Doping effects on the thermoelectric properties of pristine poly(3,4-ethylenedioxythiophene)

Abstract

Electronic and thermoelectric properties of poly(3,4-ethylenedioxythiophene) (PEDOT) depend strongly on its geometric structure and the free charge concentration in the PEDOT crystals. In this work, pristine and doped PEDOT crystals with tosylate (Tos)/tosylate anion (Tos⁻) are studied using Density Functional Theory (DFT) methods. During Tos⁻ doping, charge transfer from PEDOT chains to Tos⁻ occurs with a structural transformation (from aromatic-like to semi-quinoid-like). These changes shift the Fermi level into the valence band and exhibit metallic character with a semiconductor-metal transformation. The influence of the doping concentration on the thermoelectric properties of the pristine PEDOT, such as electric conductivity, Seebeck coefficient and power factor, was carefully studied. We found that doping affects the geometric structure, free charge concentration, and eventually leads to changes in the electronic and thermoelectric properties of PEDOT. When the Tos⁻ doping concentration is around 12.5%, a high conductivity and Seebeck coefficient can be achieved at the same time (which means a high power factor). Our investigations also show that there is a compromise between doping and the thermoelectric properties of PEDOT(Tos/Tos⁻), and doping does not always work well to improve the electrical conductivity and Seebeck coefficient for organic thermoelectric materials. This study might be beneficial to the engineering realization of PEDOT for thermoelectric applications.

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1. Introduction

Thermoelectric materials are important energy conversion materials that directly transform heat to electrical energy, being widely used in thermoelectric power generation or cooling devices.^1,2 The performance of thermoelectric materials is indicated by the thermoelectric figure of merit (ZT) ZT = S²σT/κ, where S is the thermopower or Seebeck coefficient, σ is the electronic conductivity, κ is the thermal conductivity and T is the absolute temperature. For most thermoelectric materials, S is closely related to the concentrations of electronic carriers. With an increase of carrier concentration, σ will increase and S will decrease. Therefore, to obtain a higher ZT value, optimal carrier concentrations are required to achieve a balance between S and σ. In addition, a low κ value is obviously crucial and usually this can be realized by doping or the formation of low-dimensional super-lattices.^3,4 In practical applications, a ZT value larger than 1 is required.

Presently, the most widely used thermoelectric materials are (Bi₂Te₃)-based alloys with ZT in the range of 1 to 2.5.^5,6 However, the high cost and high toxicity in their synthesis procedures limit the large-scale applications of these kind of alloy materials. Motivated by the desires of sustainable developing strategies, organic materials with extremely low-cost, good flexibility and environmental friendliness are expected to partially alleviate these burdens for thermoelectric materials at room temperature in the near future.⁷

One of the potential organic thermoelectric materials (OTEMs) is conducting polymers with special geometric structures.⁸ Previously, conducting polymers have been employed as battery electrode materials, anti-static materials, electrochromic display materials, biosensor materials and functional film materials.^9–13 Their utilization potentials as OTEMs were not discovered until the 1990s, due to the progress of electrical and thermal conductivity on conducting polymers.^14–16 However, their poor chemical stability and low ZT of 10⁻² to 10⁻³ in air have limited their practical applications.^17,18

Poly(3,4-ethylenedioxythiophene) (PEDOT) as one of conducting polymers are applied to thermoelectric fields only in recent years. The pristine PEDOT was investigated first but studies show they were not as promising as those inorganic counterparts. With the development of chemical synthesis, by doping or combing PEDOT with other carbon materials via chemical or electrochemical routes, ZT values of PEDOT are dramatically improved to the order of 10⁻² to 10⁻¹.^19–22 Within those efforts, graphene, carbon nanotubes are combined with PEDOT to form composite materials. When tosylate(Tos)/tosylate anion (Tos⁻) and polystyrene sulphonic (PSS)/polyanion (PSS⁻) are added into the PEDOT structures, ZT can reach 0.25.²³ Those doped PEDOT structures exhibited excellent chemical stability and relatively high ZT values. More recently, a higher ZT value of 0.42 was obtained by removing unoxidized PSS in doped PEDOT.²⁴

