Assembling Ï-Conjugated Molecules with Negative Gaussian

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Assembling #-Conjugated Molecules with Negative Gaussian Curvature for Efficient Carbon-Based Metal-Free Thermoelectric Material Jiabing Yu, Qiang Sun, and Puru Jena J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b08976 • Publication Date (Web): 22 Nov 2016 Downloaded from http://pubs.acs.org on November 26, 2016

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The Journal of Physical Chemistry

Assembling π-Conjugated Molecules with Negative Gaussian Curvature for Efficient Carbon-Based Metal-Free Thermoelectric Material Jiabing Yu,† Qiang Sun†, ‡, §,*, and Puru Jena§ †

Department of Materials Science and Engineering, Peking University, Beijing 100871, China

‡

Center for Applied Physics and Technology, Peking University, Beijing 100871, China

§

Department of Physics, Virginia Commonwealth University, Richmond, VA 23284, USA

Abstract Development of efficient, light-weight, cost-effective, and environmentally-friendly thermoelectric materials is critical for energy conversion devices. However, none of the existing thermoelectric materials satisfy these requirements. Here, we predict a novel carbon-based metal-free thermoelectric material named bct-C80S16 composed of π-conjugated saddleshaped molecular unit with a negative Gaussian curvature, leading to low lattice thermal conductivity while maintaining a high charge mobility. The resulting peak figure of merit (ZT) of 2.41 at 1000K is much larger than that of conventional Bi- or Pb-based thermoelectric materials. Additionally, bctC80S16 is highly porous and light with a mass density of 1.11 3 g/cm . The high thermoelectric performance and low mass density would make this metal-free semiconducting materials promising for practical applications in space-based technologies.

Introduction Thermoelectric (TE) materials can convert solar thermal energy and waste heat generated by power plants, vehicles, or even living beings into electricity, thus, playing an important role not only in sustainable energy but also for a clean environment. The energy conversion efficiency of a TE material at temperature T is evaluated by the figure of merit 2 (ZT= S σT/κ), which depends on the Seebeck coefficient (S), electrical conductivity (σ), and thermal conductivity (κ). However, the efficiency of the state-of-the-art TE materials 1 such as Bi-Te-based alloys (ZT = 1.4 at 400K) and Pb-Te2 based alloys (ZT = 1.6 at 700 K) are less competitive with 3 other energy conversion systems. Moreover, these materials are toxic and not environment friendly. The TE performance of current metal-free and light-weight TE materials such as 4,5 Si-Ge-based alloys (ZT = 1.3 at 900 °C) is also unsatisfactory. Thus, searching for new thermoelectric materials containing abundant, low-cost and non-toxic elements with high ZT is highly desirable.

In this study we report a promising metal-free TE material belonging to carbon-based semiconductors which generally have a low thermal conductivity and low density. In fact, as early as 1967, Hamann studied thermoelectric properties of 6 copper phthalocyanine single crystals. Unfortunately the ZT value of conventional organic TE materials was not high due 7,8 to the low Seebeck coefficient and electrical conductivity. Considering that highly ordered π-conjugated single crystals can exhibit higher conductivity than amorphous polymers, we attempt to use π-conjugated small molecules as structural units to design a new thermoelectric material. Here, the tetrathio[8]circulene (TT8C) molecule (Figure 1a), synthe9 sized recently by Wong and coworkers , is selected as the building block, owing to its particular π-conjugated saddlelike structure (Figure 1b). We show that such a metal-free TE material (labeled bct-C80S16) displays high charge mobility while maintaining low thermal conductivity due to its particular geometric structure with negative Gaussian curvature. The resulting peak ZT is 2.41 at 1000K. The geometric and electronic structures are calculated within density functional theory (DFT) while the TE transport properties are estimated 10 using semi-classical Boltzmann transport theory . The computational details can be found in the Supporting Information (SI).

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Figure 1 (a) Structural formula of TT8C molecule. (b) An illustration of the saddle-shaped geometric structure of TT8C molecule. (c) The crystal structure of bct-C80S16. The grey and yellow balls represent carbon and sulfur atoms, respectively.

