figure 5, the trend of

Figure 6. Radial distribution functions g(r), with respect to platelet centers of masses in the bulk for the systems s7, s9, s10, and s11 (sampled during the last 15 ns of the simulation). σs = −640 mC/m2.

a bulk region is found at large r, i.e., g(r) = 1. The presence of peaks up to D ≈ 80 Å shows, however, that relatively large tactoids with a interplatelet distance equal to around 7.5 Å are still present. When the side chain length of the comb copolymer is increased, i.e., system s10, a repulsive g(r) for the whole plotted r-range is observed (green curve). In full agreement with the free energy calculations, replacing the comb copolymer with a block copolymer with the same neutral block length, s11 (black curve), leads to a somewhat more attractive system characterized by the formation of small independent tactoids. This is manifested by a shift in the maximum of g(r) at larger r. Although illustrative, the radial distribution functions plotted here should be treated with caution since, as we will see below, the kinetics toward equilibrium of the dispersions is greatly affected by the presence of copolymers. Cluster and Time Correlation Analysis. As shortly discussed in relation to the calculated free energy curves, displaying deep global minima at short separations and a long-range repulsion, one would expect a slowdown of the platelet aggregation in the presence of copolymers and not a thermodynamic stable suspension of individual platelets. Our simulations of many platelets dispersed in aqueous solution of Ca(OH)2 and of various Ca(OH)2/copolymers provide such evidence. The slowdown in the rate of the tactoid formation in copolymer systems as compared to the polymer-free system is illustrated in Figure 7, which gives the time evolution of the platelet clustering in dispersions containing copolymers (systems s8, s9, and s10), in comparison with the corresponding polymer free dispersion, i.e., system s7. Indeed, the rate of cluster formation is found to be much slower for the copolymer systems, and the maximum cluster size is reduced as compared to the polymer free system. A platelet was defined to belong to a specific cluster, if its center of mass was separated no more than a cutoff radius rcut from any platelet center of mass of that cluster. c The most efficient stabilizing comb copolymer is P7,10 (system s10), which presents the longest neutral side chains. For example, at 50 ns, s10 consists of roughly 30 individual platelet clusters (tactoids), see Figure 7a, with the biggest one consisting of only four platelets, see Figure 7b. In comparison, lowering the side chain length for the same copolymer structure (system s9) leads to a higher maximal cluster size and a somewhat lower value in the number of clusters. This is again in line with the potential of mean forces, see inset in Figure 4, which show a larger and more long range barrier for the comb

Figure 5. Radial distribution functions g(r) with respect to platelet centers of masses in the bulk for polyelectrolyte free systems. Three surface densities are shown: σs = −175 mC/m2 (system s5), σs = −350 mC/m2 (system s6), and σs = −640 mC/m2 (system s7). For the two lowest surface charge densities, no excess divalent salt was added. Note the logarithmic scale on the y-axis. The upper right inset shows the corresponding platelet auto correlation functions. Color-coded simulation snapshots (upper left) are also shown to illustrate the systems. Note that the snapshot corresponding to the highest surface charge density (green) includes all platelets in the system.

going from a dispersed system (s5) to a completely aggregated system (s7) is shown by (i) center−center platelet radial distribution functions g(r), main figure, (ii) single-platelet auto rotational correlation functions (upper rightmost inset), and (iii) simulation snapshots. We see that unless the surface charge density is extremely high the ion correlation forces alone are not sufficient to aggregate the system. Above a threshold value (also dependent on the concentration of 2:1 salt), regularly spaced peaks in g(r) appear (system s6), which is a signature of the formation of tactoids, in which the platelets stack face to face in columns. For the lowest surface charge density, such tactoids are absent, while for the highest surface charge, the system has collapsed into one aggregate, comprising all platelets in the system (see color coded snapshots). Accordingly, the rotational autocorrelation functions show the successively slowed down relaxation of the systems with increasing surface charge densities. Note the non-monotonic behavior of the rotational autocorrelation for system s6, indicating correlations of rotational modes between different tactoids, which is a signature of liquid crystal formation. The dispersive effect of copolymers in such a system is illustrated in Figure 6 where the radial distribution functions (sampled during the last 15 ns of the simulations) are shown for systems s9, s10, and s11 in comparison with the polymerfree system s7. In accordance with the free energy calculations in Figure 4, we see that adding copolymers gives rise to a substantial stabilization of the system which otherwise forms large tactoids and finally aggregates. Already for system s9 (red curve), which contains comb copolymers with short side chains, 6717

