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Dresselhaus was among the first researchers to study magnetic and optical properties of graphite using lasers. She discovered that laser vaporization could generate carbon clusters. This method was then used by other scientists and led to the discovery of fullerenes.
She made massive contributions to the field of nanotechnology which led to groundbreaking developments in medicine, computing, and clean energy production. Her discoveries on the electrical and thermal properties of nanocarbons were extremely valuable in many areas of technology (such as electronics and optics), nanotechnology, and materials science. In the 1990s, Dresselhaus and her team started to develop more efficient thermoelectric nanomaterials to generate electricity and save energy. Her work drew the attention of the US Navy as well as the scientific community. These innovative materials have wide applications, including use in car engines, photovoltaic cells, and electronic devices.
Over the course of her career, Dresselhaus published more than 1700 papers and co-wrote eight books. She has received numerous awards for both her research and for her support and efforts to make careers in science and engineering more welcoming to women. She was the chair of the governing board of the American Institute of Physics, president of the American Physical Society (APS), and the first female president of the American Association for the Advancement of Science. Her awards include, but are not limited to, the National Medal of Science in 1990, the Enrico Fermi Award which she shared with Burton Richter in 2012. In the same year, she became the first solo recipient of the Kavli prize for her contributions to nanoscience. In 2014 she was awarded the Presidential Medal of Freedom and was inducted into the US National Inventors Hall of Fame. Dresselhaus and her colleague organized the first Women's Forum at MIT in 1971 to discuss the roles of women in science and engineering. She also appeared in a General Electric television advertisement that aimed to encourage the participation of women in STEM fields which asked “what if female scientists were celebrities?”. The APS honored her legacy by creating the Millie Dresselhaus Fund to support and empower more women in physics.
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Science details:
Dresselhaus’s theoretical and experimental work studying carbon laid the foundation for the discovery of buckminsterfullerenes, also known as “buckyballs”. These are a type of fullerene: a molecule of hexagonally arranged carbon atoms which are connected by single and double bonds. The fullerene molecule can be flat (graphene), cylindrical (carbon nanotubes), ellipsoidal, or spherical (buckyballs).
Buckyballs have the chemical formula C₆₀. It has a “truncated icosahedron“ structure that resembles a soccer ball. C₆₀ is a stable molecule that can withstand high temperatures and pressures. In solids, if the molecules are doped with alkali metals, they can be converted from semiconductors to conductors or superconductors.
In 1996, Mildred Dresselhaus, Gene Dresselhaus, and Peter C. Eklund published “Science of fullerenes and carbon nanotubes”: the first book that provides a comprehensive resource on fullerenes and discusses their applications.
Citations and resources:
https://www.nature.com/articles/543316a
https://en.wikipedia.org/wiki/Fullerene
https://en.wikipedia.org/wiki/Buckminsterfullerene#cite_ref-Dresselhaus_15-0
https://www.worldcat.org/title/science-of-fullerenes-and-carbon-nanotubes/oclc/162571937
Figures:
Left: eBook cover of “Science of fullerenes and carbon nanotubes” (1996) by Mildred Dresselhaus, Gene Dresselhaus, and Peter C. Eklund. https://www.worldcat.org/title/science-of-fullerenes-and-carbon-nanotubes/oclc/162571937
Right: Diagram of buckminsterfullerene (C₆₀) with rods connecting carbon atoms. https://en.wikipedia.org/wiki/Buckminsterfullerene#/media/File:C60-rods.png
Science details:
Graphene is an allotrope of carbon and is the strongest known material - approximately 200 times stronger than surgical steel. It is a two-dimensional crystal of carbon atoms arranged in a honeycomb lattice. It is a good thermal conductor, electrical conductor, and is transparent due to its thinness.