Results and discussion The fully relaxed structure of bct-C80S16 has a bodycentered tetragonal cell (space group I41/amd, No. 141) containing 96 atoms (80 carbon atoms and 16 sulfur atoms) with optimized lattice parameters of a = b = 16.40 Å and c = 8.25 Å. The porous metal-free framework leads to a low density of 3 1.11 g/cm , which is much smaller than the density of conven3 tional TE materials, such as Bi2Te3 (7.64 g/cm ). Figure 1c shows the anisotropic geometric figure with negative Gaussian curvature. Based on the special geometric configuration, we can expect some unusual TE transport properties, namely, the geometric structure with negative Gaussian curvature can effectively enhance anharmonic scattering thus resulting in a low lattice thermal conductivity, while the well preserved π-conjugated bonding character would give a high charge mobility. It is noteworthy that the unique geometric figure with negative Gaussian curvature leads to a typical anisotropic transmission path (see SI). The wavy feature in the “x” direction is shown in Figure S1a while the helical feature in the “z” direction is shown in Figure S1b. Predictably, the charge mobility and thermal conductivity would be much lower than that along the “x” direction. The dynamic stability of bct-C80S16 is confirmed by phonon spectrum and ab initio molecular dynamics (AIMD) simulation indicates bct-C80S16 is thermally stable at 1000K (The detailed results can be seen in SI). It is well known that studies of thermoelectric properties require an accurate band structure because the Seebeck coefficient, electrical conductivity, and electronic contribution to the thermal conductivity depend on it. So we calculated the electronic band structure and corresponding density of states (DOS) of bct-C80S16 using hybrid (HSE06) and GGA (PBE) functionals. As shown in Figure 2, the bct-C80S16 is found to be a semiconductor with a direct band gap of 1.73 (1.26) eV at HSE06 (PBE) level. The well preserved π-conjugated bonding character of TT8C molecule in bct-C80S16 crystal results in a broad highest valence band (HVB) and lowest conduction band (LCB), the highly delocalized band state would give rise to high charge mobility.

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Figure 2 Electronic band structure calculated by GGA-PBE (blue dashed lines) and HSE06 hybrid functional (red solid lines) and DOS calculated at HSE06 hybrid functional level of bct-C80S16. The Fermi energy level is shifted to 0.00 eV. Ζ(0.5,0.5,0.5), Γ(0,0,0), Χ(0,0,0.5), Ρ(0.25,0.25,0.25), Ν(0,0.5,0). On the basis of the accurate band structure, we use the semi-classical Boltzmann transport theory to calculate the electronic transport properties of bct-C80S16. Due to different transmission path in different directions caused by the anisotropic geometric structure with negative Gaussian curvature, the transport properties are much better along “x” direction than that of “z” direction. So here we only focus on discussing the transport properties along “x” direction, while the results along “z” direction can be found in SI (see Figure S3). Figure 3 shows the calculated xx tensor component of transport coefficients as a function of chemical potential at different temperatures. We note that the room temperature -1 Seebeck coefficient exceeds 2000 μV K , much larger than that of conventional bulk thermoelectric materials, such as 11 12 Bi2Te3, Bi2Se3 and SnSe , but comparable with lowdimensional and nanostructured TE materials widely studied in recent years such as graphene/h-BN super-lattice nanorib13 bons . As displayed in Figure 3a and 3b, the Seebeck coefficient shows a peak at a small chemical potential, while the electrical conductivity increases with the increase of the chemical potential. This implies that there should be a tradeoff between the Seebeck coefficient and the electrical conductivity. Figure 3c clearly indicates that the maximum power factor (PF) appears at an optimum doping level where neither the Seebeck coefficient nor the electrical conductivity reaches a maximum. Additionally, when the temperature increases the Seebeck coefficient decreases but the electric conductivity increases, causing an increase in PF. Thus, we can expect that bct-C80S16 has a favorable TE performance in the entire temperature range from 300K to 1000K.


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The Journal of Physical Chemistry relaxation time for electron (light hole) is 143 (97) fs along the “x” direction, while the value is only 8.1 (3.5) fs along the “z” direction.

Table 1 DP constant E1, elastic constant C, effective mass m*, carrier mobility μ and relaxation time τ at 300 K. e represents electron while lh and hh represent light hole and heavy hole, respectively. me represents the rest mass of electron. Along the “x” direction E1(eV)

C(GPa)

m*(me)

μc(cm /(Vs)

2

τ(fs)

e

10.44

43

0.21

1.20×103

143

lh

10.97

43

0.26

6.69×102

97

hh

10.97

43

0.54

1.04×102

32

Along the “z” direction e

2.70

1.9

1.08

13.1

8.1

lh

2.89

1.9

1.71

3.61

3.5

hh

2.89

1.9

1.71

3.61

3.5

The electronic thermal conductivity (κe) is calculated using 16 the Wiedemann-Franz law κ e = Lσ T . Here the Lorentz Figure 3 Calculated (a) Seebeck coefficient, (b) electric conductivity, and (c) power factor as a function of chemical potential along the “x” direction at different temperatures. Within the semi-classical Boltzmann theory, the electrical conductivity σ can only be calculated as a function of relaxation time τ, namely the ratio σ/τ. To study the electronic relaxation time of bct-C80S16, we apply the deformation po14,15 tential (DP) theory proposed by Bardeen and Shockley, considering that the acoustic phonons are the main scattering mechanism. The relaxation time τ of a 3D system at temperature T can be expressed as:

τ =

µc m ∗ e

=

23 2 π 1 2h 4C 3m ∗3 2 ( k BT )

32

E12

Here, m* and μc are the effective mass and carrier mobility along the transport direction, respectively. The effective mass along different directions in wave vector space can be achieved from the second derivative of the conduction and valence bands (

1 1 ∂2E = 2 2 ). The deformation potential ∗ m h ∂k

constant, defined as E1 = ∆E / ( ∆l / l0 ) , is determined by changing the lattice constant l along the transport direction. The elastic modulus can be calculated using C = (∂ 2E ∂δ 2 ) / V0 , where E is the total energy of the system, δ is the applied uniaxial strain along the transport direction, and V0 is the volume of unit cell.

