# The Effect of High-Energy Ionizing Radiation on the Mechanical Properties of a Melamine Resin, Phenol-Formaldehyde Resin, and Nitrile Rubber Blend

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## Abstract

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## 1. Introduction

_{g}, determined by the DMA (dynamic mechanical analysis) technology, achieved values higher even by 17 per cent in irradiated samples compared to heat-cured samples, due to the higher density of the formed polymeric 3D network resulting in higher stiffness of the material cured by irradiation. The authors of this paper concluded that curing of epoxy resin by EB irradiation may be particularly suitable for applications in which high thermal stability and heat resistance are required. Ref. [15] deals with the study of the thermal and mechanical properties of epoxy-diane resin cured with polyethylene-polyamine after irradiation by doses of 30, 100, and 300 kGy. The effects of individual radiation doses were investigated using standard static tensile tests, as well as with the use of TGA (thermogravimetric analysis) and DMA methods. It was found that the thermal properties of the investigated material slightly increased after EB irradiation. Mechanical properties increased after irradiation by doses of 30 kGy and 100 kGy, while at a dose of 300 kGy, they significantly decreased. The impact of EB irradiation on the mechanical and dynamic mechanical properties of cross-linked fluorocarbon rubber, natural rubber, ethylene-propylene-diene monomer of rubber, and nitrile rubber was investigated [16]. It was found that the modulus of elasticity, gel portion, the temperature of glass transition, and dynamic elastic modulus of the investigated vulcanizates increase with the increasing irradiation dose, while the elongation at break and the loss factor decrease. The authors of the paper [17] studied the mechanism of interaction between carbon fibers and phenol epoxy matrixes of polymeric composites cured by EB radiation, as well as improving their interfacial shear strength. Promising results were obtained by electrochemical processing of carbon fibers followed by subsequent application of a reagent compatible with the applied EB. The morphology of both modified and unmodified carbon fibers was characterized by the use of SEM (scanning electron microscopy), AFM (atomic force microscopy), and XPS (X-ray photoelectron spectroscopy). It was proved that acidic electrolytes are particularly well-suited to improving interfacial adhesion in the EB curing process. Alkaline groups on carbon fibers prevent cationic polymerization and improve the shear strength of EB-cured composites.

## 2. Materials and Methods

#### 2.1. Preparation of Samples

#### 2.2. Radiation Treatment

#### 2.3. Static Uniaxial Tensile Tests

^{−1}at room temperature. The mean value of at least five dumbbell specimens of each sample, prepared in accordance with standards ISO 37 or ASTM D 412 [20,21], was taken, although specimens that broke in an unusual manner were disregarded. The average engineering stress-strain curves were constructed from the obtained experimental average force vs. elongation data with a maximum relative standard deviation of 5%, and they were analyzed using the software package Matlab

^{®}Version 7.10.0.499 R2010a 64-bit (MathWorks, Natick, MA, USA).

## 3. Results and Discussion

#### 3.1. Changes in Mechanical Properties

_{g}[23], with much higher strength and lower ductility than in the non-irradiated sample.

_{g}temperature [24], with ductility smaller than in the case of application of lower radiation doses. The strength of the irradiated material at a dose of 150 kGy achieves the maximum value at the same time. The shape of the stress-strain curve at higher radiation doses corresponds to curves of the amorphous cured resins in a glassy state, at a temperature just below T

_{g}[22], with strength substantially lower than at a dose of 150 kGy, and with a corresponding ductility.

_{b}and of the tensile stress at break σ

_{b}of the investigated PS PMX3 for different radiation doses, in the form of stress-strain curves to the break of the sample, are presented in Figure 2a, while their changes with the increasing dose of irradiation are shown in Figure 2b. Vertical abscissas show the error intervals of experimental data with the corresponding standard deviation. It is evident from Figure 2a,b that up to a dose of 150 kGy, ε

_{b}decreases in a non-linear manner, but continuously, with a corresponding increase of σ

_{b}. Changes in values ε

_{b}and σ

_{b}after irradiation of the samples of PS PMX3 by radiation doses of 77 kGy, 138 kGy, and 150 kGy thus show the expected opposite trend. The value ε

