# Elastic Response of Cementitious Gels to Polycation Addition

Fabrice Brunel, Isabelle Pochard, Martin Turesson, sandrine Gauffinet, Christophe Labbez

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Fabrice Brunel, Isabelle Pochard, Martin Turesson, sandrine Gauffinet, Christophe Labbez. Elastic Response of Cementitious Gels to Polycation Addition. ACS Omega, 2017, 2 (5), pp.2148 - 2158. 10.1021/acsomega.6b00445 . hal-01716467

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ACS
OMEGA

# Elastic Response of Cementitious Gels to Polycation Addition

Fabrice Brunel,† Isabelle Pochard,‡,● Martin Turesson, Sandrine Gauffinet, and Christophe Labbez*●

ICB, UMR 6303 CNRS, Univ. Bourgogne Franche-Comté, FR-21000 Dijon, France

<figure><img src="image_3.png" /></figure>

## Supporting Information

**ABSTRACT:** The high compressive strength of cementitious materials stems from the creation of a percolated network of calcium silicate hydrate (C-S-H) nanoparticles glued together by strong $Ca^{2+}-Ca^{2+}$ correlation forces. Although strong, the ion correlation force is short range and yields poor elastic properties (elastic limit and resilience). Here, the use of polycations to partially replace $Ca^{2+}$ counterions and enhance the resilience of cementitious materials is reported. Adsorption isotherms, electrophoretic mobility, as well as small angle X-ray scattering and dynamic rheometry measurements, are performed on C-S-H gels, used as nonreactive models of cementitious systems, in the presence of different linear and branched polycations for various electrostatic coupling, that is, surface charge densities (pH) and $Ca^{2+}$ concentrations. The critical strain of the C-S-H gels was found to be improved by up to 1 order of magnitude as a result of bridging forces. At high electrostatic coupling (real cement conditions), only branched polycations are found to improve the deformation at the elastic limit. The results were corroborated by Monte Carlo simulations.

### Wraparound bridging mechanism

<figure><img src="image_4.png" /></figure>

### Surface bridging mechanism

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

## INTRODUCTION

Ordinary concrete, that is, a mix of Portland cement and aggregates, is the most highly used material in the world for housing and infrastructure construction. In addition to its good compressive strength properties, its omnipresence is explained by the low cost and the worldwide availability of the cement constituents that happen to be among the main elements of the earth's crust (Si, Ca, O).¹ However, the manufacturing of Portland cement clinker is responsible for about 5% of human-caused emissions of carbon dioxide. The environmental impact of cement production can be significantly lowered by improving its mechanical properties, as this would allow both improvement in the durability and a reduction in the amount of concrete used. Two ways can be envisaged to do this. The first, which is largely employed, consists of increasing the compressive strength by reducing the overall porosity of the final material. This is achieved by lowering the added water in the cement paste by using a fluidifying anionic comb-polyelectrolyte.²⁻⁴ The second method is improving the elasticity of the material. Within this scope, various ways have been reported from the development of composite materials⁵,⁶ to the control of defects (voids), so called macro-defect-free (MDF) cements,⁷ to the synthesis of highly-organized hybrid calcium silicate hydrate (C-S-H) mesocrystals.⁸ These approaches rely on the control of the structure at the microscale (MDF) or at the mesoscale (mesocrystal), or on the introduction of a ductile phase (composite materials). We propose here, instead, to modulate the interactions between cement hydrates by the use of cationic polyelectrolytes.

The cohesive properties of hydrated cement are due to the C-S-H nanoparticles.⁹,¹⁰ C-S-H is a phyllosilicate and presents a crystalline lamellar structure close to that of the rare

minerals tobermorite and/or jennite.¹¹,¹² Its exact structure is still an ongoing debate. The typical size of a C-S-H particle ranges between 5 and 60 nm.¹⁰ The basal plane of the C-S-H particles is covered with parallel silicate chains creating a high density of titrating silanol groups. Under normal conditions of the hydrated cement paste, this surface is in contact with an electrolyte solution saturated with calcium hydroxide (about 20 mmol/L at pH = 12.5). In such a solution, 90% of the surface silanols are deprotonated, that is, negatively charged, and counterbalanced by divalent calcium ions.¹³ The attractive force arising between such particles has been characterized by atomic force microscopy and is well described by Monte Carlo (MC) simulations including the ion-ion correlations neglected in the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory.¹³,¹⁴ Indeed, the approximate DLVO theory predicts repulsive forces between surfaces, due to the entropy of the counterions.¹⁵,¹⁶ However, including ionic correlations gives rise to a net attractive double layer interaction of purely electrostatic origin.¹⁷ This correlation attraction increases with increasing pH (more silanol groups become deprotonated) or when monovalent counterions are replaced with divalent ones ($Ca^{2+}$).¹⁸,¹⁹ The main drawback of this correlation attraction is its very short range, resulting in a low elastic deformation of the hydrated cement.¹⁹,²⁰

