Introduction

Li–ion batteries have already played an important role in powering electronic equipment, grid energy storages, tools, and vehicles [1,2,3]. Electrode materials are one of the most important composite materials for improving the performance of lithium–ion batteries [4]. Inorganic electrode materials, including LiNiO2 [5], LiCoO2 [6], LiFePO4 [7], and LiMn2O4 [8], have been researched in-depth and are extensively applied. However, inorganic materials have two disadvantages: one is limited mineral resources, particularly of Co and Ni, the other is the production or recovery of inorganic compounds that require high temperatures and the release of large quantities of carbon dioxide, which is harmful to the environment [9].

Recently, due to the unique properties, such as renewable sustainability, lower carbon dioxide emissions [10, 11], abundance of raw materials, and diverse types of structures, organic electrode materials have attracted considerable attention. To date, many organic electrode materials have been reported [12, 13], such as the conductive polymer [14, 15], organic radicals [16, 17], reduced carboxylate, and carbonyl compounds [18,19,20,21,22,23,24,25,26]. However, the disadvantages of organic compounds are that they can be easily dissolved and have low thermal tolerance, poor conductivity, and low mechanical stability [27, 28].

Organic polymers can reduce these problems because of their lower solubility, lower self-discharge rates, high mechanical strength, greater flexibility, superior thermal stability, and versatility [19, 29, 30]. These polymers include conducting polymers, radical polymers [31], polypyrrole [31], organosulfur derivatives [32, 33], and polymers with carbonyl groups [19, 34]. Recently, many new polymer electrode materials have been developed [25, 35,36,37,38,39,40,41,42,43]. In particular, Qichun Zhang et al. [44] discovered a high-performance all-plastic full battery (both the cathode and anode are poly (2,3-dithiino-1,4-benzoquinone) (PDB)). The electrode is not easily dissolved in the electrolyte, meaning that the electrode has ultra-long cycle stability. These researchers’ study demonstrated that the design and fabrication of high-performance all-plastic batteries is becoming possible.

Poly(ethylene terephthalate) (PET) material, which is highly difficult to degrade in a natural environment, has been reported as an anode material for lithium–ion batteries after a low-temperature solvothermal treatment [45], which shows that polymer waste is expected to become the electrode material of lithium–ion battery.

For many industrial polymers, their unit structures contain a carbon–oxygen double bond (C=O) in a conjugated carbonyl or carboxyl group, which is a typical characteristic for organic electrode materials of lithium–ion batteries. Thus, a theoretical screening study to find potential electrode materials from industrial polymers, which are produced on a large scale and at low cost, is required.

Previously, the single-molecule model accompanied with DFT calculation has been widely used to study small organic molecule as electrode materials for lithium–ion batteries, but it could not precisely predict the potential [46,47,48,49,50]. Recently, a high-throughput screening scheme based on the dispersion-corrected density functional theory (DFT-D) and organic crystal structure could accurately calculate the potential of organic electrode materials [16, 35, 48, 50,51,52,53,54].

For polymer materials, their crystal structures are easily deformed, and the crystallized phases always coexist with an amorphous phase, which means that it is difficult to accurately measure and describe the crystal structure of polymers. In the present study, the charge/discharge potentials of 11 reported polymer electrode materials for lithium–ion batteries was collected, and the experimental values were fitted linearly with the values of ΔEpoly (as shown in Eq. (2b)) calculated with a single-molecule model. After a mathematical treatment, a semi-empirical formula to predict charge/discharge potential of polymer electrode materials was set up, which was further applied to predicted more than 20 industrial polymers as electrode materials. Several materials with high potential and capacity are specified in the paper, and the calculation results demonstrate that the electronegativities of the substituents could adjust the charge/discharge potential of the polymer electrode materials for lithium–ion batteries.

Computational method

The Amsterdam Density Functional program package (ADF, version 2017) was applied in this study; geometries were optimized using the Perdew−Burke−Ernzerhof (PBE) exchange−correlation (xc) potential as implemented in the Amsterdam Density Functional-BAND (ADF2017) package [35, 36, 53, 55]. The double-ζ polarized (DZP) sets, the zeroth-order regular approximation (ZORA), normal numerical quality, and the large frozen core technology were applied in this work. A conductor-like screening model (COSMO) was used here to describe the acetonitrile solvent environment, and the dielectric constant was selected as 37.5 for the acetonitrile solvent. ADF-BAND uses chain periodicity, DZP basis is set with large frozen core, and the unit cell consists of repeating units. Constructing a one-dimensional chain periodic structure in ADF-BAND based on a single molecular model. The chain periodic structures were optimized.

