Patent Grant
10598614
The present invention relates to single-walled carbon nanotubes (SWCNTs), which may be used for thermoelectric (TE) power generation. The development of inexpensive and efficient TE materials offers the prospect of converting waste heat into pollution-free electricity in standalone power generation systems, cogeneration architectures (e.g., coupled to a photovoltaic module), and/or cooling systems (e.g., microprocessor cooling). It is desirable for efficient TE materials to be good at conducting electricity but not heat, so that a thermal gradient may be maintained to produce the TE effect. However, this is challenging for most material systems, because the electrical and thermal conductivities are typically related to each other via the charge carrier density, such that the thermal conductivity increases as the electrical conductivity increases. Decoupling the electrical and thermal conductivities has been achieved in some inorganic semiconductors (ISCs), such as bismuth telluride (Bi2Te3), although further improvements in these materials are likely to require the development of complex and/or nanoscale structures. Complex fabrication strategies, combined with material cost, scarcity, toxicity, and disposal, may significantly limit the potential for large-scale deployment of TE devices based on such materials.
The size-tunable physical properties of solution-phase processable nanomaterials may enable diverse strategies for energy harvesting/storage and inexpensive, bottom-up approaches for fabricating devices with unique form and function (e.g., flexible, lightweight, and/or wearable). Nanostructuring of bulk ISCs has shown particular promise for improving TE energy conversion devices, which convert thermal energy from waste and natural heat sources into electricity, due to the beneficial formation of nanoscale interfaces. However, the best-performing ISCs are incompatible with applications that require the TE generator to adopt irregular, or even flexible, form factors.
In contrast, nanostructured organic semiconductors (OSCs), including SWCNTs, offer a number of intriguing technological characteristics for TE applications, such as earth-abundant raw materials, low-cost deposition, and flexible form factors. Despite their promising electronic properties, SWCNTs have received little attention in the context of TE energy conversion, although several studies have focused on the use of SWCNTs as inclusions in composite materials based on conducting polymers. Two recent studies demonstrated higher thermopowers for films enriched in semiconducting (s-SWCNT) species than those containing significant fractions of metallic (m-SWCNT) species. Beyond these results, little has been known about the detailed dependence of the TE power factor and the thermal conductivity on the SWCNT diameter, electronic structure, and carrier density. Although large thermal conductivities (κ>1,000 W m−1 K−1) have been observed for individual SWCNTs, much lower values (κ<35 W m−1 K−1) have been obtained for mats of nanotube ropes or bundles.
Exemplary embodiments of the invention provide methods for determining desired doping conditions for a semiconducting single-walled carbon nanotube (s-SWCNT). One exemplary method includes doping each of a plurality of s-SWCNT networks under a respective set of doping conditions; determining a TE power factor as a function of a fractional bleach of an absorption spectrum for the plurality of s-SWCNT networks doped under the respective sets of doping conditions; and using the function to identify one of the TE power factors within a range of the fractional bleach of the absorption spectrum, wherein the identified TE power factor corresponds to the desired doping conditions.
The doping may include immersing the s-SWCNT network in a solution comprising a charge-transfer dopant until a charge carrier doping level of the s-SWCNT network is saturated; and subsequently reducing the charge carrier doping level of the s-SWCNT network. The charge-transfer dopant may include triethyloxonium hexachloroantimonate (OA).
Alternatively, the doping may include sequentially immersing the s-SWCNT network in solutions comprising increasing concentrations of the charge-transfer dopant. The charge-transfer dopant may include OA.
The method may include controlling a band gap of the s-SWCNT network by adjusting a diameter of carbon nanotubes of the s-SWCNT network. The band gap may be controlled to have a value between approximately 1.0 eV and approximately 1.2 eV.
The method may also include removing at least a portion of a polymer wrapped around carbon nanotubes of the s-SWCNT network. Further, the method may also include, before determining the desired doping conditions, selectively extracting s-SWCNTs from polydisperse SWCNT soot using polyfluorene-based polymers; and performing ultrasonic spray deposition of the s-SWCNTs to form the s-SWCNT networks.
The method may also include doping an s-SWCNT network under the desired doping conditions. The identified TE power factor may be a maximum TE power factor within the range of the fractional bleach of the absorption spectrum. The identified TE power factor may be at least 340 μW m−1 K−2.
According to another aspect of the invention, a composition is provided. The composition includes a doped s-SWCNT network, wherein the s-SWCNT network has a TE power factor of at least 340 μW m−1 K−2. The s-SWCNT network may have a band gap between approximately 1.0 eV and approximately 1.2 eV. The s-SWCNT network may be doped with OA.
Other objects, advantages, and novel features of the present invention will become apparent from the following detailed description of the invention when considered in conjunction with the accompanying figures.
Exemplary embodiments of the invention provide s-SWCNT networks with a carefully controlled chirality distribution (or bandgap) and carrier density that are capable of achieving large TE power factors, higher than 340 μW m−1 K−2, comparable to the best-performing conducting polymers and larger than previously observed for carbon nanotube films. Controlling the carrier doping according to exemplary embodiments of the invention significantly reduces the thermal conductivity κ relative to undoped s-SWCNT networks. Removing a polymer wrapped around the carbon nanotubes improves the TE properties of the s-SWCNT networks.
