Cement hydration is recognized as a complex physicochemical process and many attempts have been made to describe and quantify the kinetics of hydration. Many of the developed models explicitly consider the effects of cement particle size distribution (PSD) and curing temperature on kinetics. However, considerably less consideration has been given to the influence of the starting water-to-cement mass ratio (w/c) on the developing hydration. From a practical viewpoint, predicting the change in degree of hydration at specific points in time due to a change in the starting w/c would be extremely useful to field engineers, researchers, and ready-mix concrete producers.
Computer models have definitively demonstrated the importance of spatial considerations in influencing hydration kinetics [1, 2]. An example would be the influence of w/c on achieved degrees of hydration. At ages of 1 d and beyond, higher w/c cement pastes generally exhibit a higher degree of hydration than lower w/c pastes [2]. At least partially, this is due to the fact that in a higher w/c paste, there is more space available for the dissolution of reactants and the nucleation/precipitation of hydration products. More specifically, according to Power's model for cement hydration [3], for w/c less than about 0.36, there is insufficient capillary pore space available for the complete hydration of the cement. In this case, the maximum achievable degree of hydration can be estimated as (w/c)/0.36. This in turn implies that at later ages, pastes with w/c > 0.36 will achieve a higher degree of hydration (e.g., 1.0) than those with w/c < 0.36, and the ratio of the higher w/c paste degree of hydration to that of the lower one will approach some asymptotic value greater than 100 %. For example, in comparing the relative degree of hydration of a w/c=0.4 cement paste to a w/c=0.3 paste, both under saturated curing conditions, one should find an asymptotic value of (1.0/(0.3/0.36))*100=120 %. Conversely, pastes with two different w/c > 0.36 cured under saturated conditions can both achieve a degree of hydration approaching 1.0 at infinite time, and thus the ratio of their degrees of hydration should asymptote to a value of 100 %. These same spatial considerations will surely influence the ratio of degrees of hydration at intermediate ages.
In this paper, simple models for the kinetics of cement hydration based on spatial considerations will be presented and compared to available experimental data. The basic approach taken is to consider the hydration kinetics from a local perspective, but using global parameters. The probability for any given "unit" of cement within the cement paste volume to react is related to an instantaneous hydration rate. The resulting differential equations are then solved to yield functions that represent the degree of cement hydration vs. time, α(t). Solutions to these equations are graphically compared to experimental data, both in terms of individual cumulative degree of hydration vs. time curves and in terms of the influence of w/c on achieved hydration.