−8

-2 17,18

number is set to 2.45×10 W Ω K . To estimate the lattice thermal conductivity of bct-C80S16, the Boltzmann transport equation for the phonons is adopted. According to our calculations, the thermal conductivity of bct-C80S16 is anisotropic and the thermal conductivity along the “x” direction is larger than that along the “z” direction, well consistent with the structural feature. The lattice thermal conductivity of bctC80S16 at 300K along the “x” (“z”) directions is 1.08 (0.59) W -1 -1 m K . These values are close to the thermal conductivity of most organic TE materials and approach the lower limit of 8 thermal conductivity of inorganic TE materials . In Figure 4a we see that the cumulative lattice thermal conductivity reaches a constant value while the maximum mean free path (MFP) approaches 100 nm, suggesting that the MFP of bctC80S16 is shorter than 100 nm. The low lattice thermal conductivity is beneficial for a high TE performance. To further understand the origin of the low intrinsic lattice thermal conductivity, we calculate the mode Gruneisen parameters and cumulative lattice thermal conductivity. Mode Gruneisen parameters of bct-C80C16 are plotted in Figure 4b, from which we see that the absolute values of mode Gruneisen parameters of three acoustic branches are quite large, indicating that the three-phonon Umklapp scattering processes are very strong. This strong phonon-phonon anharmonic scattering causes a short mean free path of phonon. As shown in Figure 4c, when the temperature increases, the lattice thermal conductivity decreases, in line with the characteristics of the conventional semiconductors.

The calculated DP constants E1, elastic constants C, effective mass m*, carrier mobility μc, and relaxation time τ at 300 K are shown in Table 1. It is found that at room temperature the intrinsic mobility along the “x” direction is two orders of magnitude larger than the mobility along the “z” direction. This is because the particular geometric structure of bctC80S16 with negative Gaussian curve and helical configuration leads to the larger elastic constant and lighter effective mass along the “x” direction than that along the “z” direction. As expected, the intrinsic strong anisotropic mobility results in a strong anisotropic relaxation time. The room temperature



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Figure 5 ZTxx for (a) electron doping and (b) hole doping as a function of doping concentration.

Conclusion

Figure 4 (a) Cumulative lattice thermal conductivity of TT8C as a function of the MFP at 300 K. (b) Mode Gruneisen parameters of bct-C80S16. Only acoustic branches and the first three optical branches are plotted. (c) Lattice thermal conductivity for bct-C80S16 as a function of temperature. With all the transport coefficients determined, we can now evaluate the ZT value of bct-C80S16. Due to the strong anisotropy of electrical and thermal conductivity, the TE performance of bct-C80S16 shows strong anisotropy and the figure of merit along the “x” direction (ZTxx) is much better than that along the “z” direction (ZTzz). Figure 5 shows the calculated xx tensor component of ZT value as a function of doping concentration, while the zz component is shown in SI (see Figure S4). We find that the maximum ZTxx values at 300K 18 −3 are 0.89 and 0.87 at 3.7 × 10 cm electron concentration 19 −3 and 2.4 × 10 cm hole concentration, respectively. Because the maximum ZT increases steadily with temperature the maximum ZTxx values reach 2.41 and 1.61 for n-type and ptype doping, respectively at 1000K, much higher than another metal-free material SiGe alloy (ZT = 1.3 at 900 °C).

In conclusion, inspired by the recent experimental progress in synthesizing molecules with negative Gaussian curvature, we have proposed a metal-free thermoelectric material composed of TT8C molecular units. Using a multiscale approach that combines first-principles methods with semiclassical Boltzmann transport theory within the relaxation time approximation, we show that the bct-C80S16 is a semiconductor with a direct gap of 1.73eV. The unique geometric structure with negative Gaussian curvature brings about low lattice thermal conductivity while maintaining high carrier mobility, therefore the bct-C80S16 shows good TE performance with a peak ZT value of 2.41 at 1000K, which is much 4,5 better than that of SiGe alloy (ZT = 1.3 at 900 °C) , and is 12 comparable with that of SnSe (ZT = 2.6 at 923K) . Moreover, besides the TT8C unit, there are many other synthesized molecular units with negative Gaussian curvature, which may offer options to design new thermoelectric materials with different molecular units for high performance. We hope that this study will stimulate experimental effort on exploring novel efficient metal-free thermoelectric materials.

