# Structure and Performance Attributes Optimization and Ranking of Gamma Irradiated Polymer Hybrids for Industrial Application

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^{2}

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## Abstract

**:**

## 1. Introduction

- The material selection model based on fuzzy multi-attribute decision-making, proposed originally by Liao [16], is rather complex in nature and requires significantly large computational time.
- The model based on the ‘utility’ functions for multi-objective material optimization proposed by Ashby [17] is simple, but its effectiveness is questionable.
- A material selection model known as ELECTRE, based on multi-attribute decision-making, uses the theme of outranking-relationship among the attributes [18] but can only compute the partial prioritization among small numbers of alternatives.
- Bahraminasab and Jahan [19] recently used the comprehensive VIKOR model for the selection of a femoral-component for TKR. The results are satisfactory to some extent; however, this study is site-specific and needs to be amended for consideration at other replacement sites.

_{0}, HY

_{30}, HY

_{65}, HY

_{100}, respectively, were considered and tested for different properties for initial treatment. After satisfactory appreciation of the proposed model and a discussion of the best choice, the manuscript ends with conclusive remarks and future recommendations for industrial applications.

## 2. Theoretical Considerations on Optimization Model

_{1}, F

_{2}, F

_{3}, F

_{4}…..F

_{j}……F

_{n}]

_{i}is the material factor which is either a higher valued obligatory (HOV) or lower-valued obligatory (LOV) factor as far as the nature of the application is concerned.

_{ij}) while following the 11-point fuzzy conversion scales [31], which are used to assign verbal relative importance to the corresponding fuzzy numbers. There are other scales available, but in this study, an 11-point scale is used to better represent the relevance of one factor over another as shown in Figure 2.

## 3. Essential Attributes for Industrial Applications of UHMWPE

#### 3.1. Oxidation Index (OI)

^{−1}–1850 cm

^{−1}with the integrating area from 1330 cm

^{−1}–1396 cm

^{−1}. The major responsible factor affecting the value of OI is the reaction of free radicals with diffused oxygen within the matrix of UHMWPE, and these free radicals are the precursors of radiation treatment.

#### 3.2. Cross-Linking Yield

_{0}and W

_{1}are the weights of the sample before and after the extraction of each sample in boiling Xylene for 12 h.

#### 3.3. Percent Crystallinity (Xc) and Crystalline Lamellae Thickness (Lc)

^{−1}), respectively.

- T
_{m}is equal to the melting temperature of the hybrid; - T°
_{m}= the equilibrium-melting temperature of 100% crystalline PE is equal to 145.7 °C; - ρ
_{c}is the crystalline phase density, and its value is equal to 1.005 g/cm^{−3}; - σ is the surface energy which is equal to 95.7 × 10
^{−7}; - ΔHm is the enthalpy peak area of a 100% crystalline PE and its value is equal to 290 J/g.

#### 3.4. Mechanical Characteristics

## 4. Methodology

_{m}). The performance attributes which are considered in the course of this study are thermal activation energy (E

_{thermal}), oxidative activation energy (E

_{oxidation}), fracture-strain (E

_{b}), crystalline lamella thickness (Lc), yield strength (YS), and Young’s modulus (YM).

#### 4.1. Experimental

#### 4.1.1. Materials

^{3}), and acetone (99% pure, i.e., laboratory-grade) were used. All chemicals were purchased from Sigma-Aldrich Chemie, Steinheim, Germany, and used without any further purification.

#### 4.1.2. Hybrid’s Preparations and Modifications

- For samples labeled as HY-0, 0.4 phr VTES was mixed with acetone then poured into 10 g of UHMWPE powder. The admixture was mixed and dried for further treatment with boiling water for approximately 24 h
- For samples labeled as HY-30, HY-65, and HY-100, 0.4 phr VTES was mixed with acetone then poured into 10 g of UHMWPE powder. The admixture was mixed and dried for further treatment with 30, 65, and 100 kGy of gamma dose, respectively.

#### 4.1.3. Hybrid’s Characterization

_{b}), yield strength (YS), and Young’s modulus (YM), crystalline lamella thickness (Lc), thermal activation energy (E

_{thermal}), and oxidative activation energy (E

_{oxidation}), respectively. A universal tensile testing machine (Model BSS-500 kg, SANS, Transcell Technology, Shenzhen, China) was used to obtain the stress–strain curve, while DSC data was used for estimating the values of crystalline lamella thickness (Lc), thermal activation energy (E

_{thermal}), oxidative activation energy (E

_{oxidation}). The measured values of the selected attributes/properties for the optimization and ranking purpose are given in in the results and discussion section.

## 5. Attributes Based Ranking

## 6. Results and Discussion

_{b}(%), YS, and YM, also need to be considered. Thermal analysis has revealed that irradiated hybrids exhibited a higher onset thermal degradation temperature, peak melting temperature, and crystalline lamellae thickness compared with the water-treated hybrid. In addition, tensile testing has confirmed a 41% and 133% increase in YS and YM values for 100 kGy irradiated hybrids than that of water-treated hybrids. The lower value of OI and double value cross-linking density for 65 kGy irradiated hybrids, along with reasonable enhancement in YM, YS values as compared to other existing alternatives i.e., 30 and 100 kGy irradiated hybrids, make this a potential alternative among existing materials. In short, one cannot rely on single parameters or only on structural parameters, as recently reported by Ahmad A Baksh [28] for choosing the best among existing alternatives. Therefore, the abovementioned parameters are further considered for ranking purposes.