In a recent work conducted by some of us,²¹ MC simulations showed that the addition of a positively charge polyelectrolyte should also create an attractive force, comparable in magnitude but of longer range, as a result of a bridging mechanism. Prior

Received: November 30, 2016

Accepted: May 5, 2017

Published: May 17, 2017

<figure><img src="image_7.png" /></figure>
<figure><img src="image_8.png" /><figcaption>**Figure 1.** Adsorption isotherms for polycations in C-S-H suspensions (liquid-to-solid (L/S) = 50), incubated overnight at room temperature. (a) Linear polycations ($\bar{M}_w$ = 42 000 g/mol) at initial calcium concentrations ranging from 1.0 to 21.3 mM and (b) different polycations at an initial calcium concentration of 1.4 mM. The data points are averages obtained from three independent experiments. The full lines are best fit to the experimental data according to eq 1.</figcaption></figure>

to that, the possibility of intercalating linear polycations in C-S-H was investigated by two different groups.²²,²³ The long-range bridging is expected to significantly increase the deformation at the elastic limit (critical strain) of hydrated cement whilst having a small impact on the yield strength, significantly improving the resilience of the material. The bridging can be modulated by varying: (i) the chain length (i.e., molar mass), (ii) the charge density, and (iii) the structure of the polymer. This work aims to find, characterize, and rationalize the conditions for which a cement with improved resilience can be developed using polycations having different molar masses and structures. In this scope, C-S-H suspensions obtained through a pozzolanic reaction are used as the model system for cementitious materials. We determine the adsorption isotherms of the different polymers employed. The impact of the polycation on the electrokinetic charge, structure, and mechanical properties of the gels is characterized by electrophoretic mobility, small angle X-ray scattering (SAXS), and dynamic rheology, respectively. Finally, the evolution of the mechanical properties is discussed in light of MC simulations.

## RESULTS AND DISCUSSION

**Adsorption Isotherms.** Adsorption isotherms were determined for the branched and the three linear polycations at various calcium hydroxide concentrations. Figure 1a shows the adsorption data of the linear polymer of intermediate molar mass (42 000 g/mol) at increasing calcium concentrations from 1.0 to 21.3 mM and pH values ranging from 9.8 to 12.8. The full lines are the best (Levenberg-Marquardt) fit to a Langmuir isotherm, see eq 1. The fitted parameters for all polyelectrolytes, K and $\Gamma_{max}$ are given in Table 1. Note that the same behavior is observed for all polyelectrolytes, see Supporting Information (Figures S1 and S2).

In the considered range of pH (10 < pH < 13), the silanol groups of the C-S-H surface become gradually deprotonated and generate a strong negative surface charge, producing high-affinity Langmuir isotherms at the lowest calcium concentrations, stemming from electrostatic interactions between the positively charged polymers and the surface.¹³ Overall, polyelectrolyte adsorption and its affinity K decreases with

<table><caption>**Table 1.** Langmuir Constants (Equation 1) Determined from Adsorption Isotherms Using the Levenberg-Marquardt Curve-Fitting Algorithm</caption><thead><tr><th rowspan="3">[Ca<sup>2+</sup>]</th><th colspan="8">linear polycations</th></tr><tr><th colspan="2">8500 g/mol</th><th colspan="2">42 000 g/mol</th><th colspan="2">400 000 g/mol</th><th colspan="2">branched polycation</th></tr><tr><th>K</th><th>Γ<sub>max</sub></th><th>K</th><th>Γ<sub>max</sub></th><th>K</th><th>Γ<sub>max</sub></th><th>K</th><th>Γ<sub>max</sub></th></tr></thead><tbody><tr><td>1.4</td><td>7.85</td><td>181</td><td>7.87</td><td>168</td><td>0.94</td><td>182</td><td>0.52</td><td>222</td></tr><tr><td>1.0</td><td>4</td><td>170</td><td>4.72</td><td>169</td><td>2.28</td><td>166</td><td>1.95</td><td>145</td></tr><tr><td>4.7</td><td>2.9</td><td>161</td><td>1.72</td><td>159</td><td>2.74</td><td>134</td><td>2.44</td><td>258</td></tr><tr><td>7.1</td><td>1.33</td><td>130</td><td>1.18</td><td>129</td><td>0.82</td><td>119</td><td>2.27</td><td>185</td></tr></tbody></table>

increasing calcium hydroxide concentration, in good agreement with MC simulation predictions,²¹ due to the competition between polycations and Ca²⁺ as counterions to the C-S-H surface.

At the highest calcium concentrations, curves [Ca²⁺] = 18.1 and 21.3 mM, the results are more surprising: the adsorption increases almost linearly with polymer concentration. This behavior may be explained by the formation of new surfaces available for adsorption by the precipitation of Ca(OH)₂ (portlandite). Indeed, polycation adsorption is simultaneously followed by the release of calcium ions in the bulk (see Figure 2) which, given the high initial concentrations of calcium hydroxide, soon reach the solubility limit of the portlandite.

