Force Field for Tricalcium Silicate and Insight into Nanoscale Properties: Cleavage, Initial...

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Article

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 HeinzJ. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp312815g • Publication Date (Web): 03 Apr 2013

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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 Sika Technology AG, CH-8048 Zürich, Switzerland

3 Department of Civil, Environmental and Geomatic Engineering, ETH Zurich, CH-

8093 Zürich, Switzerland

*Corresponding author: [email protected]

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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).

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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 non-

covalent 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

(1)

(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

∑

∑∑∑

−

++−+−=

excl) (1,3nonbondedij

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,0

9

,0

,0

excl) (1,3nonbonded 0

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bonded ,

bonded ,

32

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,0

ij

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ij

ij

ij

ij ij

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r

ijkijk

ijk

ijk

ij

ijrpotr

qqKrrKE ijij

σ

σ

σ

σε

επεθθθ

∑

∑∑∑

−

++−+−=

excl) (1,3nonbondedij

6

,0

12

,0

,0

excl) (1,3nonbonded 0

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bonded ,

bonded ,

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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 and , 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 and 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 and well depths .

AMBER and CHARMM assume an arithmetic mean to obtain 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 and ,

even though 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 <5% if neglected (see section S1).

ii,0σ ii,0ε

ii,0σ ii,0ε

ii,0σ ii,0ε

ij,0σ

ii,0σ ii,0ε

ij,0ε

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Table 1. Force field parameters for tricalcium silicate and superficially hydrated

tricalcium silicate for use in various force fields, including PCFF, COMPASS, AMBER,

CHARMM, CVFF, OPLS-AA. Note the choice of appropriate LJ parameters and

.

I. Nonbond Charge (e) (pm) (kcal/mol)

Ca +1.5 370a [335]b (335)c 0.24a [0.28]b (0.29)c

Si +1.0 480 [450] (455) 0.40 [0.47] (0.51)

Osilicate –1.0 340 [315] (315) 0.06 [0.08] (0.07)

Ooxide –1.5 380 [350] (350) 0.06 [0.08] (0.07)

Ohydroxyl –1.05 360 [347] (347) 0.12 [0.12] (0.12)

Hhydroxyl +0.30 109.8 [108.5] (108.5) 0.013 [0.016] (0.016)

II. Bonds r0 (pm) Kr [kcal/(mol·Å2)]

Si–O (in SiO4–) 168 250

O–H (in OH–) 92.9 495

III. Angle θ0 (deg) Kθ [kcal/(mol·rad2)]

O–Si–O (in SiO4–) 109.5 160

a Values without brackets show the van-der-Waals parameters for PCFF and COMPASS

using a 9-6 LJ potential and 6th power combination rules (eq 1).

b Values in square brackets show the van-der-Waals parameters for AMBER and

CHARMM using a 12-6 LJ potential and an arithmetic combination rule for (eq 2).

ii,0σ

ii,0ε

ii,0σ ii,0ε

0σ

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c Values in parenthesis show the van-der-Waals parameters for CVFF and OPLS-AA

using a 12-6 LJ potential and a geometric combination rule for (eq 2).

2.3. Parameter Derivation. The X-ray crystal structure of tricalcium silicate served

as a basis to develop the force field parameters.74,75 The monoclinic M3 polymorph is the

primary reference as it is preferentially found in Portland cement (Figure 1b).74 The other

possible polymorphs M1 and T2 differ only in the orientation of the silicate tetrahedra.

Different orientations of some silica tetrahedra under standard conditions and increased

disorder at elevated temperature are also observed in the simulation at nanosecond time

scales in agreement with the coexistence of M3, M1, and T2 polymorphs. Equilibrium

bond lengths and angles were tested in NPT simulations to reproduce average

bond lengths and angles according to X-ray data. The vibration constants and

were chosen initially from earlier parameters for clay minerals38 and then refined by NPT

simulations to reproduce IR and Raman spectra of C3S. The Si−O stretching constant of

C3S is lower compared to layered silicates and bulk silica41 due to the absence of bonded

neighbour atoms.

Atomic charges were assigned according to an analysis of electronic deformation

densities, dipole moments, an extended Born thermodynamic cycle, trends across the

periodic table for similar compounds, and quantum-mechanical data as previously

reported.37,38 The atomic charge of +1.0e ±0.1e on silicon atoms in tetrahedral oxygen

coordination yields electrostatic contributions to the surface tension of pyrophyllite and

cleavage energies of tricalcium silicate and other silicate minerals in agreement with

0σ

ijr ,0 ijk,0θ

ijrK , ijkK ,θ

iq

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experiment.38,39,41,76 Van-der-Waals diameters were chosen consistent with data

across the periodic table, other silicates, and fine-tuned for agreement between computed

and measured lattice parameters from X-Ray data.38,77 Well depths were adjusted in

agreement with atomic polarizabilities,78 number of pairwise interactions, and computed

cell parameters from X-ray data. Details of the interpretation and assignment of

parameters are given in section S1 of the Supporting Information as well as in a recent

review article.9

3. Bulk and Surface Properties

The parameters for C3S were optimized for all energy expressions to reproduce lattice

parameters, cleavage energies, and mechanical properties in quantitative agreement with

experiment. The excellent description of bulk and surface properties by the force field

provides new insight into interfaces and anisotropy at the nanometer scale that is

fundamental for engineered building materials.

3.1. Structure and Lattice Parameters. Molecular dynamics simulation in the

NPT ensemble reproduces the crystal structure of C3S in outstanding agreement with X-

ray data for all energy expressions (Table 2). The average deviation of lattice parameters

from laboratory measurement is only 0.3%, the average Si−O bond lengths are 160 ±5

pm as in the reported crystal structure, and root mean square deviations of individual

atom positions from the X-ray pattern are low. In the course of molecular dynamics

simulation at room temperature, local disorder of some silicate tetrahedra was observed

as reported by X-ray data.74,75 SiO4 tetrahedra can have markedly variable orientation

ii,0σ

ii,0ε

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over the course of several nanoseconds while central Si atoms, Ca, and free oxide ions

remain at the same position.

Table 2. Lattice parameters of tricalcium silicate (2×3×2 multiple of the unit cell)

according to X-ray data and molecular dynamics simulation in the NPT ensemble using

the force field parameters embedded in various force fields under standard temperature

and pressure.

Method a

(nm)

b

(nm)

c

(nm)

α

(°)

β

(°)

γ

(°)

V

(nm3)

rms dev

(pm/atom)

Expt (2×3×2)a 2.447 2.121 1.8596 90 116.31 90 8.6554 0

PCFF, COMPASS 2.443 2.113 1.8685 90 116.18 90 8.6557 17

AMBER, CHARMM 2.440 2.118 1.8660 90 116.17 90 8.6548 20

CVFF, OPLS-AA 2.440 2.123 1.8654 90 116.43 90 8.6530 14

a Ref. 74.