The TE performance of a material is represented by the dimensionless figure-of-merit zT=(α2σ)T/κ, where α is the thermopower (Seebeck coefficient), σ is the electrical conductivity, α2σ is the TE power factor, κ is the thermal conductivity, and T is the absolute temperature. The thermopower α is the electromotive force ΔV generated across a material when it is subjected to the temperature difference ΔT, and is given by α=ΔV/ΔT. The TE power factor α2σ may be controlled when optimizing the figure-of-merit zT of a material system. To achieve a high figure-of-merit zT, the TE power factor α2σ may be maximized while maintaining a low thermal conductivity κ.
As discussed in further detail below, according to exemplary embodiments of the present invention, s-SWCNTs are enriched with any suitable material, such as conjugated polymers or copolymers based on various chemical moieties (for example, fluorene, thiophene, carbazole, etc), DNA, or surfactants, and are extracted from raw SWCNT soot, which may be a raw nanotube material. The s-SWCNTs are composed of carbon atoms, but may include substitutionally-doped elements, such as nitrogen or boron atoms, in place of some carbon atoms. Uniform thin films of s-SWCNTs are then formed by any suitable method, such as ultrasonic spraying. Next the s-SWCNT films are doped using a thermally stable p-type or n-type dopant. Any suitable charge-transfer dopant, such as Lewis acids or bases (such as 2,3,5,6-Tetrafluoro-tetracyanoquinodimethane (F4-TCNQ), triethyloxonium hexachloroantimonate (OA), hydrazine, and/or ethylenediamine), and/or Brönsted-Lowry acids or bases (such as nitric acid, sulphuric acid, and/or trifluoroacetic acid), may be used. Lewis or Brönsted acids will generate p-type s-SWCNT networks (where holes are majority carriers), and Lewis or Brönsted bases will generate n-type s-SWCNT networks (where electrons are majority carriers). The doping level is tuned via the amount of adsorbed dopant. By tuning the doping level, the TE power factor α2σ may be optimized.
Exemplary embodiments of the present invention provide thin films of a potentially inexpensive organic material that can efficiently convert waste heat to electricity. As discussed above, exemplary methods use enriched s-SWCNTs and tune their TE properties by using controllable amounts of dopant molecules to tune the Fermi energy of the s-SWCNTs that constitute the film. The s-SWCNTs may also have tunable colors, which may be used in TE fabrics, because they are nanomaterials with diameter-tunable bandgaps. The polymer, the diameter distribution, the electronic structure of particular s-SWCNTs, and/or the overall composition of the network may be adjusted to define the TE properties of the film. For example, if specific polymers provide large TE power factors α2σ, these polymers may be engineered into the composite to achieve higher TE power factors α2σ by providing an increase in the thermopower α at high electrical conductivity σ. Similarly, if specific s-SWCNT densities of states provide large TE power factors α2σ, these s-SWCNT densities may be engineered into the composite to achieve higher TE power factors α2σ by providing an increase in the thermopower α at high electrical conductivity σ.
In addition, highly pure single-chirality s-SWCNTs may be incorporated into otherwise polydisperse s-SWCNT composites. This may provide advantageously high thermopowers α at very high electrical conductivities. Further, films may be fabricated with tailored isotopic (or atomic) compositions to rationally incorporate phonon scattering centers. This may provide advantageously low thermal conductivities while maintaining the high thermopowers α and high electrical conductivities.
Exemplary embodiments of the present invention may maintain a very high thermopower α in an SWCNT while simultaneously realizing high electrical conductivity σ. These two properties define the TE power factor α2σ within the TE figure-of-merit zT, and are very hard to optimize simultaneously because they typically vary inversely with respect to each other. At low carrier densities, the thermopower α is typically high, while the electrical conductivity σ is low. As the carrier density rises, the thermopower α falls and the electrical conductivity σ rises. Exemplary embodiments of the present invention may utilize s-SWCNTs surrounded by a fluorene-based polymer or co-polymer host as a material that can be optimized by tuning the Fermi energy. This type of tunability may not be possible in films containing both s-SWCNTs and m-SWCNTs, because m-SWCNTs have a finite density of states (DOS) at all energies, resulting in a low intrinsic thermopower α, and are very hard to tune via molecular doping. Further, exemplary embodiments of the present invention utilize the extreme sensitivity of fluorene-based polymers or co-polymers for extracting high yields of s-SWCNTs. These polymers enable highly selective dispersion of particular distributions of SWCNTs, and these distributions can be sensitively tuned by choosing the appropriate polymer and SWCNT synthesis conditions, as discussed in further detail below.
Exemplary embodiments of the invention provide methods for fabricating and doping TE materials based on enriched s-SWCNTs. Experimental data has verified theoretical predictions that suggest that the thermopower α for s-SWCNTs can greatly exceed those experimentally obtained in related art studies (500 μV K−) at low doping densities. By controlling the doping conditions, thermopower α values can be maintained well over 100 μV K−1 even at very high carrier densities and electrical conductivity σ values, providing an optimum TE power factor α2σ of approximately 340 μW m−1 K−2 for s-SWCNTs with an electronic band gap of approximately 1.0 eV to 1.2 eV. The doping method according to exemplary embodiments of the invention significantly hinders the vibron/phonon contribution that dominates the thermal conductivity κ in undoped carbon nanotube networks.
