New Insight on the Interface between Polythiophene and

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Surfaces, Interfaces, and Applications

New Insight on the Interface between Polythiophene and Semiconductors via Molecular Dynamics Simulations Yicheng Qian, Ming Guo, Chun Li, Kedong Bi, and Yunfei Chen ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.9b09742 • Publication Date (Web): 24 Jul 2019 Downloaded from pubs.acs.org on July 25, 2019

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ACS Applied Materials & Interfaces

New Insight on the Interface between Polythiophene and Semiconductors via Molecular Dynamics Simulations Yicheng Qian, Ming Guo, Chun Li, Kedong Bi *, Yunfei Chen *

Jiangsu Key Laboratory for Design and Manufacture of Micro-Nano Biomedical Instruments, School of Mechanical Engineering, Southeast University, Nanjing, 211189, P. R. of China

KEYWORDS: interfacial strength, polythiophene, entropy, molecular dynamics

Polythiophene is considered as an effective dry adhesive and is promising to be a conductive adhesive due to its excellent properties. Here, we used steered molecular dynamics (SMD) to investigate the interfacial strength between polythiophene and various semiconductors with similar structures including silicon, silicon carbide and diamond. Energy decomposition were done to have a detailed insight into the adhesive mechanism. Particularly, we laid stress on the entropy difference of the polythiophene chain in different systems. Van der Waals interaction and electrostatic interaction both positively contributed to the adhesion between polythiophene and semiconductors while the entropy change of polythiophene, including vibrational entropy change and conformational entropy change, weakened the adhesion to some extent. Our results indicated that the combined effect of these three factors made the adhesion between 1

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polythiophene and silicon carbide the strongest among the systems we studied. Additionally, it was found that such adhesion was scarcely influenced by temperature. This simple polythiophene-semiconductor interfacial study can help optimizing the choice of semiconductor when applying the polythiophene adhesive.

INTRODUCTION Polythiophene (PTh) materials have developed significant technical interest due to the prominent mechanical properties,1 chain-oriented high thermal conductivity,2 controllable electrical conductivity3-6 and other excellent characteristics. In particular, PTh nanotubule arrays exhibit strong adhesions on various smooth surfaces after drying from the wet states to ensure enough contact area.7 These outstanding properties provide PTh a potential opportunity for application in various fields, especially in electronic packaging. In this field, a reasonable selection of the material used to connect different parts is very crucial. Initially, conventional solders including Sn and Pb were wildly used to connect devices, then the solders have been gradually replaced by conductive adhesives composed of resin matrix and conductive fillers because they are unfriendly to the environment.8, 9 However, the electrical conductivities of these new adhesives only maintain from 10-3 to 10-4 S/cm and their thermal conductivities are relatively poor as well, which strongly limits the use of them on power components. Thus, PTh is regarded as a more promising candidate for the electronic devices packaging in the future due to its excellent conductivities. Conductive adhesives are commonly used to adhere semiconductors to other 2


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objects such as ceramic substrates, so it is necessary to study the adhesion between PTh and semiconductors. Adhesion is a multifaceted, complex phenomenon and relies on various factors such as types of polymers,10-13 substrate stucture,14, 15 thermal behavior16 and humidity.15, 17-19 In order to achieve the effective adhesion in the long term, the adhesion between PTh and semiconductors should be sufficient and is hardly affected by external factors. Therefore, developing a further understanding of the adhesion mechanism at the interface between PTh and semiconductors is critical for this potential application. At present, some experiments7, 20 have been conducted on PTh adhesion from a macro perspective, but the lack of analysis on the mechanism of such adhesion at the atomic level is urged to be solved. Moreover, the alignment and conformation of PTh chains remarkably affect their properties, as demonstrated in some previous experimental studies21-25 and first-principle calculations,25 so the emphasis should be laid on the molecule conformation at the interface as well. Hence, we adopt steered molecular dynamic (SMD) simulation to understand interfacial strength between PTh and three types of semiconductors including silicon, silicon carbide and diamond in this work. During the detaching simulation, pulling force and potential of mean force (PMF) are mainly calculated with CVFF field, accompanied with the utilization of Jarzynski equality.26 Energy decomposition analysis is additionally done in order to see which term makes dominant contribution to adhesion during the detaching process and the distinction triggered by various semiconductors. In the end, we will discuss how adhesion varies within a certain temperature range. 3



