Article Cite This: J. Phys. Chem. B 2018, 122, 2023−2030
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Optical Properties of Saturated and Unsaturated Carbonyl Defects in Polyethylene Guido Roma,*,† Fabien Bruneval,† and Layla Martin-Samos‡,¶ †
DEN-Service de Recherches de Métallurgie Physique, CEA, Université Paris-Saclay, F-91191 Gif sur Yvette, France Materials Research Laboratory, University of Nova Gorica, SI-5000 Nova Gorica, Slovenia ¶ CNR-IOM DEMOCRITOS, Istituto Officina dei Materiali, c/o SISSA Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste Italy ‡
S Supporting Information *
ABSTRACT: Polyethylene (PE), one of the simplest and most used aliphatic polymers, is generally provided with a number of additives, in particular antioxidants, because of its tendency to get oxidized. Carbonyl defects, a product of the oxidation of PE, are occurring in various forms, in particular saturated ones, known as ketones, where a CO double bond substitutes a CH2 group, and various unsaturated ones, i.e., with further missing hydrogens. Many experimental investigations of the optical properties in the visible/UV range mainly attribute the photoluminescence of PE to one specific kind of unsaturated carbonyls, following analogies to the emission spectra of similar small molecules. However, the reason why saturated carbonyls should not be optically detected is not clear. We investigated the optical properties of PE with and without carbonyl defects using perturbative GW and the Bethe-Salpeter equation in order to take into account excitonic effects. We discuss the calculated excitonic states in comparison with experimental absorption/emission energies and the stability of both saturated and unsaturated carbonyl defects. We conclude that the unsaturated defects are indeed the best candidate for the luminescence of oxidized PE, and the reason is mainly due to oscillator strengths.
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INTRODUCTION Plastics are ubiquitous in our world.1 They are most commonly made by polymeric materials undergoing aging processes on time scales which, in general, are much shorter than for common inorganic materials, like metals or ceramics. A common polymer based on a very simple monomer unit (−CH2−) is polyethylene (PE), used in a variety of applications including various forms of packaging and electric cable insulators. PE is a prototypical polymer of polyolephins, a subset of the class of aliphatic (i.e., nonaromatic) polymers. Typical aging mechanisms of aliphatic polymers, and in particular of polyethylene (PE), include oxidation, generally prevented through adding antioxidant molecules, which preferentially capture oxygen in place of the polymer backbone. In the absence of antioxidants, polyethylene in air is known to accumulate a certain amount of groups containing CO double bonds. The amount of those species, is generally assessed through infrared spectroscopy.2,3 Optical spectroscopies have also been used to characterize oxidized polyolephins.4−12 However, absorption/emission of electromagnetic radiation in PE, which is a large band gap insulator, is not only a probe of the material, but can also induce damage. Indeed, aging of polymers is supposed to occur, or to be enhanced, also through electronic excitations induced by photons of sufficiently high energy; in this respect, many qualitative similarities exist between insulating polymers and ionic or ionic−covalent inorganic insulators, in which defect © 2018 American Chemical Society
production by electronic excitation has been an active research field,13 especially in alkali halides14−18 and silicon dioxide.19−21 In this framework, understanding absorption and emission of light or UV radiation from polymers, with or without defects, is of particular interest. Pure polyethylene, in spite of the simple repeated monomer, has a complex lamellar structure, including crystalline and amorphous domains. Commercial products are classified according to their density as low density or high density polyethylene (LDPE or HDPE). PE is transparent to visible light, its absorption threshold (or optical gap) being around 7− 8 eV, with a broad shoulder probably due to the complex microsctructure.22−28 Only methods able to describe realistic electron−hole interactions, like coupled-cluster equation of motion (CC-EOM) approaches, were able up to now to give quantitative estimates of this threshold energy,29 confirming exciton binding energies on the order of the eV, as usual in the case of organic compounds. When polyethylene undergoes oxidation both absorption and emission thresholds are much lower in energy. While for absorption most recent results found a threshold around 4.5 eV and further absorption peak above 5.5 eV, emission can occur below 4 eV by fluorescence and even down to less than 2.5 eV Received: December 11, 2017 Revised: January 17, 2018 Published: January 23, 2018 2023
DOI: 10.1021/acs.jpcb.7b12172 J. Phys. Chem. B 2018, 122, 2023−2030
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Figure 1. Experimental absorption/emission chart (Figure 2d from ref 11. Reprinted with permission. Copyright 2012 Institute of Electrical Engineers of Japan) on which we superimpose various experimental peak positions for fluorescence (+) and phosphorescence (×) (Osawa,6 Jacques,7 Tesseydre,30and Allen31). The filled circles represent our calculated excitonic transitions associated with fluorescence (fl.) and phosphorescence (ph.), for hexatriacontane containing saturated or α, β-unsaturated carbonyls. The size of the circles (for fluorescence) is proportional to the log of the absorption oscillation strength, in order to make visible also excitons with relatively low oscillator strength.
