Article

Inhomogeneity in Cement Hydrates: Linking Local Packing to Local Pressure

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Abstract

Nanoscale structural heterogeneities were recently revealed in computational and experimental studies of calcium silicate hydrates in hardened cement pastes. In this work their consequences for the mechanics are analyzed by computing local pressures in model samples at different overall densities, corresponding to different initial water-to-cement ratios. The correlations between pore size distributions, local density, local cohesive energy, and local pressure clearly show how in these materials structural heterogeneities may be the origin of significant mechanical heterogeneities. The results indicate that even at high density pressure, heterogeneities develop during the densification of cement hydrates and result in the coexistence of regions of high positive pressure with regions of negative pressure, in spite of the overall mechanical stability of the samples. Furthermore, the regions of negative pressure, prone to mechanical instabilities and local plastic processes, tend to be localized close to the surface of large mesopores and hence to be more significant at higher initial water content.

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... In some cases the potentials and parametrizations have been used directly and individually, e.g. in Refs. [90][91][92]. In other cases they were combined and slightly modified, such as in Refs. ...
... The distribution of local volume fractions is also useful in homogeneous precipitation models as it allows to explore heterogeneities within the configuration. Such distributions have been computed in different models [56,89,90,92,123]. The definition of the local volume for the computation of the lvf differs between models. ...
... The definition of the local volume for the computation of the lvf differs between models. It is either defined in a spherical volume of few particles diameter around each particle [90,92] or based on a 3D grid [56]. Distributions of local volume fractions for spherical and ellipsoidal particle simulations are shown in Fig. 19. a and b respectively [56,92]. ...
Article
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The nano-to-micro mesoscale is crucial for cementitious materials; here reactions and interactions between molecules produce complex mechanisms that determine the behavior of cement minerals, especially C-S-H. This manuscript reviews the current state of the art in coarse-grained and mesoscale simulations of C-S-H. These simulations leverage a rigorous statistical mechanical framework, linking atomistic description with coarse-grained modelling through several pivotal concepts: potential of mean force, ion-ion correlations between charged surfaces, and grand canonical reactive ensemble. The second part of the manuscript discusses the effective interaction potentials between C-S-H particles that are currently used, followed by methods to simulate C-S-H formation. Structural, physical and mechanical properties predicted by the existing simulations are then presented. Finally the manuscript highlights opportunities for future research, which are driving the multi-scale modelling of C-S-H but also of other mesostructured materials.
... Indeed, although polydispersity has been shown to play a critical role in controlling the packing density (and, thereby, the mechanical properties) ( Masoero et al., 2014( Masoero et al., , 2012, the role of polydispersity at constant packing density remains unclear. Similarly, although structural and mechanical heterogeneity has been pointed out to impact the nanomechanics of C-S-H gels ( Ioannidou et al., 2014;Ioannidou et al., 2017;Masoero et al., 2014 ), the role of the extent of order and disorder on macroscopic properties remains poorly understood. Meanwhile, little is known about the role of the level of order in the mesostructure of C-S-H-which has been suggested to be higher in high-density C-S-H phases ( Constantinides and Ulm, 2007;Ioannidou et al., 2016aIoannidou et al., , 2014Jennings, 20 0 0 ). ...
... It should be noted that, in the thermodynamic sense, stress is only properly defined for a large ensemble of atoms, so the physical meaning of the "stress per grain" is unclear. Nevertheless, this quantity can conveniently capture the existence of local instabilities within the gel due to competitive inter-grain forces ( Ioannidou et al., 2017 ). ...
... Note that this local stress does not result in any macroscopic stress, namely, the grains experiencing some positive or negative shear stress mutually compensate each other so that the overall structure remains at zero stress. The presence of such eigenstress is a manifestation of the out-of-equilibrium nature of disordered C-S-H and arises from the fact that the grain precipitate in a random fashion, so that the addition of new grains in a preexisting rigid structure necessarily involves some non-optimal contact among grains and, hence, the formation of some local stress ( Ioannidou et al., 2017 ). A visual inspection of the local stress map (see Fig. 9 a) reveals that the stress distribution is highly heterogeneous, that is, most of the stress is concentrated in some local clusters of interconnected grains. ...
