Hydrogen Emission and Macromolecular Radiation-Induced Defects

Article pubs.acs.org/JPCB

Hydrogen Emission and Macromolecular Radiation-Induced Defects in Polyethylene Irradiated under an Inert Atmosphere: The Role of Energy Transfers toward trans-Vinylene Unsaturations A. Ventura,† Y. Ngono-Ravache,*,† H. Marie,† D. Levavasseur-Marie,† R. Legay,‡ V. Dauvois,§ T. Chenal,∥ M. Visseaux,∥ and E. Balanzat† †

Centre de Recherche sur les Ions, les Matériaux et la Photonique (CIMAP), UMR 6252, CEA-CNRS, Boulevard Henri Becquerel, BP 5133, 14070 Cedex 5, France ‡ Laboratoire de Chimie Moléculaire et Thioorganique (LCMT), UMR 6507, 6 Boulevard Maréchal Juin, 14000 Caen, France § Laboratoire de Radiolyse et de la Matière Organique (LRMO), CEA Saclay, 91191 Gif-sur-Yvette Cedex, France ∥ Univ. Lille, CNRS, ENSCL, Centrale Lille, Univ. Artois, UMR 8181, Unité de Catalyse et de Chimie du Solide (UCCS), F-59000 Lille, France S Supporting Information *

ABSTRACT: This article is aimed at studying the evolution of H2 release as well as radiation-induced defects in polyethylene (PE), as a function of the irradiation dose under anoxic conditions. We analyze the influence of the energy transfers and trapping toward radiation-induced defects on the evolution of the radiation chemical yields with dose. One key objective herein is to quantify the contribution of these transfers toward trans-vinylene (TV) on H2 emission. For this purpose, pure PE was irradiated in a large dose domain and H2 emission was compared to that in predoped PEs containing chemically inserted TV groups irradiated at low doses. In parallel, evolutions of the concentrations of the TV groups and minor defects (vinyl and trans−trans-diene) as a function of dose were considered. Moreover, measuring simultaneously H2 and unsaturated groups had allowed inferring the cross-linking evolution with dose. With this methodology, we have succeeded in quantifying the efficiency of TVs and cross-links as energy traps and, using simple models, in fully describing the evolution of all of the radiation chemical yields. Besides, irradiations were performed using either low linear energy transfer irradiations (electron beams, γ rays) or ion beams, with the objective to assess the influence of the high ionization and excitation densities induced by the latter on PE ageing and energy transfer processes.

1. INTRODUCTION

trans-diene (TTD) and polyenes (with increasing dose) (Figure S1, Supporting Information). TVs are predominant among unsaturated defects. Their radiation chemical yields at initial dose, GTV(0), are between14,15 1.0 × 10−7 and 2.5 × 10−7 mol J−1. Among gases created in PE irradiated at low LET, H2 is by far the most important. It represents more than 99% of the emitted gases. This value slightly varies with the degree of branching of the PE under study.3,11,16−18 The remaining gases are composed of hydrocarbons of low masses.4 When the irradiation dose (D) is continually increased, alkene concentrations show a common trend: they increase with increasing dose and then level off. This means that Galkenes decreases with increasing dose down to zero at saturation. The yield decrease comes from a competition between the creation

Polyethylene (PE) behavior under ionizing radiations has been thoroughly studied for over six decades. Early studies basically concern low linear energy transfer (LET) (γ rays or electron beams) irradiations and were for instance reviewed by Ungar1 and in different chapters of the book edited by Dole.2 Effects of high LET on PE were less studied. However, some detailed works either on gas emission3,4 or on macromolecular defect creation5−8 have been undertaken. Under anoxic conditions and at low LET, macromolecular defects such as cross-linking (XL), chain scissions (S), or unsaturated bonds are created, along with gas emission. As PE is a cross-linking polymer, chain scissions, although existing, are reduced. The corresponding radiation chemical yields at initial dose, hereafter denoted as Gx(0) for the defect x, are GS(0) ∼ 0.25 × 10−7 mol J−1 and GXL(0) ∼ 2 × 10−7 mol J−1 for chain scissions1,9,10 and cross-links,1,10−13 respectively. Unsaturated bonds created in PE are trans-vinylene (TV), vinyl (V), trans− © XXXX American Chemical Society

Received: May 4, 2016 Revised: August 30, 2016

A

DOI: 10.1021/acs.jpcb.6b04503 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

In this work, we aim to specifically assess the contribution of TV on the evolution of GH2 as a function of the dose. For this purpose, tailored polymers containing solely TV groups, with increasing concentrations ([TV]0) up to 4.33 mol kg−1, and containing few side chains and thus few tertiary carbons, were synthesized. Moreover, these polymers, called hereafter predoped PEs or TV-PEs, possess the same backbone structure. TV-PEs were irradiated at low doses and the evolution of GH2 with [TV]0 was compared to GH2 obtained as a function of the radiation-induced TV concentration ([TV]radio, also denoted as CTV(D)) in pure PE. For completion, unsaturated defects (TV and other alkenes) were monitored in situ in pure PE. Measuring concurrently (for the same polymer under the same irradiation conditions) GH2 and GTV, as a function of the dose, is critically important as it allows relating GH2 and [TV]radio. Last but not the least, quantifying H2 emission in such a manner and the creation of the major unsaturated bonds allowed deducing the evolution of XL with increasing dose and consequently studying their influence on energy transfers. Irradiations were performed under a helium atmosphere using γ rays, 1 MeV electron beams, or swift heavy ions (SHIs). The use of SHI enables the assessment of the influence of high densities of ionization and excitation on energy transfers inside the polymers and their influence on gas emission and macromolecular defect creation. Indeed, the structure of energy deposition in polymers by γ rays and accelerated electrons is very different from the one induced by SHI. The first group of radiations deposits their energy in a rather homogeneous way, whereas accelerated ions deposit their energy along their path in a reduced cylinder called the track. SHIs have LET at least 3 orders of magnitude higher than electrons. The huge amount of energy locally deposited by SHI, within the track, triggers specific damage processes involving complex molecular rearrangements and collective motions of atoms. This leads, in some cases, to the creation of specific defects or to the variation in the spatial distribution of defects. As an example, V group creation, quite reduced under low LET irradiations, can become very important under high LET.36

of defects and their destruction under irradiation. The destruction of native V groups present in some linear lowdensity PEs was observed at low doses and was assigned to various phenomena.10,14,15 In the first mechanism, V group destruction was assigned to the addition of radiation-induced alkyl or hydrogen radicals on V groups.19−21 The second mechanism also implies the addition of hydrogen radicals on the unsaturations, but in this case, the addition of radicals occurs only after they have diffused to the amorphous regions of the polymer.22,23 The third mechanism is associated with the migration of electronic excitations, created in other parts of the polymer, to CC double bonds and their subsequent “trapping”. This induces the formation of a triplet excited state, which takes part in reactions with neighboring molecules.14 This third mechanism is parallel to the model proposed by Partridge on PE,24−26 based on the work of Raymonda and Katsuura on C9 alkanes,27,28 concerning the fast exciton migration along the polymer chain and its trapping on odd molecules and groups present in the polymer backbone. Since these early works, great improvement has been made in the comprehension of the phenomena involved in energy transfers in polymers using the combination of molecular probes and pulse radiolysis.29,30 Apart from electronic excitation transfers, energy transfers can also occur through charge transfers and their subsequent neutralization to form highly excited states. As a consequence, in the following, we will refer to all of these transfers as energy transfers, regardless of the actual process involved. GH2 also decreases with increasing dose. The evolution of GH2 with increasing dose has been less studied. Yet, the decrease in GH2 can be assigned to the very same mechanism as that in V groups, namely, energy transfers. Energy transfers occur in polymers and have been used since decades for the radiation stabilization of aliphatic polymers by the addition of aromatic compounds, acting as energy sinks.31 Hence, GH2 was shown to drastically decrease on adding various stabilizers either in the polymer bulk or in the polymer backbone as in copolymers.32,33 In the frame of his work on the exciton model, Partridge24 has proposed the trapping of exciton on groups with absorption energies comprised between 7.5 and 9.5 eV. As experimentally shown by Partridge himself, CC unsaturated bonds are part of these odd groups. As energy transfer, through charge transfers,34 has also been shown to occur between alkanes of different ionization energies, inducing changes in the hydrogen yield, the influence of tertiary carbons, settled through crosslinking, may not be neglected. To the best of our knowledge, the hypothesis that GH2 decrease under irradiation is more certainly due to energy transfers to double bonds, rather than to the depletion of H atom reservoir, was first proposed by Seguchi,35 as quoted from his article “a double bond formed by detachment of hydrogen protects the hydrogen detachment from PE surrounding the double bond.” However, and because the model he proposed was only supported by H2 release measurements, quite strong hypotheses needed to be made for quantitatively analyzing the protection efficiency. For instance, concentrations of TV were determined from the values of GH2, considering, at any dose, a 1/1 ratio between TV creation and cross-linking. Besides, the influence of the tertiary carbons, stemming from cross-linking, was not taken into account.

