# Presentation: 638971

## A New Model for Predicting Hydration Kinetics and Microstructure Development in Cement Paste

**Jeff Bullard**
**NIST**

- ACBM Technical Review, March 2006

**Notes:**
This work grows out of the VCCTL consortium effort.  Some members represented here.
 Idea is to push the hydration modeling work, addressing as many shortcomings of current models as possible.
 To motivate why we are doing this, and what we are trying to achieve with a new model, we need to review:
What makes hydration microstructure modeling difficult?
What can current models do well, and what they can’t do well

## 
Tricalcium Silicate (idealized)

Dissolution
Ca3SiO5 + 3 H2O  3 Ca2+ + H2SiO42- + 4 OH-

Growth of C-S-H
x Ca2+ + H2SiO42- + 2(x-1) OH-  CaOx–SiO2–H2O

Growth of Portlandite
Ca2+ + 2 OH-  Ca(OH)2

Value of x depends on local pore solution 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-  CaOx–SiO2–H2O
- _Growth of Portlandite_
- Ca2+ + 2 OH-  Ca(OH)2
- Value of x depends on local pore solution chemistry

**Modeling Challenges:  ****Chemistry**

**Notes:**
Don’t need an exhaustive review of hydration chemistry or reactions
Point is that hydration involves the dissolution of ionic species from several anhydrous minerals
Common ion effects
Mechanisms of dissolution, diffusion, nucleation, growth
Hydration products do not have fixed composition

## 	Tricalcium Aluminate (idealized)

	Net Reactions Without Gypsum or CH
2 C3A + 27 H  C2AH8 + C4AH19  C3AH6 
C3A + 6 H  C3AH6      (> 30 °C)

Net Reactions With CH
C3A + CH + 12 H  C4AH13

Net Reactions With Gypsum (> 2-3%)
C3A + 3 CSH2 + 26 H  C6AS3H32      (initial)

_**	**__**Net Reactions**__ Without Gypsum or CH_
- 2 C3A + 27 H  C2AH8 + C4AH19  C3AH6
- C3A + 6 H  C3AH6      (> 30 °C)
_**Net Reactions **__With CH_
- C3A + CH + 12 H  C4AH13
_**Net Reactions **__With Gypsum (> 2-3%)_
- C3A + 3 C_S_H2 + 26 H  C6A_S_3H32      (initial)

**Modeling Challenges:  ****Chemistry**

**Notes:**
Reactions that happen depend on the reactants available in time and space
Successful model must be able to automatically handle
Multiple simultaneous reactions
Temperature dependence of rates (kinetics) and solubility (thermodynamics)

## Modeling Challenges:  Structure

**Modeling Challenges:  ****Structure**

- ACBM Technical Review, March 2006

- Micro-scale

- 75 μm

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

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

**Notes:**
The local microstructure influences kinetics and the properties that we are trying to track

Two main effects on kinetics: WATER AVAILABILITY and C-S-H BARRIER GROWTH

## Modeling Challenges:  Structure

**Modeling Challenges:  ****Structure**

- ACBM Technical Review, March 2006

- Nano-scale

- 50 nm

- CaxSiO(2+x)·H2O

**Porosity**

- “IP”

- “OP”

***Micrograph courtesy of I.G. Richardson,***
***University of Leeds***

**Notes:**
Another challenge is that the structure depends on the power of your microscope.
At least two “types” of C-S-H: what determines where/when they form
Structure at nanometer length scales influences properties and is INFLUENCED BY THE CURING CONDITIONS... (see next slide)

## Modeling Challenges:  Structure

- C3S Paste, 20°C, 8 yr

- C3S Paste, 80°C, 8 d

- “IP”

- “OP”

- “IP”

- “OP”

***Micrographs courtesy of I.G. Richardson,***
***University of Leeds***

**Modeling Challenges:  ****Structure**

**Notes:**
With these challenges (chemical and structural) in mind, let’s review what the current microstructure models can (and can’t) do to address these challenges...

## CEMHYD3D (NIST)

- Digital image basis

**Some Available Models**

- ACBM Technical Review, March 2006

**Notes:**
Make first two points, then switch to next slide...

## K

- Ca

- Si

**K**

- Al

- ... X-ray element
-      maps ...

