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SP-267—4
Influence of TiO2 Nanoparticles on
Early C3S Hydration
by B.Y. Lee, J.J. Thomas, M. Treager, and K.E. Kurtis
Synopsis: The effect of nano-anatase titanium dioxide (TiO2) powder on early age hydration kinetics of
tricalcium silicate (C3S) was investigated. Isothermal calorimetry was performed on C3S pastes with 0,
10, and 15% of TiO2 addition by weight, and two mathematical models–the Avrami model and the
boundary nucleation model (BN model)–were fitted to the data. The addition of TiO2 accelerated the
rate of hydration, increased the peak reaction rate, and increased the degree of hydration at 12 and
24 hours. The model fits demonstrate that the BN model better captures the kinetics of the reaction,
particularly in the deceleration period, than the Avrami model. The increase in the ratio of rate
parameters (kB/kG) of the BN model with TiO2 addition suggests that hydration product is formed on or
near the surfaces of TiO2 particles, as well as on the C3S surface. These results demonstrate that the
addition of TiO2 nanoparticles accelerates the early hydration by providing additional nucleation sites,
forming the foundation for future optimization of photocatalytic and other nanoparticle-containing
cements.
Keywords: Avrami model; kinetics; modeling; nucleation; titanium dioxide.
35
36
Lee et al.
ACI member Bo Yeon Lee is a PhD Candidate in the School of Civil and Environmental Engineering at Georgia
Institute of Technology, Atlanta, GA, where she also received her MS. She received her BS in architectural engineering from Yonsei University in Korea.
Jeffrey J. Thomas is a Research Associate Professor in the Department of Civil and Environmental Engineering at
Northwestern University. His research interests include modeling of the nanostructure and hydration kinetics of
cement-based materials.
Matthew Treager is an undergraduate in the School of Civil and Environmental Engineering at Georgia Institute
of Technology in Atlanta, GA.
ACI member Kimberly E. Kurtis is Associate Professor in the School of Civil and Environmental Engineering at
Georgia Institute of Technology. She is Chair of ACI Committee 236, Materials Science of Concrete, and is a
member of ACI Committee 201, Durability of Concrete; E802, Teaching Methods and Educational Materials, and
the Educational Activities Committee.
INTRODUCTION
Tricalcium silicate (3CaO·SiO2 or C3S) comprises about 50 to 70% of ordinary portland cement, and it hydrates
to form calcium silicate hydrate (C-S-H) gel, the primary binding constituent in ordinary concrete. It is of primary
importance to understand the hydration kinetics of C3S to predict the hydration kinetics of Portland cement (Fujii
and Kondo 1974; Tarrida et al. 1995; Berliner et al. 1998; Damasceni et al. 2002). There have been attempts to
approximate the kinetics of C3S hydration mathematically, and several mathematical models have been developed. The Avrami nucleation and growth model (Avrami 1939, 1940, 1941) is the most widely used model to
predict the early age hydration rate (Brown et al. 1985; FitzGerald et al. 1998; Thomas and Jennings 1999).
Recently, Thomas (2007) suggested that the boundary nucleation model (BN model), developed by Cahn
(1956) to describe a solid-solid phase transformation in a polycrystalline material, could better approximate
the process of C3S hydration than the Avrami model. While the Avrami model assumes that nucleation occurs
randomly throughout the transforming volume, the BN model assumes that nucleation is favored at grain boundaries, similar to the observation that C3S hydration occurs by the outward growth of hydration products from the
surface of the hydrating grains into the surrounding water-filled porosity. The BN model takes into account the
effect of the surface area of the starting material, which, in the case of hydrating cement or C3S, is known to have
a strong effect on the hydration kinetics.
In this research, early hydration of C3S was examined with two different addition levels of insoluble, nanoanatase titanium dioxide (TiO2) particles along with a control C3S without TiO2. The anatase form of TiO2 is known
for its photocatalytic smog-abating, self-cleaning, and biocidal capacities, which are especially efficient in nanocrystalline form (Carp et al. 2004; Fujishima and Zhang 2006). The addition of TiO2 to cement-based materials is
increasingly being researched and has been used in applications in various parts of the world (Beeldens 2007;
Kawakami et al. 2007; Poon and Cheung 2007; Jayapalan et al. 2009). The objective of this research is to verify
whether the surface area provided by nano-sized TiO2 affects the cement hydration rate and whether such an
effect can be captured by mathematical modeling. The model fit results from both the Avrami model and the BN
model will be compared, and the role of TiO2 in early age cement hydration will be discussed.