2. EXPERIMENTAL SECTION 2.1. Materials. 2.1.1. Polymers Synthesis. Pure PE was obtained from the hydrogenation of a commercial PE from Atochem (PE ATO), via the method described by Doi et al., in the presence of Wilkinson’s catalyst, using triphenylphosphine as a co-catalyst.37 As the aim of this study is to evaluate the influence of alkenes on the PE behavior under ionizing radiations, special care was taken to avoid the presence of any type of such groups in this material. The commercial PE, PE ATO, was quantitatively hydrogenated to ensure zero alkene content. PE ATO contains only V groups, as analyzed by Fourier transform infrared (FTIR) spectroscopy. Although these groups are fully hydrogenated after 15 min, the hydrogenation reaction was conducted for 2 h to ensure that any potential TV group present in the polymer was saturated (Figure S2). TV-PEs were synthesized through a two-step procedure: the synthesis of highly (95.4% according to nuclear magnetic resonance (NMR) analysis) trans-1,4-stereoregular polybutadiene (tPB) followed by homogeneous catalytic hydrogenation. The tPB was obtained by coordination catalysis using the B


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The Journal of Physical Chemistry B Cp*Nd(BH4)2(THF)x/MgnBuEt trans-stereospecific catalytic system.38 This polymerization reaction provides polymers with high M̅ n and narrow distributions Đ when the [Mg]/[Nd] ratio equals 1. All TV-PEs were obtained after the hydrogenation of tPB, stemming from a unique synthesis batch (Figure S3). The hydrogenation of the tPB was performed following the same procedure as described above. In TV-PEs, [TV]0 was varied through the modulation of the hydrogenation time. When present, V and cis-vinylene groups are hydrogenated before TV ones. 2.1.2. Material Characteristics. Polymers were characterized using 1H NMR and FTIR spectroscopy. An FTIR spectrum of a film of pure PE and the related band assignments are presented in Figure 1 and Table 1, respectively.

Table 1. Assignments of IR Bands in Virgin Pure PE and TVPEs39−41 wavenumber (cm−1)

assignment

1473

−CH2− symmetric in-plane bending: δCH2

1463

crystalline phase −CH2− symmetric in-plane bending : δCH2

1377

−CH3 symmetric in-plane bending: δsCH3

1368

−CH2− symmetric out-of-plane bending: ωCH2

1352

crystalline phase −CH2− symmetric out-of-plane bending: ωCH2

1304

amorphous phase −CH2− symmetric out-of-plane bending: ωCH2

1261

amorphous phase −CH2− symmetric out-of-plane bending: ωCH2

1176

−CH2− symmetric out-of-plane bending: ωCH2

1088

crystalline phase39 backbone C−C stretching: νC−C −CH2− symmetric out-of-plane bending: ωCH2

1050

−CH2− asymmetric out-of-plane bending: τCH2

1023 965 887

crystalline phase39 backbone C−C stretching: νC−C TV CH symmetric out-of-plane bending: ωCH −CH3 asymmetric in-plane bending: rCH3

818 and 804 730

backbone C−C stretching: νC−C −CH2− in-phase asymmetric in-plane bending: rCH2

720

crystalline phase −CH2− in-phase asymmetric in-plane bending: rCH2 crystalline phase + amorphous phase

Figure 1. FTIR spectrum of a pure PE film, of 28.6 μm thickness, acquired at an angle of 55° using a polarized light.

An excerpt of the infrared (IR) spectra of pure PE and TV-PEs, in the region of CH wagg vibrations, is presented in Figure 2. As shown in this figure, there is no absorption band related to V groups (909 cm−1) or vinylene groups (965 and 985 cm−1 for TV and TTD, respectively). The presence of cis-vinylene was ruled out because of the absence of the corresponding CH wagg absorption band in the 730−650 cm−1 region, underlying the rCH2 massif (Table 1). Moreover, no absorption band related to CC stretching vibrations is present in the 1662− 1632 cm−1 region. The ratio of chain branching in pure PE was calculated from 1 H NMR and is equal to 13 tertiary carbon atoms (CIII) for 1000 carbon atoms (Figure S4). The most important difference in the spectra of predoped TV-PEs, as compared to pure PE, is the presence of the band at 965 cm−1, related to TV, in the former. An excerpt of the IR spectra of TV-PEs, with different [TV]0 and the associated assignments are presented in Figure 2 and Table 1, respectively. The hydrogenation procedure used is known to preserve the polymer backbone.37,42,43 As a consequence, as all of the TVPEs were obtained through the hydrogenation of the same tPB, their structures, in terms of concentrations in pendant chains

Figure 2. FTIR spectral region corresponding to bands related to  CH wagg vibrations. Spectra acquired on thin films, at the same thickness (20 μm), at an angle of 55° using polarized light. From bottom to top: pure PE and TV-PE with [TV]0 of 4.47 × 10−3, 4.05 × 10−2, 4.32 × 10−1, and 4.33 mol kg−1. Baselines shifted.

C


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Table 2. Irradiation Conditions for Pure PE Irradiated at High Doses, under a Helium Atmosphere, Using Electron or Ion Beams electron beams irradiation atmosphere film thickness (μm) beam particles energy (MeV/A) particles energy (MeV) particles LET (MeV cm2 mg−1) particles LET (keV/μm) dose rate (kGy h−1) maximum dose (MGy)

heavy ions

in situ FTIR (CESIR)

in situ MS (CIGALE)

in situ FTIR (CESIR)

in situ MS (CIGALE)

helium 600 mbar 24.6 electrons

helium 4 mbar 37 electrons

(1) 2 × 10−3 a (1.9 × 10−1) 1710 11.7

(1) 2 × 10−3 a (1.9 × 10−1) 650 9.7

helium 1000 mbar 44.3 20 Ne 12.55 (251 MeV) 4.1b (390) 250 9.6

helium 4 mbar 66 20 Ne 12.55 (251 MeV) 4.1b (390) 250 8.4

a

From the NIST tables. bCalculated with SRIM, based on the TRIM code.44 CESIR (chamber for on-line analyses by IR spectroscopy) and CIGALE (chamber for irradiation and on-line gas analysis) are acronyms of homemade devices.

γ Rays and electron beam present a huge difference in dose rates. Despite this, the two irradiations are considered equivalent because γ rays are used only for H2 yield at low doses, and we have found no evidence of the influence of dose rate on H2 emission or the creation of macromolecular defects at low doses. 2.2.1. Setup and Sample Characteristics. Most of the analyses in this study were carried out on-line. Irradiations were then performed in a sequential pattern, and analyses were conducted after each dose step. The dose step was fixed at 25 kGy for hydrogen analysis and was variable for macromolecular defect analyses. Irradiations at low doses were performed in sealed glass ampoules, for subsequent off-line gas analyses. For on-line hydrogen analyses, polymers were irradiated and analyzed in a specific setup equipped with a mass spectrometer (CIGALE). Analyses were performed in the residual gas analysis (RGA) mode, using a RC RGA analyzer (HAL 7) from Hiden Analytical, equipped with a quadrupole and a secondary electron multiplier (SEM). Quantification was obtained through calibration curves. The setup, as well as the quantification procedure, is thoroughly described in a previous article.45 For off-line gas analyses, polymers were irradiated in the form of stacks of thin films inserted in 20 cm3 (8 cm3 for 36Ar ion beams) sealed glass ampoules, under He. The resulting radiolysis gases were analyzed using a quantitative gas mass spectrometer (MAT-271; Thermo Fisher, a direct inlet gas mass spectrometer with a magnetic sector), with a detection limit of about 1 ppm, depending on the gas matrix and mass interferences.46 To evaluate and correct the impact of the difference in dosimetry on GH2, two identical polymers were irradiated simultaneously with electron beams for on-line analyses and in sealed glass ampoules with γ rays for of f-line analyses. The same procedure was applied for on-line analyses with Ne beams and of f-line analysis with Ar beams. Macromolecular defects were analyzed on-line using a specific setup (CESIR) that allowed us to irradiate and acquire the FTIR spectra without removing the sample from the cell. As a consequence, first, oxidation was avoided and second, as exactly the same area of the sample was irradiated and probed all along the experiment, inconveniences due to possible local thickness variations were avoided. Moreover, multiple samples could be irradiated concomitantly, saving irradiation time.

