Force Field for Tricalcium Silicate and Insight into Nanoscale

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Force Field for Tricalcium Silicate and Insight into Nanoscale Properties: Cleavage, Initial Hydration, and Adsorption of Organic Molecules Ratan Kishore Mishra, Robert Johann Flatt, and Hendrik Heinz J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp312815g • Publication Date (Web): 03 Apr 2013 Downloaded from http://pubs.acs.org on April 16, 2013

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The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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The Journal of Physical Chemistry

Force Field for Tricalcium Silicate and Insight into Nanoscale Properties: Cleavage, Initial Hydration, and Adsorption of Organic Molecules

Ratan K. Mishra,1 Robert J. Flatt2,3 and Hendrik Heinz1*

1

Department of Polymer Engineering, University of Akron, Akron, OH44325, USA 2

3

Sika Technology AG, CH-8048 Zürich, Switzerland

Department of Civil, Environmental and Geomatic Engineering, ETH Zurich, CH8093 Zürich, Switzerland

*

Corresponding author: [email protected]

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ACS Paragon Plus Environment


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Abstract Improvements in the sustainability and durability of building materials depend on understanding interfacial properties of various mineral phases at the nanometer scale. Tricalcium silicate (C3S) is the major constituent of cement clinker and we present and validate a force field for atomistic simulations that provides excellent agreement with available experimental data, including X-ray structures, cleavage energies, elastic moduli, and IR spectra. Using this model and available measurements, we quantify key surface and interface properties of the dry and superficially hydrated mineral. An extensive set of possible cleavage planes shows cleavage energies in a range of 1300 to 1600 mJ/m2 that are consistent with the observation of faceted crystallites with an aspect ratio near one. Using pure and hydroxylated surface models that represent the first step in the hydration reaction, we examined the adsorption mechanism of several organic amines and alcohols at different temperatures. Strong attraction between -20 and -50 kcal/mol is found as a result of complexation of superficial calcium ions, electrostatic interactions, and hydrogen bonds on the ionic surface. Agglomeration of cleaved C3S surfaces in the absence of organic molecules was found to recover less than half the original cleavage energy (~450 mJ/m2) associated with reduced Coulomb interactions between reconstructed surfaces. Additional adsorption of organic compounds below monolayer coverage reduced the attraction between even surfaces to less than 5% of the original cleavage energy (~50 mJ/m2) related to their action as spacers between cleaved surfaces and mitigation of local electric fields. Computed agglomeration energies for a series of adsorbed organic compounds correlate with the reduction in surface forces in the form of measured grinding efficiencies. The force field is extensible to other cement phases and

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compatible with many platforms for molecular simulations (PCFF, COMPASS, CHARMM, AMBER, OPLS-AA, CVFF).

Keywords building materials, concrete, silicates, molecular dynamics, surface forces, interatomic potentials

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1. Introduction Concrete is the most widely used man-made material world-wide several times ahead of brick, steel, and wood.1-3 The annual production exceeds 10 cubic kilometers, including 3 billion tons of cement, and leaves a significant environmental footprint due to intense energy consumption and release of CO2 that accounts for 5-7% of global CO2 emissions.4,5 The environmental burden is projected to increase as developing economies have a need for expanding the built infrastructure.5,6 Accordingly, major efforts in academia and industry are deployed to reduce energy consumption and CO2 release.7 These global challenges can only be met by expanding the depth of fundamental understanding of cement materials, which significantly depends on insight at the nanometer scale.8,9 Many physical and chemical properties of cement materials still remain unclear due to limitations of experimental techniques and the need for advanced modeling and simulation increases to support a broader, deeper and more concerted scientific approach for sustainable development. Cement is a solid mixture of various minerals that includes tricalcium silicate with Mg, Al, and Fe impurities in the low percent range (50-70%, also called “alite”), dicalcium silicate containing similar metal substitutions (15-30%, also called “belite”), tricalcium aluminate (5-10%), and a ferrite phase (10-15%).1 Accordingly, tricalcium silicate is the predominant mineral phase in cement and often abbreviated as C3S (Figure 1).10 Approaches to reduce the environmental impact of cement production focus largely on replacement of part of the original cement by so-called Supplementary Cementitious Materials (SCMs) that include slag, fly-ash, limestone, silica fume, and metakaolin.6 The reactivity of SCMs upon hydration is typically lower than of original cement and may