A comparison of all investigated polycations at a calcium concentration of 1.4 mM and pH = 9.8 is presented in Figure 1b. Although the polycations show a much greater adsorption capacity than that of small oligocations, as predicted by MC simulations,²¹ the high molecular weight linear (400 000 g/mol) and branched polycations show significantly lower adsorption than that of smaller polycations. A possible explanation for this is the decrease in the specific surface available for adsorption with the degree of polymerization as a result of the globular-like conformation of the long polymers and the aggregated state of the C-S-H dispersions as revealed by SAXS, see the Supporting Information (Figures S3 and S4 and Tables S1-S3).

The release of Ca²⁺ upon addition of the polycation is illustrated in Figure 2. Except for the two highest calcium
<figure><img src="image_9.png" /><figcaption>**Figure 2.** Evolution of the bulk calcium concentration as a function of the amount of polycations introduced. (a) Linear polycation (M̄<sub>w</sub> = 42 000 g/mol) at various initial calcium concentrations (from 1.0 to 21.3 mM). (b) Different polycations at an initial calcium concentration of 1.4 mM. All samples were incubated overnight at room temperature before analysis.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 3.** Electrophoretic mobility of C-S-H particle suspensions (L/S = 50) as a function of added polycation, measured with the electro-acoustic-based ZetaProbe Analyzer. (a) Linear polycation (M̄<sub>w</sub> = 42 000 g/mol) at various initial Ca(OH)<sub>2</sub> concentrations and (b) different polycations at an initial Ca(OH)<sub>2</sub> concentration of 1.4 mM.</figcaption></figure>

concentrations, the bulk Ca²⁺ concentration is observed to increase with polycation addition, whatever the polycation, c.f. Figure 2b, and to reach a plateau, which is analogous to the polycation isotherms, c.f. Figure 1. The near constant Ca²⁺ concentration observed at the two highest Ca(OH)₂ concentrations, c.f. Figure 2a, upon polycation addition may indicate that, in these cases, the released Ca²⁺ precipitates with OH⁻ to form portlandite.

Finally, one can notice that the Ca²⁺ release is significantly lower in the case of the branched polycations, see Figure 2. This is explained by the presence of carboxylate functional groups which form ion pairs with Ca²⁺.³ This also results in an increase in the adsorption affinity of these polymers with increasing Ca²⁺ concentration, see Table 1.

**Charge Reversal.** As has been already shown by experiments and MC simulations, when no polymer is added, a charge reversal of C-S-H occurs upon increasing Ca²⁺ concentration and pH.¹³ This can happen because C-S-H is highly negatively charged and the solution contains multivalent

counterions, here Ca²⁺, which accumulate in a thin layer close to the solid surface. The ion-ion correlations have been shown to be responsible for this phenomenon. Similarly, small oligocations have also been observed and predicted to overcharge the C-S-H particles at low calcium hydroxide concentration.²¹ From these results, one can reasonably expect that a polycation would cause a strong charge reversal of C-S-H. This is indeed the case, as can be seen in Figure 3. At the lowest calcium hydroxide concentration, μₑ increases from -1 × 10⁻⁸, for a polyelectrolyte free solution, to +1.5 × 10⁻⁸ m² V⁻¹ s⁻¹ when the surface is saturated with polyelectrolyte (M̄<sub>w</sub> = 42 000 g/mol). At the highest Ca²⁺ concentration, although weakly, the electrophoretic mobility still increases with polyelectrolyte concentration. This shows that even in these unfavorable conditions, polycations can still compete with Ca²⁺ at the C-S-H surface in agreement with the adsorption isotherms. Also, in line with the adsorption data, the electrophoretic mobility decreases with the degree of polymerization, see Figure 3b.
<figure><img src="image_11.png" /><figcaption>**Figure 4.** Strain sweep measurements of concentrated C–S–H suspensions (i.e., centrifugation pellets) with different concentrations of branched polycation introduced at an initial Ca(OH)₂ concentration of (a) 1.4 mM and (b) 21.3 mM. The frequency is 1 rad/s. All tests were carried out in the parallel plate geometry (diameter = 15 mm).</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Figure 5.** Values of the critical strain of the C–S–H gels (obtained by centrifugation) vs the amount of polycation added for the different types of polycation and for various initial Ca(OH)₂ concentrations: (a–c) low concentrations; (d–f) high concentrations. The frequency is 1 rad/s. All tests were carried out with the parallel plate geometry (diameter = 15 mm).</figcaption></figure>

