# Optimization of Mechanical Properties for Polyoxymethylene/Glass Fiber/Polytetrafluoroethylene Composites Using Response Surface Methodology

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}), alumina (Al

_{2}O

_{3}) and polytetrafluoroethylene (PTFE) in micro- or nano-sized particles and other polymeric materials such as polyethylene oxide (PEO), polylactic acid (PLA), etc. [7,8,9,10,12,13,16,17].

## 2. Materials and Methods

#### 2.1. Materials

^{3}and a melting temperature of 178 °C. Polytetrafluoroethylene (PTFE) microparticles with an average particle size of 12 µm, density of 0.425 g/cm

^{3}, and specific surface area of 1.5–3.0 m

^{2}/g were also purchased from Du Pont. The PTFE etch solution was prepared in the lab using sodium naphthalene with a density of 0.45 g/cm

^{3}. Tetrahydrofuran, purchased from J.T. Bakker, (Phillipsburg, NJ, USA) was used as a solvent to dissolve the salt.

#### 2.2. Preparation of PTFE Microparticles Etch Solution

^{3}of acetone was added to the PTFE and stirred for 5 min with 525 rpm. Upon completion of the first wash cycle, the solution was left to settle, followed by pouring away the upper liquid. Another two wash cycles were repeated. The process was then followed by rinsing of the solid using 200 cm

^{3}of distilled water. Stirrer speed of 525 rpm was used for rinsing. After each rinse cycle, the solid was left to settle and the upper portion containing mainly dissolved sodium salt in distilled water was poured away prior to the next rinse cycle. A total of five rinse cycles were performed to completely separate the etched PTFE micro powder from the sodium salt. The residue containing only the etched PTFE micro powder in distilled water was then placed in a petri dish of 150 mm diameter. This formed a PTFE layer of approximately 1 mm thick. An incubator with a temperature of 40 °C was used to dry the solution for 48 h. The etched PTFE was then removed from the petri dish and placed in a lab container in a dark environment to prevent exposure to light.

#### 2.3. Preparation of POM Composites

#### 2.4. Model Development Using Response Surface Methodology (RSM)

#### 2.5. Statistical Analysis and Model Fitting

^{2}, signifies the level of fit of the polynomial model, with values between 0 and 1. R

^{2}is one of the measures for variability reduction of a response in statistical modeling. As more terms are added, the value of R

^{2}increases without consideration of the statistical significance of these additional terms. The goal is to obtain R

^{2}values close to 1. Adjusted R

^{2}(R

^{2}

_{adj}) takes into consideration only the terms that are statistically significant. A lower value of R

^{2}

_{adj}than R

^{2}indicates no necessity of adding extra terms into the model.

#### 2.6. Optimization of Mechanical Properties Using the Desirability Method

#### 2.7. Morphology Analysis Using Scanning Electron Microscopy (SEM)

#### 2.8. Mechanical Testing

## 3. Results and Discussion

#### 3.1. Morphology Analysis Using SEM

#### 3.1.1. Surface Microscopy of Etched PTFE

#### 3.1.2. Morphology of POM/GF/PTFE Fractured Surfaces

#### 3.2. RSM Analysis of Mechanical Properties

#### 3.3. ANOVA Analysis and Model Fitting for Tensile Strength of POM Composite

^{2}, A

^{2}B, and AB

^{2}are significant for the tensile strength of POM composites. The coefficient of determination, R

^{2}, is one of the measures resulting in a reduction of response variability. The R

^{2}of 0.9720 is very close to 1, in agreement that the model comprises the best fit data. The R

^{2}

_{adj}value of 0.9328 suggests the model is sufficient without needing to consider additional terms. An adequate precision measures the signal to noise ratio, and a value greater than 4 is desirable. A precision value of 17.698 indicates an adequate signal. This model can be used to navigate the design space.

^{2}of 0.9720 and R

^{2}

_{adj}of 0.9328 along with the residual analysis adequately fit the model to ethe xperimental data.

#### 3.4. ANOVA Analysis and Model Fitting for Elasticity Modulus of POM Composites

^{2}of 0.9542 is very close to 1, in agreement that the model comprises the best fit data. The R

^{2}

_{adj}value of 0.9450 suggests the model is sufficient without needing to consider additional terms. Adequate precision measures the signal to noise ratio and a value of greater than 4 is desirable. The adequate precision value of 30.038 indicates an adequate signal. This model can be used to navigate the design space.

