Symmetry, Fullerenes, Nanotechnology and Other Stuff · Symmetry, Fullerenes, Nanotechnology and...
Transcript of Symmetry, Fullerenes, Nanotechnology and Other Stuff · Symmetry, Fullerenes, Nanotechnology and...
Symmetry, Fullerenes, Nanotechnology and Other Stuff H. C. Dorn
Virginia Tech
Alpha helix Protein St. Etienne du Mont (Paris) Spiral Staircase (Tel Aviv)
M. Hargittai and I. Hargittai Visual Symmetry,
World Scientific, 2009
University of Virginia, February 12, 2011
neon.otago.ac.nz/chemlect/chem203/symmetrylectures/molecularsymmetry.pdf
Symmetry Operation Decision Tree
120! Rotation Three-fold, C3
90! Rotation Four-fold, C4
1 3
1 2 3 2
Rotational Symmetry Elements
Examples of Rotational Symmetry
Automobiles, Planes, and Ships M. Hargittai and I. Hargittai
Visual Symmetry, World Scientific, 2009
Symmetry and Music
J. S. Bach Contrapunctus
XVIII
B. Bartok
Microcosmos
6-Fold Rotational Symmetry of Snow Flakes
M. C. Escher 1893-1972
Symmetry in Architecture and Art
Buckminster Fuller
1895-1983
M. Hargittai and I. Hargittai Visual Symmetry,
World Scientific, 2009
Chirality “Handedness”
Nearly Mirror (Bilateral) Symmetry of Orchids:
Doubling the left-hand side of
orchid picture (middle)
Doubling the right-hand side of
orchid picture (middle)
M. Hargittai and I. Hargittai Visual Symmetry,
World Scientific, 2009
Doubling the left-hand side of Alan A. MacKay’s middle picture
Doubling the right-hand side of Alan A. MacKay’s
middle picture
“Less Perfect” Mirror Symmetry of Alan L. Mackay’s Picture
Mirror Symmetry of the Human Face
M. Hargittai and I. Hargittai Visual Symmetry,
World Scientific, 2009
Chirality of Molecules
Louis Pasteur 1822-1895
Sodium Ammonium Tartrate Crystals from Wine Lees
L(+)tartaric acid (most common) and D(-) tartaric acid
M. Hargittai and I. Hargittai Visual Symmetry,
World Scientific, 2009
Right Hand Version Left Hand Version
Ethambutol
Treats tuberculosis C a u s e s blindness
Penicillamine Treats joints V e r y toxic
Naproxen
Reduces pain, inflammation T o x i c for the liver (but risks heart disease)
Propxyphene*
Pain reliever D a r von Novrad Cough medicine
Norgestrol No harmful effect C o n t r a c eptive
Asparagine
Bitter S w e e t
Carvone Caraway sme l l S p e a r m i nt smell
Limonene
Orange sm e l l P i n e smell *Note that the names of the respective medications are each other’s mirror images, Darvon® versus Novrad®
Molecules, Medical Drugs, and Chirality
M. Hargittai and I. Hargittai Visual Symmetry,
World Scientific, 2009
Left-Handed and Right handed Carvone: Chiral Mirror Image Molecules with Different Odors
Molecules, Walnuts, and Symmetry
M. Hargittai and I. Hargittai Visual Symmetry,
World Scientific, 2009
Nanotechnology
The Big
and
Small of it
Buckyballs and Nanotechnology!
Richard Feynman “There’s Plenty of Room at the Bottom”
Cal Tech, Dec. 29, 1959
Origins of Nanotechnology
Why can’t we write the entire 24
Volumes of the Encyclopedia
Brittanica on the head of a pin?
How do we write small?
Miniaturizing the Computer?
Problems of Lubrication
A hundred Tiny Hands
Atoms in a Small World
Nanotechnology: A Matter of Size and Control
1 nm = 10-9 m Think very small (“nano” = 1 billionth of a meter) = 10 H atoms; or, 1 human hair = 100,000 nanometers!
