MATERIALS

RELATED APPLICATIONS

This application claims priority under 35 U.S.C. § 119(e) to U.S. Provisional

Application Serial No. 61/906,616, filed November 20, 2013, and entitled "Carbon Dioxide Reduction over Single Wall Carbon Nanotubes," the contents of which are incorporated herein by reference in their entirety for all purposes.

FIELD

Embodiments described herein generally relate to layered, carbon-containing materials for use in reducing carbon dioxide, and associated systems and methods.

BACKGROUND

Man-made carbon dioxide (C0 ₂ ) emissions have increased dramatically in the last 100 years as a result of the ever expanding demand for fossil fuels. At the beginning of the 20 ^th century, annual global oil consumption was about 150 million barrels. Today that amount is consumed in less than two days. Similarly, since 1985 global use of coal has more than doubled, going from about 70 quadrillion BTU annually to over 150 quadrillion BTU today. Advances in the global thermal data record and in the climate models have demonstrated accelerated warming. In 2007, the Intergovernmental Panel on Climate Change (IPCC) concluded that undeniable global warming was very likely man-made (95% confidence), laying much of the blame on the increase in global C0 ₂ emissions from fossil fuels. Moreover, carbon dioxide emissions are projected to increase in coming decades due to economic and population growth around the world.

BRIEF DESCRIPTION OF THE DRAWINGS

Many aspects of the present disclosure can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present disclosure. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views. FIGS. 1A and IB are graphical representations of an example of a cell used for carbon dioxide reduction with single wall carbon nanotubes in accordance with various embodiments of the present disclosure.

FIG. 2 is a plot illustrating an example of a chrono-amperometry response of a SWNT film in accordance with various embodiments of the present disclosure.

FIG. 3 is a plot illustrating examples of cyclic voltammograms of a SWNT film electrode in Ar and CO ₂ saturated electrolyte in accordance with various embodiments of the present disclosure.

FIG. 4 is a plot illustrating linear sweep voltammograms of a SWNT disk electrode at different rotation rates in accordance with various embodiments of the present disclosure.

FIG. 5 is a plot illustrating an example of C0 ₂ reduction activity of a SWNT film before and after electrochemical activation in accordance with various embodiments of the present disclosure.

DETAILED DESCRIPTION

Disclosed herein are various examples related to carbon dioxide reduction with electrodes comprising layered, carbon-containing materials (e.g., single wall carbon nanotube films).

Carbon-based fuels have advantages that make them difficult to replace. The greatest of these is perhaps the enormous existing infrastructure for their distribution and use. Carbon-based fuels also possess a high energy density compared to other fuels. Accordingly, there is little incentive to find alternatives. In light of this reality, catalytic conversion of the waste C0 ₂ back to a usable fuel and/or commodity chemicals using renewable (solar, wind, wave) or deep (nuclear) energy sources have been considered to reduce C0 ₂ levels. Wholesale catalytic conversion of C0 ₂ would impact the global carbon balance by recycling the C0 ₂ into useful fuels, making the corresponding rewards (stabilization of global C0 ₂ and temperatures) enormous.

Only a few precious metal catalysts exhibit high catalytic conversion of CO ₂ at low overpotential. The overpotential is defined as the voltage beyond the thermodynamic minimum voltage for the reaction to proceed for the catalyst. For example, a silver catalyst has

demonstrated CO ₂ reduction at a low overpotential of -0.17 V in an ionic liquid medium.

Similarly, a hydrogenated palladium (Pd) electrode showed CO ₂ reduction at an overpotential of -0.20 V in the presence of pyridinium within the electrolyte. However, no non-precious metal catalysts have exhibited C0 ₂ reduction at such low overpotentials. Among the best non-precious metal catalysts is iron 5,10,15,20-tetrakis(2,6-dihydroxylphenyl)-porphyrin (Fe TDHPP), which has exhibited a C0 ₂ reduction at an overpotential of -0.43 V. Ni-cyclam and Mn-based carbonyl complexes showed efficient C0 ₂ reduction in acetonitrile at overpotentials of -0.55 V and -0.51 V, respectively. Some copper and zinc oxide based electrodes have shown carbon dioxide reduction activity in aqueous electrolyte within an overpotential range of -0.3 V to -0.7 V.

In the present disclosure, electrochemical reduction of C0 ₂ over layered, carbon- containing materials, such as single wall carbon nanotube films, is demonstrated at remarkably low overpotentials. Examples of suitable layered, carbon-containing materials include, but are not limited to, carbon nanotubes (e.g., single wall carbon nanotubes, multi-wall carbon nanotubes), carbon-carbon compacts (e.g., composites comprising carbon particles and a carbonized polymer binder), carbon nanofibers (e.g., stacked cup carbon nanofibers), multilayer graphene films (e.g., double-layer graphene, triple-layer graphene), reduced graphene oxide, pyrolytic graphite (e.g., highly ordered pyrolytic graphite), and microcrystalline graphite (e.g., amorphous graphite).

It has been recognized within the context of this invention that certain carbon-containing materials are capable of catalyzing C0 ₂ reduction at low overpotentials. In some embodiments, the carbon-containing material comprises a plurality of sp bonded carbon atoms. A material comprising a plurality of sp 2 bonded carbon atoms may, in some cases, be referred to as an sp 2 bonded carbon material. In some embodiments, the percentage of carbon atoms in an sp bonded carbon material that are sp bonded is at least about 50%, at least about 60%, at least about 70%, at least about 80%, at least about 90%, at least about 95%, at least about 99%, or about 100%. In certain cases, the percentage of carbon atoms in an sp 2 bonded carbon material that are sp 2 bonded is in the range of about 50% to about 100%, about 60% to about 100%, about 70% to about 100%, about 80% to about 100%, about 90% to about 100%, about 95% to about 100%, or about 99% to about 100%. In some embodiments, an sp bonded carbon material comprises one or more aromatic rings (e.g., a network of aromatic rings) comprising at least a portion of the sp bonded carbon atoms.