^{2}of 0.9542 and R

^{2}

_{adj}of 0.9450 along with the residual analysis adequately fit the model to the experimental data.

#### 3.5. ANOVA Analysis and Model Fitting for Toughness of POM Composites

^{2}, and B

^{2}are significant for the toughness of POM composites. The coefficient of determination, R

^{2}of 0.8988 is close to 1, in agreement that the model comprises of best fit data. The R

^{2}

_{adj}value of 0.8482 suggests the model is sufficient without needing to consider additional terms. An adequate precision measures the signal to noise ratio, and a value of greater than 4 is desirable. The adequate precision value of 15.760 indicates an adequate signal. This model can be used to navigate the design space.

^{2}(0.8988) and R

^{2}

_{adj}(0.8482) along with the residual analysis adequately fit the model to experimental data.

^{3}, with a PTFE etch time of 5 min. With PTFE constant at 9.5%, toughness gradually decreases as the PTFE etch time is increased, reaching a low of 2000 kJ/m

^{3}at a PTFE etch time of 10 to 14 min before increasing slightly.

#### 3.6. ANOVA Analysis and Model Fitting for Hardness of POM Composites

^{2}were significant for the hardness of POM composites. The coefficient of determination, R

^{2}, of 0.9800 is very close to 1, in agreement that the model comprises of best fit data. The R

^{2}

_{adj}value of 0.9657 suggests the model is sufficient without needing to consider additional terms. Adequate precision measures the signal to noise ratio and a value of greater than 4 is desirable. The precision value of 26.444 indicates an adequate signal. This model can be used to navigate the design space.

^{2}(0.9800) and R

^{2}

_{adj}(0.9657), along with the residual analysis, adequately fit the model to the experimental data.

#### 3.7. Overall Desirability for Mechanical Properties for POM Composites

^{3}, and the hardness is 115.0 HRR.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**SEM micrographs of fractured surfaces for POM composites with (

**a**) 4.0% PTFE etched for 10 min; (

**b**) 17.3% PTFE etched for 10 min; (

**c**) 9.5% PTFE etched for 2.9 min; (

**d**) 9.5% PTFE etched for 17.1 min.

**Figure 3.**Stress vs. strain curves comparing effects of PTFE content and etch time on POM composites.

**Figure 4.**Stochastic error and deterministic portion for tensile strength of POM composites as (

**a**) normal probability plot for residuals; (

**b**) predicted versus actual values.

**Figure 5.**3D response surface plot (

**a**) with 2D contour plot; (

**b**) of the effects of PTFE content and PTFE etch time on tensile strength of POM composites.

**Figure 6.**Stochastic error and deterministic portion for elasticity modulus of POM composites as (

**a**) normal probability plot for residuals; (

**b**) predicted versus actual values.

**Figure 7.**3D response surface plot (

**a**) with 2D contour plot; (

**b**) of the effects of PTFE content and PTFE etch time on elasticity modulus of POM composites.

**Figure 8.**Stochastic error and deterministic portion for toughness of POM composites as (

**a**) normal probability plot for residuals; (

**b**) predicted versus actual values.

**Figure 9.**3D response surface plot (

**a**) with 2D contour plot; (

**b**) of the effects of PTFE content and PTFE etch time on toughness of POM composites.

**Figure 10.**Stochastic error and deterministic portion for hardness of POM composites as (

**a**) normal probability plot for residuals; (

**b**) predicted versus actual values.

**Figure 11.**3D response surface plot (

**a**) with 2D contour plot; (

**b**) of the effects of PTFE content and PTFE etch time on hardness of POM composites.

**Figure 12.**3D response surface plot (

**a**) with 2D contour plot; (

**b**) of desirability function applied to multiple responses.

Input Variables | Symbol | Axial (−√2) | Low (−1) | Mid (0) | High (+1) | Axial (+√2) |
---|---|---|---|---|---|---|

PTFE content (%) | A | 1.7 | 4 | 9.5 | 15 | 17.3 |

PTFE etch time (min) | B | 2.9 | 5 | 10 | 15 | 17.1 |

**Table 2.**Central composite design (CCD) in uncoded factors with tensile strength, elasticity modulus, toughness, and hardness as responses.