**Critical Strain.** The typical nonlinear oscillatory responses (strain sweep measurements) of the C–S–H gels ($G' > G''$ not shown) at various added amounts of polycation and calcium hydroxide concentrations are shown in Figure 4 in comparison to the pure C–S–H gels at $\omega = 1$ rad/s. At low strain, all curves show a typical plateau in the elastic modulus, $G'$, characteristic

of the viscoelastic domain, followed by a drop when the gel starts to yield, from which the critical strain, $\gamma_c$, can be identified. Although most of the following discussion will concentrate on $\gamma_c$, one can also notice a second shoulder in the $G' = f(\gamma)$ curve as the strain increases. This second critical strain, sometimes called the “upper critical strain”, also varies
<figure><img src="image_13.png" /><figcaption>**Figure 6.** Schematic representation of the wraparound bridging mechanism and re-stabilization with increasing polycation concentration.</figcaption></figure>

with the polyelectrolyte and Ca(OH)₂ concentrations. These two discontinuities are also present in the G'' curves, not shown, indicating that our gels yield through two different mechanisms. This behavior is well established for colloids in the glass regime, that is, high volume fraction, and is attributed firstly to bound breaking and secondly to cage breaking. More recently, this has been observed as well in the gel region. However, its physical origin is still a subject of debate.²⁴⁻²⁶ On the other hand, the first yield strain can reasonably be attributed to the breakup of the sample microstructure, and therefore to its elastic limit.

$\gamma_c$ values are reported in Figure 5 as a function of the amount of polycation added at various Ca(OH)₂ concentrations for the linear and branched polycations. Without the polycations, all of the C-S-H samples exhibit a limited elasticity, that is, small $\gamma_c$, similar to previously reported values on hydrated cement.²⁷ The latter is found to increase slightly from 0.03 to 0.08% with increasing Ca(OH)₂ concentration. However, a significant gain in $\gamma_c$ (deformation at the elastic limit) can be found when polycations are added. The results in Figure 5 can be divided into two distinct regions, that is the low and high Ca(OH)₂ concentrations. At the lowest Ca(OH)₂ concentration, see Figure 5a-c, a sharp increase in $\gamma_c$ is observed, increasing up to 1 order of magnitude, upon a small addition of polycation. $\gamma_c$ is then found to peak at about 1 g/L of polycation and, upon further addition (i.e., adsorption), drops rapidly in response to the suspension re-stabilization induced by the strong over-charging of C-S-H particles by the polycations. Remarkably, the same qualitative behavior is observed for the linear and branched polymers and is, thus, not affected by the specific structure of the polycations. The magnitude of $\gamma_c$, however, depends strongly on the molecular weight (# degree of polymerization), see Figure 5a,b. That is, $\gamma_c$ is found to increase with $M_w$. Furthermore, addition of the low molar mass linear polycation, $\bar{M}_w$ = 8500 g/mol, does not result in any significant gain in $\gamma_c$ (not shown) but instead leads to fluidizing, clearly indicating that the $M_w$ is here a critical parameter. Below, we will argue that the observed increase in critical strain is a consequence of a wraparound bridging mechanism characterized by the bridging of particles or small particle aggregates with polyelectrolyte chains coiled around two or several of them. At high Ca(OH)₂ concentrations, linear polycations have virtually no effect on $\gamma_c$, but when the branched polycations are used, a continuous increase in $\gamma_c$ with polymer concentration is

observed, compare Figure 5f with Figure 5d-e. This result points to a bridging distinct from the previous one at low Ca(OH)₂ concentration and as we will show below, can be rationalized as a surface bridging mechanism.

*Wraparound Bridging Mechanism.* At the lowest Ca(OH)₂ concentration, the sequence observed (i.e., flocculation/coagulation at colloidal charge equivalence followed by redispersion in the presence of an excess of polyelectrolyte) has been reported for many other systems.²⁸ Examples include oppositely charged synthetic polyelectrolytes adsorbed on colloidal particles,²⁷,²⁹⁻³⁵ surfactant micelles,³⁶⁻³⁸ and proteins, as well as complexation of DNA to latex particles, dendrimers, and proteins.³⁹,⁴⁰ It is also largely exploited in industry, like for example, the pulp industry.⁴¹⁻⁴⁵ Substantial theoretical and simulation efforts have also been devoted to such systems. On the basis of a simple electrostatic model for the polyelectrolyte, a pearl necklace model, solved with MC simulations, Åkesson et al. were the first to show the important attractive contribution of the polymer connectivity to the interaction force between surfaces.⁴⁶ The attraction results from the polyelectrolyte chains stretching between the charged surfaces, that is, polyelectrolyte bridging, and was found to be significantly larger than the van der Waals interaction. Granfeldt et al. applied MC simulations to investigate the interaction between two spherical colloids with grafted polyelectrolytes in a system where the polyelectrolytes and particles are comparable in size.⁴⁷ The width of the interaction well was found to be significantly larger than that for a planar system. Finally, the structure and phase behavior of many charged spherical colloid solutions with different amounts of oppositely charged polyelectrolytes have also been investigated using MC simulations at the level of the primitive model (PM).⁴⁰,⁴⁸ Although simple, the model can reproduce the qualitative trend observed experimentally.

