Presentation at Holcim, May 1, 2002

1
A New Model for Predicting Hydration Kinetics and
Microstructure Development in Cement Paste
Jeff Bullard NIST
ACBM Technical Review, March 2006
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Modeling Challenges Chemistry

• Tricalcium Silicate (idealized)
• Dissolution
• Ca3SiO5 3 H2O ? 3 Ca2 H2SiO42- 4 OH-
• Growth of C-S-H
• x Ca2 H2SiO42- 2(x-1) OH- ? CaOxSiO2H2O
• Growth of Portlandite
• Ca2 2 OH- ? Ca(OH)2
• Value of x depends on local pore solution
  chemistry

3
Modeling Challenges Chemistry

• Tricalcium Aluminate (idealized)
• Net Reactions Without Gypsum or CH
• 2 C3A 27 H ? C2AH8 C4AH19 ? C3AH6
• C3A 6 H ? C3AH6 (gt 30 C)
• Net Reactions With CH
• C3A CH 12 H ? C4AH13
• Net Reactions With Gypsum (gt 2-3)
• C3A 3 CSH2 26 H ? C6AS3H32 (initial)

4
Modeling Challenges Structure
Micro-scale

• Kinetic Implications
• Nucleation sites
• C-S-H growth diffusion barrier
• Water availability

75 µm

• Property Implications
• Porosity forms 3-D percolating network
• Solids may begin as percolating (or not) soft
  clusters later form stiff percolating network

ACBM Technical Review, March 2006
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Modeling Challenges Structure
Nano-scale
IP
OP
Porosity
Micrograph courtesy of I.G. Richardson, University
of Leeds
50 nm
CaxSiO(2x)H2O
ACBM Technical Review, March 2006
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Modeling Challenges Structure
Nano-scale
C3S Paste, 20C, 8 yr
IP
OP
IP
Micrographs courtesy of I.G. Richardson, Universit
y of Leeds
OP
C3S Paste, 80C, 8 d
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Some Available Models

• CEMHYD3D (NIST)
• Digital image basis

ACBM Technical Review, March 2006
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SEM/BSE Image
Ca
Si
Al
Particle Size Distribution
K
K
X-ray element maps
segment image into phases
Measure autocorrelation fns on majority phases
Contributors D. Bentz and P. Stutzman
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Some Available Models

• CEMHYD3D (NIST)
• Digital image basis
• Accurate microstructure representation
• Rule-based to mimic reaction and diffusion

ACBM Technical Review, March 2006
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CEMHYD3D

• Cellular automaton approach
• Each volume element is an independent agent that
  can
• Dissolve
• Diffuse
• React

Pore solution
Stepwise random walk on lattice
Collisions between agents, governed by reaction
rules
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Some Available Models

• CEMHYD3D (NIST)
• Digital image basis
• Accurate microstructure representation
• Rule-based to mimic reaction and diffusion
• Little or no kinetic information
• Magic resolution of 1 µm
• Primarily interpolative

ACBM Technical Review, March 2006
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Some Available Models

• HYMOSTRUC (TU Delft) IPK (EPFL)
• Continuum basis
• Chemically homogenized particles
• Hydration modeled as growth of interparticle
  contacts
• Phenomenological kinetic equations (e.g.
  Johnson-Avrami-Mehl)
• Not easily extensible

ACBM Technical Review, March 2006
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New Model HydratiCA

• Discretize on regular grid
• Retain power of CEMHYD3D microstructure
  representation
• Stochastic methods for diffusion and reaction
• Algorithms are mechanistically based, and
  converge to standard PDE rate equations
• Scalable and extensible
• Applies to general aqueous mineral systems

ACBM Technical Review, March 2006
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Mesh Class
Dimensions, resolution, clock, phase stats,
thermal condition, moisture conditions, databases
Node Class
neighbors, volume, materials, methods for
transport and rx
Derived Material Classes
Material Database Class
(Liquid, Solid, Gel, Crystal, Solute)
Methods for material-specific behavior encoded
here
Reaction Database Class
ID, reactants, products, molar stoichiometric
coefficients, reaction enthalpy, activation
enthalpy, equilibrium constant baseline rate
constant
Base Material Class
ID, composition, ?, ?, Cp, porosity,
mobility, virtual methods for
material-specific behavior
Ion Database Class
ID, mol wt, radius, intrinsic diffusivity,
charge (immutable)
ACBM Technical Review, March 2006
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HydratiCA Modeling Aqueous Diffusion
ACBM Technical Review, March 2006
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HydratiCA Modeling Aqueous Diffusion

• Based on a random walker algorithm
• Each computational node contains a number of
  cells of solute and water
• In any time step, each cell can execute a single
  step in a random direction
• Probability of stepping is proportional to the
  solute mobility and the time increment

p D Dt/l2
ACBM Technical Review, March 2006
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Non-steady state diffusion of neutral solute
15 mM
5 mM
l
l
l
100 µm