RESEARCH SIGNIFICANCE
Photocatalytic cementitious materials hold promise in the construction industry due to their potential for
smog-abatement, self-cleaning abilities, and biocidal applications (Carp et al. 2004; Fujishima and Zhang
2006). However, while practical use of these materials continues to grow, little has been published describing
the influence of photocatalytic nanoparticles on early age behavior of such cementitious materials (Jayapalan
et al. 2009). This research examines the influence of photocatalytic titanium dioxide dosage rates on early age
hydration of C3S by isothermal calorimetry, and compares it with two existing models on hydration kinetics. The
aim is to better understand the influence of the nanoparticles on hydration of Portland cement, forming the basis
for anticipating the influence of these nanoparticles on setting time, rate of strength gain, and durability.
THEORETICAL BACKGROUND
For the purpose of this research, it is useful to first review the hydration models considered.
1
THEORETICAL BACKGROUND
2
of Concrete:
Thereview
NexttheBig
Thing
Is Small
3
ForNanotechnology
the purpose of this research,
it is useful to first
hydration
models
considered.37
4
Avrami nucleation
growth
model and growth model
5 and
Avrami
nucleation
The theory was
first
treated
by
Kolmogorov
(1937),
Johnson
and Mehl (1939),
Avrami
(1939,
1941)
6
The theory
was first
treated
by Kolmogorov
(1937),and
Johnson
and
Mehl1940,
(1939),
andtoAvrami (1939, 19
explain the kinetics
of
phase
change
of
metals.
The
main
assumptions
made
were
that
the
new
phase
is
nucle7
1941) to explain the kinetics of phase change of metals. The main assumptions made were that the new phase
8 and
nucleated
by grain
germ centers
nuclei and
thatnew
the grain
of the new
phase arethroughout
randomly distributed
ated by germ nuclei
that the
of the
phasecenters
are randomly
distributed
the matrix.throughout the mat
9 mathematical
Due to its simple
mathematical
theory
has been
adapted
for
C
S
Due to its simple
form, the
theory hasform,
been the
widely
adapted
for Cwidely
S
hydration
(Brown
et
al. 1985; (Brown et al. 19
3 hydration
3
101998;FitzGerald
et al.Jennings
1998; Thomas
final forms
theintroduced
equations will
FitzGerald et al.
Thomas and
1999). and
OnlyJennings
the final1999).
formsOnly
of thethe
equations
willofbe
here.be introduced here.
11 volume The
transformed
volume of
fraction
X asbea written
functionas,
of time can be written as,
The transformed
fraction
X as a function
time can
12
n
(1)
13
X = 1 − exp[− (k avrX t=) 1] – exp –(kavrt)n
14
where the effective
constant
kavr, as rate
proposed
by kAvrami,
is a function of constant linear growth rate, G, and
15 rate
where
the effective
constant
avr, as proposed by Avrami, is a function of constant linear growth rate, G, a
either of the rate
of
nucleation
per
unit
of
untransformed
volume,
Iv, or the number
of nuclei
pernumber
unit volume,
Nv0,per unit volume, N
16
either of the rate of nucleation per unit of untransformed
volume,
Iv, or the
of nuclei
and n is an exponent
that
depends
on
the
dimensionality
of
the
product
that
forms.
17
and n is an exponent that depends on the dimensionality of the product that forms.
The hydration
canhydration
be obtained
differentiating
Eq. (1)
respect to time,
berespect
writtentoas,
18 rate, whichThe
rate,by
which
can be obtained
bywith
differentiating
Eq. (1)can
with
time, can be written as,
19
n
n
n = Ankn n(t
t0)n–1
(2)
20
R = AnkRavr
(t − t 0 avr
) −1 –exp(
−[exp(–[k
k avr (t −avr
t 0(t)]–)t0)] )
21
where R is the22
hydration
is ahydration
normalization
to match constant
isothermal
calorimetry
data,calorimetry
and t0 is the
whererate,
R isAthe
rate, Aconstant
is a normalization
to match
isothermal
data, and t0 is the ti
time delay between
the
time
of
mixing
and
the
start
of
nucleation
and
growth
kinetics.
