2.2 Cement Chemistry

As with the development of any cellular-automaton-type model, rules must be selected to govern the state transitions occurring at each lattice element (site) of the microstructure. For cement, this requires a detailed understanding of the chemical reactions occurring when cement reacts with water. Review articles describing cement chemistry are available (Brown 1991, Gartner and Gaidis 1989, RILEM Technical Committee 66-MMH 1986) but, as will be outlined below, a well defined quantitative account is still lacking. This section provides a generally plausible outline of cement hydration, which should be viewed as a simplification of the complicated and poorly understood processes taking place in real cement. For example, the composition of the cement particles is conventionally broken down into several pure phases, but this is an idealization. Real particles may have regions which are not pure, but are hybrids of different proportions of silicate, ferrite and aluminate; in oil well cements the situation is particularly complicated (Bergstrom et al 1991/92). The 'true' chemical composition of the cement phases remains an open question. Attempts have been made since the time of Bogue (1929) to predict such phase compositions starting from oxide analyses of the original clinker but, although these predictions are still widely used, e.g. for furnishing American Petroleum Institute (API) specifications of oil well cements, they can only be regarded as approximations. The amorphous gels and crystalline products produced during hydration may also have a variety of chemical forms (Taylor 1990).

The most widely used cement is portland cement. The four major Bogue clinker phases present in portland cement are tricalcium silicate (C₃S), dicalcium silicate (C₂S), tricalcium aluminate (C₃A), and tetracalcium aluminoferrite (C₄AF); the clinker is ground with gypsum (CH₂). The formulae in parentheses use the standard cement chemistry abbreviations: C = CaO, S = SiO_2, A = Al₂O ₃, F = Fe₂O₃, = SO₃, and H = H₂O. Densities and molar volumes for all phases relevant to our models, taken from the cement literature (Lu et al 1993, Mindess and Young 1981, Young and Hansen 1987), are given in table 1.

Table 1: Densities and molar volumes of cementitious materials
Compound Name	Compound Formula	Density (g cm-3)	Molar Volume (cm-3 mol -1)
Tricalcium silicate	C3S	3.21	71
Dicalcium silicate	C2S	3.28	52.4
Tricalcium aluminate	C3A	3.03	89.1
Tetracalcium aluminoferrite	C4AF	3.73	128
Gypsum	CH2	2.32	74.2
Calcium silicate hydrate	C1.7SH4	1.85	124
Pozzolanic C-S-H	C1.1SH2.1	1.97	81
Calcium hydroxide	CH	2.24	33.1
Ettringite	C6A3H32	1.75	715
Monosulphate	C4AH12	1.99	313
Hydrogarnet	C3AH6	2.52	150
Iron hydroxide	FH3	2.2	95.2

The reactions used in our cement microstructure models are summarized in Figure 1. The numbers below each reaction equation indicate the volume units of each phase required to balance that particular chemical reaction. Knowing the molar volumes and the reaction stoichiometries, these volume stoichiometries can be easily calculated for each reaction. Since Bogue phases are only approximations, so too are these idealized cement hydration reactions. Indeed, there is considerable controversy in the cement chemistry literature concerning what reactions are actually occurring, what are their spatial distributions, which are slow or fast, what are the mechanistic details and even the exact chemical composition of the species that may exist during hydration. It is a virtue of the CA approach that we can deliberately avoid pursuing an overdetailed chemical description, and still obtain realistic physical properties of the evolving dynamical system.

As seen in Figure 1, the silicate reactions are simpler than those for the aluminate and ferrite phases of portland cement. Tricalcium silicate is the major component of portland cement; it is generally present in a mass fraction of 50-70%, and is considered to be responsible for controlling many of the ultimate properties of cement-based materials including transport and strength properties. When C₃S reacts with water, a nanoporous, amorphous calcium silicate hydrate (C-S-H ) gel is redeposited on the surfaces of the original C₃S and and on previously deposited C-S-H , while calcium hydroxide (CH) crystals nucleate and grow in the available capillary pore space. As time proceeds, the C-S-H gel polymerizes, but we do not include this process in our list of reactions. The reactions for C₂S are similar, but less CH is formed due to the lower Ca/Si molar ratio of the initial C₂S. Additionally, in portland cement, the C₂S typically reacts at a much slower rate than the C₃S. Due to the extensive use of pozzolanic materials such as silica fume and fly ash in concrete, the pozzolanic reaction between calcium hydroxide and reactive silica has been included in the list of reactions. The stoichiometry for this reaction is based on recently published data (Lu et al 1993) and is an approximation as it is likely to vary with water-to-cement (w/c) ratio and silica fume content.