When a small amount of polyelectrolyte is added, below the charge equivalence, distinct clusters are formed as a result of bridging forces, stabilized by long-range electrostatic repulsions. At the colloidal charge equivalence, the system becomes unstable, and a large and loose aggregate of particles and polyelectrolytes is formed. In an excess of polyelectrolyte, the large aggregate melts into a mixture of individual particles and small clusters that are sterically and electrostatically stabilized. Although in some cases the attraction could be attributed to van der Waals forces, uncertainty in the choice of the Hamaker
<figure><img src="image_14.png" /><figcaption>**Figure 7.** (Left) Interaction free energies, *W*<sub>s</sub>(*h*), for the investigated polymers. As a reference, the interaction free energy in the presence of divalent ions only (green curve) is presented. (Right) Snapshot simultaneously showing typical configurations of linear, <sup>5</sup>P<sub>L</sub> (black beads), and branched, <sup>5</sup>P<sub>6</sub><sup>10</sup> (red beads) polycations when the distance between charged surfaces is 4 nm. For clarity, only the neutral monomers of the branched polycations are shown.</figcaption></figure>

constant leads to ambiguities in this explanation. Note as well that such an argument was used to explain surface forces measured with an atomic force microscope with a colloidal probe setup where the size of the colloidal particles are considerably larger than the persistent length of the polymer.³⁴ In any case, the gain in the critical strain of 1 order of magnitude observed here cannot be explained by a van der Waals type of interaction.

Our results can thus be rationalized as follows, see Figure 6. At the low Ca(OH)₂ concentration, the C–S–H particles bear a small negative charge and form a weak gel as a result of the weak correlation force,¹⁸ giving rise to a small critical strain. The gel consists of small aggregates of C–S–H particles as revealed by SAXS, see Supporting Information. As polycations are added, they compete with and partially replace the calcium counterions. At charge equivalence, a homogeneous gel of C–S–H and polyelectrolytes is formed. The gel network is formed by polyelectrolyte chains wrapped around different particles and/or small clusters of C–S–H. The polymer gives rise to a wide attractive well in the effective pair potential, which, in turn, results in a large critical strain. When the polymer radius of gyration to particle/cluster radius ratio is much lower than 1, the range of the attraction is very limited and the critical strain is dramatically reduced. Above the charge equivalence, the homogeneous gel melts into a mixture of small clusters and individual C–S–H particles overcharged by polyelectrolytes and the critical strain collapses.

**Surface Bridging Mechanism.** At large Ca(OH)₂ concentration, the C–S–H particles are highly charged,¹³ experience strong ion–ion correlation forces,¹⁸ and form a strong gel with large and dense aggregates, as revealed by SAXS data (see Supporting Information), much larger than the radius of gyration of the polymers. In those gels, the critical strain, thus, corresponds to the bound breaking between these large aggregates. Considering their size, there is no possibility of a “wraparound” type of polymer bridging mechanism. Instead, the polymers form large walls (aggregates) which, to a good approximation, can be considered to be infinite and flat. The system can be described as a polyelectrolyte solution confined between two parallel and infinite charged surfaces. The variation in critical strain can be interpreted as a change in

the width of the well of the surface interaction free energy, $W_s(h)$.

$W_s(h)$ was calculated for the three different branched polymers, namely, $^5P_3^{10}$, $^5P_6^{10}$, and $^5P_{12}^{10}$, and one linear polymer, $^5P_L$ using the model described in Figure 9. The results are summarized in Figure 7. As a reference, a polymer free system with only divalent counterions, neutralizing the surfaces, is presented. In this case, the attraction is short ranged (around 20 Å) with a free energy minimum at around 8 Å, arising from strong ion–ion correlations. Replacing the ions with linear polymers ($^5P_L$) gives rise to a somewhat longer range of attraction (≈40 Å) showing a minimum at around $h = 11$ Å. In this situation, the attraction is a mix of ion–ion correlations and bridging attraction.⁴⁹ Switching to the branched polymers ($^5P_n^{10}$), the picture completely changes, with a prominent shift in the position of the surface free energy minimum and an extended range of attraction. In particular, the free energy minimum lies at 40 Å due to the greater bond length between the side chain monomers. What is more, the range and magnitude of attraction increase from $n = 3$ to 12.