AUTHOR INFORMATION Corresponding Author *[email protected]

Notes The authors declare no competing financial interests.

ACKNOWLEDGMENT


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Q.S. acknowledges the support from the National Natural Science Foundation of China (NSFC-21173007, 11274023), from the National Grand Fundamental Research 973 Program of China (2012CB921404); P.J. acknowledges support by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award # DE-FG02-96ER45579.

Supporting Information Detailed calculation methods, optimized structures, dynamic and thermal stability, band structures, and thermoelectric transport coefficients along “z” direction.

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(7) O. Bubnova and X. Crispin. Towards polymer-based organic thermoelectric generators. Energy Environ. Sci. 2012, 5, 93459362. (8) Q. Zhang, Y. Sun, W. Xu, and D. Zhu. Organic thermoelectric materials: emerging green energy materials converting heat to electricity directly and efficiently. Adv. Mater. 2014, 26, 6829-6851. (9) X. Xiong, C. L. Deng, B. F. Minaev, G. V. Baryshnikov, X. S. Peng, and H. N. Wong. Tetrathio and Tetraseleno [8] circulenes: Synthesis, Structures, and Properties. Chem. Asian J. 2015, 10, 969975. (10) G. S. Nolas, J. Sharp, and J. Goldsmid, Thermoelectrics: basic principles and new materials developments (Springer Science & Business Media, 2001), Vol. 45. (11) S. Mishra, S. Satpathy, and O. Jepsen. Electronic structure and thermoelectric properties of bismuth telluride and bismuth selenide. J. Phys. Condens. Matter 1997, 9, 461. (12) L.-D. Zhao, S.-H. Lo, Y. Zhang, H. Sun, G. Tan, C. Uher, C. Wolverton, V. P. Dravid, and M. G. Kanatzidis. Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals. Nature 2014, 508, 373-377. (13) Y. Yokomizo and J. Nakamura. Giant Seebeck coefficient of the graphene/h-BN superlattices. Appl. Phys. Lett. 2013, 103, 113901. (14) J. Bardeen and W. Shockley. Deformation potentials and mobilities in non-polar crystals. Phys. Rev. 1950, 80, 72. (15) Z. Shuai, L. Wang, and C. Song, in Theory of Charge Transport in Carbon Electronic Materials (Springer, 2012), pp. 67-88. (16) A. Bejan and A. D. Kraus, Heat transfer handbook (John Wiley & Sons, 2003), Vol. 1. (17) J. Zhou, C. Jin, J. H. Seol, X. Li, and L. Shi. Thermoelectric properties of individual electrodeposited bismuth telluride nanowires. Appl. Phys. Lett. 2005, 87, 133109. (18) S. Sumithra, N. J. Takas, D. K. Misra, W. M. Nolting, P. Poudeu, and K. L. Stokes. Enhancement in thermoelectric figure of merit in nanostructured Bi2Te3 with semimetal nanoinclusions. Adv. Energy Mater. 2011, 1, 1141-1147.



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Table of Contents Graphic


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(a) Structural formula of TT8C molecule. (b) An illustration of the saddle-shaped geometric structure of TT8C molecule. (c) The crystal structure of bct-C80S16. The grey and yellow balls represent carbon and sulfur atoms, respectively. Figure 1 63x53mm (600 x 600 DPI)



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Electronic band structure calculated by GGA-PBE (blue dashed lines) and HSE06 hybrid functional (red solid lines) and DOS calculated at HSE06 hybrid functional level of bct-C80S16. The Fermi energy level is shifted to 0.00 eV. Ζ(-0.5,0.5,0.5), Γ(0,0,0), Χ(0,0,0.5), Ρ(0.25,0.25,0.25), Ν(0,0.5,0). Figure 2 65x56mm (600 x 600 DPI)


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Calculated (a) Seebeck coefficient, (b) electric con-ductivity, and (c) power factor as a function of chemical potential along the “x” direction at different temperatures. Figure 3 91x112mm (600 x 600 DPI)



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(a) Cumulative lattice thermal conductivity of TT8C as a function of the MFP at 300 K. (b) Mode Gruneisen pa-rameters of bct-C80S16. Only acoustic branches and the first three optical branches are plotted. (c) Lattice thermal con-ductivity for bct-C80S16 as a function of temperature. Figure 4 150x302mm (600 x 600 DPI)


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ZTxx for (a) electron doping and (b) hole doping as a function of doping concentration. Figure 5 103x141mm (600 x 600 DPI)


Assembling Ï-Conjugated Molecules with Negative Gaussian

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