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affect key engineering properties of concrete such as workability, strength and durability. The search for solutions inspired fundamental studies of the surface reactivity of cement minerals,11-18 the reactivity of nanostructures of cement hydrates,19-21 the development of mechanical properties produced by these hydrates,22-24 and the properties of SCMs.6 A broad range of experimental approaches such as XRD, SANS,20 in-situ TEM imaging,21 nanoindentation,25,26 colloidal probe measurements of adhesion forces,27 zeta potentials, IR, and Raman spectroscopy,14,28 NMR,29-31 and calorimetry32 has been employed. Nevertheless, insight into interfacial processes, reaction kinetics, and nanoscale structure evolution remains challenging due to the difficulty to monitor interfaces and to interpret available data. Key solutions to retain the reactivity of cement-SCM blends include enhancement of the reactivity of the original cement component by finer grinding33,34 or increasing the reactivity of tricalcium silicate by specific means. Finer grinding requires more energy to cleave mineral surfaces and was found to be more efficient using organic additives referred to as grinding aids. However, the governing surface forces of cleavage and agglomeration are only coarsely understood and underlying mechanisms of surface interactions with organic molecules have remained uncertain.7,33 It is the aim of this work to systematically discuss surface properties, adsorption of organic molecules, and agglomeration at the molecular scale using newly developed, validated force fields. On the other hand, the feasibility of an increase in the reactivity of the main phase of cement (C3S) involves an on-going debate over properties of C3S-water interfaces and their role on the rate-limiting step of cement hydration.16,18,35 In this work, we also examine the very first step of hydration using models. Further structural and dynamic chemical insight

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into the aqueous interfaces of C3S and its hydration products supported by atomistic models may have profound implications on tuning reaction rates and practical applications. Interfacial properties of hydrated cement phases also play an important role for the adsorption of polymeric additives that contribute to enhanced durability of concrete.8 The objective of this paper is (a) to advance fundamental understanding of the main phase of cement through the development, validation, and application of a reliable force field for tricalcium silicate, Ca3SiO5 (Figure 1), (b) to apply the model to characterize surface, cleavage, initial hydration, and nanoscale mechanical properties that have been difficult to quantify through measurements, and (c) to describe specific details of surface interactions with a series of organic molecules and resulting modification in surface forces (agglomeration energies) that guide in approaches toward energy savings. No empirical potentials have yet been reported for this important mineral and we employed an approach that has proven to be particularly effective in predicting interfacial properties of clay minerals, silica, metals, as well as sulfates and phosphates.9,36-41 Intermolecular potentials for similar minerals have often been limited by coarse approximations of atomic charges, overestimated surface energies, requirements of fixed atoms, and energy expressions that are not compatible with force fields for organic compounds and biopolymers.42-62 The present parameterization is accurate, requires no fixed atoms, is broadly applicable as part of many biomolecular and materials oriented force fields, and guides in the development of dependable force fields for other cement phases.9 The outline of this paper is as follows. In section 2, we present the force field for tricalcium silicate and initial hydrated surfaces. In section 3, bulk and surface properties

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are validated according to model and experiment, showing excellent agreement of key properties and systematic new insight into direction-dependent elastic moduli, cleavage energies of {h k l} facets, and equilibrium crystal morphology. In section 4, we analyze the surface interactions and adsorption energies of the organic compounds triisopropanol amine (TIPA), triethanol amine (TEA), MDIPA (N-Methyl-diisopropanolamine), and glycerine used in cement production.33,49,63 We explain the mechanism of agglomeration and the reduction of agglomeration energies in the presence of these molecules in agreement with observed grinding efficiencies in a ball mill. Conclusions and perspectives are presented in section 5, followed by computational and experimental details in section 6.

Figure 1. (a) The role of tricalcium silicate in building materials and (b) a structural model of the common M3 polymorph (1×2×1 unit cells, a = 1.2235 nm). 7 of 64



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2. Force Field Parameters for Ca3SiO5 In this section, prior simulation studies and limitations of force fields of related minerals are discussed, followed by the description of parameters for tricalcium silicate and initially hydrated surfaces that are compatible with many different energy expressions. Validation of the parameters is discussed in the next main section 3 as it reveals significant new insight into surface and mechanical properties. 2.1. Related Prior Studies and Challenges. To our knowledge, no computational study on tricalcium silicate has yet been reported while numerous related inorganic materials have been investigated.9,36-62 Examples of prior studies by other research teams include the development of force field parameters for silica,42 mica,43 an adaptation of the universal force field for ettringite,44 Born-Mayer-Huggins (BMH) models for CSH gel,45 the use of MNDO approaches for xonotlite,46 nonbonded parameters for calcium hydroxide, ettringite, and tobermorite,47 force fields for tobermorite structures derived using GULP,48 Born-Mayer-Huggins potentials for silica,49 general parameters for clay minerals (CLAYFF),50 polarizable Buckingham parameters for wollastonite using formal charges,51 calcite-organic interactions using detailed Buckingham parameters,52 silica parameters without surface ionization,53 tobermorite aqueous interfaces using CLAYFF,54 hydrotalcite interfaces with organic molecules,55 QM studies on xonotlite and hydrogen bonding using Car-Parrinello MD,56 surfaces of Ca(OH)2, Mg(OH)2, quartz, and ceria using

