Charge transport behavior in gamma‐ray irradiated poly(ethylene terephthalate) estimated by surface potential decay

National Natural Science Foundation of China, Grant/Award Numbers: 51677127, 51677128, 51707132, 51707133 Abstract This study reports on the variation in charge transport behaviour of poly (ethylene terephthalate) (PET) caused by gamma‐ray irradiation estimated by means of surface potential decay (SPD) measurement. The 100 μm‐thick PET specimens were exposed to Co gamma rays to a maximum total dose of 1000 kGy. The SPD test was carried out to obtain charge transport related parameters via various models, and the effect of gamma‐ray on the transport behaviour was examined. Furthermore, Fourier transform infrared spectrum, gel content, ultraviolet‐visible spectroscopy, X‐ray photoelectron spectroscopy, differential scanning calorimetry and polarized optical microscope were employed to characterize the change in material structure induced by the irradiation. The test results indicated that with the growth in the total dose, the deep trap centre was basically unchanged, whereas the shallow trap centre became shallower. In addition, the trap density tended to decrease. The carrier mobility in PET increased with the total dose, and the charge transport manner conformed well to the hopping model. It is suggested that the formation of oxygen‐based groups from the irradiation induced oxidation reaction tends to encourage the charge transport, while the decrease of amorphous region gives rise to the reduction in trap density.


| INTRODUCTION
Recently the safety of electrical equipment installed in nuclear power plant (NPP) has received extensive attentions. Polymer materials have been widely used as insulation in NPPs and are inevitably exposed to the radiation environment [1]. Due to the impact of the irradiation ray, the degradation of the material occurs through various types of reactions such as chain scission, oxidation and crosslinking, which accelerates the ageing and possibly leads to the dielectric breakdown of polymer insulation thus threatening the safe operation of NPP [2]. Therefore, the understanding of the irradiation effect on the insulation performance of polymeric material is of great significance for the safety of NPP.
Over the past decades, many investigations have been performed on the electrical performance of polymer insulating materials with respect to gamma-ray irradiation. Y. Ohki et al. have investigated the change in electrical property of poly(ether ether ketone) (PEEK) exposed to gamma-ray irradiation. It was found that the conductivity of PEEK increased whereas the complex dielectric permittivity decreased with the irradiation dose [3]. G. Chen et al. have found that the positive charge was presented in low density polyethylene (LDPE) irradiated in air to total doses of 100 kGy, whereas only a small amount of charge existed in LDPE irradiated in vacuum or in nitrogen [4]. Y. Gao et al. have studied the surface charge behaviour on gamma-ray irradiated poly(butylene naphthalate) (PBN), it was pointed out that the rate of the charge decay decreased with the increase in total dose to 1000 kGy [5]. D.M. Min et al. have reported that the number of trap centres in silicone rubber (SiR) increased firstly then decreased as the irradiation dose changed from 0 to 225 kGy [6]. The trap distribution in isotactic polypropylene (i-PP) irradiated by gamma-rays to a maximum dose of 100 kGy was studied by S. Mouaci et al., the increase in the number of traps with the irradiation has been revealed [7]. In short, it has been demonstrated that the change in chemical and physical structures of insulating polymer could result in the variation in charge transport behaviour, which would in turn affect the electrical performance of the insulating material in NPP [8].
Poly(ethylene terephthalate) (PET) has excellent mechanical strength, good chemical stability and superior resistance to irradiation even up to 30 MGy, which makes it a promising candidate to be used as insulating material in NPP [9]. Studies with respect to the gamma-ray irradiation on ageing mechanism of PET have been performed. D.H. Jeon et al. have focused on the effect of gamma-ray irradiation on physicochemical properties of PET. It was found that the permeability, the thermal properties and the surface resistivity of the irradiated PET were not significantly changed with the total dose from 0 to 200 kGy [10]. M. Miyamoto et al. have compared the dielectric properties between poly(ethylene naphthalate) (PEN) and PET with gamma-ray irradiation, the increase in the complex permittivity of PET has been found with the total dose, whereas such increase was hardly observed in PEN [11]. N. Belkahla et al. have demonstrated the influence of gammaray irradiation on electrical conduction in PET. It was proposed that the increase in direct current after the irradiation was due to the chain scission of the macromolecules induced by the irradiation [12]. Although researches have been conducted to understand the change in mechanical, thermal or dielectric property of PET caused by gamma-ray irradiation, the charge transport behaviour has been rarely focused on.
