by: Dr. James J. Beaudoin
A colloidal model for the nanostructure of
hydrated cement paste was proposed by
Jennings [1] in 2000 and has been referred
to as CM-I. This was later refined in 2008
[2] and referred to as CM-II. The model is
essentially a hybrid incorporating many
features of the Feldman-Sereda (F-S)
layered model and the colloidal Powers-Brownyard
( P-B) model. A substantial amount of the
input data for the computations at the core
of the Jennings (J)-model is based on the
publications of Feldman [3-6] that relate to
a detailed assessment of the completely
irreversible water sorption isotherm and the
nanostructural implications of the helium
inflow experiments. The J-model is used to
provide explanations for certain aspects of
the physical and chemical behavior of cement
paste and relies heavily on ‘granular’
behavior analogies. The focus in this note
will be on the refined model as this is the
most recent colloidal-based model at the
time of writing. The primary features of the
model (CM-II) will be described. This will
be followed by a discussion of the main
tenets of the model. Alternate points of
view and critical commentary is integrated
into the discussion.
The C-S-H is modeled as a network of
prismatic-shaped aggregates or particles
referred to as ‘globules’ for consistency
with the original model (CM-I). A schematic
of the model is illustrated in Figure 1. The
particles have a least dimension of about 5
nm and the other dimensions vary from
30-60nm.The particles are depicted as having
outer surface and internal porosity as well
as interlayer space. The model utilizes
three types of pores: pores within the
‘globule’ referred to as intraglobular pores
(IGP); small gel pores (SGP) (1-3 nm in
diameter) trapped between the globules that
are percolated to the outer regions; large
gel pores (LGP) (3-12 nm in diameter) or
space created as a result of the overlap of
globular flocs. Clusters of ‘globules’ pack
together in two packing densities termed
high density (HD) C-S-H and low density
C-S-H (LD) C-S-H. The C-S-H ,itself, is
considered intrinsically similar, the
difference due solely to the porosity as a
result of the packing arrangement.
Figure 1. A schematic
of the Jennings model for C-S-H
There are a number of difficulties with the
J-model. Some of these are discussed as
follows. First the issue of correct density
values for C-S-H is important. The J-Model
uses a value of 2.604 g/cm3
for saturated ‘globules’ based on small
angle neutron scattering (SANS) measurements
[7]. Earlier work by Powers and Brownyard
cited density values of 2.60g/cm3 for
D-dried cement paste when lime-saturated
water was used as a displacement fluid [8].
This is similar to the density of quartz
(2.60-2.65 g/cm3). This value
would likely represent the density of the
silicate sheets (including the Ca-O
backbone) themselves as the water enters the
space between the layers and thus the volume
occupied by interlayer water would not be
considered as part of the solid. This is
also the case for the density value of 2.85
g/cm3 reported by Brunauer and
Greenberg [9]. Density values of D-dried
hydrated cement pastes determined using
helium and methanol as displacement fluids
(Feldman, [10] were about 2.20-2.30g/cm3.
Heller and Taylor [11] reported values of
2.00-2.20g/cm3 for
semi-crystalline C-S-H (I) obtained by
calculation using crystallographic data.
Cement paste density values determined at
the 11%RH condition using helium, water ,or
methanol as displacement fluids had values
of about 2.30-2.40g/cm3 for all
fluids. A value of 2.18 g/cm3
was obtained for hydrated C3S from which
calcium hydroxide had been depleted i.e.
essentially for C-S-H [12]. A density value
of phase pure C-S-H (I) (2.40g/cm3 ,C/S= 0.80) was
determined experimentally by the writers
using helium pycnometry. Density values
reported to be 2.35 and 2.45 g/cm3
for C-S-H were also obtained by atomistic
modeling using Monte Carlo algorithms and
geometrical calculi for the saturated and
dry state, respectively. Further , the unit
cell dimensions for C-S-H reported by
Pellenq et. al [13] are in error. The
density value would be significantly lower
than the estimate based on neutron
scattering experiments. The SANS value of
2.60 g/cm3 was incorrectly
considered as a validation of their
atomistic numerical model.
Changes in density of the C-S-H on
first-drying from 11%RH and adsorption back
to 11%RH are explained by the J-model as
follows. Water,on drying, is removed from
the interlayer space and the surface both
of which act to increase the density.
