Polymer morphology and interfacial charge transfer dominate over energy-dependent scattering in organic-inorganic thermoelectrics

Hybrid (organic-inorganic) materials have emerged as a promising class of thermoelectric materials, achieving power factors (S2σ) exceeding those of either constituent. The mechanism of this enhancement is still under debate, and pinpointing the underlying physics has proven difficult. In this work, we combine transport measurements with theoretical simulations and first principles calculations on a prototypical PEDOT:PSS-Te(Cux) nanowire hybrid material system to understand the effect of templating and charge redistribution on the thermoelectric performance. Further, we apply the recently developed Kang-Snyder charge transport model to show that scattering of holes in the hybrid system, defined by the energy-dependent scattering parameter, remains the same as in the host polymer matrix; performance is instead dictated by polymer morphology manifested in an energy-independent transport coefficient. We build upon this language to explain thermoelectric behavior in a variety of PEDOT and P3HT based hybrids acting as a guide for future work in multiphase materials.

language to explain thermoelectric behavior in a variety of PEDOT and P3HT based hybrids acting as a guide for future work in multiphase materials.

Introduction
New, emerging classes of organic semiconductors, polymers, and organic-inorganic composite materials have penetrated into areas of optoelectronics previously dominated by inorganic materials. Organic light emitting diodes have reached wide commercial availability, and organicinorganic hybrid photovoltaics have shown an unparalleled rate of efficiency improvement. 1,2 Such solution-processable materials avoid the need for energy-intensive fabrication steps and instead utilize inexpensive, scalable, roll-to-roll techniques. 3 In particular, progress in this area has been driven by the development of materials based on poly (3,4-ethylenedioxythiophene), (PEDOT). 4,5 PEDOT-based materials have demonstrated remarkably high conductivities, outperforming all other conductive polymer classes and driving tremendous interest in the use of soft materials in flexible electronics and thermoelectrics. [6][7][8] Soft thermoelectric materials can realize flexible energy generation or heating-cooling devices with conformal geometries, enabling a new portfolio of applications for thermoelectric technologies. 3 Of particular interest are hybrid soft nanomaterialsan emerging material class that combines organic and inorganic components to yield fundamentally new properties. [9][10][11][12] In hybrid systems, recent studies have focused on the use of strategies such as interfacial transport, structural/morphological effects, and modifications to the energy dependence of carrier scattering to improve electronic and thermoelectric performance. [13][14][15] However, it has proven difficult to establish the fundamental physics driving these performance enhancements. The most challenging of the proposed design strategies to evaluate is the role of energy dependent scattering, a phenomenon frequently and contentiously implicated in high performing thermoelectric materials. 16,17 More generally, advanced design of high performing soft thermoelectric materials has been stymied by the fact that transport in these systems is complex and resists description by a unified transport model. Development of next generation soft hybrid materials and modules requires improved understanding of the carrier transport physics in complex multiphase systems. Kang and Snyder recently proposed a generalized charge transport model (henceforth referred to as Kang-Snyder Model) for conducting polymers, which marks a significant advance in the theoretical tools available to the soft thermoelectrics field. 18,19 In this model, the thermoelectric transport of conducting polymers has been modeled using energy independent parameter, E0 and energy dependent parameter 's' over a large range of conductivity. In addition, vital to the theory developed is the energy-dependent scattering parameter s, which distinguishes the majority of conducting polymers (s = 3) from the class of PEDOT-based materials (s = 1). However, these two parameters are difficult to uniquely measure. Additionally, this first report did not cover hybrid organic-inorganic materials, which creates an important gap in the relevant material classes that requires further investigation.
Here, we apply this Kang-Snyder framework to a set of hybrid thermoelectric materials to identify the physics responsible for favorable thermoelectric transport in these systems. We begin with a model system of tellurium nanowires coated with PEDOT:PSS. This system was chosen due to its high thermoelectric performance (ZT ~ 0.1 at room temperature), facile solution-based synthesis, and well-defined single crystalline inorganic phase. 10,11,13 Further, we have previously shown that this material can be easily converted to tellurium-alloy heterowires. 10 For example, using copper as the alloying material results in PEDOT:PSS-Te-Cu1.75Te heteronanowires. It has been observed that formation of small amounts of alloy subphases yields improvement in the thermoelectric performance of these materials. However, whether the observed transport properties are dictated by the organic phase, inorganic phase, or interfacial properties is an open question. Here, we use a full suite of experiments, transport modeling, molecular dynamics, and first principles calculations to describe the exact nature of the organic-inorganic interactions. We also show that the Kang-Snyder framework can be applied effectively to hybrid systems, extending the theoretical tools available to experimentalists. In this way, we seek to fill an important gap in knowledge in this body of literature and inform the direction of future experimental work.

