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Vanishing Thermal Conductance of Carbon Nanotube upon Encapsulation by Zig-Zag Sulfur Chain Sayantanu Koley, Sabyasachi Sen, and Swapan Chakrabarti J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b01121 • Publication Date (Web): 23 May 2018 Downloaded from http://pubs.acs.org on May 23, 2018

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The Journal of Physical Chemistry Letters

Vanishing Thermal Conductance of Carbon Nanotube upon Encapsulation by Zig-zag Sulfur Chain Sayantanu Koley,

†Department

†

‡

Sabyasachi Sen,

and Swapan Chakrabarti

∗,†

of Chemistry, University of Calcutta, 92, A. P. C. Road, Kolkata-700009, India

‡Department

of Physics, JIS College of Engineering, Block-A, Phase-III, Kalyani, Nadia, PIN- 741235, India.

E-mail: [email protected]

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Herein we report an unprecedented enhancement of thermoelectric properties of a single walled carbon nanotube upon encapsulation of a zig-zag sulfur chain inside the nanocore. Our calculations on a 70 Å long [5, 5] carbon nanotube reveals that the encapsulation of zig-zag sulfur chain will lead to 107 % increase in the thermoelectric gure of merit and concomitant quenching of thermal conductance by 90%. We have noticed that nite transmission gradient at the Fermi level combined with destructive quantum interference at the sulfur sites and structural conformation dependent scattering induced damping of phonon transmission are attributed to the dramatic improvement of thermoelectric behavior of this material. This nding indeed will help circumvent the long standing problem in the fabrication of carbon nanotube based ultrafast device.

Graphical TOC Entry

Keywords American Chemical Society, LATEX

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The conversion of waste heat into electricity with an aim to address the global challenges related to eco-friendly clean energy is the need of the hour and therefore demands special endeavor from the scientic community involving physics, chemistry and material science as well. 1,2 Historically, the rst experimental realization of thermoelectric eect was achieved date back to 1821 and the eld is now quite developed with its cornucopia lled with a large number of high performance thermoelectric (TE) materials, namely, Mg3 (Sb, Bi)2 , Cu2 Se, CuInSe2 Bi2 Te3 , PbTe, SiGe, Cu2 S, to mention a few. 310 The performance of a TE material is usually dened by a dimensionless gure of merit, ZT =

Ge S 2 T , k

where Ge , S and k are the

electrical conductance, Seebeck coecient and thermal conductance, respectively. It is quite obvious that the enhancement of Ge , S and a simultaneous lowering of k will be the key route to increase the ZT value vis-à-vis the eciency of a TE material. In this context, the hitherto existing experimental and theoretical results suggest that, band convergence, carrier mobility, anharmonicity, spin-orbit coupling, nano-structuring etc. are the decisive factors in controlling the net ZT value of the bulk TE materials. 1117 Apart from the bulk TE material, thermoelectricity with high ZT value has also been observed in molecular break-junction set up as well. 1820

Figure 1: Pictorial representation of linear and zig-zag sulfur chain encapsulated single walled carbon nanotube. Nevertheless, the research interest in the eld of TE is not conned only to nd material 3



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with thermodynamically unlimited ZT value rather nding ways to reduce thermal conductance of electronic material having tantalizing prospect in device fabrication is equally important. For example, carbon nanotube (CNT) could be used as single electron transistor, eld eect transistor and electron-hole bound super current generator. 21,22 However, very large thermal conductance of CNT is actually disadvantageous to use it in large scale ultrafast device fabrication. In this context, a recent experiment shows a new ray of hope where it has been found that encapsulation of Er@C82 or Gd@C82 in CNT can reduce the thermal conductance of these CNT-peapods by 35-50%. 23 This ground-breaking observation actually motivates us to discover new CNT based materials that could have even lower thermal conductance. In this letter, we report that the thermal conductance of a single wall CNT (SWCNT) encapsulated zig-zag sulfur chain (Z@SWCNT) can be suppressed by 90% and the ZT can be increased by 108 times compared to pristine SWCNT. The investigations were performed on 35 and 70 Å long zig-zag and linear sulfur chain containing SWCNT (L@SWCNT) and these thermally stable systems have already been synthesized by Fujimori

et al.

