Final Size of Particles versus Temperature

Obviously the rate of particle growth at a given temperature becomes e. ceedingly slow when the difference in solubility of the smallest versus the largest particles has become negligible. - j. i. . 

Thus at 90 C, for example, the solubility of massive silica formed is about 350 ppm, and the size above which growth is slow at 90 C is about 8 nm. If we assume growth occurs until all the particles are within the size range of kl0% or 7.2-8.8 nm, then using the expression 10 , the range of solubility is between 1.39 x 350 and 1.31 X 350, or 487 and 459, that is, a solubility difference of 28 ppm. 

At 30 C the solubility of massive silica is 70 ppm (SiOj made at 8S C) and growth becomes slow at 3.5 nm diameter. A similar calculation, assuming the expression 10 , gives for a 10% spread in particle sizes a range in solubilities of 137-121, or a difference of 16 ppm. 

For a quantitative study of spontaneous growth, data are needed on the particle 

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