Article
The colloidal calcium–silicate–hydrate (C–S–H) gel largely controls the strength of concrete. However, little remains known about how the structural features of the C–S–H gel control its mechanical properties. Here, based on coarse-grained mesoscale simulations, we investigate the effect of grain polydispersity and structural disorder on the nanomechanics of C–S–H. Our simulations offer a good agreement with nanoindentation data over a large range of packing density values. We show that, at constant packing density, stiffness and hardness are not affected by the polydispersity in grain sizes. In contrast, the level of disorder is found to play a critical role. We demonstrate that, in contrast to the case of ordered C–S–H models, the elastic response of disordered C–S–H gels is governed by the existence of stress heterogeneity and nanoyielding within its structure. These results highlight the intrinsically disordered nature of C–S–H and the crucial role of order and disorder in controlling gels’ mechanical properties.
... Figure 3 shows such structural heterogeneities developed during the out-ofequilibrium process of particle precipitation interacting with LJ potential. Hardened cement paste exhibits a broad heterogeneity of local volume fractions ηlocal 15,53 . After thresholding the configuration for increasing local volume fractions, an underlying percolating network of highly packed (>64% RCP) particles is revealed. ...
... Here, we move further to understand also the role of particles with local volume fraction below 60%. Figure 4 shows the correlations between local volume fractions and local pressure Plocal in a configuration of hardened cement paste where the total eigenstress (at the level of the simulation box) has been relaxed (~10kPa) 53 . In the population of particles with local volume fractions larger than 60% a tail towards positive local pressure is observed, hence overall particles are under compression. ...
Chapter
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Cement hydrates named C-S-H are the main products of the reaction of cement with water. The C-S-H phase is the most important phase of cement paste as it glues all other phases together in a solid rock-like material. C-S-H gels form and densify via out-of-equilibrium precipitation and aggregation of nano-grains during cement hydration. In this chapter, the link between the making and densification of C-S-H gels and amorphous solids is discussed by coarse-grained models based on the evolution of interaction potentials and an out-of-equilibrium simulation approach for particle precipitation. In particular, we characterize and correlate mesoscale structural and mechanical heterogeneities resulting into residual local eigenstresses. This underlying microscopic picture explains recent macroscopic measurements of the volume change of hydrating cement in fully saturated conditions.
... A. Mesoscale model of hardened cement paste. Ioannidou's et al. mesoscale C-S-H model (18,23) was used to calculate the water adsorption/desorption by DFT simulations. The precipitation of C-S-H nano-grains and settings was simulated using the approach recently proposed in Ref. (15). ...
... The effective interparticle forces between cement hydrates depends on the concentration of calcium ions in the solution and changes during the hydration (51,52). In precious works, the microstructure of C-S-H gels at early hydration stages was investigated using attracto-repulsive potential arising from ion-ion correlation forces (15,23). ...
Preprint
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... The C-S-H data were isolated from the cement samples by spatially correlating nanoindentation data and energy dispersive X-ray spectrometry and elemental mapping data. The comparison of these data highlights the fact the densest part (η>0.6) of the material spans the whole structure in a complex, loadbearing network, which dominates the nano-indentation experiments 33,35 . ...
Chapter
Full-text available
Cement is the most used building material on earth, yet its properties are inexactly understood and not fully controlled. Cement hydrates named C-S-H (Calcium-Silicate-Hydrate) are the most abundant phase in hydrated cement paste and are responsible for gluing all other hydration products and unreacted cement together. A source of complexity in modelling C-S-H is that the structure is amorphous, multiscale with fully interconnected porosity spanning from a few nm up to mm. The focus of this chapter is modeling approaches that allow connecting structure and mechanics of C-S-H at the mesoscale (the scale that spans from few nm up to the micron) from the early stages of hydration, the setting and up to the hardened cement paste. The modelling approach reviewed here is of reduced complexity based on coarse-graining with emphasis on the effective interactions between C-S-H particles. It addresses the mesoscale of C-S-H and has provided a unified framework for understanding the microstructure of C-S-H and reconciling data from many different experimental techniques. A consistent picture is presented covering (1) the reactive solidification of cement, (2) the origin of the observed microstructure of C-S-H, and (3) its link to mechanics. This provides a powerful predictive tool for nanoscale design of cement.