MATERIALS AND METHODS Materials PTh with Cα-Cα conjunction structure was investigated because this structure was a dominant product via electrically chemical polymerization and had good conductivity upon the maximum overlap of the C-C interring carbon pz orbitals.27-29 In our work, there were ten repeated units in our single PTh chains with terminal hydrogen atoms at both sides, whose structure parameters referred to a previous article.30 This selection of chain length was reasonable according to some previous experimental31-33 and MD simulation works.34 Silicon, silicon carbide and diamond crystals were chosen as the substrates on the account that silicon is the material most commonly used and other two materials, which have wide band gap and unique physical and chemical properties, are ideal for making high-frequency devices in the future. In this paper, silicon and diamond both existed in a diamond cubic lattice structure while zinc-blende structure was more suitable for silicon carbide. The (001) contact surface of the substrate was cleaved in Material Studio software, whose thickness was over 10 Å. Although the zincblende structure of silicon carbide is not yet commercially available, its high electron mobility, nearly 1000 cm2/V‧s, will be a major advantage among all kinds of structures of silicon carbide in future. Interatomic potentials The interatomic potential for all kinds of semiconductors in our work was described 4


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by Tersoff potential which had been successfully applied to study these materials and the parameters were taken from a previous article.35 Simultaneously, the CVFF force field36 was recognized to be more proper for the interatomic potential of PTh and the interaction between PTh and semiconductors because it can be applied to calculate a large number of organic molecules and is more accurate in terms of the structure and binding energy of the computing system after continuous enhancement. The potential function in CVFF is symbolized by the superposition of bonded interactions and nonbonded interactions. The bonded terms are composed of bond stretch, bond angle bending and dihedral angle torsion terms while the non-bonded part contains electrostatic and van der Waals terms. The CVFF potential function used in this work is shown as,

E  K b  b  b0   K θ    0   K φ 1  d cos n0  2

2



b



     ij   qi q j ij    4 ij          r   i,j  r  rij  i,j ij  ij    12

6

(1)

where b0, θ0 and φ0 are equilibrium bond length, equilibrium bond angle and dihedral angle respectively, Kb, Kθ and Kφ are the corresponding constants, b and θ are the actual bond length and bond angle. εij and σij decide the minimum and zero values of the van der Waals term which is described by 12-6 Lennard-Jones potential, and rij is the distance between two particles with the charge qi and qj. Steered molecular dynamics (SMD) simulations Classical molecular dynamics (MD) simulation is a suitable tool to study adhesion

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at the atomic level. Here, SMD, which has been widely used for the investigation on various materials,10-12,

37

is selected among various methods. Compared with other

quasi-static methods like umbrella sampling38 and thermodynamic integration,39 the superiority of this non-equilibrium one is the improvement of efficiency when ensuring accuracy, which induces relatively accurate variation of energies within the nanosecond time scale. During the SMD process, a reaction coordinate was selected to indicate the position of the target molecule during the movement for the purpose of studying the variation of free energy. The free energy profile as a function of the reaction coordinate was called ΔG (PMF). In this implementation, we used a virtual spring to limit the constant moving speed, v, of the target molecule along the reaction coordinates. The driving force FSMD applied to the target molecule is defined as,

FSMD  K spring  R  R0 

(2)

where Kspring is the spring constant and R0 is the distance from the end of spring to the tether point. The calculation of the averaged adhesion work is based on the Jarzynski equation, which uncovers the relationship between the free energy difference during the equilibrium process and the work done through the non-equilibrium process. The Jarzynski equation26 is described as,

 G   W  exp     exp     kBT   kBT 

(3)

where kB is the Boltzmann constant, T is the temperature of the system, W is the work done throughout the detaching process and the angular bracket indicates the ensemble average of the sampled quantity. Furthermore, our study benefited from the 6