Results and discussion

As shown in Fig. 1, 11 reported polymer electrode materials were researched by theoretical methods [51], and one of the materials, poly(2,3-dithiino-1,4-benzoquinone) (PDB)) [44], is discussed in detail to present the calculation process.

Fig. 1
figure 1

Structures of the 11 types of reported industrial polymer materials. (1) Polyethylene terephthalate (PET); (2) polyimide-2; (3) polyimide-3; (4) urea-perylene diimide polymer; (5) poly(2,3-dithiino-1,4-benzoquinone); (6) 3,4,9,10-perylenetetracarboxylicacid-dianhydride(PTCDA) sulfide polymers; (7) N,N0-diallyl-2,3,5,6-tetraketopiperazine; (8) poly(2,5-dihydroxy-1,4-benzoquinonyl sulfide; (9) poly(5-amino-1,4-dyhydroxy anthraquinone); (10) poly(2,5-dihydroxy-1,4-benzoquinone-3,6-methylene); (11) poly(anthraquinonyl sulfide)

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The lithiated/delithiated structures of PDB (as shown in Fig. 2) are all fully optimized in acetonitrile with a relative permittivity of 37.5 through a single-molecule model, and the carbonyl group was considered the most suitable location for lithium. The lithiated/delithiated process can be simply explained as the double-bond breaking down into single bonds during the lithiation process and single bonds returning double bonds during delithiation [21,22,23,24,25]. In this way, the reaction occurred only near a single molecule, and each lithium only connected to an oxygen atom, as shown in Fig. 2 b.

Fig. 2
figure 2

a Structure of the delithiated PDB; b the structure of the lithiated PDB

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The band structure of PDB is shown in Fig. 3. Figure 3 a shows the energy band structure and DOS (density of states) before lithium insertion, and Fig. 3 b shows the energy band structure and DOS after lithium insertion.

Fig. 3
figure 3

a On the left is the energy band before the lithium is inserted, and on the right is the DOS; b on the left is the energy band after the lithium is inserted, and on the right is the DOS

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The band structure of PDB in the vicinity of the Fermi level is presented in Fig. 3; among the states, α, β, and γ are three different states near the Fermi level. For delithium, the α state was occupied, which was the valence band maximum (VBM); β and γ states are both unoccupied; and β was the conductor band minimum (CBM). The band gap between α and β was approximately 0.8 eV. After lithium was embedded, the electrons go into the β band, and the Fermi level goes to the top of β band. The occupied β state becomes VBM, γ becomes CBM, and the band gap between β and γ decreases to 0.47 eV, which suggests that they are typical semiconductors. The band gaps were all small, but the energy bands (α, β, and γ) were flat, which implies they were all local states.

Before lithiation, the β state was the LUMO (lowest unoccupied molecular orbit), and the charges were primarily distributed around carbon–carbon double bonds, as shown in Fig. 4 a. After lithiation, the electrons accompanied with lithium ions were transferred into the conjugated molecular orbit, and the β state changes to the HOMO (highest occupied molecular orbit), in which charges are mainly distributed around the carbon atoms directly bonding to the carbonyl groups and carbonyl carbon atoms, as shown in Fig. 4 b.

Fig. 4
figure 4

a LUMO before lithium intercalation; b the HOMO after lithium intercalation

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When the crystal structure is known, the total energy of lithium crystal and materials can be determined; therefore, potentials can be calculated according to the following formula:

$$ {V}_{\mathrm{cal}}=\frac{-\left({E}_{\mathrm{A}-\underset{\mathrm{n}}{L}i}-E-\mathrm{A} nE\right)}{nF} $$
(1)

where n is the number of transferred electrons, F is the Faraday constant, EA is the total energy for the electrode material with delithiation state, EA-Lin is that with lithiation state, ELi is the total energy of lithium metal, and Vcal is the calculated potential.

However, the crystal structures of many polymers are not known; therefore, we cannot determine the total energy of the polymer crystal. Therefore, a single-molecule model was used for the study and calculated using the Eq. (2a):

$$ {V}_{\mathrm{pre}}=k\frac{-\left({E}_{\mathrm{A}-{\mathrm{Li}}_n}-{E}_{\mathrm{A}}\right)}{nF}+c $$
(2a)

which could be further simplified as the following:

$$ {V}_{\mathrm{pre}}=k\Delta {E}_{\mathrm{poly}}+c\kern0.72em \mathrm{and}\kern0.5em \Delta {E}_{\mathrm{poly}}=\frac{-\left({E}_{\mathrm{A}-{\mathrm{Li}}_n}-{E}_{\mathrm{A}}\right)}{nF} $$
(2b)

EA and EA-Lin are calculated with the single molecular model; k and c are unknown and the correction value.