Each carbon atom in graphene has four valence (outer shell) electrons, three of which are connected to the three nearest neighbors by sigma-bonds, which are very strong covalent bonds, giving graphene its mechanical properties (i.e. strength and flexibility). The last valence electron is a free pi electron that contributes to the conduction band of the entire sheet of graphene. The free pi electrons behave like massless Dirac fermions (quasiparticles with spin ½ which have distinct antiparticles) which move at relativistic speeds along graphene’s plane. These are responsible for graphene’s thermal and electrical properties.
Citations and resources:
https://en.wikipedia.org/wiki/Graphene
https://en.wikipedia.org/wiki/Graphene_lens
https://www.physicscentral.com/explore/action/graphene.cfm
https://www.youtube.com/watch?v=eh3dA8xnZ4Y
Figures:
Top: Sigma (dark blue) and pi (magenta) bonds in graphene. Sigma bonds are due to the overlap of sp2 hybrid orbitals which are parallel to the plane of graphene. Pi bonds are due to tunneling (pink arrow) between the pz orbitals which are perpendicular to the plane of graphene. https://en.wikipedia.org/wiki/Graphene#/media/File:Graphene_-_sigma_and_pi_bonds.svg
Bottom: Depiction of a flat sheet of graphene with carbon atoms in a honeycomb lattice. https://analyticalscience.wiley.com/do/10.1002/gitlab.15487/full/#media-1
Science details:
Band structure is a description of the energy levels of electrons in solids. Similar to how electrons in an atom are allowed discrete energies, electrons in solids are shared between atoms and have discrete bands of allowed energies. This is because atoms are in close proximity to each other so energies are perturbed through quantum mechanical interactions. The outermost (highest energy) electrons in the solid occupy the “valence band”, where the states are semi or fully filled. The “conduction band” gives the next highest energy levels which are normally empty states. The band structure of metals has no gap between the valence and conduction bands, meaning the most energetic electrons can jump to higher energy levels without adding energy to the solid. This is why metals are good electrical conductors. Insulators have a large gap between the valence and conduction band, called the “forbidden gap” (band gap), meaning extra energy is needed for the electrons to move to higher energy levels. This additional energy could be several eV for one electron, meaning insulators will not conduct electricity even when a voltage is applied. Semiconductors have narrow forbidden gaps, small enough that electrons can jump from the valence to the conduction band if a small amount of energy is applied.
Citations and resources:
https://www.britannica.com/science/band-theory
https://jqi.umd.edu/glossary/band-structure
https://solidstate.quantumtinkerer.tudelft.nl/13_semiconductors/
Figures:
Energy bands of metals (left), semiconductors (middle), and insulators (right). Metals have overlapping conduction (blue) and valence (red) bands. Semiconductors have a narrow band gap between the valence and conduction bands. Insulators have a large band gap between bands. The y-axis marks increasing energy from bottom to top, and the Fermi energy marks the center of the band gaps. https://energyeducation.ca/encyclopedia/Band_gap
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The energy E of a massive particle is related to its momentum and mass (p, m) by E=p²/2m, whereas the energy of a massless particle is related to its momentum and speed (p, v) by E=pv. This linear relationship means that the conduction and valence bands are connected at a single point. The band structure of graphene has both band gaps and points where electrons will flow without added energy, meaning it is both a semiconductor and a metal. Graphene’s electrons can either be described by the Schrodinger equation for massive particles, or by a two-dimensional Dirac equation for massless particles, depending on their momentum and energy.
Citations and resources:
https://www.youtube.com/watch?v=OdR0VqfSRdM
https://en.wikipedia.org/wiki/Electronic_properties_of_graphene
https://www.sciencedirect.com/science/article/pii/S1742706121004293
Figures:
Left: 3D plot of energy (E) of a massive particle on the z-axis against wavevectors (k) in the y and x direction. The energy is linearly proportional to the wavevector, giving the band structure a conic shape where the valence (orange) and conduction (blue) bands meet at a point.
