Some References: Colloids – A lot of what I presented is in -"Thermodynamics and Hydrodynamics of Hard Spheres; the role of gravity.", P. M. Chaikin, in.

Some References:Colloids – A lot of what I presented is in -"Thermodynamics and Hydrodynamics of Hard Spheres; the role of gravity.", P. M. Chaikin, in Soft and Fragile Matter, Nonequilibrium Dynamics, Metastability and Flow, ed. By M. E. Cates and M. R. Evans, (Institute of Physics Publishing, London, 2000) and there are more general references and it is a good volume. Some of our stuff: Z. Cheng, W.B. Russel, and P.M. Chaikin "Controlled growth ofhard-sphere colloidal crystals", Nature 401, 893 - 895 (1999)."Crystallization Kinetics of Hard Spheres in Microgravity in the Coexistence Regime: Interactions between Growing Crystallites", Zhengdong Cheng, P. M. Chaikin,Jixiang Zhu, W. B. Russel, and W. V. Meyer, Phys. Rev. Lett. {\bf 88}, 015501 (2002)."Colloidal hard-sphere crystallization kinetics in microgravity and normal gravity", ZD Cheng ,JX Zhu ,WB Russel ,WV Meyer ,PM Chaikin,APPLIED OPTICS {\bf 40}, 4146-4151 (2001). "Phase diagram of hard spheres", Cheng Z, Chaikin PM, Russel WB, Meyer WV, Zhu J, Rogers RB, Ottewill RH, MATERIALS \& DESIGN,{\bf 22}, 529-534 (2001).Phonons in an Entropic Crystal Zhengdong Cheng, Jixiang Zhu,William B. Russel, P. M. Chaikin, Phys. Rev. Lett. 85, 1460 (2000)Nature of the divergence in low shear viscosity of colloidal hard-sphere dispersions, Cheng ZD, Zhu JX, Chaikin PM, Phan SE, Russel WB, PHYSICAL REVIEW E65 (4): art. no. 041405 Part 1 APR 2002  Good diblock references:F. S. Bates, and G. H. Fredickson, Physics Today Feb, 1999F. S. Bates, Science, 251, 898 Some of our stuff is in:C. Harrison, D.H. Adamson, Z. Cheng, J.M. Sebastian, S.Sethuraman, D.A. Huse, R.A. Register, and P.M. Chaikin,"Mechanisms of Ordering in Striped Patterns", Science, 290,1558-1560 (2000).R. R. Li, P. D. Dapkus, M. E. Thompson, W. G. Jeong C.Harrison, P. M. Chaikin, R. A. Register,D. H. Adamson, DenseArrays of Ordered GaAs Nanostructures by Selective Area Growth onSubstrates Patterned by Block Copolymer Lithography, APPL PHYSLETT 76: (13) 1689-1691 (2000)  

Diblock Copolymer Nanolithography

PB

50 nm

SILICONSUBSTRATE

PB

PB

SILICON

60 nm

Lamellae

Cylinders Spheres

polymer B

Diblock CopolymerIn bulk and at equilibrium, diblock copolymers exhibitmicrophase separated morphologies due to theincompatibility between two blocks and connectivityconstraint, and self-assemble in well ordered structures.

Spherical

Cylindrical

Lamellar

SA

CA

L~10Disordered

0.5 fA

XN

SA CA

LSBCB

X=Flory Huggins Interaction ParameterN=Degree of PolymerizaionfA=Volume Fraction of A Block

Monolayers on a substrate

PB

50 nm

SILICON

collaboration with R.R. Li, P.D. Dapkus, and M.E. Thompson (USC)

use MOCVD to selectively grow GaAs dots on substrate, through holes in removable “mask”

GaAs GaAs

GaAs GaAs

ozone

CF4 RIE

MOCVD

wet etch

polymer SiNx (15 nm)

GaAs GaAs

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 300

10

20

30

40

50

60

70

height above SiNx (TMAFM)

dot diameter(FESEM)

GaAs (001)

TMAFM tip

GaAs Dots Have Narrow Size Distribution

Num

ber

of D

ots

diameter:23 ± 3 nm

overall height:14 ± 2 nm

tapping-mode atomic force microscopy (TMAFM)

103

104

105

106

102

103

2(nan

om

eter

s)

Annealing Time (seconds)10

310

410

510

6

102

103

-1/2 (

nan

om

eter

s)

Annealing Time (seconds)

Orientational Correlation length Average Distance between Disclinations

2 ~ -1/2 t1/4

466 K395 K

Fred, 0.5 pointblur. Figure 2.

A B

C

500 nm

S U B S T R A T E

ISLAND(3 cylinder layers)OFF-ISLAND

(two cylinder layers)

D

DEPTH PROFILING AN ISLAND

MIDDLETOP

BOTTOM

Nature Feb. 6,1965

Topological equivalent

For Circular area two loops are essential

Two Loops Three loops and one Triradius

Disclinations : “5” and “7”

Analysis of a micrograph

100 nm

0 /3

Steps : 1. Locate Spheres2. Triangulate Lattice3. Locate disclinations4. Locate dislocations5. Create orientation field6. Color-map

09169878

Measuring Correlation Length 6

• All sphere centers are located and the inter-sphere triangulation lattice produces the local “bond-orientation” angle.

• We define e6i(x) as our hexatic order parameter to calculate 6, similar to 2.

~130 nm~4.5 d0250 nm

Correlation FunctionImages

0 500 1000

0.0

0.2

0.4

0.6

0.8

1.0

B 09169878

g6(r)~e(-r/)

nanometers

Time Dependence of Correlation Length

104

106

108

10

100

6

Time/(a2/D)

104

105t1/4shift data by aT,

taking 398K as reference

t/aT

(nm)

ColorLookup Table

40nmStep Edge

dislocations

“perfect alignment with Mask and Pressure

Substrate

Without mask

Mask

Substrate

With mask

PS/PI

S. Chou C. Harrison, P. Chaikin, & R. Register

Effect of Diblock Copolymers on the Quantum Hall Effect

The periodic modulation induced by the triangular polymer lattice lifts the degeneracy of the Landau levels, creating a commensurability-related sub-band structure (Hofstadter butterfly) which should cause extra peaks to appear in the longitudinal resistance.

Hal

l Res

ista

nce

Rxy

(k

)30

25

20

15

10

5

0

Longitudinal R

esistance Rxx (k

)

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Magnetic Field B (T)0 2 4 6 8 10 12

T=0.3Kunpatterned

Longitudinal R

esistance Rxx (k

)

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Magnetic Field B (T)0 2 4 6 8 10 12

T=0.3Kpatterned Vg=0.1

Chaikin, Register, Shayegan, Bhatt

a

1 m