The physics of cement cohesion Abhay Goyal*+ Department of Physics, Institute for Soft Matter Synthesis and Metrology, Georgetown University, Washington, D.C. 20057, USA Ivan Palaia* Universit´eParis-Saclay, CNRS, LPTMS, 91405, Orsay, France and Department of Physics and Astronomy, University College London, London, WC1E 6BT, United Kingdom Katerina Ioannidou Laboratoire de M´ecanique et G´enieCivil, CNRS, Universit´ede Montpellier, 34090 Montpellier, France Massachusetts Institute of Technology/CNRS/Aix-Marseille University Joint Laboratory, Cambridge, MA 02139 and Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 Franz-Josef Ulm Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 Henri van Damme Ecole´ Sup´erieure de Physique et Chimie Industrielle de la Ville de Paris, 10 rue Vauquelin, 75005 Paris, France Roland J.-M. Pellenq Massachusetts Institute of Technology/CNRS/Aix-Marseille University Joint Laboratory, Cambridge, MA 02139 and Department of Physics, Georgetown University, Washington, D.C. 20057, USA Emmanuel Trizac Universit´eParis-Saclay, CNRS, LPTMS, 91405, Orsay, France Emanuela Del Gado+ Department of Physics, Institute for Soft Matter Synthesis and Metrology, Georgetown University, Washington, D.C. 20057, USA (Dated: August 31, 2021) Cement is one of the most produced materials solid cement paste and open new paths for science in the world. A major player in greenhouse gas and technologies of construction materials. emissions, it is the main binding agent in con- crete, to which it provides a cohesive strength that rapidly increases during setting. Under- I. Introduction standing how such cohesion emerges has been a major obstacle to advances in cement science Concrete, made by mixing cement with water, sand and technology. Here, we combine computational and rocks, is by far the most used man-made substance statistical mechanics and theory to demonstrate on earth. With a world population projected to grow how cement cohesion results from the organiza- past 9 billion by mid-century, there is need for more and tion of interlocked ions and water, progressively better infrastructure [1], with no other material that can arXiv:2108.03145v1 [physics.app-ph] 6 Aug 2021 confined in nano-slits between charged surfaces replace concrete to meet our needs for housing, shelter, of Calcium-Silicate-Hydrates. Due to the wa- or bridges. However, concrete as it is now is not sus- ter/ions interlocking, dielectric screening is dras- tainable, since cement production alone is responsible tically reduced and ionic correlations are proven for significant amounts of man-made greenhouse gases. significantly stronger than previously thought, While even a slight reduction of its carbon footprint will dictating the evolution of the nano-scale interac- dramatically reduce global anthropogenic CO2 emissions, tions during cement hydration. By developing a meeting emission-reduction targets for new constructions quantitative analytical prediction of cement co- calls for deeper scientific understanding of cement prop- hesion based on Coulombic forces, we reconcile a erties and performance [2]. novel fundamental understanding of cement hy- The dissolution of cement grains in water and dration with the fully atomistic description of the re-precipitation of various hydration products, with 2 Calcium-Silicate-Hydrates (C{S{H) being the most im- emerging physical picture against an analytical theory portant [3, 4], drives the setting of cement into a progres- that distills the essential ingredients of the net interac- sively harder solid that binds together concrete and de- tions beyond the traditional PM assumptions, for a range termines its mechanics [5]. During this process, strongly of materials and systems in similar strong electrostatic cohesive forces develop from the accumulation and con- coupling conditions. finement of ions in solution between the surfaces of C{S{ H, whose surface charge progressively increases over time [6{8]. II. Results Net attractive interactions between equally charged surfaces in ionic solutions are common in colloidal ma- The intricacy of chemical reactions during cement hy- terials or biological systems [9{15]. The comprehensive dration and setting makes it hard to identify the fun- analytical theory developed nearly a century ago by Der- damental physical mechanisms that control cement co- jaguin, Landau, Verwey and Overbeek (DLVO), which hesion. C{S{H is a non-stoichiometric compound, with relies on a mean-field approximation treating the ions as structure and composition variability, even more pro- an uncorrelated continuum, captures some of these cases nounced at the earlier stages of the hydration [4, 21, 30, [9]. For cement hydration products like C{S{H, how- 31]. The charged surfaces of C{S{H nanoparticles con- ever, the DLVO description is inapplicable since the ions fine ions and water in nanometer sized pores [18, 32] and 2+ in solution are mostly multivalent (such as Ca ) and studies of titration