Effect of Particle Size Distribution on Hydration Kinetics
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EFFECT OF PARTICLE SIZE DISTRIBUTION ON HYDRATION KINETICS
James M. Pommersheim Bucknell University, Lewisburg,
PA 17837
ABSTRACT A general method has been developed for determining the effects of particle size distribution (PSD) on the kinetics of hydration. Given the PSD and the kinetic rate for particles having a single size, expressions can be derived for the variation of the total degree of hydration with time. The method was applied to PSD and kinetic functions typical of cement systems that account for reaction, diffusion and expansion of spherical A key The PSD was found to critically affect the kinetics. hydrate layers.
feature of the theory follows with time those particles that have become totally hydrated, so-called "dead" particles.
This produces a dead-particle
hydration curve having approximately the same shape and location as the overall hydration curve. It can be represented analytically in all cases and gives a measure of the disguise provided by the distribution.
INTRODUCTION When a dispersion of different sized particles undergoes a chemical reaction, such as in the hydration of portland cement, the progress of the reaction will differ for each sized particle. In general, the smaller sized
particles will react or hydrate faster, a consequence of their larger surface to volume ratio. If
the degree of reaction for an individual particle
of original size r is ar, then the overall degree of hydration a of the dispersion is
given by: rmax
a - f
r W(r) dr
(I)
rmin where rmin is the size of the smallest particle, rmax is the size of the largest particle, and W(r) is the particle size distribution (PSD), the weight fraction of particles having size r. Since W(r) includes all sized particles it follows that: rmax f W(r) rmin
dr - 1.
(2)
Equation I shows the exact way in which the kinetics (ar) and particle size W(r) are coupled. For a continuous distribution the individual degrees of hydration for each sized particle are summed. If all the particles have a single size, it follows from equations 1 and 2 that a - ar- Since there is a discrete but large number of particles in most size ranges, the use of an integral rather than a summation is usually justified. This paper examines the important effect that particle size distribution has on reaction kinetics. Specifically, typical distributions and kinetics for the hydration of the constituents of portland cement are examined and combined to obtain expressions for according to equation 1. Results are interpreted in terms of how the PSD disguises the hydration of individual particles.
Mat. Res. Soc. Symp. Proc. Vol. 85. ' 1987 Matenals Research Society
302
PARTICLE SIZE DISTRIBUTION Little data exists on particle size distributions for portland cement systems. Brown and Galuk [1] have used a modified Weibull distribution to fit data, while Knudsen [2] earlier used both the exponential and double exponential distributions. Knudsen reported [3] that the exponential distribution could fit the PSD of cement over 95% of its range. Part of the
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