Synthesis and Structure.
Synthesis of tellurium nanowires coated in PEDOT:PSS (PEDOT:PSS-Te NWs) and conversion to Te-Cu1.75Te heterostructures (PEDOT:PSS-Te(Cux) NWs) were performed as previously reported (Details in Methods). 10,11 The synthesis of the tellurium nanowires is performed in the presence of PEDOT:PSS, which has been posited to act both as a stabilizing ligand and as a structure-directing agent (Figure 1a). 11,13 Te-Cu1.75Te heterowires have a curved appearance as a result of alloy domains appearing at 'kinked' portions of the wires. Representative high-

Morphology and Interactions.
To probe the organic-inorganic interactions involved in carrier transport in this material system, we perform extensive Molecular Dynamics (MD) simulations and Density Functional Theory (DFT) calculations. Specifically, MD simulations uncover detailed information about adhesion and polymer morphology/structural changes in the vicinity of the Te nanowire and Cu1.75Te heteronanowire surfaces. These analyses strongly suggest that structural templating effects occur during synthesis. Templating effects have been widely hypothesized to occur in such processes, but direct evidence has been lacking so far. 13 As a complement to our structural analyses, DFT is used to investigate the electronic effects that arise at the organic-inorganic interface. In particular, we estimate the amount of charge transfer between the organic and inorganic phases and probe the evolution of the electronic Density of States (DOS).

Molecular dynamics (MD) simulations of the organic-inorganic interface.
The MD simulations (details in Methods and Supplementary Note 1) reveal self-alignment of PEDOT chains at the organic-inorganic interface for both Te and Cu1.75Te NW surfaces. This selfalignment is only observed for the PEDOT chains in the vicinity of Te and the Cu1.75Te surfaces, while the PSS remains unaligned. This phenomenon is clearly distinguished by comparing the structures and concentration profiles before and after simulated annealing (Figure 1e Simulated annealing (details in Methods) reveal that PEDOT chains tend to align in a planar configuration on both Te and Cu1.75Te surfaces, although self-assembly is observed on the Te surface and not the Cu1.75Te (Supplementary Figure 5). We attribute this phenomenon to stronger interaction between PEDOT and the Cu1.75Te surface, resulting in reduced movement of the PEDOT chains on the Cu1.75Te surface (Supplementary Movies 6-7).

Density functional theory (DFT) calculations to probe nature of interactions at the interface.
To complement our understanding of polymer templating on the inorganic NW surfaces, DFT was used to calculate adsorption energies of PEDOT/PSS on these surfaces. Here, we consider a charged polaronic PEDOT hexamer (EDOT6) +2 and deprotonated PSS oligomer (SS6) -2 in a planar configuration close to the inorganic surface, as is predicted from MD simulations. At the Te NWorganic interface, adsorption energies of -0.42 eV and -0.31 eV per monomer were obtained for charged PEDOT and PSS, respectively, consistent with MD results that the Te surface is primarily occupied by adsorbed, aligned PEDOT. On the other hand, the PEDOT-Cu1.75Te adsorption energy is -0.56 eV, indicating an even stronger interaction.
Since MD and DFT both demonstrate the importance of the PEDOT-inorganic interaction at the interface in this system, further calculations were performed to determine the density of states and charge density difference at this interface. Figure 2a depicts the calculated charge density difference between (EDOT6) +2 and the Te surface, where a decrease in the electron density is represented in blue and electron density enrichment in red. Furthermore, using these charge density differences, charge transfer rates were extracted, yielding important insight into the electronic effects occurring at the organic-inorganic interface.
The maximum charge transfer rates from the inorganic surface to the first layer of (neutral) PEDOT chains on the surface were determined to be -0.078 and -0.144 for Te and Cu1.75Te, respectively. Charge transfer rates are higher for the charged (EDOT6) +2 bipolaron, calculated to be -0.186 and -0.239 for Te and Cu1.75Te, respectively (Table S1). Note that a negative quantity here represents electron transfer from the inorganic surface to the organic PEDOT chains (i.e. hole transfer from the organic PEDOT chain to the inorganic surface). In every case, this charge transfer provides a de-doping effect of holes in the p-type PEDOT chains, which plays a key role in understanding the thermoelectric trends in these hybrid systems (Table 1). This de-doping effect is stronger for the doped PEDOT bipolaron compared to pristine PEDOT chains and also stronger for PEDOT on the Cu1.75Te surface compared to PEDOT on the Te surface. The charge transfer and de-doping effect is only observed for the first two layer of PEDOT chains and vanished for higher distances. As for the nature of the bonding between the organic and inorganic components, the weak charge density difference and atomic distances between organic and inorganic constituents,  Combined with the MD results, the DFT calculations strongly suggest that the interaction between the PEDOT and Te/Cu1.75Te surface is a templating effect; charge transfer does occur at this interface, but no chemical bonding takes place between the organic and inorganic phases.
Hence, we expect that thermoelectric behavior in p-type PEDOT-Te hybrids is dominated by transport through the organic PEDOT matrix. This conclusion runs contrary to previous reports that have instead emphasized the role of the inorganic phase or change in the energy-dependent carrier scattering at interfaces as key drivers of the thermoelectric properties of hybrid materials. 14,15,26 Additionally, our results depict that the organic-inorganic interface in such hybrid systems is rich in aligned and extended PEDOT chains in addition to intra-chain charge redistribution. We conclude that alignment of PEDOT molecules at the organic-inorganic interface and charge transfer at the interface both play key roles in the high thermoelectric performance observed in the PEDOT:PSS-Te hybrid system, building upon earlier hypotheses proposing increased electrical conductivity at the interface. 11 Seebeck and electrical conductivity analysis