3.2. Vibration Spectra. Force constants for bond stretching and angle bending in

the force field reproduce wavenumbers in IR and Raman spectra from experimental

measurements qualitatively well (Figure 2).79 The main features comprise the Si−O bond

stretching vibration near 950 cm-1 and the O−Si−O angle bending vibration near 500 cm-1

(Figure 2). The agreement in wavenumbers is limited to about ±100 cm-1. Intensities and

broadening of the experimental signals cannot be reproduced by classical force fields

related to the simplification of the electronic structure.

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Figure 2. Comparison of computed and experimental IR spectra of tricalcium silicate (ref.

61). The computational signature is the same for all chosen energy expressions.

3.3. Mechanical Properties. Mechanical properties play a dominant role for the

stability of concrete and building structures (Table 3). The agreement between computed

and experimental elastic moduli and Poisson ratios is excellent and enables quantitative

insight beyond available measurements. The computed bulk modulus matches the bulk

modulus measured under standard conditions.22,80 We also find that C3S is anisotropic

(Figure 1b). The mineral possesses a layered structure in the z direction and is more

compressible in this direction compared to the x and y directions (Table 3). This

anisotropy is reflected in Young’s moduli of 103 GPa in the z direction and 152 GPa as

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well as 176 GPa in the x and y directions, respectively. In experiment, such direction-

dependent measurements have not yet been reported as C3S crystallizes poorly.74,81

Measured Young’s moduli are, therefore, rather distributed (118-147 GPa)22,80 and

likely represent average values over different crystallite orientations. All measurements

fall within the range of the three ideal values of Young’s moduli according to the

simulation. The computed Poisson ratios also indicate the anisotropy and, on average,

agree with experimental values. For example, compression in z direction will yield only a

small expansion in y direction related to the high value of and thus yields a

comparatively small Poisson ratio of 0.20. On the other hand, compression in x or y

direction will cause a significant expansion in the z direction, related to lower resistance

, and leads to higher Poisson ratios and of 0.37 and 0.30, respectively.

yE

yzν

zE zxνzyν

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Table 3. Bulk modulus, Young’s moduli (in GPa), and Poisson ratios of tricalcium

silicate at 0.1-1.5 GPa stress in computation and experiment.

Bulk Modulus Computed Experiment

K 105 ± 5 105.2a

Young’s Moduli Computed Experiment

Ex 152 ± 6 135 ± 7, 147 ± 5b and 117.6a

(direction unknown) Ey 176 ± 3

Ez 103 ± 11

Poisson Ratios Computed Experiment

νxy 0.303 ± 0.042

νxz 0.273 ± 0.043

νyx 0.225 ± 0.021 0.314a

(direction unknown) νyz 0.197 ± 0.027

νzx 0.372± 0.041

νzy 0.299 ± 0.058

a Ref 22. Measurement uncertainty is <10%. b Ref. 80.

3.4. Cleavage Energy. Cleavage and agglomeration of cement particles play a key

role in cement grinding, hydration, interaction with organic modifiers, hardening, and

ultimately, in the stability of concrete building structures. The number of possible (h k l)

cleavage planes of the dry mineral is in principle unlimited (Figure 1a). The likelihood of

cleavage of a given plane depends on the possibility of energetically favourable

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distributions of calcium, silicate, and oxide ions. The analysis of atomic and molecular

layers perpendicular to a potential cleavage plane (h k l) reveals repetitive sequences of

charges, such as … +3e, −3e, +3e, −3e … for a given cross-sectional area (Figure 3). The

total charge per layer area determines the dominant Coulomb contribution to the cohesive

energy. Simulations show that an equal distribution of charged moieties on the cleaved

surfaces is energetically favorable, such as the distribution of −3e as −1.5e and −1.5e on

the two surfaces upon cleavage. The equal distribution of the charge leads to electrically

neutral surfaces with a net charge of zero, minimizes local electric fields, and reduces the

distance dependence of the cleavage energy. Equal distribution of ionic species thus leads

to equilibrium cleavage with the lowest possible cleavage energy. We focus on

equilibrium cleavage in this work, and the analysis of unequal charge distributions39,82

remains as a future challenge.

The analysis of cleavage planes of different spatial orientation indicates a range of

cleavage energies between 1300 and 1600 mJ/m2 (Table 4). A number of low energy

cleavage planes correlate with the direction of the cell vectors (Figure 4). The abundance

of small ionic species in the crystal allows the placement of cleavage planes in many

different directions without significant interference from covalent bonds. These potential

surface environments of calcium cations, silicate anions, and oxide anions upon cleavage

have a certain degree of similarity. The total energy of cleavage is composed primarily of

Coulomb energy (96%), minor contributions of van-der-Waals energy (3%), and

marginal contributions from internal energy such as bonds and angles (1%) according to

the energy expressions (equations 1 and 2). This distribution is consistent with the high

degree of ionic bonding in the mineral. Low energy surfaces with average cleavage

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energies of 1340 ±50 mJ/m2 constitute the majority of the surface area. In spite of

electrically neutral cleavage, all cleavage planes exhibit a minor distance dependence of

the cleavage energy. This distance dependence augments some cleavage energies more

than 50 mJ/m2 for surface separations between 10 nm and infinity and reduces the

cleavage energy when the surfaces are closer than 10 nm. The magnitude of distance

dependence is uniquely determined by the average moments of dipoles and multipoles on

the cleaved surface (h k l), i.e., by the magnitude of charges and distances between

cations and anions for a given cleavage plane.

The comparison of computed cleavage energies with experiment is not directly

conceivable, as cleavage energies are not known for tricalcium silicate. However,

cleavage energies have been reported for CaO and Ca(OH)2 as 1310 and 1180 mJ/m2

with uncertainties of ±200 and ±100 mJ/m2, respectively.83 The structure of Ca3SiO5 can

be regarded as 2 CaO · CaSiO3 or 3 CaO · SiO2 (“C3S”) and is similar to CaO in polarity.

Therefore, the computed surface-averaged cleavage energy of 1340 mJ/m2 for C3S is in

good agreement with 1310 mJ/m2 measured for CaO, especially given the large

uncertainty. In addition, Ca(OH)2 is less polar than CaO and Ca3SiO5 due to the presence

of hydroxide and shows a lower cleavage energy (in contrast to CaO, the positive charge

in Ca(OH)2 is shared by hydrogen and calcium). The reliability of the force field with

respect to surface and interface energies is also supported by the ability of closely related

parameters to reproduce cleavage energies of mica and montmorillonite, electrostatic and

Lifshitz-van-der-Waals contributions to the surface tension of pyrophyllite, as well as

hydration energies and water contact angles on various silica surfaces.9,38,39,41,76

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It has been shown that the strong cohesive energy of significantly ionic minerals

typically leads to very small entropic contributions upon cleavage.39,82 Thus, cleavage

energies reported in Table 4 can be regarded equal to free energies of cleavage.

A solid-vapor surface tension remains difficult to define as surface cations

rearrange irreversibly upon cleavage and hydration easily occurs (section 4). In either

case, the surface structure loses correlation with original lattice features. Depending on

whether free energies of cleavage or of agglomeration would still be considered an

estimate of , the surface-averaged value could range from 1340 ± 50 mJ/m2 to 450 ±

50 mJ/m2 without hydration, and much lower values after hydration (section 4.3).