Buckingham

potentials,57

Buckingham

potentials

for

non-hydrated

hydroxypapatite,58 hydrotalcite interactions with humic acids,59 a CSH model using

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GULP60 and CLAYFF,61 as well as a CSH model on the basis of Born-Mayer-Huggins potentials.62 Few studies have achieved force field parameterizations with less than 50% deviations in interfacial energies from experiment,47,55,56 however, due to several challenges: (1) The best performance of force fields can be achieved when the balance of covalent and ionic contributions to bonding is represented according to true mineral chemistry.9,37 Many interatomic potentials employed formal charges, however, e.g., Born-Mayer-Huggins, GULP, and Buckingham potentials. The balance of covalent versus ionic bonding is then not adequately represented37 and computed interfacial properties deviate from experiment up to several multiples.38 Also smaller imbalances between atomic charges in the model and the true electronic structure, as verifiable by electron deformation densities, dipole moments, and the extended Born model,37 introduce significant errors. For example, the atomic charge of Si in tetrahedral oxygen coordination is +1.1±0.2e,37 yet a different value of +2.1e used in CLAYFF50 causes computed surface tensions of clay minerals to overestimate experimental values up to 100%9,38 and interfacial properties of tricalcium silicate cannot be reproduced. The origin of these difficulties lies in the neglect of covalent bonding by assuming exclusively noncovalent interactions, which require stronger ionic forces to maintain structural stability. (2) General force fields without validation for inorganic compounds such as UFF may deliver random properties.36,44 (3) Repulsive and dispersive van-der-Waals parameters in Lennard-Jones or Buckingham potentials often correlate only coarsely with atomic radii and atomic polarizabilities, and available experimental data for cleavage energies, hydration energies, and surface tensions have been rarely employed to validate and refine

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force fields. (4) Some parameter sets assume chemically unrealistic surfaces, for example, dangling oxygen atoms instead of protonated groups lead to excessive layering of interfacial water. (5) Many energy expressions for minerals (BMH models, extended Buckingham potentials) are not compatible or difficult to combine with existing force fields for organic and biological compounds such as PCFF,64 COMPASS,65 CVFF,66 OPLS-AA,67 AMBER,68 and CHARMM.69 Details of challenges for the reliability of force fields, further including defect sites, surface reconstruction, temperature, and pressure,41,70-73 have been recently reviewed.9 Solutions for the above challenges have been identified by our team since 2003 and lead to force fields for inorganic compounds with less than 10% deviation in interfacial properties from experiment.36-41 In parallel, Kalinichev et al47,54,55,59 and Cygan et al.50 developed nonbonded force fields (CLAYFF) for a range of minerals that also addressed many challenges but include the limitations in polarity and interfacial properties described above. In our approach, we attribute a key role to physically and chemically justified atomic charges to precisely reflect covalent and ionic contributions to chemical bonding. Many examples of atomic charges, supported by measurements and by reproducible chemical first principles, were reported and explained for a variety of inorganic compounds in 2004, to avoid widely scattered charges from DFT and HF “first principles” calculations that depend on tens of available setup choices.37 Parameters for tricalcium silicate were originally developed in 2003 along with mica (initially unpublished due to intellectual property commitments),36 and recently introduced along with parameters of over twenty minerals, including clay minerals, cement phases, aluminates, and phosphates, under the name INTERFACE force field.9 These parameters