Figure 2. Structures of polyethylene chains with saturated or unsaturated carbonyl defects. The oxygen atom is red, hydrogens are blue and carbons are yellow.
an explanation of emission energies caused by charge recombination in EL experiments. Although the quasiparticle band structure is here much improved thanks to the fraction of Hartree−Fock exchange, excitonic effects are still out of the scope of the theoretical framework employed. Another interesting recent work tries to interpret the experimental PL signatures with excitation energies calculated with a configuration-interaction approach, however the comparison of calculations with experiments is not conclusive.11 Excitonic effects can be, conversely, included either in the Bethe−Salpeter equation (BSE) or in time-dependent DFT (TDDFT). The latter was recently used to exploit the results of reflectivity measurement of degraded paper,35,36 where cellulose, at variance with PE, is a polymer with aromatic units. The authors analyze various types of CO containing groups, showing that different groups can have similar absorption thresholds but different shapes of the absorption cross sections. In the present paper we make use of the former approach, the BSE, to calculate excitonic spectra of PE based on single particle eigenvalues obtained in the framework of the GW perturbative approach. In order to predict, or at least to recognize, the spectral features of a specific chemical group, or a defect, one needs to answer three questions. What are the allowed energies of the absorbed/emitted photons? What is the absorption/emission cross section (related to the oscillator strengths) associated with those transitions? What is the expected concentration of the chemical group we are looking for? In this work we consider those three aspects comparing saturated and unsaturated carbonyl groups in polyethylene.
by phosphorescence, with a longer time delay. The position of experimental peaks, together with our calculated exciton energies, are summarized in Figure 1, where we superimpose them to an emission/absorption experimental chart from ref 11. Experimental resonances show up as shoulders in significantly broadened spectra. These features in the optical spectra have in general been associated with α,β-unsaturated carbonyls, also called enone groups, formed by a CO unit with two adjacent missing hydrogen atoms on the same side of the CO bond. It is not clear why saturated carbonyls (i.e., simple CO bonds supplanting a −CH2− group, also named ketones) should not be equally taken into account. For the sake of clarity, as the nomenclature of these chain defects varies with the authors, we show in Figure 2, the relaxed structures of the two mentioned defects. Our theoretical points for the fluorescence of unsaturated carbonyl defects in Figure 1 are in fair agreement with the experimental emission called α in the experimental chart. The γ emission is much less discussed in the original paper. Its decay with time, for example, is not given, making it difficult to say whether we can assign it to phosphorescence or not. In any case, we postpone further discussion to end of the paper, as we need at this point a deeper view on the context and on our approach. Attempts to understand in detail the origin of photoluminescence (PL) be it fluorescence or phosphorescence and electro-luminescence (EL)32 in oxidized polyethylene are still scarce. A first pioneering work dealing with defected PE chains and the possible trapping of excitons is the work by Ceresoli and co-workers;33 although leading to precious qualitive insights (exciton trapping, dynamical effects, structural evolutions), the underlying framework (semilocal density functional theory, DFT) could not lead to a quantitative description of optical absorption/emission. A much more recent work,34 based on hybrid functionals and charge transition levels of various types of defective groups, attempts
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METHOD Our approach is based on density functional theory (DFT) for structural optimizations and formation energies, and on the GW-BSE37 approach for optical properties. 2024
DOI: 10.1021/acs.jpcb.7b12172 J. Phys. Chem. B 2018, 122, 2023−2030
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Figure 3. Calculated photoabsorption cross section for crystalline PE (on the left) and for alkane chains of varying lentghs (on the right). For the former, we show the position of exciton states (green impulses), the first few of which are almost fully dark.