This surface bridging mechanism can be explained in the following way.²¹,⁴⁹ At large surface separation, the polyelectrolyte chains collapse onto the surfaces, due to the strong electrostatic attraction. Such configurations have a low entropy, but the energy cost for the charged monomers to extend out of the surface is even greater. As the surface separation decreases and as the monomers start to feel the electrostatic attraction of the other surface, this energy cost drops and is accompanied with a substantial entropy gain as the polymer chains stretch across the confined space in between the surfaces (the aggregates). The extent of bridging and the resulting attraction is of course affected by the separation between the charged monomers and the internal entropy of the polymer and is the key to understanding the difference between the linear and branched polycations. Indeed, with the linear polymer, independent of polymerization degree, the most favorable case is found at a separation corresponding to the monomer–monomer separation²¹,⁴⁶ and is thus rather limited. On the other hand, for the branched polymers, bridging occurs at considerably larger separations as a result of a much greater charged monomer–charged monomer separation and the gain in internal entropy associated with the side chains.
This is illustrated in Figure 7, which shows a simulation snapshot of typical configurations of the linear and branched polycations at a surface separation of 4 nm. As can be seen, the linear polymer lies in a flat configuration on the surface, whereas the branched one stretches from one surface to the other, creating a long-range bridging interaction. Finally, recalling that the polymers compete with Ca²⁺ ions at the C-S-H surface, it is quite straightforward to understand that this competition is the main reason for the continuous increase in the observed γ_c with concentration of the branched polycations.

## ■ CONCLUSIONS

Cationic polymers were successfully adsorbed onto negatively charged C-S-H particles. Two different regimes can be identified that lead to an increase in the critical strain (i.e., resilience) through polycation adsorption:

**At Low Calcium Concentration.** The negatively charged surface exhibits a strong affinity for polycations. Under these conditions, a small addition of polycation neutralizes the surface charge of C-S-H (i.e., μ_e ≈ 0) and more importantly, increases the critical strain by 1 order of magnitude. This effect is attributed to a wraparound bridging mechanism, where the polymer chains wrap around the C-S-H particles and/or small aggregates thus forming strong C-S-H/polyelectrolyte gels. With increasing polyelectrolyte concentration, the adsorption reaches a saturation plateau and the gel is redispersed into C-S-H clusters overcharged by polycations (μ_e ≫ 0).

**At High Calcium Concentration (Normal Cement Conditions).** C-S-H particles form large and dense aggregates and the critical strain of the C-S-H gels is observed to increase only with branched polycations. In accord with MC simulations, this result is best explained by a surface bridging mechanism, that is, the surface bridging of large C-S-H aggregates by polymers. Increasing the charged monomer-charged monomer separation and internal entropy of the polymers (for the same backbone length), that is, going from linear to branched polymers, is found to enlarge the range of bridging attraction. This gives plenty of room to further improve the resilience of the material by optimizing the polymer structure, notably, the length of the charged branches.

Although there is still a way to go, in particular with the application to the real cement system, these results open a new route toward resilient and tough cementitious materials.

## ■ EXPERIMENTAL SECTION

**C-S-H Suspensions Preparation.** The C-S-H mother suspensions were prepared by mixing pure calcium oxide, colloidal silica (fumed silica AEROSIL 200), and distilled-deionized milli-Q water. Proportions were chosen to obtain C-S-H suspensions in equilibrium with different calcium hydroxide concentrations, having different Ca/Si stoichiometric ratios (from 0.66 to 1.5), and a L/S weight ratio of 50 (see Table 2). The calcium oxide powder was obtained from decarbonated calcium carbonate in a furnace at 1000 °C for 4 h. The suspensions were aged for 3 weeks under strong shaking conditions before use. The Ca/Si ratio of samples was controlled directly on the solids by alkali fusion and also by the difference between the added amount of reactants and the remaining calcium and silicon amount in the C-S-H equilibrium solutions. Concentrations of Ca²⁺ and silicate in

<table><caption>**Table 2.** Masses of CaO and SiO₂ Used To Produce 250 mL of C-S-H Suspensions of Various Calcium to Silicon Stoichiometric Ratios (Ca/Si) and the Corresponding Calcium and Silica Concentrations and pH of the Liquid Phase<sup>a</sup></caption><thead><tr><th>Ca/Si</th><th>CaO (g)</th><th>SiO<sub>2</sub> (g)</th><th>Ca<sup>2+</sup> (mM)</th><th>Si (mM)</th><th>pH</th></tr></thead><tbody><tr><td>0.66</td><td>1.89</td><td>3.09</td><td>1.36</td><td>3.21</td><td>9.8</td></tr><tr><td>0.8</td><td>2.27</td><td>3.04</td><td>0.95</td><td>0.95</td><td>10.7</td></tr><tr><td>1</td><td>2.45</td><td>2.59</td><td>4.67</td><td>N.A.</td><td>12.2</td></tr><tr><td>1.2</td><td>2.73</td><td>2.36</td><td>7.09</td><td>N.A.</td><td>12.5</td></tr><tr><td>1.35</td><td>2.86</td><td>2.17</td><td>18.06</td><td>N.A.</td><td>12.8</td></tr><tr><td>1.5</td><td>3.07</td><td>1.98</td><td>21.30</td><td>N.A.</td><td>12.8</td></tr></tbody></table>

<sup>a</sup>The dilution of the sample used did not allow us to determine concentrations below 100 μM with enough accuracy and are not reported.

solution were determined by ICP-EOS. The absence of carbonation and portlandite was controlled by DRX and by the obtained solubilities. The used synthesis protocol, sample preparations, and analysis methods, as well as the solubility data of C-S-H, are well established and are detailed elsewhere.<sup>50,51</sup>

The adsorption and electrophoretic experiments described below were conducted at equilibrium on samples prepared by subdividing the mother suspensions in batches to which the desired amount of polyelectrolyte was added. The determination of structure and mechanical properties was performed by synchrotron-based SAXS (described in the Supporting Information) and dynamic rheology measurements on pellets obtained after centrifugation of the equilibrated batches.