Right: 3D plot of energy (E) of a massless particle on the z-axis against wavevectors (k) in the y and x direction. The energy is related to the square wavevector, giving the band structure a parabolic shape. Two paraboloids are overlaid on top of each other, showing one band structure with a band gap separating the valence and conduction bands.
https://www.pnas.org/content/pnas/107/34/14999/F3.large.jpg?width=800&height=600&carousel=1
Science details:
Each carbon atom contributes a free pi electron to the conduction band of the entire sheet of graphene. For first nearest-neighbor interactions, the energy of the free electron is dependent on its wavevector (or momentum) in the plane parallel to the sheet of graphene, taken to be the xy plane. The positive and negative energies correspond to the conduction and valence bands, respectively. The bands meet at six vertices in the plane, called the Dirac points. Near those points, the energy is linearly dependent on the wavevector, much like a massless relativistic particle. This means that for certain energies, the electrons can be described pseudo-relativistically by a 2D Dirac equation.
There are 12 possible paths that the free electrons can take that correspond to the first nearest-neighbor interactions. The band structure reveals two properties of graphene, the first being that it can be metallic: there are 6 directions (given by the Dirac points where energy E=0) along which current can flow in zigzag paths in the plane. The second property is that graphene can be a semiconductor: the other 6 directions correspond to the energy gaps in the band structure. This means that electrons cannot flow along those paths without some external energy input.
Citations and resources:
https://www.physicscentral.com/explore/action/graphene.cfm
https://www.youtube.com/watch?v=eh3dA8xnZ4Y
https://www.youtube.com/watch?v=OdR0VqfSRdM
https://en.wikipedia.org/wiki/Electronic_properties_of_graphene
Figures:
Electronic band structure of graphene. In the plane made by the wavevectors in the x and y direction, the valence and conduction bands touch each other at six vertices (Dirac points). The right inset shows a closeup of the conic band structure near a Dirac point, showing that in those regions the dispersion relation is similar to that of a massless Dirac particle. The equation for the dispersion relation, where energy (E) is a function of the wavevector (k) in the x and y directions, is given below. https://physics.aps.org/articles/v4/25
Science details:
Carbon nanotubes are an allotrope of carbon. The structure of an ideal single-wall carbon nanotube (SWCNT) can be thought of as an infinitely long sheet of graphene rolled into a cylinder. The fixed length of the carbon-carbon bonds on the cylinder’s surface constrains the diameter to around 1 nm. Because of this small cross-section, electrons can only propagate along the tubular axis which makes the carbon nanotube a one-dimensional conductor. Two or three SWCNTs can be nested together to form multi-wall carbon nanotubes (MWCNTs). Some SWCNTs are metallic, whereas some are semiconductors, depending on their geometry. They have high tensile strength and thermal conductivity because of their nanostructure and the carbon bonds’ strength.
Citations and resources:
https://en.wikipedia.org/wiki/Carbon_nanotube
Figures:
3D renderings of single and multi-wall carbon nanotubes. https://worldofnanoscience.weebly.com/nanotube--carbon-fiber-overview.html
Science details:
The different configurations of SWCNTs are given by their “(n,m) notation”. This describes the hexagonal arrangement of carbon atoms which determines the electrical properties of the SWCNT. Imagine an infinitely long tube being sliced parallel to its axis and unrolled into a sheet of graphene. When unrolled, an atom (denoted by A) is split into two halves at opposite ends of the sheet (A1 and A2) and a line, which measures the tube’s circumference, is drawn connecting them. Two linearly independent basis vectors u and v are used to describe how the half atom A1 is connected to two of its nearest neighbor atoms. The vector that starts at A1 and connects to A2 is given by a linear combination: cₖ=nu+mv, where cₖ is called the “chiral vector”. The integers n and m give the SWCNT’s (n,m) notation and describe the tube’s geometry.
This hypothetical process can also be reversed. This would mean starting with a graphene sheet and constructing the chiral vector cₖ that points from A1 to A2, with the (n,m) notation corresponding to cₖ=nu+mv. The sheet would then be rolled into a tube, connecting A1 to A2, with the tube’s axis perpendicular to cₖ.