Due to the great progress made on the experiments, theoretical investigations are also performed to exploit the potentials of PEDOT. The earlier theoretical work about PEDOT was done by A. Dkhissi, C. Alemán et al., focusing on the electronic properties of PEDOT oligomer.^25–27 Their studies showed that the pristine PEDOT has aromatic-like characters while doped PEDOT have semi-quinoid-like structures within the framework of Density Functional Theory (DFT). Various functional such as HF, B3LYP, PBE are employed to describe the charge distributions, molecular distortion etc. for doped PEDOT oligomers. Ahméd Dkhissi used the molecular dynamic simulations to investigate the stable structures of doped PEDOT, providing an important reference to the investigations of stable PEDOT structures under doping.²⁸ However, previous theoretical studies are mainly about PEDOT oligomer, the investigations on the crystalline structures of ordered PEDOT are relatively rare. In 2008, E. G. Kim et al. studied the crystalline structures for Tos⁻ doped PEDOT with DFT. They found that doping would change the geometric and electronic structures, leading to the transition of PEDOT lattice from semiconductor to semi-metal.²⁹ Annika Lenz et al. obtained the geometric and electronic structure of PEDOT : PSS and investigated the influences of PSS⁻ doping concentration on optical parameters by the DFT methods.³⁰

However, doping effects on the thermoelectric properties of PEDOT has not yet been fully explained in detail, such as the effects on S, σ and thermoelectric power factor (S²σ). In this paper, we then focus on the Tos/Tos⁻ doping effects in the pristine PEDOT crystals and study their thermoelectric properties by using the DFT methods. We found that doping did modify the thermoelectric properties of PEDOT with improved σ and S if an optimal concentration is carefully adopted. These improvements primarily originate from the change of basic structure with aromatic-like structure to semi-quinoid-like structure, as well as the introduction of positive charge in PEDOT chains. The degree of changes is determined by an optimal Tos⁻ doping concentration, in which the S coefficient and σ can be maximized simultaneously.

2. Methods

All the calculations are performed by using the CASTEP module in Materials Studio® with the general exchange and correlation functional of Perdewe–Burkee–Ernzerhof (PBE) within the framework of the generalized gradient approximation (GGA).^31,32 The selection of PBE is on the basis of following considerations: (1) computation costs. Compared with other functional like B3LYP, PBE0, the calculation times are much less; (2) PBE functionals have been applied to well describe the charge transfer and molecular distortion for the doped PEDOT^27–29 and also π–π stacking interactions between molecular crystals.^33–35 Since the doped PEDOT exhibits high orderliness and lattice symmetry in this work, we choose PBE as the exchange and correlation functions without considering other limitations. More accurate computations like using advanced functional are expected in our future work. The cutoff energy is set as 380 eV for pristine PEDOT and 340 eV for doped PEDOT, respectively, with 9 × 7 × 9 Monkhorst Pack mesh of k-points.

The initial geometric structures and lattice constants of pristine and doped PEDOTs are built in an orthorhombic unit cell on the basis of the experimental data.^29,36 For the pristine PEDOT crystal, the lattice constants are set as a = 7.60 Å, b = 10.52 Å, c = 7.935 Å. For the doped PEDOT crystals, we consider two types of doping. The first is the Tos anion doping (Tos⁻), the second is the molecular doping (with Tos doping). During all geometric optimization of PEDOT, the lattice constants in all three directions are fixed to the experimental values and the coordinates for each atom are totally relaxed. Since GGA/PBE overestimates lattice parameters in general, this treatment would relieve the overestimations resulting from lattice parameters optimization by GGA/PBE.

Seebeck coefficient S is characterized by a local change of the density of states (DOS) g(E) near Fermi level according to the Mahan–Sofo theory.^37,38 S is expressed as:

where S depends on the electrical conductivity σ(E) = n(E)qμ(E) taken at Fermi energy E_F and carrier density n(E) = g(E)f(E) taken at the energy level E, f(E) is Fermi function, q is the carrier charge and μ(E) is the mobility, k_B is the Boltzmann constant.

Eqn (1) implies that there are two mechanisms to increase S: an increased energy-dependence of μ(E); or an increased energy-dependence of n(E) by a local increase/decrease for electrons/holes in E, which corresponds to a large change of the density of states (DOS) g(E) near Fermi level.

