Determination, Modeling and Evaluation of Kinetics of 223Ra Sorption on Hydroxyapatite and Titanium Dioxide Nanoparticles
Abstract
:1. Introduction
2. Materials and Methods
2.1. Preparation of 223Ra Stock Solution
2.2. Britton–Robinson Buffer Solution
2.3. Sorbent Material Preparation
2.4. Determination of Kinetic Dependences
2.5. Kinetic Models for Two-Phase Systems
2.6. Procedure of the Experimental Data Evaluation
3. Results and Discussion
3.1. Parameters of nHAp and nTiO2
3.2. Evaluation of Kinetic Dependence
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Control Process | Model Abbreviation | Differential Equation | Equation # |
---|---|---|---|
Mass transfer | DM | dq/dt = KDM × (q* − q) | (3) |
Film diffusion | FD | dq/dt = KFD × (c − c*) | (4) |
KFD = 3 × D/(δ × R × hs) | (5) | ||
Diffusion | ID | dq/dt = KID × (c − c*)/{[1 − (q/q*)]−1/3 − 1} | (6) |
in an inert layer | KID = 3 × D/(R2 × hs) | (7) | |
Diffusion | RLD | dq/dt = KRLD × (q* − q)/{[1 − (q/q*)]−1/3 − 1} | (8) |
in a reacted layer | KRLD = 3 × D/(R2 × hs) | (9) | |
Chemical reaction | CR | dq/dt = KCR × rCR × [1 − (q/q*)]2/3 | (10) |
in the reaction zone, | KCR = 3/(R × hs) | (11) | |
e.g., 1st order reversible reaction | RCR = KCR × (c − c*) | (12) | |
Gel diffusion | GD | dq/dt = KGD × [(q* − q0)2 − (q − q0)2]/(q − q0) | (13) |
KGD = D × π2/(2 × R2) | (14) | ||
Following balance equations hold: | |||
dq/dt = −r × dc/dt | (15) | ||
if c is the integration variable: q = r × (c0 − c) + q0 | (16) | ||
if q is the integration variable: c = c0 − (q − q0)/r | (17) | ||
Equilibrium equations used: q* = Kd × c, and c* = q/Kd | (18) |
Parameter | Unit | nHAp | nTiO2 |
---|---|---|---|
Specific surface area | (m2·kg−1) | 117 ± 8 | 330 ± 10 |
Crystallite size | (nm) | 5.18 | 2.64 |
Equivalent diameter | (nm) | 21.7 ± 6.9 | 5.3 ± 1.7 |
Surface edge sites | (mol·kg−1) | 5.10 ± 1.20 | 0.20 ± 0.01 |
Surface layer sites | (mol·kg−1) | 0.15 ± 0.01 | 0.67 ± 0.01 |
pH applicability | pH | 5–10 | 2–10 |
Specific mass | (g·cm−3) | 3.14–3.21 | 3.90–4.30 |
Experiment No. | nHAp | nTiO2 | ||||
---|---|---|---|---|---|---|
c0 | Kd | r | c0 | Kd | r | |
(mol·Laq−1) | (Laq∙kg−1) | (Laq∙kg−1) | (mol·Laq−1) | (Laq∙kg−1) | (Laq∙kg−1) | |
1 | 9.92 × 10−12 | 3.03 × 104 | 1000 | 1.01 × 10−11 | 5.90 × 104 | 1000 |
2 | 9.46 × 10−12 | 1.55 × 104 | 1000 | 1.05 × 10−11 | 1.25 × 105 | 1000 |
3 | 1.12 × 10−11 | 1.54 × 104 | 1000 | 9.86 × 10−12 | 1.52 × 105 | 1000 |
Mean value ± σes * | 1.02 × 10−11 ± 0.07 × 10−11 | 2.04 × 104 ± 0.70 × 104 | 1000 | 1.01 × 10−11 ± 0.03 × 10−11 | 1.12 × 105 ± 0.39 × 105 | 1000 |
Sorbent | Experiment No. | WSOS/DF | |||||
---|---|---|---|---|---|---|---|
DM | FD | ID | RLD | CR | GD | ||
nHAp | 1 | 59.70 | 1860 | 5.35 | 5.47 | 1320 | 40.30 |
2 | 8.28 | 186 | 7.45 | 7.25 | 92.60 | 10.10 | |
3 | 8.06 | 461 | 2.60 | 2.71 | 250 | 27.60 | |
Mean value ± σes * | 25.34 ± 24.29 | 835.67 ± 732.96 | 5.13 ± 1.99 | 5.14 ± 1.87 | 554.20 ± 545.30 | 26.00 ± 12.38 | |
nTiO2 | 1 | 48.70 | 54.70 | 6.72 | 7.63 | 52.80 | 9.99 |
2 | 5.76 | 757 | 1.23 | 3.18 | 36.30 | 9.42 | |
3 | 33.40 | 258 | 8.09 | 16.10 | 239 | 5.43 | |
Mean value ± σes * | 29.29 ± 17.77 | 356.57 ± 295.06 | 5.35 ± 2.97 | 8.96 ± 5.36 | 109.37 ± 91.91 | 8.27 ± 2.04 |
Sorbent | Experiment No.: | KRLD ± σ (cm3·g−1·min−1) | Mean * KRLD ± σes (cm3·g−1·min−1) | Mean * D ± σes (cm2·min−1) | Mean * t1/2 ± σes (min) |
---|---|---|---|---|---|
nHAp | 1 | 1.24 × 10−1 | 5.03 × 10−1 ± 2.72 × 10−1 | 2.50 × 10−12 ± 1.80 × 10−12 | 0.75 ± 0.18 |
2 | 7.53 × 10−1 | ||||
3 | 6.31 × 10−1 | ||||
nTiO2 | 1 | 2.82 × 10−2 | 4.01 × 10−2 ± 2.44 × 10−2 | 1.60 × 10−14 ± 0.96 × 10−14 | 0.51 ± 0.32 |
2 | 1.80 × 10−2 | ||||
3 | 0.74 × 10−2 |
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Suchánková, P.; Kukleva, E.; Štamberg, K.; Nykl, P.; Sakmár, M.; Vlk, M.; Kozempel, J. Determination, Modeling and Evaluation of Kinetics of 223Ra Sorption on Hydroxyapatite and Titanium Dioxide Nanoparticles. Materials 2020, 13, 1915. https://doi.org/10.3390/ma13081915
Suchánková P, Kukleva E, Štamberg K, Nykl P, Sakmár M, Vlk M, Kozempel J. Determination, Modeling and Evaluation of Kinetics of 223Ra Sorption on Hydroxyapatite and Titanium Dioxide Nanoparticles. Materials. 2020; 13(8):1915. https://doi.org/10.3390/ma13081915
Chicago/Turabian StyleSuchánková, Petra, Ekaterina Kukleva, Karel Štamberg, Pavel Nykl, Michal Sakmár, Martin Vlk, and Ján Kozempel. 2020. "Determination, Modeling and Evaluation of Kinetics of 223Ra Sorption on Hydroxyapatite and Titanium Dioxide Nanoparticles" Materials 13, no. 8: 1915. https://doi.org/10.3390/ma13081915