First-principles density functional theory (DFT) calculations of the DOS and thermopower for representative m- and s-SWCNTs have been performed. In the diffusive transport regime, the thermopower can be expressed with the Mott formula:
The energy-dependent electrical conductivity is given by σ(E)=e2Ne(E)D(E), a product of the DOS and diffusion constant, which both depend on energy. In the low-temperature approximation, the thermpower value can be expressed as a log term:
and the thermopower approximately equates to the addition of a ballistic term and a diffusive term, α≈αball+αdiff. Thus the total thermopower can be written as:
where the first term describes the ballistic contribution, due to the shape of the DOS, and the second term describes the diffusive contribution. In this example, only the ballistic contribution to the thermopower was calculated. Initial work suggests that the diffusive term is a simple constant with the same sign as the ballistic term, meaning that the total achievable thermopower may be slightly larger than is estimated here.
In the low-temperature approximation, the thermopower value can be expressed as a log term:
where E is the energy, Ef is the energy of the Fermi level, the first term inside the square brackets is the ballistic (or intrinsic) contribution to the thermopower due to the shape of the DOS N(E), the second term is the diffusive (or extrinsic) contribution, due to the energy-dependence of the diffusion coefficient D(E), kB is the Boltzmann constant, T is the absolute temperature, and e is elementary charge. In this example, only the ballistic contribution to the thermopower was calculated based on Equation (4), but the contribution from the diffusive component could also be determined as discussed above.
In this example, Projected-Augmented Wave (PAW) and Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional were employed as implemented in Vienna Ab Initio Simulation Package (VASP). A plane wave basis set with a kinetic energy cutoff of 400 eV was used, and all atomic positions were relaxed until forces are less than 0.025 eV/Å. For the calculations of the electronic DOS, the (500×1×1), (40×1×1) and (20×1×1) Γ-centered k-points samplings were used for (9,9), (7,5) and (10,8) SWCNT, respectively, and a Gaussian broadening of 0.02 eV was applied.
As discussed above, the primary representative semiconducting species studied by DFT were the (7,5) and (10,8) s-SWCNTs, whereas the primary metallic species was the (9,9) m-SWCNT. For the calculations of the electronic DOS, the (500×1×1), (40×1×1) and (20×1×1) Γ-centered k-points samplings were used for (9,9), (7,5) and (10,8) SWCNT, respectively, and a Gaussian broadening of 0.02 eV was applied. In order to rule out possible effects due to the reduced size of the unit cell of the (9,9) m-SWCNT, calculations were also carried out on the zigzag (10,0) and (16,0) s-SWCNTs, which have similar diameters to the (7,5) and (10,9) s-SWCNTs, respectively, but much smaller unit cells, similar in size to the (9,9) m-SWCNT.
The DFT calculations demonstrate that the peak of the intrinsic thermopower α of two model s-SWCNTs is nearly an order of magnitude higher than that of the (9,9) m-SWCNT, qualitatively consistent with recent experimental results from the related art. However, the magnitude of the predicted thermopowers α for the s-SWCNTs is dramatically higher than values obtained in recent experiments from the related art. A small Fermi energy shift, ΔEF, of only approximately 60 meV in either direction produces the maximum thermopower α of approximately 1,300 μV K−1 and 800 μV K−1 for the (7,5) and (10,8) s-SWCNTs shown in
Exemplary embodiments of the invention provide highly tailored s-SWCNT thin films with finely controlled SWCNT chirality distribution and carrier density.
To generate enriched semiconducting samples, s-SWCNTs may be selectively extracted from polydisperse SWCNT soot using fluorene-based polymers or co-polymers, such as those shown in
For example, to prepare polymer:s-SWCNT dispersions, four different SWCNT source materials may be used: (1) SWCNTs synthesized by LV at a furnace temperature of approximately 1125° C.; (2) commercially obtained “SG65i” material synthesized from cobalt molybdenum catalysis of CoMoCAT®; (3) commercially obtained raw HiPCO® material synthesized by high-pressure disproportionation of CO; and (4) commercially obtained raw Tuball™ SWCNTs. The raw LV SWCNTs, HiPCO® SWCNTs, and Tuball™ SWCNTs are all presumed to contain metallic and semiconducting tubes in a roughly 1:3 ratio, whereas the CoMoCAT® material is enriched in s-SWCNTs and the (6,5) s-SWCNT in particular. The SWCNTs may be dispersed in a fluorene-based polymer or co-polymer solution generated by dissolving polymer in toluene at a concentration between 0.4-2 mg/mL. The polymers used may include poly[(9,9-dioctylfluorenyl-2,7-diyl)-alt-co-(6,6′-{2,2′-bipyridine})] (PFO-BPy), poly[(9,9-dihexylfluorenyl-2,7-diyl)-co-(9,10-anthracene)] (PFH-A), and/or poly(9,9-dioctylfluorenyl-2,7-diyl) (PFO). These fluorene-based polymers selectively wrap s-SWCNTs, allowing for a SWCNT dispersion with a less than 1% m-SWCNT impurity level. Although these three fluorene-based polymers select only semiconducting tubes, each polymer selects a different population of s-SWCNTs. PFO-BPy selects large diameter tubes with no preference for particular chiralities, PFH-A selects near-armchair s-SWCNTs and disperses a much narrower chirality distribution, and PFO selects only (7,5) tubes from the SG65i material even though the precursor material is predominantly composed of (6,5) s-SWCNTs. For further detail concerning the technique for generating high-yield dispersions of s-SWCNTs using a fluorene-based semiconducting polymer that selectively wraps semiconducting nanotubes with a range of large diameters, see Guillot, S. L. et al. Precision printing and optical modeling of ultrathin SWCNT/C60 heterojunction solar cells. Nanoscale 7, 6556-6566 (2015) and Mistry, K. S., Larsen, B. A. & Blackburn, J. L. High-Yield Dispersions of Large-Diameter Semiconducting Single-Walled Carbon Nanotubes with Tunable Narrow Chirality Distributions. ACS Nano 7, 2231-2239 (2013), the entire disclosures of which are incorporated by reference herein.
