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(How) Can C-S-H Growth BehaviorBe Predicted?

Jeff Bullard

Materials and Construction Research DivisionNational Institute of Standards and Technology

Gaithersburg, Maryland USA

Questions from a Modeling Perspective

VCCTL Consortium


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Objectives of Modeling

Primary purposes of modeling are to:

Gain Insight: Distill real system into one with simplerphysics/chemistry that you think are relevant. Analyzebehavior of model to better understand qualitative behavior

of the real system. Represents a research tool.

Predict: Use basic mathematical equations, perhaps withsome physical basis, having fitting parameters that can becalibrated to experiment. Use to interpolate predictions onsimilar systems... an empirical approach.

Both: Build as much realistic physics/chemistry back intothe research tool to gain better quantitative predictions.Represents a design tool.


3/15

A Sampling of Cement Hydration Models

HYMOSTRUC (TU Delft):

multi-parameter semi-empirical equation for kinetics, based onPSD, w/c ratio, and clinker composition

C-S-H assumed as a continuous layer around spherical particles

IC (EPFL): modeling platform for representing microstructure

user-defined kinetic equations (Avrami-type, multi-parametersemi-empirical, etc.)

user specifies growth rules for C-S-H and CH

CEMHYD3D (NIST):

discretized, heterogeneous particles

probabilistic rules for dissolution, nucleation, growth

rules calibrated to simulate OPC hydration


4/15

Materials Science Microstructure Models

Cellular Automaton Models

:

Used to simulate dendrite growth and morphology duringsolidification, recrystallization, grain growth, etc.

Crystallographic orientation dependence

Phase Field Models: Based on localized reduction in free energy using TDGL

Captures phase separation, solidification, coarsening, sintering

Parameters directly linked to local composition and phasevolume fraction


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Localized Kinetic Description

Let be a material parameter that can be distributed heterogeneously in a system(like a microstructure representation)

In any volume element small enough that and all other parameters areapproximately homogeneously distributed, then

Examples:

Rate of change of = (Kinetic factor)(Thermodynamic driving force)

c =Dc

kT

2

[C] = k+ {A}{B}

1

K

Keq

Single component diffusion

Rate of elementary reaction

A + BC


6/15

Why is a Localized Description Important?

1. Cement paste has heterogeneous phase distribution and composition

2. Dissolution, nucleation, and growth are mediated by pore solution.

3. Driving force, e.g. saturation index, for each phase is generally different from pointto point

4. Location and morphology of precipitated phases is inherently localized

5. The parameters describing the process are actual physical/chemical properties ofthe materials comprising the system, instead of model-dependent empiricalparameters

6. Any change to the system that affects local driving force or kinetics can be

accommodated naturally

w/c, particle size distribution, temperature, chemicaladditives.


7/15

Why is a Localized Description Important?

1 m 1 m

I.G. Richardson, Cem. Concr. Res. 34 (2004) 1733

IP

OP

M.G. Juenger et al, J. Mater. Sci. Lett. 22 (2003)1335

P.E. Stutzman, Ch. 14 in FHWA Petrographic Manual,

FHWA-HRT-04-150 (2006)

Morphology of C-S-H varies significantly over smalldistances.

Therefore, morphology appears to be governed bysome differences in local growth conditions:

(solution chemistry, confinement ... ?)


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What are the Effects of Length Scale?

I.G. Richardson, Cem. Concr. Res. 34 (2004) 1733A. Allen J. Thomas, H. Jennings , Nature Mater. 6(2007) 311

If C-S-H is built from 5-nm bricks, then

1. What determines how the bricks assemble together at greater length scales?

2. How can bricks collectively know whether to grow as foils, fibers, etc., andwhat determines the fiber width and length?


9/15

What are the Effects of Solution Chemistry?