3. Results and discussion

3.1 Stable geometric structure

Fig. 1 shows the optimized structures from our computations. To get clear pictures on the structures, the pristine PEDOT, Tos⁻ doped PEDOT with different concentrations, and Tos doped PEDOT (molecular doping) are shown for comparisons. As can be seen, in the pristine PEDOT crystal, one (layer) periodic structure along lattice direction b is presented with a stacking distance of 3.745 Å between chain backbones along lattice direction a (Fig. 1a). The stacking is the result of π–π stacking interactions between adjacent thiophene rings with shifting one thiophene ring along the chain extension direction.^29,39 A small rotated angle (around 10°) is also presented between lattice direction b and the plane of PEDOT chain, which are the results of interactions between adjacent PEDOT layers.

Fig. 1 The stable geometric structures for pristine PEDOT and doped PEDOT crystals with one view,. (a) the pristine PEDOT; (b) 8.3% Tos⁻ doped PEDOT; (c) 12.5% Tos⁻ doped PEDOT: (d) 16.7% Tos⁻ doped PEDOT; (e) 25% Tos⁻ doped PEDOT; (f) 50% Tos⁻ doped PEDOT; (g) 25% Tos doped PEDOT (molecular doping). Colors: red-O atom; gray-C atom; dark gray-H atom; yellow-S atom.

For the Tos⁻ doped PEDOT crystals (Fig. 1b–f), periodic Tos/Tos⁻ and PEDOT layer are alternately arranged and the π–π stacking interactions between adjacent thiophene rings are still kept in PEDOT layers. However, from the microscopic views, obvious structural changes can be found in PEDOT layers when we compared the structures before and after doping. In brief, the complete planarization thiophene backbones with aromatic-like structures in the doped PEDOT layers, as well as the rotated PEDOT chains closing to the SO₃⁻ of Tos⁻ are changed (Fig. 1b–g). The interactions between Tos/Tos⁻ and PEDOT layers could eliminate the partly rotated angle of PEDOT chains that close to the SO₃H/SO₃⁻ on Tos/Tos⁻. As an example, detailed structural changes in PEDOT layers are showed in Table 1 (only pristine, 12.5% and 25% Tos⁻ doped, and 25% Tos doped PEDOT are shown). It can be seen that, doping would lengthen the C=C bonds and shorten the single C–C bonds in intra-ring of PEDOT backbones. With the increase of doping concentrations, the length of C=C bond and C–C bond in PEDOT layer are tending to be equal, as shown in Table 1 for the case of 12.5% and 25.0% Tos⁻ doped PEDOT. Data under other concentrations are not shown since they exhibit similar behaviors. Note that the length of C–C bonds in inter-ring has changes with doping concentrations. However, we didn't find the similar tendency of equality between C=C and C–C bonds exhibiting in PEDOT layer as that in inter-ring. The inter-ring bonds lengths decreased with doping concentrations. The structural changes indicate that doped PEDOT chains present semi-quinoid-like characteristics, in which the inter-ring bonds remain lager than intra-ring bonds. Therefore, when Tos⁻ are mingled in pristine PEDOT crystal, a structure transformation from aromatic-like to semi-quinoid-like will occur.^25,40,41 Meanwhile, for molecular doping (here we just show the case of 25% Tos doping), only small changes (seen in Table 1) of bond-length are presented, comparing to the pristine PEDOT. Interestingly, molecular doping with even higher concentrations (i.e., 50%) will not change the properties in an obvious way, e.g., intra-ring and inter-ring bonds. Further numerical investigations with higher Tos⁻ doping concentrations show that the thermoelectric properties after doping depend strongly on the interplay of intra-ring and inter-ring bonds. Higher Tos⁻ doping concentration (less than 50%) leads to lager change of bond length, while high Tos doping is only with undiscerned changes. We therefore will mainly focus on the case of Tos⁻ doping in the following.

Table 1 The changes of the bond length in PEDOT chains for pristine PEDOT crystal and doped PEDOT crystals

Crystal	Intra-ring bonds length (Å)		Inter-ring bonds length (Å)	Lattice constants
	C=C	1.387	1.421	a = 7.60 Å,
	C–C	1.405		b = 10.52 Å
				c = 7.935 Å
12.5% Tos^− doping	C=C	1.396	1.418	a = 13.60 Å
	C–C	1.402		b = 14.00 Å
				c = 7.80 Å
25.0% Tos^− doping	C=C	1.400	1.417	a = 6.80 Å
	C–C	1.401		b = 14.00 Å
				c = 7.8 Å
25.0% Tos doping	C=C	1.391	1.424	a = 6.80 Å
	C–C	1.403		b = 14.00 Å
				c = 7.8 Å

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3.2 The electronic structures