and chain length, are assumed to be identical. Therefore, the average molecular weight, M̅ n, the dispersity index, Đ, and the content in tertiary carbons in TV-PEs are equal to 178 000 g mol−1, 1.13, and 5 carbons for 1000 carbons in the chain, respectively.38 One can expect that when increasing the concentration of TV, the crystalline ratio of the polymers should decrease as compared to pure PE. We did not measure accurately the crystalline fraction of the TV-PEs. Yet, for comparison purposes, its evolution with [TV]0 was estimated using the massif at 720 cm−1 related to the in-phase CH2 rocking vibration mode, as explained in Figure S5. The decrease in the crystalline ratio for the samples with the highest TV content is relatively modest, around 20%. 2.2. Irradiation Conditions. Irradiations were performed at room temperature under a helium atmosphere using γ rays, 1 MeV electron beams, or swift heavy ions. All of the irradiation conditions, including doses, dose rates, irradiation atmosphere, and sample thicknesses, are gathered in Tables 2 and 3. For comparison purposes between different irradiation types, the ion beam fluence (ϕ) was transformed into dose, in Gy, through the relation D = q·LET·ϕ, with q = 1.6 × 10−7 when LET is expressed in MeV mg−1 cm2 and ϕ in cm−2. The same formula can be used to transform the flux into dose rate. Table 3. Irradiation Conditions for Pure PE and TV-PEs Irradiated at Low Doses Using γ Rays or Ion Beams high LET irradiation low LET irradiation

medium energy

high energy

device

glass ampoules

CIGALE

irradiation atmosphere average film thickness (μm) beam particle energy (MeV/A) particle energy (MeV) particle LET (MeV cm2 mg−1) particle LET (keV/μm) dose rate (kGy h−1) irradiation doses (kGy)

800 mbar He 30

4 mbar He 35

glass ampoules 600 mbar He 30

γ rays

20

Ne 13 (260) 4a

36

(380) 250 25

(247) 125 25

a

0.58 75 and 130

Ar 87 (3132) 2.6a

Calculated with SRIM, based on the TRIM code.44 D


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The Journal of Physical Chemistry B Polymers were irradiated in the form of thin films to enable FTIR analysis, in the transmission mode, without band saturation. Interference fringes were avoided by recording the spectra, with polarized light, at the Brewster angle (55°). The FTIR spectra were recorded using a Nicolet Nexus 570 IR spectrometer, equipped with an MCTA detector, at a resolution of 2 cm−1. A total of 256 scans were averaged for improving the signal-to-noise ratio. This is necessary for accurate defect quantification because very low irradiation doses were also used. 2.2.2. Beam Characteristics. Some of the irradiations (of fline analyses) were performed using γ rays from a cobalt source, at IONISOS (Dagneux, France). Electron beam irradiations were performed at the SIRIUS platform (Laboratoire des Solides Irradiés, Ecole polytechnique, France). Experiments with ion beams were performed at the Grand Accélérateur National d’Ions Lourds (GANIL, Caen, France), on the medium-energy line facility (IRASME) for the 20Ne beams and on the high-energy line facility (IRRABAT) for the 36 Ar beams. High-energy Ar beams were chosen to allow the beam to pass through the glass wall without losing too much energy and to allow LET close to that of Ne beams. In any sample, the projectile range was by far much larger than the sample thickness. In other respects, the beam energy was high enough to guarantee a rather constant LET over the sample thickness. In all cases, the relative decrease in the projectile energy in the sample was below 25%. For both electron and ion beams, an x,y-scanned beam was used to ensure a homogeneous irradiation field over the sample surfaces. Details of the dosimetry and systematic errors on dose are presented in section D of Supporting Information. 2.3. Spectra and Data Analyses. 2.3.1. Gas Mass Spectrometry and RGA Spectra. Gas mass spectrometry analyses were performed for polymers irradiated in sealed glass ampoules. Instantaneous gas emission yield at a given dose, GH2(D), expressed in mol J−1, is obtained via eq 1 below. G H2(D) =

nH2 ΔD·m

=

Pf ·%vol ·Vfree R ·T ·ΔD ·m

is the sample thickness. The molar extinction coefficients used for quantification are 155, 141, and 331 kg mol−1 cm−1, for 965 cm −1 (TV), 909 cm −1 (V), and 985 cm −1 (TTD), respectively.47 Absorbances were obtained either using the Omnic software or through spectrum deconvolution of the 920−1000 cm−1 region (Figure S6). 2.3.3. Errors on Radiation Chemical Yields. Errors on the radiation chemical yields of both H2 emission and macromolecular defects, and their possible influence when comparing data obtained under different irradiation conditions, are discussed in section D of Supporting Information.

3. RESULTS 3.1. Pure PE. Pure PE was irradiated with 1 MeV electron beams and 20Ne ion beams at doses as high as 10 MGy. Irradiating at such high doses enables one to follow all radiation chemical yields with increasing dose and thus with increasing concentrations in radiation-induced macromolecular defects. In particular, measuring GH2 in pure PE as a function of the dose, and then as a function of the concentration of radiationinduced macromolecular defects, in pure PE allows comparison with GH2(0), at low doses, as a function of the concentration of chemically inserted TV in TV-PE. 3.1.1. Molecular Hydrogen. Molecular hydrogen represents almost all of the emitted gases in pure PE, irradiated either with electrons or with ion beams in the LET domain used in this work.48 Figure 3 represents the evolution of GH2 as a function of the dose in pure PE irradiated with either 1 MeV electron beams or 20 Ne ion beams. For both irradiation conditions, GH2 decreases with increasing dose, as observed by previous authors,35 and then almost stabilizes at high doses. The values at stabilization of GH2 are equal to ≈2 × 10−7 and ≈3 × 10−7 mol J−1 at low

(1)

In this equation, nH2 is the number of moles of molecular hydrogen emitted by radiolysis during the dose step, ΔD, and m is the sample mass in kg, Pf is the total pressure in the glass tube after irradiation in Pa, %vol is the hydrogen volume fraction determined by gas mass spectrometry, Vfree is the free volume in the glass ampoule in m3, R is the gas constant (8.314 J mol−1 K−1), and T is the temperature during analysis in K. For RGA analyses, the same equation applies but the H2 partial pressure (Pf · %vol) was extracted by analyzing the time evolution of IH2/IHe, following injection in the spectrometer, as briefly described in the Supporting Information (section D) and in detail in a previously published work.45 2.3.2. Infrared Spectra. Molecular defects analyzed by FTIR are essentially of the alkene type: TV, V, and TTD. These defects were, respectively, monitored via the 965, 909, and 985 cm−1 absorption bands. These bands are assigned to the trans C−H wagging, CH2 wagging, and trans C−H wagging in the trans−trans configuration, respectively.39,40 The concentration of a vibrator is linked to the absorbance through the Beer−Lambert law A = ε·C·l. In this equation, A is the absorbance, C (mol kg−1) is the vibrator concentration, ε (mol−1 kg cm−1) is the molar extinction coefficient, and l (cm)

Figure 3. Evolution of the radiation chemical yield of hydrogen emission as a function of the dose in pure PE irradiated under a helium atmosphere using electron beams (solid circles) and 20Ne ion beams (solid squares). The dashed line represents the evolution of H2 yield assuming that it is proportional to the concentration of H atoms in the polymer. E


