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X/n c. 0. 1. n c -k. The Effect of Size on Properties. Scaling Laws in 1-, 2-, and 3-Dimensions. “Labors of the Months” (Norwich, England, ca. 1480). The ruby color is probably due to embedded gold nanoparticles.). David Stroud, OSU Physics.

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Presentation Transcript
slide1

X/nc

0

1

nc-k

The Effect of Size on Properties

Scaling Laws in 1-, 2-, and 3-Dimensions

slide2
“Labors of the Months” (Norwich, England, ca. 1480). The ruby color is probably due to embedded gold nanoparticles.)

David Stroud, OSU Physics

the lycurgus cup glass british museum 4 th century a d
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)

lycurgus cup illuminated from within
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

what is the origin of the color answer surface plasmons
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.

slide9

Length scale relates differently to the number of particles for 1D, 2D, and 3D growth

n

n2

n3

Length Scale 

slide11

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.

slide12

-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

slide13

-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

slide14

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

slide15

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

slide16

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