of the surface silanol groups indicate confined between surfaces whose surface charge density that during early hydration, as a result of the chang- − 2 rapidly reaches values up to ' 3 to 5e =nm in the lay- ing solution chemistry, the surface charge of C{S{H in- ers of hardened C{S{H [4, 8, 16]. Sure enough, DLVO creases with increasing pH, coupled to the combined pre- theory does not predict any cohesion for cement [7, 8]. cipitation of calcium hydroxide [31]. Experimental and Monte-Carlo simulations of a primitive model for ion simulation efforts over the last decade have clarified the confinement (PM), instead, have proven that ions, con- atomistic details of the final hardened C{S{H, in terms fined in water between charged surfaces, can induce net of atomic pair distribution functions, composition vari- attractive forces for a range of surface charge densities ability, and even cohesive strength [4, 20, 21, 23, 24]. relevant to C{S{H [6, 17, 18], due to the correlations However, a direct link between the surface charge and that stem from the discrete nature of ions. Nevertheless, chemistry, the emerging nanoscale cohesion, and the fi- these PM studies predict cohesive strengths at most of nal material properties is missing. ' 60 MPa in clear contradiction with experiments and To address this question we have used a semi-atomistic with the fully atomistic understanding of hardened C{ computational approach, in which ions and water are rep- S{H achieved over the last 10 years [4, 8, 19{21]. The resented explicitly while the C{S{H surface properties at cohesive strength of hardened cement is 100 times larger different hydration stages are recapitulated through sur- than that, and the presence of water is limited to a few face charge densities σ from 1e−=nm2 to 3e−=nm2. C{ molecules per ion, whereas it is treated as a bulk dielec- S{H is often characterized in terms of Ca/Si ratios, and, tric continuum in the PM approach. There is therefore a with pH values typical of cement hydration, the range of knowledge gap in the fundamental understanding of how surface charge densities considered here approximately nanoscale cohesive forces emerge during cement hydra- correspond to the relevant range of Ca/Si ratios between tion, as different chemical reactions drive the increase of 1 and 2 [16, 30, 33]. Representing C{S{H surfaces with the surface charge of cement hydrates and the ion con- smooth, uniformly charged walls is clearly a simplifica- finement [22]. tion, since their strongly heterogeneous nature is known We now fill this gap with 3D numerical simulations [21], but it is essential to the extended spatio-temporal that feature a simple but molecular description of ions analysis performed here. Thanks to this simplification, and water, providing a quantitative picture of how ce- in fact, we can extensively sample ion and water struc- ment cohesion develops during hydration. When one ture and dynamics in Molecular Dynamics and Grand- considers explicitly the role of water, it becomes clear Canonical Monte Carlo simulations, and extract the net how its capability to restructure and re-orient around the pressure ions and water induce between the confining C{ ions drives the optimized organization of interlocked ion- S{H charged surfaces. water structures that determine the net cohesive forces In our 3D study, C{S{H surfaces are planar (walls), and their evolution. consistent with the platelet-like morphology of the As ion confinement and surface charge density increase, nanoparticles [30, 32, 34] and the ions confined in be- with dramatically weakened water dielectric screening, tween them, neutralizing the surface charge, are Calcium electrostatic forces and discreteness effects are dramat- (Ca2+).To reasonable approximation, this represents the ically amplified and glue together the ion-water-surface most relevant portion of the ions confined between C{ assembly into a highly cohesive state. While we quanti- S{H surfaces during cement hydration [6, 8, 16]. The tatively recover several key experimental findings in real walls have periodic boundaries alongx ^ andy ^ and are cement [23{28] and the main features of the fully atom- separated by a distance D along thez ^ direction. For istic description of hardened C{S{H [16, 29], we test the (Ca2+) and C{S{H surfaces we include both short-range 3 a b 8 Å 20 Å c d D = 20 Å D = 8 Å FIG. 1. Results from simulations with PM and SPC/E water at σ = 1e−=nm2. Here and in subsequent figures all data are averaged over 106 MD steps after having reached equilibrium. Error bars are smaller than the symbol sizes. In (a) we show the net pressure between the C-S-H surfaces. With explicit water, we obtain negative pressures|i.e. net attraction|that cannot be found with the PM approach, even considering an increased effective ion size due to hydration. This stems from much stronger ion-ion correlations seen in (b), where we plot the ion pair correlation in the xy plane at D = 8 A and D = 20 A.