**Polyelectrolytes.** Poly(diallyldimethylammonium chloride) linear polycations, see Figure 8a, with various molecular weight distributions were used: M̄w = 8500 g/mol from PolyScience, M̄w = 42 000 and 400 000 g/mol from Sigma-Aldrich. The molar masses were determined from the value of the intrinsic viscosity, in 0.5 M NaCl, according to the MHKS coefficient given by Dautzenberg et al.<sup>52</sup> In addition, a branched copolymer with M̄w = 200 000 g/mol was also studied. This polyelectrolyte was obtained from the polymerization of (3-acrylamidopropyl) trimethylammonium chloride (BCQuat) with acrylic acid (weight ratio BCQuat/acrylic acid = 8.5, i.e., molar ratio BCQuat/acrylic acid = 3). The copolymer was synthesized and provided by Bozzetto Group, Filago, Italy. The repeating unit of the branched polycation is shown in Figure 8b.

**Adsorption.** Various batches of pure C-S-H suspensions with different calcium hydroxide concentrations were prepared with a L/S ratio of 50.0 (in weight) and a volume of 10.0 mL. All of these samples were obtained from the corresponding initial mother C-S-H suspensions whose preparation protocol is described above. Polycation solutions (250 μL) of different concentrations were added to these batches. After 48 h incubation under shaking conditions at room temperature (293 K), samples were centrifuged (9000 rpm for 15 min). The supernatants were recovered in which polyelectrolyte, calcium, and silicate contents were measured using Total Organic Carbon analysis (Shimadzu TOC-5000A) and inductively coupled plasma-optical emission spectrometry (Vista Pro Varian), respectively. The adsorbed amounts of polymer were then deduced from subtracting the remaining content in the supernatant from the added amount in the initial suspensions. See the SI for more details.
<figure><img src="image_15.png" /><figcaption>Figure 8. Chemical structure of (a) the linear poly(diallyldimethylammonium chloride) and (b) the branched copolymer of (3-acrylamidopropyl)trimethylammonium chloride (BCQuat) with acrylic acid.</figcaption></figure>

The adsorption data were fitted with a Langmuir isotherm, defined as

$$ \Gamma = \Gamma_{\max} \left( \frac{K_c}{1 + K_c} \right) \qquad (1) $$

where c is the equilibrium bulk concentration, Γ is the amount of adsorbed polymer (in milligram per gram of C-S-H), Γmax is the maximum amount of adsorbed polymer, and K is the Langmuir equilibrium constant (K and Γmax define the substrate surface affinity and the surface saturation, respectively).

**Electrophoretic Mobility.** The electrophoretic mobilities of the C-S-H suspensions were determined using an electroacoustic-based ZetaProbe Analyzer (Colloidal Dynamics Inc., Warwick, RI). The electrophoretic mobility was measured by successively adding a polymer solution to 250 mL of C-S-H suspension (L/S = 50). For the low molecular mass polymer, the waiting time between polymer addition and measurement was 1 h. In the case of the higher molecular mass polymers, a 24 h equilibration time was needed, due to their slower adsorption kinetics.

**Dynamic Rheometry.** Dynamic rheometry in a strain sweep mode was used to measure the critical strain, γc, of the C-S-H pellets obtained after centrifugation of the samples used in the polycation adsorption experiments. We used a classic parallel plate geometry, modified to keep the sample in water-saturated air. A sample consists of a disk of paste (volume fraction around 0.04), with a diameter of 50 mm and a 2 mm gap. Given these dimensions and the characteristics of the rheometer, the lowest measurable strain was 0.01% (10⁻⁴). As mentioned above, we focus our attention on γc which is, to a great extent, independent of the particle volume fraction.⁵³,⁵⁴ The latter was thus not controlled with special care. In addition, due to the preparation method (centrifugation), the volume fraction is largely governed by the magnitude of the interparticle interactions (and centrifugal speed). The dynamic elastic modulus (G') is, on the other hand, very sensitive to the particle volume fraction. Consequently, its variation between samples was not considered in detail. The rheological measurements were made with a controlled strain rheometer (AERES II Rheometric Scientific), whereby the sample is submitted to a sinusoidal strain, and the stress response is