- ... segment image into **phases **...

- SEM/BSE Image...

- Measure autocorrelation fns on majority phases

- ... Particle Size Distribution ...

_**Contributors**_**:  D. Bentz and P. Stutzman**

## CEMHYD3D (NIST)

- Digital image basis
- Accurate microstructure representation
- Rule-based to mimic reaction and diffusion

**Some Available Models**

- ACBM Technical Review, March 2006

**Notes:**
Make first two points, then switch to next slide...

## 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”

**Notes:**
One of the advantages of an Internet-based system is the worldwide accessibility it provides.  The cement images database can be accessed anywhere worldwide using a Web browser (Netscape, Internet Explorer, etc.)  The files can also be downloaded from an anonymous ftp site maintained at NIST.  The site is at ftp.nist.gov  and the files are in subdirectories under the pub/bfrl/bentz/CEMHYD3D/images directory.

## 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

**Some Available Models**

- ACBM Technical Review, March 2006

**Notes:**
Make first two points, then switch to next slide...

## 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

**Some Available Models**

- ACBM Technical Review, March 2006

## 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

**New Model: ****HydratiCA**

- ACBM Technical Review, March 2006

**Notes:**
New model should retain as much of the power of current microstructure models as possible, yet
Incorporates real kinetics (reductionist approach).  Parameters that can be measured and mean something
Is able to be extended to new cement compositions with minimum effort
Exhibits numerical convergence

## Mesh Class

_**Node Class**_

- neighbors, volume, materials,
- methods for transport and rx

_**Base Material Class**_

- (Liquid, Solid, Gel, Crystal, Solute)

_**Ion Database Class**_

- ID, mol wt, radius, intrinsic diffusivity, charge
- (immutable)

- Dimensions, resolution, clock, phase stats, thermal condition, moisture conditions, databases

- ID, composition, ,  , Cp, porosity,
- mobility, virtual methods for material-specific behavior

_**Derived Material Classes**_

- Methods for material-specific behavior
- encoded here

_**Material Database Class**_

_**Reaction Database Class**_

- ID, reactants, products, molar stoichiometric coefficients, reaction enthalpy, activation enthalpy, equilibrium constant baseline rate constant

- ACBM Technical Review, March 2006

**Notes:**
HydratiCA is object-oriented, written in C++.  Allows materials to be treated in customized ways.  “Automatic” behavior of different materials

## HydratiCA:  Modeling Aqueous Diffusion

- ACBM Technical Review, March 2006

## p = D t/2

- ACBM Technical Review, March 2006

- 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 t/2

## Non-steady state diffusion of neutral solute

- 15 mM

- 5 mM

- 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

## Non-steady state diffusion of neutral solute

**Non-steady state diffusion of neutral solute**

- ACBM Technical Review, March 2006

## HydratiCA:  Ionic Diffusion

- ACBM Technical Review, March 2006

- 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

## Coupled diffusion of ions

**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

## HydratiCA:  Modeling Chemical Reactions

- ACBM Technical Review, March 2006

## HydratiCA:  Modeling Chemical Reactions

- ACBM Technical Review, March 2006

- 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

- a A + b B   c C

*k*

## HydratiCA:  Modeling Equilibrium

- ACBM Technical Review, March 2006

- a A + b B   c C

*k**f*

- c C   a A + b B

*k**r*

- At equilibrium:

## Solution

- Ca(OH)2

- Periodic

- Periodic

- Periodic

- Periodic

**10 x 10 x 10 nodes**
**Node spacing**** ********= 3 μm**
**T = 298 K**

**HydratiCA:  Modeling Reactions**

- ACBM Technical Review, March 2006

- Ca(OH)2        Ca2+ + 2OH-

*k**f* = 2.17x10-7 moles/m2/s
*k**r* = 3.29x10-3 moles/m2/s

*k**f*

*k**r*

## HydratiCA:  Chemical Equilibrium

- ACBM Technical Review, March 2006

**HydratiCA:  Chemical Equilibrium**

- Equilibrium

- Precipitation

- Dissolution

- Ca(OH)2        Ca2+ + 2OH-

*k**f*

*k**r*

*k**f* = 2.17x10-7 moles/m2/s
*k**r* = 3.29x10-3 moles/m2/s

## HydratiCA:  Temperature Effects

- x

- *

- Hr

- Hp

- H*rev

- H*f

**HydratiCA:  Temperature Effects**

- ACBM Technical Review, March 2006

**Notes:**
The (thermodynamic) influence of temperature on solubility is captured by the (kinetic) activation enthalpies of the forward and reverse reactions.