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Table 4. Parameters Used in the Data Modeling of Yield Evolutions as a Function of the Dose in Pure PE Irradiated with Electron or Ions Beams under an Anoxic Atmospherea beam −1

GX(0) (mol J )

b (Gy−1) C(∞)i/C(∞)e v (monomers) α

electrons ions ions/electr. electrons ions

TVb

TTDb −7

1.52 × 10 2.0 × 10−7 1.31 4.34 × 10−7 2.91 × 10−7 1.96

Vb −7

0.188 × 10 0.224 × 10−7 1.19 3.70 × 10−7 1.99 × 10−7 2.21

H2 −7

0.060 × 10 0.104 × 10−7 1.74 4.49 × 10−7 1.54 × 10−7 5.09

4.06 × 10 4.65 × 10−7 e 1.14

−7 f

2.08 × 10 1.79 × 10−7 f 0.86

1.54 × 10−7

2.21 × 10−7

67d 67e 0.45d 0.54e

electrons ions electrons ions

TVh with energy transfer

XL −7 c

30g

67 0.45

a GX(0) is the yield for the defect X at low doses, b is the first-order destruction parameter (CX(∞) = GX(0)/b), v is the radiation-protection volume, α is the fraction of nonscavengeable energy, C(∞)i/C(∞)e is the ratio of concentrations at saturation under ion (i) and electron (e) irradiations. b Using eq 8 stemming from the zero-order formation and first-order destruction kinetics. cDeduced by fitting GH2 = f([TV]radio) using eq 5 with values of v and α obtained from electron irradiation of TV-PE (d). dDeduced by fitting GH2,[TV]0(0) = f([TV]0) (electron irradiation), without any fixed parameter, using eq 4. eDeduced by fitting GH2,[TV]0(0) = f([TV]0) (ion irradiation) using the value of v obtained from electron irradiation (d). f GXL was fitted using a linear expression with dose GXL = GXL(0) + δ.D with δ = −1.85 × 10−15 and 1.03 × 10−14 mol kg−1 J−2 for electron and ion irradiation, respectively. gUsing eq 5, deduced by fitting GH2 = f([TV]radio) (electron irradiation), fixing valkenes = 67 and α = 0.45. hUsing eq 7, deduced by fitting GTV(D) (electron irradiation), at fixed values of valkenes = 67, vXL = 30 and α = 0.45, obtained from the adjustment of the curve GH2 = f([TV]radio) (electron irradiation).

already shown in previous studies.6,7,14,50,51 This behavior, observed both under electron and 20Ne beams, signals the decrease in the radiation chemical yields of creation of these defects with increasing dose. Figure 4 presents the evolution, as a function of the dose, of the concentration of TV groups, CTV, in pure PE irradiated with either 1 MeV electron beams or 20Ne ion beams. From this figure, it appears that the saturation of TV concentration occurs at a dose similar to that for the stabilization of GH2.

and high LET, respectively. These values correspond, respectively, to ≈50 and ≈65% of the value of GH2 in pure PE at the initial dose (GH2(0)). The initial values of GH2 were extracted using the fitting procedure presented in Section 4.2. GH2(0) equals 4.06 × 10−7 and 4.65 × 10−7 mol J−1 for electron and ion beam irradiations, respectively (Table 4). The value of GH2(0) obtained in pure PE under low LET irradiations is close to the one proposed by Seguchi35 at 4.0 × 10−7 mol J−1 at 10 kGy and higher than some of those collected in the literature, mostly in early studies. These values are ranged3,11,18,49 from 2.3 × 10−7 to 4.2 × 10−7 mol J−1. This dispersion can be explained by the presence of various concentrations of V groups resulting from the polymerization procedure in these polymers, by the analysis methods (for instance, measurement of the total gas pressure is less accurate), or by the dose applied. Indeed, many studies were performed at doses varying between 100 and 1000 kGy and, as shown, GH2 decreases with increasing dose. The dashed line in Figure 3 represents the evolution of GH2 as a function of the dose under electron irradiation, assuming that the H2 emission yield is proportional to the H atom reservoir in the polymer. This line is very far from the experimental data and confirms, as already proposed by Seguchi,35 that the reduction in H2 yield with increasing dose is not linked to the reduction in the number of H atoms in the polymer. This reduction in GH2 is not linked to the decrease in the sample mass either, as (1) it is observed from the lowest doses and (2) PE is a cross-linking polymer, and at the LET used in this study, chain fragmentation in PE being almost inexistent,48 the gas release only concerns H2. 3.1.2. Macromolecular Defects. The evolution of the three most important alkene groups created in PE under an inert atmosphere, namely, TV, TTD, and V, was followed as a function of the irradiation dose. The curves related to all of the three alkenes present a tendency to saturate at high doses, as

Figure 4. Evolution of the concentration of TV as a function of the dose in pure PE irradiated under a helium atmosphere using electron beams (solid circles) and 20Ne ion beams (solid squares). Dashed lines correspond to best fits using eq 8 and the solid line is the best fit using eq 7. The curve-fitting parameters are gathered in Table 4. F


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results are in line with those previously obtained in the laboratory using the commercial PE, PE ATO.7 3.2. Molecular Hydrogen Emission in Predoped PEs (TV-PEs). As indicated above, to assess the effect of TV on the decrease in GH2, PEs containing TV were synthesized. These polymers were then irradiated at relatively low doses (75 and 130 kGy for γ irradiations and 25 kGy for ion irradiations), and hydrogen emission was quantified. The use of low doses allows preventing the formation of new defects that would compete with native TV whose effect is sought. The value of the radiation chemical yield of H2, for a TV-PE with a given initial concentration of TV, GH2,[TV]0(0), stemming from γ irradiations is actually an average value because two irradiation doses were used. Figure 6 shows the evolution of the average GH2,[TV]0(0) value as a function of the initial concentration of TV, [TV]0, in predoped PEs for γ and ion (20Ne and 36Ar) irradiations. GH2,[TV]0(0) decreases with increasing [TV]0 in the predoped polymer. The decrease rate, very rapid at the lowest concentrations, reduces with increasing concentrations and then almost nullifies at the highest concentrations of the study. The value of GH2,[TV]0(0) at the stabilization is about 52 and 45% its value when [TV]0 tends to 0 for ion and electron irradiations, respectively. These are roughly the same ratios as those of GH2 in pure PE irradiated at high doses, especially for low LET irradiations. We demonstrate here, experimentally, the contribution of TV in the reduction of hydrogen release in PE irradiated at high doses under an inert atmosphere. The decrease pattern of GH2,[TV]0(0) with the increase in [TV]0 is similar for both irradiation conditions (Figure 6). However, GH2,[TV]0(0) appears higher by 10−30%, depending on the value of [TV]0, at high LET compared to low LET. This behavior can be assigned to various parameters, which are discussed in Section 4.2. The stabilization effect of TV appears to be only modestly affected by the LET: the heterogeneity of the energy deposition induced at high LET has no dramatic influence. For the sake of completeness, it should be considered that parameters other than the initial content of TV could influence GH2, the most apparent of these being the crystallinity. The literature reports dispersed and somehow inconsistent results on the role of crystallinity in GH2. However, in a recent work and literature survey, Ferry et al. concluded that GH2 is very likely not influenced by crystallinity.52

A similar evolution of the concentration, as a function of the dose, as above, is observed for minor alkenes that are V and TTD, in pure PE irradiated with both electron and 20Ne beams, as shown in Figure 5. TTD groups appear to be created at a higher level than V groups, in pure PE irradiated with low LET particles (GTTD(0) = 1.9 × 10−8 mol J−1, whereas GV(0) = 6.0 × 10−9 mol J−1) (Table 4). This result is in agreement with the literature results.1,10,50

Figure 5. Evolution of V (open) and TTD (solid) group concentration as a function of the dose in pure PE irradiated under a helium atmosphere using electron beams (circles) and 20Ne ion beams (squares). Dashed lines: best fits using eq 8.