In this study, the charge transport behaviour in PET subjected to gamma-ray of 1000 kGy at most has been investigated by surface potential decay (SPD) measurement. The possible changes in chemical and the physical property caused by the irradiation have been characterized by Fourier transform infrared spectrum (FTIR), gel content, ultraviolet-visible spectroscopy (UV-Vis), X-ray photoelectron spectroscopy (XPS), differential scanning calorimetry (DSC) and polarized optical microscope (POM). The possible nature of the irradiation tailored charge transport in PET has been demonstrated on the basis of material microstructure. Obtained results revealed the acceleration in the charge transport caused by the irradiation through introducing oxygen based groups into the backbone of PET and tailoring the amorphous region.

| Sample preparation
The 100-μm-thick PET sample was purchased from Shanghai Feixia Rubber, China, the dimension was 10 � 10 cm. Figure 1 gives the molecular structure of the PET. A 60 Co gamma source was employed to irradiate the sample in air at room temperature. The dose rate was reasonably controlled from 10 to 130 Gy/h in order to ensure the penetration of oxygen, which was an important factor of irradiation ageing for PET. The total doses were accumulated to 100, 500 and 1000 kGy, respectively.

| Charge transport behavior estimation
Charge transport behaviour has been estimated through SPD measurement. The schematic diagram for SPD measurement is shown in Figure 2, a detailed introduction to the test circuit could be found in our previous publication [13]. In this work, the SPD test was performed at 17 � 2°C with the relative humidity of ∼20%. The potentials of �5 kV and �2 kV were applied on the needle and the grid electrodes respectively, the charging time was 10 min. Afterwards the surface potential was recorded by the probe connected with an electrostatic voltmeter (Trek 347-3-H-CE), thus trap distribution, carrier mobility as well as field dependent conductivity were derived to estimate the charge transport behaviour [14].

| Material structure characterization
FTIR spectra in a transmittance mode was employed to observe the possible change in chemical composition of PET with the same settings in [15]. The crosslinking degree was measured through Soxhlet extractor by means of 40% and 60% w/w solutions of 1,1,2,2-tetrachloroethane and phenol at 140°C for 6 h. The protocol for gel fraction analysis has been reported in our previous publication [16]. The DSC was conducted with a heating/cooling rate of 10°C/min within 25 to 300°C, and the melting enthalpy for 100%-crystalline PET was selected as 140 (J/g) [17]. The change in chemical composition of sample surface layers (less than 5 nm) were examined by XPS measurement (ESCALAB250xi). The pressure in chamber during measurement was under 10 À 6 mbar and the photoelectrons were generated with Al/Kα X-ray source using monochromator. The optical property of the sample was investigated by using a UV-Vis spectrum (Shimadzu UV-3100 PC) in the wavelength range of 320-800 nm. The crystal morphology of the sample was measured by POM (59XF, Shanghai Optical Instrument Factory No.1) following the procedure as described in [18], the average grain size was determined by averaging the sizes of no less than five grains presented in the POM image. Figure 3 shows the normalized SPD behaviour for positive and negative charges. The surface potential of each sample decays with a nonlinear trend with the lapse of time, which indicates the continuous de-trapping of charges from shallow and deep traps [16]. The potential decay behaviour is changed with the total dose as shown in Figure 3a, b, which suggests the variation in charge transport characteristics. The decay of both positive and negative potential is in good agreement with the bi-exponential curve. Therefore, the fitting curves are used to calculate the trap distribution of the sample. The trap depth ΔE and the trap density N(E) could be calculated by [19,20]:

| Charge transport behavior
where k is the Boltzmann's constant, T is the Kelvin temperature, v is the attempt to escape frequency, t is the decay time, ε 0 is the permittivity of vacuum, ε r is the relative permittivity of the material, q is the elementary charge, L is the thickness of the sample and U s is the surface potential. Accordingly, the relationship between the N(E) and the ΔE represents the trap distribution. Figure 4 depicts the typical trap distribution of the unirradiated sample and the separation of measured trap into shallow and deep trap individually. The centres of deep and shallow traps are marked by the black circles. As shown in Figure 4a, the trap depth of hole ranges from 0.65 to1.05 eV, the trap centres are at 0.92 and 0.812 eV, respectively. Figure 4b shows the trap centres for electron at 0.912 and 0.808 eV. It is considered that the trap centres would have remarkable influence on charge transport behaviour of the sample due to their higher densities, thus are selected for discussion in the following parts [21]. Figure 5 depicts the effect of gamma-ray irradiation dose on the trap centre of PET. As seen from Figure 5a, the change of the deep trap centre is negligible (∼0.92 eV) with the total dose, however, the shallow trap centre decreases from 0.82 to 0.79 eV. For the electron trap, the variation manner of trap centre is similar to that of hole trap centre. The deep trap centre is basically unchanged and shallow trap centre becomes shallower due to the gamma-ray irradiation.