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are thermodynamically consistent among themselves and with other force fields (PCFF, COMPASS, CVFF, OPLS-AA, AMBER, CHARMM) to accurately simulate interfaces with water, polymers, and biomolecules.9 The force field parameters for tricalcium silicate are described here and aim at the accurate representation of physical and chemical properties on the atomic scale as well as on the macroscopic scale (Table 1). We employ four atom types for C3S that distinguish Ca2+ ions, Si and O in silicate ions, O2‒ ions, as well as two additional atom types for oxygen and hydrogen as part of the initially hydrated, hydroxylated surfaces. A key aspect of the parameterization is the representation of atomic charges in agreement with known electron deformation densities, dipole moments, electrostatic contributions to surface tensions, cleavage energies, and consistency of these properties with similar compounds across the periodic table as previously described (Table 1).37 The assignment of van-der-Waals parameters and bonded parameters follows guidelines leading to thermodynamic consistency of the parameters, transferability, and flexibility for extensions (see sections 2.3 and S1 for details).9,38,40 Bonded parameters are assigned to pairs of atoms that are connected by covalent bonding more than by ionic bonding, and nonbond parameters are assigned to all atoms. Accordingly, (1) Si-O bonds comprise bonded terms as well as nonbond terms since the bond length of 160 pm is short and ionization of the valence electrons moderate (+1.0e out of 4e on Si, ‒1.0e out of ‒2e on O).74 (2) Ca2+ ions and oxide ions comprise only nonbond terms in agreement with large Ca···Ooxide and Ca···Osilicate distances near 240 pm and strong ionization of valence electrons (+1.5e out of +2e on Ca2+ and ‒1.5e out of ‒2e on O2‒).74

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2.2. Choice of Energy Expressions. The thermodynamically consistent integration of mineral parameters into materials-oriented and biomolecular force fields with existing parameters for solvents, polymers, biomolecules enables simulations of mineral-water and mineral-organic interfaces.9,36-41 This concept allows quantitative insight into interfacial properties for a broad range of multiphase materials. The energy expression for tricalcium silicate and hydrated surfaces was thus chosen identical with several such force fields to achieve broad applicability, including PCFF,64 COMPASS (eq 1),65 CVFF,66 OPLS-AA,67 AMBER,68 and CHARMM (eq 2):69

E pot =

∑

K r ,ij (rij − r0,ij ) 2 +

ij bonded

∑

1

K θ ,ijk (θ ijk − θ 0,ijk ) 2 +

4πε 0 ε r

ijk bonded

∑ ij nonbonded (1,3 excl)

E pot =

∑

K r , ij ( rij − r0,ij ) 2 +

ij bonded

∑

K θ ,ijk (θ ijk − θ 0,ijk ) 2 +

ijk bonded


ij nonbonded (1,3 excl)

 σ 0, ij ε 0,ij 2    σ ij 

1 4πε 0 ε r

qi q j

∑

+

(1)

9

 σ  − 3 0,ij  σ   ij


 σ 0, ij ε 0,ij   σ ij 

rij

12

qi q j rij

   

   

6

6

   

+

 σ  − 2 0,ij  σ   ij

(2)    

The energy expression comprises terms for quadratic bond stretching, quadratic angle bending, Coulomb interactions, and van-der-Waals interactions. High order cubic and quartic terms, torsion potentials, out-of-plane, and cross-terms are not needed for tricalcium silicate and thus zero.36,38,41 The energy expressions of PCFF, COMPASS, AMBER, CHARMM, CVFF, and OPLS-AA, nevertheless, exhibit some differences that we have taken into account by

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development and testing of individual Lennard-Jones (LJ) parameters for each energy expression (Table 1 and section S1 in the Supporting Information for details). Differences involve the type of LJ potential, combination rules for σ 0,ii and ε 0,ii , and scaling of nonbond interactions between 1,4 bonded atoms. Since tricalcium silicate contains no 1,4 bonded atoms (Figure 1b), no adjustments for scaling of nonbond interactions were necessary. The force fields PCFF and COMPASS are identical and thus use the same set of parameters including a 9-6 LJ potential for van der-Waals interactions (eq 1). AMBER, CHARMM, CVFF, and OPLS-AA use a 12-6 Lennard-Jones potential instead (eq 2). This is a major difference and requires adjustments in LJ parameters σ 0,ii and ε 0,ii while atomic charges and bonded parameters remain the same (Table 1).9,38,40 The group of force fields AMBER, CHARMM, CVFF, and OPLS-AA was further differentiated according to combination rules for van-der-Waals diameters σ 0,ii and well depths ε 0,ii . AMBER and CHARMM assume an arithmetic mean to obtain σ 0,ij values between different atom types while CVFF and OPLS-AA use a geometric mean, thus leading to two slightly different 12-6 LJ parameter sets (Table 1 and section S1 in the Supporting Information for details). The two subgroups differ slightly in values of σ 0,ii and ε 0,ii , even though ε 0,ij is always obtained as a geometric mean. Resulting differences in 12-6 LJ parameters due to distinct combination rules in the two subgroups are small, however, and computed cleavage energies would deviate TEA > TIPA > MDIPA in comparison to an initial cleavage energy of 1340 mJ/m2 at 363 K (Figure 11). The reduction in agglomeration energy in comparison to cleavage energies may thus reach 96%. The trend in computed agglomeration energies for the grinding aids matches observations in decreasing energy demand in the ball mill.88 MDIPA and TIPA are the most effective grinding aids according to both measurements and calculations. The analysis of simulation results helps establish correlations between molecular structure and reduction of surface forces. The reduction in agglomeration energy is caused by specific molecule-surface interactions, including a certain thickness of the organic layer between a pair of cleaved surfaces as well as the ability of additives to weaken remaining dipole moments and possible uneven charge balances between the mineral surfaces (Figure 10).39,76,89 For example, glycerine binds more tightly and