The diameter (or band gap) is determined by the synthetic conditions used to make the s-SWCNT networks. For example, polymers such as PFO, PFH-A, PFO-BPy, SMP, PF-PD, or similar fluorene-based polymers or co-polymers may be used to control which specific s-SWCNTs are selected from the raw starting material. The band gap may be controlled to have any suitable value. For example, for reasons discussed in further detail below, the band gap may be controlled to have a value between approximately 1.0 eV and approximately 1.2 eV. For example, the polymer PFH-A and the HiPCO® material may be used to achieve this band gap. The HiPCO® material contains a distribution of s-SWCNTs whose band gaps lie close to this range, and the chemical interactions between PFH-A and a specific subset of s-SWCNTs results in a sample enriched in s-SWCNTs with a band gap of approximately 1.1 eV. The subset of s-SWCNTs is determined by the choice of starting SWCNT material and the conjugated polymer. This combination may be determined by any suitable method, such as the method disclosed in Mistry, K. S., Larsen, B. A. & Blackburn, J. L. High-Yield Dispersions of Large-Diameter Semiconducting Single-Walled Carbon Nanotubes with Tunable Narrow Chirality Distributions. ACS Nano 7, 2231-2239 (2013), the entire disclosure of which is incorporated herein by reference.
Once the s-SWCNTs are dispersed in the polymer, the majority of the excess polymer may be removed during consecutive 20-hour ultracentrifuge runs until the solution reaches a mass ratio between 1:1 and 2:1 polymer:s-SWCNTs, which is determined after each centrifuge run from the absorption spectra of the solution using the Beer-Lambert Law A=εcl, where A is the absorbance, ε is the decadic molar extinction coefficient, c is the concentration, and l is the path length.
The high quality s-SWCNT networks shown in
In the example discussed above, after the initial film deposition, a toluene soak removed excess fluorene-based polymer or co-polymer, leaving polymer wrapped s-SWCNTs in a mass ratio of approximately 1:1 polymer:s-SWCNTs, and enabling close physical contact and efficient electronic coupling between s-SWCNTs, as indicated by broadened exciton transitions such as those shown in
The large density of holes (approximately 1×1020 cm−3 for a fully doped film) injected by adsorbed OA molecules strongly bleaches the exciton transitions of the s-SWCNTs, as shown by the dashed line labeled “heavily doped film” in
where AreaS
In this example, the thermopower (Seebeck) measurements were performed on a system that uses copper (Cu) blocks for temperature control and making electrical contact to the film. Indium pads were first pressed onto the s-SWCNT films to ensure good Ohmic and thermal contact to the Cu blocks. The spacing between the Cu blocks was 4 mm, so the minimum possible spacing between the indium pads was approximately 6 mm. However, the typical spacing between the indium pads (for greater than 90% of the measurements) employed in this example is approximately 16-20 mm. Resistive heaters connected to each of the blocks produced the temperature gradient, which was measured by a differential thermocouple. At least four different temperature gradients (between −3 and +3 K) were measured for each sample, with the slope of the best-fit line for these points being used for the reported thermopower α, corrected for the contributions of all other components of the electrical circuit (i.e., the Seebeck voltage due to the copper/indium contacts). Based on the physical dimensions of the system, the estimated error in the thermopower α reported by the system was less than 10%.
While it is difficult to directly correlate ΔA/A0(S11) with the actual carrier density within the s-SWCNT film for a broad range of injected carrier densities, the carrier density may be estimated within a fully doped film based on the approximate size of the exciton. To fully bleach the S11 exciton, the carrier density (per unit length of SWCNT) will be such that there is approximately one hole per unit length Lcor, where Lcor is the correlation length or exciton size. Lcor has been determined to be in the range of approximately 2 nm, so full S11 bleaching occurs for hole densities in the range of approximately 0.5 nm−1. The absorbance cross section of (7,5) SWCNTs has been estimated experimentally to be in the range of approximately 1.6×1017 cm2/C atom, and the number of atoms per nanometer of SWCNT can be determined geometrically to be [119.7×d(n,m)], where d(n,m) is the diameter of the carbon nanotube with an (n,m) chiral index. Using the absorbance coefficient of the films and a full-packed SWCNT density (for (7,5) SWCNTs) of approximately 1.12 g/cm3, the films can be estimated to have a density of approximately 0.42 g/cm3 (approximately 40% filling fraction). Since (7,5) SWCNTs have approximately 99 C atoms/nm, this density translates to a carrier density of approximately 1×1020 holes/cm3 for a fully doped s-SWCNT thin film.