In some embodiments, the carbon-containing material has a relatively high percentage of carbon. In certain cases, the atomic percent of carbon in the carbon-containing material (e.g., the percent ratio of the number of carbon atoms to the total number of atoms) is at least about 50%, at least about 60%, at least about 70%, at least about 80%, at least about 90%, at least about 95%, or at least about 99%. The atomic percent of carbon in the carbon-containing material is, in some cases, in the range of about 50% to about 99%, about 60% to about 99%, about 70% to about 99%, about 80% to about 99%, about 90% to about 99%, or about 95% to about 99%. In certain embodiments, the carbon-containing material is substantially free of heteroatoms. In some cases, the carbon-containing material comprises one or more heteroatoms. As used herein, a

heteroatom refers to an atom that is not carbon or hydrogen (e.g., oxygen, nitrogen).

In some embodiments, the carbon-containing material has a relatively high electrical conductivity. In certain cases, for example, delocalized pi electrons from one or more aromatic rings (e.g., a network of aromatic rings) facilitate charge transport throughout the carbon- containing material. Accordingly, in some cases, the carbon-containing material has a relatively low resistance. In some embodiments, the carbon-containing material has a sheet resistance of about 1000 ohms/sq or less, about 500 ohms/sq or less, about 200 ohms/sq or less, about 100 ohms/sq or less, about 50 ohms/sq or less, about 20 ohms/sq or less, or about 10 ohms/sq or less. In some embodiments, the carbon-containing material has a sheet resistance in the range of about 10 ohms/sq to about 20 ohms/sq, about 10 ohms/sq to about 50 ohms/sq, about 10 ohms/sq to about 100 ohms/sq, about 10 ohms/sq to about 200 ohms/sq, about 10 ohms/sq to about 500 ohms/sq, or about 10 ohms/sq to about 1000 ohms/sq. Sheet resistance may be measured according to any method known in the art. For example, sheet resistance may be measured using a four-point probe.

In some embodiments, the carbon-containing material comprises a plurality of

discontinuous, electrically conductive structures in electrical communication with each other. For example, in certain embodiments, the carbon-containing material may comprise a plurality of electrically conductive carbon nanotubes and/or electrically conductive carbon particles (e.g., graphitic particles). The plurality of discontinuous, electrically conductive structures may, in some cases, comprise sp bonded carbons. In some embodiments, the plurality of electrically conductive structures may be arranged such that charge is able to propagate through the carbon- containing material (e.g., the electrically conductive structures may form an electrically conductive network).

It has also been recognized within the context of this invention that a carbon-containing material having a layered structure may be capable of catalyzing C0 ₂ reduction at low overpotentials. As used herein, a layered structure refers to a structure comprising a plurality of layers (e.g., sheets), where at least a portion of one layer is separated from at least a portion of an adjacent layer by a finite space. In some cases, a layer may comprise an amount of a material (e.g., a carbon-containing material) bounded by a space (e.g., a finite space) or other boundary. A layer of the layered structure may, in some cases, be substantially continuous. In some embodiments, a layer of the layered structure may comprise a plurality of individual,

discontinuous structures (e.g., carbon nanotubes). A layer may have any suitable shape. For example, a layer of the layered structure may be substantially planar, substantially cylindrical, substantially spherical, or irregularly shaped. A layer may, in some cases, comprise one or more protrusions. According to some embodiments, a layered structure may comprise one or more bundles of carbon nanotubes (e.g., SWNTs).

The layered, carbon-containing material may have any suitable structure. In some cases, the layered structure comprises a plurality of substantially parallel layers. In some embodiments, at least two adjacent layers are held together by van der Waals forces. In some embodiments, at least two adjacent layers are held together by at least one covalent bond, at least one ionic bond, and/or at least one hydrogen bond.

According to some embodiments, the space between at least two adjacent layers may be sufficiently large for one or more ions (e.g., anions, cations) and/or one or more neutral molecules to be intercalated between the two layers. The one or more ions may be monatomic or polyatomic. In certain cases, the one or more ions and/or neutral molecules may comprise one or more heteroatoms. In some embodiments, the space between at least two adjacent layers is at least about 0.1 nm, at least about 0.5 nm, at least about 1 nm, at least about 2 nm, at least about 5 nm, or at least about 10 nm. In some embodiments, the space between at least two adjacent layers is in the range of about 0.1 nm to about 0.5 nm, about 0.1 nm to about 1 nm, about 0.1 nm to about 2 nm, about 0.1 nm to about 5 nm, about 0.1 nm to about 10 nm, about 0.5 nm to about 1 nm, about 0.5 nm to about 2 nm, about 0.5 nm to about 5 nm, about 0.5 nm to about 10 nm, about 1 nm to about 2 nm, about 1 nm to about 5 nm, about 1 nm to about 10 nm, or about 5 nm to about 10 nm.

In some embodiments, the layered, carbon-containing material comprises a plurality of carbon nanotubes (CNTs). A carbon nanotube (CNT) generally refers to a substantially cylindrical nanostructure comprising a layer of graphene. In some embodiments, a CNT may be a single wall carbon nanotube (e.g., a CNT comprising a single layer of graphene). In alternative embodiments, a CNT may be a multi-wall carbon nanotube (e.g., a CNT comprising two or more layers of graphene). In some embodiments, the percentage of CNTs in the carbon-containing material that are SWNTs is relatively high. For example, the percentage of CNTs in the carbon- containing material that are SWNTs may be at least about 50%, at least about 60%, at least about 70%, at least about 80%, at least about 90%, at least about 95%, at least about 99%, or about 100%. In certain cases, the percentage of CNTs in the carbon-containing material that are SWNTs is in the range of about 50% to about 100%, about 60% to about 100%, about 70% to about 100%, about 80% to about 100%, about 90% to about 100%, about 95% to about 100%, or about 99% to about 100%.

In some embodiments, two or more CNTs may associate with each other and form a bundle. The CNTs in a bundle may be held together by van der Waals forces. In some cases, a CNT bundle comprises at least about 2 CNTs, at least about 5 CNTs, at least about 10 CNTs, at least about 30 CNTs, at least about 50 CNTs, at least about 70 CNTs, at least about 100 CNTs, at least about 200 CNTs, at least about 500 CNTs, at least about 700 CNTs, or at least about 1000 CNTs. In some embodiments, a CNT bundle has a diameter of at least about 5 nm, at least about 10 nm, at least about 20 nm, at least about 50 nm, or at least about 100 nm, at least about 200 nm, or at least about 500 nm. A layered, carbon-containing material may, in some cases, comprise one or more CNT bundles. In some cases, at least two CNT bundles of the layered, carbon- containing material are held together by van der Waals forces.