24

To address the

origin of this spectacular thermoelectric behavior of the studied material, we have performed density functional theory based non-equilibrium Green function(NEGF) calculations and evaluated the important physical parameters, namely transmission gradient at the Fermi level, transmission pathways, electrical and phonon transmission as well. To begin our investigation, we have considered 35 and 70 Å long [5, 5] SWCNT having diameter 7.05 Å. The L@SWCNT and Z@SWCNT devices are depicted in Figs. 1(a) and 1(b), respectively. The pristine and sulfur containing SWCNTs are optimized using Slater-Koster method 25 in combination with self-consistent CP2K basis set. From the optimized structures of sulfur encapsulated SWCNTs, it is found that all the sulfur-sulfur bond lengths are not equal and it lies in the range of 1.96-2.10 Å and this is fully consistent with the universal Peierls instability eect observed in 1D or quasi-1D system. It is also to be noted that the calculated bond length agrees quite well with the average experimental 4


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sulfur-sulfur bond length of 1.97Å. 24 After the optimization, we have performed the phonon transport calculation using ReaxFF potential. 26 All the optimization and transport related calculations are carried out using ATK 2016.4 27,28 software and the computation of thermoelectric parameters have been done up to a maximum temperature of 800 K since beyond this temperature the sulfur encapsulated SWCNTs are not stable. Earlier it was found that anharmonicity will be be important if the temperature exceeds 1000 K. 29 Moreover, it is to be noted that the experimental thermal conductance data for SWCNT is available up to 800 K which ensures excitation of all the normal modes and due to these reasons, we have performed all the calculations up to 800 K. 30 The relevant results on the thermoelectric properties of the pristine SWCNT, L@SWCNT and Z@SWCNT having tube length of 70 Å are presented in Fig. 2 and the corresponding results on 35 Å long SWCNT are given in the Supporting Information. Nonetheless, Fig. 2(a)depicts the variation of ZT with temperature which clearly demonstrates that both pristine SWCNT and L@SWCNT have very low ZT. In particular, the pristine SWCNT has a maximum ZT value of 1.09 × 10−6 and for the L@SWCNT, the corresponding ZT is 3.31 × 10−4 at 800 K. The Fig. 2(a) also reveals that, in case of Z@SWCNT, ZT increases signicantly and reaches the maximum value of 0.18 which actually is 107 % higher than the pristine SWCNT. Earlier Kodama

et al.

found

that the incorporation of Gd@C82 and Er@C82 in CNT helps increase the ZT value up to 200-400% only, indicating that the present in silico nding on ZT value is unquestionably far more superior than other CNT based materials. To understand the origin of this huge enhancement of ZT of Z@SWCNT with respect to the pristine analog, let us rst examine the temperature dependence of Seebeck coecient, electrical and thermal conductance, the key physical parameters directly involved in determining the ZT value of a TE material. In the present context, Fig. 2(b) provides necessary information about the variation of electrical conductance with temperature. A closer inspection of the gure reveals that the electrical conductance of pristine SWCNT and L@SWCNT could reach a maximum value of 1.31 × 10−4 and 3.76 × 10−4 Siemens, respectively while 5



Figure 2: Temperature dependence of (a) ZT, (b) electrical conductance, (c) Seebeck coecient and(d) thermal conductance of pristine and sulfur chain encapsulated SWCNT (length=70 Å) the corresponding value for Z@SWCNT is slightly lower than the other two devices having the highest value 3.47 × 10−5 at 800K. This merely indicates that the electrical conductance is not playing the major role in shaping up the high ZT value of Z@SWCNT in comparison to the other two systems. To proceed further, let us now turn our attention on another factor which is also directly proportional to the ZT of a TE material, that is, the Seebeck coecient and the relevant results are shown in Fig. 2(c). The Seebeck coecient of pristine SWCNT and L@SWCNT are more or less same and their maximum values are found to be 2.61 × 10−7 and 3.14 × 10−6 V/K, respectively. However, a huge change in the value of Seebeck coecient has been observed for Z@SWCNT with a maximum value of 1.02 × 10−4 V/K which of course is 103 times higher than pristine SWCNT. Since ZT is proportional to the square of S, a thousand fold increase in S will result into a 106 times enhancement of ZT. Apart from these two factors, it is also well known that the thermal conductance also plays signicant role on the TE eciency of a material. The change in thermal conductance of the devices with increasing temperature has been displayed in Fig. 2(d). Here the curves reveal that, amongst the three studied systems, the thermal conductance of L@SWCNT is the highest while that of Z@SWCNT has the minimum value keeping the pristine SWCNT