Figure 1: Cement model reactions -
numbers indicate volume stoichiometries

Tricalcium aluminate, C₃A, is generally the fastest reacting phase in portland cement. In fact, gypsum is specifically added to portland cement to slow down this reaction, thus avoiding 'flash set' of the material. Because the aluminate phase is critical to early hydration properties, it is of great interest in oil well cementing. When gypsum is not present in the system, C₃A reacts with water to form a variety of crystalline hydration products, with hydrogarnet, C₃AH₆, being the ultimately stable hydration product. Reactions are much more complex in the presence of gypsum. In this case, the C₃A will react with the gypsum to form ettringite, C₆A₃H₃₂, whose crystals are often observed to grow as needles within the cement paste. Microscopic analysis has shown the wide range of morphologies of growing ettringite crystals and their sensitivity to additives such as sucrose retarders and to temperature (Kuzel and Pöllmann 1991). When all of the gypsum is consumed, the ettringite may decompose, reacting with more of the C₃A to form the monosulphate phase, C₄AH₁₂. Additionally, ettringite is unstable above 60 ºC, exemplifying that cement reactions are a function of temperature as well as solution concentrations. Ambient conditions are assumed in this paper. The sulfate ions are generally more mobile than the aluminate ions so that ettringite forms either in solution or at the surfaces of the aluminate phases in cement paste. There is also evidence that the ettringite changes from a gel to a crystalline form during cement hydration: application of ATR/FTIR techniques to measure changes in chemical composition during hydration does not indicate any C-S-H formation at early time, but the attainment of a steady level of ettringite (though this does not preclude a phase change of ettringite, such as from gel to crystalline form) (Jones 1992).

The reactions of the ferrite phase, C₄AF, are the least well understood of those occurring during portland cement hydration. The ferrite phase is often said to react slowly (in comparison to the other phases) and only contributes to long−term properties of cements (although exceptions to this have been noted in the presence of special additives (Chiesi et al 1992), and the bulk A//F ratio does have a strong effect on thickening time in oil well cements). In the present work, we have assumed that the reactions of the ferrite phase are similar to those of tricalcium aluminate, with the production of extra calcium hydroxide and iron (III) hydroxide FH₃ to account for the extra calcium and iron present in the C₄AF phase, based on experimental evidence given by Brown (1987). No density information was available in the literature for the iron hydroxide gel forming in cement paste, so the value of 2.2 g cm^-3 given in Table 1 was assumed.

Cement hydration does not proceed at a fixed rate. The evolution of hydrating cement can be qualitatively characterized by the heat evolution curve sketched in Figure 2 (Nelson 1990). The process can be broken down into five stages: (1) preinduction, (2) induction, (3) acceleration, (4) deceleration and (5) diffusion limited.

The major activity during each stage is described qualitatively as follows:

(1) Preinduction - This is the initial rapid hydration that occurs when the particles of cement are exposed to water, releasing a large amount of heat. Duration: On the order of minutes.

(2) Induction - A period of reduced hydration activity. The reason why the hydration is inhibited during this time period is not clear, although many theories have been proposed. Duration: On the order of 1-2 h.

(3) Acceleration - The rate of hydration increases. This is the beginning of the period during which the cement paste will achieve set. The major portion of the silicates hydrates and the cement solidifies. Duration: On the order of hours.

(4) Deceleration - The hydration rate decreases as the hydrated material covers the particles. Duration: On the order of hours to days.

(5) Diffusion Limited - Hydration and aggregation occur at a very low rate. Reactions are limited by the rate of diffusion of species through the dense pore network. Duration: On the order of days to years.

The set point of a cement slurry can be defined operationally as the condition when the hydrating cement system provides a measurable resistance to penetration; a standard test for set time of hydraulic cement is given in ASTM C191 (1990). In oil well cementing the analogous measure used is the thickening time. It is defined as the time taken to reach a certain torque when stirring a cement (in a 'consistometer'). The measurement determines how long a cement slurry can be pumped; details of the standard test are given in the API standard API Spec 10 (1982). Both measurements are designed to meet engineering needs, but relating results to simple underlying physical transformations that occur during hydration is difficult; a recent study by Chen and Odler (1992) provides a valuable discussion of this subject. Our model, however, suggests a new measurement can be directly related to percolation: as the particles of cement become covered in C-S-H , a point in time is reached at which a continuous solid structure has percolated throughout the cement paste (Bentz and Garboczi 1991b). The model provides the insight that the percolation transition might be quite sharp, and that beyond this point the cement slurry should be able to support shear stresses, and thus permit shear wave propagation. The CA-based model suggested an ultrasonic shear wave experiment, which has subsequently been performed, confirming these conjectures (D'Angelo et al 1992). The similarity between the onset of percolation in the CA model and the onset of shear wave propagation in ultrasonic experiments is discussed further in Section 4.