The comparison of results obtained under electron beam irradiation with those obtained under ion beam irradiation gives insight into the LET effect on alkene creation. This effect depends on the group considered. It is similar for TV and TTD and depends on the dose: reduced at low doses and significant at high doses, at the plateau. As an example, the values of GTV(0) are close at both low and high LET, but the concentration at the plateau at high LET is almost twice as much as the value at low LET (Table 4). More precisely, GTV(0) is equal to 1.52 × 10−7 and 2.0 × 10−7 mol J−1 for electron beams and ion beams, respectively, and CTV(∞) equals 0.35 and 0.69 mol kg−1 at low and high LET, respectively (Table 4). An important LET effect exists on V creation, in the entire dose domain. This behavior was previously observed and assigned to the need for high densities of ionization for V groups to be created.5,7 The initial radiation chemical yield GV(0) is 6.0 × 10−9 mol J−1 at low LET and 1.0 × 10−8 mol J−1 at high LET (Table 4). The value of GV(0) at high LET is almost twice its value at low LET. The ratio of CV between ion beam and electron beam is even higher at the plateau, with CV(∞) = 0.013 and 0.068 mol kg−1 at low and high LET, respectively. For ion irradiation, saturation is not observed. The maximum dose used is far below the saturation dose, making the adjustments less accurate. Nevertheless, CV(∞) is undoubtedly at least five times larger at high LET. These

4. DATA PROCESSING, MODELING, AND DISCUSSION 4.1. Estimation of the Yield in Cross-Linking. Direct measurement of cross-linking as a function of the dose, in a cross-linking-type polymer, is extremely difficult. At the molecular level, C−C bonds involving tertiary carbons do not present any remarkable IR absorption band. Tertiary carbons can be quantified using 13C NMR. Yet, in the case of homogeneous distribution of cross-linking in the polymer, this necessitates either high temperatures to dissolve PE or solid-state magic angle spinning (MAS) cross-polarization. Using high temperatures for dissolution must be prevented because of further reactions of the remaining radicals at very low doses and difficulties or even the impossibility of dissolving the irradiated polymer at higher doses, owing to cross-linkings. G


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Figure 7. Evolution of the cross-linking radiation chemical yield as a function of the irradiation dose, in pure PE irradiated under a helium atmosphere using electron beams (dots) and Ne ion beams (squares).

Figure 6. Evolution of GH2,[TV]0(0), the H2 emission yield at low doses in predoped PE, as a function of the initial concentration of TV in TVPEs irradiated under a helium atmosphere using γ rays (solid circles) and heavy ions (solid squares). The lines represent the evolutions calculated from eq 4. Parameters of the fits are gathered in Table 4.

extensively in the literature. Tentative assessment of this effect on PE was made, through the study of the evolution of mechanical properties associated with the measurement of gel fractions, with no clear indication other than the creation of heterogeneously distributed cross-links at high LET.55,56 Most of the studies on the effect of LET on cross-linking polymers were performed using polystyrene (PS). As far as the gel fraction is concerned, the effect of LET on GXL(0) in PS is not straightforward.17,57 Nevertheless, using appropriate conditions (monodisperse PS and GPC), GXL was shown to increase with increasing LET.58 However, an increase in GXL with increasing LET in PS does not imply an increase in GXL in all cross-linking polymers. As a matter of fact, PS contains aromatic cycles whose sensitivity to LET has been demonstrated by different authors (e.g., LaVerne59) and that play an important role in the evolution of this polymer with increasing LET. The evolution of GXL as a function of the LET, in PE, remains an open question. However, as it was shown in various cross-linking and degrading polymers that cross-links are created in the form of “gel dots”58 or “gel strings,”60 in the wake of a unique ion, one can expect that for a given average dose in the polymer, the local GXL in a given track would be higher than GXL in the same polymer irradiated with low LET at the same dose. 4.2. Modeling and Discussion. In this section, results obtained at low LET (electron beam and γ rays) are analyzed and discussed separately from those obtained under high LET using ion beams. The analysis of the sensibility of the fit to the values of the parameters is presented in the Supporting Information (section F). 4.2.1. Low LET. 4.2.1.1. Hydrogen Emission. As said above, one main goal of this study is to assess, experimentally, the role of TV as energy sinks and their influence on the decrease in molecular hydrogen emission in pure PE with increasing dose. For this purpose, we have compared the evolution of the initial hydrogen yield as a function of the concentration of native TV (GH2,[TV]0(0) = f([TV]0)) in TV-PEs (Figure 7) with the evolution of the hydrogen yield as a function of the radiation-

On the other hand, solid-state MAS−NMR is a highly timedemanding task. As a matter of fact, data on cross-linking in PE come quasiexclusively from studies at the macromolecular level and, to the best of our knowledge, were exclusively obtained at low doses due to a rapid gel formation. In the course of this study, the yield in cross-linking was not determined experimentally. Nevertheless, as we have performed a thorough quantification of both H2 emission and unsaturated bond creation, in the same samples and under similar irradiation conditions, the cross-linking yield in pure PE, as a function of the dose, can be deduced considering the following material balance G XL(D) = G H2(D) − GTV (D) − 2*GTTD(D) − G V (D) (2)

Still, one must be aware that, even if not visible or difficult to extract from the IR spectra, other defects might be formed; very likely in minute yields. Therefore, the material balance in eq 2 can be marginally modified. Figure 7 shows the evolution of GXL as a function of the dose, in pure PE irradiated with electron or ion beams. We show here a first result of the evolution of XL as a function of dose, up to quite high doses. It appears that the cross-linking yield, in pure PE irradiated with electron beams, is constant all through the dose range used. At high LET, one might see in Figure 7 a slight tendency for GXL to increase with increasing dose. For ion beam irradiation, GXL represents an average yield on the entire polymer volume. At low LET and low doses, the mean value of GXL(0) is 2.1 × 10−7 mol J−1 (Table 4) and is coherent with values given in the literature,53,54 ranging from 1.7 × 10−7 ± 0.2 × 10−7 to 2 × 10−7 ± 0.4 × 10−7 mol J−1. It is worth noting that GXL(0) does not depend markedly on LET. The effect of LET on [XL] in PE has not been discussed H


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when considering the fact that CXL and CTV are very close at low doses, one can infer that XLs are weaker energy sinks. Other radiation-induced alkenes such as TTD and V are meant to be as good energy sinks as TV. However, as their concentrations are far below the TV concentration (Figures 4 and 5) at any dose, their effects should not notably affect GH2. The simplest way of assessing the role of a defect X as an energy sink is to consider that C2H4 ethyl moieties present in a sphere of volume v, centered on a given X group, are totally inhibited in terms of H2 creation. The radius of this sphere corresponds to a “capture radius” and is related to the maximum distance an excitation or a charge can cover before being annihilated. In such a case, when the defect concentration is high enough, GH2 tends toward zero. As this is not the case here, then, either the C2H4 moieties present in the volume v are partially protected or a fraction of the H2 created comes from “in-site” or “in-cage” processes that could not be affected by energy transfers (nonscavengeable energy). These are two different ways of describing the same concept. In the first case, there is a probability for an “excitation” to escape the influence of a given X group. In the second case, there is a probability that H2 can be created anywhere. For instance, Partridge24 has suggested that a certain ratio of the energy is localized on C−H bonds and cannot be scavenged. When X groups are randomly distributed in the polymer volume, as is the case of TV in predoped TV-PEs, the polymer fraction, f, not affected by the presence of X can be expressed through a Poisson law following eq 3.

induced TV concentration in pure PE (GH2 = f([TV]radio)). The last curve is derived from two curves, namely, the evolution of GH2 as a function of the irradiation dose, on one hand (Figure 3), and the evolution of TV concentration, [TV]radio (also denoted as CTV(D)), as a function of the irradiation dose, on the other hand (Figure 4). Replacing the x axis of the graph in Figure 3 by the y axis of the graph in Figure 4 gives the evolution GH2 = f([TV]radio) in pure PE. The curves representing the evolutions GH2,[TV]0(0) = f([TV]0) and GH2 = f([TV]radio) for TV-PEs and pure PE irradiated under an inert atmosphere with γ rays and electron beams, respectively, are presented in Figure 8. The curves are

f = e−ν·c ′

(3)

The radiation chemical yield of H2, at low doses and at a given TV concentration, in the entire polymer, GH2,c′(0), is then given by eq 4. G H2, c ′(0)

Figure 8. Evolution of the relative radiation chemical yield of emission of molecular hydrogen as a function of the concentration of radiationinduced TV in pure PE irradiated with 1 MeV electron beams (solid circle); evolution of the relative initial chemical yield of emission of molecular hydrogen as a function of the concentration of chemically inserted TV in predoped PE irradiated with γ rays (open circles). Lines correspond to curve fitting: dashed line for pure PE (eq 5) and solid line for TV-PE (eq 4). The inset is a zoom of the main figure in the region of low concentrations of TV. Fitting parameters are gathered in Table 4. In this figure, GH2,[TV]0=0(0) corresponds to GH2,c′→0(0) obtained by fitting the curve GH2,[TV]0(0) = f([TV]0) using eq 4.