SVγ

SVγ

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Figure 3. Schematic of cleavage, surface relaxation, and agglomeration of a possible (h k

l) plane of tricalcium silicate in vacuum. (a) Bulk mineral. (b) Equilibrium cleavage

assuming equal partition of ionic species between the two nascent surfaces. (c)

Relaxation of superficial groups at larger separation. Equal partition of ionic groups

minimizes local electric fields and the cleavage energy. Unequal partition of ionic groups

results in charged surfaces and possible attraction beyond micrometers. (d)

Agglomeration of the reconstructed cleaved surfaces leads to an imperfect boundary and

only partial recovery of the cohesive energy.

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Figure 4. Crystal structure and possible cleavage planes of tricalcium silicate viewed

perpendicular to the three coordinate axes of the unit cell. (a) Projection perpendicular to

the b axis onto the horizontal ac plane. Black dashed lines indicate cleavage planes

parallel to the bc plane (except (10 0 -3)) and perpendicular to the ac plane. The grey

dashed rectangle indicates the smallest possible rectangular super cell. (b) Projection

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perpendicular to the c axis onto the ab plane (a axis points 26.3º downward). Black

dashed lines indicate cleavage planes parallel to the ac plane and perpendicular to the ab

plane. (c) Projection perpendicular to the axis a onto the bc plane (the c axis points 26.3º

downward). Black dashed lines indicate cleavage planes parallel to the ab plane and at an

angle of 116.3º/63.7º to the bc plane. Cm symmetry leads to several geometrically

identical planes with the same cleavage energies, for example, (100) and (200), (300) and

(-300), (800) and (-800), (010) and (020). Other planes resemble each other but are not

identical, such as (001), (003), and (00-3); (00-8) and (008).

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Table 4. Computed cleavage energy of several cleavage planes of tricalcium silicate.

Equivalent or similar (~) cleavage planes according to Cm (c1m1) symmetry are

indicated. Experimental values for similar minerals CaO and Ca(OH)2 are also shown

(not known for Ca3SiO5).

Miller Index Cleavage Energya (mJ/m2)

(1 0 0), (2 0 0) 1534 ± 56

(3 0 0), (-3 0 0) 1590 ±31

(8 0 0), (-8 0 0) 1401 ± 35

(0 1 0), (0 2 0) 1329 ± 37

(0 4 0), (0 -4 0) 1324 ± 25

(0 0 1) ~ (0 0 3) ~ (0 0 -3) 1335± 25

(0 0 2) 1350 ± 31

(0 0 8) ~ (0 0 -8) 1436 ± 30

(-10 0 3) 1385 ± 38

Surface-averaged cleavage energies (mJ/m2)

Ca3SiO5 Computed 1340 ± 50

Ca3SiO5 Experimental N.A.

CaO Experimental 1310 ± 200b

Ca(OH)2 Experimental 1180 ± 100b

a Increases by more than 50 mJ/m2 at separations exceeding 10 nm. b Ref. 83.

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3.5 Equilibrium Particle Shape. The comparatively small anisotropy of the

surface-averaged cleavage energy suggests a somewhat irregular crystallite shape of low

aspect ratio in thermodynamic equilibrium. The Wulff construction, using surface

energies as normal vectors to the identified (h k l) planes, is qualitatively consistent with

SEM data for tricalcium silicate in Portland cement and in dental root filling materials

(Figure 5).81 Deviations from this shape may occur related to nonequilibrium cleavage

and the presence of many cleavage planes of similar energy.

Figure 5. Possible equilibrium shape of C3S based on directional cleavage energies in

Table 4.

4. Adsorption of Organic Molecules and Agglomeration Forces

Experimental investigations of the adsorption of organic molecules and agglomeration

forces between particle surfaces have remained difficult due to the inaccessibility and

high reactivity of the surfaces of the micro and nanostructured particles. Much of the

laboratory evidence has been based on indirect measures such as heats of adsorption and

energy savings during ball milling. Common organic additives include low molecular

weight amines and alcohols (Scheme 1). In the following, we report fundamental insight

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into adsorption and agglomeration processes on representative even tricalcium silicate

surfaces in comparison to available data (Figure 6).

Scheme 1. Structure of triisopropanolamine (TIPA), triethanolamine (TEA), N-methyl-

diisopropanolamine (MDIPA), and glycerine used as additives (grinding aids) in cement.

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Figure 6. Schematic of the calculation of adsorption energies (a, b) and

agglomeration energies using molecular dynamics simulation (c, d, e). Simulations

(a) of a molecule adsorbed onto the surface and (b) detached from the surface were

employed for the analysis of adsorption energies. Simulations of agglomerated (c) and

cleaved surfaces (d, e) were employed for the analysis of agglomeration energies. The

distribution of adsorbed molecules ranges from (d) equal distribution on both surfaces to

(e) one-sided distribution on one separate surface. E represents the average total energy

of a simulation box and A the cross-sectional area of one surface.

4.1. Composition of the Surface and Initial Hydration. A fundamental aspect to

characterize adsorption of molecules onto freshly cleaved surfaces is the surface

composition. Cleaved surfaces in the dry state lead to maximum cohesion (see section

4.3), however, the influence of humidity, the addition of organic molecules in solution,

and possible dehydration of mineral additives (e.g. gypsum) in cement lead to instant

reactions of C3S with water and different degrees of surface hydration.

The first step upon hydration is the conversion of superficial oxide ions to

hydroxide ions (Figure 7). The reaction is a consequence of the instability of oxide ions

in water (the pKa value of hydroxide is estimated to be >30).84 Initial surface interactions

with organic modifiers such as grinding aids after cleavage and subsequent

agglomeration therefore likely involve hydroxylated and dry surfaces. In the model, the

hydration of oxide ions is approximated as

, (6)

Eads

Eagg

H2+0.41eO−0.82e + O−1.5e → 2 O−1.05eH 0.30e

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followed by relaxation of all superficial ions (Table 1). The reaction leads to twice as

many hydroxide groups than initial oxide ions on the surface, which unsettles the C3S

surface structure with a disordered pattern of hydroxide groups upon relaxation (Figure 8).

Further hydration events are beyond the scope of this work and could be

described using extensions of this model. They include the hydration and dissolution of

orthosilicate ions to H2SiO42– and H3SiO4

– ions on the C3S surface,85,86 dissolution of

calcium hydroxide, oligomerization of individual silicate species and deposition of

oligomeric C-S-H gels. These hydration processes proceed over hours, days and years on

the surface while the core of the particles remains tricalcium silicate.

Figure 7. The first step of partial dissolution of C3S involves hydration of superficial

oxide ions and leads to a hydroxylated C3S surface (refs. 85, 86). Models of dry surfaces

were employed for the analysis of cleavage energies and hydroxylated models for the

analysis of adsorption and agglomeration energies.