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independence of speed in this equation. Then ΔG is calculated from the deformation of the previous equation given as,

 W  G   kBT log exp     kBT 

(4)

Previous papers26, 40, 41 revealed that the second-order scheme, however, yielded better results on the free energy profile than the exponential one (4) since statistical errors, which were almost excluded in low-order cumulant estimation, might dominate the systematic error when only a limited number of trajectories were actually sampled. The second-order expression26 is described as,

G  W 

W2  W

2

2kBT

(5)

Energy Decomposition In order to make a detailed analysis of the free energy change through the detaching process, the decomposition formula26 is adopted described as,

G  E  T S  EvdW  Ecoul  T S

(6)

where ΔE is the potential energy change term, which can be further decomposed into van der Waals interaction energy change ΔEvdW and electrostatic interaction energy change ΔEcoul, and ΔS is the entropy change. ΔG was calculated according to Equation (5), and the potential energy changes including van der Waals energy change and electrostatic energy change were obtained in LAMMPS. Subsequently, the entropy change could be calculated by Equation (6) with these simulation results above. Simulation Details 7



The model consisted of a substrate made of crystalline semiconductor (silicon, silicon carbide or diamond) and a single PTh chain laying on the substrate. For convenience, these three systems were shortly referred to as PSI, PSC and PSD systems respectively. The symmetrically straight PTh chain was reasonably chosen as the typical starting configuration in our simulation, as illustrated in Figure 1. Periodic boundary conditions were applied in x- and y- directions while non-periodic boundary conditions were applied in the z- direction. The box dimensions in x- and y- directions were 53.9 Å × 53.9 Å, 52.1 Å × 52.1 Å, 53.6 Å × 53.6 Å respectively in PSI, PSC and PSD systems and the length of the PTh chain was 39.8 Å. Thus, the substrate was adequately large in x- and y-direction to avoid the boundary effect on the PTh chain, and the interaction between the single PTh chain and its counterparts in the mirrors did not happen across the boundaries on the ground that the atomistic interactions were truncated at 10 Å in our simulation. MD simulations were implemented using LAMMPS package42 with a timestep of 1 fs in the following process. Partial charges of all atoms in the simulation were calculated by the charge equilibrium (QEq) method.43 In our simulation, the charge balance was performed every timestep and the charges were updated before the energy calculations. The first set of results were all done at 300 K, and the effect of temperature on all systems was studied at 250 K-500 K with the intervals of 50 K.

8


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Figure 1.

The Cα-Cα conjunction structure of PTh with ten repeated units.

Then the model was subjected to a geometry optimization using the conjugate gradient algorithm, and a dynamic equilibration run of 500 ps in NVT ensemble was carried out to relax the model conformation followed by another 500 ps in NPT ensemble, where 1 atmosphere was only applied in x- and y-direction. Subsequently, SMD method was performed in NVT ensemble with a spring constant of 1000 pN/Å and constant velocity of 10 Å/ns26, where the direction was vertical to the surface of the substrate. The spring force was applied on the terminal carbon atom in the backbone of the chain. Consequently, the distance between this carbon atom and the contact surface of the substrate was selected as the reaction coordinate. Ten SMD trajectories were sampled to minimize the system errors by using second-order cumulant expansion of Jarzynski equality.

RESULTS AND DISCUSSIONS Adhesion strength comparison In order to calculate the interfacial strength between chains and substrates at room temperature, the adsorbed single chain is stripped from different substrate surfaces. The entire detaching process is divided into several phases (Figure 2b-f). The PSI system is exemplified here due to the similar free energy curves of these three systems. In the first stage, the force value is raised continuously to a critical value (Figure 2b-c) in order to complete the initial separation. Then, as the binding area continues to decrease, 9



as shown in Figure 2c-e, the required force is demonstrated in the form of fluctuation. Especially, the regular oscillation happens in PSD system. At last, the PTh chain evolves to a free conformation which is not restricted by the substrate in the model (Figure 2e-f). There is no apparent deformation happening in the chain, indicating the integrity of the PTh chain throughout the detaching process.

