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Application of GRAAL model to the resumption of
International Simple Glass alteration
M. Fournier, P. Frugier, S. Gin
To cite this version:
M. Fournier, P. Frugier, S. Gin. Application of GRAAL model to the resumption of International
Simple Glass alteration. npj Materials Degradation, Nature Research 2018, 2, pp.21.
�10.1038/s41529-018-0043-4�. �cea-02339738�
Application of GRAAL model to the resumption of International Simple
Glass alteration
Maxime Fournier, Pierre Frugier, Stéphane Gin
S
UPPLEMENTARY
I
NFORMATION
Supplementary Note 1 Assumptions
for modeling zeolites nucleation-growth
Supplementary Figure 1: In the proposed approach,
nucleation occurs at a constant rate on the gel surface area (glass surface area). The nuclei surface area available for zeolites growth is therefore proportional to the time t: S tc
nn tn
. The zeolites growth occurs is in a single direction, forming needles.Supplementary Figure 2: In seeded tests, the growth
surface area Sc, corresponding to the seeds surface area
introduced into the medium at the initial time, is independent of time. The seeds growth is represented by the unidirectional growth of a set of needles.
Supplementary Note 2 Gel description
in an alkaline environment
Supplementary Figure 3: In order to integrate the RA
phenomenon to the GRAAL model, a new gel composition domain was defined. This domain integrates a passivating (PRI) and three non-passivating end-members (SiAlCa, SiZrNa, and SiZr0.1Na0.2). Two secondary phases (Na-P2 zeolites and CSH0.8) also play a role in controlling the activities in solution.
Phase controlling activity during Element the plateau stage the RA stage
Al SiAlCa (NPEM) zeolite Na-P2 (PII)
Ca CSH0.8 (PII) CSH0.8 (PII)
Si PRI SiZr0.1Na0.2 (NPEM)
Zr SiZrNa (NPEM) SiZr0.1Na0.2 (NPEM)
Supplementary Table 1: Amorphous layer
end-members are constructed to ensure the control of Al, Ca, Si, and Zr activities before and during a RA. Activity control could be ensured by the PRI, the gel non-passivating end-members (NPEM), or the secondary phases (PII). The end-member SiZr0.1Na0.2 controls both Si and Zr activities during the RA because it has the stoichiometry of the “final gel” towards which the system tends. Boron activity is imposed by the glass dissolution kinetics and Na activity is imposed by a flux corresponding to NaOH additions used to maintain the pH1. t= 0 S, gel surface t +t t +2·t nucleation unidirectional growth
n, nuclei specific surface area
t= 0
Sc, seeds surface area
t +t t +2·t unidirectionnal growth Al Na Ca Zr Si SiAlCa PRI CSH0.8 zeolite Na-P2 SiZrNa SiZr0.1Na0.2 -31 -4 0,25 -9,55 2,2 -9 -35 -25 -15 -5 5 log K
Supplementary Note 3 Modeling supplementary results
Supplementary Figure 4: Comparisons between modeled and experimental concentrations at pH 10.1. Experimental
B, Si, Na, and Al 1 (diamonds) and modeled (dashed line for = 1 and dotted line for 0) concentrations in (a)
unseeded and (b) seeded tests conducted at pH 10.1 maintained by adding NaOH in static conditions, at 90°C, S/V = 1,770 m-1. 0 2 4 6 8 10 12 0 100 200 300 [B] (mmol·L -1) time (d) 0 5 10 15 20 25 0 100 200 300 [Na] (mmol·L -1) time (d) 0 0.05 0.1 0.15 0.2 0.25 0 100 200 300 [Al] (mmol·L -1) time (d) 0 2 4 6 8 10 12 0 100 200 300 [Si] (mmol·L -1) time (d)
a
0 10 20 30 40 50 60 70 0 100 200 300 [B] (mmol·L -1) time (d) 0 20 40 60 80 100 0 100 200 300 [Na] (mmol·L -1) time (d) 0 0.05 0.1 0.15 0.2 0.25 0 100 200 300 [Al] (mmol·L -1) time (d) 0 5 10 15 20 25 30 35 0 100 200 300 [Si] (mmol·L -1) time (d)b
Supplementary Figure 5: Comparisons between modeled and experimental concentrations at pH 10.4. Experimental
B, Si, Na, and Al 1 (diamonds) and modeled (dashed line for = 1 and dotted line for 0) concentrations in (a)
unseeded and (b) seeded tests conducted at pH 10.4 maintained by adding NaOH in static conditions, at 90°C, S/V = 1,770 m-1. 0 20 40 60 80 100 120 140 0 100 200 300 [B] (mmol·L -1) time (d) 0 30 60 90 120 150 180 0 100 200 300 [Na] (mmol·L -1) time (d) 0 0.1 0.2 0.3 0 100 200 300 [Al] (mmol·L -1) time (d) 0 20 40 60 80 0 100 200 300 [Si] (mmol·L -1) time (d)
a
0 20 40 60 80 100 120 0 100 200 300 [B] (mmol·L -1) time (d) 0 30 60 90 120 150 180 0 100 200 300 [Na] (mmol·L -1) time (d) 0 0.1 0.2 0.3 0 100 200 300 [Al] (mmol·L -1) time (d) 0 20 40 60 80 0 100 200 300 [Si] (mmol·L -1) time (d)b
Supplementary Figure 6: Comparisons between modeled and experimental concentrations at pH 11. Experimental
B, Si, Na, and Al 1 (diamonds) and modeled (dashed line for = 1 and dotted line for 0) concentrations in (a)
unseeded and (b) seeded tests conducted at pH 11 maintained by adding NaOH in static conditions, at 90°C, S/V = 1,770 m-1. 0 100 200 300 400 0 25 50 75 [B] (mmol·L -1) time (d) 0 200 400 600 800 0 25 50 75 [Na] (mmol·L -1) time (d) 0 0.4 0.8 1.2 1.6 2 0 25 50 75 100 [Al] (mmol·L -1) time (d) 0 50 100 150 200 0 25 50 75 100 [Si] (mmol·L -1) time (d)