functional calculations for the molecules,47 unless otherwise specified. Although the choice of the xc-functional has an influence on the final results, a comparison of LDA and PBE0 xc-functionals as starting points shows only a shift on the order of 0.3 eV in the excitonic states and relatively small variations of the oscillator strengths (see the Supporting Information), as could be expected from a previous assessment.48 Formation energies of the defects were calculated both for the periodic solid and the alkane molecules. For the latter we checked several approximations, including the PBE0 hybrid functional and the random phase approximation (RPA) to the total energy, which is calculated in the MOLGW code using the polarizability calculation.49,50 For the calculation of formation free energies, the oxygen chemical potential was fixed as the energy of the oxygen molecule plus the rotational and configurational free energy at the given temperature and partial pressure. The vibrational and electronic entropy terms are neglected in the free energy both of the solid and the molecules. For hydrogen, we chose the thermodynamical condition in which the hydrogen reservoir is fixed by hydrogens belonging to end chain CH3 groups through the reaction:
We model polyethylene both with a perfect orthorhombic crystal and with isolated molecules of varying length. Atomic configurations have been optimized using the PWSCF module of the Quantum-Espresso software package.38 We used the optB86b+vdW exchange correlation functional39 in order to provide a good description of van der Waals interchain interactions. Pseudopotentials, norm-conserving (nc) for C and H and both nc and ultrasoft for oxygen, were generated with the optimized B86b exchange39 and Perdew86 for correlation.40 For the unit cell of the orthorhombic crystal, containing 12 atoms, we sampled the Brillouin zone (BZ) with a 3 × 3 × 6 Γ-centered Monkhorst−Pack mesh. Equivalent kpoint sampling was maintained for relaxations of supercells. Defect formation energies were calculated in a 2 × 2 × 5 supercell (240 atoms without defects) or in 2 × 1 × 4 supercell for convergence checks. Relaxations were pursued until forces were all below 10−3 Ry/bohr. For finite size alkane chains the relaxations were performed in body-centered tetragonal unit cells in order to maximize the chain ends distance. The cells were 40 × 40 bohr wide in the plane perpendicular to the chain and, in the direction parallel to the chain, they were exceeding the molecule length by at least 45 bohr. Excited state geometries were obtained by fixing the occupations of the electronic states accordingly. Calculations of the photoabsorption cross sections were performed in the framework of many-body perturbation theory with the GW approximation (one-shot G0W0) followed by solving the Bethe−Salpeter equation with the GW spectrum. For the alkane molecules we used the MOLGW code41,42 with an augmented double-ζ polarized Gaussian basis set (aug-ccpVDZ). For the periodic solid we used the SaX code,43 which implements GW and the BSE on a plane wave basis set. The polarizability cutoff was set at 8 Ry. For defects in the crystal we used a 2 × 1 × 4 supercell with more than 600 empty bands and the BZ sampled by the Γ point only. We used the TammDancoff approximation for solving the BSE for the periodic solid, but not for the molecules. Concerning the frequency convolution in the GW self-energy operator, MOLGW performs it analytically thanks to the spectral decomposition of the screened Coulomb interaction W, while SaX applies a Godby−Needs44,45 plasmon pole model, giving a reliable description of electronic screening.46 G0W0 calculations were done on top of optB86b+vdW DFT calculations for the solid and starting from PBE0 hybrid
P + 2H ↔ P + P
(1)
where a terminated polymer chain P splits into two through the incorporation of two hydrogen atoms. The corresponding chemical potential is easily obtained by fitting the energy of CnH2n+2 molecules with a linear function of n (E(n) = a × n + b) and taking μH = b/2. The formation energy of charged defects for the solid, calculated with supercells and periodic boundary conditions, were corrected for spurious image interaction with the monopole Madelung term.