The layered, carbon-containing material comprising a plurality of CNTs (e.g., SWNTs) may, in certain embodiments, exhibit a relatively high electrical conductivity. In some embodiments, at least a portion of the CNTs in the layered, carbon-containing material are electrically conductive. For example, at least a portion of the CNTs may be metallic nanotubes or semiconducting nanotubes doped with a charge transfer species (e.g., bromine, iodine, alkali metals). According to some embodiments, the electrically conductive CNTs may be in electrical communication, such that charge may be transported throughout the layered, carbon-containing material.

In some cases, the CNTs of the layered, carbon-containing material have relatively small diameters. In certain embodiments, at least a portion of the CNTs have a diameter of about 100 nm or less, about 50 nm or less, about 20 nm or less, about 10 nm or less, about 5 nm or less, about 2 nm or less, or about 1 nm or less. In some embodiments, at least a portion of the CNTs have a diameter in the range of about 1 nm to about 2 nm, about 1 nm to about 5 nm, about 1 nm to about 10 nm, about 1 nm to about 20 nm, about 1 nm to about 50 nm, or about 1 nm to about 100 nm. In some embodiments, the number average diameter of the CNTs in the layered, carbon-containing material is in the range of about 1 nm to about 2 nm, about 1 nm to about 5 nm, about 1 nm to about 10 nm, about 1 nm to about 20 nm, about 1 nm to about 50 nm, or about 1 nm to about 100 nm. In certain cases, substantially all of the CNTs in the layered, carbon- containing material have a diameter in the range of about 1 nm to about 2 nm, about 1 nm to about 5 nm, about 1 nm to about 10 nm, about 1 nm to about 20 nm, about 1 nm to about 50 nm, or about 1 nm to about 100 nm.

The CNTs described herein may be described according to any method known in the art. Non-limiting examples of suitable methods include chemical vapor deposition, laser ablation, and thermal plasma methods.

In some embodiments, the layered, carbon-containing material comprises a carbon-carbon compact. As used herein, a carbon-carbon compact refers to a composite comprising a plurality of carbon particles (e.g., graphitic particles) and a carbonized polymer binder. For example, a carbon-carbon compact may be formed by pyrolyzing a plurality of carbon particles in a polymer binder (e.g., subjecting the carbon particles and polymer binder to a temperature of at least about 1000 °C under an inert atmosphere), such that the polymer binder is carbonized. In some embodiments, the carbon particles comprise a plurality of sp bonded carbons. For example, the carbon particles may, in some cases, be graphitic particles (e.g., particles comprising one or more graphene sheets). In some embodiments, the carbon particles may be relatively small. For example, the carbon particles may have a number average maximum cross- sectional dimension of about 50 μιη or less, about 20 μιη or less, about 10 μιη or less, about 5 μιη or less, about 1 μιη or less, about 500 nm or less, about 200 nm or less, about 100 nm or less, about 50 nm or less, about 20 nm or less. In some embodiments, the carbon particles may have a number average maximum cross- sectional dimension in the range of about 20 nm to about 50 nm, about 20 nm to about 100 nm, about 20 nm to about 200 nm, about 20 nm to about 500 nm, about 20 nm to about 1 μιη, about 20 nm to about 5 μιη, about 20 nm to about 10 μιη, about 20 nm to about 20 μιη, or about 20 nm to about 50 μιη. As used herein, the maximum cross- sectional dimension of a particle refers to the largest distance between two opposed boundaries of the particle that may be measured (e.g., diameter). The carbon particles may have any suitable shape. For example, at least a portion of the carbon particles may be substantially spherical, substantially flake-shaped, substantially needle-shaped, irregularly shaped, or any other shape.

In some embodiments, the carbon particles are embedded in a polymer prior to pyrolysis. The polymer may be any polymer consisting of carbon, hydrogen, and oxygen that is capable of being carbonized. Examples of suitable polymers include, but are not limited to, poly(furfuryl alcohol), polyethylene, poly(methyl methacrylate), phenolic resins, and graphite cement. In some cases, polymers comprising elements other than carbon, hydrogen, and oxygen may be used. Non-limiting examples of suitable polymers include polyaniline, polypyrrole, and polythiophene. The polymer may be selected such that after carbonization, the carbon-carbon compact has relatively high electrical conductivity.

In some embodiments, at least a portion of the plurality of carbon particles are electrically conductive. In some cases, a plurality of the electrically conductive carbon particles are in electrical communication with each other. For example, the plurality of carbon particles may form a network facilitating charge transport throughout the carbon-carbon compact.

In some embodiments, the layered, carbon-containing material comprises a plurality of carbon nanofibers. A carbon nanofiber generally refers to a carbon nanostructure comprising graphene layers arranged as stacked cones, cups, and/or plates. In some embodiments, the carbon nanofiber is substantially tubular. In some embodiments, at least a portion of the carbon nanofibers have a diameter of at least about 10 nm, at least about 20 nm, at least about 50 nm, at least about 70 nm, at least about 100 nm, at least about 150 nm, at least about 200 nm, at least about 500 nm, at least about 700 nm, or at least about 1 μιη. In some embodiments, at least a portion of the plurality of carbon nanofibers have a diameter in the range of about 10 nm to about 20 nm, about 10 nm to about 50 nm, about 10 nm to about 70 nm, about 10 nm to about 100 nm, about 10 nm to about 150 nm, about 10 nm to about 200 nm, about 10 nm to about 500 nm, about 10 nm to about 700 nm, about 10 nm to about 1 μιη, about 50 nm to about 100 nm, about 50 nm to about 150 nm, about 50 nm to about 200 nm, about 50 nm to about 500 nm, about 50 nm to about 700 nm, about 50 nm to about 1 μιη, about 100 nm to about 200 nm, about 100 nm to about 500 nm, about 100 nm to about 700 nm, or about 100 nm to about 1 μιη. In some embodiments, the number average diameter of the carbon nanofibers in the layered, carbon- containing material is in the range of about 10 nm to about 20 nm, about 10 nm to about 50 nm, about 10 nm to about 70 nm, about 10 nm to about 100 nm, about 10 nm to about 150 nm, about 10 nm to about 200 nm, about 10 nm to about 500 nm, about 10 nm to about 700 nm, about 10 nm to about 1 μιη, about 50 nm to about 100 nm, about 50 nm to about 150 nm, about 50 nm to about 200 nm, about 50 nm to about 500 nm, about 50 nm to about 700 nm, about 50 nm to about 1 μιη, about 100 nm to about 200 nm, about 100 nm to about 500 nm, about 100 nm to about 700 nm, or about 100 nm to about 1 μιη.