4.2. Interaction with Organic Additives. The structure and dynamics of organic

compounds on hydroxylated and dry C3S surfaces were investigated at temperatures of

Ca2+ Ca2+ SiO44– O2– Ca2+

Ca2+ SiO44– O2– Ca2+ Ca2+

Solution

Solid

H2O

OH–

Ca2+ Ca2+ SiO44– OH– Ca2+

Ca2+ SiO44– O2– Ca2+ Ca2+

Protonation

of oxide

Dry C3S Hydroxylated C3S

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25 °C and 110 °C on energetically stable (040) surfaces (Figure 8). 110 °C corresponds to

the average grinding temperature of ball mills in a cement plant.

The hydroxylated C3S surfaces are characteristically disordered, especially in the

top layer, showing superficial hydroxide, rotation of the silicate anions as observed in X-

ray structures74,75 as well as partial pullout of individual silicate ions (see circular

highlights in Figure 8). The analysis of adsorbed TIPA, TEA, MDIPA, and glycerine

molecules (Scheme 1) indicates close contacts of hydroxyl groups in the organic

molecules with superficial calcium ions as well as hydrogen bonds and other polar

interactions (Figure 8a,b). Hydrogen bonds arise from the interaction of hydroxyl groups

of the molecules to silicate and hydroxide groups on the C3S surface. Glycerine possesses

more conformational freedom and binds tighter to the surface in comparison to the

tertiary amines TIPA and TEA (Figure 8c). This trend is also reflected in stronger

adsorption (i.e. larger negative value of adsorption energy) (Figure 9). Surface defects are

also targets for adsorbed molecules and disorder was somewhat higher at 383 K

compared to 298 K as demonstrated by the larger distance of individual ions from the

basal plane (see horizontal dashed lines in Figure 8b). The presence of oxide ions on the

dry surfaces in the presence of water or alcohol molecules is unlikely as reactions to

hydroxide and alkoxide occur (Figure 8c), however, adsorption energies were analyzed

both on hydroxylated and dry surfaces for comparison (Figure 9).

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Figure 8. Representative snapshots of organic molecules adsorbed on hydroxylated and

dry (040) surfaces of tricalcium silicate in molecular dynamics simulation. (a) TEA on

the hydroxylated tricalcium silicate surface, showing adsorption by hydrogen bonds and

coordination of superficial Ca ions by hydroxyl groups (see inset). Circular highlights

indicate surface reconstruction. (b) Snapshot of TIPA on the hydroxylated surface at 383

K and 298 K. Horizontal dashed lines along with circular and elliptical highlights indicate

increased disorder of the surface at 383 K. (c) Snapshot of glycerine on the hydroxylated

and dry surfaces at 383 K. The distance of glycerine to superficial ions is smaller in

comparison to the tertiary amino alcohols and results in stronger binding.

Adsorption energies were computed in a range of -18 to -55 kcal/mol (Figure 9).

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The magnitude of adsorption can be understood assuming an approximate strength of

O···Ca2+ coordination of -8 kcal/mol, of a hydrogen bond of ~ -4 kcal/mol, as well as

further multipolar interactions (Figure 8).84 An increase in adsorption strength, equivalent

to a decrease in adsorption energy to further below zero, was found in the order TEA <

TIPA, MDIPA < glycerine irrespective of surface type and temperature. The dry surface

at 298 K showed the strongest adsorption and only minor differentiation among the four

compounds. The same surface at 383 K showed reduced adsorption and significant

differences in adsorption energy among the four molecules. Similar trends for all

compounds, although overall 10-30% weaker attraction, were observed on the

hydroxylated surface at 298 K and 383 K. Adsorption on the hydroxylated surface is

reduced at 383 K but remains nevertheless in a substantial range of -18 to -37 kcal/mol.

In particular, adsorption of TEA and TIPA decreases considerably when the temperature

rises from 298 K to 383 K while the values are similar for MDIPA and glycerine. The

stronger temperature dependence of adsorption of the tertiary amine alcohols TEA and

TIPA may be associated with the release of conformation restraints in the bound state at

higher temperature in contrast to less conformation restraints for the near-linear flexible

MDIPA and glycerol molecules at either temperature. The results also show clearly that

the adsorption energy depends on surface-molecule interactions and does not correlate

with the volatility of the organic liquids. The volatility depends on molecule-molecule

interactions only and boiling points of 335.4 ºC, 306 ºC, 248 ºC and 290 ºC for TEA,

TIPA, MDIPA, and glycerine84 do not correlate with the order of adsorption energies.

Adsorption energies expressed per unit mass, instead of per mole, indicate even stronger

adsorption of glycerine and reduce differences between chemically similar TEA and TIPA

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(Figure S1).

0

-20

-40

-60

-80

-100 Hydrox. C

3S at 298 K

Hydrox. C3S at 383 K

Dry C3S at 298 K

Dry C3S at 383 K

Adsorption energy (kcal/mol)

TEA TIPA MDIPA Glycerine

Figure 9. Computed adsorption energy of TEA, TIPA, MDIPA, and glycerine on

hydroxylated and dry (040) surfaces of tricalcium silicate. Adsorption is stronger at lower

temperature compared to higher temperature, and also stronger on dry surfaces compared

to hydroxylated surfaces.

4.3. Origin and Prediction of Agglomeration Forces. Agglomeration of particles

due to electrostatic forces plays a key role during grinding of cement clinker in a ball

mill. Strong agglomeration of the particles reduces the efficiency of the ball mill because

part of the energy that would be used to cleave particles is repeatedly used to break up

agglomerates (Figure 10a). Moreover, agglomerating particles also tend to coat the

milling media, reducing the efficiency of shocks by distributing the stresses at impact

over a network of many particles. Finally, agglomeration also affects the efficiency of the

separator. Industrial ball mills are coupled with a cyclone-based separator that selects

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particles fine enough as the product and recycles others at the head of the ball mill

(Figure 10a). The milling process usually occurs at 110 ºC with a separator temperature

of 90 ºC.

Figure 10. Agglomeration of mineral surfaces and the role of adsorbed molecules on the

nanometer scale. (a) The separator mechanism of cement clinker in a ball mill shows the

collection of fine cement particles (upper left corner) while coarse particles or

agglomerates of ground particles are rejected for further grinding until the desired particle

size is reached. (b, c) Snapshots of glycerine molecules confined between cleaved particle

surfaces below monolayer coverage in the top view indicate residual mobility during tens

of nanoseconds (movement of molecules highlighted in purple and blue from b to c). (d)

The surface-bound organic molecules act as a spacer to reduce agglomeration of the

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highly polar surfaces (side view). The interfacial gap between tricalcium silicate surfaces

at monolayer coverage or above lowers agglomeration energies up to 95% in comparison

to cleavage energies. (e, f) The distribution of adsorbed molecules on cleaved surfaces

can vary between equal and one-sided.

We quantified the agglomeration energy through simulation of the buried interfaces,

including neat and hydrated (040) surfaces in the absence and in the presence of organic

capping agents (Figures 6b and 11). As shown in section 3, neat surfaces of C3S tend to

attract each other upon cleavage due to strong Coulomb interactions (Figure 3). This

attraction causes the formation of particle agglomerates (Figure 10a). The energy upon

agglomeration of cleaved surfaces is less than the original cleavage energy (Figure 11)

because rearrangements of superficial ions as part of the cleavage process change the

surface structure. Reversal into a perfect crystal lattice would require a spatial fit between

the cleaved surfaces as well as very high activation barriers to relocate displaced

superficial ions into crystallographic positions. Even if a spatial fit could be achieved, the

activation barriers are not accessible during ordinary temperatures. Agglomeration

energies of locally even, dry surfaces are 450 mJ/m2 at 363 K according to the

computation, which is about 60% less than the original cleavage energy of 1340 mJ/m2.