Figure 2.

Top view (a) of initial PSI system and representative side snapshots (b-f)

during the whole detaching process. The work profile done in ten trajectories and free energy curves estimated by exponential averaged form (1) and the second-order cumulant expansion form of Jarzynski equation (2) are all plotted in Figure 3. The first derivative of the free energy curve, as shown in Figure 4, is considered as the force that needs to be applied to complete the detaching process, the maximum of which is the so-called adhesion force.

10


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Figure 3.

The work profile in ten trajectories (gray lines) and the free energy curves

estimated by exponential averaged form (red lines) and the second-order cumulant expansion formula of Jarzynski equation (blue lines) in (a) PSI, (b) PSC and (c) PSD systems. The embedded patterns, where purple atoms represent silicon atoms and yellow ones represent carbon atoms, demonstrate the unit cell structures of corresponding substrates in different systems. 11



It is observed that great difference of values exists in both the free energy profile and the force curve in different systems. According to the results of the second-order expansion, the adhesion energy in PSI system, totally about 46.86 kcal/mol, is the smallest, while that in PSC system presents the highest PMF value of nearly 148.07 kcal/mol among these three systems. These results reasonably agree with the simulation results of the PTh-CNT/BNNT system.34 The adhesion force ranks similarly with the numerical order of adhesion energy for the reason that a stronger interfacial binding energy requires a larger detaching force. The highest adhesion force is 346.48 pN in PSC system, much higher than those in PSI and PSD systems. Moreover, it is found that the force presents a more regular oscillation in PSD than that in other systems.

Figure 4.

The second-order free energy profile and detaching force curve in (a) PSI, 12


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(b) PSC and (c) PSD systems during the detaching process. The dotted lines with five letters b-f respectively on the top correspond to the phenomenon in Figure 2b-f. Energy decomposition comparison A deeper analysis of free energy change ΔG during the detaching process was conducted to understand the contribution of various energy terms to the total energy among these three systems according to Equation (6). Since the substrate is regarded as a hard substance and its structure remains unchanged, its vibration change and deformation can be ignored. Thus, it is assumed that the change in entropy totally comes from the PTh chain itself. The changes of all sub-energies during the detaching process are obtained respectively in these three models, as displayed in Table 1. Table 1.

Change of each sub-energy during detaching process

Energy (kcal/mol)

ΔG

ΔE

ΔEvdW

ΔEcoul

TΔS

PSI

46.86

163.36

19.11

144.25

116.50

PSC

148.07

411.10

44.11

366.99

263.03

PSD

109.22

138.29

136.64

1.65

29.07

The difference of the van der Waals energy exists in these systems. The well depth of the potential describing carbon (ε0=0.16 kcal/mol) is drastically larger than that describing silicon (ε0=0.04 kcal/mol). Consequently, the higher the proportion of carbon in the substrate is, the stronger the van der Waals interaction between the substrate and the PTh chain will be, leading to a greater contribution to the total energy change in PSD system. 13



It is also found that electrostatic interaction plays a major role in PSI and PSC system while it contributes little in PSD system. The contribution of electrostatic interaction to the adhesion is somewhat complicated from the perspective of the electronegativity χ of various elements. Carbon (χ=123.21 kcal/mol) and sulfur (χ=159.76 kcal/mol) are the main atoms in the PTh chain and the substrates in these systems only contain silicon (χ=96.11 kcal/mol) and carbon atoms. In regard to PSD system, since diamond is made up of carbon atoms, the electronegativity difference between PTh and diamond is so little that rare charge is triggered in diamond. This means the electrostatic energy at the interface can be neglected in PSD system. In PSI, however, owing to the electronegativity difference between silicon and the main atoms of PTh, the surface silicon atoms possessed weak positive charges while the chain was mainly negatively charged, which consequently brought certain electrostatic interaction to strengthen the interface. As to PSC system, the electrostatic interaction occupied a larger proportion of adhesion energy than others. On one hand, it is attributed to the interfacial charge generated by the electronegativity difference, just like the origin of electrostatic interaction in PSI system. On the other hand, the larger electrostatic interaction is triggered by the polar covalent bonds formed inside the silicon carbide according to the frontier molecular orbital theory.44 The existence of this kind of bonds means that the carbons force the shared electrons closer to them, making silicon atoms exhibit larger positive partial charges compared to that in PSI system. The polarity of the silicon carbide, thereby increasing the electrostatic energy between PTh and the substrate, is extraordinary beneficial to adhesion. Therefore, the electrostatic part 14