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flexibly to the surface compared to the other molecules (Figures 8 and 9). Adsorption is stronger but the agglomeration energy of glycerine-covered surfaces is higher than for TEA, TIPA, and MDIPA, and the effect as a dispersant is accordingly weaker. A subnanometer thickness of the adsorbed organic layer on the cleaved surfaces appears to be sufficient to eliminate the majority of attractive Coulomb forces between cleaved surfaces. A critical distance for the reduction of strong Coulomb forces of just under 0.5 nm

was

also

identified

for

layered

silicates

with

and

without

surface

modification.39,76,89,90 Larger amounts of grinding aids per surface area could reduce agglomeration further and lowest values may be expected for multi-layer adsorption when the surface tension of the surface-adsorbed molecules becomes the limiting factor, i.e., in a range of 20 to 70 mJ/m2 depending on composition and temperature. The trends in computed agglomeration energies between two (or multiple) surfaces provide useful criteria to estimate the energy efficiency of grinding in a ball mill. In contrast, adsorption energies on isolated surfaces or volatilities of bulk organic liquid show no correlation with agglomeration energies since they relate to different processes. In summary, molecular simulations explain the mechanism of organic adsorption and quantify agglomeration of particle surfaces. The models can also provide specific guidance for the modification of nanoscale interfaces to lower energy costs in conjunction with laboratory tests. Follow-up studies may examine in more detail the influence of specific facets, surface shape, larger superstructures, and nonequilibrium cleavage on surface forces and dispersion processes.

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500

HC: Hydroxylated C3S

2

Agglomeration Energy, mJ/m

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400 300 200 100 0 C3S

HC

HC-Gly HC-TEA HC-TIPA HC-MDIPA

Figure 11. Computed agglomeration energy of dry and hydroxylated cleaved C3S (040) surfaces in the absence and in the presence of the molecular grinding aids glycerine, TEA, TIPA, and MDIPA at 363 K. The reduction in agglomeration energy can be seen.

Table 5. Amount of capping agents for the computation of agglomeration energies on the hydroxylated tricalcium silicate (040) surface at 363 K. Dosage

Surface Area

No of

(mg/m2)

(nm2)

molecules

C3S-TIPA

0.21

12.32

8

C3S-TEA

0.20

12.32

10

C3S-MDIPA

0.20

12.32

10

C3S-Gly

0.20

12.32

16

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5. Conclusions We present force field parameters for tricalcium silicate (C3S) that reproduce atomicscale, bulk, and surface properties in quantitative agreement with available laboratory data and are fully integrated into harmonic force fields for organic and biological compounds. The models were applied to quantify cleavage energies, anisotropic mechanical properties, the adsorption of organic additives, as well as the approximate agglomeration of surfaces in cement particles. The results facilitate fundamental understanding of the major mineral phase in cement, initial hydration, and cohesive properties that have remained difficult to access by measurements and contribute to meet sustainability and durability challenges of cement-based materials. The force field parameters are the first available to-date and compatible with the energy expressions of PCFF, COMPASS, AMBER, CHARMM, CVFF, OPLS-AA in thermodynamic consistency with parameters for organic molecules, biomolecules, solvents as well as other minerals and metals.9 The average deviation in unit cell parameters from X-Ray data is less than 0.5%, computed vibrational frequencies agree with measured IR and Raman spectra within 100 cm-1. Spatially averaged elastic properties and cleavage energies of different crystal planes are of the same accuracy as available laboratory data ( MDIPA > TIPA ~ TEA. Stronger adsorption (i.e. adsorption energy further below zero) correlates with more surface interaction but not with lower volatility of the organic liquid (i.e. higher boiling point) as interactions within the pure liquid are different. Agglomeration energies between cleaved surfaces with and without adsorbed alcohols (“grinding aids”) were computed to explain reductions in surface forces and describe a clear trend in the effectiveness of specific molecules. Surface reconstruction after cleavage and shielding of Coulomb interactions by the organic modifiers between cleaved surfaces reduce agglomeration energies by up to 96% compared to the cleavage energy. The trend in reduction of surface agglomeration was found to be MDIPA > TIPA > TEA > glycerine below monolayer coverage, in correlation with experimental observations. The difference is related to the thickness of the organic layer and differences in binding geometry and mobility, although we also note that calculations of the agglomeration energy on even surfaces may not be enough to differentiate the effectiveness in complete detail. The models presented and evaluated here are a first step towards quantitative simulation of cement materials from the nanoscale. Further extensions to other cement phases and reactive models are feasible.