To identify the value of k and c, 11 reported polymer electrode materials were collected [44, 51], and their experimental potentials are listed in Table 1. A linear fitting between the calculation values of △Epoly and the values of the experimental potentials is present in Fig. 5, which implies k = 1, c = − 0.45, R2 = 0.59. Ideally, the slope of the equation should be one. In fact, the slope after fitting was the same as the ideal slope, and the intercept was − 0.45 V. Non-zero intercepts can be derived from the energy difference of lithium in a single-molecule model and the system error between the “computing” and “experimental” environments.

$$ {V}_{\mathrm{pre}}=\frac{-\left({E}_{\mathrm{A}-{\mathrm{Li}}_n}-{E}_{\mathrm{A}}\right)}{nF}-0.45 $$
(2c)
Table 1 Values of △Epoly and experimental potentials of the 11 types of industrial polymer materials
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Figure 5
figure 5

Linear relationship between experimental potential and △Epoly

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The verification results of the experiment and calculation are shown in the Fig. 5, where R2 = 0.59, indicating that the experimental and calculated values fit well. The present work is purely theoretical, and the possibilities of 26 industry polymers to be applied as electrode of Li–ion battery have been simulated. The related experiments are out of the present work. Recently, in another published paper (Solid State Ionics 317 (2018) 164–169), PET was reported as electrode material of Li–ion battery, and its experimental potential (about 0.9 V) is very close to the theoretical value (about 0.82 V) reported in the present work, which further verifies the theoretical method.

In this paper, we apply Eq. (2c) to predict the potentials of the polymer electrode materials for lithium–ion batteries. For the other 26 types of industrial polymer materials, which are not reported previously, their molecular structures are listed in Fig. 6. The predicted potentials are shown in Fig. 7. The potentials of 3 types of materials were higher than 2.0 V, 11 types of materials were between 1.5 and 2.0 V, and 12 types of materials were lower than 1.5 V. Materials with a potential higher than 1.5 V can be used as cathode materials.

Fig. 6
figure 6

Structures of 26 types of industrial polymer materials. (1) Polybutylene terephthalate; (2) poly-p-phenylene terephthamide; (3) 3,3′-ODPA/ODA/PA; (4) polyethylene terephthalate; (5) polyethylene-2,6-naphtalate; (6) poly(p-phenylene terephthalate); (7) polyterephthalic acid to naphthalenediol; (8) 3,4′-ODPA/ODA/PA (PAA); (9) PAI-1; (10) PAI-2; (11) fluorinated polyimide-1; (12) fluorinated polyimide-2; (13) fluorinated polyimide-3; (14) polyimide-1; (15) polyimide-2; (16) polypyromellitic diphenyl sulfide; (17) polypyromellitic diphenyl ether imine; (18) polybenzophenone tetracarboxylic acid p-dimethylcyclohexaneimine; (19) polybenzophenone tetracarboxylic acid dimethylcyclohexaneimine; (20) polyimide-3; (21) polybenzophenone tetraformyl triphenyl disulfide imine; (22) polybiphenyltetramethyleneimine; (23) polypyromellitic diphenylmethaneimine; (24) polydiphenyl ether tetraamine diamine; (25) polyethylene terephthalate; (26) polyetherketoneketone

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Fig. 7
figure 7

Predicted potentials of 26 types of industrial polymer materials

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Figure 8 shows that the theoretical capacities of 6 types of materials are higher than 274 mAh/g (the capacity of LiCoO2), and of 21 types are higher than 170 mAh/g (the capacity of LiFePO4). Most polymer materials have a higher capacity compared with inorganic materials.

Fig. 8
figure 8

Theoretical capacity of 26 types of industrial polymer materials

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The band gaps of the 26 types of industrial polymer materials are shown in Fig. 9, in which the blue bars represent the delithiated states, and the red bars represent the lithiated states. For each material, the band gap of the delithiated state is significantly different from the lithiated state, which is primarily observed because the intercalated lithium ions greatly change the interaction between industrial polymers. The band gap of LiFePO4 is 3.1 eV, the band gap of NCM (nickel cobalt manganese ternary material) is 1.95 eV, and the band gap of sulfur is about 3.1 eV. The band gaps of the 26 materials are all less than 2.7 eV, and the band gaps of most materials are smaller than that of typical inorganic materials, indicating that the polymer materials have good electronic conductivity.