Removal of water from the IGP spaces with
‘fixed’ boundaries has the effect of
decreasing density values, the net effect of
removal of water from all three locations
being a density increase. The assertion that
both the volume and mass change from the
first two locations are the same amount on
drying is erroneous. For example, the
separation of the length-change isotherm
into ‘reversible’ and ‘irreversible’
components indicates that the ‘reversible’
length-change on drying is < 0.01% whereas
the ‘irreversible’ length-change > 0.35%.
The separation itself is ‘model-less’. The
‘reversible’ isotherm ,however, is by
definition attributed to surface adsorption
as the latter is a thermodynamically
reversible process. It is clear then that
there are significant differences in the
magnitude of volume change due to the
removal of adsorbed water and interlayer
water. The assumption that the IGP
boundaries are fixed is unlikely as the
structural collapse of the layers on drying
would bring the surfaces closer together.
Water in the IGP, if present, would appear
to be under a similar force field as the
interlayer water. It is also concluded on
the basis of similar density values
estimated after resorption to 11% RH that
water does not re-enter the layers of the
C-S-H at this humidity but rather resides on
the surface and in the IGP. This explanation
is untenable as given the location of the
IGP, water in the J-model would have to
enter the interlayer in order to reach the
IGP sites. Further , the scanning loops
emanating from the adsorption branch, in the
water mass-change isotherm indicate that
there is significant irreversibility at very
low humidity levels. This irreversibility
can be readily explained by the entry and
exit of some of the interlayer water on
adsorption even at humidities <11%RH. The
increase in density on first drying is due
to the removal of interlayer water. The
sharp decrease is due to the collapse of
layers not allowing helium to enter fully in
40 hours. The increase in density on
rewetting then can only be explained by
water returning to the interlayer structure
without an equivalent re-expansion. The
density increase at higher humidities is due
to the large volume increase because of the
swelling of the layers as more water is
associated with the structure.
The arguments advanced for the J-model based
on thermodynamics would also appear to be
invalid. The rationale for surface area
contributions including surfaces of the IGP
spaces is based on water adsorption
calculations. These are untenable due to the
irreversible nature of the isotherms. B.E.T
surface area calculations require data
representing ‘reversible’ adsorption
processes. In addition, helium inflow into
the cement paste nanostructure with the
exception of low water/cement ratio pastes
reaches equilibrium in 40 hours. Helium
penetrates all the available space. Density
values determined by accounting for
interlayer space detected by helium are
consistent with values for C-S-H based on
X-ray crystallographic determinations [10]
i.e. 2.20-2.40. Helium gas can flow into
nanospaces <1nm in size instantaneously [4].
Density values of , for example, porous
vycor glass (mean pore size <3nm) determined
using helium pycnometry agree with standard
values [10].This calls into question the
existence of IGP spaces. A value for the
density of water of about 2.0g/cm3
is estimated using the J-model as only the
outside surface water is considered to
change the measured volume. Feldman’s
estimate of 1.20± 0.08 g/cm3 for
the density of interlayer water (based on
the F-S model) is more realistic and
consistent with water densities for
interlayer water in clay systems [14]. The
J-model provides estimates of water density
of about 1.20 g/cm3 in the
region of the isotherm between 11-40% RH.
This region is the flattest part of the
isotherm and it would be expected that the
bulk of the interlayer water would have
previously entered the system at humidities
< 11%RH. The density value for the water in
this region is accurate and reflects the
incremental amount of interlayer water that
has intercalated between the C-S-H
layers.
The packing of ‘globules’ into different
arrangements appears to be a useful concept.
It allows properties to vary without
changing the globular structure. In this
respect it is compatible with the F-S model
where aggregates of layers can ‘pack’ into
connected arrays. The constancy of water
surface area is however an issue. The
calculation itself is ‘model-less’ and
meaningless as indicated in the previous
discussions. Since the water isotherm is
totally irreversible a B.E.T. surface area
calculation is invalid.
The J-model postulates the existence of
small gel porosity (SGP) trapped between
‘globules’ and percolated to the outside
surfaces. This is compatible with the F-S
model for paste at low porosity (low
water/cement ratio) and the Daimon model.