Note
that
there
23
delay between the time of mixing and the start of nucleation and growth kinetics. Note are
thatfour
there are four paramet
parameters varying,
which are
A, kavr
, t0A,and
Avrami
been
to describe
C3S C S hydration,
24
varying,
which
are
kavrn.
, t0While
and n.the
While
the model
Avramihas
model
hasused
beenwidely
used widely
to describe
3
hydration, the25
heterogeneous
nucleation
process
that
occurs
during
cement
hydration
may
not
be
best
described
heterogeneous nucleation process that occurs during cement hydration may not be best described by a homogene
by a homogeneous
(Garraultetetal.
al.2006;
2006;
Thomas
2007).
26 nucleation
nucleation assumption
assumption (Garrault
Thomas
2007).
27
Boundary nucleation
model nucleation model
28
Boundary
The boundary
nucleation
andboundary
growth model
(BN model)
wasmodel
first developed
bywas
Cahn
(1956),
to describe
the
29
The
nucleation
and growth
(BN model)
first
developed
by Cahn
(1956), to describe
kinetics of nucleation
and
growth
of
a
polycrystalline
material.
The
key
assumption
is
that
nucleation
is
permitted
30
kinetics of nucleation and growth of a polycrystalline material. The key assumption is that nucleation is permitted
to occur only on
boundaries,
unlike the
Avrami model
assumes
that nucleation
occurs
at nucleation
randomly occurs at random
31internal
occur
only on internal
boundaries,
unlikewhich
the Avrami
model
which assumes
that
32
distributed
locations
everywhere
within volume.
the untransformed
Fortransformed
the BN model,
the transformed volu
distributed locations
everywhere
within the
untransformed
For the BNvolume.
model, the
volume
33
fraction
function
of time, X, is given by:
fraction as a function
of time,asX,a is
given by
34
35
36
(
(
))
Gt
X = 1 − exp ⎡− 2OvB ∫ 1 − exp − Y e dy ⎤
⎢⎣
⎥⎦
0
πI B 2 3 ⎡ 3 y 2
2 y 3 ⎤ (if t > y/G)
e
where
Y =
3
G t ⎢1 − 2 2 + 3 3 ⎥
G t ⎦
⎣ G t
(3)
37
(if t < y/G)
Ye = 0
38
Notetemporary
that y and variables
Ye are temporary
variablesafter
that integration.
disappear after
integration.
In Eq. 3,
depends
Note that y 39
and Ye are
that disappear
In Eq.
(3), X depends
onXjust
threeon just three well40
defined
physical
parameters:
G,
the
linear
growth
rate
of
transformed
phase,
I
,
the
nucleation
rate per unit area o
B
well-defined physical parameters: G, the linear growth
B rate of transformed phase, IB, the nucleation rate per unit
41
untransformed
boundary,
and
O
,
the
boundary
area
per
unit
volume.
v
B
area of untransformed boundary, and Ov , the boundary area per unit volume.
42
In order to apply the BN model to C3S hydration rate data, some slight modifications must be made (Thom
In order to apply the BN model to C3S hydration rate data, some
slight modifications must be made (Thomas
43
2007). Eq. (3) must be numerically integrated to obtain the transformation rate, dX/dt. Also, the scaling parame
2007). Eq. (3) must be numerically integrated to obtain the transformation rate, dX/dt. Also, the scaling param44
A and the time constant t0, described above in conjunction with the Avrami model (Eq. 2), are introduced.
eter A and the time constant t0, described above
in conjunction with the Avrami model (Eq. (2)), are introduced.