The electronic structures for pristine and doped PEDOT crystals are showed in Fig. 2. Based on our numerical efforts, only four structures are selected to perform the band gap calculations. The Kohn–Sham one-electron band gap for pristine PEDOT crystal (Fig. 2a) and doped PEDOT (Fig. 2b–d) is 0.45 eV and zero, respectively. The band-gap for pristine PEDOT is closed to other DFT computations (0.37 eV) with slight difference of 0.08 eV, may originate from the different exchange-correlation functional used in the calculations.²⁹ The 0.45 eV band gap indicates that the pristine PEDOT presents similar properties to the inorganic semiconductors. For the Tos⁻ doped PEDOT (12.5% and 25.0%, Fig. 2b and c), Tos⁻ makes the Fermi level shift into valence band and then the structures exhibit metallic characters comparing to pristine PEDOT.^42–44 These metallic characters only present in the PEDOT layers and can be reflected by the splitting of subbands in the ΓZ and XU zone and the flatted subbands in the UY zone, as shown in Fig. 2. Splitting of subbands means the charge can transport along lattice a, c directions; the flatted subbands in the UY zone implies the charge is restrained along lattice b direction.^29,45 The much bigger subbands splitting in the ΓZ zone than that of in the XU zone indicates that the introduced free charge in PEDOT layers transports more easily along the extension direction of the chain (lattice c direction). The small splitting in the XU zone may originate from the intra-stack interactions between adjacent PEDOT chains.⁴⁶

Fig. 2 The band structures (a) for pristine PEDOT crystal, band gap is 0.452 eV; (b) for the 12.5% Tos⁻ doped PEDOT crystal; (c) for the 25.0% Tos⁻ doped PEDOT crystal; (d) for the 25.0% Tos doped PEDOT crystal.

The comparisons of band diagrams for the 12.5% and 25.0% Tos⁻ doped PEDOT (Fig. 2b and c) show that the higher Tos⁻ doping density will promote a much larger shift of Fermi level (0.25 eV for 12.5% Tos⁻ doping and 0.5 eV for 25.0% Tos⁻ doping). Note that when the doping density reaches 50%, this shift is close to 0.6 eV while the computation costs are much higher. In addition, for the 12.5% Tos⁻ doped PEDOT crystal, some impurity levels away from the Fermi level are introduced in the valance band and conduction band. For the 25.0% Tos⁻ doped PEDOT crystal, impurity levels don't appear in a large scale near Fermi level. This holds for much higher doping concentrations like in the case of 50% Tos⁻ doping. For molecular doping (i.e., 25% Tos doping and more), impurity levels appear near the top of valance band and the Fermi level is located between the top of valance band and the partial impurity levels. Compared with Tos⁻ doping, molecular doping doesn't prompt a transformation from semiconductor character to metallic character. Thus, we can conclude that molecular doping is not an effective way to improve the conductivity for PEDOT. Note that although the Tos⁻ doped PEDOT layers exhibit metallic characters, this improvement is still under limited range and depends strongly on the doping materials according to our simulations. Further work needs to be done with the optimization of materials, structures and other issues.

Table 2 lists the amount of charge in PEDOT layers for pristine and doped PEDOT crystals on the basis of charge analysis. It can be seen that the electric neutrality is kept in the pristine PEDOT and the Tos doped PEDOT crystal; while in the Tos⁻ doped case, charge transfer occurs and the charge is nearly uniformly distributed on whole PEDOT chains. The introduction of positive charge in PEDOT chains means that some electrons are taken away from fully filled valence band maximum, resulting in a shift of Fermi level.

Table 2 The charge in pristine and doped PEDOT chain with Tos(Tos⁻) in a unit cell; T1 mean all EDOTs in a unit cell; T2 means two EDOTs are along the same chain direction in the unit cell

Crystal		Charge (e)
Pristine PEDOT	T1	0.00
Doped PEDOT with 12.5% Tos^− doping	T1	+1.00
	T2	+0.26	+0.28	+0.24	+0.22
	Tos^−	−1.00
Doped PEDOT with 25.0% Tos^− doping	Total EDOTs	+1.00
	One EDOT	+0.25	+0.28	+0.22	+0.25
	Tos^−	−1.00
Molecular doping (doped PEDOT with 25.0% Tos doping)	T1	0.00
	Tos	0.00