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Figure 7. (a) Number of observed platelet-clusters and (b) size of the largest platelet-cluster as a function of the simulation time, for systems s7, s8, s9, and s10. The inset in panel b shows the fast and complete aggregation of system s7 for a cluster cutoff, rcut = 4.5 nm.

copolymer with the longest neutral side chain length, i.e., Pc7,10. With a lower copolymer concentration (system s8), with on average 2 copolymers/plate, the brush layers of copolymers on the platelet surfaces create less steric side chain repulsion, and, consequently, a faster aggregation into bigger tactoids is found. For example, at t = 50 ns, system s8 displays only 10 individual clusters, with up to 14 platelets per tactoid. Note that the difference in clustering for system s7 with respect to the choice of rcut comes from the aggregation between tactoids stacked together and arranged in a perpendicular fashion, as seen in the snapshot of Figure 5. On the contrary, for the copolymer-containing systems, no marked difference between the two different choices of rcut was observed, meaning that no tactoid−tactoid aggregation was observed during these simulations (not shown). Another way to look at the stabilizing effect of the copolymer is to calculate time rotational autocorrelation functions for the different system studied. This is what is presented in Figure 8

Discussion in Regard to Experiments. Unfortunately, a direct comparison between these simulation predictions and experiments is difficult since similar experimental investigations do not exist. However, indirect macroscopic measurements of viscosity and dynamic rheology in cementitious systems35−39 reveal the same trends. That is, the elastic modulus and viscosity of a freshly hydrated cement paste, when mixed with hydrophilic comb copolymer, are generally observed to increase with a decreasing degree of polymerization of the hydrophilic neutral side chains and when lowering the copolymer dosage. This is in full agreement with the simulated aggregation rates (and free energy barriers). On the other hand, the slowdown of the simulated aggregation rates may in part clarify the mechanisms involved in the dormant period, so far not well understood, observed during the hydration of cement when mixed with comb copolymer solutions. Indeed, very similarly to the behavior of the aggregation rates reported here, this period of slow hydration kinetics is observed to be increasing as the stabilizing effect of the polymer becomes more efficient; see for example ref 35. Although the growth of the individual C−S−H particles is not accounted for in our simulations, which is known to be greatly affected by the presence of comb copolymers,20,40 this assumption deserves, to our opinion, further theoretical and experimental investigations since it is generally accepted that the C−S−H nanoplatelet networks formed during cement hydration41 are the result of the continuous aggregation/germination growth of new C−S−H platelets in contact with previous ones. A slowdown of the C− S−H aggregation kinetics should therefore impart cement hydration kinetics. Finally, one should also mention that for a similar copolymer to platelet size ratio the same aggregation mechanism was observed from SAXS measurements20 on diluted C−S−H/copolymers dispersions, i.e., the growth of individual C−S−H tactoids; see Figure 17, case (b), in ref 20. The snapshots in Figure 9 show the largest tactoid and the surrounding divalent ions and copolymers formed in the presence of comb polymers (system s9 at t = 50 ns) and block copolymers (system s11 at t = 100 ns). We see that the comb copolymers are located on the surfaces of the terminal platelets of the tactoids, creating comb copolymer end-caps, preventing rapid aggregation of tactoids. The stepwise increment of the maximum tactoid size, seen in Figure 7b, shows that the tactoids grow by merging smaller (copolymer end-capped) tactoids and not by single platelet addition. In the case of the block copolymer (system s11), polymer intercalation between platelets in the tactoids is found. The intercalation is explained by a bridging mechanism characterized in Figure 4 by a significantly deep minimum in the free energy between two

Figure 8. Platelet rotational autocorrelation functions for systems s7− s11.

for systems s7−s11, sampled at large t. We see that the lowest relaxation time is obtained for system s10, indicating faster rotational modes, which is coherent with Figure 7, displaying the largest amount of individual clusters (containing few platelets per tactoids) for system s10. The polymer free system (s7) is also shown in Figure 8. Due to the formation of a large aggregate, the rotational relaxation time is very slow, and we observe an almost immobile cluster. We also see that loading the system with more polymers creates a faster relaxation time (compare system s8 and s9). System s11, containing the block copolymer, shows a relaxation time somewhat lower than for system s9, indicating fairly good stabilization. 6718