45
The threeB physical parameters OvB, IB, and G are correlated such that the kinetic profile is described by t
The three physical
parameters
O
,
I
,
and
G
are
such by
thatThomas
the kinetic
profile is described by two
v
B
46
independent rate constants kB andcorrelated
kG as proposed
(2007):
independent rate constants kB and kG as proposed
by Thomas (2007):
1/
4
47
k B = (I B OvB ) G 3 / 4
kB = (IBOvB)1/4G3/4
48
kG = OvB G
(4)
k = O BG
49
Thus fits made with the BN model Ghave vfour varying parameters: A, t0, kB, and kG. If any one of the physi
50
parameters in Eq. 4 are known independently, then the other two can be calculated from the fitted values of the r
Thus fits made with the BN model have four varying parameters: A, t0, kB, and kG. If any one of the physical
parameters in Eq. (4) are known independently, then the other two can be calculated from the fitted values of the
rate constants. For the case of a hydrating C3S paste, the value of OvB can be calculated by dividing the measured
surface area of the C3S powder by the calculated volume occupied by the3hydration products after complete
hydration, allowing G and IB to be determined from the fits.
38
Lee et al.
Each of the rate constants represents different physical behavior: kB describes the rate of transformation on
the internal boundaries (the surface of particles), whereas kG describes the rate of transformation in the bulk
matrix (the pore space between the particles). The ratio of these two rate constants (kB/kG) can be used to identify
the type of kinetic behavior. If kB/kG is very large, then the hydrated products will be densely populated on or
very near the nucleation sites (i.e., the C3S surface in the case of C3S hydration). If kB/kG is very small, then the
hydrated products will form evenly throughout the paste, approaching the condition of the Avrami model.
EXPERIMENTAL PROCEDURE
Materials
Pure tricalcium silicate (C3S) powder was obtained from the Lafarge Research Center in Lyon, France. The chemical
composition of C3S was analyzed by quantitative x-ray diffraction (QXRD) using Cu-Ka radiation, which gave C3S =
98.43%, C2S = 1.46%, and CaO = 0.10% by mass fraction (Fig. 1). Particle size distribution was measured in ethanol
slurry using Microtrac X-100 laser particle analyzer (Fig. 2). The median diameter of the C3S sample was measured
to be 7.754 mm. Using an empirical relationship between surface area of cement and particle size distribution developed by Zhang and Napiermunn (1995), the surface area of C3S was found to be 0.291 m2/g (1420 ft2/lb).
The anatase titanium dioxide (AMT-100, Tayca Corp.) used was 93% pure with an average crystal size of 6 nm
and a pH of 7. The manufacturer-provided surface area was 280 m2/g (1.37 × 106 ft2/lb).
Experiment
Three different C3S pastes were prepared at 0%, 10%, and 15% addition rate of TiO2 by mass; note that the
TiO2 was dosed in addition to, not by weight replacement, for cement. This approach keeps the cement content
constant among the different pastes, which simplifies interpretation of calorimetry data. The water to cement
ratio (w/c) was kept constant at 0.50, which resulted in a stiffer mix as more of the high surface area TiO2 was added.
The rate of hydration was measured by isothermal calorimetry (TAM AIR, TA instruments) at 20°C (68°F), which
has precision of ±20 mW and accuracy greater than 95%. All the materials were equilibrated at 20°C (68°F) for
24 hours prior to the testing. The TiO2 was hand mixed with deionized water for 1 minute, and then the C3S was
added and hand mixed for another 2 min. Samples were placed into the calorimeter less than 5 minutes after
mixing with C3S. The calorimetry data from the initial 15 minutes after mixing were excluded for both of the model
fits as some time is required for the samples to be equilibrated within the instrument.
RESULTS AND DISCUSSION
Figure 3 shows the rate of hydration per gram of C3S for the first 40 h after mixing for each of the pastes examined; corresponding cumulative heat data for the first 80 hours is presented in Fig. 4. Recall that the C3S content
and w/c for each paste remains constant, while the dosage of TiO2 nanoparticles varies among 0, 10, and 15%.