## HydratiCA:  Temperature Effects

**HydratiCA:  Temperature Effects**

- ACBM Technical Review, March 2006

**Notes:**
Because the temperature effects are accounted in the kinetic terms, HydratiCA captures both temperature effects simultaneously:  (1) accelerated reaction kinetics at higher temperatures; (2) modified solubility (thermodynamic) at different temperatures.

## 

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).

- 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

**HydratiCA:  Nucleation**

**Notes:**
The physics of nucleation involves the product of two terms: (1) a VERY large exponential prefactor, and (2) an exponential term that has a VERY large negative exponent.  The balance of these two terms is extremely sensitive to the local environments (local saturation index).

Note that the nucleation work depends explicitly on the saturation index:  this reflects the dependence of the size of the critical nucleus on the bulk driving force for precipitation.

## Solution

- Inert

- Periodic

- Periodic

- Periodic

- Periodic

**10 x 10 x 10 nodes**
**Node spacing**** ********= 3 μm**
**T = 298 K**

**HydratiCA:  Modeling Nucleation**

- ACBM Technical Review, March 2006

- Ca(OH)2        Ca2+ + 2OH-

*k**f* = 2.17x10-7 moles/m2/s
*k**r* = 3.29x10-3 moles/m2/s

*k**f*

*k**r*

## HydratiCA:  Nucleation

- Ca2+ + 2OH-                 Ca(OH)2

- ACBM Technical Review, March 2006

## Nucleation sites distinguished by

_**Dirt Speck in Water**_

_**Surface Nucleation**_

**Nucleation sites distinguished by**
**nucleation work**

- ACBM Technical Review, March 2006

## HydratiCA:  Modeling Hydration of C3S

- ACBM Technical Review, March 2006

## 
Requires assumptions about chemical reactions and mechanisms
Alternative theories can, in principle, be tested by HydratiCA
First theory tested:  Garrault and Nonat, Langmuir 17, 8131–8138 (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.

- Requires assumptions about chemical reactions and mechanisms
- Alternative theories can, in principle, be tested by HydratiCA
- First theory tested:  Garrault and Nonat, *Langmuir* 17, 8131–8138 (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.

**HydratiCA:  Hydration of C****3****S**

- ACBM Technical Review, March 2006

**Notes:**
HydratiCA partially captures autocatalytic behavior of precipitation reactions without any modifications.  When the precipitate exceeds the node volume, the number of growth sites per precipitate increases roughly as the volume of the precipitate.  To capture very early age behavior, we may need to make the growth rate of supercritical embryos depend explicitly on their size while they are still smaller than the node size.

## H2O

- C3S

- Periodic

- Periodic

- Periodic

- Periodic

**25 x 25 x 25 nodes**
**Node spacing**** ********= 4 μm**
**T = 298 K**

- w/c = 0.3125
- 4 m2/kg

**HydratiCA:  Hydration of C****3****S**

- ACBM Technical Review, March 2006

## HydratiCA:  Hydration of C3S

- For this **original choice** of parameters, the silicate concentration reaches a local maximum at about 6 minutes.

**HydratiCA:  Hydration of C****3****S**

- ACBM Technical Review, March 2006

## 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.

**HydratiCA:  Hydration of C****3****S**

- ACBM Technical Review, March 2006

## HydratiCA:  Hydration of C3S

- Control Variables:
*k*diss = 1.0 x 10-4 mole/s
- Nuc rate coefficient = 109 s-1
- CSH transport factor = 0.3 P

**HydratiCA:  Hydration of C****3****S**

- ACBM Technical Review, March 2006

## 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

**HydratiCA:  Hydration of C****3****S**

- ACBM Technical Review, March 2006