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On the Validity of Colloidal Models for Hydrated Cement Paste

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.

Jennings globular model for C-S-H in hydrated Portland cement
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].


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.


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