- Oxidation strength is the first and foremost requirement; therefore, the lowest value of OI and higher value of E
_{oxidation}are required. OI is considered as a LOV factor, while E_{oxidation}is labeled as an HOV factor. - Higher cross-linking yield is the major reason for treating/modifying UHMWPE since its introduction. Therefore, GC (which is ASTM standard for measuring the cross-linking yield) is labeled as an HOV factor.
- The major advantage of UHMWPE-based material is that the mechanical energy, which is usually absorbed through the crystalline phase, is dissipated via its long-chain vibrations, and all-trans interphase regions play the role of transferring the absorbed energy from the crystalline phase to an amorphous one. Therefore, higher contents of crystalline centers are beneficial for the efficient dissipation of absorbed mechanical energy into the surroundings. A higher value of (%) Xc is therefore required, thus justifying its labeling as an HOV factor.
- The importance of T
_{m}(°C) and E_{Thermal}(KJ/mol) contributions are negligible and cannot be neglected when considering the long-term service characteristics of UHMWPE-based biomaterials. As a result, in this study, these factors are labeled as LOV factors. - Usually, crystallite centers are the major source for the dissipation of mechanical energy via long-chain vibrations. In this regard, the mobility of crystalline lamellae for the process of energy dissipation should be higher, which points towards the importance of crystalline lamellae of an adequate thickness for the increased efficacy of UHMWPE as energy dissipaters. In this study, Lc (nm) is included in the list of LOV factors.

_{ij}and r

_{ji}among the i

^{th}and j

^{th}factor. After finalizing the graph, the next step was to write the adjacency matrix, as given below, following the steps mentioned in Section 2.

_{m}, and performance attributes, i.e., E

_{thermal}, E

_{oxidation}, E

_{b}, Lc, YS, and YM), these are normalized while using their importance as HOV and LOV factors.

_{i}/v

_{j}, where, vi is the factor quantitative measure for the i

^{th}alternative and vj is the factor quantitative measure for the j

^{th}alternative, having a larger factor value from the enlisted possible alternatives. It is worth mentioning here that this ratio is only valid for those factors whose higher values are enviable in an application context. For LOV factors (the factors with lower desirable measure), the normalized values are calculated by v

_{j}/v

_{i}, where vj is the factor quantitative measure for the j

^{th}alternative having lower factor-value from enlisted possible alternatives. The quantitative values of structural attributes, i.e., OI, GC, Xc, and Tm, and performance attributes, i.e., E

_{thermal}, E

_{oxidation}, E

_{b}, Lc, YS, and YM), (given in Table 2) are normalized while using their importance as HOV and LOV factors.

_{m}, and E

_{thermal}, Eb, YM, YS are the major responsible factors. These factors need to be considered for obtaining an optimum solution for the problems as opposed to the study by Ahmad A Baksh [28], where only three structure parameters, i.e., OI, GC, and Xc (%), were considered for ranking the alternatives.

_{b}, as given in Table 1, for the 65 kGy irradiated sample is the reason for placing HY-65 as the ranked number one hybrid. The optimization methodology in this paper for selecting suitable alternative for the industrial community is simple and can be extended by including more attributes. Moreover, the methodologies not only give an analysis of the alternatives, but also serves as a visualization of the correlation factors while utilizing the graphical representation. The measurements of the factors and their relative significance are used together to rank the alternatives, and consequently, give a stronger evaluation of the alternatives. Furthermore, using the concept of a permanent matrix is more beneficial for the more accurate evaluation of factors. It contains all possible structural components of the factors and their relative significance, and it, therefore also characterizes the considered selection issue in a more indisputable way.

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Self-descriptive material selection graph for this study with mentioned HOV and LOV factor and weight–age of relative importance’s among each factor.

**Figure 5.**Rainbow color representation of decision matrices for HY-0 (

**top right**side), HY-30 (

**top left**side), HY-65 (

**bottom left**side), and HY-100 (

**bottom right**side).

**Table 1.**Measured values of selected attributes/properties for establishing structural–property optimization and ranking of hybrids.

Material Attribute/Property | UHMWPE/Silane Hybrids | |||
---|---|---|---|---|

HY-0 | HY-30 | HY-65 | HY-100 | |

OI | 0.17 | 0.42 | 0.24 | 0.54 |

Gel Contents (%) | 84.7 | 90.1 | 91 | 75 |

Xc (%) | 50.1 | 54.3 | 52.2 | 53.9 |

T_{m} (°C) | 137.1 | 133.3 | 133.7 | 131.8 |

Lc (nm) | 10.8 | 7.5 | 7.8 | 6.7 |

E_{oxidation (eV)} | 122 | 133 | 170 | 190 |

E_{Thermal (eV)} | 446 | 440 | 370 | 361 |

E_{b} (%) | 357 | 452 | 360 | 324 |

YS (MPa) | 21.7 | 22.7 | 25.3 | 30.7 |

YM (MPa) | 422 | 738 | 817 | 984 |

**Table 2.**Adjacency matrix from the material selection graph (Figure 3) with relative importance among the attributes as off-diagonal elements obtained from 11-point fuzzy logic conversation scale.