G H2, c ′→ 0(0)

= α + (1 − α) e−ν·c ′ (4)

In this equation, GH2,c′→0(0) represents the radiation chemical yield of H2, at low doses, when the concentration c′ tends toward 0, v is the protection volume, expressed as the number of ethyl groups, and c′ is the relative concentration of X. It represents the ratio between the concentration of X and the concentration of ethyl groups. α is related to the efficiency of energy transfers (considering partial inhibition and/or nonscavengeable processes). When α = 0, no H2 is formed in the protected polymer fraction. When α = 1, GH2,c′(0) = GH2,c′→0(0), and no energy is transferred to the energy sink. At high c′, GH2,c′(0) tends toward α.GH2,c′→0(0). Therefore,

close to each other up to a [TV] of about 0.2 mol kg−1. This value corresponds to [TV]radio at 2 MGy and represents the 2/ 3rd of the concentration at saturation of TV, in pure PE. This consequently means that the role of TV in the stabilization of pure PE under low LET irradiation is preponderant up to around 2 MGy. Above 0.2 mol kg−1, the two curves split and, at a given [TV], the H2 yield in irradiated pure PE is smaller. At such high doses, PE is already highly modified and factors other than energy transfers on the sole TV groups might be considered. Indeed, defects other than TV are created under irradiation. Therefore, at low doses, the fact that the hydrogen yields are similar in irradiated pure PE and in predoped PE implies that the other radiation-induced defects are either less effective as energy sinks, or created in minute amounts. As a matter of fact,

α=

G H2, c ′→∞(0) G H2, c ′→ 0(0)

. In this relation, GH2,c′→∞(0) is the hydrogen

yield at high [TV]0 and at low doses. The best least-squares fits of experimental data using eq 4 are plotted in Figure 6. This equation has three free parameters, GH2,c′→0(0), α, and v. For γ-irradiated TV-PEs samples, their values are 4.21 × 10−7 mol J−1, 0.45 and 67, respectively. In contrast to TV-PEs that contain essentially TV as energy sinks, irradiated pure PE contains various types of defects and thus various potential energy sinks. Considering that all the radiation-induced defects contribute to the energy trapping and consequently to the decrease in GH2 with dose, and also I


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4.2.1.2. Macromolecular Defects in Pure PE. In pure PE, the creation of H2 and macromolecular defects can be represented by the mechanism below.

assuming that the fraction of nonscavengeable energy does not depend on the energy sink type (a unique α for all of the defects), eq 4 becomes G H2 G H2(0)

4

= α + (1 − α) exp(−∑ νi·ci) i=1

(5)

In this equation, the subscript i stands for the different radiation-induced defects, that is, TV, TTD, V, and XL. Equation 5 has six free parameters: GH2(0), α, and the four volumes of protection vi. As it is unrealistic to deduce all of the four vi values from data fitting, we have considered that all alkenes have the same trapping efficiency (vTV = vV = vTTD). This hypothesis does not have a major practical impact because, due to their relatively low concentrations, trapping on TTD and V has a very limited influence on GH2. To calculate GH2 at any dose, and thus at the corresponding [TV]radio, using eq 5, experimental values of radiation-induced [TV], [V], and [TTD] were expressed as a function of the dose using eq 8 (Table 4). Equation 8 is used here irrespective of its actual meaning in terms of kinetic processes. The evolution of XLs as a function of the dose was simply considered linear (caption of Table 4). Experimental data representing the evolution of H2 yield as a function of the concentration of radiation-induced TV, [TV]radio, along with the curve fitting from eq 5, are plotted in Figure 8. For this fitting, we have considered α = 0.45 and valkenes = 67 (i.e., the same values as for the curve GH2,[TV]0(0) = f([TV]0) in TV-PEs). This leads to vXL = 30 and GH2(0) = 4.06 × 10−7 mol J−1. The values of GH2(0) in pure PE and GH2,c′→0(0) in TV-PEs when [TV]0 is close to zero should be identical but are found to be slightly different. We assign this difference in values to the difference in the content in tertiary carbons in the two polymers, as discussed in Supporting Information. As a consequence of the lower energy trapping efficiency of XL compared to TV, at low doses, [XL] is very close to [TV]radio but has less influence on GH2. At higher doses, the influence of XL becomes more important, leading to a split between the curves GH2,[TV]0(0) = f([TV]0) and GH2 = f([TV]radio). As a matter of fact, at high doses [XL] ≫ [TV]radio because [TV]radio saturates, whereas [XL] does not (Figures 4 and 7). Therefore, the lesser efficiency of XL, compared to TV, is offset by its much larger concentration. In his work, Seguchi35 ended up with a protection volume of TV of 400 units of ethylene groups, much higher than the value we found (67 units). Part of the difference comes from the simplified analysis done in this earlier work and part comes from differences in the raw data. As a matter of fact, and for unknown reasons, GH2 in the ultrahigh molecular weight PE (UHM-PE) in this earlier work decreases faster with increasing dose than in our experiments. To determine the difference in the protection volume stemming exclusively from the difference in raw data between the cited reference and our data, eq 5 was applied to T. Seguchi’s data. Fitting these data with α = 0.45 and vXL = 30 gives a volume of protection around a given TV group of 220 units instead of 400 units in the original publication.

PH → PH*, PH+ + e−

(a1)

PH+ + e− → PH*

(a2)

PH* → PH + Q (de‐excitation)

(b1)

PH* → TV + H 2

(b2)

PH* → P° + H°

(b3)

Reaction b2, leading to the direct and concomitant creation of TV and H2, is minor.56 The polymer carbon-centered radical, P°, created during reaction b3 can react readily in the cage with the parent H° to give H2 and TV (reaction c1), recombine to form the initial polymer or react with a PH, either in the vicinity of its creation or after diffusion (reaction c2) P° + H° → H 2 + TV

(c1)

H° + PH → P° + H 2

(c2)

P° can evolve into cross-linking through addition or into TV through dismutation

P° + P° → XL

(d1)

P° + P° → TV + PH

(d2)

On the basis of these reactions (a1−d2), any process reducing H2 emission through the limitation of PH decomposition (reactions b3 and c2) is likely to have an equivalent effect on the creation of TV. Therefore, one can also consider that the creation component of TV in pure PE is also affected by energy transfers. For the same reasons, identical parameters (valkenes, vXL, and α) as for the curve GH2 = f([TV]radio) are used when applying eq 7 to Figure 4. To the best of our knowledge, the eventuality of the reduction of TV creation by energy transfers has not been considered so far. The evolution of the concentration of a given alkene, Cx(D), with dose is most traditionally described by a zero-order formation and a first-order destruction kinetics, according to eq 6. DCx = Gx (0) − b·Cx(D) dD

(6)

In this equation, b represents the destruction constant and Gx(0) is the yield in x at low doses. The simplest way to introduce the effect of energy transfer in the TV dynamics is first to consider that the creation term is affected in a similar way as H2 is, and second to keep a firstorder destruction term. Taking into account this destruction term was revealed mandatory (Supporting Information, section F). Hence, GTV is stated according to eq 7 4

D[TV] = GTV (0) ·(α + (1 − α) exp(−∑ νi·ci)) dD i=1 − b·[TV]

(7)

Equation 7 has been integrated numerically and used to fit experimental data. For γ-irradiated pure PE, Figure 4 shows the result of a curve fitting operated using the same parameters as those used for GH2 = f([TV]radio), which are valkenes = 67, vXL = 30, and α = 0.45. The model perfectly fits the data and gives J