The precise, highly controlled assembly of atoms and molecules into new materials and devices with unique, possibly revolutionary properties
Individual iron atoms positioned in an oval “corral” on a copper surface, using a scanning tunneling microscope --IBM Almaden Research Center
Carbon Nanotubes • 100 times stronger than steel • Conduct electricity better than copper • Conduct heat better than diamonds • Depending on current, can either: - Act as a metal (conductor) - Act as semiconductor (transistor) • Markets now exist for nanotubes as raw material
Single wall carbon nanotube with attached protein receptors
Allotropes of Carbon
6
C 12.011
CARBON Diamond
Graphite Rods New Carbonaceous Nanomaterials
Smalley, Kroto, and Curl (1984-5)
Large Fullerenes
Laser Apparatus
C60, Fullerenes, BuckyBalls! 0.2 m 0.7 nm
Dr. Richard Smalley,
Nobel Laureate,1996
Leukemia Victim,
October 2005
Fullerenes (Buckyballs)
Icosahedral (Ih) Fullerene C60:
120 Symmetry Operations !
M. Hargittai and I. Hargittai Visual Symmetry,
World Scientific, 2009
Solubility of C60 and C70
C60 dissolved in toluene
C70 dissolved in toluene
graphite in toluene (not dissolved)
C70 dissolved in toluene
Green food coloring in water
C60 dissolved in ortho- dichlorobenzene
Slide 19
Hexagon and Pentagon Motifs
Devil’s Postpile
National Monument, CA
Euler: Properties of Polyhedra
! Euler’s Theorem ! " + f = e + 2 f = faces e= edges " = vertices
For a fullerene with n carbons, Cn n = "#e = 3n/2 f = n/2 + 2
Dodecahedron C20
Euler (Continued)
(5p + 6h)/3 = n
f = p + h (p =pentagons and h = hexagons)
p + h = n/2 + 2
Solution is p = 12, h = n/2 -10
Fullerene C60 Diameter =0.7 nm
120 Symmetry Elements !
Soccer Ball Diameter = 0.3 m
Carbon Nanotubes
Single-wall Carbon Nanotubes:
A Major Application
TU Delft/Gripp Design!Nature 412 (2001)
Two-dimensional imaging of electronic wavefunctions in carbon nanotubes
S.G. LEMAY, et al. Nature 412, 617 - 620 (2001)
Single Walled Carbon Nanotubes (Don Bethune, IBM)
Jan ‘93: 2% Co burn – “rubbery soot” and “spider web structures”
Single Wall Carbon Nanotubes
0 1 2 3 Diameter (nm)
- Bethune, et al., Nature 363, 605 (1993) • Iijima & Ichihashi, Nature 363, 603 (1993) - Fe catalyst, with methane
CNano’09 Conference, Santorini Island October, 2009
Nanotube Types
Armchair, Metal, n=m; n=integer, m=o, zigzag; n not equal to m, chiral (n-m multiples of 3, narrow bandgap)
The structure of a nanotube can be specified by a vector, (n,m), which defines how the graphene sheet is rolled up. To produce a nanotube with the indices (6,3), say, the sheet is rolled up so that the atom labelled (0,0) is superimposed on the one labelled (6,3). It can be seen from the figure that m = 0 f all zig-zag tubes,
while n = m for all armchair tubes.
Nanotube Structure (Graphene Sheet Roll-Up) http://ipn2.epfl.ch/CHBU/NTbasics1.htm
NASA Space Elevator
Carbon Nanohorns, Nano Onions, and Graphene
Carbon Nanohorns
Nano Onions
Graphene
Nobel Prize 2010
Geim and Novoselov
Gedanken Experiment in Science Education
Gedanken Horse Race (t=0)
Gedanken Horse Race (t= $)
Gedanken Horse Race (t= $)
Gedanken Horse Race (t= 2$)
Gedanken Horse Race (t= 2$)
Time Symmetry T: t (-t)
Magnetic Resonance Imaging (MRI)
Over 150 million MRI Diagnostic Procedures/Year Between
25-50% Require the use of MRI Contrast Agent (over 1 billion $/
year market for MRI Contrast Agents