... It should be noted that, in the thermodynamic sense, stress is only properly defined for a large ensemble of atoms, so that the physical meaning of the "stress per atom" is unclear. Nevertheless, this quantity can conveniently capture the existence of local instabilities within the gel due to competitive interatomic forces (Ioannidou et al., 2017). Based on this framework, we compute the local stress experienced by each Si atom, since the silicate chains constitute the rigidity backbone of C-S-H. ...
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Topological constraint theory (TCT) classifies disordered networks as flexible, stressed-rigid, or isostatic based on the balance between the number of topological constraints and degrees of freedom. In contrast with the predictions from a mean-field enumeration of the constraints, the isostatic state—wherein the network is rigid but free of stress—has been suggested to be achieved within a range of compositions, the intermediate phase, rather than at a fixed threshold. However, our understanding of the nature and potential structural signatures of the intermediate phase remains elusive. Here, based on molecular dynamics simulations of calcium–silicate–hydrate systems with varying compositions, we seek for some mechanical and structural signatures of the intermediate phase. We show that this system exhibits a composition-driven rigidity transition. We find that the fracture toughness, fracture energy, mechanical reversibility, and creep compliance exhibit an anomalous behavior within a compositional window at the vicinity of the isostatic threshold. These features are argued to constitute a mechanical signature of an intermediate phase. Notably, we identify a clear structural signature of the intermediate phase in the medium-range order of this system, which is indicative of an optimal space-filling tendency. Based on these simulations, we demonstrate that the intermediate phase observed in this system arises from a bifurcation between the rigidity and stress transitions. These features might be revealed to be generic to isostatic disordered networks.
... By the end of hydration, C-S-H becomes denser and denser, and its nanoscale features (including the interlayer distances and chemical compositions usually described in terms of Ca/Si ratio) play a predominant role in most observations and studies (16,21,29). Nevertheless, the earlier-stage mesoscale morphology controls the development of larger pores and contributes to local stresses in the initial gel network, which have consequences for the long-term evolution of the material and its interactions with the environment (5,43,44,(50)(51)(52)(53). The change in shape of the nanoscale interactions, with competing attraction and repulsion and a notable increase of the attraction strength with surface charge density during hydration, largely controls the morphology of the mesoscale structures that build the gel network and can markedly steer compressive or tensile stresses as the material progressively densifies and solidifies. ...
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Cement is the most produced material in the world. A major player in greenhouse gas emissions, it is the main binding agent in concrete, providing a cohesive strength that rapidly increases during setting. Understanding how such cohesion emerges is a major obstacle to advances in cement science and technology. Here, we combine computational statistical mechanics and theory to demonstrate how cement cohesion arises from the organization of interlocked ions and water, progressively confined in nanoslits between charged surfaces of calcium-silicate-hydrates. Because of the water/ions interlocking, dielectric screening is drastically reduced and ionic correlations are proven notably stronger than previously thought, dictating the evolution of nanoscale interactions during cement hydration. By developing a quantitative analytical prediction of cement cohesion based on Coulombic forces, we reconcile a fundamental understanding of cement hydration with the fully atomistic description of the solid cement paste and open new paths for scientific design of construction materials.
... By the end of hydration, C-S-H becomes denser and denser, and its nanoscale features (including the interlayer distances and chemical compositions usually described in terms of Ca/Si ratio) play a predominant role in most observations and studies [16,21,29]. Nevertheless, the earlier stage mesoscale morphology controls the development of larger pores and contributes to local stresses in the initial gel network, which have consequences for the long term evolution of the material and its interactions with the environment [5,43,44,[50][51][52][53]. The change in shape of the nanoscale interactions, with competing attraction and repulsion and a striking increase of the attraction strength with surface charge density during hydration, largely controls the morphology of the mesoscale structures that build the gel network and can dramatically steer compressive or tensile stresses as the material progressively densifies and solidifies. ...