Multiple control experiments demonstrate that the remaining fluorene-based polymer or co-polymer in the s-SWCNT networks does not contribute to the measured electrical conductivity σ. A comparison was performed of the basic charge transport properties of polymer-wrapped LV s-SWCNT films with the transport properties of LV SWCNT films prepared without fluorene-based polymers or co-polymers. To prepare SWCNT films according to exemplary embodiments of the invention, SWCNTs that are dispersed with carboxymethyl cellulose (CMC) in aqueous suspension may first be spray-coat mixed (⅓ metallic, ⅔ semiconducting). The CMC may then be digested from the film with nitric acid, leaving a well-connected network of heavily p-type SWCNTs devoid of residual polymer. The typically reported figures of merit are plotted for these transparent SWCNT films, the optical transmittance at 550 nm (T550) and sheet resistance (Rsh in Ω/sq.) in
The T550/Rsh values for heavily doped LV s-SWCNT networks employing both PFH-A and PFO-BPy polymers follow the same trend as the p-type films prepared according to the CMC process. This correlation suggests that the fluorene-based polymer or co-polymer does not enhance hole transport within the p-type s-SWCNT films. The temperature-dependent resistance of heavily doped polymer-wrapped LV s-SWCNT films was also compared to that of SWCNT films prepared without fluorene-based polymer or co-polymer (not shown). In all cases, the resistance decreases with increasing temperature, indicating a thermally activated conduction mechanism that was previously ascribed to barriers associated with tube-tube junctions. Taken together, these experiments help to confirm that the electrical properties measured in
At very high doping densities of the polymer:s-SWCNT networks there is also a decrease in the intensity of the lowest energy absorption band attributed to the polymer, and the appearance of a red-shifted shoulder in the absorption spectrum.
These control experiments were carried out in the solution phase to avoid complications arising from spectral features due to interchain interactions in the solid state.
To rationalize the doping behavior of the fluorene-based polymers or co-polymers, the valence level offsets between a model system are considered: PFO and the (7,5) s-SWCNT. Schuettfort, T., Nish, A. & Nicholas, R. J. Observation of a Type II Heterojunction in a Highly Ordered Polymer-Carbon Nanotube Nanohybrid Structure. Nano Lett. 9, 3871-3876 (2009) estimated the valence level offset to be approximately 500 meV for the (7,5) SWCNT. From Bindl, D. J. et al. Free Carrier Generation and Recombination in Polymer-Wrapped Semiconducting Carbon Nanotube Films and Heterojunctions. J. Phys. Chem. Lett. 4, 3550-3559 (2013), the (9,7) ionization potential has been estimated to be in the range of 5.18 eV. Taking into account the difference in electronic band gaps of the (9,7) and (7,5) SWCNTs, this places the ionization potential of the (7,5) SWCNT in the range of approximately 5.36 eV. Janietz, S. et al. Electrochemical determination of the ionization potential and electron affinity of poly(9,9-dioctylfluorene). Appl. Phys. Lett. 73, 2453-2455 (1998) finds an ionization potential of approximately 5.8 eV for PFO. This translates to an estimated offset of approximately 440 meV between the (7,5) SWCNTs and PFO. This offset would grow to approximately 600 meV for the LV SWCNTs in this example.
This implies that the polymer is not significantly doped (i.e., exhibits negligible absorption features due to polaron formation) until fairly large shifts occur in the Fermi level (ΔEF>approximately 500 meV). This doping of the polymer can be observed in two ways. Firstly, the absorbance spectra shows that the fluorene-based polymers are doped by OA at high surface concentrations of OA, i.e. the highest doping levels as shown in
The doping of the polymer can also be seen by a sudden change in the FWHM in the XPS C1s peak. In one example, core-level and work function XPS measurements were performed. The XPS core-level peaks were calibrated using a cleaned gold (Au) standard, which includes measuring the Fermi level and core-levels of Au. The core-level spectra were collected with a pass energy of 11.85 eV and a step size of 0.10 eV. This gives an uncertainty in the peak position of ±0.05 eV. The work function was determined by analyzing the secondary-electron cutoff region of the spectrum. Since this is a photon-energy independent measurement, the secondary-electron spectra were calibrated using ultraviolet photoelectron spectroscopy of Au, which captures both the Fermi-edge and secondary-electron cutoff region in one calibration scan. These measurements were taken with a pass energy of 2.95 eV and a step size of 0.025 eV. This gives an uncertainty in the work function of ±0.025 eV. The XPS measurements were performed under ultra-high vacuum (UHV) conditions (10-10 Torr). The samples did not exhibit signs of X-ray damage or sample charging during the XPS measurements (each sample was under vacuum for less than 30 mins).