_{b}= 180.9% at 150 kGy versus the value ε

_{b}= 332.4% at a dose of 138 kGy is approximately 1.84 times lower, and compared to the value ε

_{b}= 426% at 77 kGy, it is approximately 2.36 times lower. The value σ

_{b}= 7.681 MPa at 150 kGy is versus the value σ

_{b}= 4.441 MPa at 138 kGy more than 1.73 times higher, and compared to the value σ

_{b}= 2.466 MPa at 77 kGy, it is approximately 3.12 times higher. The identified changes of values ε

_{b}and σ

_{b}demonstrate the changes in the mechanical properties of the irradiated PS PMX3 in this interval of radiation doses in terms of a significant reduction in its total ductility (ε

_{b}), while at the same time, its tensile strength (σ

_{b}) significantly increases due to the prevalence of cross-linking reactions over the intensity of the reactions of polymer chain scission and degradation of intermolecular cross-links initiated by the absorbed high-energy EB radiation [25]. Higher radiation doses produce more cross-links between macromolecular chains of irradiated material, resulting in an increase in resistance to the release of intermolecular forces by mechanical loading, or in an increase in its stiffness. At higher radiation doses, the polymeric network becomes tighter, and it restricts the internal mobility of the chains, thereby increasing the resistance of the irradiated material to its mechanical damage, or its strength [26]. Higher density of 3D structures of polymeric network and limited mobility of polymeric chains, i.e., higher stiffness, as well as strength of material due to irradiation by higher radiation doses, also prevent the structural reorganization of polymeric chains during its tensile stress, which significantly reduces the ability of PS PMX3 to be plastically deformed by drawing, or its ductility [27]. At radiation doses above 150 kGy, the dependence of both ε

_{b}and σ

_{b}on the magnitude of the dose of the absorbed EB radiation is non-monotonic. At 180 kGy σ

_{b,}it drops to the value of 6.637 MPa, while ε

_{b}rises to 281.2%; at 190 kGy, σ

_{b}and ε

_{b}simultaneously drop to 3.172 MPa and 54.39%, while at a dose of 284 kGy, σ

_{b}and ε

_{b}simultaneously increase to the values of 5.041 MPa and 107.5%, respectively. At a dose of 180 kGy, due to the dominance of the degradation processes over the radiation, cross-linking prevails over the degradation of transverse inter-molecular bonds between the chains of the polymeric network over their production, which makes the network less tight. The lower density of bonds reduces the size of intermolecular interactions and releases limited mobility of chains, which is accompanied by observed decreases in strength (σ

_{b}) and increased ductility (ε

_{b}) of the irradiated material. During further increases of the radiation dose, the changes of ε

_{b}and σ

_{b}show the same trend with an analogous course, so it is possible to assume that further degradation of the radiation-induced polymeric network of the irradiated material will occur. The ε

_{b}and σ

_{b}values for the non-irradiated sample could not be determined, as it was not ruptured under the given conditions of the tensile tests.

_{m}and the modulus M 40 of the investigated PS PMX3 for the virgin sample and the samples irradiated with different doses of EB radiation are presented in Figure 3a, and their changes with the increasing dose of absorbed radiation are shown in Figure 3b. For clarity, Figure 3a shows the entire stress-strain curves till completion of the tensile tests, not only after they have been torn apart, as in Figure 2a. It is evident from Figure 3a,b that up to a dose of 150 kGy both σ

_{m}and M 40 are non-linear, but they grow monotonously. The values σ

_{m}= 3.23 MPa at 77 kGy, σ

_{m}= 4.734 MPa at 138 kGy and σ

_{m}= 7.674 MPa at 150 kGy, compared to the non-irradiated sample σ

_{m}= 2.143 MPa, are approximately 1.5, 2.1, and 3.6 times higher, respectively. Values of the modulus M 40 = 2.598 MPa at 77 kGy, M 40 = 3.059 MPa at 138 kGy and M 40 = 4.3110 MPa at 150 kGy, compared to M 40 = 2.13 MPa for a non-irradiated sample, are approximately 1.2, 1.4, and 2 times higher, respectively. The recorded changes in the values of σ

