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Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr. Ron Rusay Diablo Valley College University of California, Berkeley / Lawrence Livermore National Laboratory

Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

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Page 1: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Nanotechnology: a chemist’s constructivist view

Mathematical Modeling, Technology and Bridging to the

Nano-realm in Teaching Undergraduate Chemistry

Dr. Ron Rusay

Diablo Valley College University of California, Berkeley / Lawrence Livermore

National Laboratory

Page 2: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Nanotechnology : Perspectives & Perceptions

• How small is small?• The width of a human hair is ~ 50,000 nanometers

nanometer = 1 billionth of a meter (1/1,000,000,000 m; i.e., 50,000 x 10 -9 meters) • It takes about 200 human hairs lined up side by side to equal 1 cm

….more than 500 per inch.

QuickTime™ and aVideo decompressor

are needed to see this picture.

Page 3: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

1/50 of ~ 50,000 nanometers

Page 4: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

What is considered too large for the nano realm?Powers of 10 (10 x)

http://www.eamesoffice.com/powers_of_ten/powers_of_ten.htmlhttp://www.powersof10.com/

Earth = 12,760,000 meters wide (12.76 x 10 6), 12.76 million meters

Plant Cell = 0.00001276 meters wide (12.76 x 10 -6) (12.76 millionths of a meter) (12,760 nanometers!)

Page 5: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Nanotechnology: A Brief Chronology

• Feynman’s miniaturization: prescience and seminal views (1959)http://www.zyvex.com/nanotech/feynman.html

• Nanotechnology, (Journal’s first issue: 1990)http://www.iop.org/EJ/journal/0957-4484

• Curl, Kroto, Smalley: Nobel prize (1996); Fullerene, Nano tubes, http://www.nobel.se/chemistry/laureates/1996/

• National, Regional, Local Initiatives eg.– US: http://www.nano.gov/

– UK: http://www.nano.org.uk/

– Molecular Foundry (LBL): http://www.foundry.lbl.gov/ – Nano High School: http://www.lbl.gov/nanohigh/nanoscience_links.html

Page 6: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

“Nanotechnology”• Regarded as < 1,000 nanometers ~1/50 the diameter of a

human hair. (Basically anything less than a micron (10-6 m). Chemists typically

think in mental views and images of < 1 nanometer.)

• Can be defined as the science of arranging and re-arranging atoms. (Manufacturing at a molecular level.)

• Two commonly used terms that broadly describe Nanotechnology: – Positional assembly

http://www.zyvex.com/nanotech/CDAarticle.html

– Self replication http://www.zyvex.com/nanotech/selfRep.html

Page 7: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Nano-scale: Models of Atoms & Molecules

• Rutherford (1913-1917)• Atoms, molecules, and nucleii

Page 8: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

• 1 nm = 10 Å• An atom vs. a nucleus ~10,000 x larger

~ 0.1 nm

Nucleus =1/10,000of the atom

Anders Jöns Ångström(1814-1874)

1 Å = 10 picometers = 0.1 nanometers = 10-4 microns = 10-8 centimeters

Page 9: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

• Resultant Molecular Dipoles > 0• Solubility: Polar molecules that

dissolve or are dissolved in like molecules

Molecular Size, Shape & PropertiesOzone and Water

• The Lotus flower• Water & dirt repellancy

0.1278 nm

Page 11: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

DNA: Size, Shape & Self Assemblyhttp://www.umass.edu/microbio/chime/beta/pe_alpha/atlas/atlas.htm

Views & Algorithms

10.85 Å10.85 Å

QuickTime™ and aAnimation decompressorare needed to see this picture.

Several formats are commonly used but all rely on plotting atoms in 3 dimensional space; .pdb is one of the most popular.

Page 13: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

http://www.rcsb.org/pdb/

PROTEIN DATA BANK

What are PDB files? http://chemistry.Gsu.EDU/glactone/PDB/pdb.htmlThe PDB format (Protein Data Bank), from the Research Collaboratory for Structural Bioinformatics) is a standard file format for the XYZ coordinates of atoms in a molecule.