As the addition level of TiO2 nanoparticles increased, the rate of hydration was accelerated. For example, the
rate peak (or greatest power evolved with time) occurs 123 min. earlier for the 10% TiO2 paste and 200 min.
earlier for 15% TiO2 compared to the peak for the ordinary paste (Fig. 3). Furthermore, the peak heights in the
rate curve occurring at 6.5, 7.7, and 9.8 hours after mixing, were increased by 11.0% and 11.9%, respectively, for
10 and 15% TiO2 paste, when compared to pure C3S paste. The total heat of hydration (Fig. 4) data demonstrate
that the pastes containing TiO2 experience greater heat evolution than the ordinary paste in the first 20 hours
before the energy evolved begins to slow. In comparison, the 0% TiO2 (pure C3S) paste releases energy more
slowly initially, but continues to steadily increase through the 80 hours of data collected. These data suggest that
the addition of TiO2 particles to cement paste may affect early age hydration by decreasing the time to set and
increasing the rate of early strength development.
The degree of hydration, a, of a C3S paste can be calculated by dividing the heat of hydration at a given time by
the enthalpy of reaction of C3S, which has been reported to be DH = –121 kJ/mol (Thomas et al. 2009). The values
of a at 12 and 24 hours for each paste are listed in Table 1. The increasing a with higher levels of TiO2 shows that
these pastes have achieved greater degrees of hydration by 12 and 24 hours, as suggested by the faster hydration rate described above. In particular, increases in a at 12 hours of 42.86 and 51.43%, respectively, for 10 and
15% TiO2 when compared to the reference paste are notable. By 24 hours, the acceleratory effect of the TiO2 is
less than at 12 hours; increases in a at 24 hours are 19.30 and 21.05%, respectively, at 10 and 15% TiO2, when
compared to the reference C3S paste. It should be recalled that the TiO2 particles added to these pastes are not
known to react with water or calcium silicates. Therefore, an alternative explanation for the observed increase in
early age C3S reaction in the presence of these nanoparticles must be sought.
Nanotechnology of Concrete: The Next Big Thing Is Small 39
Both the Avrami model and the BN model were fit to the experimental data for each of the samples (see Fig. 5 to
7). Fitting was performed manually using least mean square error to obtain the closest fit around the rate peak.
The two rate parameters kB and kG for the BN model were first derived with a fixed OvB calculated from the surface
area of the C3S powder (OvB =0.44 m2/cm3 [77.6 ft2/in.3]) and then G and IB for different pastes were calculated
using the relationships in Eq. (4). The fit parameters are listed in Table 2 for the Avrami model and in Table 3 for
the BN model. Figures 5 to 7 show the rate of hydration data with both fits for each of the three pastes examined.
For the C3S paste, the BN model clearly provides a better fit than the Avrami model to the hydration rate
behavior, as was previously shown for C3S hydration under different conditions by Thomas (2007). While both
models closely approximate the early hydration reaction of C3S in the acceleration period (for all of the pastes),
the BN model more closely captures the hydration behavior of the deceleration period after the rate peak. The
divergence with the Avrami model occurs in the deceleration period and suggests that the conditions of random
nucleation assumed by that model do not apply to pure C3S hydration. The BN model also better represents the
early age hydration of C3S mixed with TiO2 than the Avrami model. Again, the improvements in the fit are especially notable in the down slope region. This suggests that nucleation is spatially nonrandom and is likely related
to the surface area of the solid phases available for product nucleation and growth.
Further, an increase in the kG/kG ratio of the BN model is found as the TiO2 dosage (and solid surface area)
increases (Table 3). This suggests that the presence of additional surface area, provided by the increasing
amounts of TiO2, promotes hydration product formation, which occurs on or near the surfaces of the particles
according to the model assumptions. This implies that the addition of TiO2 powder supplied additional nucleation sites to accelerate the hydration. It is also proposed that by providing additional nucleation sites away from
the reacting C3S particles, the start of diffusion-controlled hydration kinetics is delayed, increasing the amount
of early nucleation and growth hydration, as has been proposed for other nucleating materials (Thomas et al.
2009). Such behavior would account for both the acceleration in reaction rate and the increase in peak height
observed in the presence of TiO2 nanoparticles.