Thermoelectric properties and modelling using Kang-Snyder model.
Armed with structural and morphological insight, we now correlate our measurements of thermoelectric transport with the observed and simulated structures. Figure 3a depicts the electrical conductivity and Seebeck coefficient of the PEDOT:PSS-CuTe hybrid system as a function of copper loading. In the absence of a robust transport model for hybrid systems, researchers have previously had to rely on mean field theories. One commonly used model for multicomponent hybrids/composites is effective medium theory, which predicts that the Seebeck coefficient of the composite must lie between that of the individual materials (∼190 μV/K for PEDOT:PSS-Te and ∼10 μV/K for PEDOT:PSS-Cu1.75Te at room temperature). 25 Effective medium theory, therefore, fails to capture the observed enhancement of the Seebeck coefficient at low (~5%) Cu loading.
This deviation had originally been speculated to be due to a change in the energy-dependence of carrier scattering upon introduction of Cu. Also, while the Cu loading in the composite is being varied, the overall inorganic content (Te and Cu) is controlled (typically 60-80%). 10,13 The recently published Kang-Snyder model provides an opportunity to clarify this conundrum. Kang and Snyder showed that this framework handles pure polymeric systems well (including PEDOT); this makes the PEDOT:PSS-CuTe system a suitable candidate, since the PEDOT domains are known to be pivotal for charge transport in these hybrid materials. Further, PEDOT:PSS-CuTe is an excellent test case, since the effects of energy dependent scattering, (de-)doping, and morphology intermingle in a complex fashion. Given that the model independently treats the energy-dependent scattering (through the parameter s), doping (through the reduced chemical potential η), and energy-independent transport parameter 0 ( ), such an analysis can provide insight that is both critical and previously inaccessible. According to this model, energy dependent conductivity, ( , ) can be written as: such that the total conductivity is given by: Using from Eq. 1 and integration by parts, the total conductivity can be written as: where F is Fermi integral and  = − is reduced chemical potential and Et is the transport energy, below which there is no contribution to the conductivity even at finite temperature.. The corresponding Seebeck coefficient can be written as: The  value was determined by using experimental Seebeck coefficient in Eq. 3 for a particular value of s. When applying the model for pure polymers, Kang and Snyder observed that traditional semiconducting polymers (e.g. polyacetalyene) follow s = 3 dependence, whereas PEDOT-based systems exhibit s = 1 dependence. In hybrid systems, it can therefore be presumed that, if transport in the polymer phase dominates the overall material properties, the energy dependence of transport (i.e. s) will remain the same as for the pure polymer matrix. If, on the other hand, transport in the hybrid material is modified by a change in the energy dependence of carrier scattering, it would be expected that s would also change. Therefore, to validate the hypothesis that the Seebeck enhancement observed in the PEDOT:PSS-Te(Cux) system is due to altered energy dependence of scattering, it is necessary that a change in the parameter s is observed upon introduction of Cu.
For this goal, the Seebeck coefficient of the PEDOT:PSS-Te(Cux) hybrid system is plotted as a function of the conductivity (Figure 3b) and fit to the Kang-Snyder Charge Transport model. 18 We observe that the experimental data lie on the s= 1 CT model curve ( Figure 3b) with 0 ( ) = 5.47 / . Thus, the s dependence is unchanged between the pure PEDOT:PSS and its hybrid.
Note, however, that while the Kang-Snyder model captures large trends in the S vs sigma curve, small changes such as electron filtering cannot be isolated. Hence, in order to understand the nonmonotonic trend in the Seebeck and conductivity, we study in detail the effect of (de-)doping and templating on the hybrid system (Table 2). Combining our experimental and theoretical results, we conclude that the complex thermoelectric trends of these hybrid films are dictated by the interaction of several effects. First, as suggested by extensive MD simulations, upon the formation of PEDOT:PSS-Te NWs, there is a templating effect for PEDOT moities on the inorganic surface.
This phenomenon results in an increase of hole mobility in the interfacial polymer, increasing the electrical conductivity of the PEDOT:PSS-Te composite relative to the pristine polymer. This templating effect is weakened by the addition of Cu, which disrupts the inorganic surfaces and produces "kinked" inorganic morphologies. Secondly, detailed DFT calculations are indicative of charge transfer between the organic and inorganic phases, resulting in a de-doping effect of the ptype PEDOT chains (Table 1 and Supplementary Table 1). In the low Cu loading regime, this dedoping effect is relatively strong, and contributes directly to the increased Seebeck coefficient and moderately decreased electronic conductivity observed here. This is contrary to previous hypotheses that a change in the energy dependence of carrier scattering is solely responsible for the non-monotonic thermoelectric trends observed in this range.
Upon further addition of Cu, a third effect emerges; Cu loading above 10% is associated with an increase in with only a nominal change in the E 0 value (Table 3). This trend indicates that the addition of Cu introduces carriers into the film and modifies the transport through a doping channel. Previous reports on this material system have suggested that positively charged Cu ions, in addition to reacting with the inorganic phase, also remain in the PEDOT phase as ionic species.
These remaining Cu ions likely interact with the PEDOT chains to increase the carrier concentration in the organic phase. This effect dominates at high Cu loading, which is associated with a strong increase in the reduced chemical potential. Note that s=2 and s=3 do not fit the experimental data for any value of the transport coefficient, 0 ( ) (Figure 3b is plotted on loglog scale). While, for a fixed 0 , is modulated by charge redistribution between the organic and inorganic phases and doping from Cu ions, only a change in morphology (templating, or kinked surfaces) can change 0 .