_{m}and M 40 after application of radiation doses of 77 kGy, 138 kGy, and 150 kGy demonstrate the expected increase in tensile strength of the irradiated PS PMX3 with a simultaneous increase in stiffness at the initial stages of deformation, which can also be attributed to the prevailing radiation-induced cross-linking reactions over the degradation processes in the irradiated material, with the mechanism described above. At radiation doses above 150 kGy, as with at ε

_{b}and σ

_{b}, the dependencies of both σ

_{m}and M 40 on the magnitude of the dose of the absorbed radiation are non-monotonic, but they exhibit the same trend with an analogous course. At 180 kGy, the value σ

_{m}drops to 6.682 MPa and M 40 drops to 3.67 MPa; at 190 kGy, the value σ

_{m}drops to 3.476 and M 40 drops to 3.21 MPa, due to the induction-induced reduction of strength and an increase of the ductility of the sample due to the predominance of the degradation processes over the forming processes of the polymer network with the mechanism described above. At a dose of 284 kGy, the values of σ

_{m}and M 40 simultaneously increase to 5.551 MPa and 3.931 MPa, respectively. However, this increase in σ

_{m}and M 40, as well as the increase of ε

_{b}and σ

_{b}at the radiation dose of 284 kGy, is due to the continued degradation of the sample material, and not to the subsequent process of formation of the polymeric network or by the radiation-induced change of crystallinity of PS PMX3 [28]. Due to the chemical composition of the irradiated material, it can be assumed that at high radiation doses, the cross-linked nitrile rubber therein becomes completely disintegrated, and it thereby transforms to a filler dispersed in the polymeric matrix of the blend of melamine and phenol-formaldehyde resin of the composite created by the high-energy EB irradiation with mechanical properties quite different from those of the original polymer system. However, this assumption will need to be verified in ongoing research using the DSC, DMTA, TGA, and FT-IR techniques, or other diagnostic techniques.

_{b}, which is typical for brittle amorphous polymers, such as cross-linked reactoplasts, including the cured resins [24]. During all other applied radiation doses, the tensile response of the irradiated PS exhibits signs of the tensile response of more ductile materials with significantly lower stiffness and strength [23]. From the point of view of enhancement of mechanical properties of the investigated PS PMX3 with its irradiation by high-energy EB radiation, it is possible to consider the radiation dose of 150 kGy as optimal.

#### 3.2. Regression Analysis

_{b}and σ

_{b}), and in Figure 5a,b (for σ

_{m}and M 40).

_{i}, θ

_{i}, m

_{i}, and δ represent unknown but the correct coefficients of the model that have been reliably estimated in the process of parametric fitting of experimental data using the Trust Region algorithm of non-linear least squares method [29] in the device ‘CF Tool’ of the Matlab

^{®}software package. The following is then valid for the model coefficients Δy

_{i}:

_{i}pertains to critical points of the curve y = y (x) where a significant change in the velocity of its trend takes place, and N is the number of these critical points. The negative value of the quotient in the model exponent then represents a decreasing trend, while its positive value represents the increasing trend of y(x). The coefficient δ represents a non-constant error parameter of the model, which will be discussed later.

^{k}

^{−1}of the Weibull’s distribution approximates the constants Δy

_{i}, the scale parameter b = ±1/θ

_{i}and the shape parameter, or the Weibull modulus k = m

_{i}. Since the sum (ΣΔy

_{i}+ δ) approximates the initial values of the respective mechanical characteristics y(0) and θ

_{i}of the radiation dose at the critical points of the curve y = y(x), the values Δy

_{i}and θ

_{i}depend on the initial physical state of the irradiated sample of material, its properties and conditions of irradiation, while the Weibull’s moduli m

_{i}reflect the statistics of transverse intermolecular bonds breaking due to EB irradiation with different radiation doses. Since the breaking of bonds is conditioned by overcoming the energy barrier of intermolecular forces, the values of the coefficients m