A further decrease to 240 mJ/m2 agglomeration energy occurs upon hydration, which is

80% less than the initial cleavage energy. The reason for the decrease in surface forces

upon hydration is the diminished strength of superficial Coulomb interactions. The

remaining agglomeration energy is still significant and comparable to the equilibrium

cleavage energy of mica layers in vacuum of 375 mJ/m2.38,87 Actual agglomeration

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energies are likely lower than the equilibrium limit as micrometer-size particles are

irregular and experience no continuous contact area. Therefore, agglomeration energies in

the range 240 to 450 mJ/m2 may be regarded as an upper limit after equilibrium cleavage

of tricalcium silicate surfaces in the absence of organic modification. In principle, the

magnitude of cleavage and agglomeration energies could also be higher in case of

nonequilibrium cleavage with unequal distribution of cations which is, however, beyond

the scope of this work.39,82

The addition of a concentrated solution of molecular modifiers (“grinding aids”)

onto the particles during grinding leads to their dispersion on existing and freshly cleaved

surfaces and further reduces cohesion (Figures 10 and 11). Agglomeration energies for

surface coverage below molecular monolayers (Table 5) are between 110 and 50 mJ/m2

in the order glycerine > 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 sub-

nanometer 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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0

100

200

300

400

500 HC: Hydroxylated C3S

Agglomeration Energy, mJ/m

2

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

(mg/m2)

Surface Area

(nm2)

No of

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 atomic-

scale, 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 (<10% uncertainty) and provide insight into anisotropies and

particle shape that has remained elusive in measurements. The analysis of more than 20

different (h k l) cleavage planes indicates different surface environments upon cleavage

and initial stages of hydration (h k l) with cleavage energies in a range of 1300 to 1600

mJ/m2 and an equilibrium particle shape of low aspect ratio.

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The model was further employed to investigate adsorption mechanisms of several

organic molecules on hydroxylated and dry surfaces of C3S at room temperature and at

grinding temperatures near 383 K. The mechanism of adsorption of the molecules

involves coordination of Ca2+ ions, hydrogen bonds, and other polar interactions with the

surface. Simulation results show that adsorption is weaker on hydroxylated C3S surfaces

than on dry surfaces and the adsorption strength decreases in the order glycerine >

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 and monitoring of the relative

decrease in box volume . The triaxial stress was varied from 0.1 to 1.5 GPa and

plotted versus to compute the bulk modulus as an average slope:

. (3)

Young’s moduli Ex , Ey , Ez in x, y, and z directions were similarly computed using a

series of gradually increasing uniaxial stress ( , , ) and standard pressure in

the other directions. The uniaxial stress was varied from 0.1 to 1.5 GPa and plotted versus

σ

VV /∂ σ

VV /∂

VVK∂∂

=σ

σ xxσ yy σ zz

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the corresponding uniaxial strains ( , , ) to calculate the Young’s moduli as an

average slope:

, , (4)

The Poisson ratios were computed from the same set of simulations under uniaxial

stress in direction j using the average ratio of strains to . For example,

was obtained from the average expansion strain of the super cell in

the x direction in relation to the compressive strain in the y direction under uniaxial

compressive stress .

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):

(5)

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

xxεyyε zzε

Ex = ∂σ xx /∂εxx yyyyyE εσ ∂∂= / zzzzzE εσ ∂∂= /

vij

iiε jjε

yyxxxyv εε /−= xxε

yyε

σ yy

A

EEE

togetherseparated

cleavage2

−=

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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 and

(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 direction-

dependent 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

Eseparate Etogether

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average energies and 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

132

2E

EEEagg −

+= , whereby 32 EE = in the absence of organic molecules (Figure 6).

In the presence of grinding aids, the assumption of an arithmetic mean of E2 and E3 for

the separated state rather than 12 EEEagg −= 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

EcloseE far

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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.

References

(1) Taylor, H. F. W. Cement Chemistry, ed. 2; Academic Press, London, 1997.

(2) Aïtcin, P. C. Cements of Yesterday and Today – Concrete of Tomorrow. Cem.

Concr. Res. 2000, 30, 1349-1359.

(3) Gartner, E. M. at 31st Cement and Concrete Science Conference - Novel

Developments and Innovation in Cementitious Materials. Imperial College, London,

UK, September, 2011.

(4) Scrivener, K. L. The Concrete Conundrum. Chemistry World 2008, 5, 62-66.

(5) Sharp, J. H.; Gartner, E. M.; MacPhee, D. E. Novel Cement Systems

(Sustainability). Session 2 of the Fred Glasser Cement Science Symposium. Adv.

Cem. Res. 2010, 22, 195-202.

Page 51 of 64



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

52 of 64

(6) Lothenbach, B.; Scrivener, K.; Hooton, R. D. Supplementary Cementitious

Materials. Cem. Concr. Res. 2011, 41, 1244-1256.

(7) Schneider, M.; Romer, M.; Tschudin, M.; Bolio, H. Sustainable Cement Production

– Present and Future. Cement Concrete Res. 2011, 41, 642-650.

(8) Flatt, R. J.; Roussel, N.; Cheeseman, C. R.Concrete : An Eco Material that Needs to

be Improved. J. Eur. Ceram. Soc. 2012, 32, 2787-2798.

(9) Heinz, H.; Lin, T. Z.; Mishra, R. K.; Emami, F. S. Thermodynamically Consistent

Force Fields for the Assembly of Inorganic, Organic, and Biological Nanostructures:

The INTERFACE Force Field. Langmuir 2013, 29, 1754-1765.

(10) Tricalcium silicate abbreviates as C3S related to the stoichiometric perception as a

mixture of oxides 3 CaO · SiO2. Possible defects include Mg2+ for Ca2+, 2 AlO45- for

2 SiO44- · O2-, and similarly 2 FeO4

5- for 2 SiO44- · O2- (formal charges shown to

indicate stoichiometry).

(11) Birchall, J. D.; Howard, A. J.; Bailey J. E. On the Hydration of Portland Cement.

Proc. Royal Soc. London A 1978, 360, 445-453.

(12) Jawed, I.; Skalny, J. Surface Phenomena during Tricalcium Silicate Hydration. J.

Colloid Interface Sci. 1982, 85, 235-243.

(13) Tzschichholz, F.; Herrmann, H. J.; Zanni, H. A Reaction-Diffusion Model for the

Hydration/Setting of Cement. Phys. Rev. E 1996, 53, 2629-2637.

(14) Yu, P.; Kirkpatrick, R. J.; Poe, B.; McMillan, P. F.; Cong X. Structure of Calcium

Silicate Hydrate (C-S-H): Near-, Mid-, and Far-Infrared Spectroscopy. J. Am.