A few lines from a PDB file for a DNA base pair structure AUTHOR GENERATED BY GLACTONESEQRES 1 A 1 GSEQRES 1 B 1 CATOM 1 P G A 1 -6.620 6.196 2.089ATOM 2 OXT G A 1 -6.904 7.627 1.869ATOM 3 O2P G A 1 -7.438 5.244 1.299ATOM 4 O5' G A 1 -5.074 5.900 1.839ATOM 5 C5' G A 1 -4.102 6.424 2.779ATOM 6 C4' G A 1 -2.830 6.792 2.049ATOM 7 O4' G A 1 -2.044 5.576 1.839ATOM 8 C3' G A 1 -2.997 7.378 0.649

The last three columns are the XYZ coordinates of the atoms. PDB format can be applied to any molecule, very small to very large. It includess enormous on-line libraries of molecules.

Page 15: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Proteins: Size, Shape & Self Assemblyhttp://www.stark.kent.edu/~cearley/PChem/protein/protein.htm

Page 16: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Protein Shape: Forces, Bonds, Self Assembly,Folding

10-40kJ/mol

700-4,000kJ/mol

150-1000kJ/mol

0.05-40kJ/mol

Ion-dipole(Dissolving)40-600kJ/mol

Page 17: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Globular proteins:A larger number of atoms rolled into relative small volumes

RNA polymerase II-transcription factor J. Biol. Chem., Vol. 274, Issue 11, 6813-6816, 1999

The yellow dashed line is ~ 110-Å

Protein sizes are most often referred to by their molecular masses (daltons; 1 amu = 1 dalton),not by their dimensions because of their globular nature.

Page 18: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

The Ribosome: RNA Proteins

227 Å

Crystal structure of a part of the ribosome at 5.5 Å Resolution. (1GIX): Contains the 30S Ribosome Subunit, three tRNA, and mRNA molecules

(2001) Noller, Ramakrishnan, Steitz~ 50 proteins + 1,000s nucleotides

Page 19: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Interactions:Large proteins (Enzymes) with small molecules (Substrates)

Page 21: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Three different smell receptors.Three different smell receptors.

Page 22: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Modeling and SmellModeling and SmellFour different molecules fitting the same smell receptor.Four different molecules fitting the same smell receptor.

Page 24: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Enzyme interaction: neurotransmission

The interaction of a globular protein, The interaction of a globular protein, acetylcholinesterase, with a relatively small acetylcholinesterase, with a relatively small molecule, acetylcholine. molecule, acetylcholine.

Richard Short (Cornell University)

QuickTime™ and aYUV420 codec decompressorare needed to see this picture.

Page 25: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Acetylcholine, Nerves & NeurotransmissionThe Neuron: Shapes and Spaces

QuickTime™ and aGIF decompressor

are needed to see this picture.

Page 26: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Acetylcholine: OP Pesticides and Nerve gases

Page 27: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Trypsin: Hydrolysis

Acetylcholinesterase works in Acetylcholinesterase works in a similar way to the digestion a similar way to the digestion proteins.proteins.

Page 28: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Another Way to Inhibit EnzymesThe Importance of Shape

Statins:Inhbiting cholesterol biosynthesis

Page 29: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Hemoglobin and Oxygen TransportAn allosteric effect & sickle cell anemiahttp://ep.llnl.gov/msds/Columbia/slide8-3.html

BPG

Oxygen

Page 30: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Heme

NN

NN NN

NN

Fe 2+

HH33CC

HH33CC CHCH33

CHCH33

CHCH22CHCH22COCO22HH

CHCH CHCH22

HH22CC CHCH

HOHO22CCHCCH22CHCH22

• Heme is the coenzyme that binds oxygen in hemoglobin (transport) and myoglobin (storage in muscles)

• Molecule surrounding the iron is a type of porphyrin. • Important in Photodynamic therapy (PDT)• The U.S. would still be a British colony except for porphyria, a medical condition in “blue bloods”.

