The Effect of Size on Properties

1. X/nc 0 1 nc-k The Effect of Size on Properties Scaling Laws in 1-, 2-, and 3-Dimensions

2. “Labors of the Months” (Norwich, England, ca. 1480). The ruby color is probably due to embedded gold nanoparticles.) David Stroud, OSU Physics

3. The Lycurgus Cup (glass; British Museum; 4th century A. D.) David Stroud, OSU Physics When illuminated from outside, it appears green. However, when Illuminated from within the cup, it glows red. Red color is due to very small amounts of gold powder (about 40 parts per million)

4. Lycurgus Cup illuminated from within When illuminated from within, the Lycurgus cup glows red. The red color is due to tiny gold particles embedded in the glass, which have an absorption peak at around 520 nm

5. What is the origin of the color? Answer: ``surface plasmons’’ • An SP is a natural oscillation of the electron gas inside a goldnanosphere. • SP frequency depends on the dielectricfunction of the gold, and the shape of the nanoparticle. (not to scale) Ionic background electron sphere Electron cloud oscillates with frequency of SP; ions provide restoring force.

7. Sean Murdock, Executive Director, AtomWorks 3/31/03

8. Sean Murdock, Executive Director, AtomWorks 3/31/03

9. Length scale relates differently to the number of particles for 1D, 2D, and 3D growth n n2 n3 Length Scale 

10. Carbon Chains, Growth in 1-D

11. Which structure is more stable at infinity? ―≡―≡―≡―≡― or = = = = = = = = = acetylenic cumulenic avg. bond enthalpy = 141.9 kcal/mol avg. bond enthalpy = 146.7 kcal/mol Hartree-Fock (Eeq) more stable by 3.9 kcal/mol per carbon avg. bond enthalpies: C-C is 83.2 kcal/mol, C=C is 146.7 kcal/mol, C≡C is 200.5 kcal/mol Brown T.L., LeMay H.E., and Bursten, B.E. Chemistry The Central Science 8th Ed. Karpfen, A. Ab-initio studies on polymers I: The linear infinite polyyne, J. Phys. C: Solid State Phys. Vol. 12, 1979.

12. -CC-CC-CC-CC-CC-CC-CC- =C=C=C=C=C=C=C=C=C=C=C=C=C=C= Infinitely-Long Linear Carbon Chains Ab-Initio (G3) and PM3 Free Energy cumulenic -132.0 kcal/mol -131.3 kcal/mol Polyyne acetylenic -134.9 kcal/mol PM3 -134.6 kcal/mol Polyene pure -long carbon  1/Length # of Carbon Atoms

13. -CC-CC-CC-CC-CC-CC-CC- Geometry =C=C=C=C=C=C=C=C=C=C=C=C=C=C= G3 theory - MP2(full)/6-31G* eq. geometry single bond double bond 10 8 6 triple bond 4 2

14. 2-D Growth PM3 Graphene Sheet RC-C= 1.408(9)Å 6 13 22 33 70 48 30 61 16 46 33 22 13 6 1/length number of C atoms

15. 3-D Growth volume per Ni atom=VNi AW density (1 mol/6.022x1023 atoms)(1 Å/1x10-8 cm)3 (58.69 g/mol)/(8.90 g/cm3)= 11.0 Å3 11.0 Å3 =(4/3) rNi3 [3(11.0 Å3 )/(4)]1/3 =1.38 Å=rNi cluster volume Vclusrter nNiVNi (4/3)rcluster3 =nNi (4/3)rNi3 rcluster3 =nNi rNi3 rcluster=nNi1/3rNi 1/length number of Ni atoms

16. X/nc 0 1 nc-k Extrapolating finite clusters to bulk for k-dimensional growth X=ΔGAB, -CC-CC-CC- X=mass, H-CC-CC-CC-H X=mass, -CC-CC-CC- X=ΔGAB, H-CC-CC-CC-H

19. energy of quantum unit of light the PHOTON

43. Electron in a 8x8x8 Bohr Box (0.52 Ang./Bohr) DVR_3Dgeneral_11b11b11.mcd