Testing the Grambow Glass Dissolution Model by Comparing it With Monte Carlo Simulation Results
- PDF / 817,692 Bytes
- 11 Pages / 391.5 x 623.16 pts Page_size
- 9 Downloads / 173 Views
409 Mat. Res. Soc. Symp. Proc. Vol. 556 © 1999 Materials Research Society
REVIEW OF THE SIMULATIONS
GRAMBOW
MODEL
AND
THE
MONTE
CARLO
The Grambow model According to the Grambow model, glass dissolution is governed by silica dissolution: Si02 + 2H,0 =
(1)
Si(OH)4
In this reaction there are two silica states: non dissolved SiO 2 and dissolved Si(OH) 4. The Grambow (glass dissolution) rate law, which is also based on two silica states, is given by
J,= kI- C+
(2)
J,
where Jrate is the silica dissolution rate, k is the initial dissolution rate, C is the concentration of dissolved silica, y is the "silica saturation concentration" and Jf,, is the "final dissolution rate". The final dissolution rate is added to account for experimental results. There is no theoretical explanation for it and it is also often omitted in the Grambow rate law. The glass region where fast dissolving components have already leached out of the glass is called the gel layer. In the original Grambow model, the rate law is applied at the pristine glass/gel surface. From there, dissolved silica diffuses through the gel layer towards the solution. This leads to another model parameter, the diffusion coefficient Dgei of silica in the gel layer. So, the Grambow model is not equivalent to applying the Grambow rate law at the gel/water interface. The Monte Carlo simulations In this paper, we use two versions of our Monte Carlo model: (1) a "two component" version in which we consider the glass to be a random mixture of a network former with low solubility (which we call "silica") and an easily dissolving component (which we call "sodium") [9-11], and (2) a "one component" version in which we consider the glass as consisting of silica only. Up to now, the two component version can only accommodate a zero surface to volume ratio (due to an infinite solution volume). The one component version can also handle non zero surface to volume ratios, which makes it possible to use it for verifying the Grambow rate law. The reason why we developed a one component version for non zero surface to volume ratios is that we did not want to use excessive computation time for sodium dissolution processes. Apart from the final dissolution rate, sodium dissolution processes are not included in the Grambow rate law anyway. In the one component model, we simulate dissolution on a microscopic scale and track the evolution of the system as a function of time. All particles (which are either silica or water) are assumed to lie in a diamond lattice. This assumption is not crucial, but makes it easy to define a neighboring position and to handle volume exclusion. A diamond lattice is chosen because (1) it is three dimensional and (2) a coordination number of four is the best representation for the tetrahedral silica configuration. Initially, the system is assumed to consist primarily of a gel layer where each lattice site bears a water particle with probability p and a silica particle with probability (l-p). In fact, this gel is the glass of the two component 410
Data Loading...