Effect of the total irradiation dose on the trap density of PET is depicted in Figure 6. Due to the difference in the structure of the material and the change in the structure of the material induced by the gamma-ray irradiation, the data -437 dispersion of the trap density is very significant. In order to ensure the rationality of the experimental data, each group of experiments under different irradiation doses were carried out 5 times. Based on the overall experimental results, the linear fitting method was used to fit the average of the experimental data. As shown in Figure 6a, b, for the shallow hole trap, the density decreases from 1.4 � 10 19 to 1.0 � 10 19 m À 3 ·eV À 1 with the total dose. Meanwhile, the decrease in the deep trap density is induced by the gamma-ray irradiation from 1.9 � 10 21 to 1.8 � 10 21 m À 3 ·eV À 1 . For the electron trap, both the shallow and the deep trap density decrease sharply with the total dose, as shown in Figure 6c, d, which is in agreement with the trend of the regression line. Hence, the regression line in the Figure 6 is reasonable. It is suggested that the gamma-ray irradiation reduces the trap density.
Moreover, the carrier mobility μ is also used to characterize the charge transport process of PET, which can be calculated by SPD curve. The μ can be expressed as [22]: where t T is the time at which the charge moves from the surface to the grounded electrode. The detail of the calculation method for t T has been stated in our earlier publication [23]. U s0 is the initial surface potential. Figure 7 summarized the effect of gamma-ray irradiation on the carrier mobility of PET. The carrier mobility of both hole and electron of PET is in the level of 10 À 15 m 2 ·V À 1 ·s À 1 . The hole mobility is 5.0 � 10 À 15 m 2 ·V À 1 ·s À 1 and the electron mobility is 6.3 � 10 À 15 m 2 ·V À 1 ·s À 1 for un-irradiated sample.
Compared with the virgin sample, the mobility of the irradiated sample for hole and electron increase to 8.0 � 10 À 15 and 8.4 � 10 À 15 m 2 ·V À 1 ·s À 1 , respectively. It is suggested that the carrier transport appears to be accelerated by the irradiation.
Provided that the charge mainly transports through the bulk of the material during the SPD process, the bulk conductivity of material σ can be derived by [24]: In order to further identify the mechanism of conduction in PET, the charge transport models, that is Poole-Frenkel (PF) and hopping have been employed. For the PF model, the field dependent conductivity is represented as exponential function of the square root of the electric field [25]: where β PF is the PF coefficient, which can be expressed as: ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi q πϵ 0 ϵ r L r ð6Þ Figure 8 shows the dependence of the conductivity upon the square root of U s for PET irradiated with various total doses. The experimental results are in good agreement with the fitting curves, hence the β PF can be calculated by the slope of fitting curve. With the decrease of the U 0:5 s , the conductivity decreases remarkably. The values of ε r obtained from the Equation (6) are in the range of 0.1-0.5, which are lower as compared with the reasonable values for polymeric insulating materials (higher than 2). It reveals that the PF conduction model is not suitable for the observed decay process.
