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



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)



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



Chirality of Molecules

Louis Pasteur 1822-1895

Sodium Ammonium Tartrate Crystals from Wine Lees

L(+)tartaric acid (most common) and D(-) tartaric acid



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



Left-Handed and Right handed Carvone: Chiral Mirror Image Molecules with Different Odors

Molecules, Walnuts, and Symmetry



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 !



Solubility of C60 and C70

C60 dissolved in toluene


graphite in toluene (not dissolved)


Green food coloring in water

C60 dissolved in ortho- dichlorobenzene

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= 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

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