_{i}depend on the magnitude of the activation energy of the individual relaxation events observed at the applied radiation doses due to the release of the polymeric chains with respect to the relevant type of motion corresponding to the given primary as well as secondary relaxation event [33]. At the same time, the degree of chains mobility is determined by the actual physical state of the polymer. In the glassy state, it is limited only to local movements of individual molecules, vibrations, bending and stretching of bonds, rotation of lateral molecular groups, and movement of only a few main chains. In the area of the glass transition, significant movement of lateral groups is possible, as well as gradual movement and reptation of the main chains, which transforms to a large-scale movement of segments and whole chains in a rubbery state. The state of viscous flow allows for the sliding of whole macromolecular chains and global translations of entire polymer molecules between entanglements with subsequent decay of the polymeric material as a whole [34]. Since the critical condition for radiation-induced polymer cross-linking is, in addition to the formation of secondary radicals in its amorphous regions, also the sufficiently high mobility of the chains which are carried by these secondary radicals, the radiation cross-linking by ionizing radiation is an optimal rubbery, or visco-elastic state with high mobility of entire chains [28]. Since the sensitivity of the individual tensile characteristics ε

_{b}, σ

_{b}, σ

_{m}, and M 40 to the magnitude of the absorbed radiation dose is different, it can be naturally expected that values of the parameters m

_{i}for their description with the use of the model (1) will also be different.

_{i}, θ

_{i}, and m

_{i}, i.e., on the initial physical state of the irradiated material sample, its properties and conditions of irradiation, as well as on the activation energies of the relaxation events initiated by individual radiation doses of the absorbed radiation that together determine the intensity of radiation-induced generation of cross-links and formation of polymer network.

_{i}, m

_{i}and δ, estimated in the process of parametric fitting of the experimental data, coefficients θ

_{i}and percentage deviations of the coefficients Δy(0) from their experimental values, as well as the statistical parameters ‘goodness of fit’ SSE, RMSE, R

^{2}and Adj-R

^{2}[35], are listed in Table 2 (for ε

_{b}and σ

_{b}) and Table 3 (for σ

_{m}and M 40). Due to the aforementioned low number of available experimental data, it was impossible to identify the coefficients θ

_{i}by parametric fitting of the experimental data; therefore, they were estimated directly from the graphical interpretation of the functional dependencies of the monitored mechanical characteristics of the irradiated material.

^{2}and Adj-R

^{2}to one (or their equality at the value of one), and low values of deviations Δy(0) show the relatively high performance of the found model. However, due to the low amount of available experimental data, more detailed statistical analysis of the descriptive and predictive capabilities of the model was not possible, and it will be necessary to realize this within the framework of ongoing research.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**(

**a**) Experimental average engineering stress-strain curves of non-irradiated polymeric system PMX3 and of polymeric system PMX3 modified by various radiation doses of ionizing EB radiation; (

**b**) Detailed representation of the linear region of the stress-strain curves.

**Figure 2.**(

**a**) Presentation of the values of strain at the break ε

_{b}and of stress at break σ

_{b}of the polymeric system PMX4 for various radiation doses; (

**b**) The effect of the radiation dose on the values of strain at break ε

_{b}and stress at break σ

_{b}of the polymeric system PMX3.

**Figure 3.**(

**a**) Presentation of the strength limit values σ

_{m}and the modulus M 40 of the polymeric system PMX3 for the virgin sample and for the samples irradiated with different radiation doses; (

**b**) Effect of the radiation dose on the strength limit values σ

_{m}and the modulus M 40 of the polymeric system PMX3.

**Figure 4.**(

**a**) Regression analysis of the functional dependence of strain at break ε

_{b}on the radiation dose; (

**b**) Regression analysis of the functional dependence of stress at break σ

_{b}on the radiation dose.

**Figure 5.**(

**a**) Regression analysis of the functional dependence of the strength limit σ

_{m}on the radiation dose; (

**b**) Regression analysis of the functional dependence of the modulus M 40 on the radiation dose.

**Table 1.**Experimental values of mechanical characteristics ε

_{b}, σ

_{b}, σ

_{m}and M 40 for the virgin sample of PMX3 polymer system and samples irradiated with individual radiation doses.