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material in between them. Since thermal conductance is inversely proportional to ZT, the decrease in thermal conductance of Z@SWCNT will indeed help increase its ZT up to 107 % with respect to the other two systems. It is to be noted that, all the TE parameters along with the relevant discussions for the devices having 35 Å length are provided in the Supporting Information le. A comparison of Fig. S1 of Supporting Information with Fig.2 shows that the trend of Seebeck coecient values of 35 Å long Z@SWCNT is dierent from that of 70 Å long Z@SWCNT. This is due to the fact that the nature of the single molecular orbital which involved with the transport (highest occupied molecular orbital)process changes with the variation in the length of the nanotube. Furthermore, the value of S attains saturation for 70 Å long Z@SWCNT, however in case of 35 Å long Z@SWCNT, it continues to increase with the rise of temperature. In the present scenario, the temperature dierence between the electrodes actually drives the holes to move from hot to cold electrode that produces current and, with the increase in temperature dierence, electrons will indeed start owing through the LUMO level in the same direction leading to the saturation in the value of Seebeck coecient. 31 This saturation phenomenon has been found in case of the longer chain system since the LUMO level of the longer chain system is closer to the Fermi level compared to the LUMO of the smaller chain analog. To address this unprecedented increase of the ZT value of Z@SWCNT compared to the pristine analog, we need to shed light on the question like how the large enhancement of S with a concommitant decrease of Ge and

k are taking place for Z@SWCNT. In the present context, let us rst recall the denition of Seebeck coecient which usually is expressed as S=-∆V/∆T. Here ∆V represents the voltage dierence originated from the temperature dierence, ∆T between the electrodes. In a molecular break-junction set up, S can further be expressed as a function of the transmission function following the equation, 32

S=

2 −π 2 kB T δ ln(τ (E)) [ ]E=EF 3|e| δE

7


(1)


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(E) Figure 3: (a) δτδE versus energy plot, (b) electronic transmission plot of the devices and tranmission pathways of (c)L@SWCNT, (d)Z@SWCNT of the device having length 70 Å. The arrows indicate angular distribution of electron transport, blue and red arrows indicate electron transport along the length of SWCNT and green arrows indicate electron transport perpendicular to the length of SWCNT.

where kB is the Boltzmann constant, τ (E) is the transmission function and EF is the (E) ) Fermi energy. The above equation clearly tells us that the slope of the transmission function( δτδE

at the EF is crucial in determining the value of S at a particular temperature. Fig. 3(a) illustrates the variation of

δτ (E) δE

as a function of energy and the curves reveal that the

δτ (E) δE

at EF for both SWCNT and L@SWCNT is almost zero while Z@SWCNT exhibits a nite slope at EF with a reasonable value of -2.88. This nite slope indeed leads to a large Seebeck coecient of Z@SWCNT and makes it dierent from the other two systems in terms of TE eciency. The negative slope also indicates that the Z@SWCNT will act as a p-type thermoelectric material and this nding is quite consistent with the negative gradient of the density of states at the EF . Besides, the presence of the highest occupied molecular orbital closer to the EF also supports p-type behavior of the system. The variation of gradient of DOS along with the molecular orbitals are presented in the Supporting Information. The above equation also suggests that Seebeck coecient depends on the reciprocal of the electronic 8


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transmission, (τ (E)) and according to Fig. 3(b), τ (E) value is the lowest for Z@SWCNT, leading to the highest value of the Seebeck coecient. In the next step, to get insight into the role of electrical conductance, Ge on the ZT values of the studied materials, it is useful to start the discussion by introducing the famous Landauer-Buttiker equation, 3335

2e I= h

Z

∞

(fL − fR )τ (E)dE

(2)

−∞

where fL and fR are the Fermi functions of the left and right electrode, respectively. The equation suggests that Ge is directly proportional to the net transmission of the electronic waves, τ (E) through the device. Keeping this factor in mind, we have plotted the electronic transmission spectra of the devices as a function of energy and the results are shown in Fig. 3(b). From this gure, it is apparent that the pristine SWCNT hardly has any τ (E) value at the EF while this contribution is quite appreciable for both the sulfur chain encapsulated SWCNTs. Looking at Fig. 3(b), it is also evident that the L@SWCNT has higher τ (E) value at EF compared to the Z@SWCNT and as a consequence, the electrical conductance of L@SWCNT will be larger than that of the zig-zag analog. To nd a molecular origin of this in silico observation, we have computed the transmission pathways of the L@SWCNT and the Z@SWCNT and those are represented in Figs. 3(c) and 3(d) respectively and the corresponding results for the pristine SWCNT are supplied in the Supplimental Material. It is worth recalling that the transmission pathways are actually the pictorial illustration of local bond contribution to the net transmission coecient 36 and the analysis of the transmission vectors is now a very useful technique to probe the nature of the interference pattern associated with the transmission of the electronic waves. Fig. 3(c) elucidates that the transmission vectors of L@SWCNT are mostly phase coherent which eventually leads to constructive interference vis-à-vis higher transmission. On the other hand, due to a phase dierence of

π 2

(green arrows) of the transmission vectors at each sulfur atom of the zig-zag

9



chain, the propagating electronic waves will encounter destructive interference and is evident from Fig. 3(d). Moreover, Figs 3(c) and 3(d) also suggest that back scattering event is more pronounced in case of Z@SWCNT which further substantiate the origin of higher electrical conductance of L@SWCNT in comparison to Z@SWCNT.