Validation of Kang-Snyder model for other PEDOT and P3HT based hybrid films.
In order to determine if this is generally true for PEDOT:PSS based films, we applied the Kang-Snyder model to different systems (Figure 4a). Half-closed circles (olive) symbols show Seebeck and conductivity data on PEDOT:PSS films that are doped using an electrochemical transistor configuration. 27 Here, PEDOT:PSS is tuned by changing its oxidation state (de-doping) to obtain the optimal power factor, with presumably no change to the PEDOT morphology.
Electrochemically doped PEDOS-C6 (a derivative of PEDOT) also exhibits Seebeck and conductivity data (purple close triangles) that lie on the s=1 curve with same 0 ( ) value. 28 Open square (pink) symbols represent the Seebeck coefficient as a function of conductivity for PEDOT:Tosylate (Tos) system, 4 where the insulating PSS polyanions are replaced by the small anion Tos, which improves inter-chain π-π interaction of PEDOT chains. The PEDOT:Tos Seebeck and conductivity data also lie on the s= 1 curve, albeit with a larger value of 0 ( ). This is expected due to better alignment of PEDOT chains evidenced by Grazing Incidence Wide-Angle X-ray Scattering (GIWAXS) where the PEDOT:Tos contains well-ordered crystallite grains surrounded by some amorphous PEDOT:PSS regions. This is distinctly improved from the electrochemically doped PEDOT samples described above. 0 ( ) value is further improved in the PEDOT:Tos-Pyridine+triblock copolymer system by controlling the oxidation rate as well as crystallization of oxidized PEDOT which further reduces film defects. 29  Figure 7). The associated Seebeck increase is due to a de-doping effect, as η is observed to decrease slightly when Cu loading is increased from 0 to 10%. With further loading of Cu, the Seebeck decreases and the conductivity increases (further details about the de-doping and doping can be found in Supplementary Note 4).
In this regime, there is presumably little change in the PEDOT morphology at the organicinorganic interface, and the increased conductivity and reduced Seebeck are a result of a doping effect associated with additional copper loading. Hence, both 10% and 50% Cu loading samples lie on the s=1 curve with same 0 ( ) values (Figure 4a). Coupled with other PEDOT-based hybrids (Figure 4a), we can conclude generally that the energy-dependence of carrier scattering is independent of the type of doping, or indeed the inorganic constituent, contrary to many reports in the literature. This result provides key evidence that carrier transport in hybrid films occurs predominantly through PEDOT itself (to corroborate this, we also performed experiments on Te NWs in an insulating polymer matrix: details can be found in Supplementary Figure 17). Counterions and inorganic constituents impact transport mainly via the transport parameter, 0 ( ),which can be attributed to morphological/templating effects in the PEDOT phase. The increase in 0 ( ) in hybrid materials can be qualitatively understood as enhancing the effective mobility of the itinerant carriers within the PEDOT polymer matrix. It is interesting, albeit counter-intuitive, that this can occur as a result of introducing numerous new potential scattering interfaces in the material via addition of inorganic components or secondary phases. However, that introduction of inorganic species can provide templating effects in polymers which lead to structural or behavioural modifications is well-known.
To gain deeper insight into the transport coefficient, 0 ( ), we performed temperature dependent Seebeck and conductivity measurements on these hybrid films. The reduced chemical potential with respect to room temperature value, does not change significantly with lowering temperature as shown in Figure 4b (24%, 35% and 40% for 0, 10 and 50 % Cu loading respectively from room temperature value). The temperature dependence of 0 ( ) can be written based hybrids. The value of power factor is hypothesized to be lower in P3HT based systems because of a low value of σE 0 due to side alkyl side-chains; although alkyl chains help to make these solution processable, it degrades the alignment and orientation of the P3HT polymer chains 40,41 . Hypothetically, if a P3HT-based hybrid film with σE 0 approaching 10 S/cm is manufactured, the power factor would be as high as 10 mW/mK 2 . Therefore, it is clear that, so far, the key to high thermoelectric performance in these complex hybrid systems has been the advantage gained by physical interfacial interactions and exploiting polymeric templating effects capable of enhancing carrier transport in the organic phase, rather than modifying the energy dependence of scattering. in the organic phase that enhance mobility of charge carries. These are three well-defined routes that can be impactful in the near future.