The hopping conduction model is described as the charge transport process in which the carriers de-trap from traps by thermal excitation and move to empty traps. The field dependent conductivity can be expressed by [26]: where δ is the average hopping distance, N is the carrier density and ϕ is the average hopping barrier height. The field 438dependent conductivity of PET sample with various total doses is shown in Figure 9. The fitting curve based on hopping model is in good agreement with the measured values. Based on the Equation (7), the average hopping distance a could be derived. It is found that the value of δ is about tens of nm, as shown in Figure 10, which is in agreement with the values for polymeric insulating material reported in previous work [27]. The average hopping distance increases from 27.8 to 53.4 nm with the total dose, as depicted in Figure 10. Thus, it is proposed that the hopping conduction model is more suitable to describe the charge transport behaviour of the PET sample in this work.
Besides, the de-trapping probability of captured charges can be described by coefficient P de (E T ) and thus the residence time τ de (E T ) for charge trapped can be given by [28]: where E T is the trap depth. The residence time of carriers can be calculated from the above equation. When the trap depths are 0.65 and 1.1 eV at 298 K, the residence times are 9.6 � 10 À 1 and 3.9 � 107 s, respectively. The de-trapping time for charge located by the shallow trap is much shorter than that by the deep trap. The charge can hop between shallow traps easily, thereby the overall charge hopping process in the bulk is considered to be mainly determined by the shallow traps. The dependence of average hopping distance upon the density of shallow trap can be observed in Figure 10. It can be observed that the average hopping distance tends to increase with the decrease in the density of shallow trap centre, which should be ascribed to the irradiation caused variation in the microstructure of test sample.

| Material structure characterization
The PET molecules are composed of a couple of functional groups, for example ethyl group, ester groups and aromatic ring, as shown in Figure 1, which consist chemical bonds like C-H, C-C, C-O, C¼O and aromatic ring. Figure 11 shows FTIR spectra for the virgin and the irradiated PET. Due to the stretching absorption of C-O group, two absorption peaks exist at 1240 and 1096 cm À 1 . An absorption peak at 1720 cm À 1 is attributed to the stretching vibration of the C¼O bond in the ester group. For the ethyl group, two kinds of bonds exist at 2964 and 725 cm À 1 . These bands are assigned to the stretching vibration of C-H bond. The absorption peaks at 3080, 1578 and 1408 cm À 1 are associated with the stretching vibration of the aromatic ring [29]. It has been reported that the oxidation reaction could generate -OH and -COOH groups under gamma-ray irradiation in air, and results in the increase of the concentration of C¼O group with the total irradiation dose [30].
However, in this work, the absorption peak intensities of the main functional groups for PET are not changed obviously and no more absorption peaks appear or disappear. Indeed, in the given FTIR spectra, the characteristic wavenumbers of oxidized species are already occupied by those for PET, as seen from the unirradiated sample spectrum. Hence, no significant structure changes are observed with the irradiation.
The formation of three-dimensional network structure induced by cross-linking reaction in polymers is related to the irradiation dose, the irradiation time and the oxygen concentration. The increase of the free radical concentration in the sample with the irradiation will enhance the formation possibility of the three-dimensional network structure, however, the gel content of the PET remains zero with the irradiation in this work. It is deduced from such a fact that no three-dimensional network structure is generated with the irradiation.
The UV-Vis spectra of samples irradiated with various total doses in the wavelength range from 320 to 800 nm are depicted in Figure 12. It can be seen that the absorption edge shifts towards the higher wavelength side and the sample colour becomes darker with the irradiation. Y. Ohki et al. have investigated that the colouring in UV-Vis spectra is commonly observed when carbonyls or their derivatives are induced [31]. It indicates that the oxidation reaction occurs with the irradiation.