Ceram. Soc. 1999, 82, 742-748.

(15) Bullard, J. W. A Determination of Hydration Mechanisms for Tricalcium Silicate

Page 52 of 64



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

53 of 64

Using a Kinetic Cellular Automaton Model. J. Am. Ceram. Soc. 2008, 91, 2088-

2097.

(16) Juilland, P.; Gallucci, E.; Flatt, R.; Scrivener, K. Dissolution Theory Induction

Period in Alite Hydration. Cement Concrete Res. 2010, 40, 831-844.

(17) Skinner, L. B.; Chae, S. R.; Benmore, C. J.; Wenk, H. R.; Monteiro, P. J. M.

Nanostructure of Calcium Silicate Hydrates in Cements. Phys. Rev. Lett. 2010,

104, 195502.

(18) Bullard, J. W.; Jennings, H. M.; Livingston, R. A.; Nonat, A.; Scherer, G. W.;

Schweitzer, J. S.; Scrivener, K. L.; Thomas, J. J. Mechanisms of Cement Hydration.

Cem. Concr. Res. 2011, 41, 1208-1223.

(19) Nonat, A. The Structure and Stoichiometry of CSH. Cem. Concr. Res. 2004, 34,

1521-1528.

(20) Allen, A. J.; Thomas, J. J.; Jennings, H. M. Composition and Density of Nanoscale

Calcium–Silicate–Hydrate in Cement. Nature Materials 2007, 6, 311-316.

(21) Richardson, I. G. The Calcium Silicate Hydrates. Cem. Concr. Res. 2008, 38, 137-

158.

(22) Boumiz, A.; Sorrentino, D.; Vernet, C.; Tenoudji, F. C. Modelling the development

of the elastic moduli as a function of the hydration degree of cement pastes and

mortars, In: Proceedings of the 2nd International RILEM Symposium on Hydration

and Setting, Nonat, A., ed.; RILEM, Dijon, France, 1997, pp. 295-316.

(23) Kovler, K.; Roussel, N. Properties of Fresh and Hardened Concrete. Cem. Concr.

Res. 2011, 41, 775-792.

Page 53 of 64



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

54 of 64

(24) Masoero, E.; Del Gado, E.; Pellenq, R. J. M.; Ulm, F. J.; Yip, S. Nanostructure

and Nanomechanics of Cement: Polydisperse Colloidal Packing. Phys. Rev.

Lett. 2012, 15, 155503.

(25) Ulm, F. J.; Van Damme, M.; Bobko, C.; Ortega, J. A.; Tai, K.; Ortiz, C. Statistical

Indentation Techniques for Hydrated Nanocomposites: Concrete, Bone, and Shale.

J. Am. Ceram. Soc. 2007, 90, 2677-2692.

(26) Lura, P.; Trtik, P.; Muench, B. Validity of Recent Approaches for Statistical

Nanoindentation of Cement Pastes. Cem. Concr. Composites 2011, 33, 457-465.

(27) Flatt, R. J.; Schober, I.; Raphael, E.; Plassard, C.; Lesniewska, E. Conformation of

Adsorbed Comb Copolymer Dispersants. Langmuir 2009, 25, 845-855.

(28) Plank, J.; Hirsch, C. Impact of Zeta Potential of Early Cement Hydration Phases

on Superplasticizer Adsorption. Cement Concrete Res. 2007, 37, 537-542.

(29) Cong, X. D.; Kirkpatrick, R. J. 29Si MAS NMR Study of the Structure

of Calcium Silicate Hydrate. Adv. Cem. Based Mat. 1996, 3, 144-156.

(30) Tran, T. T.; Herfort, D.; Jakobsen, H. J.; Skibsted, J. Site Preferences of Fluoride

Guest Ions in the Calcium Silicate Phases of Portland Cement from 29Si{19F} CP-

REDOR NMR Spectroscopy. J. Am. Chem. Soc. 2009, 131, 14170-14171.

(31) McDonald, P. J.; Korb, J. P.; Mitchell, J.; Monteilhet, L. Surface Relaxation and

Chemical Exchange in Hydrating Cement Pastes: A Two-Dimensional NMR

Relaxation Study. Phys. Rev. E 2005, 72, 011409.

(32) Thomas, J. J.; Jennings, H. M.; Chen, J. J. Influence of Nucleation Seeding on the

Hydration Mechanisms of Tricalcium Silicate and Cement. J. Phys. Chem. C 2009,

113, 4327-4334.

Page 54 of 64



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

55 of 64

(33) Sohoni, S.; Sridhar, R.; Mandal, G. The Effect of Grinding Aids on the Fine

Grinding of Limestone, Quartz and Portland Cement Clinker. Powder Tech.

1991, 67, 277-286.

(34) Bentz, D. P.; Garboczi, E. J.; Haecker, C. J.; Jensen, O. M. Effects of Cement

Particle Size Distribution on Performance Properties of Portland Cement-Based

Materials. Cem. Concr. Res. 1999, 29, 1663-1671.

(35) Gartner, E. M.; Jennings, H. M. Thermodynamics of Calcium Silicate Hydrates and

Their Solutions. J. Am. Ceram. Soc. 1987, 70, 743-749.

(36) Heinz, H.; Castelijns, H. J.; Suter, U. W. Structure and Phase Transitions of Alkyl

Chains on Mica. J. Am. Chem. Soc. 2003, 125, 9500-9510.

(37) Heinz, H.; Suter, U. W. Atomic Charges for Classical Simulations of Polar Systems.

J. Phys. Chem. B 2004, 108, 18341-18352.

(38) Heinz, H.; Koerner, H.; Anderson, K.L.; Vaia, R.A.; Farmer, B. L. Force Field for

Phyllosilicates and Dynamics of Octadecylammonium Chains

Grafted to Montmorillonite. Chem. Mater. 2005, 17, 5658-5669.

(39) Heinz, H.; Vaia, R. A.; Farmer, B. L. Interaction Energy and Surface

Reconstruction between Sheets of Layered Silicates. J. Chem. Phys. 2006, 124,

224713.

(40) Heinz, H.; Vaia, R. A.; Farmer, B. L.; Naik, R. R. Accurate Simulation of Surfaces

and Interfaces of FCC Metals Using 12-6 and 9-6 Lennard-Jones Potentials. J. Phys.

Chem. C 2008, 112, 17281-17290.

(41) Patwardhan, S. V.; Emami, F. S.; Berry, R. J.; Jones, S. E.; Naik, R. R.;

Deschaume, O.; Heinz, H.; Perry, C. C. Chemistry of Aqueous Silica Nanoparticle

Page 55 of 64



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

56 of 64

Surfaces and the Mechanism of Selective Peptide Adsorption. J. Am. Chem. Soc.

2012, 134, 6244-6256.

(42) van Beest, B. W. H.; Kramer, G. J.; Van Santen, R. A. Force Fields for Silicas and

Aluminophosphates Based on Ab-initio Calculations. Phys. Rev. Lett. 1990, 64,

1955-1958.

(43) Collins, D. R.; Catlow, C. R. A. Computer Simulation of Structures and Cohesive

Properties of Micas. Am. Mineral. 1992, 77, 1172-1181.

