The Application of Box–Behnken Design for Investigating the Supercritical CO2 Foaming Process: A Case Study of Thermoplastic Polyurethane 85A
Abstract
1. Introduction
2. Results
3. Discussion
4. Materials and Methods
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Exp. No. | P (bar) | T (°C) | t (h) | Expansion Ratio (-) |
---|---|---|---|---|
A1 | 100 | 100 | 2 | 1.81 |
A2 | 80 | 100 | 2 | 1.38 |
A3 | 120 | 100 | 2 | 2.02 |
A4 | 100 | 60 | 2 | 1.08 |
A5 | 100 | 80 | 2 | 1.30 |
A6 | 100 | 120 | 2 | 3.18 |
A7 | 100 | 140 | 2 | 5.44 |
A8 | 100 | 160 | 2 | 1.29 |
A9 | 100 | 100 | 4 | 1.83 |
A10 | 100 | 80 | 4 | 1.26 |
A11 | 100 | 120 | 4 | 3.07 |
A12 | 120 | 100 | 4 | 1.85 |
Independent Variable | Symbol | Level | ||
---|---|---|---|---|
−1 | 0 | 1 | ||
A: Saturation pressure | P (bar) | 80 | 100 | 120 |
B: Saturation temperature | T (°C) | 100 | 120 | 140 |
C: Immersion time | t (hr) | 2 | 4 | 6 |
Exp. No. | Operating Parameter | Results | ||||
---|---|---|---|---|---|---|
P (bar) | T (°C) | t (hr) | Exp. Ratio (-) | Pore Size (μm) | Cell Density (cells/cm3) | |
B1 | 100 | 120 | 4 | 2.87 | 11.3 | 109 |
B2 | 100 | 120 | 4 | 2.42 | 11.2 | 109 |
B3 | 80 | 140 | 4 | 6.00 | 52.7 | 107 |
B4 | 120 | 120 | 6 | 2.92 | 7.8 | 109 |
B5 | 100 | 120 | 4 | 2.56 | 9.7 | 109 |
B6 | 100 | 100 | 2 | 1.56 | 6.7 | 109 |
B7 | 100 | 140 | 2 | 5.88 | 22.6 | 108 |
B8 | 100 | 120 | 4 | 2.50 | 9.7 | 109 |
B9 | 120 | 120 | 2 | 2.86 | 9.2 | 109 |
B10 | 100 | 100 | 6 | 1.53 | 7.2 | 109 |
B11 | 80 | 120 | 2 | 2.03 | 47.0 | 107 |
B12 | 120 | 140 | 4 | 5.43 | 12.7 | 109 |
B13 | 100 | 140 | 6 | 6.22 | 19.5 | 108 |
B14 | 80 | 100 | 4 | 1.35 | 34.9 | 106 |
B15 | 80 | 120 | 6 | 2.09 | 45.7 | 107 |
B16 | 120 | 100 | 4 | 1.80 | 5.4 | 109 |
B17 | 100 | 120 | 4 | 2.46 | 11.2 | 109 |
Results | Model | ||
---|---|---|---|
Linear | 2FI | Quadratic | |
Expansion ratio | |||
R2 | 0.8428 | 0.8493 | 0.9867 |
p-value of lack of fit test | 0.0040 | 0.0022 | 0.0814 |
Mean pore size | |||
R2 | 0.7506 | 0.7583 | 0.9978 |
p-value of lack of fit test | <0.0001 | <0.0001 | 0.1702 |
Response | Equation | AARD (%) |
---|---|---|
Expansion ratio (-) | 22.42 + 0.145 A − 0.559 B − 0.316 C − 0.0003 A2 + 0.003007 B2 + 0.0082 C2 − 0.00064 AB + 0.00231 BC | 7.1 |
Mean pore size (μm) | 389.9 − 7.43 A + 0.365 B − 1.95 C + 0.03654 A2 + 0.003 B2 + 0.55 C2 − 0.00656 × 10−3 AB − 0.0225 BC | 6.0 |
Exp. No. | P (bar) | T (°C) | t (h) | Expansion Ratio (-) | Pore Size (μm) | ||
---|---|---|---|---|---|---|---|
Exp. (a) | Pred. (b) | Exp. (a) | Pred. (b) | ||||
C1 | 120 | 140 | 4.7 | 5.54 | 5.69 | 12.7 | 12.4 |
C2 | 80 | 140 | 6 | 6.76 | 5.98 | 60.6 | 55.0 |
Source | p-Value (a) | |
---|---|---|
Expansion Ratio (-) | Mean Pore Size (μm) | |
Model | <0.0001 | <0.0001 |
A | 0.1044 | <0.0001 |
B | <0.0001 | <0.0001 |
C | 0.6186 | 0.1393 |
A2 | 0.4277 | <0.0001 |
B2 | <0.0001 | 0.0663 |
C2 | 0.8245 | 0.0052 |
AB | 0.1241 | 0.0023 |
AC | 1.0000 | 0.9657 |
BC | 0.5464 | 0.1532 |
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Khudaida, S.H.; Yen, S.-K.; Su, C.-S. The Application of Box–Behnken Design for Investigating the Supercritical CO2 Foaming Process: A Case Study of Thermoplastic Polyurethane 85A. Molecules 2024, 29, 363. https://doi.org/10.3390/molecules29020363
Khudaida SH, Yen S-K, Su C-S. The Application of Box–Behnken Design for Investigating the Supercritical CO2 Foaming Process: A Case Study of Thermoplastic Polyurethane 85A. Molecules. 2024; 29(2):363. https://doi.org/10.3390/molecules29020363
Chicago/Turabian StyleKhudaida, Salal Hasan, Shih-Kuo Yen, and Chie-Shaan Su. 2024. "The Application of Box–Behnken Design for Investigating the Supercritical CO2 Foaming Process: A Case Study of Thermoplastic Polyurethane 85A" Molecules 29, no. 2: 363. https://doi.org/10.3390/molecules29020363
APA StyleKhudaida, S. H., Yen, S.-K., & Su, C.-S. (2024). The Application of Box–Behnken Design for Investigating the Supercritical CO2 Foaming Process: A Case Study of Thermoplastic Polyurethane 85A. Molecules, 29(2), 363. https://doi.org/10.3390/molecules29020363