Band Electronic Structures of Polyphenanthrene and Polyacene

The undoped, LiC8, LiC4, and LiC2 stages for both polymers are computed and analyzed. PA-type moieties in a-C materials should be doped preferentially...
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2534

J. Phys. Chem. B 2001, 105, 2534-2538

Band Electronic Structures of Polyphenanthrene and Polyacene Doped with Lithium Galia Madjarova† and Tokio Yamabe* Institute for Fundamental Chemistry, 34-4 Takano-Nishihiraki-cho, Sakyo-ku, Kyoto 606-8103, Japan ReceiVed: October 6, 2000; In Final Form: January 9, 2001

The band electronic structures of polyphenanthrene (PPh) and polyacene (PA) doped with lithium are calculated and analyzed at the extended Hu¨ckel level of theory to elucidate the lithium storage mechanism in amorphous carbon (a-C) electrode materials used for the lithium-ion rechargeable battery. The undoped, LiC8, LiC4, and LiC2 stages for both polymers are computed and analyzed. PA-type moieties in a-C materials should be doped preferentially in the initial stages of doping because of the deep unoccupied levels relevant to the PA-type edge structure. PPh should possess greater doping capability than PA especially in heavy doping stages, because there is a high density of states (DOS) above the Fermi level in PPh. The Fermi levels of PPh(LiC2) and PA(LiC2) lie just below the Li bands; thus, the upper limit of Li doping in a-C materials is likely the LiC2 stage. The irreversible capacity loss observed in the charging-discharging process in a-C materials may be attributed to the low-lying levels relevant to the PA-type edge structure.

Introduction

CHART 1

The lithium-ion rechargeable battery has a tremendous role in modern technological applications. It is currently the best energy storage device for various portable electronic products and vehicles, and its use will be significantly expanded in the near future. A typical lithium-ion rechargeable battery consists of suitably chosen lithium intercalation compounds for the electrodes; lithium transition metal oxides are used for the cathode, and carbonaceous materials are used for the anode. The main issue we address in this article is the mechanism of lithium doping in possible carbonaceous materials. Various types of carbonaceous materials from highly ordered to disordered carbons have been investigated experimentally and theoretically. The mechanism of lithium storage in graphite and highly graphitic materials is well characterized and understood,1-3 but their reversible capacity of 372 mAh/g is only about one tenth of that of lithium metal (3800 mAh/g). Recently, extensive studies have been devoted to amorphous carbon (a-C) electrode materials that can show high capacity that ranges from 600 to 1100 mAh/g.1,4-8 Despite a large amount of work, there is no satisfactory answer for the lithium storage mechanism in a-C materials. Polyacenic semiconductor (PAS) materials, prepared from phenol-formaldehyde resin at relatively low temperatures,5a,b belong to a typical a-C material. They show rechargeable capacity of 850 mAh/g and can store lithium ions up to an [Li]/[C] atomic ratio of 0.5. Recently, using isotropic pitch as a row material, a new carbonaceous material with a discharge capacity of 1017 mAh/g and efficiency of 81.5% has been reported. According to the solid-state 13C NMR results, a crystallite of this material consists of graphene sheets shaped like a disk; therefore, authors5c call this material polycyclic aromatic hydrocarbons (PAHs), different from PAS. Structural analyses of PAS and PAH materials5c have demonstrated that they have the content similar to aromatic carbons but the different shape of graphene sheets, that is, different edge † Permanent address: Faculty of Chemistry, University of Sofia, Sofia1126, Bulgaria. * To whom correspondence should be addressed. E-mail: [email protected]