Note that the FWHM of the fully doped SWCNT/PFO film in
As discussed above, exemplary embodiments of the invention control the carrier density and Fermi energy of s-SWCNT films. Exemplary embodiments of the invention may perform p-type doping of polymer:s-SWCNT networks by immersing networks in a solution of OA in DCE, modifying a procedure described in Chandra, B., Afzali, A., Khare, N., El-Ashry, M. M. & Tulevski, G. S. Stable Charge-Transfer Doping of Transparent Single-Walled Carbon Nanotube Films. Chem. Mater. 22, 5179-5183 (2010), the entire disclosure of which is incorporated by reference herein. The procedure described in Chandra attempts to achieve a maximum (or saturated) doping level. In contrast, exemplary embodiments of the present invention provide control over the doping level within the s-SWCNT network. For example, as discussed below, the desired doping level may be chosen to optimize the TE power factor α2σ of the s-SWCNT network.
In one exemplary embodiment of the invention, the doping level of the s-SWCNT network may be controlled by first saturating the doping level of the s-SWCNT network, such that the s-SWCNT network is fully doped, and then removing charge carriers from the s-SWCNT network to reach the desired doping level. For example, the saturating may include a single step of immersing the s-SWCNT network in a concentrated OA solution at approximately 78° C. for at least approximately 1 minute. The OA solution may have a concentration greater than approximately 1 mg/mL, and the solvent may be DCE or any other appropriate solvent. Alternatively, the saturating may include a plurality of steps of immersing the s-SWCNT network in OA solutions having various immersion times, concentrations, and/or temperatures. In general, concentrations of OA above approximately 1 mg/mL lead to very heavy doping, essentially fully quenching the S11 SWCNT optical transition, and partial to full quenching of the S22 and polymer optical transitions, as shown in
For example, for the Solid SPR sample discussed below, full doping is achieved by immersion in a 3 mg/mL solution of OA in DCE at 78° C. for 10 minutes, affording a TE power factor of ˜150 μW m−1 K−2. A peak TE power factor of approximately 340-350 μW m−1 K−2 is then achieved by immersion of the fully doped sample in acetone at room temperature for between 1 and 3 minutes.
In another exemplary embodiment of the invention, the doping level may be controlled by adding the dopant until the desired doping level is reached. This may be performed in one or more steps. For example, the adding of the dopant may include a single step of immersing the s-SWCNT network in an OA solution until the desired doping level is reached, or a plurality of steps of immersing the s-SWCNT network in OA solutions having increasing concentrations until the desired doping level is reached. Concentrations of OA as low as approximately 1-5 ng/mL may be used to achieve very low doping levels. For example, a peak TE power factor of approximately 100 μW m−1 K−2 can be obtained for a PFH-A:LV s-SWCNT network by immersion of the undoped film in a solution of OA at concentrations between 1 and 8.4 μg/mL in DCE at 78° C. for 10 minutes.
After the desired doping level has been achieved, the film may be immersed for no more than approximately 3 seconds in acetone in order to remove excess OA and byproducts.
As shown in
Surface-bound OA produces strong Sb and Cl signals, as shown in
XPS measurements can also be used to track the chemical potential of charge carriers injected by the OA dopants.
Correlation of XPS and absorbance data for a series of controllably doped films allows calibration of the Fermi level shift (ΔEF) as a function of the relative bleach of the S11 absorption transition. Here, ΔEF is calculated according to the shift in EC1s between the undoped and doped s-SWCNT networks, i.e., ΔEF=EC1s,undoped−EC1s,doped, and ΔA/A0 (S11) is calculated as described above. The data in
As an initial guide for TE power factor studies,
In this example, the electronic band gap (Eg,elec) was determined by the addition of the optical band gap (Eg,opt) and the exciton binding energy (Eb), assuming a dielectric constant ε=4: i.e., Eg,elec=Eg,opt+Eb, ε=4. The binding energies of the S11 excitons are described by the analytical function:
where d is the SWCNT diameter in nm and ξ=(−1)ν·cos(3θ/d), where ν=(n−m) mod 3. Accordingly, for SWCNTs in vacuum (ε=1.846), A=0.6724 eV nm, B=−4.910×10−2 eV nm2, C=4.577×10−2 eV nm2, and D=−8.325×10−3 eV nm3. To re-calculate the binding energy for SWCNTs in a medium with a given dielectric constant, the scaling law (Eb∝ε−1.4) applies. For the calculations above, the diameter of each SWCNT is taken from Weisman, R. & Bachilo, S. Dependence of optical transition energies on structure for single-walled carbon nanotubes in aqueous suspension: An empirical Kataura plot. Nano Lett. 3, 1235-1238 (2003), the entire disclosure of which is incorporated by reference herein, and the optical gap may be taken either from the same document or from photoluminescence excitation maps on SWCNT dispersions.
Table 1 below shows the calculated binding energies (Eb) and Optical/Electronic Band Gaps (Eg) for various SWCNTs considered, either experimentally or theoretically.
Eg,elec
of approximately 1.1-1.2 eV (
d
of approximately 1-1.1 nm).