These type of pores have been detected by
helium inflow experiments as described
previously.
The J-model assigns irreversible shrinkage
to drying from 100-50% RH. It appears then
that these are ascribed mainly to capillary
effects. The F-S model attributes these
effects primarily to the region of humidity
< 11%RH. The latter is based on the
observation that the ‘irreversible’ length
change accounts for about 80% of the length
change ,most of which occurs below 11%RH.
Further the length-change isotherm is
completely irreversible exhibiting large
primary and secondary hysteresis. This is
contrary to the assertion based on the
J-model that drying is mostly reversible
below 50% RH. The J-model argues that
irreversible shrinkage involves a ‘pushing’
of the globule flocs closer together through
the action of meniscus effects i.e.
compressive stress on the solid. This is
consistent with some aspects of a layered
model (F-S) and correlates with an increased
degree of polymerization of the silicates
and the observed reductions in surface area.
In an attempt to assess length-change below
40% RH Jennings applied the Bangham
equations using Eglobule = 60GPa
[2] and a surface area value of 70m2/g.
Length change was far lower than that
observed. The values for Eglobule
and surface area are reasonable. The
difficulty is that the equations must be
applied to the ‘reversible’ portion of the
isotherm and not the ‘total’ water isotherm
for reasons discussed previously. Jennings
argues that the large shrinkages of 1% or
more that have been measured directly for
small regions of C-S-H using microscopic
techniques [2] was the motivation for the
development of a colloidal model and
suggests that the shrinkage at low RH’s is
due to the removal of interlayer water. It
would appear that on this basis the F-S
model is more appropriate. Large local
deformations ,then, can easily be
rationalized by a layered model as opposed
to a ‘globular’ model.
The J-model rationalizes the creep process
as beginning when the SGP are full and
increases as the LGPs fill at higher
humidities. In the J-model creep involves
reorientation of the globules producing
denser local packing and perhaps reducing
the surface area. This argument would appear
to be wanting as creep of cement paste has
been shown to occur in the ‘dry’ state.
Further, relaxation experiments performed on
pure C-S-H, have shown that at any given
equilibrium condition with respect to
moisture content the basal spacing does not
change when the specimens are subjected to a
sustained load. The predominating mechanism,
then, would appear to be one that involves
‘sliding of C-S-H sheets. A reorientation
of aggregates of ‘sheets’ is possible but
it is likely a minor contributor to the
process.
Aging is associated with volume
change/collapse of the LGP in the J-model.
The globules deform as water is removed and
re-enters the interlayer spaces. It is
argued that there are several ways of
rearranging the globules to collapse the LGP.
The process of pulling water out of the LGP
causes them to collapse with the greatest
effect occurring while the meniscus is
outside the gel. It is suggested here that
aging as described by the F-S model is more
consistent with experimental observations
[15]. In the F-S model aging is ascribed to
the creation of new interlayer space as the
silicate sheets translate and layer surfaces
approach each other under sustained stress.
Examination of the ‘irreversible’ water
isotherm indicates that length-change on
drying from the saturated state is
insignificant until humidities below 11%RH
are reached where shrinkage can exceed
0.20%.This clearly indicates that the role
of menisci in this regard is not likely a
factor. The meniscus effect on ‘reversible’
desorption is greater. However the effect is
small as the total ‘reversible shrinkage’ at
humidities above 40%RH (where the meniscus
ruptures) is about 0.05%.
Slow diffusion of water on drying is
attributed to the desorption of hindered or
load-bearing water (J-model) that is
accompanied by rearrangement of the
globules. The arguments contravening the
necessity of introducing this concept
follows in a brief discussion of the idea of
disjoining pressure.
Further discussion of the validity of
applying the concept of ‘disjoining
pressure’ to explain volume change
behavior in the adsorption region is
useful. It is very difficult to reconcile
this idea with the basic parameters
governing physical adsorption. Consider the
following argument. The adsorbed film is in
a state of compression, normal to the
surface. There is also a two dimensional
spreading pressure tangential to the
surface. Some rupture of the solid may take
place due to the tangential spreading
pressure force or by a shear force created
by an isotropic expansion of the
‘crystallites’ or a decrease of their
surface free energy. The movement of the
solid will , however , involve other terms
in the equation for the total free energy
(i.e. dG surface phase = VdP –
SdT- Sdγ + μ1dn1 + μ2dn2).