Page 31: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Myoglobin

N-terminusN-terminus

C-terminusC-terminus Heme

Page 32: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

myosin-actin: muscle

Some Examples of Structural Proteins http://info.bio.cmu.edu/courses/03231/ProtStruc/ProtStruc.htm

collagen: connective tissue

Michael Ferenczi

Page 33: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Mechanical proteinsPathogens & Cell Invasion

http://ep.llnl.gov/msds/Staph-infection/infection.html

Streptococcus pyogenes96,000 x

Vincent A. Fischetti Ph.D., Rockefeller University

Page 34: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Human’s total ~ 100 x 10 6 immunoproteins

AntibodiesProlific Immunoproteins

Immunoglobin

Human Genome ~30,000 proteins

Combinatorial syntheses from libraries of 250, 10, and 6 possible contributors

Page 35: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Gecko & it’s toe, setae, spatulae6000x Magnification

http://micro.magnet.fsu.edu/primer/java/electronmicroscopy/magnify1/index.html

Geim, Nature Materials (2003) Glue-free Adhesive100 x 10 6 hairs/cm2

Full et. al., Nature (2000)5,000 setae / mm2

600x frictional force; 10-7 Newtons per seta

Page 36: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

The “Lotus Effect” Biomimicry

http://www.bfi.org/Trimtab/spring01/biomimicry.htm

• Lotus petals have micrometer-scale roughness, resulting in water contact angles up to 170°

• See the Left image in the illustration on the right.

Wax

Page 37: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

The “Lotus Effect” Biomimicry

http://www.sciencemag.org/cgi/content/full/299/5611/1377/DC1

• Isotactic polypropylene (i-PP) melted between two glass slides and subsequent crystallization provided a smooth surface. Atomic force microscopy tests indicated that the surface had root mean square (rms) roughness of 10 nm.

• A) The water drop on the resulting surface had a contact angle of 104° ± 2

• B) the water drop on a superhydrophobic i-PP coating surface has a contact angle of 160°.

Science, 299, (2003), pp. 1377-1380, H. Yldrm Erbil, A. Levent Demirel, Yonca Avc, Olcay Mert

Page 38: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

ColloidsHydro- philes & phobes

Page 39: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Hydrophilic and Hydrophobic

Colloids

Page 40: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Colloids

Page 41: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Bridging to the Nano realmMolecular Modeling: Visualizations & Predictions

Modeling Methods:• Numerical Methods

• Integral Method

• Ab Initio Methods

• Semi-Empirical MO-SCF Methods

• Approximate MO Methods 

Page 42: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Web MOhttp://c4.cabrillo.cc.ca.us/projects/webmo/index.html

login: dvc1 password:chem

• Web MO Project: undergraduate molecular modeling college consortium

• Web-based, free, instructional service• Uses MOPAC 7 & GAMESS 2000, others

to be added• Modeling tools, activities and lessons are

under construction

Page 43: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Web MOhttp://c4.cabrillo.cc.ca.us/projects/webmo/index.html

login: dvc1 password:chem

• Output:– Dipole moment– Bond Orders– Partial Charges– Vibrational Modes– Molecular Orbitals– Ultraviolet-Visible-Infrared Graphics– NMR Chemical Shifts

Page 44: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

0.143 nm

Web MO Visual Output

Color coded electron density distribution: blue-lowest, red highest, green balanced

Page 45: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

• 1) S-(+)- caraway1) S-(+)- caraway R-(-)- spearmint R-(-)- spearmint

• 2) Ambrox-Ambergris

http://ep.llnl.gov/msds/orgchem/Chem226/Mol-Modl-II.html#ambergris

Examples of Planned Web MO Projects

Page 46: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

• 3) d- and l- tartaric acid

Examples of Planned Web MO Projects

Page 47: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Modeling & Energy Calculations of Acetylene Lawrence Berkeley Laboratory (LBL)

Example of a Web MO Project

C

C

H

H

Page 48: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

C

C

H

H

Calculated image (Philippe Sautet)

orbital

pz

TIP

H

O+

Imaging: acetylene on Pd(111) at 28 K

Molecular Image Tip cruising altitude ~700 pmΔz = 20 pm

Surface atomic profile

Tip cruising altitude ~500 pm

Δz = 2 pm

1 cm(± 1 μm)

The STM image is a map of the pi-orbital of distorted acetylene

Why don’t we see the Pd atoms?Because the tip needs to be very close to image the Pd atoms and would knock the molecule away

If the tip was made as big as an airplane, it would be flying at 1 cm from the surface and waving up an down by 1 micrometer

M. Salmeron (LBL)

Page 49: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Excitation of frustrated rotational modes in acetylene molecules on Pd(111) at T = 30 K

Tip

e-

((( ) ( )))

M. Salmeron (LBL)

QuickTime™ and aYUV420 codec decompressorare needed to see this picture.