The measured thermopower α shown in
To explicitly compare the experimentally obtained thermopower α to the first-principles calculations, the calibration curve generated in
In order to evaluate the TE performance beyond the TE power factor α2σ, the in-plane thermal conductance of an LV s-SWCNT:polymer network deposited onto a micromachined silicon nitride (Si—N) platform was measured. These structures, formed from patterned 500 nm thick low-stress Si—N, consisted of two islands connected by an approximately 90 micron wide, approximately 2 mm long Si—N beam that forms the sample growth stage. Note the lateral dimension (over which the temperature gradient is established) is enormous compared to the sample film thickness, ensuring the experiment is sensitive only to in-plane heat flow. Each island contains a heater, a thermistor, and electrical leads formed from patterned Cr/Pt (thickness 10 nm/40 nm). This allows accurate control and measurement of thermal gradients on the thin films.
In one example, a micromachined suspended Si—N thermal isolation platform measurement technique shown in
Before sample deposition, a protective 10 nm layer of amorphous Al2O3 was deposited on the platforms through a shadow mask that leaves the sample electrical leads exposed. The platform was then exposed to OA under the same conditions as occur in the doping step. This step can leave dopant molecules attached to the Si—N, and can cause small (approximately 10 nW K−1) reductions in the background Si—N thermal conductance due to phonon scattering. The background thermal conductance of the platform was then measured by recording the island temperatures as a function of applied power and employing a simple 2-body thermal model. After this measurement, the film was ultrasonically sprayed through another shadow mask (see
The undoped network adds a large contribution to the total thermal conductance relative to the conductance of the bare Si—N beam.
The large drop in κ suggests that the addition of the dopant not only contributes holes to the SWCNT-polymer hybrid but also adds scattering centers for phonons. This intriguing result provides strong evidence that the thermal conductivity κ in s-SWCNT networks is dominated by phonons, with a very small electronic contribution, and can be significantly reduced by appropriate doping strategies, even at very high electrical conductivity σ (e.g. greater than 100,000 S m−1). As discussed above, reducing the thermal conductivity κ may increase the figure of merit zT. Beyond doping strategies, network morphology and isotope composition may be controlled as rational routes towards further reducing the thermal conductivity κ (and increasing zT) by interfacial phonon scattering.
Although the zT values for neat s-SWCNT networks according to exemplary embodiments of the invention are still low (zT≈0.01-0.05), the weak correlation of both the thermopower α and the thermal conductivity κ to the electrical conductivity σ observed here provides a new framework for understanding the role of s-SWCNTs in TE applications. Additionally, zT may be further improved by optimizing the operational temperature T range, as illustrated by the temperature dependence of the TE properties shown in
The thermopower α and TE power factor α2σ as functions of the electrical conductivity σ do not always follow the same trends when a sample is doped sequentially or de-doped from its fully doped state.
The methods of preparing an s-SWCNT network discussed above result in a polymer being wrapped around the carbon nanotubes of the s-SWCNT network. However, the TE properties of the s-SWCNT network may be further improved by removing at least a portion of the wrapped polymer. For example, an H-bonded supramolecular polymer (SP) may be used to selectively disperse s-SWCNTs. After the s-SWCNTs are dispersed by the SP, the SP may be disassembled and removed by disrupting the H-bonds, allowing for the production of samples enriched with s-SWCNTs and containing no residual polymer. The SP may be dissolved after thin-film deposition. As discussed in further detail below, removal of the H-bonded supramolecular polymer after thin-film deposition results in (1) enhanced carrier doping and electrical conductivity σ, (2) enhanced charge carrier mobility, and (3) approximately a factor of 2 increase in the TE power factor α2σ.
Three s-SWCNT network samples were prepared by LV. The first sample was “PFOBPy:LV”, a control sample of LV s-SWCNTs dispersed by poly[(9,9-dioctylfluorenyl-2,7-diyl)-alt-co-(6,6′-{2,2′-bipyridine})] (PFO-BPy) in which a polymer is wrapped around the carbon nanotubes of the s-SWCNT network. The second sample was “Solid SPR,” a sample of LV s-SWCNTs that were dispersed using the H-bonded SP, where the SP was removed by treatment with trifluoroacetic acid (TFA) after network deposition. The third sample was “Solution SPR”, a sample of LV s-SWCNTs that were dispersed using the H-bonded SP, where the SP was removed by treatment with TFA in solution prior to network deposition.
The three samples displayed in
The absorption spectra of the doped s-SWCNT networks shown in
The differences observed in
In all cases, the electrical conductivity data in
The trends shown in
Accordingly, improving the charge carrier mobility generates large improvements in the attainable TE power factor α2σ. This conclusion can be understood by considering the dependencies of the conductivity σ and thermopower α on the carrier density n. While the conductivity σ is directly proportional to carrier density n, the thermopower α is inversely proportional to the carrier density n:
where kB is the Boltzmann constant, e is the elementary charge, h is the Planck constant, m* is the charge carrier effective mass, T is the absolute temperature, and n is the charge carrier density.
A higher hole mobility implies that a given conductivity σ can be reached at a lower carrier density n. In turn, Equation (7) implies that at a given conductivity σ, the s-SWCNT thin film with the highest hole mobility will also have the highest thermopower α.