The t0 parameter in both the Avrami model and the BN model graphically shifts the curves either to the right
or to the left, depending on the sign. A positive t0 value can be interpreted as an induction period, shifting the
curves to the right. On the other hand, a negative t0 found in the BN model fits suggests that the TiO2 particles
have an effect of promoting the nucleation rate at a very early age. Note that the differences seen in t0 between
the 0% paste and the 10 and 15% pastes in the case of the BN model are 2.2 and 3.0 hours, respectively, which
are on the order of magnitude of the acceleration noted previously with respect to the peak heights seen in Fig. 3.
CONCLUSIONS
The early hydration behavior of pure C3S was measured and compared to that of C3S pastes containing 10%
and 15% additions of high surface area TiO2. Two nucleation and growth models–the Avrami model and boundary
nucleation model–were applied to the experimental data. Based on the results of this study, the following
conclusions are drawn:
• The addition of high surface area TiO2 powder accelerates the early age hydration of C3S by ~2.0-3.3 hours
and increases the rate peak height by ~11-12%, an effect that is attributed to its ability to stimulate nucleation of hydration product.
• The BN model is capable of representing the kinetic behavior of C3S paste mixed with TiO2 nano-particles
and provides a better fit to the rate data than the Avrami model for all pastes tested.
• The increase in the ratio of the rate constants from the BN model (kB/kG) with addition of TiO2 suggests that
the formation of hydration products is linked to the increase in available nucleation sites (i.e., increase in
solid surface area) provided by the TiO2 nanoparticles.
Observations such as these which show that the early rate of hydration can be altered through the addition
of unreactive TiO2 particles suggest that the setting behavior, strength development, and permeability of photocatalytic and other Portland cements can be optimized by controlling compositional variables and particle size.
ACKNOWLEDGMENTS
This material is based upon work supported by the National Science Foundation under Grant No. CMMI-0825373. The
authors are grateful to Lafarge for providing the C3S used. The authors thank Matthew Treager and Sarah Fredrich for their
help. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and
do not necessarily reflect the views of the National Science Foundation.
40
Lee et al.
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Zhang, Y.M., and Napiermunn, T.J., “Effects of Particle-Size Distribution, Surface-Area and Chemical-Composition on Portland-Cement Strength,” Powder Technology, V. 83, No. 3, 1995, pp. 245-252.
Table 1—Cumulative heat of hydration and degree of hydration, a, of TiO2-blended C3S pastes at 12 and 24 hours
TiO2 added (%)
Cumulative heat (12 h), kJ/mol
a (12 h)
0
10
15
42.65
60.15
64.70
0.35
0.50
0.53
Cumulative heat (24 h),
kJ/mol
68.76
82.13
83.85
a (24 h)
0.57
0.68
0.69
Nanotechnology of Concrete: The Next Big Thing Is Small
Table 2—Fit parameters A, t0, kavr and n for Avrami model
TiO2, %
A, kJ/mol
t0, h
kavr, h–1
n
0
10
15
56.718
64.116
59.184
2.700
0.180
0.042
0.1190
0.1144
0.1320
2.90
2.97
2.80
Table 3—Fit parameters A, t0, kG, kB and kB/kG for boundary nucleation model
TiO2, %
A, kJ/mol
t0, h
kB, h–1
kG, h–1
kB/kG
IB (mm–2h)–1
G, mm/h
0
10
15
71.514
85.488
87.954
1.2
-1.0
-1.8
0.1030
0.0990
0.1043
0.0824
0.0734
0.0656
1.2500
1.3488
1.5899
0.0390
0.0471
0.0811
0.1871
0.1666
0.1490
Fig. 1—Diffraction pattern for cement sample compared to reference pattern for C3S.
Fig. 2—Particle size distribution and cumulative particle size of C3S powder examined.
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Lee et al.
Fig. 3—Hydration rate of TiO2-blended C3S pastes.
Fig. 4—Cumulative heat of hydration of TiO2-blended C3S pastes.
Nanotechnology of Concrete: The Next Big Thing Is Small
Fig. 5—Rate of hydration with 0% TiO2 – Experiment versus Avrami and BN models.
Fig. 6—Rate of hydration with 10% TiO2 – Experiment versus Avrami and BN models.
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Fig. 7—Rate of hydration with 15% TiO2 – Experiment versus Avrami and BN models.