Parameters | OI | GC (%) | Xc (%) | T_{m} (°C) | Lc (nm) | E_{oxidation (eV)} | E_{Thermal (eV)} | E_{b} (%) | YS (MPa) | YM (MPa) |
---|---|---|---|---|---|---|---|---|---|---|

OI | R_{1} | 0.5 | 0.745 | 0.955 | 0.955 | 0.665 | 0.955 | 0.745 | 0.665 | 0.745 |

GC (%) | 0.5 | R_{2} | 0.745 | 0.955 | 0.955 | 0.745 | 0.955 | 0.745 | 0.665 | 0.745 |

Xc (%) | 0.255 | 0.255 | R_{3} | 0.255 | 0.5 | 0.665 | 0.335 | 0.41 | 0.5 | 0.5 |

T_{m} (°C) | 0.045 | 0.045 | 0.745 | R_{4} | 0.5 | 0.59 | 0.5 | 0.59 | 0.665 | 0.665 |

Lc (nm) | 0.045 | 0.045 | 0.5 | 0.5 | R_{5} | 0.59 | 0.5 | 0.59 | 0.665 | 0.665 |

E_{oxidation (eV)} | 0.335 | 0.255 | 0.335 | 0.41 | 0.41 | R_{6} | 0.41 | 0.335 | 0.41 | 0.335 |

E_{Thermal (eV)} | 0.045 | 0.045 | 0.665 | 0.5 | 0.5 | 0.59 | R_{7} | 0.335 | 0.41 | 0.41 |

E_{b} (%) | 0.255 | 0.255 | 0.590 | 0.41 | 0.41 | 0.665 | 0.665 | R_{8} | 0.335 | 0.41 |

YS (MPa) | 0.335 | 0.335 | 0.5 | 0.335 | 0.335 | 0.59 | 0.59 | 0.665 | R_{9} | 0.5 |

YM (MPa) | 0.255 | 0.255 | 0.5 | 0.335 | 0.335 | 0.665 | 0.59 | 0.59 | 0.5 | R_{10} |

_{1}, R

_{2},….Ri….R

_{10}are the normalized values of each attribute/factor of the respective hybrids under investigation in this study.

Material Attribute/Property | UHMWPE/Silane Hybrids | |||
---|---|---|---|---|

HY-0 | HY-30 | HY-65 | HY-100 | |

OI | 1.00 | 0.40 | 0.71 | 0.31 |

Gel Contents (%) | 0.93 | 0.99 | 1.00 | 0.82 |

Xc (%) | 0.92 | 1.00 | 0.96 | 0.99 |

T_{m} (°C) | 0.96 | 0.99 | 0.99 | 1.00 |

Lc (nm) | 0.62 | 0.90 | 0.86 | 1.00 |

E_{oxidation (eV)} | 0.64 | 0.70 | 0.89 | 1.00 |

E_{Thermal (eV)} | 0.81 | 0.82 | 0.98 | 1.00 |

E_{b} (%) | 0.79 | 1.00 | 0.80 | 0.72 |

YS (MPa) | 0.71 | 0.74 | 0.82 | 1.00 |

YM (MPa) | 0.43 | 0.75 | 0.83 | 1.00 |

Sample | Suitability Index Value | Ranking |
---|---|---|

HY-0 | 2488.43 | 4th |

HY-30 | 2637.2 | 3rd |

HY-65 | 3050.24 | 1st |

HY-100 | 2890.47 | 2nd |

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**MDPI and ACS Style**

Serbaya, S.H.; Abualsauod, E.H.; Basingab, M.S.; Bukhari, H.; Rizwan, A.; Mehmood, M.S.
Structure and Performance Attributes Optimization and Ranking of Gamma Irradiated Polymer Hybrids for Industrial Application. *Polymers* **2022**, *14*, 47.
https://doi.org/10.3390/polym14010047

**AMA Style**

Serbaya SH, Abualsauod EH, Basingab MS, Bukhari H, Rizwan A, Mehmood MS.
Structure and Performance Attributes Optimization and Ranking of Gamma Irradiated Polymer Hybrids for Industrial Application. *Polymers*. 2022; 14(1):47.
https://doi.org/10.3390/polym14010047

**Chicago/Turabian Style**

Serbaya, Suhail H., Emad H. Abualsauod, Mohammed Salem Basingab, Hatim Bukhari, Ali Rizwan, and Malik Sajjad Mehmood.
2022. "Structure and Performance Attributes Optimization and Ranking of Gamma Irradiated Polymer Hybrids for Industrial Application" *Polymers* 14, no. 1: 47.
https://doi.org/10.3390/polym14010047