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by the long range free energy barrier, appearing in response to overlapping brushes of neutral side chains, and by the short ranged ion−ion free energy attraction found in potential of mean force calculations between two platelets in a parallel (face-to-face) configuration. The stabilizing effect of the copolymer was found to be all the more important as the dosage and the degree of polymerization of the neutral side chain of copolymers were large, in full agreement with experiments. Tactoids are found to grow in a stepwise fashion,44 by merging smaller (polymer end-capped) tactoids into bigger ones, keeping a polymer end-capped tactoid configuration, a phenomenon also observed experimentally for sufficiently large copolymers. Unlike comb copolymers, block copolymers intercalate in between charged nanoplatelets of the tactoids, due to a bridging mechanism. This last finding sheds more light on the mecanisms at play in the recent synthesis of a cementitious hybrid mesocrystal.

Figure 9. Simulation snapshots showing the largest tactoid, with its neighboring copolymers and divalent ions for (left) system s9 (comb copolymers) at t = 100 ns, and (right) system s11 (block copolymers) at t = 50 ns. The platelet sites are shown in dark gray; divalent ions in light green; copolymer backbones in red and neutral side chain monomers in light gray.

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ASSOCIATED CONTENT

S Supporting Information *

plates at around h = 15 Å. At t = 100 ns, roughly 75 copolymers (spread over 13 separate intercalation sites) were found to be intercalated, thus, giving on average six incorporated polymers per intercalation site. At the same time 25 individual tactoids were found with a maximum tactoid size of 4. This means that roughly 50% of the tactoids (13/25) contained intercalated copolymers. Instead, no polymer intercalation was observed for any of the systems containing comb copolymers as a result of a too large loss in the internal entropy of the neutral side chains as compared to the gain in the backbone bridging contribution to the energy. This prediction is in full agreement with experimental observations, see for example ref 42, and allows one to rationalize the long-standing question of why comb copolymers never intercalate in like-charged C−S−H tactoids while they apparently do in oppositely charged platelet systems, like for example aluminate hydrates.43 Indeed, in the latter, the bridging contribution to the energy should be much greater due to the direct polymer adsorption to the bare charged surface of the platelets. What is more, the intercalation of block copolymer into like-charged platelet tactoids predicted here is in full agreement with the recent experimental finding of hybrid C−S−H mesocrystals in the presence of similar block copolymers.21 From our previous simulation studies on clays, one can reasonably argue that at higher simulated particle volume fractions, one should also find conditions for which hybrid nanoplatet mesocrystals are formed. In any case, this work constitutes the first brick toward the understanding of the self-assembly of C−S−H nanoplatelet in like-charged block copolymer solutions.

Simulation details are included. This material is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Authors

*(M.T.) E-mail: [email protected]. *(C.L.) E-mail: [email protected]. Present Address ‡

(M.T.) Chemical Center, Lund University, P.O. Box 124, S221 00, Lund, Sweden. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the Wenner-Gren Foundation and the support of the CRI from the University of Burgundy (https:// haydn2005.u-bourgogne.fr/CRI-CCUB) to access their computer facilities are gratefully acknowledged. The authors also thank Prof. Bo Jönsson (Lund university), Dr. A. Picker, Prof. H. Cölfen (university of Konstanz), and Dr. L. Nicoleau (BASF) for valuable discussions.

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REFERENCES

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CONCLUSIONS To summarize, we have studied the behavior of highly negatively charged nanoplatelets in a Ca2+ salt solution, both in the absence and presence of different types of neutral-anionic copolyelectrolytes. For high enough platelet surface charge density (in polymer-free systems), the platelets stack face-toface in tactoid clusters, which eventually aggregate, a phenomenon driven by ion−ion correlations at the origin of the cohesive properties of C−S−H particles in a cement slurry. When mixing copolymers into such systems, polymer adsorption occurs on the platelets, via a calcium-mediated adsorption mechanism which dramatically slows down the kinetics of platelet aggregation. This behavior was rationalized 6719

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