(44) Coveney, P. V.; Humphries, W. Molecular Modelling of the Mechanism of Action

of Phosphonate Retarders on Hydrating Cements. J. Chem. Soc.-Faraday Trans.

1996, 92, 831-841.

(45) Faucon, P.; Delaye, J. M.; Virlet, J.; Jacquinot, J. F.; Adenot, F. Study of the

Structural Properties of the C-S-H(I) by Molecular Dynamics Simulation. Cem.

Concr. Res. 1997, 27, 1581-1590.

(46) Bell, I. S.; Coveney, P. V. Molecular Modelling of the Mechanism of Action of

Borate Retarders on Hydrating Cements at High Temperature. Molecular

Simulation 1998, 20, 331-356.

(47) Kalinichev, A. G.; Kirkpatrick, R. J. Molecular Dynamics Modeling of Chloride

Binding to the Surfaces of Calcium Hydroxide, Hydrated Calcium Aluminate, and

Calcium Silicate Phases. Chem. Mater. 2002, 14, 3539-3549.

(48) Gmira, A.; Zabat, M.; Pellenq, R. J. M.; Van Damme, H. Microscopic Physical

Basis of the Poromechanical Behavior of Cement-Based Materials. Mater. Struct.

2004, 37, 3-14.

Page 56 of 64



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

57 of 64

(49) Su, X. T.; Garofalini, S. H. Atomistic Structure of Calcium Silicate Intergranular

Films Between Prism and Basal Planes in Silicon Nitride: A Molecular Dynamics

Study. J. Mater. Res. 2004, 19, 752-758.

(50) Cygan, R. T.; Liang, J. J.; Kalinichev, A. G. Molecular Models of Hydroxide,

Oxyhydroxide, and Clay Phases and the Development of a General Force Field. J.

Phys. Chem. B 2004, 108, 1255-1266.

(51) Kundu, T. K.; Rao, K. H.; Parker, S. C. Competitive Adsorption on Wollastonite:

An Atomistic Simulation Approach. J. Phys. Chem. B 2005, 109, 11286-11295.

(52) Perry, T. D.; Cygan, R. T.; Mitchell, R. Molecular Models of Alginic Acid:

Interactions with Calcium Ions and Calcite Surfaces. Geochimica et Cosmochimica

Acta 2006, 70, 3508-3532.

(53) Cruz-Chu, E. R.; Aksimentiev, A.; Schulten, K. Water-Silica Force Field for

Simulating Nanodevices. J. Phys. Chem. B 2006, 110, 21497-21508.

(54) Kalinichev, A. G.; Wang, J. W.; Kirkpatrick, R. J. Molecular Dynamics Modeling

of the Structure, Dynamics and Energetics of Mineral-water Interfaces: Application

to Cement Materials. Cem. Concr. Res. 2007, 37, 337-347.

(55) Kumar, P. P.; Kalinichev, A. G.; Kirkpatrick, R. J. Molecular Dynamics Simulation

of the Energetics and Structure of Layered Double Hydroxides Intercalated with

Carboxylic Acids. J. Phys. Chem. C 2007, 111, 13517-13523.

(56) Churakov, S. V.; Mandaliev, P. Structure of the Hydrogen Bonds and Silica Defects

in the Tetrahedral Double Chain of Xonotlite. Cem. Concr. Res. 2008, 38, 300-311.

Page 57 of 64



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

58 of 64

(57) Allen, J. P.; Gren, W.; Molinari, M.; Arrouvel, C.; Maglia, F.; Parker, S. C.

Atomistic Modelling of Adsorption and Segregation at Inorganic Solid Interfaces.

Mol. Simul. 2009, 35, 584-608.

(58) de Leeuw, N. H. Computer Simulations of Structures and Properties of the

Biomaterial Hydroxyapatite. J. Mater. Chem. 2010, 20, 5376-5389.

(59) Kalinichev, A. G.; Kumar, P. P.; Kirkpatrick, R. J. Molecular Dynamics Computer

Simulations of the Effects of Hydrogen Bonding on the Properties of Layered

Double Hydroxides Intercalated with Organic Acids. Phil. Mag. 2010, 90, 2475-

2488.

(60) Pellenq, R. J. M.; Kushima, A.; Shahsavari, R.; Van Vliet, K. J.; Buehler, M. J.; Yip,

S.; Ulm, F. J. A realistic molecular model of cement hydrates. Proc. Natl. Acad. Sci.

USA 2009, 38, 16102-16107.

(61) Shahsavari, R.; Pellenq, R. J. M.; Ulm, F. J. Empirical Force Fields for Complex

Hydrated Calcio-Silicate Layered Materials. Phys. Chem. Chem. Phys. 2011, 13,

1002-1011.

(62) Dolado, J. S.; Griebel, M.; Hamaekers, J.; Heber, F. The Nano-Branched Structure

of Cementitious Calcium-Silicate-Hydrate Gel. J. Mater. Chem. 2011, 21, 4445-

4449.

(63) Serafin, F. G. Amide Grinding Aid (U.S. Patent No. 3,459,570, August 5, 1969).

(64) (a) Sun, H.; Mumby, S. J.; Maple, J. R.; Hagler, A. T. An Ab-initio CFF93 All-

atom Force Field for Polycarbonates. J. Am. Chem. Soc. 1994, 116, 2978-2987. (b)

Maple, J. R., Thacher, T. S., Dinur, U.; Hagler, A. T. Biosym Force Field Research

Results in New Techniques for the Extraction of Inter and Intramolecular Forces.

Page 58 of 64



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

59 of 64

Chem. Des. Autom. News 1990, 5, 5-10. (c) Sun, H. Force Field for Computation of

Conformational Energies, Structures, and Vibrational Frequencies of Aromatic

Polyesters. J. Comput. Chem. 1994, 15, 752-768. (d) Hill, J.-R.; Sauer, J. Molecular

Mechanics Potential for Silica and Zeolite Catalysts Based on Ab-initio

Calculations. 1. Dense and Microporous Silica. J. Phys. Chem. 1994, 98, 1238-1244.

(e) Sun, H. Ab-initio Calculations and Force-Field Development for Computer

Simulation of Polysilanes. Macromolecules 1995, 28, 701-712.

(65) Sun, H. COMPASS: An Ab-initio Force-Field Optimized for Condensed-Phase

Applications - Overview with Details on Alkane and Benzene Compounds. J. Phys.

Chem. B 1998, 102, 7338-7364.

(66) Dauber-Osguthorpe, P.; Roberts, V. A.; Osguthorpe, D. J.; Wolff, J.; Genest, M.;

Hagler, A. T. Structure and Energetics of Ligand Binding to Proteins: Escherichia

coli Dihydrofolate Reductase-Trimethoprim, A Drug-Receptor System. Proteins:

Struct. Funct. Genetics 1988, 4, 31-47.

(67) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. Development and Testing of the

OPLS All-Atom Force Field on Conformational Energetics and Properties of

Organic Liquids. J. Am. Chem. Soc. 1996, 118, 11225-11236.