The carbon nanofibers described herein may be described according to any method known in the art. Non-limiting examples of suitable methods include chemical vapor deposition, laser ablation, and thermal plasma methods.

As used herein, the term "graphene" is given its ordinary meaning in the art and generally refers to a single atomic layer of carbon atoms that are covalently bound to each other (e.g., sp bonded carbons). The sp bonded carbons form repeating units that generally comprise 6- membered rings. In some cases, a graphene layer comprises a basal plane comprising a fused network of aromatic rings and a perimeter or edge comprising the terminal carbon atoms of the fused network. The basal plane may, in some cases, be flat or buckled. As used herein, the term "graphite" refers to two or more layers of graphene.

The layered, carbon-containing materials described herein may be synthesized according to any method known in the art. For example, fabrication of SWNT thin films on filtration membranes is described in U.S. Patent No. 7,261,852, issued on August 28, 2007, which is hereby incorporated by reference in its entirety. Briefly, SWNTs in a homogeneous surfactant suspension are vacuum or pressure filtered to the surface of a filtration membrane. The pores of the filtration membrane are too small for the SWNTs to efficiently permeate (typically about 0.1 μιη - 0.22 μιη), resulting in the nanotubes assembling as a thin film on the top surface of the membrane. In some embodiments, the filtration membrane makes up part of the completed device.

In addition, the filtration membrane may be lyophobic to prevent leakage of the electrolyte from the cell volume. The permeation of water through the lyophobic membrane during assembly of the SWNT film can be facilitated by excess surfactant in the aqueous SWNT surfactant suspension. The surfactant may subsequently be washed out of the SWNT film and the filtration membrane by washing with a solvent in which the surfactant is highly soluble. The SWNT film may then permitted to dry, consolidating the SWNTs as a continuous, electrically conducting film. Non-limiting examples of lyophobic membranes include

polytetrafluoroethylene (PTFE, trade name Teflon) and hydrophobic modified polyamides (trade name hydrophobic modified Nylon). In some embodiments of the invention, the porous membrane can be constructed of a hydrophobic polymer, for example, tetrafluoroethylene (PTFE), polyvinylidene fluoride (PVDF), polyethylene, polypropylene, polyester, or

hydrophobic polyamide. In other embodiments of the invention, the porous membrane can be a polymer generally considered hydrophilic, where the surface has been treated to achieve a hydrophobic surface. A metal may be evaporated along one edge of the SWNT film with sufficient overlap to make electrical contact to the nanotubes. The electrode may then be used.

In some embodiments, an electrode comprises a carbon-containing material described herein. The carbon-containing material may, in some cases, be an sp bonded carbon material.

An electrode comprising an sp 2 bonded carbon material may be referred to as an sp 2 bonded carbon electrode. In some embodiments, the electrode comprises a single layer of the carbon- containing material (e.g., sp bonded carbon material). In some cases, the electrode comprises a plurality of layers of the carbon-containing material (e.g., the electrode comprises a layered, carbon-containing material).

In certain embodiments, the electrode comprises a layered, carbon-containing material having the form of a foam and/or a felt. Accordingly, the electrode may comprise a plurality of pores (e.g., conduits, voids, passageways). In some embodiments, the electrode has a porosity of at least about 10% by volume, at least about 20% by volume, at least about 30% by volume, at least about 40% by volume, at least about 50% by volume, at least about 60% by volume, at least about 70% by volume, at least about 80% by volume or at least about 90% by volume. In some cases, the porosity of the electrode is in the range of about 10% to about 20% by volume, about 10% to about 30% by volume, about 10% to about 40% by volume, about 10% to about 50% by volume, about 10% to about 60% by volume, about 10% to about 70% by volume, about 10% to about 80% by volume, about 10% to about 90% by volume, about 20% to about 30% by volume, about 20% to about 40% by volume, about 20% to about 50% by volume, about 20% to about 60% by volume, about 20% to about 70% by volume, about 20% to about 80% by volume, about 20% to about 90% by volume, about 40% to about 50% by volume, about 40% to about 60% by volume, about 40% to about 70% by volume, about 40% to about 80% by volume, about 40% to about 90% by volume, about 60% to about 70% by volume, about 60% to about 80% by volume, or about 60% to about 90% by volume.

In some embodiments, the average pore size (e.g., number average maximum cross- sectional dimension) of the plurality of pores of the electrode is relatively large. For example, the average pore size may be at least about 1 μιη, at least about 2 μιη, at least about 5 μιη, at least about 10 μιη, at least about 20 μιη, at least about 50 μιη, at least about 100 μιη, at least about 200 μιη, at least about 500 μιη, at least about 1 mm, at least about 2 mm, or at least about 5 mm. In some embodiments, the average pore size is in the range of about 1 μιη to about 2 μιη, about 1 μιη to about 5 μιη, about 1 μιη to about 10 μιη, about 1 μιη to about 20 μιη, about 1 μιη to about 50 μιη, about 1 μιη to about 100 μιη, about 1 μιη to about 200 μιη, about 1 μιη to about 500 μιη, about 1 μιη to about 1 mm, about 1 μιη to about 2 mm, about 1 μιη to about 5 mm, about 10 μιη to about 20 μιη, about 10 μιη to about 50 μιη, about 10 μιη to about 100 μιη, about 10 μιη to about 200 μιη, about 10 μιη to about 500 μιη, about 10 μιη to about 1 mm, about 10 μιη to about 2 mm, about 10 μιη to about 5 mm, about 100 μιη to about 200 μιη, about 100 μιη to about 500 μιη, about 100 μιη to about 1 mm, about 100 μιη to about 2 mm, about 100 μιη to about 5 mm, about 1 mm to about 2 mm, or about 1 mm to about 5 mm. The pores may have any suitable shape. For example, at least a portion of the pores may have a substantially circular,

substantially elliptical, substantially polygonal, or irregular cross section.