Synthesis and Characterization. Synthesis of PEDOT:PSS-Te NWs and PEDOT:PSS-Te(Cux)
NWs closely followed previous methods. 10,11 All steps in the procedure are carried out in aqueous solution in the presence of air, with high reproducibility over many separate experiments. As shown in our previous report, during conversion to PEDOT:PSS-Te(Cux) NWs, mobile copper ions penetrate the PEDOT:PSS surface layer to react with the Te core and form isolated alloy domains of Cu1.75Te. 10 During this process, the nanowires undergo a transition from rigid rods ( Figure 1a) to curved wires, with alloy domains appearing at 'kinked' portions of the wires ( Figure   1b). The resulting nanostructures are Te-Cu1.75Te heterowires. The extent of copper loading in each sample was directly measured using Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES). After synthesis, x-ray diffraction (XRD), scanning electron microscopy (SEM), and x-ray photoelectron spectroscopy (XPS) were used to confirm the material structure and properties. Representative data can be found in the Supplementary Information   (Supplementary Figures 10-11) and are consistent with our previous report on these materials. 10 43 Ten annealing cycles between 300 K and 1300 K were carried out for equilibrium followed by 5000 steps smart minimization. The total annealing time is at least 5 ns with 0.5 fs time step and Nosé-Hoover Thermostat method is adopted for temperature control. Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS) 44 is used to evaluate the atomic forces. 45,46 A summation method of non- surfaces respectively (Supplementary Figures 2-3). Each simulation was repeated at least three times with simulated annealing protocol for different amorphous polymers to investigate structural changes.
Six EDOT12 and three SS24 oligomers were used to calculate interaction energies with the Te and Cu1.75Te NW surfaces (Supplementary Figure 4). Similarly, six EDOT12 oligomers distributed randomly onto the NW surface was used to study directional preference and self-assembly of chains on surfaces (Supplementary Figure 5). Data availability statement: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.