PTFE Content (A) | PTFE Etch Time (B) | Tensile Strength (MPa) | Elasticity Modulus (MPa) | Toughness (kJ/m^{3}) | Hardness (HRR) |
---|---|---|---|---|---|

1.7 | 10.0 | 106.8 ± 1.6 | 8377 ± 132 | 1636 ± 102 | 115.5 ± 0.6 |

4.0 | 5.0 | 111.9 ± 1.6 | 8287 ± 73 | 2020 ± 114 | 115.7 ± 0.3 |

4.0 | 15.0 | 108.9 ± 2.4 | 8301 ± 110 | 1836 ± 147 | 115.6 ± 0.3 |

9.5 | 10.0 | 107.5 ± 1.4 | 8046 ± 108 | 2013 ± 87 | 114.4 ± 0.4 |

9.5 | 10.0 | 108.6 ± 1.7 | 8087 ± 90 | 2021 ± 106 | 114.6 ± 0.7 |

9.5 | 17.1 | 107.7 ± 1.9 | 8069 ± 129 | 2090 ± 92 | 114.7 ± 0.6 |

9.5 | 10.0 | 107.2 ± 1.8 | 8057 ± 86 | 2014 ± 97 | 114.6 ± 0.3 |

9.5 | 10.0 | 108.1 ± 0.9 | 8067 ± 48 | 2025 ± 105 | 114.1 ± 0.3 |

9.5 | 2.9 | 108.2 ± 1.2 | 8048 ± 48 | 2149 ± 101 | 114.8 ± 0.3 |

9.5 | 10.0 | 108.0 ± 1.2 | 8118 ± 99 | 1909 ± 119 | 114.0 ± 0.6 |

15.0 | 5.0 | 105.1 ± 1.9 | 7884 ± 76 | 2032 ± 113 | 112.8 ± 0.3 |

15.0 | 15.0 | 102.0 ± 2.1 | 7803 ± 75 | 1879 ± 134 | 112.9 ± 0.3 |

17.3 | 10.0 | 101.7 ± 3.3 | 7867 ± 113 | 1805 ± 150 | 111.8 ± 0.2 |

**Table 3.**Analyses of variance (ANOVA) for response surface model for tensile strength of POM composites using CCD.

Source | Sum of Squares | df | Mean Square | F | Prob. > F | |
---|---|---|---|---|---|---|

Model | 88.44 | 7 | 12.63 | 24.80 | 0.0014 | significant |

A | 13.06 | 1 | 13.06 | 25.62 | 0.0039 | |

B | 0.15 | 1 | 0.15 | 0.30 | 0.6093 | |

AB | 6.25 × 10^{−4} | 1 | 6.25 × 10^{−4} | 1.23 × 10^{−3} | 0.9734 | |

A^{2} | 17.31 | 1 | 17.31 | 33.98 | 0.0021 | |

B^{2} | 0.46 | 1 | 0.46 | 0.90 | 0.3853 | |

A^{2}B | 3.53 | 1 | 3.53 | 6.92 | 0.0465 | |

AB^{2} | 5.29 | 1 | 5.29 | 10.38 | 0.0234 | |

Residual | 2.55 | 5 | 0.51 | |||

Lack of Fit | 1.44 | 1 | 1.44 | 5.17 | 0.0853 | not significant |

Pure Error | 1.11 | 4 | 0.28 | |||

Cor Total | 90.99 | 12 |

^{2}, 0.9720; R

^{2}

_{adj}, 0.9328; Adequate precision, 17.968.

**Table 4.**Analyses of variance (ANOVA) for response surface model for elasticity modulus of POM composites using CCD.

Source | Sum of Squares | df | Mean Square | F | Prob. > F | |
---|---|---|---|---|---|---|

Model | 3.353 × 10^{5} | 5 | 67,068.87 | 49.85 | <0.0001 | significant |

A | 3.288 × 10^{5} | 1 | 3.288 × 10^{5} | 244.38 | <0.0001 | |

B | 164.62 | 1 | 164.62 | 0.12 | 0.7368 | |

AB | 2244.00 | 1 | 2244.00 | 1.67 | 0.2376 | |

A^{2} | 2299.33 | 1 | 2299.33 | 1.71 | 0.2324 | |

B^{2} | 1306.86 | 1 | 1306.86 | 0.97 | 0.3572 | |

Residual | 9418.45 | 7 | 1345.49 | |||

Lack of Fit | 6145.04 | 3 | 2048.35 | 2.50 | 0.1982 | not significant |

Pure Error | 3273.41 | 4 | 818.35 | |||

Cor Total | 3.448 × 10^{5} | 12 |

^{2}, 0.9542; R

^{2}

_{adj}, 0.9450; Adequate precision, 30.038.