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6. Computational Methods In this section, details of molecular models, force fields, simulation protocols, data analysis, and uncertainties are described. 6.1. Models. Models of three-dimensional periodic super-cells of tricalcium silicate were built using the known X-ray crystal structure of the M3 monoclinic polymorph of C3S.74 For the optimization of force field parameters, small models and super cells of 2×3×2 unit cells were employed (2.447×2.121×1.8596 nm3). Subsequent tests with larger cells showed the same accuracy in computed cell parameters, cleavage energies, vibration spectra, and elastic moduli. For the calculation of cleavage energies of each (h k l) plane, a customized super cell was employed in which two coordinate axes define a plane parallel to the desired (h k l) cleavage plane. This setup simplifies the creation of the surfaces under periodic boundary conditions (Figure 4). The customized super cells included multiples of the original unit cell as well as multiples of a rectangular cell with different orientation of the coordinate system (see Table S2 in the Supporting Information for details). The rectangular cell is of the same translation symmetry and density as the original unit cell (see Figure 4a, smallest unit is 1.2185×0.7035×2.5275 nm3).40 Models of unified surfaces before cleavage were chosen approximately 2.5×2.5 nm2 in lateral dimension and with a vertical thickness of 6 nm (Table S2). Models of the cleaved (h k l) surfaces were prepared by dissection of the unified mineral slab at the specified plane assuming a stoichiometric distribution of cations and anions to minimize local electric fields (Figure

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3b), followed by relaxation of the surfaces (see Figure 3c, section 3.4., and section 6.3.)76 The two surface slabs were of about 3.0 nm thickness after cleavage. To examine adsorption of organic molecules and agglomeration energies, models of dry and hydroxylated tricalcium silicate surfaces were prepared from the low energy (040) cleavage plane using rectangular simulation boxes of 2.437×43×2.527 nm3 size. Molecular models of the hydroxylated tricalcium silicate surface were built from the dry (040) surface by hydration of superficial oxide ions to hydroxide (Figure 7). This process involved the conversion of oxide ions in the top ionic layer to hydroxide and further stoichiometric addition of hydroxide ions using the graphical user interface91 followed by relaxation through molecular dynamics. The thickness of individual mineral slabs for the calculation of adsorption energies was chosen about 3 nm and the box height was increased to 43 nm normal to the surface to avoid residual interactions of ionic species with vertical periodic images (Figure 6a,b). The surface coverage for the calculation of adsorption energies was two molecules per surface, leading to negligible interactions between the two molecules upon adsorption and increased accuracy of the computed adsorption energy per molecule. For the calculation of agglomeration energies, two mineral slabs of about 3 nm thickness were employed in configurations together and separated by 20 nm (Figure 6c,d,e). Organic additives were initially placed within 3 to 5 Å on one or both inner surfaces at a given surface coverage to investigate adsorption and agglomeration energies, respectively. The surface coverage in the simulation of agglomeration energies was chosen according to the typical dosage in cement plants, which is 500 g solution per ton of cement with a concentration of 40% organic additive by mass. We assumed a specific surface area of cement particles of 1.0 m2/g determined