Preprint
Full-text available
Cement is one of the most produced materials in the world. A major player in greenhouse gas emissions, it is the main binding agent in concrete, to which it provides a cohesive strength that rapidly increases during setting. Understanding how such cohesion emerges has been a major obstacle to advances in cement science and technology. Here, we combine computational statistical mechanics and theory to demonstrate how cement cohesion results from the organization of interlocked ions and water, progressively confined in nano-slits between charged surfaces of Calcium-Silicate-Hydrates. Due to the water/ions interlocking, dielectric screening is drastically reduced and ionic correlations are proven significantly stronger than previously thought, dictating the evolution of the nano-scale interactions during cement hydration. By developing a quantitative analytical prediction of cement cohesion based on Coulombic forces, we reconcile a novel fundamental understanding of cement hydration with the fully atomistic description of the solid cement paste and open new paths for science and technologies of construction materials.
... Reactive heterogeneous materials such as cement have residual stresses due to the out-of-equilibrium solidification process [51][52][53]. The cement paste structure analyzed here has accumulated tensile eigen-stress of -47 MPa through the precipitation of nano-grains [54,55]. Figure 4 shows how capillary forces affect the relaxation of two different samples, young cement paste sample with initial tensile eigen-stresses (-47MPa) and hardened sample (the relaxed version of the young sample). ...
Article
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We propose a theoretical framework to calculate capillary stresses in complex mesoporous materials, such as moist sand, nanoporous hydrates, and drying colloidal films. Molecular simulations are mapped onto a phase-field model of the liquid-vapor mixture, whose inhomogeneous stress tensor is integrated over Voronoi polyhedra in order to calculate equal and opposite forces between each pair of neighboring grains. The method is illustrated by simulations of moisture-induced forces in small clusters and random packings of spherical grains using lattice-gas Density Functional Theory. For a nano-granular model of cement hydrates, this approach reproduces the hysteretic water sorption/desorption isotherms and predicts drying shrinkage strain isotherm in good agreement with experiments. We show that capillary stress is an effective mechanism for internal stress relaxation in colloidal random packings, which contributes to the extraordinary durability of cement paste.
... In return, the energy barrier is associated with the maximum magnitude of the eigenstress max | σ * |, with a temperature dependence according to Eq. (7) consistent with its role as an energy barrier. According to this conjecture, the eigenstress represents but a mean force field which -if relaxed-entails the measured incremental swelling or shrinkage, much akin to mesoscale colloidal simulations carried out in an NpT-ensemble ( Ioannidou et al., 2017a ). More specifically, in terms of Eq. (9) , repulsion is associated with the η 2 -term, and the attraction with the η 4 -term. ...
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Volume changes in chemically reactive materials, such as hydrating cement, play a critical role in many engineering applications that require precise estimates of stress and pressure developments. But a means to determine bulk volume changes in the absence of other deformation mechanisms related to thermal, pressure and load variations, is still missing. Herein, we present such a measuring devise, and a hybrid experimental–theoretical technique that permits the determination of colloidal eigenstresses. Applied to cementitious materials, it is found that bulk volume changes in saturated cement pastes at constant pressure and temperature conditions result from a competition of repulsive and attractive phenomena that originate from the relative distance of the solid particles – much as Henry Louis Le Châtelier, the father of modern cement science, had conjectured in the late 19th century. Precipitation of hydration products in confined spaces entails a repulsion, whereas the concurrent reduction in interparticle distance entails activation of attractive forces in charged colloidal particles. This cross-over from repulsion to attraction can be viewed as a phase transition between a liquid state (below the solid percolation) and the limit packing of hard spheres, separated by an energy barrier that defines the temperature-dependent eigenstress magnitude.