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allows PSC to be of great superiority among these three systems, and this enhancement can be confirmed by the experiment on other similar materials such as GaAs7 and the MD simulation of PTh-CNT/BNNT interface34 in the previous researches. The adhesion energy significantly increases due to more electrostatic interactions when CNT is replaced by BNNT, in common with the results influenced by the substitution for diamond with silicon carbide in our work. The change in entropy cannot be ignored as well. The entropy change is actually unfavorable for the combination of a single chain with other materials and this phenomenon was also introduced in a previous work.45 Table 1 implies that PSD system experienced the smallest entropy change after completing the process while that in PSC is the biggest, and the explanation of this result can be divided into two aspects, the vibrational entropy change and the conformational entropy change. For one thing, the total interaction potential ΔE hugely constrains the spontaneous vibration of the PTh chain, resulting in the big vibrational entropy change between the actual chain state and the free chain state. For another, the inhomogeneous charge distribution at the interface restrains the chain conformation to some extent. Atoms with bigger negative charges in the PTh chain are inclined to approach atoms with positive charges on the substrate surface and make the rings in the PTh chain tilted.

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Figure 5.

Top views of the conformation of the single PTh chain after relaxation in

(a) PSI, (b) PSC and (c) PSD and corresponding side views of them (d-f). To further confirm the analysis of entropy changes in these systems, different chain conformations were demonstrated in Figure 5. The radial distribution function (RDF) and radius of gyration (Rg) are used to provide qualitative information for the description of orientation and flexibility of the PTh chain. RDF (g(r)) shows the probability distribution of B atoms existing around the reference atoms A with the distance r between them, which is calculated46 as follows, g r  

nB  B 4 r 2 r 1

(7)

where ρB is the number of B atoms in the unit volume and nB is the number of B atoms around A atoms in a spherical shell of radius r with the thickness Δr. Here, A represents surface atoms and B symbolizes atoms in the single PTh chain, and Figure 6 illustrates the RDF of atoms in the PTh chain from the surface atoms after proper equilibration. In regard to the flexibility of the chain, Rg is an important measurement defined as,12

16


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Rg 

1 n 2 ri  rc  n i 1

rc 

1 n  ri n i 1

(8)

(9)

where n is the number of atoms, ri is the location of the ith atom and rc is the location of the center of mass. The Rg variation of the PTh chain with time during equilibration is illustrated in Figure 7.

Figure 6.

The RDFs of surface atoms with all kinds of atoms in (a) PSI, (b) PSC and

(c) PSD are calculated by averaging the last 5000 timesteps in equilibrium. C1 (pink lines) represents the carbon atoms directly connected to sulfur atoms while C2 (green lines) symbolizes other carbon atoms in the PTh chain.

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Figure 7.

The Rg variation of a single PTh chain with time in all three systems.

According to our results, chains are more unconstrained in PSI and PSD systems than that in PSC system since ΔE in them are much smaller than that in PSC system, which means smaller vibrational entropy changes in PSI and PSD systems. The remarkable entropy difference between PSI and PSD systems is attributed to the different conformational entropy changes in PTh chains caused by the electrostatic interactions. In PSD system, the chain appears parallel to the substrate surface as illustrated in Figure 5c because of little electrostatic interaction and five-membered rings maintain an alternating symmetrical state similar to the initial state, which means little conformational entropy change. However, due to the effect of inhomogeneous charge distribution at the interface, the five-membered rings in the chain are tilted in PSI system as shown in Figure 5a, leading to the obvious non-spontaneous structural orientation. The different peak positions of various atoms in Figure 6a implies that different atoms tend to have various distances from the substrate surface, which confirms the oblique state of the rings of the PTh chain in PSI system, and this nonspontaneous orientation reasonably brings about the greater conformational entropy 18