In some cases, an electrode comprising a layered, carbon-containing material has a relatively large surface area. As used herein, the term "surface area" refers to bulk surface area (e.g., the area of all surfaces of the electrode that a fluid, such as a liquid electrolyte, may be able to contact). In some embodiments, the electrode has a surface area of at least about 100 m /g, at least about 200 m 2 /g, at least about 500 m 2 /g, at least about 700 m 2 /g, or at least about 1000 m 2 /g. In some embodiments, the electrode has a surface area in the range of about 100 m /g to about 200 m ² /g, about 100 m ² /g to about 500 m ² /g, about 100 m ² /g to about 700 m ² /g ₅ about 100 m ² /g to about 1000 m ² /g, about 200 m ² /g to about 500 m ² /g ₅ about 200 m ² /g to about 700 m ² /g ₅ about 200 m ² /g to about 1000 m ² /g, or about 500 m ² /g to about 1000 m ² /g.

In certain embodiments, the electrode comprising a layered, carbon-containing material has a relatively low density. In some cases, the density of the electrode is about 5 g/cm or less, about 2 g/cm 3 or less, about 1 g/cm 3 or less, about 0.5 g/cm 3 or less, about 0.2 g/cm 3 or less, or about 0.1 g/cm or less. In some embodiments, the density of the electrode is in the range of about 0.1 g/cm 3 to about 0.2 g/cm 3 , 0.1 g/cm 3 to about 0.5 g/cm 3 , 0.1 g/cm 3 to about 1 g/cm 3 , 0.1 g/cm 3 to about 2 g/cm 3 , or about 0.1 g/cm 3 to about 5 g/cm 3.

According to some embodiments, an electrode comprising a layered, carbon-containing material may be used to electrochemically reduce carbon dioxide. In some embodiments, C0 ₂ reduction may initiate at a relatively low overpotential. In certain cases, C0 ₂ reduction may initiate at an overpotential of about 1 V or less, about 0.7 V or less, about 0.5 V or less, about 0.2 V or less, about 0.1 V or less, about 0.05 V or less, or about 0.01 V or less. In some

embodiments, C0 ₂ reduction may initiate at an overpotential in the range of about 0.01 V to about 0.05 V, about 0.01 V to about 0.1 V, about 0.01 V to about 0.2 V, about 0.01 V to about 0.5 V, about 0.01 V to about 0.7 V, about 0.01 V to about 1 V, about 0.05 V to about 0.1 V, about 0.05 V to about 0.2 V, about 0.05 V to about 0.5 V, about 0.05 V to about 0.7 V, about 0.05 V to about 1 V, about 0.1 V to about 0.5 V, about 0.1 V to about 0.7 V, about 0.1 V to about 1 V, about 0.2 V to about 0.5 V, about 0.2 V to about 0.7 V, about 0.2 V to about 1 V, or about 0.5 V to about 1 V.

The electrode may have any suitable thickness. In some embodiments, the electrode has a thickness of about 5000 μιη or less, about 2000 μιη or less, about 1000 μιη or less, about 500 μιη or less, about 200 μιη or less, about 100 μιη or less, about 50 μιη or less, about 20 μιη or less, about 10 μιη or less, about 5 μιη or less, about 2 μιη or less, about 1.5 μιη or less, about 1 μιη or less, about 500 nm or less, about 100 nm or less, about 50 nm or less, about 20 nm or less, or about 10 nm or less. In some embodiments, the electrode has a thickness in the range of about 10 nm to about 20 nm, about 10 nm to about 50 nm, about 10 nm to about 100 nm, about 10 nm to about 500 nm, about 10 nm to about 1 μιη, about 10 nm to about 1.5 μιη, about 10 nm to about 2 μιη, about 10 nm to about 5 μιη, about 10 nm to about 10 μιη, about 10 nm to about 20 μιη, about 10 nm to about 50 μιη, about 10 nm to about 100 μιη, about 10 nm to about 200 μιη, about 10 nm to about 500 μιη, about 10 nm to about 1000 μιη, about 10 nm to about 2000 μιη, about 10 nm to about 5000 μιη, about 50 nm to about 100 nm, about 50 nm to about 500 nm, about 50 nm to about 1 μιη, about 50 nm to about 1.5 μιη, about 50 nm to about 2 μιη, about 50 nm to about 5 μιη, about 50 nm to about 10 μιη, about 50 nm to about 20 μιη, about 50 nm to about 50 μιη, about 50 nm to about 100 μιη, about 50 nm to about 200 μιη, about 50 nm to about 500 μιη, about 50 nm to about 1000 μιη, about 50 nm to about 2000 μιη, about 50 nm to about 5000 μιη, about 100 nm to about 500 nm, about 100 nm to about 1 μιη, about 100 nm to about 1.5 μιη, about 100 nm to about 2 μιη, about 100 nm to about 5 μιη, about 100 nm to about 10 μιη, about 100 nm to about 20 μηι, about 100 nm to about 50 μηι, about 100 nm to about 100 μηι, about 100 nm to about 200 μηι, about 100 nm to about 500 μιη, about 100 nm to about 1000 μιη, about 100 nm to about 2000 μιη, about 100 nm to about 5000 μιη, about 500 nm to about 1 μιη, about 500 nm to about 1.5 μιη, about 500 nm to about 2 μιη, about 500 nm to about 5 μιη, about 500 nm to about 10 μιη, about 500 nm to about 20 μιη, about 500 nm to about 50 μιη, about 500 nm to about 100 μιη, about 500 nm to about 200 μιη, about 500 nm to about 500 μιη, about 500 nm to about 1000 μιη, about 500 nm to about 2000 μιη, about 500 nm to about 5000 μιη, about 1 μιη to about 2 μιη, about 1 μιη to about 5 μιη, about 1 μιη to about 10 μιη, about 1 μιη to about 20 μιη, about 1 μιη to about 50 μιη, about 1 μιη to about 100 μιη, about 1 μιη to about 200 μιη, about 1 μιη to about 500 μιη, about 1 μιη to about 1000 μιη, about 1 μιη to about 2000 μιη, about 1 μιη to about 5000 μιη, about 10 μιη to about 20 μιη, about 10 μιη to about 50 μιη, about 10 μιη to about 100 μιη, about 10 μιη to about 200 μιη, about 10 μιη to about 500 μιη, about 10 μηι to about 1000 μιη, about 10 μιη to about 2000 μηι, about 10 μιη to about 5000 μιη, about 100 μηι to about 200 μιη, about 100 μιη to about 500 μιη, about 100 μηι to about 1000 μιη, about 100 μιη to about 2000 μηι, about 100 μιη to about 5000 μιη, about 1000 μηι to about 2000 μιη, or about 1000 μιη to about 5000 μιη.