Page 50: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

0.1

1

10

100

-300-250-200-150-100-500Tip Bias (mV)

Log

(Hop

s/s) 253 pA

-37mV

0

8

16

24

32

0 50 100 150 200 250 300 350 400 450current (pA)

rota

tion

s p

er

secon

d

1.72 seconds

V = 20 mV

0

50

100

150

200 1

2,3

Pd

Pd

Pd1

23

Pd

Pd

Pd

2

Measuring the excitation rate

Tip fixed at position 1:

Curr

ent

(pA

)

((( ) ( )))

x

Center of molecule

M. Salmeron (LBL)

Page 51: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Excitation of translations of C2H2 molecules:

R = 150 M R = 94 M R = 0.55 G

Rotation by electron excitation:

R = 10.5 M

Translation by direct contact (orbital overlap):

z ~ +0.8 Åz ~ -0.2 Å

z ~ - 1 Å

Tip

z

((( ) ( )))

Trajectories of molecule pushed by the tipM. Salmeron (LBL)

Page 52: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

http://www.foundry.lbl.gov/

• Inorganic Nanostructures (A.P. Alivisatos)

• Nanofabrication (J. Bokor)

• Organic Polymer/Biopolymer Synthesis (J.M.J. Frechet)

• Biological Nanostructures (C.R. Bertozzi)

• Imaging and Manipulation (M.B. Salmeron)

• Theory of Nanostructured Materials (S.G. Louie)

Page 53: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Invited speakers:

• Pat Dehmer, Office of Basic Energy Sciences

• Paul Alivisatos, Director, Molecular Foundry

• Grant Willson, University of Texas at Austin

• Roberto Car, Princeton University

• Vicki Colvin, Rice University

• Mike Roukes, California Institute of Technology

• Mike Garner, Intel (invited)

___________________________

• Capabilities of the Foundry facilities and affiliated laboratories

• Types of projects that could be pursued in the facilities and affiliated laboratories

• Procedures for writing and review of proposals

• Logistics of working at the Foundry• A special session exploring the application of single molecule characterization and

manipulation techniques•Sessions dedicated to issues related for the call for proposals for research in the two-year

ramp-up period while the Foundry building is under construction.

Page 54: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Crystals for the ClassroomBridging the realms of the macro and atomic/nano scale

http://crystals.llnl.gov

• A modular collection of teaching-learning tools for undergraduate chemistry courses that can be adapted to teach various Science, Technology, Engineering and mathematics (STEM) topics and concepts

Page 55: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

• Chemistry lessons are embedded in the story of NIF ( The National Ignition Facility) http://crystals.llnl.gov/nif-kdp-frameset.html

• Learning activities were developed relative to the context of the research and science behind NIF.

Crystals for the ClassroomBridging the realms of the macro and atomic/nano scale

http://crystals.llnl.gov

Page 56: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

• Web based, distributed freely • Activities provide a diverse collection that support a wide variety of

learning and teaching styles: http://ep.llnl.gov/msds/Chem120/learning.html

Crystals for the ClassroomBridging the realms of the macro and atomic/nano scale

http://crystals.llnl.gov

Page 57: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Instructor - StudentActivities, Exercises & Resources

http://crystals.llnl.gov• Seeing - Hearing - Doing

• Powerpoint Presentations

• Visualizations: Time lapsed Growth

QuickTime™ and aSorenson Video decompressorare needed to see this picture.

Page 58: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

• Seeing - Hearing - Doing

• Powerpoint Presentations

• Visualizations: Time lapsed Growth

• Simulations: Fusion - Fission

Instructor - StudentActivities, Exercises & Resources

http://crystals.llnl.gov

Page 59: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

• Seeing - Hearing - Doing• Powerpoint Presentations• Visualizations: Time lapsed Growth• Simulations: Fusion - Fission• President Truman’s Announcement• Numerical and Graphical Problems• Student Worksheets• Glossary• Debate on Nuclear Energy• Writing Exercises• Interpreting Research Data• Experimentation

Instructor - StudentActivities, Exercises & Resources

http://crystals.llnl.gov

Page 60: Nanotechnology: a chemist’s constructivist view Mathematical Modeling, Technology and Bridging to the Nano-realm in Teaching Undergraduate Chemistry Dr

Acknowledgements

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