Furthermore, the optical band gap, which is defined as the energy gap from the top of the valance band to the bottom of the conduction band, could be calculated from the UV-Vis spectra. The relationship among the optical band gap, the absorption coefficient and the incident photon energy is expressed as [32]: where αhv is the optical absorption coefficient, A is a constant, hv is the energy of the incident photons, E g is the value of the optical energy gap, n is the power which characterizes the electronic transition. The value of n as 1/2, F I G U R E 1 1 FTIR spectra for the virgin and the irradiated PET. FTIR, Fourier transform infrared spectrum; PET, poly (ethylene terephthalate) F I G U R E 1 2 UV-Vis spectra of PET with various total doses. PET, poly (ethylene terephthalate) 3/2, 2 and 3 stands for direct allowed, direct forbidden, indirect allowed and indirect forbidden transitions, respectively. In this work, n ¼ 1/2 and 2 are used to analyse the variation of band gap energy for PET. Figure 13 shows the relationship between the αhv and the hv for PET with various irradiation doses. The direct and indirect band gaps can be deduced from the intersection of the extrapolated lines from the straight parts of the curve with the photon energy axis, as marked by the red circles. It is obvious that both direct and indirect band gaps both tend to decrease with the total dose, which suggests that the gamma-ray irradiation narrows the band gap of PET. XPS is performed to assist the analysis of the irradiation induced structure change of the sample. The elemental compositions of PET surface exposed to the irradiation with various total doses are depicted in Figure 14. The atomic percentages of O and C for the un-irradiated sample are 25.3% and 74.7%, respectively, which are close to the data reported earlier with 27.97% for O and 72.03% for C [33]. The ratio of O to C calculated from Figure 14 increases, which indicates that the oxidation reaction occurs with the irradiation.
The spectra of C 1s and O 1s for the virgin PET have been fitted by the AVANTAGE software, as shown in Figure 15. The C 1s spectra consists of three main bonds in Figure 15a, that is C-C and C-H bonds (carbon atoms in phenyl ring) at a binding energy of 284.4 eV, C-O bond (methylene carbon atoms singly bonded to oxygen) at 286.1 eV, and O¼C-O bond (ester carbon atoms) at 288.5 eV. The O 1s peak for the virgin sample shown in Figure 15b is composed of two components, that is O¼C bond (oxygen atoms in carbonyl) at 531.5 eV, and O-C bond (oxygen atoms in ester) at 533.0 eV [34].
The atomic percentages of C and O of PET with various irradiation doses are shown in Figure 16. For the O 1s spectra, as shown in Figure 16a, the relative percentage decreases for C¼O bond but increases for C-O bond with the total dose. According to the UV-Vis spectra, the oxidation reaction occurs with the irradiation and the number of the functional groups containing oxygen should increase. It is then considered that the amount of the C-O and the C¼O bond increases with the irradiation, whereas the number of the C-O bond rises faster than that of the C¼O bond. It is un-available to exactly point out the variation of the oxygen atom in C 1s spectra since three carbon-containing functional groups are included in the PET. As a matter of fact, the resistance to the irradiation of PET is high due to the presence of the phenyl ring [35]. It is assumed that the percentage of carbon atom in the phenyl ring is unchanged and the percentage of carbon atom with various irradiation doses except for the phenyl ring is shown in Figure  16b. The methylene carbon atom bonded to the oxygen and the ester carbon atom both increase with the irradiation dose, which means that the concentration of the oxygen-containing functional groups increases thereby in support again of the occurance of oxidation reaction. Figure 17 depicts the melting and the crystallization behaviours of PET samples. The melting temperature T m , crystallization temperature T c , melting enthalpy ΔH f , crystallinity X c and lamellar thickness L of the sample are summarized in Table 1. As shown in Figure 17a, the melting curve for the un-irradiated sample has a single endothermic peak at ∼250°C. The T m moves to higher temperature after the irradiation. According to the T m , the lamellar thickness L of PET can be calculated from Thomson-Gibbs equation [36]: where T m0 is the equilibrium melting temperature of an infinite crystal, σ e is the surface free energy per unit area of the basal plane, ΔH m is the melting enthalpy per unit volume. These values are selected as: T m0 ¼ 564 K, ΔH m ¼ 2.1 � 108 J/m 3 , σ e ¼ 0.106 J/m 2 . The average lamellar  Abbreviations: DSC, differential scanning calorimetry; PET, poly (ethylene terephthalate).