(68) Pearlman, D.A.; Case, D. A.; Caldwell, J. W.; Ross, W. S.; Cheatham, T. E.;

DeBolt, S.; Ferguson, D.; Seibel, G.; Kollman, P. AMBER, a Package of Computer

Programs for Applying Molecular Mechanics, Normal Mode Analysis, Molecular

Dynamics and Free Energy Calculations to Simulate the Structural and Energetic

Properties of Molecules. Comp. Phys. Comm. 1995, 91, 1-41.

Page 59 of 64



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

60 of 64

(69) MacKerell, A. D., Jr. et al. All-Atom Empirical Potential for Molecular Modeling

and Dynamics Studies of Proteins. J. Phys. Chem. B 1998, 102, 3586-3616.

(70) Heinz, H.; Suter, U. W. Surface Structure of Organoclays. Angew. Chem. Int. Ed.

2004, 43, 2239-2243.

(71) Heinz, H.; Vaia, R. A.; Koerner, H.; Farmer, B. L. Photoisomerization of

Azobenzene Grafted to Montmorillonite: Simulation and Experimental Challenges.

Chem. Mater. 2008, 20, 6444-6456.

(72) Zartman, G. D.; Liu, H.; Akdim, B.; Pachter, R.; Heinz, H. Nanoscale Tensile,

Shear, and Failure Properties of Layered Silicates as a Function of Cation Density

and Stress. J. Phys. Chem. C 2010, 114, 1763-1772.

(73) Feng, J.; Pandey, R. B.; Berry, R. J.; Farmer, B. L.; Naik, R. R.; Heinz, H.

Adsorption Mechanism of Single Amino Acid and Surfactant Molecules to Au {111}

Surfaces in Aqueous Solution: Design Rules for Metal-Binding Molecules. Soft

Matter 2011, 7, 2113-2120.

(74) Mumme, W. G. Crystal Structure of Tricalcium Silicate from a Portland Cement

Clinker and its Application to Quantitative XRD Analysis. Neues Jahrbuch fur

Mineralogie 1995, 4, 145-160.

(75) Jeffery, J. W. The Crystal Structure of Tricalcium Silicate. Acta Crystallographica

1952, 5, 26-35.

(76) Fu, Y. T.; Heinz, H. Cleavage Energy of Alkylammonium-Modified

Montmorillonite and Relation to Exfoliation in Nanocomposites: Influence of

Cation Density, Head Group Structure, and Chain Length. Chem. Mater. 2010, 22,

1595-1605.

Page 60 of 64



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

61 of 64

(77) Batsanov, S. S. Van der Waals Radii of Elements. Inorganic Mater. 2001, 37, 871-

885.

(78) Halgren, T. A. Representation of van der Waals (vdW) Interactions in Molecular

Mechanics Force Fields: Potential Form, Combination Rules, and vdW Parameters.

J. Am. Chem. Soc. 1992, 114, 7827-7843.

(79) (a) Ghosh, S. N.; Chatterjee, A. K. Absorption and Reflection Infra-red Spectra of

Major Cement Minerals, Clinkers, and Cements. J. Mater. Sci. 1974, 9, 1577-1584

(b) Delgado, A. H.; Paroli, R. M.; Beaudoin, J. J. Comparison of IR Techniques for

the Characterization of Construction Cement Minerals and Hydrated Products.

Appl. Spectroscopy 1996, 50, 970-976 (c) Hughes, T. L.; Methven, C. M.; Jones, T.

G. J.; Pelham, S. E.; Fletcher, P.; Hall, C. Determining Cement Composition by

Fourier Transform Infrared Spectroscopy. Adv. Cem. Based Mater. 1995, 2, 91-104.

(80) Velez, K.; Maximilien, S.; Damidot, D.; Fantozzi, G.; Sorrentino, F. Determination

by Nanoindentation of Elastic Modulus and Hardness of Pure Constituents of

Portland Cement Clinker. Cem. Concr. Res. 2001, 31, 555-561.

(81) Camilleri, J.; Montesin, F. E.; Brady, K.; Sweeney, R.; Curtis, R. V.; Ford, T. R. P.

The Constitution of Mineral Trioxide Aggregate. Dental Mater. 2005, 21, 297-303.

(82) Giese, R. F. Surface Energy Calculations for Muscovite. Nature 1974, 248, 580-581.

(83) Brunauer, S.; Kantro, D. L.; Weise, C. H. The Surface Energies of Calcium Oxide

and Calcium Hydroxide. Canadian J. Chem. 1956, 34, 729-742.

(84) CRC Handbook of Chemistry and Physics, ed. 89th, Lide, D. R., ed.; CRC Press,

Boca Raton, FL, 2008.

Page 61 of 64



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

62 of 64

(85) Barret, P.; Menetrier, D.; Bertrandie, D. Mechanism of C3S Dissolution and

Problem of the Congruency in the Very Initial Period and Later On. Cem. Concr.

Res. 1983, 13, 728-738.

(86) Taylor, H. F. W. et al. The Hydration of Tricalcium Silicate. Mater. Struct. 1984, 17,

457-468.

(87) Giese, R. F.; van Oss, C. J. Colloid and Surface Properties of Clays and Related

Minerals; Marcel Dekker: New York, 2002.

(88) Marazzani, B.; Kurz, C.; Burge, C.; Muller, T. Dialkanolamine als Additive zum

Mahlen von Feststoffen (European Patent No. 2,527,307 A1, November 28, 2012).

(89) Fu, Y. T.; Heinz, H. Structure and Cleavage Energy of Surfactant-Modified Clay

Minerals: Influence of CEC, Head Group, and Chain Length. Philosophical Mag.

2010, 90, 2415-2424.

(90) Heinz, H. Clay Minerals for Nanocomposites and Biotechnology: Surface

Modification, Dynamics and Responses to Stimuli. Clay Minerals 2012, 47, 205-

230.

(91) Materials Studio 4.0, Cerius2, and Discover programs; Accelrys, Inc., San Diego,

2006.

(92) Brunauer, S.; Emmett, P. H.; Teller, E. Adsorption of Gases in Multimolecular

Layers. J. Am. Chem. Soc. 1938, 60, 309-319.

(93) Andersen, H. C. Molecular Dynamics Simulations at Constant Pressure and/or

Temperature. J. Chem. Phys. 1980, 72, 2384-2393.

(94) Parrinello, M.; Rahman, A. Polymorphic Transitions in Single Crystals: A New

Molecular Dynamics Method. J. Appl. Phys. 1981, 52, 7182-7190.

Page 62 of 64



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

63 of 64

(95) Roosen, A. R.; McCormack, R. P.; Carter, W. C. Wulffman: A Tool for the

Calculation and Display of Crystal Shapes. Comput. Mater. Sci. 1998, 11, 16-26.

See also: http://www.ctcms.nist.gov/wulffman/index.html.

(96) Heinz, H. Computational Screening of Biomolecular Adsorption and Self-Assembly

on Nanoscale Surfaces. J. Comput. Chem. 2010, 31, 1564-1568.

(97) Plimpton, S. J. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J.

Comp. Phys. 1995, 117, 1-19.

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