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The Journal of Physical Chemistry B GTV(0) = 1.54 × 10−7 mol J−1 and b = 2.21 × 10−7 Gy−1. Therefore, experimental data are fully compatible with a TV creation affected by energy transfers. We have also adjusted the evolution of TV as a function of the dose using eq 8 (that is for α = 0 and vi = 0) obtained from the integration of eq 6 Cx(D) = Cx(∞) − (Cx(∞) − Cx(0)) e−b·D

In predoped TV-PE, the difference between low LET results and high LET results lies in GH2,c′→0(0) and α. These differences can be due to various parameters, among which, the difference in the dosimetry, the applied dose during the analysis step, or the excitation/ionization density. Only a small difference is observed in GH2,c′→0(0) between γ and ion irradiations, the ion irradiation yield being 10% higher. When considering the evolution of GH2 with dose (Figure 3), the expected difference in GH2,c′→0(0), due to the lower dose applied during the irradiation step intended for analyses with ion beams (25 kGy) than with γ rays (75 and 130 kGy), is estimated at roughly 5%. So, with this correction made, the difference is a ca. 5% excess for ion irradiation. Besides, when comparing γ and ion irradiations, the systematic errors in dose have to be considered and they are surely higher than the 5% difference estimated. Therefore, it can be concluded that the LET influence on GH2,c′→0(0) , if any, is smaller than the experimental error. This conclusion is different from the results reported by Chang and Laverne,3 showing a much higher increase (≈40%) when comparing GH2 from high-density PE (HDPE), under γ and 5-MeV He irradiations. The LETs in both studies are similar. The studies differ in that the cited studies used thick samples, leading to a great variation of LET through the sample (0.62 and 2.7 MeV cm2 mg−1 at, respectively, the sample entrance and the Bragg peak) and in the ion velocity (from 1.25 MeV/A to zero). Although the ion velocity also plays an important role, as it affects the radial energy deposition,61 leading to a smaller track radius and a denser core at lower velocities, it is difficult to justify such a high difference in H2 yields. It is easier to deduce the effect of LET on the ratio of nonscavengeable energy, α. As α is related to the evolution of the yields with [TV]0 and not to the absolute value of the yields

(8)

In this equation, b represents the destruction constant; Cx(0), Cx(D), and Cx(∞) are, respectively, the concentration in the defect x, before irradiation, at a dose D, and at saturation. Logically, the values of b obtained when considering the influence of energy transfers on the creation component of TV are lower than those obtained with the historical model (eq 8) (Table 4 and Figure 4). There is almost a factor of two (1.73) between the two situations. The same analysis as above has been applied to TTD and V groups (not shown in the corresponding figures) with the same conclusion: data are fully compatible with defect creation affected by energy transfers, exactly as GH2 is. The destruction factors b are reduced by very similar amounts (1.73 and 1.88, for TTD and V, respectively), when considering energy transfers. As shown in Figure 5, CV, the concentration of V groups in pure PE increases with increasing dose and shows a tendency to saturate at higher doses. In early studies, V groups present in the pristine PE were shown to be consumed readily under irradiation, from the lowest doses.14,15 In pure PE irradiated with electron beams, CV at saturation is equal to 0.013 mol kg−1. This concentration is much lower than the concentration of V structurally present (0.1 mol kg−1) in PE used in the aforementioned studies.14 Aside from any complex kinetics analysis, in these polymers, the native CV being much higher than the radiation-induced CV(∞) in pure PE, a decrease in CV with increasing dose is expected. One would expect, as cross-links were shown to act as energy sinks and as their creation is related to H2 emission, that their creation would also be affected by energy sinks and present the same pattern as that of TV. But the results show a different pattern. At high doses, the behavior of XL could be explained by their supplementary creation through the “destruction” of alkene groups. 4.2.2. High LET. 4.2.2.1. H2 Emission. As TV groups are homogeneously distributed in predoped TV-PEs irradiated with ion beams, the curve presenting the evolution of GH2,c′→0 as a function of [TV]0 was fitted using eq 4. The best fit values are slightly different from those obtained with low LET irradiations: GH2,c′→0(0) = 4.65 × 10−7 mol J−1, v = 57, and α = 0.54 (not shown in Figure 6). When v is fixed at 67 (the value at low LET), the curve fitting (Figure 6) is almost as good (GH2,c′→0(0) = 4.65 × 10−7 mol J−1 and α = 0.54). However, on setting α at 0.45 (value for low LET), the curve fitting becomes very poor (not shown in Figure 6) and leads to values of v and GH2,c′→0(0) of 21 and 4.47 × 10−7, respectively. The value of v can comfortably be considered as an intrinsic parameter of a given defect/material couple because it depends either on the difference in the excitation energies or on the difference in ionization potentials between the host polymer and the chemical defect considered. Hence, the selected parameter set for 20Ne beam irradiation is v = 67 (value at low LET), GH2,c′→0(0) = 4.65 × 10−7 mol J−1, and α = 0.54.

(α =

G H2, c ′→∞(0) G H2, c ′→ 0(0)

), this parameter is little affected by systematic

errors that equally affect GH2,c′→0 and GH2,c′→∞. Even if the LET influence on α is small, ≈20%, it is likely higher than the error bars. Accordingly, at high LET, the fraction of nonscavengeable hydrogen appears to be slightly higher. This is not completely unexpected when considering the proximity of initial species in the ion tracks. In the presence of domains with high densities of initial events or intermediary species, reactions with the closest neighbors are favored. The same comparisons as those for low LET irradiations were applied for ion beam irradiations, to quantify the influence of TV in energy transfers. The resulting curves are presented in Figure 9. Now, GH2,[TV]0(0) = f([TV]0) in TV-PEs and GH2 = f([TV]radio) in pure PE are superimposed in the entire dose domain studied, that is up to 9.5 MGy, and not only below ≈2 MGy, as was the case at low LET. Modeling GH2 = f([TV]radio) in pure PE irradiated at high LET using strictly the very same model as that for low LET appears not applicable because radiation-induced defects are not homogeneously spread in the polymer, conversely to what is assumed in the model. Nevertheless, using this model (eq 5) in this particular case gives insight into the influence of the heterogeneous distribution of macromolecular defects on G(H2), provided the influence of the energy deposition structure of ion on the ratio of nonscavengeable energy is accounted for. Indeed, if one considers a homogeneous K


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emission under irradiation in these tailored polymers and (2) the measurement, in a wide dose range (up to ≈10 MGy), of the H2 release, concurrently with the creation of alkene groups (TV, TTD, and V), in pure PE. The analysis of the evolution of the H2 emission yield, measured at low doses, with the TV content of predoped PEs has given the energy trapping efficiency of this alkene. The volume that a TV is able to radiation-protect contains ca. 70 ethylene monomer units. This is a relatively small number, indicating a short-range protection in a sphere having a radius of ca. 4 monomer size. Despite the modest value of this volume, the consequences of energy trapping on the dose evolution of the radiolysis of PE are very critical. Besides, the radiation protection by the alkenes is not complete. Roughly half of the energy escapes the trapping processes, either because of in-site or in-cage defect creation or because all excitations and ions created in the protection volume of a given TV group are not fully trapped on this group. The concurrent measurement of the H2 release and alkene creation has allowed, for the first time, accurate estimation of the evolution of the cross-linking yield with dose. This yield is remarkably constant in the entire dose domain, at low LET, whereas the other yields (H2 and alkenes) tend to a saturation value at high doses. We have shown that cross-links also contribute to the energy trapping but with a weaker efficiency restricted to the closest monomer neighbors, as the actual concerned volume is of ≈30 ethylene monomer units. Despite this, the energy trapping on cross-links becomes important at high doses, owing to the steady value of the cross-linking yield with dose. On the basis of these facts, we have proposed a model able to fully describe the evolutions of the yields of all the defects by setting a reduced number of physico-chemical-sound hypotheses. We have assumed that the fraction of nonscavengeable energy is the same for all of the radiation-induced defects and that the energy trapping efficiency is identical for all of the alkenes. The alkene kinetic evolution was historically described by a zero-order creation and a first-order destruction. The zeroorder creation is discarded in the proposed model, as creation is affected (is decreased when dose increases) by the creation of all of the radiation-induced defects. Yet, this sole effect does not describe the evolution with dose, observed experimentally for alkenes; the destruction of alkenes must be accounted for. In fact, we have retained a first-order destruction. The destruction factor becomes then typically twice as smaller when considering the energy transfers toward radiation-induced defects. Finally, we have explored the effect of high LETs by performing ion irradiations. At high LET, the fraction of nonscavengeable energy slightly but noticeably increases. For all alkenes, the concentration at saturation, at high doses, is significantly increased under irradiation at high LET. Finally, as previously reported in the literature, the initial creation yield of TTD is rather insensitive toward LET, whereas the V yield markedly increases as the LET increases.