structures.5c A Li storage mechanism in the PAHs with a very high capacity was proposed. The Li species located at phenanthrene-edge carbon plays an important role in Li storage. These situations have led us to investigate the electronic features of PAHs and Li-doped PAHs. Numerous one-dimensional (1-D) PAHs have been investigated theoretically and numerically by Whangbo et al.,9 Kertesz et al.,10 Bre´das et al.,11 Klein et al.,12 Tanaka, Yamabe, and coworkers,13 Tyutyulkov et al.,14 and Fujita and co-workers.15 The electronic properties of PAHs strongly depend on their size and especially their edge structure.12-20 According to their edge structures, PAHs can usually be classified into two main groups: “phenanthrene-edge type” (or arm-chair-edge type) and “acene-edge type” (or zigzag-edge type), as indicated in Chart 1. The two structures show remarkably different electronic features. Polyphenanthrene (PPh) and polyacene (PA) are typical 1-D polymers that involve the two distinct edge structures. PPh and PA can be viewed as prototypes of carbon-ladder polymers and nanosized a-C materials. In fact, according to the structural description5c of the synthesized PAS and PAHs materials, they consist of both types of polyacene and polyphenanthrene edge structures, in different ratios depending on raw material, temperature treatment, and experimental conditions. PPh and PA investigated here were used like a model system to emphasize the importance of the different edge structures of a-C materials. In this article, we discuss a change in the electronic structures of these polymers in different stages of doping to increase our knowledge on the lithium storage mechanism in a-C electrode materials. Theoretical studies at various levels have clarified that PPh is energetically more favorable than PA. The band structures

10.1021/jp003678+ CCC: $20.00 © 2001 American Chemical Society Published on Web 03/08/2001

Lithium Doped Polyphenanthrene and Polyacene

J. Phys. Chem. B, Vol. 105, No. 13, 2001 2535

CHART 2

Figure 2. Model systems with different degrees of Li-doping. Solid and open circles show ring-over-site positions of Li atoms up and down a polymer plane, respectively.

finite value of DOS at the Fermi level in PA is a consequence of the band tails of the very small band gap. In this article, we discuss how lithium doping occurs in PPh and PA. Models and Method of Calculation

Figure 1. Band structure and DOS of PPh and PA. The dotted lines and dark areas in the DOS-π indicate the Fermi level and a contribution from C 2pz orbitals, respectively.

and density of states (DOS) curves of PPh and PA with the geometries indicated in Chart 2, determined from cluster calculations at the HF/6-31G* level,21 are shown in Figure 1. Here we adopted the unit cell doubled (C8H4) for PA, so that we can compare PPh and PA directly. The dark area in the DOS curves indicates the contribution of π bands, and the dotted line marks the Fermi level (EF). PPh has a band gap (∼2.2 eV) larger than that of a single polyacetylene (CH)x chain (1.4 eV), whereas PA has a very small band gap (∼0.1 eV). Thus, PPh is electronically hard and PA is electronically soft. This difference can be derived from a detailed orbital interaction analysis of anthracene and phenanthrene.19b PA is a typical example of a second-order Peierls distortion.10,22 The bond alternation of PA is fundamentally different from that of (CH)x in that the significant bond-length difference in polyacetylene (1.4 ( 0.04 Å) is a first-order effect, whereas the small bond-length difference in PA (1.4 ( 0.015 Å) is a second-order effect. The

Band electronic structure calculations for the polymers and fragment molecular orbital (FMO) analyses23 were performed at the extended Hu¨ckel level of theory24 with the YAeHMOP program.25 This method is reliable in orbital levels, band gaps, and orbital interactions. The parameters used for carbon, hydrogen, and lithium atoms are C 2s (Hii ) -21.4 eV, ζ ) 1.625), C 2p (Hii ) -11.4 eV, ζ ) 1.625), Li 2s (Hii ) -5.342 eV, ζ ) 0.645), Li 2p (Hii ) -3.499 eV, ζ ) 0.524), and H 1s (Hii ) -13.6 eV, ζ ) 1.3), where Hii and ζ are the orbital ionization potentials and the Slater exponents, respectively. A 200-k point set was used for band structure and DOS calculations. Lattice sums up to the fifth-nearest neighbors were taken into account. The geometries in Chart 2 were obtained from ab initio calculations of PPh and PA clusters at the HF/6-31G* level21 with the Gaussian 98 program.26 In all band structure and DOS calculations, we used the doubled unit cell for undoped and doped PA to make it isoelectronic with the corresponding unit cell of PPh and allow a direct comparison of the two systems. We also used the FMO method within the extended Hu¨ckel approximation to see the electronic features of the lithium-carbon interactions in Li-doped PPh and PA. The models shown in Figure 2 are Li-doped PPh and PA at various doping levels. Molecular orbital calculations showed that the energetically favored site for a lithium dopant is the site over the center of a benzene ring.20 Solid and opened circles here show ring-over-site positions of Li ions up and down a polymer plane, respectively. PPh(LiC8) and PA(LiC8) contain a lithium ion over every two benzene rings; PPh(LiC4) and PA(LiC4) contain a lithium ion over every benzene ring; PPh(LiC2) and PA(LiC2) have two lithium ions on both sides