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OPTICAL SIGNATURES First of all we present the results for pure PE, in Figure 3. We show the results we obtained for crystalline PE with the orthorhombic structure (Figure 3a) and those for alkane chain molecules CnH2n+2 of varying length (Figure 3b). For the former, having used for the relaxation an exchange-correlation functional including a van der Waals term, our theoretical equilibrium structure is in good agreement with the experimental geometry, better than previous LDA results51 (see Supporting Informations for details). The two models give similar absorption thresholds, with small contributions starting around 7 eV or slightly above and a clear peak around 8 eV for 2025
DOI: 10.1021/acs.jpcb.7b12172 J. Phys. Chem. B 2018, 122, 2023−2030
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Figure 4. Cross sections associated with absorptionfrom the ground state (blueish lines)and emission (fluorescence)from the ground state configuration of the first singlet excited state (reddish lines)for saturated and α, β-unsaturated carbonyls in alkane chains. The darkest line is the photoabsorption cross section of the alkane chain without defects, for reference. The triangles indicate the position of the singlet−triplet transitions in the ground state configuration of the first triplet state, associated with phosphorescence. The colored blue/pink regions represent the width of experimental absorption/emission bands from ref 30.
Figure 5. Absorption spectrum for the saturated and α, β-unsaturated carbonyl defects in crystalline polyethylene. The colored blue/pink regions represent the width of experimental absorption/emission bands from ref 30.
of alkane molecules, the oscillator’s strengths for the saturated carbonyl are much lower than those of the unsaturated one. For the latter, the first two excitonic states occur at 2.4 and 5.4 eV, but the first strong absorption peak is slightly above, at 5.7 eV. For the saturated carbonyl, although the first exciton is as low as 2.9 eV, its oscillator strength is very small and only the second exciton, at 6.4 eV, and another at 6.9 eV have nonnegligible oscillator strength inside the optical gap of PE. The absorption peak at 5.7 (5.1) eV for unsaturated carbonyls for the solid (molecules) is in good agreement with one of the main experimental absorption peaks (see Figure 1). Calculated emission peaks from S1 states are at higher energy than the experimental values, especially for the solid. However, experimental spectra are quite broadened, probably also due to structural effects. Moreover, some fluorescence peaks might be related to transitions between two defect excited states, like S2 to S1 in saturated carbonyl, which are not considered here. In relation to possible emission from higher excited states, we noted that the first optically active exciton of the saturated carbonyl defect has no contribution from HOMO−LUMO single particle wave functions pair, but is mostly represented by HOMO−LUMO+1 excitations. We then checked if the oscillator strengths or exciton energies in the geometry of the second singlet excited state, S2, were significantly different from those at the S1 geometry. We show the comparison in Figure 6; the photoabsorption cross section is still much lower than for
the solid, slightly above for the molecules; this shift, coming from the choice of the underlying xc-functional, is discussed in the last section of the Supporting Information. The calculated absorption threshold is in good agreement with the reported experimental values.22−28 In the left panel, for the crystalline solid, we show the positions of the excitonic states: the first three of them are almost fully dark. We now turn to the defects signatures. We calculated the excitonic structure for CnH2nO and CnH2n−2O for simulating saturated and α, β-unsaturated carbonyl defects, up to n = 36 and in some cases n = 44. In Figure 4 we show a comparison of the optical signatures of these two defects. For both defects we consider the singlet−singlet excitations of the ground state which we associate with absorptionthe singlet−singlet spectrum of the system in the ground state configuration of the first excited singlet state (S1)which we associate with short delay (fluorescence) emissionand the singlet−triplet excitations in the ground state configurations of the triplet state (T1); these forbidden transitions may be responsible for long delay emissions (phosphorescence). The peaks associated with the unsaturated carbonyl are much stronger than those of the saturated one. The clear absorption peak at 5.1 eV is not the first excitonic state: one at 3.0 eV is also present, but its oscillator strength is so small that it is not visible in the spectrum. In Figure 5, we show the absorption spectrum for the same defects in crystalline PE. As in the case 2026