In some embodiments, the electrode may be used in a device (e.g., a C0 ₂ reduction cell) designed to catalyze C0 ₂ electroreduction. The C0 ₂ reduction cell may, in some embodiments, comprise a working electrode comprising a layered, carbon-containing material (e.g., SWNTs), a counter electrode, and an electrolyte. The counter electrode may comprise any electrically conductive material. Examples of suitable materials for the counter electrode include, but are not limited to, platinum (Pt), palladium (Pd), nickel (Ni), stainless steel, glassy carbon, and semiconducting oxides. In certain embodiments, the counter electrode may catalyze oxygen evolution. In some embodiments, the electrolyte may be positioned between the working electrode and the counter electrode. In certain embodiments, the electrolyte may be in direct contact with the working electrode. According to some embodiments, the electrolyte may comprise dissolved C0 ₂ . The electrolyte may be a liquid electrolyte or a solid electrolyte. In cases where the electrolyte is a liquid electrolyte, the C0 ₂ reduction cell may comprise a three- phase interface where the solid working electrode, liquid electrolyte, and gaseous C0 ₂ meet. In some embodiments, the three-phase interface may have a relatively large surface area.

In some embodiments, the C0 ₂ reduction cell further comprises a separator positioned between the working electrode and the counter electrode. In some cases, the separator is positioned between a first chamber comprising the working electrode and a second, separate chamber comprising the counter electrode. In some embodiments, the first chamber may comprise a first electrolyte, and the second chamber may comprise a second electrolyte. The first and second electrolytes may be the same or different. The separator may, in some cases, permit transport of certain ions (e.g., electrolyte ions). In some cases, the separator inhibits transport of reaction products. One of ordinary skill in the art would be able to select an appropriate separator material.

The C0 ₂ reduction cell may, in some embodiments, comprise a porous membrane.

According to some embodiments, the porous membrane comprises a first side and a second side opposite the first side. In some cases, a carbon-containing material (e.g., a layered, carbon- containing material) is disposed on the first side of the porous membrane. In some cases, the second side comprises a lyophobic and/or hydrophobic material. In some cases, CO ₂ may diffuse through the porous membrane.

According to some embodiments, the C0 ₂ reduction cell further comprises a power supply (e.g., a battery). In some cases, the power supply is connected to the working electrode by a contact electrode. For example, the contact electrode may overlap a portion of the working electrode. The contact electrode may comprise any electrically conductive material. Non- limiting examples of suitable materials for the contact electrode include Pt, Pd, Ni, stainless steel, glassy carbon, and semiconducting oxides.

In operation, the power supply may, optionally, provide power (e.g., apply voltage) to the working electrode. In some embodiments, the working electrode has a relatively high specific capacitance. For example, in some cases, the working electrode has a specific capacitance of at least about 1 F/g, at least about 5 F/g, at least about 10 F/g, at least about 50 F/g, at least about 100 F/g, at least about 200 F/g, at least about 300 F/g, at least about 400 F/g, at least about 500 F/g, at least about 600 F/g, at least about 700 F/g, at least about 800 F/g, at least about 900 F/g, or at least about 1000 F/g. In some embodiments, the working electrode has a specific capacitance in the range of about 1 F/g to about 5 F/g, about 1 F/g to about 10 F/g, about 1 F/g to about 50 F/g, about 1 F/g to about 100 F/g, about 1 F/g to about 200 F/g, about 1 F/g to about 300 F/g, about 1 F/g to about 400 F/g, about 1 F/g to about 500 F/g, about 1 F/g to about 600 F/g, about 1 F/g to about 700 F/g, about 1 F/g to about 800 F/g, about 1 F/g to about 900 F/g, about 1 F/g to about 1000 F/g, about 10 F/g to about 50 F/g, about 10 F/g to about 100 F/g, about 10 F/g to about 200 F/g, about 10 F/g to about 300 F/g, about 10 F/g to about 400 F/g, about 10 F/g to about 500 F/g, about 10 F/g to about 600 F/g, about 10 F/g to about 700 F/g, about 10 F/g to about 800 F/g, about 10 F/g to about 900 F/g, about 10 F/g to about 1000 F/g, about 100 F/g to about 200 F/g, about 100 F/g to about 300 F/g, about 100 F/g to about 400 F/g, about 100 F/g to about 500 F/g, about 100 F/g to about 600 F/g, about 100 F/g to about 700 F/g, about 100 F/g to about 800 F/g, about 100 F/g to about 900 F/g, about 100 F/g to about 1000 F/g, or about 500 F/g to about 1000 F/g. Specific capacitance may be obtained according to any method known in the art. For example, specific capacitance may be calculated from measurements made using cyclic voltammetry.

In some embodiments, the working electrode may come into contact with at least a portion of dissolved C0 ₂ in the electrolyte. Upon contact with the layered, carbon-containing material of the working electrode, the C0 ₂ may be reduced to one or more products. Non- limiting examples of reaction products include formate, carbon monoxide, methanol, ethanol, methane, ethane, acetic acid, formaldehyde, and acetaldehyde. In some embodiments, the one or more reaction products may be gases and/or liquids. The reaction products may, in some cases, be collected and stored for later use. In some embodiments, a C0 ₂ reduction current is generated.

Some aspects are directed to methods of reducing carbon dioxide. According to some embodiments, a method may comprise the step of providing an electrolyte including dissolved C0 ₂ to an electrode (e.g., an sp bonded carbon electrode). In some embodiments, the method further comprises reducing the dissolved C0 ₂ via electroreduction. The reducing step may, for example, occur through powering the electrode. In some cases, the electrode may be powered by applying voltage from a power supply to the electrode (e.g., through a contact electrode in electrical communication with the power supply and the electrode).

The method may, optionally, comprise the step of mixing C0 ₂ with the electrolyte to produce the electrolyte including dissolved C0 ₂ . In some cases, the C0 ₂ may be remotely mixed with the electrolyte. In certain embodiments, the C0 ₂ may diffuse through a membrane (e.g., a lyophobic, porous membrane) to mix with the electrolyte.