2536 J. Phys. Chem. B, Vol. 105, No. 13, 2001

Madjarova and Yamabe

Figure 3. Band structure and DOS of PPh(LiC8) and PA(LiC8). The dotted lines are the Fermi level. Dark areas in DOS-π and DOS-Li indicate contributions from C 2pz orbitals and Li 2s, 2px, 2py, and 2pz orbitals to the total DOS, respectively.

of a benzene ring. The LiC2 models look unrealistic, but such high doping states have been observed frequently in a-C materials, although the still unknown structure of lithium dopants in heavy doping stages is a recent issue of debate.1,4-8 The distance between a lithium ion and the center of a benzene ring was fixed to be 1.85 Å, half of the interlayer distance of the lithium intercalation compound LiC6. PPh(LiC2) and PA(LiC2) can model a-C materials that are highly doped with lithium provided that lithium is adsorbed on both sides of a single carbon sheet. Results and Discussion Doping Capability. According to Yata et al.,5a the capacity of Li-doped a-C materials, Q (mAh/g), has close relevance to the [Li]/[C] atomic ratio, as indicated in eq 1.

[Li]/[C] ) {3.6(12 + [H]/[C])Q}/96500

(1)

According to this equation, lithium content increases as a function of the [H]/[C] atomic ratio. Because the PPh and PA models in Figure 2 have the same values in the [Li]/[C] and [H]/[C] atomic ratios for a given degree of doping, the difference in the electronic features that we will see later in this article is due to the intrinsic nature of these polymers. The comparison of the electronic structures of Li-doped PPh and PA will explain their different doping capability. The doping process in PPh and PA can be viewed as the process in which empty π bands of the polymers are gradually filled by electrons of lithium dopants. In initial stages of doping, which can be simulated by the LiC8 models, the band structures in the vicinity of the Fermi levels of PPh(LiC8) and PA(LiC8) are not affected significantly by lithium dopants. The frontier orbital bands that consist of π orbitals are almost identical with

Figure 4. Band structure and DOS of PPh(LiC4) and PA(LiC4). The dotted lines are the Fermi level. Dark areas in DOS-π and DOS-Li indicate contributions from C 2pz orbitals and Li 2s, 2px, 2py, and 2pz orbitals to the total DOS, respectively.

those of the undoped PPh and PA, as shown in Figures 1 and 3. The lowest unoccupied crystal orbital (LUCO) bands of the undoped polymers are now partially filled. The newly filled levels in PA(LiC8) are low-lying in energy, whereas those in PPh(LiC8) are relatively high-lying because of the existence of the large band gap. In fact, the bottom of the LUCO band at k ) 0 for PA is -10.7 eV, and that for PPh is -9.6 eV. In view of the band structures of PPh(LiC8) and PA(LiC8), we conclude that lithium doping would take place preferentially in PA-type polymers in the initial stages of doping, because the levels of PA that are filled in the initial stages of doping are very deep in energy. Further doping will result in gradual occupation of the LUCO bands and lead to the rise of the Fermi levels. These theoretical analyses lead us to conclude that if a-C materials involve both phenanthrene- and acene-edge structures, acene-edge moieties are preferentially doped in the very initial stages of doping. The next stages of doping can be modeled by PPh(LiC4) and PA(LiC4), as shown in Figure 4. The [Li]/[C] atomic ratio at this doping level is higher than that of graphite intercalation compound LiC6. The Fermi level of PA(LiC4) goes up remarkably in comparison with that of PA(LiC8), whereas the Fermi level of PPh(LiC4) remains almost unchanged compared with that of PPh(LiC8). This remarkable contrast is because there is high DOS in the region of -10 to -8 eV in PPh, whereas there is low DOS in the same region of energy in PA. In fact, there are two bands in PPh in the region above -9.5 eV. Therefore, PPh should possess greater doping capability than PA especially in the heavy doping stages. We consider that phenanthreneedge moieties in a-C materials should play an important role in the high-capacity performance.