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by the BET method.92 Alternatively, the specific surface area of cement is also often measured with the empirical method of Blaine, which yields substantially lower values, typically around 0.3 m2/g (see additional details in section S2 in the Supporting Information). The BET surface coverage corresponds to an incomplete molecular monolayer of about 70% surface coverage (Table 5). Molecular models of C3S, the organic molecules TIPA, TEA, MDIPA, glycerine (Scheme 1), and inorganic-organic structures were constructed using the graphical interfaces of Cerius2 and Materials Studio.91 6.2. Force Field. The optimization of force field parameters for tricalcium silicate was carried out using the functional form of PCFF. Equivalent parameter sets for the energy expressions CVFF, OPLS-AA, CHARMM, and AMBER were obtained by changes in LJ parameters and renewed evaluation using the functional forms of CVFF and CHARMM.9 The analysis of adsorption of organic additives on tricalcium silicate surfaces and of agglomeration energies was carried out using the C3S-PCFF force field. 6.3. Simulation Details and Analysis. The optimization of force field parameters involved several hundred molecular mechanics minimizations and molecular dynamics (MD) simulations using the Discover program.91 Final testing of the crystal structure and cell parameters was carried out by MD simulations in the isothermal-isobaric (NPT) ensemble under standard pressure (0.0001 GPa) and temperature (298.15 K) using the Andersen93 thermostat, Parrinello-Rahman94 pressure control, a time step of 0.5 fs (increases precision of pressure control compared to a time step of 1 fs), a spherical cutoff of van der Waals interactions at 1.2 nm, and Ewald summation of Coulomb interactions with an accuracy of 10-5 kcal/mol. Simulation times of 300 ps were sufficient

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to sample average crystal lattice parameters (a, b, c, α, β, γ), and tests over tens of nanoseconds showed no changes. The computation of vibration spectra was carried out multiple times using different parameter sets and functional forms. Each computation proceeded in two steps. First, MD simulation of the equilibrium crystal structure was carried out in the NPT ensemble for 5 ps using a time step of 1 fs and collection of snapshots every 1 fs. Second, the vibration spectrum (superposition of IR and Raman spectra) was obtained as a Fourier transform of the velocity autocorrelation function of all atoms of this trajectory.38,91 The calculation of elastic properties involved MD simulations of a pre-equilibrated tricalcium silicate super cell under standard conditions in the NPT ensemble under a set of applied triaxial and uniaxial stress tensors, using a time step of 0.5 fs and an accuracy of 10-4 kcal/mol for the Ewald summation of Coulomb interactions. The duration of individual simulations was 20 ps for initial equilibration followed by 80 ps for recording average stress, cell parameters, and thermodynamic data. Longer simulation times had negligible influence on the results. The bulk modulus K was obtained using a series of simulations with gradually increasing triaxial stress σ and monitoring of the relative decrease in box volume ∂V / V . The triaxial stress σ was varied from 0.1 to 1.5 GPa and plotted versus ∂V / V to compute the bulk modulus as an average slope:

K =V

∂σ . ∂V

(3)

Young’s moduli E x , E y , Ez in x, y, and z directions were similarly computed using a series of gradually increasing uniaxial stress ( σ xx , σ yy , σ zz ) and standard pressure in the other directions. The uniaxial stress was varied from 0.1 to 1.5 GPa and plotted versus

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the corresponding uniaxial strains ( ε xx , ε yy , ε zz ) to calculate the Young’s moduli as an average slope:

Ex = ∂σ xx / ∂ε xx , E y = ∂σ yy / ∂ε yy , E z = ∂σ zz / ∂ε zz

(4)

The Poisson ratios vij were computed from the same set of simulations under uniaxial stress in direction j using the average ratio of strains ε ii to ε jj . For example,

v xy = −ε xx / ε yy was obtained from the average expansion strain ε xx of the super cell in the x direction in relation to the compressive strain ε yy in the y direction under uniaxial compressive stress σ yy . The cleavage energy39,76 of each (h k l) facet was computed as a difference in average energy of two cleaved surfaces in equilibrium (Figure 3c) and the corresponding homogeneous mineral slab (Figure 3a):

Ecleavage =

Eseparated − Etogether

(5)

2A

The procedure involved three steps. First, the equilibrium distribution of cations and anions on the surfaces of the cleaved and unified mineral slabs was determined by a series of temperature gradient molecular dynamics simulations in the NVT ensemble (relaxation process from Figure 3b to Figure 3c).76 This procedure involved coordinate constraints on all mineral atoms below a flexible top layer of ionic moieties on the mineral surfaces and a gradient from high (10000 K) to low (298 K) temperature during 10-30 ps MD. The configuration of lowest energy was confirmed for each cleaved (h k l) surface by convergence of different initial cation distributions to the same final configuration in the course of temperature gradient relaxation and then chosen for