FIGS. 1A and IB show exemplary schematic illustrations of a cell designed for C0 ₂ reduction, according to certain embodiments. Referring to FIGS. 1A and IB, shown are top and side views (respectively) of an example of a metal electrode contacted SWNT film on a porous membrane and a cell, which was used in testing. The cell is described in PCT Application No. PCT/US2010/031995 filed on April 22, 2010, which is hereby incorporated by reference in its entirety. In the example of FIGS. 1A and IB, the SWNT film 101 is disposed on the underlying, lyophobic, porous membrane 103. A contact electrode 102 overlaps a portion of an edge of the SWNT film 101. The cell body 104, including an electrolyte volume (or chamber) 105 which holds the electrolyte, may be fabricated from, e.g., solid Teflon or other appropriate material. The electrolyte volume 105 has an opening 106 extending through the cell sidewall.

A seal such as, e.g., a captured O-ring 107, surrounds the sidewall opening 106 in the cell body 104. The seal is formed against the SWNT film 101 when the membrane 103 supporting the SWNT film 101 is pressed up against the O-ring 107 by the gas flow cover 108. The gas flow cover 108 includes a gas inlet fitting 110 aligned with a first through hole (or passage) 111 leading to a gas chamber 112. A second through hole (or passage) 113 leads to a gas outlet fitting 114 of the gas flow cover 108. The gas flow cover 108 may be fabricated from Plexiglass or other appropriate material and can be secured to the cell body 104 by fasteners such as, e.g., 4 screws (not shown) that pass through openings 109 in the gas flow cover 108. As shown in FIG. 1, another electrode 117 was provided on the opposite side of the electrolyte volume 105 and sealed against an O-ring 116 by pressure from cover 118.

The electrolyte volume (or chamber) 105 included an electrolyte gas purge tube (and fitting) 120, which extended from the electrolyte volume 105 through a top cover, as illustrated in FIG. IB, to purge the cell with inert gas prior to measurements. For three terminal chrono- amperometric measurements, a counter electrode 121 (e.g., a glassy carbon electrode or a platinum flag electrode) and a reference electrode 122 (e.g., an Ag/AgCl electrode) were included in the electrolyte volume 105.

In testing and use, the SWNT film 101 side of the membrane 103 was placed across the sidewall opening 106 in the cell body 104, and a leak free seal was formed around the perimeter of the opening 106 using a compliant O-ring. During testing, to avoid electrochemical dissolution of the metallic electrode 102 that makes contact with the SWNT film 101, the metal was arranged to lie beyond the boundary of the seal 107 away from the electrolyte. In operation, the cell is filled with electrolyte, which wets the SWNT film 101 through to the membrane surface. However, because of the lyophobicity of the membrane 103, the electrolyte does not penetrate into its open pore structure. The opposite side of the membrane 103 is exposed to a gas phase medium including C0 ₂ in the gas chamber 112. The C0 ₂ permeates by diffusion through the pores of the membrane 103 at the three-phase interface including the gas or vapor phase carbon dioxide, the (solid) SWNT film, and the liquid electrolyte. At the three phase interface, C0 ₂ dissolves into the surface layer of the electrolyte, wetting the SWNTs, and is reduced electrochemically upon contact with the SWNTs.

TABLE 1 shows various reaction pathways that may be present at the SWNT film 101 electrode during operation of the cell of FIGS. 1A and IB. TABLE 1 also indicates the number of electrons involved, products, and the thermodynamic potentials for the reaction pathways (referenced to a normal hydrogen electrode (NHE)).

TABLE 1

Referring next to FIG. 2, shown is an example of the results of a three terminal chrono- amperometry measurement on the SWNT film working electrode (a 1.5 μιη thick SWNT film 101 on a PTFE membrane 103) in dimethylformamide (DMF) with 0.1M tetrabutylammonium hexafluorophosphate (TBAPF ₆ ) and 2M water (H ₂ 0). Similar results were also obtained with 0.1M tetrabutylammonium tetrafiuoroborate (TBABF ₄ ) salt in DMF with 2M H ₂ 0. The electrolyte was purged with argon (Ar) for 1 hour prior to the measurement to remove the dissolved oxygen. The electrolyte was kept under an argon blanket while the back side of the porous membrane 103 was exposed, via the gas chamber 112, to Ar 203 or C0 ₂ 206 as indicated in the plot of FIG. 2. Upon such gas exposure, the SWNT film working electrode was adjusted to -0.79 V versus NHE.

It can be seen that immediately upon exposure to the C0 ₂ , an appreciable reduction current was obtained at -0.79 V vs. NHE (an overpotential of only 0.10 V relative to the thermodynamic potential for CO production). The electrolytes used here were used to allow direct comparison with iron 5,10,15,20-tetrakis(2,6-dihydroxylphenyl)-porphyrin (Fe TDHPP) catalyst, which has shown the highest C0 ₂ reduction activity among the nonprecious metal based catalysts. The Fe TDHPP catalyst evidenced a C0 ₂ reduction current of 0.31 mA/cm at a potential of -1.16 V vs. NHE (an overpotential of -0.47 V relative to the thermodynamic potential for CO production), whereas the SWNT film electrode showed C0 ₂ reduction currents of 0.42 mA/cm at -0.79 V vs. NHE (an overpotential of 0.1 V). As indicted in TABLE 1, possible products include HCOOH, CO, CH ₃ OH, CH ₄ , C ₂ H ₄ , all of which may be useful. The low overpotential for the reaction is remarkable. Also of note in the plot 203 of FIG. 2 is the stability of the reaction during the C0 ₂ exposure 206.

FIG. 3 shows an example of cyclic voltammograms (CV) of a SWNT film (e.g., a 1.5 μιη thick SWNT film 101 on a PTFE membrane 103) electrode in DMF with 0.1M TBABF ₄ and 2M H ₂ 0. The electrolyte was saturated with Ar or C0 ₂ by purging with the respective gases for 1 hour prior to each measurement. Curves 303 and 306 are the CVs (scan rate 10 mV/s) in the Ar and C0 ₂ saturated electrolyte, respectively. In the absence of C0 ₂ (i.e., when Ar purged), the current likely corresponds to hydrogen reduction (as a precursor to H evolution) from the water in the DMF. In the presence of C0 ₂ , its reduction initiates at just below 0.4 V (vs. NHE), evidencing less than 50 mV overpotential with respect to the thermodynamic potential of methane production.