recorded. Details on the determination of γc can be found elsewhere.²⁶

**Model and Simulations.** We did not attempt to model the C-S-H system in all atomic detail, but instead we aimed at a mesoscopic model that contains the basic physical ingredients to be able to predict the broad (qualitative) trends observed in the interparticle forces when adding polymers. The PM of electrolyte solution is such an alternative, wherein all ions and polyions are considered explicitly and water is treated as a dielectric continuum, characterized by its dielectric permittivity, εr = 78.5 (at room temperature). The PM which uses a dielectric continuum for the solvent and hardcore interactions for the finite size of the ions cannot account for water structuring effects, dispersion interactions, polarization, and so forth, that become important at interparticle distances corresponding to one-two water layers, see, for example, refs 55–57. However, the PM was shown to reproduce the broad trends found in the interparticle interactions simulated with a molecular solvent at the Stockmayer level of description.⁵⁸⁻⁶⁰ Following our previous studies,⁴,¹³,¹⁸,²¹,⁴⁹ the C-S-H dispersion is (reduced) modeled as two planar parallel surfaces, mimicking two large C-S-H aggregates. In addition, as we are here only interested in the qualitative trend of the interparticular forces, particularly their range, as the calcium counterions are replaced by polycations, we further simplified the model by assuming that (i) the C-S-H surfaces bear a uniform surface charge density σ set to a constant value of -320 mC/m² and (ii) the C-S-H surface charge is exactly compensated by linear or branched model polymers introduced into the slit between C-S-H surfaces and maintained constant at all surface separations, rendering the system salt free.

Figure 9 schematically shows the system setup together with the repeating unit of our branched polymer model, consisting of 10 freely joined monomers. This unit is repeated n times with n equal to 3, 6, or 12. The bond length a between the monomers in the backbone was fixed to 5 Å. Each side chain carries two monomers, separated by a fixed bond b of 10 Å, set accordingly to the branched polymer used (BCQUAT). All monomers consist of impenetrable spheres with a diameter of 4 Å. Furthermore, positive point charges are centered in the outermost side chain monomers, mimicking the quaternary ammonium groups. The carboxylate group in the backbone was
<figure><img src="image_16.png" /><figcaption>**Figure 9.** Sketch of the model system (left figure) with two uniformly charged surfaces, mimicking two C–S–H platelets, separated by a distance *h*. The total charge of the polymers in the slit matches the total surface charge. The right figure shows the repeating unit of the polymer model for BCQuat, with positively charged terminal side chain monomers, nomenclature $^{a}P_{n}^{b}$.</figcaption></figure>

treated as neutral, due to the calcium-rich electrolyte solution, effectively neutralizing this moiety. Linear polycations were modeled in the same manner with freely joined positively charged monomers, separated by a fixed bond length *a* of 5 Å. In the following discussion, the nomenclature of a branched polymer according to Figure 9 will be denoted, $^{a}P_{n}^{b}$, and the linear polymer will be denoted $^{a}P_{L}$.

The system described in Figure 9 was simulated with a MC method in the Canonical ensemble (constant number of particles, volume, and temperature), following the Metropolis procedure.⁶¹ Further details are given in the Supporting Information.

## ■ ASSOCIATED CONTENT

### ■ Supporting Information

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsomega.6b00445.

(S1) Details of sample preparation for adsorption measurements; (S2) polymer adsorption and bulk calcium concentration data; (Figure S1) adsorption isotherms at various initial calcium concentrations of the linear and branched polycations; (Figures S2 and S3) evolution of the bulk calcium concentration as a function of amount of polycation introduced for various polycations and Ca(OH)₂ conditions; (S3) details of the synchroton-SAXS measurements; (Figures S4 and S5) SAXS patterns and their fit of C–S–H gels with and without polycation, varying the type of polycation and the bulk Ca(OH)₂ concentration; (Tables S1 and S2) summary of SAXS fitting parameters; (S4) details of the model and MC simulations; (Figure S6) sketch of the model system (PDF)

## ■ AUTHOR INFORMATION

### Corresponding Author

*E-mail: christophe.labbez@u-bourgogne.fr. Phone: +33 (0)3 80396176.

### ORCID

Isabelle Pochard: 0000-0001-7938-960X
Christophe Labbez: 0000-0001-6652-6329

### Present Addresses

†UTINAM, UMR 6213, CNRS, Univ. Bourgogne Franche-Comté, FR-25000 Besançon, France (I.P.).

†C2P2, UMR 5265, UCBL - CNRS - CPE, FR-69616 Villeurbanne, France (F.B.).

### Notes

The authors declare no competing financial interest.

## ■ ACKNOWLEDGMENTS

We thank Maurizio Bellotto for providing the branched polycation, Danièle Perrey for her help with the titration measurements of calcium and silicate, Aurélien Thureau for his help on the SOLEIL Synchrotron: SWING beamline as well as B. Jonsson, M. Vandamme, A. Nonat, B. Cabane, and H. Coelfen for discussions on and help with the manuscript. This work was supported by the “Agence Nationale de la Recherche” grant number ANR-BRIDGE-10-JCJC-080901. M.T. acknowledges financial support from the Wennergren Foundation and Conseil Regional de Bourgogne.

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