The terms μ1 and μ2
are the chemical potentials of the
adsorbate and adsorbent respectively. Also n1
and n2 are the molar quantities
of the adsorbate and adsorbent respectively.
The other terms are defined as: V=volume of
adsorbate; S = entropy; γ + surface energy.
The Gibbs-Bangham equation fully accounts
for the ‘reversible’ length change
using a valid application of thermodynamic
principles without the necessity of invoking
the abstract concept of
‘disjoining pressure’. It is noted here
that, for example, the swelling of clays can
involve the intercalation of several layers
of water into the interlayer regions. This
occurs at relatively high humidities and has
been referred to as a form of disjoining
pressure. This is distinct from the low
humidity ‘hindered’ adsorption effect
(adsorption region of the isotherm)
described by the P-B model as synonymous to ‘disjoining pressure’.
Jennings argues that the reduction in
surface energy as surfaces come into close
proximity is probably the driving force for
natural aging. This is attributed to a
measurable decrease in the LGP and a
possible rearrangement of the SGP. The F-S
model attributes the reduction in surface
energy to layered surfaces coming closer
together resulting in an increase in the
amount of interlayer space. An increase in
solid volume on drying as measured by
helium pycnometry supports this view[15].
References
1.
Jennings H. M. (2000). A model for
the microstructure of calcium silicate
hydrate in cement paste, Cem. Concr. Res.,
30(1), pp.101-116.
2.
Jennings H. M. (2008). Refinements to
colloidal model of C-S-H in cement: CM-II,
Cem. Concr. Res., 38(3), pp.275-289.
3.
Feldman R. F. (1970). Sorption and
length-change scanning isotherms of methanol
and water on hydrated Portland cement,
Proc. 5th Int. Symp. Chem. Cem.,
Tokyo, Vol.III, pp.53-66.
4.
Feldman R. F. (1971). The flow of
helium into the interlayer spaces of
hydrated cement paste, Cem. Concr. Res.,1(3),
pp. 285-300.
5.
Feldman R. F. (1972). Helium flow and
density measurement of the hydrated calcium
silicate-water system, Cem. Concr. Res.,
2(1), pp. 123-136.
6.
Feldman R. F. (1973). Helium flow
characteristics of rewetted specimens of
dried Portland cement paste, Cem. Concr,
Res., 3(6), pp. 777-790.
7.
Allen A. J., Thomas J. J. and
Jennings H. M. (2007). Composition and
density of nanoscale
calcium-silicate-hydrate in cement,
Nature Materials, 6(4), pp. 311-316.
8.
Powers T. C. and Brownyard T. L.
(1947). Physical properties of hardened
cement paste. Part 5. Studies of hardened
cement paste by means of specific volume
measurements. J. Am. Conc. Inst. Proc.,
Vol 43., pp.669-712.
9.
Brunauer S. and Greenberg S. (1962).
The hydration of tricalcium silicate and β-dicalcium
silicate at room temperature, Proc. 4th
Int. Symp. Chem. Cem., London, Vol. I,
pp. 135-163.
10. Feldman R. F. (1972). Density and
porosity studies of hydrated Portland
cement, Cement Technology, 3(1), pp.
5-14.
11. Heller L. and Taylor H.F.W. (1956).
Crystallographic data for the calcium
silicates, HMSO London, 79p.
12. Young J. F. and Hansen W. (1987).
Volume relationship for C-S-H formation
based on hydration stoichiometry, Proc.
Mater. Res. Soc. Symp. Vol. 85, pp.
313-322.
13.
Pellenq R.J.-M. et al.
(2009). A realistic molecular model of
cement hydrates, Proc. Nat. Acad. Sci.
USA., 106(38), pp. 16102-16107.
14. Martin R. T. (1962). Adsorbed water
on clay: A review. Proc. 9th
Nat. Conf. Clay and Clay Min. Ed. A.
Swineford, Pergamon Press, New York, p28.
15. Feldman R. F. (1972). Mechanism of
creep of hydrated Portland cement paste,
Cem. Concr. Res., 2(5), pp.521-540. |