Citations and resources:
https://en.wikipedia.org/wiki/Carbon_nanotube
Figures:
Left: Diagram of a sheet of graphene (hexagonal lattice of carbon atoms), with the basis vectors of the plane given by u and v. Four arrows show four possible chiral vectors cₖ=nu+mv, with (n,m)=(1,3) (blue), and (3,3), (3,1), (4,0) (red). https://en.wikipedia.org/wiki/File:Nanotube_strip_master.pdf
Right: Diagram of a hypothetically unrolled carbon nanotube, the background is a desaturated hexagonal lattice of carbon atoms with the unrolled nanotube overlaid in saturated colors. Two halves of an atom A are marked as A1 (left) and A2 (right). The chiral vector connecting A1 to A2 is shown by a blue arrow which measures the circumference of the nanotube. The basis vectors in the plane are given by vectors u and v. Three parameters are given at the top right: d is the approximate diameter of the nanotube, α is the angle from u to cₖ, the chiral vector cₖ=nu+mv with (n,m) = (3,1). https://en.wikipedia.org/wiki/File:Nanotube_strip_%2B03_%2B01.pdf
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The three types of SWNTs are “zigzag”, “armchair”, and “chiral”. If the (n,m) nanotube has m=0 then it is a zigzag nanotube. If the (n,m) nanotube has n=m and m≠0 then it is an armchair nanotube. Chiral nanotubes have m>0 and m≠n (meaning zigzag and armchair nanotubes are achiral). If n=m, the SWCNT will be metallic (MWCNTs are always metallic). If n−m is a multiple of 3 and n≠m, then the nanotube is quasi-metallic with a very small band gap. Otherwise, it will be a semiconductor.
Citations and resources:
https://en.wikipedia.org/wiki/Carbon_nanotube
Figures:
Top: Diagrams of armchair (left), zigzag (middle), and chiral (right) single-wall carbon nanotubes.
Bottom: Schematic of a hexagonal lattice with three chiral vectors for each type of SWCNTs. The basis vectors given by a₁ and a₂, the three chiral vectors all start at (n,m)=(0,0). The zigzag nanotube’s vector ends at (9,0), and the armchair nanotube’s vector ends at (5,5). The chiral nanotube’s vector ends at the point C with (n,m)=(8,4) with the chiral angle denoted by θ and the tube axis is perpendicular to the chiral vector.
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Raman scattering is the inelastic scattering of photons by a material. When photons strike a molecule, many undergo Rayleigh scattering: photons are elastically scattered, meaning they have the same energy (frequency and wavelength) as the incident photons but change direction. Raman scattering occurs when the molecule gains or loses some of the incident photons’ energy, which changes the molecule’s vibrational mode. In both Raman and Rayleigh scattering the final state of the molecule has the same electronic energy as the initial state, but the vibrational energy will change in Raman scattering. The absorption of a photon excites the molecule to a virtual energy state before re-emission. In Stokes Raman scattering, vibrational energy is gained by the molecule and the emitted photon’s vibrational energy is lower than that of the incident photon. In anti-Stokes Raman scattering, the molecule loses vibrational energy and the emitted photon has higher vibrational energy than the incident photon.
Citations and resources:
https://en.wikipedia.org/wiki/Raman_scattering
Figures:
Left: Depiction of a molecule being struck by incident light (green, frequency=ν_incident) which is then scattered. In Rayleigh scattering, the emitted light (green) has frequency ν_scattered=ν_incident. In Raman scattering, the emitted light (red) has frequency ν_scattered≠ν_incident. Adapted from https://www.horiba.com/usa/raman-imaging-and-spectroscopy/
Right: Energy level diagram showing the states involved in Rayleigh and Raman scattering. The vibrational energy states are labeled from 0 to 4. Infrared absorption (leftmost blue arrow) involves excitation from 0 to 1. In Rayleigh scattering, the molecule is initially in state 0 then enters a virtual energy state (blue arrow) then returns to state 0 (red arrow). In Stokes Raman scattering, the molecule is initially in state 0 then enters the virtual energy state (blue arrow) then descends to state 1 (green arrow). In anti-Stokes Raman scattering, the molecule is initially in state 1 then enters the virtual energy state (blue arrow) then descends to state 0 (purple arrow). https://en.wikipedia.org/wiki/Raman_spectroscopy#/media/File:Raman_energy_levels.svg
Science details:
Raman spectroscopy can give information about the vibrational modes of molecules. In practice, the light source is usually a laser which directs monochromatic light onto a sample. The photons from the laser then interact with the sample (the molecular vibrations or phonons in the solid) which changes the energy of the scattered photons. Modern detectors are charge-coupled devices (CCDs) which capture the scattered light.