Several studies have indicated a compositionrange for C-S-H gel

C-S-H(I) has Ca/Si ~ 1.2 and forms insolutions with low Ca/Si ratios. Reported toform a dense layer on C3S surfaces

C-S-H(II) has Ca/Si ~ 2 and forms in solutionswith high Ca/Si ratios. Reported to be lessdense, less protective on C3S

S. Garrault-Gauffinet and A. Nonat, J. Crystal Growth 200 (1999) 565

S. Garrault-Gauffinet and A. Nonat, Langmuir 17(2001) 8131

Pore solution chemistry also influences the

kinetics of hydration dramatically

Nonat and coworkers also argue that solutionchemistry affects the growth anisotropy of C-S-Hnuclei on C3S surfaces


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Each lattice site has a set ofoccupation numbers, {N} ofcellsof each type of substance. = C

Cells at a given node can, with defined probability

Diffuse, with specific mobility, to a neighboring node

React with other cells at that node according to values of {N}and a given rate constant for the reaction

HydratiCA: Operating Principles

Site0 Site1 Site n

. . .


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C3S Hydration Simulation

25

m

Real-shape particlesobtained by FIB (R. Flattand L. Holzer)

w/c = 1.4


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= 1.0 m/site, with C-S-H(m)

log Ksp(C3S) = 0.48

log Ksp(C-S-H(m)) = -17.1

Open points are experimental

data from Garrault and Nonat

C3S Simulations

0 5 10 15 20 25time (min)

100

101

102

103

[H2

SiO4

2-](mol/L)

11 mmol/L experiment


[Ca2+

] = 11 mmol/L

[Ca2+

] = 22 mmol/L

Experimental data from S. Garrault and A.Nonat, Langmuir, 17 8131-8138 (2001)

0 100 200 300 400 500 600time (min)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

DegreeofHydration



[Ca2+

] = 11 mmol/L

[Ca

2+

] = 22 mmol/L

Unconstrained


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0 200 400 600 800t (min)

0.00

0.05

0.10

0.15

0.20

D

egree

ofHydration

22 mM Ca(OH)2

fixed

20 mM Ca(OH)2

20 mM CaCl2

Tricalcium Silicate, w/s = 0.75

375 m2/kg

Control

0 100 200 300 400t (min)

0.000

0.005

0.010

0.015

Ca(OH)2VolumeFraction

20 mM Ca(OH)2

20 mM CaCl2


375 m2/kg

Control

0 200 400 600 800t (min)

0.000

0.020

0.040

0.060

0.080

C-S-H

VolumeFraction

20 mM Ca(OH)2

20 mM CaCl2


375 m2/kg

Control

Example: Influence of Calcium Salts

Ca(OH)2 is predicted to delay hydration ofC3S, extending the induction period andreducing hydration rates everywhere.

CaCl2 is predicted to have no effect on theinduction period, but to acceleratehydration through more rapid growth ofhydration products.


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Ongoing Questions

1. These simulations assume that reaction order is equal to the molecularity. Can weobtain experimental measurements of reaction order, i.e. rate law, for growth of C-S-Hand other complex minerals like ettringite?

2. These simulations assume that C-S-H nucleates heterogeneously on C3S surfaces, butthere are reports that C-S-H may rapidly fill capillary pore space at very early agesand then densify with time. What mechanism could explain this rapid growth?

3. How do other solution components, especially aluminates and other anions (Cl-,SO42-) affect C-S-H in terms of its growth rate constant, its composition, itsmorphology, and its density?

4. Can we characterize C3S surfaces to better understand how its dissolution rate varieswith time (see talk by Patrick Julliand) ?

5. HydratiCA simulations indicate that induction period can be modeled well byassuming either (a) low-solubility C3S surface or (b) high-solubility C3S surfaceprotected by a metastable layer of a calcium silicate hydrate (Stein & Stevels). Canexperiments be devised to distinguish between these two mechanisms?


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Outlook

Many questions persist about the nature of C-S-H growth kinetics and morphology

A model framework that uses a localized description of microstructure evolution canprovide much-needed links between solution chemistry, temperature, and materialproperties that are not provided by other kinds of cement hydration models.HydratiCA is one example.

This modeling approach requires knowledge about fundamental properties ormaterials and their interactions with water: Keq, growth and dissolution rate constants,density, activation energies, adsorption isotherms for impurities, nucleation barriers.

Also requires more research into the link between nanoscale C-S-H structure and theemergence of various C-S-H morphologies. We can build this detail into the model ifwe understand the mechanism.

As more fundamental information becomes available, it can be incorporated into thismodeling approach and make the model increasingly powerful

This will require a sustained collaboration between experimentalists and modelers

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