DOI: 10.1021/acs.jpcb.7b12172 J. Phys. Chem. B 2018, 122, 2023−2030
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For hydrogen, the chemical potential was taken as the end chain H energy in PE (see the Method section for details). The results for alkane molecules, with a comparison between several approximations for the exchange-correlation functional, are shown in Figure 7. Both defects have a negative formation energy, which means that the spontaneaous formation of carbonyl defects can be only hindered by entropy or be kinetically limited. For the periodic solid we considered several charge states of the defects, in order to determine the relevant charge transition levels, crucial in assessing their stability as a function of the Fermi level. The results, obtained with a vdW exchange-correlation functional for better description of interchain interactions, are plotted in Figure 8. For the neutral defects the formation energies are very similar to those obtained for the molecules. Negative defects with charge Q = −1 (with an unpaired spin) and Q = −2 become favorable well above midgap, with the 0/-1 charge transition levels around 6 eV above the valence band top. If we consider PE in equilibrium with gaseous oxygen with a given partial pressure (PO2), the formation free energy contains a non-negligible positive contribution from the translational entropy of the molecules. This term is more important the lower PO2 and the higher the temperature. However, as we show in Figure 9, only well above room temperature and at partial pressure well below atmospheric pressure would the formation free energy of carbonyls become positive. The comparison between parts a and b of Figure 9 shows that unsaturated carbonyls are not so easily formed at room temperaturethe formation free energy is positive and large enoughprovided that the oxygen partial pressure is low enough (typically in UHV conditions). This is not true for saturated carbonyls, which are thermodynamically unavoidable and whose formation is limited either by diffusion or by reaction kinetics, or both. An estimate of the energy barrier limiting the formation of oxygen related defects can be given on the basis of permeability of oxygen, which relies oxygen transport in the material to the oxygen partial pressure. The temperature dependence of the permeability is controlled by energy barriers for diffusing though the surface and the bulk; the reported value is on the order of 0.4 eV.52 The energy
Figure 6. Photoabsorption cross section of a saturated carbonyl defect (the C36H72O molecule) in three possible geometries, the equilibrium ones for the ground state (GS) and the S1 and S2 excited states.
the unsaturated carbonyl, however both energy and oscillator strength are clearly sensitive to structural effects. The similarity of the spectra at the S2 and ground state geometries is coherent with the fact that the CO distance is similar in those two cases (1.21 and 1.23 Å respectively), while it is noticeably elongated in the S1 (1.31 Å), as in the triplet excited state (T1). Some of the calculated singlet−triplet excitations are in fair agreement with phosphorescence emission regions, for both saturated and unsaturated carbonyls, however the lowest of the calculated transitions is below the experimental range. One point is however clear: the calculated spectra point to the fact that, if both defects are present in similar concentrations, the dominant contribution, both for the absorption and for the emission, will come from unsaturated carbonyl defects. In the following section we will address the question of their stability.
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DEFECT STABILITY The equilibrium concentrations of the saturated and unsaturated carbonyl defects are determined, at a given temperature, essentially by their formation energy and by the oxygen partial pressure. Let us first consider the formation energies. We have calculated the formation energies of the defects inserted both in the isolated molecules and in the solid. We fixed the chemical potential of oxygen as half the energy of the oxygen molecule.
Figure 7. Formation energy of saturated (a) and unsaturated carbonyl defects (b), as a function of the size of alkane molecules. Several approximations have been tested for the carbonyl, as shown. The oxygen chemical potential is taken as half the energy of an oxygen molecule, and the hydrogen chemical potential is an estimation of the energy of H in PE. 2027
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Figure 8. Formation energy of saturated (a) and α, β-unsaturated (b) carbonyl defects vs the Fermi level in solid PE, calculated at the DFT level with the optB86b+vdW xc-functional, for charge states Q = 0, −1, −2.