• C(x,y,z,0) 0
• C(0,y,z,t) 15 mM
• C(100,y,z,t) 5 mM

ACBM Technical Review, March 2006
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Non-steady state diffusion of neutral solute
ACBM Technical Review, March 2006
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HydratiCA Ionic Diffusion

• Effective mobility of a charged species is
  influenced by long-range Coulombic interactions
  with other charged species
• Local charge neutrality is required, even though
  different ions have different intrinsic diffusion
  coefficients
• HydratiCA can estimate the electrostatic
  potential at each time step, and include it in
  the electrochemical potential
• Results in biased random walk

ACBM Technical Review, March 2006
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Coupled diffusion of ions
DCa 0.7 x 10-5 cm2/s DOH 5.3 x 10-5 cm2/s
ACBM Technical Review, March 2006
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HydratiCA Modeling Chemical Reactions
ACBM Technical Review, March 2006
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HydratiCA Modeling Chemical Reactions
k
a A b B ? c C

• Reaction events are localized within a node
• List of available reactants is generated and
  compared against reaction database
• List of possible reactions is built
• Reaction randomly selected from list
• Unit reaction is executed (n cells of A and m
  cells of B are removed, p cells of C are added)
  on a probabilistic basis
• Probability proportional to rate constant k

ACBM Technical Review, March 2006
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HydratiCA Modeling Equilibrium
kf
a A b B ? c C
kr
c C ? a A b B
At equilibrium
ACBM Technical Review, March 2006
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HydratiCA Modeling Reactions
Periodic

• 10 x 10 x 10 nodes
• Node spacing l 3 µm
• T 298 K

Solution
Ca(OH)2 Ca2 2OH-
Periodic
Periodic
Ca(OH)2
kf
kr
kf 2.17x10-7 moles/m2/s kr 3.29x10-3
moles/m2/s
Periodic
ACBM Technical Review, March 2006
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HydratiCA Chemical Equilibrium
Precipitation
Ca(OH)2 Ca2 2OH-
Equilibrium
kf
kr
kf 2.17x10-7 moles/m2/s kr 3.29x10-3
moles/m2/s
Dissolution
ACBM Technical Review, March 2006
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HydratiCA Temperature Effects

DHf
DHrev
Hr
Hp
x
ACBM Technical Review, March 2006
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HydratiCA Temperature Effects
ACBM Technical Review, March 2006
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HydratiCA Nucleation

• Similar to nucleation of solid from a supercooled
  melt
• Literature review D. Kaschiev and G.M. van
  Rosmalen, Cryst. Res. Technol. 38 7-8 555-574
  (2003).

For spherical nuclei
ACBM Technical Review, March 2006
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HydratiCA Modeling Nucleation
Periodic

• 10 x 10 x 10 nodes
• Node spacing l 3 µm
• T 298 K

Solution
Ca(OH)2 Ca2 2OH-
Periodic
Periodic
Inert
kf
kr
kf 2.17x10-7 moles/m2/s kr 3.29x10-3
moles/m2/s
Periodic
ACBM Technical Review, March 2006
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HydratiCA Nucleation
Ca2 2OH- Ca(OH)2
ACBM Technical Review, March 2006
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Dirt Speck in Water
Surface Nucleation
Nucleation sites distinguished by nucleation work
ACBM Technical Review, March 2006
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HydratiCA Modeling Hydration of C3S
ACBM Technical Review, March 2006
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HydratiCA Hydration of C3S

• Requires assumptions about chemical reactions and
  mechanisms
• Alternative theories can, in principle, be tested
  by HydratiCA
• First theory tested Garrault and Nonat,
  Langmuir 17, 81318138 (2001).
• Coupled reactions
• Nucleation of C-S-H occurs on surface of C3S
• Growth of C-S-H is autocatalytic due to
  increased area of C-S-H surfaces for growth.

ACBM Technical Review, March 2006
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HydratiCA Hydration of C3S
Periodic

• 25 x 25 x 25 nodes
• Node spacing l 4 µm
• T 298 K

H2O
Periodic
Periodic
C3S
w/c 0.3125 4 m2/kg
Periodic
ACBM Technical Review, March 2006
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HydratiCA Hydration of C3S
For this original choice of parameters, the
silicate concentration reaches a local maximum at
about 6 minutes.
ACBM Technical Review, March 2006
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HydratiCA Hydration of C3S
pH increases rapidly over first few minutes,
then more slowly with increasing time as the
rates of consumption and production of OH- are
comparable.
ACBM Technical Review, March 2006
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HydratiCA Hydration of C3S

• Control Variables
• kdiss 1.0 x 10-4 mole/s
• Nuc rate coefficient 109 s-1
• CSH transport factor 0.3 P

ACBM Technical Review, March 2006
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HydratiCA Hydration of C3S

• The kinetic behavior depends on three main
  parameters
• C3S dissolution rate const.
• C-S-H nucleation work
• Homogeneous
• Heterogeneous
• C-S-H growth rate constant

Garrault/Nonat
Garrault/Nonat
ACBM Technical Review, March 2006