Statistical Modeling of Photo-Bending Actuation of Hybrid Silicones Mixed with Azobenzene Powder
Abstract
:1. Introduction
2. Materials and Methods
3. Results & Discussions
3.1. Photo-Actuation Behavior
3.2. Bending Evaluation
3.3. Model Construction
3.3.1. Model Construction for Photo-Bending
3.3.2. Model Construction for Unbending
4. Conclusions
Supplementary Materials
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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x1 | x2 | x1x2 | x12 | x22 | x12x2 | x1x22 | x13 | x23 | x12x22 | x13x2 | x1x23 | x14 | x24 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Linear | Y | Y | - | - | - | - | - | - | - | - | - | - | - | - |
2FI | Y | Y | Y | - | - | - | - | - | - | - | - | - | - | - |
Quadratic | Y | Y | Y | Y | Y | Y | Y | - | - | - | - | - | - | - |
Cubic | Y | Y | Y | Y | Y | Y | Y | Y | Y | - | - | - | - | - |
Quartic | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y |
0 wt% | 1 wt% | 5 wt% | 10 wt% | |
---|---|---|---|---|
Length from irradiated center to the tip/mm | 20.0 | 18.9 | 18.0 | 16.5 |
Width/mm | 4.9 | 4.5 | 4.9 | 5.5 |
Thickness/mm | 1.4 | 1.5 | 1.7 | 1.5 |
Light (mW/cm2) | The Value of A | |||||||
---|---|---|---|---|---|---|---|---|
0 wt% | 1 wt% | 5 wt% | 10 wt% | 0 wt% | 1 wt% | 5 wt% | 10 wt% | |
150 | 0.57 | 1.78 | 3.41 | 4.88 | 66.7 | 43.6 | 70.7 | 60.1 |
300 | 1.23 | 3.57 | 6.61 | 8.56 | 61.6 | 46.9 | 65.8 | 49.8 |
450 | 2.04 | 5.32 | 9.54 | 12.0 | 58.0 | 45.6 | 62.1 | 47.0 |
600 | 2.48 | 6.07 | 11.5 | 13.2 | 52.9 | 41.8 | 53.6 | 40.2 |
Light (mW/cm2) | The Value of A | |||||||
---|---|---|---|---|---|---|---|---|
0 wt% | 1 wt% | 5 wt% | 10 wt% | 0 wt% | 1 wt% | 5 wt% | 10 wt% | |
150 | 0.62 | 1.78 | 3.69 | 5.05 | 48.7 | 52.5 | 70.9 | 69.0 |
300 | 1.28 | 3.59 | 6.97 | 8.60 | 49.9 | 50.9 | 72.4 | 67.6 |
450 | 2.18 | 6.97 | 9.91 | 12.0 | 51.4 | 55.5 | 74.7 | 71.2 |
600 | 2.60 | 8.60 | 11.8 | 13.1 | 44.7 | 52.8 | 85.7 | 74.4 |
Source | Sequential p-Value | Lack of Fit p-Value | Adjusted R2 | Predicted R2 |
---|---|---|---|---|
Linear | 7.49 × 10−19 | 4.86 × 10−15 | 0.837 | 0.820 |
2FI | 1.42 × 10−4 | 4.62 × 10−13 | 0.880 | 0.864 |
Quadratic | 1.09 × 10−12 | 4.66 × 10−5 | 0.966 | 0.960 |
Cubic | 2.18 × 10−6 | 0.228 | 0.983 | 0.977 |
Quartic | 0.0871 | 0.619 | 0.985 | 0.977 |
Source | Sum of Squares | df | Mean Square | F-Value | p-Value |
---|---|---|---|---|---|
Model | 739. 9 | 9 | 82.2 | 311.4 | 9.14 × 10−33 |
P% | 0.69 | 1 | 0.69 | 2.6 | 0.113 |
PUV | 60.6 | 1 | 60.6 | 229.4 | 1.09 × 10−17 |
P%PUV | 22.7 | 1 | 22.7 | 86.1 | 2.62 × 10−11 |
P%2 | 35.6 | 1 | 35.6 | 134.8 | 4.60 × 10−14 |
PUV2 | 0.026 | 1 | 0.026 | 0.099 | 0.755 |
P%2PUV | 5.4 | 1 | 5.4 | 20.4 | 5.98 × 10−5 |
P%PUV2 | 1.5 | 1 | 1.5 | 5.6 | 0.0229 |
P%3 | 4.5 | 1 | 4.5 | 17.0 | 1.93 × 10−4 |
PUV3 | 1.3 | 1 | 1.3 | 4.8 | 0.0345 |
Residual | 10.0 | 38 | 0.26 | - | - |
Lack of Fit | 2.1 | 6 | 0.36 | 1.45 | 0.228 |