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thickness for PET after the irradiation is ∼15 nm as listed in Table 1. The difference in the lamellar thickness of the samples is not remarkable, however, the lamellar thicknesses of the irradiated samples are larger than that of the virgin sample. Thus, the crystallinity of PET gets increased by the irradiation. In Table 1, the X c firstly increases from 28.0% to 37.5% as the total dose rises to 100 kGy and then reduces from 37.5% to 29.4%. The T c shifts to the lower temperature with the total dose, as shown in Figure 17b. It is considered to be related to the change in the nucleating agent in PET sample caused by the irradiation. Figure 18 shows the crystal morphology of the virgin and the irradiated PET. For the un-irradiated sample in Figure 18a, the spherulites are small and dense. The crystal is not clear and the average size of the spherulite is ∼11.3 μm. As illustrated in Figure 18b-d, the average size of the spherulite increases gradually to ∼24.7 μm and the number of the spherulite in sight decreases with the total dose. The crystal boundary becomes clear as well. It indicates that the irradiation has a positive effect on the formation of larger spherulite.

| DISCUSSION
Charge transport behaviour is considered as an important issue related to electrical performances such as space charge accumulation, electrical treeing and dielectric breakdown [37][38][39]. The carrier traps in polymer have great impact on the charge transport, and are thought to be generated from physical defects (molecular weight distribution, free volume etc.) and chemical defects (broken chains, branched chains, additives and by-products etc.) [40]. As regards the present work, the change in physical and chemical structures of PET induced by the gamma-ray irradiation would lead to the variation in the charge transport behaviour. Both multiscale and multidisciplinary methods have been employed to analyse the structure change and to establish the relationship between the charge transport behaviour and the structure of PET.
In the microscopic scale, no cross-linking reaction occurs in the PET with the irradiation as the gel content depicts. FTIR, UV-Vis and XPS are employed to analyse the oxidation reaction induced by the irradiation. The relative concentration of O on the surface of PET increases from 25.3% to 27.6% with the total dose, meanwhile the sample colour becomes darker, which should be attributed to the presence of carbonyl or its derivatives induced by the irradiation [41]. Therefore, the oxidation reaction plays a dominant role during the irradiation, and such reaction becomes more serious with the total dose. The primary reason for such a behaviour is that: First, the oxygen could easily diffuse into the thin sample of 100 µm and reacts with free radicals generated by the irradiation, the free radicals are consumed during the oxidation reaction hence no three-dimensional network structure is formed even with 1000 kGy irradiation. Second, the rigid phenyl ring in PET backbone makes it difficult for the molecular chain to move and to bond with each other to form the network. For further understanding the degradation mechanism of PET, the possible chemical reactions caused by the irradiation are speculated and are depicted in Figure 19. In Figure 19a, the molecular chains of PET are broken by the gamma-ray and free radicals are generated. As the material is irradiated in oxygen containing atmosphere, the peroxy radicals and the hydroperoxides can be easily formed. Then the peroxy radicals react with molecules or recombine with each other to form the oxidation products such as carbonyl or hydroxyl groups. In addition, the hydroperoxides are decomposed to form the hydroxyl groups as depicted in Figure  19b. This is well supported by the XPS results presented in Figure 16, where the relative contents of C-O and C¼O bond enhance by 4.3% and 7% with the total dose, respectively.
In the mesoscopic scale, PET, as a semi-crystalline polymer material, contains crystal and amorphous regions [42]. In the crystal region, the chain scission is difficult to occur due to the compact crystal structure, and the oxidation reaction is hard to occur as well because the oxygen diffusion is weak. For the amorphous region, the oxygen diffusion in the amorphous region is much easier and the oxidation reaction occurs mainly at the crystal/amorphous interface or in the amorphous region [16]. The molecular chains are easy to be disrupted and the short molecular  [43], hence the crystallinity of the irradiated sample is larger than that of the virgin sample. The crystal size is also closely related to the molecular mobility. The enhancement of molecular mobility makes the average crystal size increase by 66.7%. Moreover, the formation of more integral crystals, the thicker lamella and the higher melting temperatures are influenced by molecular mobility. The boundary at crystal/amorphous regions decreases with the irradiation, as shown in Figure 17a and Figure 18.