Mechanical Characteristics | 0 kGy | 77 kGy | 138 kGy | 150 kGy | 180 kGy | 190 kGy | 284 kGy |
---|---|---|---|---|---|---|---|

ε_{b} (%) | - | 426.1 | 332.4 | 180.9 | 281.2 | 54.4 | 107.5 |

σ_{b} (MPa) | - | 2.466 | 4.441 | 7.681 | 6.637 | 3.172 | 5.041 |

σ_{m} (MPa) | 2.143 | 3.234 | 4.734 | 7.674 | 6.682 | 3.476 | 5.551 |

M 40 (MPa) | 2.132 | 2.598 | 3.059 | 4.311 | 3.672 | 3.213 | 3.931 |

**Table 2.**Results of the regression analysis of the functional dependence of ε

_{b}and σ

_{b}of the irradiated material on the magnitude of the radiation dose and statistical analysis of the quality of the found regression model.

Mechanical Characteristics | θ_{i} | Δy_{i} | m_{i} | δ | Δy(0) (%) | SSE | R^{2} | Adj-R^{2} | RMSE |
---|---|---|---|---|---|---|---|---|---|

ε_{b} (%) | 110 | 22.83 | 6.003 | 50 | 0.5904 | 8.147 × 10^{−5} | 1 | 1 | 9.026 × 10^{−3} |

150 | 355.71 | 17.051 | |||||||

σ_{b} (MPa) | 110 | 2.073 | 3.825 | 2.2 | 2.319 | 4.877 × 10^{−6} | 1 | 1 | 1.562 × 10^{−3} |

150 | 8.147 × 10^{−5} | 1.053 |

**Table 3.**Results of the regression analysis of the functional dependence of σ

_{m}and M 40 of irradiated material on the magnitude of the radiation dose and statistical analysis of the quality of the found regression model.

Mechanical Characteristics | θ_{i} | Δy_{i} | m_{i} | δ | Δy(0) (%) | SSE | R^{2} | Adj-R^{2} | RMSE |
---|---|---|---|---|---|---|---|---|---|

σ_{m} (MPa) | 77 | 0.617 | 0.287 | 0.015 | 2.143 | 7.104 × 10^{−5} | 1 | 1 | 8.429 × 10^{−3} |

138 | 0.045 | 15.261 | |||||||

150 | 1.473 | 6.897 | |||||||

M 40 (MPa) | 77 | 0.272 | 0.321 | 1.591 | 2.708 | 3.737 × 10^{−4} | 0.9999 | 0.9998 | 3.67 × 10^{−3} |

138 | 0.164 | 9.662 | |||||||

150 | 0.091 | 16.761 |

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**MDPI and ACS Style**

Kopal, I.; Vršková, J.; Labaj, I.; Ondrušová, D.; Hybler, P.; Harničárová, M.; Valíček, J.; Kušnerová, M.
The Effect of High-Energy Ionizing Radiation on the Mechanical Properties of a Melamine Resin, Phenol-Formaldehyde Resin, and Nitrile Rubber Blend. *Materials* **2018**, *11*, 2405.
https://doi.org/10.3390/ma11122405

**AMA Style**

Kopal I, Vršková J, Labaj I, Ondrušová D, Hybler P, Harničárová M, Valíček J, Kušnerová M.
The Effect of High-Energy Ionizing Radiation on the Mechanical Properties of a Melamine Resin, Phenol-Formaldehyde Resin, and Nitrile Rubber Blend. *Materials*. 2018; 11(12):2405.
https://doi.org/10.3390/ma11122405

**Chicago/Turabian Style**

Kopal, Ivan, Juliana Vršková, Ivan Labaj, Darina Ondrušová, Peter Hybler, Marta Harničárová, Jan Valíček, and Milena Kušnerová.
2018. "The Effect of High-Energy Ionizing Radiation on the Mechanical Properties of a Melamine Resin, Phenol-Formaldehyde Resin, and Nitrile Rubber Blend" *Materials* 11, no. 12: 2405.
https://doi.org/10.3390/ma11122405