a
0 50 100 150 200 250 300 0 10 20 30 [B] (mmol·L -1) time (d) 0 100 200 300 400 500 600 0 10 20 30 [Na] (mmol·L -1) time (d) 0 0.4 0.8 1.2 1.6 0 10 20 30 40 [Al] (mmol·L -1) time (d) 0 50 100 150 200 0 10 20 30 40 [Si] (mmol·L -1) time (d)b
Supplementary Figure 7: Comparisons between modeled and experimental concentrations at pH 11.3. Experimental
B, Si, Na, and Al 1 (diamonds) and modeled (dashed line for = 1 and dotted line for 0) concentrations in (a)
unseeded and (b) seeded tests conducted at pH 11.3 maintained by adding NaOH in static conditions, at 90°C, S/V = 1,770 m-1. 0 50 100 150 200 250 300 0 10 20 30 [B] (mmol·L -1) time (d) 0 200 400 600 800 0 10 20 30 [Na] (mmol·L -1) time (d) 0 0.5 1 1.5 2 0 10 20 30 40 [Al] (mmol·L -1) time (d) 0 50 100 150 200 250 0 10 20 30 40 [Si] (mmol·L -1) time (d)
a
0 50 100 150 200 250 300 0 5 10 15 [B] (mmol·L -1) time (d) 0 200 400 600 800 0 5 10 15 [Na] (mmol·L -1) time (d) 0 0.5 1 1.5 2 2.5 3 0 5 10 15 20 [Al] (mmol·L -1) time (d) 0 50 100 150 200 250 0 5 10 15 20 [Si] (mmol·L -1) time (d)b
Supplementary Discussion
The solubility of the Na-P2 zeolite seeds was
evaluated by placing synthesized seeds
1in
NaOH solutions of different molarities for one
month at 90 °C. The ratio between the seeds
“geometric” surface area (0.25 m
2·g
–1) and the
solution volume was approximately 2·10
–3m
–1.
The concentrations measured in solution were
fairly constant, indicating the early onset of
saturation
conditions
in
solution
(Supplementary Figure 8). Even at the lowest
pH tested (therefore the farthest pH from the
synthesis conditions), the dissolution of the
seeds was low and the stationary state was
reached quickly. The altered zeolite thickness
increased with the increase in the pH.
Moreover, the Si/Al ratio in solution increase,
thus deviating from 1.7, the ratio of the seeds
(Supplementary
Table
2).
The
seeds
dissolution was not congruent, implying the
slow formation of a phase with a stoichiometry
different from the starting mineral. Since the
maximum equivalent thickness of Si was only
300 nm after one month of leaching, the
quantities formed of this (or these) phase(s)
remained
low,
explaining
that
their
identification and characterization could not be
completed (not visible by SEM after 330 days
at pH ≈ 9).
pH 9,3 9,9 10,1 10,4 10,7 11,0 11,3 eThSi 37 51 69 102 109 197 299
Si/Al 5.0 5.8 5.0 4.5 3.5 3.2 2.2
Supplementary Table 2: Calculation of the equivalent
thickness in Si (eThSi, in nm) of altered zeolite after 29
days and the average Si/Al solution ratio for each pH. The seeds Si/Al ratio is 1.7.
1 Fournier, M. et al. npj Mater. Degrad. 1, 17 (2017).
Supplementary Figure 8: Concentrations of Si, Al, and
Na measured in solution during the dissolution of Na-P2 zeolite seeds in NaOH solutions of different molarities. The initial sodium concentrations were subtracted.
The solubility constant of the Na-P2 zeolite
was calculated using the CHESS code for
different pH values. This calculation required
the implementation of the following
dissolution-precipitation reaction in the database, using a
stoichiometry measured elsewhere
1:
3
2 8 4 4 4
NaAlSi O H
4 H
1Na
1Al
2 H SiO
For all the pH values studied, we calculated a
solubility constant value at each sampling time
(1, 3, 7, 14, and 28 days respectively). The
results obtained were similar for the same pH
but varied substantially from one pH to another
(Supplementary Figure 9).
1 10 0 5 10 15 20 25 30 [Na] (mmol·L -1) time (d) pH = 9,5 pH = 9,8 pH = 10,1 pH = 10,4 pH = 10,7 pH = 11,0 pH = 11,3 0.1 1 [Al] (mmol·L -1) 1 2 4 8 [Si] (mmol·L -1)Supplementary Figure 9: Data derived from calculating
the solubility constant K of the Na-P2 zeolite (a) at each sampling time and (b) on average for the different studied pH values.
The solubility constant of a mineral does not
depend on the pH. The variations observed in
Supplementary Figure 9(b) are thus related to
the uncertainties associated with log K
measurements.
The
average
solubility
constant
(log
K
4 0)
.
reasonably describes
the equilibrium between the Na-P2 zeolite and
the NaOH solutions (Supplementary Figure
10). This log K value was used in the
calculations presented in the main text.
Supplementary Figure 10: Comparison between (a) Si, (b) Al, and (c) Na concentrations measured after 29 days
(red diamonds) and those calculated using three solubility constant values for the Na-P2 zeolite: logK 4 0. (purple line), logKmin 4 3. (green
dashed line), and logKmax 3 5. (blue dashed line).
3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 9 9.5 10 10.5 11 11.5 – log K pH 1 j 3 j 7 j 14 j 29 j