Lithium Doped Polyphenanthrene and Polyacene

J. Phys. Chem. B, Vol. 105, No. 13, 2001 2537

Figure 6. Orbital interaction diagrams for Li-doped phenanthrene and anthracene partitioned in two fragments and frontier π-orbital pattern of undoped molecules. HOMO, highest occupied molecular orbital. Figure 5. Band structure and DOS of PPh(LiC2) and PA(LiC2). The dotted lines are the Fermi level. Dark areas in DOS-π and DOS-Li indicate contributions from C 2pz orbitals and Li 2s, 2px, 2py, and 2pz orbitals to the total DOS, respectively.

TABLE 1: Computed Fermi Levels (in eV) of Undoped and Doped Polyphenanthrene (PPh) and Polyacene (PA) [Li]/[C] ratio

PPh

PA

undoped LiC16 LiC8 LiC4 LiC2

-11.7 -9.4 -9.2 -8.6 -7.0

-10.8 -10.5 -9.7 -8.3 -7.0

A further increase in lithium dopants will lead to full occupation of the LUCO and (LUCO + 1) bands, as demonstrated in Figure 5. In the final stages of doping, the Fermi levels of PPh(LiC2) and PA(LiC2) go up to about -7 eV, and the band structures in the frontier orbital region are significantly perturbed by lithium dopants. Lithium dopants make significant contribution in the DOS curves in the region above -7 eV. Note that the Fermi levels of PPh(LiC2) and PA(LiC2) lie just below the bands that come from lithium dopants, as indicated by DOS-Li in Figure 5. The dark area in DOS-Li indicates contributions from Li 2s, 2px, 2py, and 2pz orbitals to the total DOS. If the doping process proceeds further, the lithium 2s bands are gradually filled, which suggests that neutral lithium atoms are produced when the [Li]/[C] atomic ratio is larger than 0.5. Such a situation cannot be viewed as doping anymore because of the lack of charge transfer. Thus, the upper limit of lithium doping in a-C materials is likely to be the LiC2 stage. Of course, the doping capability has relevance to the Fermi level, which is the most important microscopic character of extended electronic systems. The lower the Fermi level of an a-C material subjected to doping, the higher its doping capability. In the initial stages of doping that can be represented by the LiC16 and LiC8 models, the Fermi level of doped PA lies below that of doped PPh, as listed in Table 1, in which PPh-

(LiC16) and PA(LiC16) contain a lithium ion over every four benzene rings. Table 1 shows that the Fermi level of heavily doped PPh, which can be represented by PPh(LiC4), is lower than that of heavily doped PA, which can be represented by PA(LiC4). Therefore, PPh-type polymers are expected to have greater doping capability. The Fermi level rises as the degree of doping proceeds, and finally the Fermi level gets closer to the lithium 2s bands. This should lead to a slow and, eventually, to a complete ceasing of further lithium doping, which outlines the limit of effective adsorption capability for a given carbonaceous material. Lithium doping beyond this limit will have no effect with respect to capacity increase, because such lithium dopants are not ionized. This theoretical prediction consists of experimental voltage profiles. For instance, further doping over the LiC2 level for PAS material5b is accompanied with Li metal deposition on the electrode. Orbital Interaction Analyses. To characterize the orbital interactions between Li dopants and the polymers, we applied the FMO method to the Li2-phenanthrene and Li2-anthracene complexes, which can be partitioned into phenanthrene (anthracene) and lithium fragments. Although we see explicit orbital interactions at higher levels, we see no orbital interaction in the frontier orbital region, which shows that a dominant factor for the lithium doping in carbon materials is most likely to be a charge-transfer reaction. The orbital interaction diagrams for heavily doped phenanthrene and anthracene with three and six Li atoms, which correspond to the LiC4 and LiC2 models, respectively, show similar orbital interactions. In the doping process there is a transfer of electrons from Li 2s orbitals to the vacant π orbitals of the hydrocarbons. Therefore, in view of the lowest unoccupied molecular orbital (LUMO) levels, lithium affinity is higher in anthracene than in phenanthrene, but this order is reversed when we compare the (LUMO + 1) levels. This result is in good agreement with our prediction that PPh-type materials should possess greater doping