Figure 9. Pressure/temperature maps of the formation free energy for a neutral saturated (a) and unsaturated (b) carbonyl in PE (Pref = 1 bar). In the dark blue region (Gf ≤ 0) the formation of the defects is limited by diffusion or by reaction kinetics.
barrier for permeability can refer to bulk diffusion or to surface related barriers (absorption, bulk-surface exchange). Indications that surface conditions may influence the formation of chromophoric species in PE was already emitted in order to explain curious appearance disappearance of fluorescence signals from samples.53 Combining the energy barrier for permeability with calculated formation enthalpies one could find T/PO2 regions where α, β-unsaturated carbonyls are present in concentration orders of magnitude lower than saturated ones; it would be then possible to isolate the optical signatures of saturated carbonyls or, as the latter are very weak according to our calculations, to switch on and off the emission of α, βunsaturated carbonyls. This might have happened for the two samples labeled OL and HT in the work by Arai11 from which we have borrowed the chart in Figure 1. For those two samples, which were treated at high temperature (180 °C), the fluorescence emission at 4−4.5 eVwhich is clearly present in the spectrum of the sample labeled AL, used in Figure 1) has disappeared. As can be seen from our Figure 9b, at that temperature, and ambient pressure, the formation free energy of α, β-unsaturated is positive (0.2 eV) and their equilibrium concentration is on the order of a few hundred ppm. Even if the PL measurements in ref 11 were later performed at low temperature (10 K) the sample might have needed a longer time at room temperature to recover the initial concentration of α,β-unsaturated carbonyls.
Before concluding we ought to mention that, in principle, controlling the hydrogen partial pressure might be another way to control the ratio of saturated to unsaturated carbonyls.
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CONCLUSIONS In summary, we have shown, using state of the art calculations of the optical absorption spectra, that discriminating the nature of carbonyl defects in polyethylene is possible. Some absorption peaks can be identified with α,β-unsaturated carbonyl excitonic peaks, in particular, the absorption/emission feature around 5.5−6.5/4−5 eV labeled α PL.11 Saturated carbonyls, although their formation is expected to be limited only by diffusion or reaction kinetics in most temperature/pressure regimes, are not easily detectable due to their much lower optical absorption cross section. Phosphorescence emission lines coincide partially with the calculated de-excitations energies from triplet states to the singlet ground state for both defects. Further insight into the photoluminescence process should take into account the influence of the local structure of the polymer and its dynamics, also to identify nonradiative decay in competition with radiative channels. Other oxygen related species, even excluding antioxydants and fillers, are probably present. Already proposed were dienones, diketones, and aldheydes. These species, not considered here, are expected to contribute to the broad absorption/emission regions, especially to the one at lower emission energies, around 3 eV. Moreover, although we have shown that long molecules and crystalline polyethylene have qualitatively similar optical 2028
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spectra, there are quantitative differences between our calculated optical properties for isolated molecules and for the crystalline solid, which underline the importance of interchain interaction.
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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.7b12172. Technical details on the convergence of the calculated quantities with various parameters, on the theoretical equilibrium structure of crystalline polyethylene, and on the influence of the exchange-correlation functional of the starting DFT calculation on the GW-BSE results (PDF)
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AUTHOR INFORMATION
Corresponding Author
*(G.R.) E-mail:
[email protected] ORCID
Guido Roma: 0000-0002-9779-4868 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was granted access to the HPC resources of TGCC and CINES under the allocation 2016A0010906018 made by GENCI and under the allocation by CEA-DEN.
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REFERENCES
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DOI: 10.1021/acs.jpcb.7b12172 J. Phys. Chem. B 2018, 122, 2023−2030
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DOI: 10.1021/acs.jpcb.7b12172 J. Phys. Chem. B 2018, 122, 2023−2030