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change in PSI system than that in PSD system. As for PSC, the rings are flipped by the electrostatic interaction as demonstrated in Figure 5b and Figure 6b, similar to the analysis of PSI system, and this kind of orientation gives rise to a certain conformational entropy change. Furthermore, the large ΔE in PSC system strongly restricts the mobility and vibration of the chain, which makes the chain straighter than that in PSI and brings about the biggest vibrational entropy change. As to the flexibility of the chain, it is found that Rg of the PTh chain in PSI system is much smaller than those in PSC and PSD systems after equilibration, as shown in Figure 7. These results indicate that the PTh chain on silicon is much more flexible than those in PSC and PSD systems, which is consistent with the conformation results illustrated in Figure 5. This coil-like bending of the PTh chain in PSI system also results in more conformational entropy. In order to verity our entropy analysis, we took 100 samples every timestep in the last 0.1 ps of both the equilibrium process and the detaching process respectively, according to Schlitter formula,47 to calculate the conformational entropy of the PTh chain before and after detachment, then the vibrational entropy change can be calculated by subtracting the conformational entropy change from the whole entropy change. These calculations confirm our analysis in entropy change (Table S1, SI). Hence, the whole entropy change in PSC system presents to be the biggest among these three systems.

The effect of temperature Normally, the temperature of electronic devices goes up a lot during operation, so the reliability of adhesion at different temperatures was necessarily studied. The 19



temperature ranging from 250 K to 500 K is in consideration because a previous literature confirms that PTh still works effectively under the temperature up to nearly 500 K. Ten SMD trajectories were also sampled under each chosen temperature point. The changes of adhesion as a function of temperature in different systems, compared in Figure 8, suggest that the adhesion of the three systems all monotonically decrease in the testing range when the temperature increase. This result can be explained that the entropic effects endow the PTh chain with more mobility at a higher temperature and the enthalpic effects become less dominant, thereby weakening the stability of the interface and reducing the adhesion energy. This minute reduction means adhesions in these three systems are barely influenced by temperature.

Figure 8.

Adhesion energy with PTh as a function of temperature for silicon (black),

silicon carbide (red) and diamond (blue).

CONCLUSION SMD method was used to have a detailed insight into adhesion between PTh chains and three important semiconductor materials. Van der Waals energy and electrostatic 20


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energy both played a positive role in adhesion while the increase in entropy change conversely weakened the adhesion throughout the energy decomposition. Our results demonstrated that electrostatic energy contributed the most in adhesion between PTh and silicon carbide while van der Waals energy dominated the adhesion in the system composed of PTh and diamond. The entropy change can be divided into the vibrational entropy change and the conformational entropy change. The vibrational entropy was determined by the constraint originating from the total interaction potential and the nonspontaneous bending ascending from the inhomogeneous charge distribution strongly affected the conformational entropy change. Combining the factors mentioned above, it was found that interfacial adhesion energy and force between the single PTh chain and silicon carbide were the highest under the same condition. Additionally, the adhesion energy slightly attenuated with increasing temperature because of thermal motion of the molecule, which means the little influence of temperature on such adhesions. This study indicates that the PTh material, as a conductive binder, has an excellent application prospect to satisfy certain adhesion conditions in the semiconductor industry and we can optimize the semiconductor choice when using the polythiophene adhesive according to our results.

ASSOCIATED CONTENT Supporting Information. The following files are available free of charge. Additional calculation results (the influence of starting configuration, RMSD during equilibration, entropy change calculation) (PDF) 21



AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] (K. Bi), [email protected] (Y. Chen) Notes The authors declare no competing financial interest. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

ACKNOWLEDGMENTS The authors are grateful for financial support from National Natural Science Foundation of China (51575109, 51728501) and Natural Science Foundation of Jiangsu Province (BK20160072). We thank Mengtao Gu from School of Energy and Environment for the support of Material Studio Visualizer.

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New Insight on the Interface between Polythiophene and

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