Figure 9. Evolution of the relative radiation chemical yield of emission of molecular hydrogen as a function of the concentration of radiationinduced TV in pure PE irradiated with 20Ne ion beams (solid circle); evolution of the relative initial chemical yield of emission of molecular hydrogen as a function of the concentration of chemically inserted TV in predoped PE irradiated with 20Ne or 96Ar (open circles). The solid line corresponds to curve fitting using eq 4 for TV-PE. Fitting parameters are gathered in Table 4. In this figure, GH2,[TV]0=0(0) corresponds to GH2,c′→0(0) obtained by fitting the curve GH2,[TV]0(0) = f([TV]0) using eq 4. The dashed line represents the curve fitting for pure PE, using eq 5 and assuming that the defects are homogeneously spread in the polymer bulk but taking into account the influence of the specific structure of energy deposition on the nonscavengeable energy (α = 0.54).

repartition of the radiation-induced defects, using the value of α determined on TV-PEs irradiated with ion beams (α = 0.54), the difference between the curve stemming from the model (dashed line Figure 9) and the experimental data represents the influence of the heterogeneous distribution of the radiationinduced defects on the efficiency of energy transfers. The dashed curve is slightly below the experimental values and shows a small but visible difference with experimental data. Qualitatively, this shows that the nonhomogeneous distribution of radiation-induced defects makes them less effective in energy transfer processes, and this effect was expected. 4.2.2.2. Macromolecular Defects in Pure PE. A common strong trend of high LET irradiations on TV, V, or TTD groups in pure PE is to induce Calkenes(∞) values much higher than those at low LET (Section 3.1.2, Table 4), C(∞) being the concentration when creation and destruction are balanced. This does not contradict the common sense as, because of the heterogeneity of energy deposition and because of a higher α at high LET, one expects a less efficient decrease in creation when radiation-induced defects accumulate. To what extent the destruction factor is affected by LET is hard to determine.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b04503. The supporting information section gathers (1) secondary figures and calculations related to the synthesis of the polymers, (2) calculation of crystalline ratio using

5. CONCLUSIONS We have fully revisited the radiolysis of PE under anoxic conditions using a novel approach based on two pillars: (1) the synthesis of PEs predoped with TV groups and the study of H2 L


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(15) Williams, T. F.; Dole, M. Irradiation of polyethylene. 3. Influence of temperature and phase. J. Am. Chem. Soc. 1959, 81, 2919− 2926. (16) Lewis, M. B.; Coghlan, W. A. Ion-track reaction-rate model for hydrogen production from polymers. J. Nucl. Mater. 1996, 228, 302− 317. (17) Calcagno, L.; Compagnini, G.; Foti, G. Structural Modification of polymer-films by ion irradiation. Nucl. Instrum. Methods Phys. Res., Sect. B 1992, 65, 413−422. (18) Venkatesan, T.; Calcagno, L.; Elman, B. S.; Foti, G. Ion Beam Modification of Insulators; Elsevier: Amsterdam, 1987; Vol. 2. (19) Lawton, E. J.; Grubb, W. T.; Balwit, J. S. A solid state polymerization initiated by high-energy electrons. J. Polym. Sci. 1956, 19, 455−458. (20) Pearson, R. W. Mechanism of the radiation crosslinking of polyethylene. J. Polym. Sci. 1957, 25, 189−200. (21) Crook, M. A.; Lyons, B. J. Role of unsaturation in radiation chemistry of polymers. 1. Polyethylene. Trans. Faraday Soc. 1963, 59, 2334−2349. (22) Collinson, E.; Dainton, F. S.; Walker, D. C. Radiation chemistry of n-hexadecene-1. Trans. Faraday Soc. 1961, 57, 1732−1749. (23) Patel, G. N. Crystallinity and the effect of ionizing radiation in polyethylene. VI. Decay of vinyl groups. J. Polym. Sci., Polym. Phys. Ed. 1975, 13, 361−367. (24) Partridge, R. H. Excitation energy transfer in alkanes. 1. Exciton model. J. Chem. Phys. 1970, 52, 2485−2490. (25) Partridge, R. H. Excitation energy transfer in alkanes. 2. Experimental demonstration. J. Chem. Phys. 1970, 52, 2491−2500. (26) Partridge, R. H. Excitation energy transfer in alkanes. 3. Radiation chemistry of alkane polymers. J. Chem. Phys. 1970, 52, 2501−2510. (27) Katsuura, K.; Inokuti, M. Exciton Impurity Level and Its Implications to Radiation Chemistry. J. Chem. Phys. 1964, 41, 989− 993. (28) Raymonda, J. W.; Simpson, W. T. Experimental and theoretical study of sigma-bond electronic transitions in alkanes. J. Chem. Phys. 1967, 47, 430−448. (29) Zhang, G. H.; Thomas, J. K. Energy transfer via ionic processes in polymer films irradiated by 0.4 MeV electrons. J. Phys. Chem. 1996, 100, 11438−11455. (30) Thomas, J. K. Fundamental aspects of the radiolysis of solid polymers, crosslinking and degradation. Nucl. Instrum. Methods Phys. Res., Sect. B 2007, 265, 1−7. (31) Zeman, A.; Heusinger, H. Intramolecular energy transfer in gamma-irradiated alkylbenzenes. J. Phys. Chem. 1966, 70, 3374−3376. (32) Manion, J. P.; Burton, M. Radiolysis of hydrocarbon mixtures. J. Phys. Chem. 1952, 56, 560−569. (33) Burton, M.; Lipsky, S. Mechanisms of protection in radiolysis of organic systems. J. Phys. Chem. 1957, 61, 1461−1465. (34) Hardwick, T. J. Charge transfer in radiolysis of organic liquids. 1. Evidence from hydrogen gas yields. J. Phys. Chem. 1962, 66, 2132− 2138. (35) Seguchi, T. Mechanisms and kinetics of hydrogen yield from polymers by irradiation. Nucl. Instrum. Methods Phys. Res., Sect. B 2001, 185, 43−49. (36) Ngono-Ravache, Y. Spectroscopic study of chemical modifications induced by swift heavy ions on polymers: the contribution of the CIRIL Platform and the CIMAP Laboratory. In CIRIL, 30 Years of Interdisciplinary Research at GANIL; IOP Publishing Ltd: Bristol, 2015; Vol. 629. (37) Doi, Y.; Yano, A.; Soga, K.; Burfield, D. R. Hydrogenation of polybutadienes - microstructure and thermal-properties of hydrogenated polybutadienes. Macromolecules 1986, 19, 2409−2412. (38) Ventura, A.; Chenal, T.; Bria, M.; Bonnet, F.; Zinck, P.; NgonoRavache, Y.; Balanzat, E.; Visseaux, M. Trans-stereospecific polymerization of butadiene and random copolymerization with styrene using borohydrido neodymium/magnesium dialkyl catalysts. Eur. Polym. J. 2013, 49, 4130−4140.

absorption bands related to CH2 rocking vibrations, (3) details on dosimetry and errors on radiation chemical yields, (4) information on the characteristics of IR bands used for the deconvolution of the massif at 680−760 cm−1 (crystalline fraction calculation) and the massif at 920−1020 cm−1 (extraction of the absorbances of TV and TTD), and (5) modeling: analysis of the sensibility of the fits to the parameter values and secondary discussion (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: (33) 2 31 45 47 51. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to thank the GANIL, the SIRIUS facilities, and the EMIR network for the beamtime, and the technical staff of the CIMAP for CIGALE maintenance and various technical help. The members of the LCMT and LRMO laboratories are warmly thanked for their great help with NMR and mass spectroscopy, respectively.

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REFERENCES

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Hydrogen Emission and Macromolecular Radiation-Induced Defects

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