Additional Reactions

The needed physical properties of the phases found in fly ash and the relevant hydration products are summarized in Table 1. While specific gravities, molecular weights, and molar volumes are readily available in the literature [3, 7], heat of formation data have yet to be located for all of the phases. Figure 1 summarizes the proposed reactions between the fly ash and the cement phases and their hydration products, such as CH. The numbers below each reaction indicate the volume stoichiometries (on a pixel basis) which must be maintained by the computer model. Based on these volume stoichiometries, all but one of the reactions in Figure 1 are seen to further contribute to the chemical shrinkage [6] occuring during hydration, as the volume of the solid hydration products is less than that of the reactants (solids and water). The only exception to this is the conversion of primary C-S-H to "pozzolanic" C-S-H .

Table 1: Physical Properties of Proposed Components of Fly Ash

Compound Name	Compound Formula	Density (Mg/m3 )	Molar volume (cm3 /mol)	Heat of formation (k J/mol)
Silica	S	2.2	27.	-907.5
Aluminosilicate	AS	3.247	49.9
Stratlingite	C2ASH8	1.94	215.63
Anhydrite	$C\bar{S}$	2.61	52.16	-1424.6
Gypsum	$C\bar{S}H_2$	2.32	74.2	-2022.6
Calcium chloride	CaCl2	2.15	51.62	-795.8
Friedel's salt	C3A(CaCl2)H10	1.892	296.66
Calcium Hydroxide	CH	2.24	33.1	-986.1
Calcium silicate hydrate	C1.7SH4	2.12	108.	-3283
Pozzolanic C-S-H	C1.1SH3.9	1.69	101.8	-2299.1
Tricalcium aluminate	C3A	3.03	89.1	-3587.8
Dicalcium aluminosilicate	C2AS	3.05	90.
Calcium aluminodisilicate	CAS2	2.77	100.62

Figure 1: Cement-fly ash model reactions - numbers below reactions indicate volume stoichiometries.

The new version of the model allows for the conversion of primary C-S-H to pozzolanic C-S-H, for the case where there is an excess of silica due to the presence of fly ash or silica fume. The user can select to have this reaction included with or eliminated from those executed in the model through the use of a global input flag. This reaction allows for the observed reduction in the C/S ratio of C-S-H over time in systems containing pozzolans [8]. When activated, the global parameter PCSH2CSH controls the probability of a primary C-S-H pixel being converted to pozzolanic C-S-H during any given dissolution cycle of the model. The calcium liberated by this reaction is converted to diffusing CH species which can form solid CH or participate in further pozzolanic reactions with the available silica and aluminosilicates.

For the purposes of incorporating fly ash, four new diffusing species [1] have been introduced into the model: diffusing anhydrite, diffusing CaCl₂, diffusing AS, and diffusing CAS2. The silica itself does not dissolve, but diffusing CH species react at silica surfaces to form pozzolanic C-S-H . The interactions between the new diffusing species and the phases of the Portland cement are as follows:

diffusing CaCl₂: when a diffusing CaCl₂ species collides with either solid or diffusing C₃A, Friedel's salt is formed. If it collides with solid C₄AF, Friedel's salt, CH, and FH₃ are formed.

diffusing AS: when a diffusing AS species collides with either solid or diffusing CH, stratlingite is formed.

diffusing CAS2: when a diffusing CAS2 species collides with solid or diffusing C₃A, stratlingite is formed. If it collides with solid C₄AF, stratlingite, CH, and FH₃ are formed.

diffusing anhydrite: when a diffusing anhydrite species collides with either solid or diffusing gypsum, it is converted into solid gypsum.

Globally, when the model is executed under adiabatic conditions, the activation energy for the fly ash reactions (considered to be on the order of 80 kJ/mole), is used to update both the probability of a diffusing CH species reacting at a silica surface and the probability of dissolution of the aluminosilicate and calcium aluminosilicate components of the fly ash. The reactivity of the fly ash should perhaps also be a function of pH, but this has yet to be incorporated into the model. Perhaps using an exponential function to describe the pH evolution over time or as a function of degree of hydration, such as:

$$pH = pH_{init} + \gamma \times [1-\exp({\frac {-\alpha} {1-\alpha}})]$$ (1)

would provide a basis for estimating pH during the course of the hydration. In the above equation, pH_init is the initial pH of the pore solution when the cement and fly ash are mixed with water, $\gamma$ is the increase in pH during the entire course of hydration, and $\alpha$ is the degree of hydration. The reactivity of the fly ash could then be adjusted based on the current pH of the pore solution.

The new version of the model can be found in the programs disrealnew.c and hydrealnew.c in the anonymous ftp directory as described in section 1. An example annotated input datafile for the execution of disrealnew is given in Appendix C.