**Table 5.**Analyses of variance (ANOVA) for response surface model for toughness of POM composites using CCD.

Source | Sum of Squares | df | Mean Square | F | Prob. > F | |
---|---|---|---|---|---|---|

Model | 2.055 × 10^{5} | 5 | 41,102.41 | 12.59 | 0.0022 | significant |

A | 10,720.96 | 1 | 10,720.96 | 3.28 | 0.1128 | |

B | 22,150.59 | 1 | 22,150.59 | 6.79 | 0.0352 | |

AB | 252.79 | 1 | 252.79 | 0.077 | 0.7888 | |

A^{2} | 1.220 × 10^{5} | 1 | 1.220 × 10^{5} | 37.37 | 0.0005 | |

B^{2} | 31,322.35 | 1 | 31,322.35 | 9.59 | 0.0174 | |

Residual | 22,851.58 | 7 | 3264.51 | |||

Lack of Fit | 13,145.38 | 3 | 4381.79 | 1.81 | 0.2857 | not significant |

Pure Error | 9706.20 | 4 | 2426.55 | |||

Cor Total | 2.284 × 10^{5} | 12 |

^{2}, 0.8988; R

^{2}

_{adj}, 0.8482; Adequate precision, 15.760.

**Table 6.**Analyses of variance (ANOVA) for response surface model for hardness of POM composites using CCD.

Source | Sum of Squares | df | Mean Square | F | Prob. > F | |
---|---|---|---|---|---|---|

Model | 15.55 | 5 | 3.11 | 68.5 | <0.0001 | significant |

A | 14.42 | 1 | 14.42 | 317.66 | <0.0001 | |

B | 2.20 × 10^{−3} | 1 | 2.20 × 10^{−3} | 0.048 | 0.832 | |

AB | 0.013 | 1 | 0.013 | 0.29 | 0.6074 | |

A^{2} | 0.74 | 1 | 0.74 | 16.34 | 0.0049 | |

B^{2} | 0.24 | 1 | 0.24 | 5.3 | 0.0549 | |

Residual | 0.32 | 7 | 0.045 | |||

Lack of Fit | 0.016 | 3 | 5.42 × 10^{−3} | 0.072 | 0.9719 | not significant |

Pure Error | 0.3 | 4 | 0.075 | |||

Cor Total | 15.86 | 12 |

^{2}, 0.9800; R

^{2}

_{adj}, 0.9657; Adequate precision, 26.444.

Name | Goal | Lower Limit | Upper Limit | Lower Weight | Upper Weight | Importance | Desirability (d) |
---|---|---|---|---|---|---|---|

A: PTFE Content | In range | 4 | 15 | 1 | 1 | 3 | 1 |

B: PTFE Etch Time | In range | 5 | 15 | 1 | 1 | 3 | 1 |

Tensile Strength | Target = 108.0 | 101.7 | 111.9 | 1 | 1 | 3 | 0.8956 |

Elasticity Modulus | Target = 8300.0 | 7802.9 | 8377.0 | 1 | 1 | 5 | 0.7797 |

Toughness | Target = 2000.0 | 1636.3 | 2149.4 | 1 | 1 | 3 | 0.8274 |

Hardness | Target = 115.0 | 111.8 | 115.7 | 1 | 1 | 5 | 1 |

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## Share and Cite

**MDPI and ACS Style**

Kunnan Singh, J.S.; Ching, Y.C.; Abdullah, L.C.; Ching, K.Y.; Razali, S.; Gan, S.N.
Optimization of Mechanical Properties for Polyoxymethylene/Glass Fiber/Polytetrafluoroethylene Composites Using Response Surface Methodology. *Polymers* **2018**, *10*, 338.
https://doi.org/10.3390/polym10030338

**AMA Style**

Kunnan Singh JS, Ching YC, Abdullah LC, Ching KY, Razali S, Gan SN.
Optimization of Mechanical Properties for Polyoxymethylene/Glass Fiber/Polytetrafluoroethylene Composites Using Response Surface Methodology. *Polymers*. 2018; 10(3):338.
https://doi.org/10.3390/polym10030338

**Chicago/Turabian Style**

Kunnan Singh, Jasbir Singh, Yern Chee Ching, Luqman Chuah Abdullah, Kuan Yong Ching, Shaifulazuar Razali, and Seng Neon Gan.
2018. "Optimization of Mechanical Properties for Polyoxymethylene/Glass Fiber/Polytetrafluoroethylene Composites Using Response Surface Methodology" *Polymers* 10, no. 3: 338.
https://doi.org/10.3390/polym10030338