Figure 4: Phonon transmission plot of all the devices having length of 70 Å.

Figure 5: Phonon density of states of linear and zig-zag sulfur chain encapsulated SWCNT. The third factor involved with ZT is the thermal conductance and it actually plays a detrimental role in the overall performance of a TE material. Thermal conductance comes both from the electrons and phonons and for the elastic case, only the ke has signicance. It is to be noted further that according to Wiedemann-Franz law ke is related to the electrical conductance by the relation ke = Ge LT , where L is the Lorenz number and can be taken as 10


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constant for a particular type of carrier. From the previous discussion on Ge , it is obvious that ke value of L@SWCNT will be higher than that of Z@SWCNT. Meanwhile our calculations also suggest that the phonon contribution to thermal conductance, kph of Z@SWCNT is lower than that of L@SWCNT. To nd the reason behind the origin of higher phononic thermal conductance of L@SWCNT, we have calculated the phonon transmission spectra of the systems since kph is directly proportional to it and the corresponding results are presented in Fig. 4. The plots manifestly reect that the phonon transmission of Z@SWCNT is much less than that of both pristine SWCNT and L@SWCNT, indicating that kph value of Z@SWCNT should be lower compared to the other two systems. It is important to mention here that the phonon transmission spectra of 35 and 70 Å long Z@SWCNT are dierent which apparently goes against the common notion of ballistic transport. 37 However, in the ballistic transport regime, phonon transmission of SWCNT of dierent lengths should be same if and only if the two systems have equal strain and it has already been found that the strain in the structure of SWCNT changes signicanly with the alteration of length and diameter of the nanotube. 38,39 Our calculations also reveal that the nature of the phonon transmission strongly dependent on the chirality index(n,m) of the nanotube. Nevertheless, one question still remains unanswered and that is, how the encapsulation of zig-zag sulfur chain into the core of SWCNT helps decrease the phonon transmission signicantly. To get an answer, we have computed the phonon density of states (PhDOS) of both L@SWCNT and Z@SWCNT and the PhDOS plots are illustrated in Fig. 5. The gure tells us that the PhDOS of Z@SWCNT is slightly denser than its linear version and is quite puzzling since it goes against the nature of variation of the phonon transmission spectrum of the two systems. Earlier Sasikumar and Keblinski showed that the conformation of molecular chain can have signicant impact on the phonon transport in a molecular break junction set up. 40 More precisely, nonequilirium molecular dynamics based computation provides strong evidence in favor of ballistic heat transport along a straight chain polyethylene while it has been observed that the heat ow gets hindered in a twisted conformation of the same 11



material due to large increase in the phonon scattering event. Following the argument of Sasikumar and Keblinski, it is easy to understand that the rate of phonon scattering in a Z@SWCNT will be higher than linear chain analog which at the end is responsible for the lower thermal conductance of zig-zag system. Nonetheless, since k is inversely proportional to ZT, a smaller k value will further help increase the ZT value of Z@SWCNT.

Based on the above stated discussions, we conclude that pure SWCNT exhibits very poor thermoelectric properties though it could be improved to a signicant extent upon encapsulation of zig-zag sulfur chain. It has been found that thermoelectric gure of merit will be increased by 107 % while the thermal conductance could be reduced up to 90% in comparison to the pristine SWCNT. Our analyses reveal that, in case of Z@SWCNT, the nite transmission gradient leads to an enormous increase in the Seebeck coecient and at the same time, large phonon scattering actually helps decrease the thermal conductance of this material. Besides, in case of linear chain system, that means, the L@SWCNT quenching of phonon scattering makes a perfect environment for the ballistic heat transport, leading to a very high kph value. Finally, the present ndings will make an immediate impact on the carbon nanotube based ultrafast device related research.

Acknowledgement SK acknowledges UGC for senior research fellowship, SS acknowledges All India Council of Technical Education (AICTE), Govt. of India for the research funding [Ref. No.: File No.

8 − 18/RIFD/RPS/POLICY-t / 2016 − 17 Date: 14 September 2017]. SC acknowledges CRNN, University of Calcutta for providing computational resources.

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Supporting Information Available Thermoelctric properties and explanation of devices having length 35 Å ; MPSH states, gradient of DOS, PhDOS plots of Z@SWCNT; PhDOS plots of L@SWCNT;transmission pathways of SWCNT; Optimized coordinates of the two probe set up.

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