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subsequent calculations (see details in ref. 76). Second, single point energies for a series of separations of the two cleaved surfaces were determined to estimate the dependence of the cleavage energy over longer distances (5, 10, 20, 50 nm), which was small but not negligible. Third, a separated configuration with 10 nm distance between the two equilibrated mineral slabs of ~3 nm thickness (Figure 3c), as well as a homogeneous mineral slab of ~6 nm thickness were subjected to 500 ps MD simulation in the NVT ensemble with Ewald summation of Coulomb interactions of high accuracy (10-6 kcal/mol). The first 200 ps served initial equilibration and the latter 300 ps were employed to record energies for the calculation of average energies Eseparate and Etogether (eq 5). Standard deviations were determined from block averages over portions of the equilibrium trajectory as well as from repeated calculations with slightly different initial ion distributions on the surfaces close to the equilibrium distribution. The equilibrium crystal shape (Figure 5) was estimated from the directiondependent cleavage energies (Table 4) in a normal vector construction using the Wulffman program.95 The computation of adsorption energy of organic molecules on the dry and hydroxylated C3S surfaces comprised MD simulations in the NVT ensemble at temperatures of 298 K and 383 K. For each molecule at a given temperature, two simulations were carried out for the molecules 20 nm apart from the surface (isolated from each other) and adsorbed on the surface (Figure 6 a,b).96 Simulation times were 4 ns with a time step of 1 fs, of which the first 2 ns were used for equilibration and the remaining 2 ns for collection of thermodynamic data and snapshots every 400 fs. Simulations were repeated several times with different initial start structures to obtain

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average energies Eclose and E far as well as associated standard deviations. The adsorption energy varied within 1 to 2 kcal/mol per molecule depending on the position on the surface. The calculation of agglomeration energies involved NVT molecular dynamics simulation at 363 K using three different model setups of same total dimension and composition (Figure 6c,d,e). A total simulation time of 3 ns was chosen for each system, including 400 ps initial equilibration at 363.15 K temperature, 200 ps annealing at 600 K, 800 ps further equilibration at 363.15 K, and 1 ns for recording thermodynamic quantities and snapshots every 300 fs at 363.15 K. Annealing at 600 K was necessary to identify the global energy minimum of the molecules confined between the two highly polar surfaces (Figure 6d). Without annealing, divergent local minima of higher energy were commonly found from one simulation to another. The agglomeration energy was calculated as

Eagg =

E2 + E3 − E1 , whereby E2 = E3 in the absence of organic molecules (Figure 6). 2

In the presence of grinding aids, the assumption of an arithmetic mean of E2 and E3 for the separated state rather than Eagg = E2 − E1 may be more realistic, however, results differ only moderately. Standard deviations in computed agglomeration energies were determined from block averages over different portions of equilibrium trajectories as well as from repeated calculations with different initial arrangements of the molecules on the surfaces. The program LAMMPS was employed for most long molecular dynamics simulations97 in addition to Discover.91

6.4. Limitations. While the models provide insight into the most important mineral phase of cement, a number of practical and theoretical limitations provide ground for

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further study. Chemically pure C3S is a simplification of alite, which contains defects by Mg, Al, and Fe in the low percent range that could be described by cation exchange (Ca2+ → Mg2+) and Si → (Al, Fe) defects analogous to layered silicates.37,38 C3S is also only one of the phases present in cement and accurate simulations of other phases are possible.9,47 Moreover, the assumption of even surfaces is a first order simplification on the scale of nanometers. The influence of other surface topologies onto cleavage, adsorption of organic molecules, and agglomeration can be further studied using the proposed models as well as in laboratory as techniques and data become available. Some residual uncertainty arises also from the accuracy of the force field. The reliability of the force field includes minor uncertainties in atomic charges of ±0.1e and possible alternative combinations of nonbond parameters for the mineral. Also, parameters for organic molecules differ slightly from one force field to another, e.g., PCFF, COMPASS, CHARMM, AMBER, CVFF, or OPLS-AA parameters. A notable limitation is the difficulty to simulate chemical reactions such as hydration. The direct simulation of reactions may become possible through extension of the straightforward and thermodynamically consistent force field presented here with appropriate Morse potentials or other reactive potentials with an interpretable number of additional parameters. The overall accuracy of computed cleavage, adsorption, and agglomeration energy is estimated to be about ±10% compared to available experimental measurements.

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Acknowledgements We acknowledge support by Sika Technology AG, the ETH Zurich Foundation, the National Science Foundation (DMR 0955071), the University of Akron, and the Swiss Commission for Technological Innovation (KTI 13703.1 PFFLR-IW). We are also grateful for the allocation of computational resources at the Ohio Supercomputing Center.

Supporting Information Available: Details of the parameter derivation, calculation of the surface coverage, adsorption energies in kcal/g, and choice of super cells for individual (h k l) cleavage planes. This material is available free of charge at http://www.acs.org.

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Force Field for Tricalcium Silicate and Insight into Nanoscale

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