Yanfei Peng1 , Claus Borgnakke2 , Will Hansen2, Joe Biernacki3
1 USG Corporation, Libertyville, IL
2 University of Michigan, Ann Arbor, MI
3 Tennessee Technological University, Cookville, TN
Hancock and Sharp found that the general equation for reaction, based on nucleation and growth of solid state reactions, provides the basis for analyzing reaction kinetics. This equation has the form of: , where is solid state reaction such as relative degree of hydration; is ultimate relative degree of hydration, k is the rate constant (1/time) and m is a constant that varies with the process type. Model linearization for the slope m becomes a diagnostic of the reaction process over time. The characteristic ranges of m are a measure of: m~ 0.5 is a diffusion controlled process; m~ 1 is a phase-boundary controlled process; and m~ 2-3 is a chemical controlled process. The analysis applied to heat of hydration data for C3S and portland cement paste at three constant temperatures (15 0C; 23 0C and 35 0C) shows that hydration reactions are initially chemically controlled with an m value of about 2. Temperature effect on hydration during this stage can be accurately modeled using an Arrhenius type rate model, where temperature effect on rate is captured using apparent activation energy Ea. The extent of chemical control for C3S is found to be valid up to about 30 maturity hours using the Arrhenius-based maturity function M20 for equivalent hours at room temperature, 20 0C, with an apparent activation energy of about 35,000 J/mole for C3S hydration. This range covers the stage of rate increase and rapid decrease. Beyond this stage of hydration the reaction process becomes diffusion controlled with an m value of about 0.47-0.50. During this stage temperature effects on rate vanish, except for their effect on ultimate degree of hydration. The generalized model is not optimum for accurate hydration development prediction. An empirical model known as an S-curve model, where heat of hydration Q (J/g) = Qultimate * EXP (-(t/tnorm)β), was found to more accurately predict hydration development rather than process of hydration.