Pure Error | 7.9 | 32 | 0.25 | - | - |
Corrected Total | 749.9 | 47 | - | - | - |
Source | Sequential p-Value | Lack of Fit p-Value | Adjusted R2 | Predicted R2 |
---|---|---|---|---|
Linear | 0.00140 | 3.84 × 10−10 | 0.220 | 0.156 |
2FI | 0.202 | 3.75 × 10−10 | 0.232 | 0.157 |
Quadratic | 0.0253 | 1.51 × 10−9 | 0.324 | 0.225 |
Cubic | 1.76 × 10−11 | 0.107 | 0.824 | 0.761 |
Quartic | 0.0186 | 0.837 | 0.856 | 0.785 |
Source | Sum of Squares | df | Mean Square | F-Value | p-Value |
---|---|---|---|---|---|
Model | 4075.7 | 9 | 452.9 | 25.5 | 1.77 × 10−13 |
P% | 1988.5 | 1 | 1988.5 | 112.1 | 6.84 × 10−13 |
PUV | 79.1 | 1 | 79.1 | 4.5 | 0.0413 |
P% PUV | 116.7 | 1 | 116.7 | 6.6 | 0.0144 |
P%2 | 508.5 | 1 | 508.5 | 28.7 | 4.38 × 10−6 |
PUV2 | 9.8 | 1 | 9.76 | 0.55 | 0.463 |
P%2PUV | 0.24 | 1 | 0.24 | 0.01 | 0.907 |
P%PUV2 | 18.4 | 1 | 18.4 | 1.0 | 0.315 |
P%3 | 2158.7 | 1 | 2158.7 | 121.7 | 2.09 × 10−13 |
PUV3 | 16.1 | 1 | 16.1 | 0.9 | 0.346 |
Residual | 674.2 | 38 | 17.7 | - | - |
Lack of Fit | 178.7 | 6 | 29. 8 | 1.92 | 0.107 |
Pure Error | 495.5 | 32 | 15.5 | - | - |
Corrected Total | 4749.9 | 47 | - | - | - |
Source | Sequential p-Value | Lack of Fit p-Value | Adjusted R2 | Predicted R2 |
---|---|---|---|---|
Linear | 2.26 × 10−9 | 1.85 × 10−10 | 0.569 | 0.531 |
2FI | 0.277 | 1.54 × 10−10 | 0.571 | 0.528 |
Quadratic | 5.88 × 10−12 | 0.00260 | 0.869 | 0.844 |
Cubic | 3.64 × 10−4 | 0.263 | 0.915 | 0.888 |
Quartic | 0.144 | 0.493 | 0.921 | 0.884 |
Source | Sum of Squares | df | Mean Square | F-Value | p-Value |
---|---|---|---|---|---|
Model | 6718.9 | 9 | 746.5 | 57.05 | 2.53 × 10−19 |
P% | 311.3 | 1 | 311.3 | 23.79 | 1.95 × 10−5 |
PUV | 159.7 | 1 | 159.7 | 12.21 | 0.00123 |
P% PUV | 0.010 | 1 | 0.010 | 0.0 | 0.978 |
P%2 | 1313.2 | 1 | 1313.2 | 100.34 | 3.26 × 10−12 |
PUV2 | 27.3 | 1 | 27.3 | 2.08 | 0.157 |
P%2PUV | 168.3 | 1 | 168.3 | 12.86 | 9.44 × 10−4 |
P% PUV2 | 64.0 | 1 | 64.0 | 4.89 | 0.0331 |
P%3 | 101.8 | 1 | 101.8 | 7.78 | 0.00823 |
PUV3 | 14.8 | 1 | 14.8 | 1.13 | 0.294 |
Residual | 497.3 | 38 | 13.1 | - | - |
Lack of Fit | 100.7 | 6 | 16.8 | 1.35 | 0.263 |
Pure Error | 396.6 | 32 | 12.4 | - | - |
Corrected Total | 7216.2 | 47 | - | - | - |
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Taniguchi, T.; Blanc, L.; Asahi, T.; Koshima, H.; Lambert, P. Statistical Modeling of Photo-Bending Actuation of Hybrid Silicones Mixed with Azobenzene Powder. Actuators 2019, 8, 68. https://doi.org/10.3390/act8040068
Taniguchi T, Blanc L, Asahi T, Koshima H, Lambert P. Statistical Modeling of Photo-Bending Actuation of Hybrid Silicones Mixed with Azobenzene Powder. Actuators. 2019; 8(4):68. https://doi.org/10.3390/act8040068
Chicago/Turabian StyleTaniguchi, Takuya, Loïc Blanc, Toru Asahi, Hideko Koshima, and Pierre Lambert. 2019. "Statistical Modeling of Photo-Bending Actuation of Hybrid Silicones Mixed with Azobenzene Powder" Actuators 8, no. 4: 68. https://doi.org/10.3390/act8040068