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By comparing the DOS between the pristine (Fig. 3a) and Tos⁻ doped PEDOT crystals (Fig. 3b and c), we found a shift of Fermi level presented in the Tos⁻ doped case, and the results match with band calculations and charge analysis. The DOS near Fermi level is mainly contributed by the p-orbital of carbon atoms in the PEDOT chain backbones and only small part comes from the p-orbital of oxygen atoms in ethylenedioxy and sulphur atoms in thiophene ring. The special contribution of p-orbital of carbon atoms not only indicates that the carbon atoms π–π coupling forms electronic channels in the chain PEDOT backbones to transfer introduced charge, but also illustrates that the conductive characteristics of Tos⁻ doped PEDOT crystals are mainly controlled by PEDOT chains. The existence of electronic channels makes the PEDOT chains exhibited high conductivity along the extension direction of the chain. While for the molecular doping (25.0% Tos doped PEDOT as an example, Fig. 3d), the Fermi level is located on the bottom between impurity level and valance band, different with Tos⁻ doping. In general, the highest conductivity is achieved when Tos⁻ doping concentration is close to 25.0% based on our theoretical predications.

Fig. 3 The DOS and the first-order derivative near Fermi level. (a) for the pristine PEDOT crystal; (b) for the 12.5% Tos⁻ doped PEDOT crystal; (c) for the 25.0% Tos⁻ doped PEDOT crystal; (d) for the 25.0% Tos doped PEDOT crystal.

3.3 Thermoelectric properties

Considering practical applications, a large ZT is necessary to achieve high conversion efficiency. Generally, the thermal conductivity κ of conducting polymer is lower than that of its inorganic counterpart and the doping just has a minimal impact on κ. Therefore, κ is not taken into consideration and only power factor is investigated in this work. Since S and σ correlate to each other and they didn't present monotonic increase or decrease with the doping concentration, a compromise should be found between S and σ.^47,48 In this work, we did optimization to let S and σ maximized. Since doping would increase the conductivity almost monochromatically (at relatively mild doping concentrations, i.e., <25%), we will look for the case where S can be maximized.

The S coefficient is closely related to the first-order derivative (FOD) of DOS near Fermi level and their relationship is nearly monotonic according to the eqn (1).^37,38,49 Typically, S will increase with , where carrier density n(E) = g(E)f(E) taken at the energy level E, depending on the change of energy-dependence g(E) by a local increase/decrease of electrons/holes. Therefore, the S coefficient can be enhanced by obtaining a sharp DOS near Fermi level. The DOS comparisons between pristine PEDOT and doped PEDOT are shown in Fig. 3. We can see that the DOS for the 12.5% Tos⁻ doped PEDOT crystal presents most dramatic changes near Fermi level, the FOD is −31.74 (the FOD for the pristine PEDOT is −13.71). The DOS for the 25.0% Tos⁻ doped PEDOT crystal displays a smaller change near Fermi level and the FOD is −4.76. For the 25.0% Tos doped PEDOT crystal, the FOD is nearly zero and presenting large differences with Tos⁻ doping. These results indicate that although doping concentration plays an important role on σ, it doesn't mean that higher concentration could assist to reach high S too much. After numerous optimizations, we found that an appropriate doping density around 12.5% can effectively improve S coefficient while good electronic conductivity (on the order of 10³ S cm⁻¹) can be maintained. Namely, the power factor S²σ is maximized based on our calculations. Note that if only considering S coefficient improvement, Tos⁻ doping plays a negative role since heavy doping would decrease σ and S coefficient.

4. Conclusion

In summary, we use DFT methods to analyze the pristine and doped PEDOT crystals. We found that a transformation from semiconductor to metallic characters can be accomplished by Tos⁻ doping. The PEDOT chain exhibits semi-quinoid-like configuration with Tos⁻ doping in pristine PEDOT. Meanwhile, Tos⁻ doping introduced some positive charges into PEDOT layers and could be easily transported along the extension direction of the chain. It was found that the Tos⁻ doping could improve σ and S simultaneously once an appropriate concentration was found. These investigations might provide good hints to improve the ZT value of thermoelectric materials and eventually assist theoretical as well as experimental studies in near future.

Acknowledgements

The authors appreciate the constructive reviewing and suggestions from reviewers. This work was funded by the Science and Technology on Plasma Physics Laboratory in Research Center of Laser Fusion at CAEP (no. 9140c680502140c68004), and the Science and Technology Development Fund of CAEP (no. 2014A0302014).

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