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The colloidal calcium-silicate-hydrate (C-S-H) gel largely controls the mechanical properties of concrete. However, little remains known about how the structural features of the C-S-H gel control its mechanical properties. The aim of the current study is therefore to investigate the structure, mechanical properties and the crack propagation of the colloidal C-S-H gel at the mesoscale. To achieve this, Grand Canonical Monte Carlo methods were utilized to construct the colloidal C-S-H gel. The structure features were demonstrated by the pore size distribution. Subsequently, computational uniaxial tension tests were performed on the C-S-H gel specimens using a non-local peridynamics (PD) model. On the basis of the simulated stress–strain response, the Young’s modulus and tensile strength can be obtained. The modelling results show that both the strength and Young’s modulus grow exponentially with the packing fraction increasing which shows reasonable agreement with the literature, revealing the feasibility of the PD method for the investigation of mechanical performance of C-S-H gel at mesoscale.
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Chapter
In previous sections, the atomistic simulation methods have been introduced to the materials science for cement-based materials to decode the intrinsic building block of the cement hydrate at nanoscale. The molecular dynamics method exhibits the significant advantage in investigating the properties of cement-based concrete material at nanoscale and opens a novel pathway for design of construction and building materials.
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The calcium silicate hydrate (C-S-H) controls most of the final properties of the cement paste, including its mechanical performance. It is agreed that the nanometer-sized building blocks that compose the C-S-H are the origin of the mechanical properties. In this work, we employ atomistic simulations to investigate the relaxation process of C-S-H nanoparticles subjected to shear stress. In particular, we study the stress relaxation by rearrangement of these nanoparticles via sliding adjacent C-S-H layers separated by a variable interfacial distance. The simulations show that the shear strength has its maximum at the bulk interlayer space, called perfect contact interface, and decreases sharply to low values for very short interfacial distances, coinciding with the transition from 2 to 3 water layers and beginning of the water flow. The evolution of the shear strength as a function of the temperature and ionic confinement confirms that the water diffusion controls the shear strength.
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Capillary effects, such as imbibition drying cycles, impact the mechanics of granular systems over time. A multiscale poromechanics framework was applied to cement paste, which is the most common building material, experiencing broad humidity variations over the lifetime of infrastructure. First, the liquid density distribution at intermediate to high relative humidity is obtained using a lattice gas density functional method together with a realistic nanogranular model of cement hydrates. The calculated adsorption/desorption isotherms and pore size distributions are discussed and compare well with nitrogen and water experiments. The standard method for pore size distribution determination from desorption data is evaluated. Second, the integration of the Korteweg liquid stress field around each cement hydrate particle provided the capillary forces at the nanoscale. The cement mesoscale structure was relaxed under the action of the capillary forces. Local irreversible deformations of the cement nanograins assembly were identified due to liquid–solid interactions. The spatial correlations of the nonaffine displacements extend to a few tens of nanometers. Third, the Love–Weber method provided the homogenized liquid stress at the micrometer scale. The homogenization length coincided with the spatial correlation length of nonaffine displacements. Our results on the solid response to capillary stress field suggest that the micrometer-scale texture is not affected by mild drying, while nanoscale irreversible deformations still occur. These results pave the way for understanding capillary phenomena-induced stresses in heterogeneous porous media ranging from construction materials to hydrogels and living systems.
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Calcium silicates hydrates (C-S-H) are the most abundant hydration products in ordinary Portland cement paste. Yet, despite the critical role they play determining mechanical and transport properties, there is still a debate on their density and exact composition. Here, the site-specific mass density and composition of C-S-H in hydrated cement paste are determined with nanoscale resolution in a non-destructive approach. We used ptychographic X-ray computed tomography in order to determine spatially resolved mass density and water content of the C-S-H within the microstructure of the cement paste. Our findings indicate that the C-S-H at the border of hydrated alite particles have a higher density than the apparent inner-product C-S-H, which is contrary to the common expectations from previous works on hydrated cement paste.