Fig. 9
figure 9

Band gaps of 26 types of industrial polymer materials

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The predicted potentials, theoretical capacity, and band gap of 26 types of industrial polymer materials are provided in Fig. 10. Good cathode materials for lithium batteries require large potentials, high capacity, and small band gaps. There are 6 types of materials’ with theoretical capacities higher than 274 mAh/g (the capacity of LiCoO2). In the above discussion, the 20th material has high capacity, but its potential is not ideal. The potential of the ninth material is higher than 2.0 V, but the theoretical capacity of the ninth was 203.1 mAh/g, and its theoretical capacity was not ideal. Although other materials except for the 16th, 17th, and 23rd also have small band gap values before and after lithium insertion, their potential and theoretical capacity was not outstanding. There were 12 types of industrial polymer materials that have potentials below 1.5 V; therefore, those industrial polymers might be used as anode materials.

Fig. 10
figure 10

Predicted potential–theoretical capacity band gap map of 26 types of industrial polymer materials

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Thus, three industrial polymers were highlighted: 16th, 17th, and 23rd. The potentials of 16th and 17th were 2.03 V and 2.00 V, respectively, and the potential of the 23rd was 1.95 V. The capacity of the 16th and 23rd were higher than 274 mAh/g, and the capacity of the 17th was 269.4 mAh/g, which was close to 274 mAh/g. The band gaps of the 17th before and after lithium insertion were 0.93 eV and 0.53 eV, respectively. The band gaps of the 16th before and after lithium insertion were 1.69 eV and 0.51 eV, respectively. The band gaps of the 23rd before and after lithium insertion were 2.19 eV and 0.13 eV, respectively. The band gaps show that they have good electronic conductivity and dynamic performance in Li–ion batteries. The high capacity, high potential, and small band gaps were positive factors for the three industrial polymer materials to be electrode materials.

In this work, three polymer electrode materials (with a relatively high potential, high capacity, and small band gap), 16th, 17th, and 23rd, were highlighted from 26 types of industrial polymers. The 16th, 17th, and 23rd materials have similar structures and similar potentials. Therefore, the following studies of the three materials (16th, 17th, and 23rd) with similar structure were made.

It is difficult to set up a general rule to coarsely identify the potentials and band gaps of the polymers. So, we researched three different polymer materials (Fig. 11) which have the similar structure. We investigated how the heteroatom and substituent identity (X = O, S, or CH2) in the structure affected the potentials of materials. The highest potential of 2.03 V was obtained when oxygen was used as the heteroatom. The material with sulfur as the heteroatom had a potential of 2.0 V, which was slightly lower than oxygen. The material with methylene (CH2) as the substituent had the lowest potential of 1.95 V in the three polymer materials. The potentials of materials could be explained by the energy of LUMO. In the reduction process, the electrons go into the LUMO, which means that the higher the energy of LUMO is, the more difficult it is to enter. When comparing the LUMO energy values of polymers containing S, O, and CH2, we noticed that the potential values follow the order: 16th > 17th > 23rd. This behavior can be explained by the following: the methylene group is the electron-donating group, when the LUMO orbital energy value increases, the electrons will be unable to enter the LUMO orbital, meaning that that the potential is its lowest. The electronegativity of the sulfur atom was less than the electronegativity of the oxygen atom; therefore, the electron-donating ability of the sulfur atom was higher than that of the oxygen atom. This property caused the LUMO orbital energy value to be higher than that of the oxygen atom, making its potential lower than that of the oxygen atom. Therefore, a material containing a low electronegative heteroatom and an electron-donating group has a low potential value. Therefore, the electrochemical properties of materials can be improved by changing the heteroatoms in the structure.

Fig. 11
figure 11

a Potentials of the 16th, 17th, and 23rd materials; b LUMO and HOMO orbital energy values of the 16th, 17th, and 23rd materials; c repeating units of 16th, 17th, and 23rd materials

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Then, the polymer containing a high electronegative heteroatom and electron-absorbing groups has a relatively high potential and small band gap. For capacity, the material with a larger amount of carbonyl groups and a smaller molar mass has a larger theoretical capacity.

Conclusions

The charge/discharge potentials of 11 reported polymer electrode materials for lithium–ion batteries were collected, and the experimental values were fitted linearly with the values of ΔEpoly (as shown in Eq. (2b)) calculated with the single-molecule model. After the mathematical treatment, a semi-empirical formula was employed to predict charge/discharge potentials of more than 20 industrial polymers as electrode materials. The potential energy range of 26 types of industrial polymers was 0.62~2.03 V, the capacity distribution was 79.5~382.9 mAh/g−1, and all band gaps were less than 2.57 eV. The 16th, 17th, and 23rd materials are highlighted from 26 types of industrial polymers which have better electrochemical performance than the other materials in this paper. We also found that the electrochemical properties of materials can be improved by changing the heteroatoms in the structure. More polymer electrode materials can be developed with the present theoretical method. We believe that the results of this study will help in designing better electrode materials.