With the change in the structure of PET, the charge transport feature is obviously tailored. More shallower traps are introduced by carbonyl and hydroxyl groups generated from the oxidation reaction and assist the charge migration [44]. In addition, the indirect and the direct optical band gaps are closely related to the electronic excitation processes between traps. The change in band gap energy is attributed to the generation of localized electronic states in the forbidden band, which accounts for the increase of carrier mobility in the PET. Besides, the enhanced crystallinity leads to the decrease of physical defects in amorphous region to generate shallow traps.
It is proposed that the increase of the crystallinity has more remarkable influence on the trap distribution, which could be supported by the experimental results that the density of shallow trap centre tends to decrease with the total dose as shown in Figure 6.
The hopping transport mechanism for the un-irradiated and the irradiated PET is shown in Figure 20, taking electrons as example, it is considered that the trapping/de-trapping dynamics may occur at the crystal/amorphous interface with hopping between deep and shallow traps or in the amorphous region with hopping solely between shallow traps, as depicted by the hopping Route ① and ②. Charges captured by the shallow traps can be easily released to the other traps by thermal activation, while the shallow traps are mainly formed in the amorphous region [45], thus the hopping process occurs primarily in these regions (Route ②), as shown in Figure 20a. For the un-irradiated sample, the trap depth is relatively deep. Although the density of shallow trap is large, the residence time of carriers is long, which leads the carrier mobility to be low. For the irradiated sample, since the traps are shallowed by the irradiation, the residence time for the charges captured by the shallow traps could become shorter, which results in the enhancement in the carrier mobility. As the density of the F I G U R E 1 9 Possible chemical reactions in PET caused by the gamma-ray irradiation. (a) Oxidative degradation reaction, (b) Peroxy radical reaction by gamma-ray irradiation. PET, poly (ethylene terephthalate) shallow trap centre decreases, the number of the empty traps for the carrier hopping reduces, which leads to the enhancement of the average hopping distance. In short, it is concluded that the average hopping distance and the carrier mobility are mainly related to the characteristics of shallow traps. As regards the deep trap, it is noticed that with the enhancement in the total dose, the crystal structure of PET remains spherulite shape thus the deep trap centre is basically unchanged. The deep traps mainly appear at the crystal/ amorphous interface [46], thus the reduced interface region is considered as the reason for the decrease of the deep trap density.

| CONCLUSIONS
In this study, the effect of gamma-ray irradiation on the charge transport behaviour of PET has been investigated through SPD measurement. The main conclusions can be summarized as follows, i. With the increase of the total dose, the deep trap centre of PET is basically unchanged and the shallow trap centre becomes shallower, the density of deep and shallow traps decreases. The charge transport follows well with the hopping model, the average hopping distance tends to increase with the total dose, the carrier mobility increases as well ii. The oxidation products such as carbonyl and hydroxyl groups are formed, however, no cross-linking reaction occurs with the irradiation. The band gap becomes narrower with the total irradiation dose iii. As the total irradiation dose increases, the size and the regularity of crystallite tend to increase, whereas the boundary at crystal/amorphous region decreases. Compared with the virgin sample, the crystallinity of the irradiated sample become increased, which results in the decrease in the amorphous region. The melting point as well as the lamellar thickness increases, whereas the crystallization temperature decreases In summary, it is found that the charge transport in PET is accelerated by the gamma-ray irradiation through tailoring the shallow trap centre, which is achieved by introducing oxidation products acting as shallower traps and by decreasing the amorphous region thus reducing the number of shallow trap site. Such information is helpful for understanding the effect of gamma-ray irradiation on charge transport behaviour of PET and will provide a reference for the development of cable insulation material employed in NPP.

ACKNOWLEDGMENTS
Dr. Yu Gao would like to appreciate the kind help of Professor Yoshimichi Ohki from the Waseda University, Japan who allows him a six-week academic visiting in the Waseda Univeristy and authorizes him to use the experiment apparatus in the Kagami Memorial Research Institute for Materials Science and Technology. This work in financially supported by National Nature Science Foundation of China