2538 J. Phys. Chem. B, Vol. 105, No. 13, 2001 capability than PA-type materials, especially in the heavy doping stages. Discharging Mechanism. The basic requirement toward carbon materials used as the anode is, of course, high capacity for reversible lithium-ion adsorption at a potential close to that of the lithium metal. In the first charging-discharging cycle, a considerable amount of Li atoms remains in PAS and PAH materials.5 The capacity loss is a serious problem in applying these materials to lithium-ion rechargeable battery because it reduces the cycle performance. For instance, the irreversible capacity of PAS material amounts to 250 mAh/g, which corresponds to about 30% of the total reversible capacity (850 mAh/g). Let us consider a possible origin of the irreversible capacity loss on the basis of the band structure calculations of doped PPh and PA. In Figure 3 we found that electrons of lithium dopants are transferred to very deep levels of PA in initial stages of doping, whereas electrons of lithium dopants are transferred to relatively shallow levels of PPh. An almost identical fact was seen in the FMO analyses in Figure 6. In the discharging process, electrons leave the anode, and at the same time lithium ions diffuse spontaneously into the electrolyte. We think that electrons occupying the very-low-lying levels and lithium ions cannot leave spontaneously during the discharging process. This again suggests that PPh-type polymers should perform better as the negative electrode for the lithium-ion rechargeable battery. Conclusions We conducted band electronic structure calculations of Lidoped PPh and PA at the extended Hu¨ckel level of theory to deepen our understanding of the charging-discharging process in a-C materials used for the anode of lithium-ion rechargeable battery. PPh and PA are prototypes of carbon-ladder polymers that involve two distinct edge structures and show different electronic features. We computed and analyzed the nondoped, LiC8, LiC4, and LiC2 stages for PPh and PA and derived the following conclusions. (1) PA-type moieties in a-C materials should be doped preferentially in the initial stages of doping because of the deep unoccupied levels relevant to the PA-type edge structure. (2) PPh-type polymers should possess greater doping capability than PA-type polymers in heavy doping stages, because there is high DOS above the Fermi level in PPh. (3) The Fermi levels of PPh(LiC2) and PA(LiC2) lie just below the lithium 2s bands; thus, the upper limit of lithium doping in a-C materials is likely to be the LiC2 stage. (4) The irreversible capacity loss observed in the charging-discharging process in PAS and PAHs materials can be attributed to the deep occupied levels that arise from the PA-type edge structure. Acknowledgment. We thank Professor Kazunari Yoshizawa of Kyoto University for fruitful discussions and comments. This work was supported by the “Research for the Future” Program from the Japan Society for the Promotion of Science (JSPS-RFTF96P00206). Computational time was provided by the Supercomputer Laboratory of Kyoto University and the Computer Center of the Institute for Molecular Science. References and Notes (1) (a) Dahn, J. R.; Zheng, T.; Xue, J. S. Science 1995, 270, 590. (b) Dahn, J. R. Phys. ReV. B 1991, 44, 9170. (2) He´rold, A. In Physics of Intercalation Compounds; Pietronero, L., Tosati, E., Eds.; Springer: Berlin, 1981; p 7. (3) Rabii, S.; Holzwarth, N. A. W.; Li, G.; Moscovici, J.; Loupias, G.; Guerard, D.; Nalimova, V. Mol. Cryst. Liq. Crys. 1994, 245, 13.

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