The Raman spectrum is the intensity of scattered light as a function of the frequency difference between the scattered and incident light, called the “Raman shift” (usually denoted by Δν). This is directly related to the shift in energy following the Raman scattering and can reveal information about the vibrational modes of the sample. These vibrational modes are unique to a molecule’s chemical bonds, therefore different molecules will have different Raman spectra. Analysis of the Raman spectrum can give information about a sample’s chemical impurities, mass density, elastic constants, doping, defects in its structure, number of graphene layers, nanotube diameter, chirality, curvature, electrical properties (such as metallicity or semiconductivity), and more.
Citations and resources:
https://en.wikipedia.org/wiki/Raman_spectroscopy
https://www.nanophoton.net/applications/nano-carbon/cnt-high-resolution
Figures:
Left: Schematic of a Raman spectroscopy setup. In the sample chamber, a laser beam is directed onto a sample using a focusing lens. The scattered light is directed to the entrance slit of a spectrometer using a beam splitter, filter, and focusing lens. In the spectrometer, the light is reflected onto a grating then into a CCD detector. https://en.wikipedia.org/wiki/File:Setup_Raman_Spectroscopy_adapted_from_Thomas_Schmid_and_Petra_Dariz_in_Heritage_2(2)_(2019)_1662-1683.png
_(2019)_1662-1683.png){kind=link}
Right: Raman intensity is plotted against Raman shift (in cm⁻¹) for a carbon nanotube. Three prominent peaks appear in the Raman spectrum: the radial breathing mode (RBM) which has the shortest peak, the D band, and the G band which has the highest peak. https://www.nanophoton.net/applications/nano-carbon/cnt-high-resolution
Science details:
Analysis of a carbon nanostructure’s Raman spectrum can give information about its chemical impurities, mass density, elastic constants, doping, defects in its structure, number of graphene layers, nanotube diameter, chirality, curvature, electrical properties (such as metallicity or semiconductivity), and more.
There are three significant features in the Raman spectrum that can characterize a carbon nanostructure: the radial breathing mode (RBM), D band, and G’ band. The RBM relates the diameter of a carbon nanotube to its optical transition energy. Both the D and G’ bands reveal information about the nanomaterial’s electronic and geometrical structure. The G’ band occurs during stretching of the carbon-carbon bonds in the material. This feature is similar in the Raman spectra of graphenes and nanotubes. Both the D band and the D’ band are used to identify disorder in the sp2 network of carbon structures such as diamondlike carbon, amorphous carbon, carbon nanofibers and nanotubes.
Citations and resources:
https://en.wikipedia.org/wiki/Raman_spectroscopy
https://www.nanophoton.net/applications/nano-carbon/cnt-high-resolution
Figures:
Raman spectra of different nanocarbons from Dresselhaus et al.: “Perspectives on Carbon Nanotubes and Graphene Raman Spectroscopy”. Raman intensity is plotted against Raman shift for several nanocarbons, listed from top to bottom: graphene, highly oriented pyrolytic graphite (HOPG), single-wall nanotube (SWNT), damaged graphene, single-wall nanohorn (SWHN), and amorphous carbon. https://www.hindawi.com/journals/isrn/2012/234216/fig5/
Slides by: Katherine Savard