Accordingly, to achieve a highly conductive s-SWCNT network from a polymer-enriched dispersion, exemplary embodiments of the invention may limit the level of nanotube bundling in the s-SWCNT network and eliminate as much of the insulating (wrapped) polymer as possible. The use of a removable SP for s-SWCNT enrichment, and its subsequent dissolution after thin-film deposition, produce dramatic improvements in the TE performance of the s-SWCNT networks. These advances push the performance of the approximately 1.3 nm diameter LV networks into the same range recently demonstrated for both HiPCO s-SWCNTs (<d>≈1.1 nm, with residual polyfluorene) and high-performance PEDOT-based organic thermoelectrics. These methods may also be applied to s-SWCNTs with diameters in the range of 1-1.1 nm, which can produce TE power factors α2σ of approximately 350 μW/m·K2, even at a polymer:SWCNT mass ratio of approximately 1:1.
Based on the above, exemplary embodiments of the present invention provide methods for determining desired doping conditions for an s-SWCNT network. The method may begin by spray depositing an s-SWCNT film as discussed above. The film may be treated to remove excess polymer from the film surface, and/or to remove the degradable wrapping polymer from the film. The thickness d of the film may then be measured by any suitable method, such as AFM or stylus profilometry of a scratch or masked edge of the film. In addition, an absorption spectrum of the undoped film may be measured.
A sample of the film may then be fully doped by immersing the film in a concentrated solution (greater than 1 mg/mL) of a charge-transfer dopant for at least approximately 1 minute at approximately 78° C., followed by subsequent de-doping by immersing the film in a suitable solvent at an appropriate temperature and time of immersion. Alternatively, a sample of the film may be incrementally doped by sequential immersion in solutions having increasing concentrations (such as between 1 ng/mL and 1 mg/mL) of the charge-transfer dopant in a suitable solvent. Once the sample has been doped, the absorption spectrum, sheet resistance Rsh, and thermopower α may be measured. The sheet resistance Rsh may be measured by any suitable method, such as linear 4-point probe resistivity, 4-point probe resistivity in the van der Pauw geometry, or 2-point probe resistivity. The absorption spectrum and thermopower α may be measured by the methods discussed above.
The doping of the sample may be performed under different doping conditions, such as dopant concentration, immersion time, and/or temperature. As discussed in further detail below, this provides data at multiple doping levels that can be used to generate plots to assist in determining doping conditions that result in a desired doping level of the s-SWCNT network.
In one example, the absorption spectrum is integrated over a suitable range to determine the area Ai under the absorption spectrum. The range may include the first (S11) excitonic absorption peak envelope, or the first (S11) and second (S22) excitonic absorption peak envelopes. Preferably, the range does not include other spectral features that are not associated with the s-SWCNT, as including the other spectral features could result in an incorrect fractional bleach of the absorption spectrum. The fractional bleach due to charge carrier doping is then determined according to:
where A0 is the area under the absorption spectrum of the undoped film, Ai is the area under the absorption spectrum of the film at a specific doping level, and ΔA is the change in the area between the undoped and doped film.
The sheet resistance Rsh may be converted to electrical conductivity σ according to:
The TE power factor may then be calculated as α2σ.
As shown in
The fractional bleach of the absorption spectrum ΔA/A0 may serve as a proxy for the doping level of the s-SWCNT network. Accordingly, as shown in
The foregoing disclosure has been set forth merely to illustrate the invention and is not intended to be limiting. Since modifications of the disclosed embodiments incorporating the spirit and substance of the invention may occur to persons skilled in the art, the invention should be construed to include everything within the scope of the appended claims and equivalents thereof.
This application claims priority under 35 U.S.C. § 119 to U.S. Provisional Patent Application No. 62/191,911, filed on Jul. 13, 2015, U.S. Provisional Patent Application No. 62/211,064, filed on Aug. 28, 2015, and U.S. Provisional Patent Application No. 62/316,709, filed on Apr. 1, 2016, the contents of which are hereby incorporated by reference in their entireties.
The United States Government has rights in this invention under Contract No. DE-AC36-08GO28308 between the United States Department of Energy and the Alliance for Sustainable Energy, LLC, the Manager and Operator of the National Renewable Energy Laboratory.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/US2016/042085 | 7/13/2016 | WO | 00 |
| Publishing Document | Publishing Date | Country | Kind |
|---|---|---|---|
| WO2017/011551 | 1/19/2017 | WO | A |
| Number | Name | Date | Kind |
|---|---|---|---|
| 20120052308 | El-Ashry et al. | Mar 2012 | A1 |
| 20120070612 | Lee et al. | Mar 2012 | A1 |
| 20130312806 | Carroll | Nov 2013 | A1 |
| 20140230871 | Nishio et al. | Aug 2014 | A1 |
| Number | Date | Country |
|---|---|---|
| 2 763 200 | Jun 2014 | EP |
| WO 2012054504 | Apr 2012 | WO |
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| Number | Date | Country | |
|---|---|---|---|
| 20180194629 A1 | Jul 2018 | US |
| Number | Date | Country | |
|---|---|---|---|
| 62191911 | Jul 2015 | US | |
| 62211064 | Aug 2015 | US | |
| 62316709 | Apr 2016 | US |