A rotating ring disk electrode (RRDE) measurement was also performed on a SWNT film transferred onto a glassy carbon disk electrode. To transfer the nanotubes onto the disk electrode, a SWNT film (300 nm) was fabricated on a PTFE membrane (0.2 μιη pore) using a filtration method. The SWNT film (5 mm diameter) with PTFE membrane was placed on top of the glassy carbon disk electrode (5 mm diameter) with the nanotubes facing the disk. A single drop of methanol was placed on the back side of the PTFE membrane to wet the PTFE, thereby delaminating the film from the SWNT film electrode and facilitating intimate contact between the nanotubes and the glassy carbon electrode as the methanol evaporated. Once the disk completely dried, the PTFE membrane was slowly removed leaving behind the SWNT film on the glassy carbon disk. The glassy carbon electrode containing the SWNT film was then mounted onto the RRDE set up (using a setup manufactured by Pine Instrument). The C0 ₂ reduction measurement was performed in DMF with 0.1M TBABF ₄ and 2M H ₂ 0. The electrolyte was purged with Ar for 1 hour to remove dissolved oxygen and other gases, followed by purging for another hour with pure C0 ₂ to saturate the electrolyte.

Measurements were performed with a C0 ₂ blanket over the electrolyte. CV curves obtained in the Ar and C0 ₂ saturated electrolyte in the glass electrochemical cell were very similar to curves obtained in Teflon cell. FIG. 4 shows examples of a linear sweep voltammetry (LSV) (with a scan rate of 10 mV/s) of the SWNT film electrode at different rotation speeds - curve 403 at 800 rpm, curve 406 at 1000 rpm, curve 409 at 1200 rpm, curve 412 at 1400 rpm and curve 415 at 1600 rpm. The currents increase with rotation speed, suggesting that the reduction currents may be diffusion limited. This suggests that the cathodic currents of the SWNT film may be due to reduction of the dissolved C0 ₂ in the electrolyte.

An activation process, which is described in a PCT Application No PCT/US2011/065569 filed on December 16, 2011, which is hereby incorporated by reference in its entirety, can enhance the C0 ₂ reduction over the activated SWNTs. A SWNT film 101 (about 1.5 μιη thick) working electrode was fabricated on PTFE membrane 103 using a vacuum filtration method. A thicker SWNT film coupled to carbon paper was used to make electrical connection to the SWNT working electrode. Activation of the SWNTs comprises contacting the SWNT film 101 with an acid solution for a sufficient period of time with a number of cathodic cycles induced over the course of the exposure. The SWNT working electrode was activated in 1M nitric acid in the electrochemical cell using glassy carbon as the counter electrode and an Ag/AgCl reference electrode. After the electrochemical activation of the SWNT film 101, the electrochemical cell was washed with copious amounts of water to remove any residual acid and the SWNT film 101 was washed in two overnight water baths (12 hours each) and 8 subsequent water baths (2 hours each). Finally, the SWNT film 101 was rinsed with DMF electrolyte (0.1M TBABF ₄ and 2M H ₂ 0) and then bathed in this electrolyte for 2 hours before its replacement for the measurement. The electrolyte was subsequently purged with Ar for 1 hour to remove dissolved 0 ₂ and other gases followed by saturation with pure C0 ₂ .

A C0 ₂ blanket was maintained over the electrolyte during the measurements. A linear sweep voltammogram (with a scan rate of 10 mV/s) was recorded on the activated SWNT film 101 electrode using a glassy carbon counter electrode. FIG. 5 shows the C0 ₂ reduction currents on SWNT film before (curve 503) and after (curve 506) the electrochemical activation. As can be seen, the activated the SWNT film 101 showed higher C0 ₂ reduction currents and also an anodically shifted onset potential, implying a greater activity of the SWNT film towards the C0 ₂ reduction once activated.

A working embodiment of a device designed to catalyze C0 ₂ electroreduction can include the following features: 1) a working electrode consisting of SWNTs, or other layered, sp bonded carbon (e.g., graphitic carbon compact) materials; 2) a counterelectrode (e.g., Pt, Pd, Ni, stainless steel, glassy carbon, oxide semiconductor or other electrical conductor); 3) a liquid electrolyte or a solid electrolyte membrane in electrical communication with both electrodes; 4) a separator that permits liquid electrolyte ion transport across it but minimizes the exchange of reaction products between the working electrode and the counter electrode (i.e., the electrodes occupying compartments effectively separated by this separator); and/or 5) the facility to collect the reaction products of the C0 ₂ electroreduction reaction.

In some embodiments the electrodes are made porous, and C0 ₂ saturated electrolyte is forced through the C0 ₂ reduction electrode to maximize the electrode exposure to the C0 ₂ to be reduced.

Possible electrolyte systems include: non-aqueous solvents such as, e.g., methanol, acetonitrile, dimethylsulfoxide, tetrahydrofuran and their mixtures with water, as well as other non-aqueous solvents in which the C0 ₂ saturation concentration exceeds that available in pure water, mixed with electrolyte salts which can include (but are not limited to): lithium, sodium or potassium tetralkylammonium cations with one or more of hexafluorophosphate,

tetrafluoroborate, or perchlorate anions. Alternatively, the electrolyte can consist of water miscible ionic liquids such as (but not limited to): 1,3-dialkylimidazolium cation with the foregoing anions, 1,3-dialkylpyrrolidinium cation with the foregoing anions. Different electrolytes including acids or bases may also be mixed into these systems. Distinct electrolytes may be used in the two separated compartments.

It should be emphasized that the above-described embodiments of the present disclosure are merely possible examples of implementations set forth for a clear understanding of the principles of the disclosure. Many variations and modifications may be made to the above- described embodiment(s) without departing substantially from the spirit and principles of the disclosure. All such modifications and variations are intended to be included herein within the scope of this disclosure and protected by the following claims. It should be noted that ratios, concentrations, amounts, and other numerical data may be expressed herein in a range format. It is to be understood that such a range format is used for convenience and brevity, and thus, should be interpreted in a flexible manner to include not only the numerical values explicitly recited as the limits of the range, but also to include all the individual numerical values or sub-ranges encompassed within that range as if each numerical value and sub-range is explicitly recited. To illustrate, a concentration range of "about 0.1% to about 5%" should be interpreted to include not only the explicitly recited concentration of about 0.1 wt% to about 5 wt%, but also include individual concentrations (e.g., 1%, 2%, 3%, and 4%) and the sub-ranges (e.g., 0.5%, 1.1%, 2.2%, 3.3%, and 4.4%) within the indicated range. The term "about" can include traditional rounding according to significant figures of numerical values. In addition, the phrase "about 'x' to 'y" includes "about Y to about 'y'".