Structure Formation, Melting and the
Optical Properties of
Gold/DNA Nanocomposites
Sung Yong Park and David Stroud
Department of Physics, Ohio State University,
Columbus, OH 43210.
Work Supported by NSF DMR04-13395 and DMR01-04987.
Calculations carried out using facilities of the Ohio
Supercomputer Center
1. Introduction
DNA/Au nanoparticle colloids and linking strands
Linker DNA
Linker DNA
R. Elghanian, et. al., Science 277, 1078 (1997).
R. Jin, et. al, J. Am. Chem. Soc. 125, 1643 (2003).
Recent Experiments
Measured Melting Curves
DNA/Au
DNA only
Particle-size dependence
of Melting
Particle
diameter
DNA only
DNA/Au
R.Elghanian, et. al., Science 277, 1078 (1997).
C.-H. Kiang, Physica A 321, 164 (2003).
Recent Experiments: Rebound Effect
R. Jin, et. al, J. Am. Chem. Soc. 125, 1643 (2003).
2. Calculation of Optical
Properties
Maxwell’s Equations
Strategy: Consider each particle as a single dipole
Comparison DDA with more accurate method
(89 13nm Au particle)
K.L. Kelly, et. al, CSE, (2001).
3. Structure at low
temperature
Recipe for Reaction Limited Aggregations
1. Irrevesible process of bonding
2. Slow reaction (fractal dimension 2.1)
Cf. DLCA (lower fractal dimension)
At low T, this system satisfies these conditions.
TEM Images of Linked DNA Gold Nanoparticles
Aggregate of 13 nm diameter DNA/gold nanocomposites
Increased magnification image
http://www.chem.nwu.edu/~mkngrp/view1.html
Comparison with fast process
Gold-MUA nanoparticles
(mercaptoundecanoic acid)
Y. Kim, et. al, Nano Lett. 1, 165 (2001).
Morphology dependence of extinction cross section
?
Theory
Experiment
Comparison of size dependence of the extinction cross section
RLCA cluster
Simple Cubic Cluster
4. Melting Transition
My strategy for explaining the results in experiments
o Model the system as simply as possible
1. DNA hybridization
o Two-state model
o “Multiple link per bond” effect
2. Cluster configuration at given temperature T
o Bond percolation model
o Reaction limited cluster aggregation model
3. Calculation of Extinction Cross Section
o Discrete Dipole Approximation (Draine & Flatau, 1994)
o Dilute cluster limit
1. DNA hybridization
Two State Model
S  S D
[ S ][ S ]
 K  exp(  G )
T
[ D]
G  a(T  TM )  b(T  TM )
3
probability that DNA pair remains hybidized is
[D ] : Concentration of duplex
: Total concentration of DNA
We treat p as static probability.
1. DNA hybridization
Particle-size dependence of
avg. no of DNA per bond <n>
“multiple DNA per bond” effect
n
p
n
peff=1-(1-p)
= Prob. that pair of Au
particles have > 1 DNA links
Particle diameter
Temperature dependence of Peff
My strategy for explaining the results in experiments
o Model the system as simply as possible
1. DNA hybridization
o Two-state model
o “Multiple link per bond” effect
2. Cluster configuration at given temperature T
o Bond percolation model
o Reaction limited cluster aggregation model
3. Calculation of Extinction Cross Section
o Discrete Dipole Approximation (Draine & Flatau, 1994)
o Dilute cluster limit
Schematics of melting for a regular square lattice
1. Prepare the low-T config.
2. Cut bonds with prob. 1-p
3. Place the connected clusters into
larger box with random position
and random orientation.
Our model: melting of a regular simple cubic cluster
p=0.95
p=0.50
p=0.25>pc
Bond percolation
threshold
p=0.0
p=0.15<pc
My strategy for explaining the results in experiments
o Model the system as simply as possible
1. DNA hybridization
o Two-state model
o “Multiple link per bond” effect
2. Cluster configuration at given temperature T
o Bond percolation model
o Reaction limited cluster aggregation model
3. Calculation of Extinction Cross Section
o Discrete Dipole Approximation (Draine & Flatau, 1994)
o Dilute cluster limit
Calculation of extinction cross section
Using Discrete Dipole Approximation (DDA)
Dilute Cluster Limit
Temperature dependence of extinction cross section at 520nm
DNA only
DNA only (higher concentration)
D
Theory vs. Experiment
Temperature dependence of
extinction cross section at 520nm
DNA only
DNA/Au
DNA only
DNA only
DNA/Au
DNA only
(higher concentration)
Theory
Experiment
5. Effects of Restructuring
If T increases, bonding becomes reversible.
Thus it becomes compact cluster.
Thus, the model to mimic this feature is needed.
o Bond percolation model
+ Reaction limited cluster aggregation model
RLCA case
Radius of gyration
Slope=fractal dimension
=2.1
With RLCA + BP
Long time: 3.0
Short time=2.1
P=0.9
N MC=0
N MC=7000
RLCA
N MC=7000
MC=70000
N MC=70000
6. Summary
DNA/Au nanocomposite system
Linker DNA
1. Expected phase diagram
Gel-sol
transition
0
melting
transition
R. Elghanian, et. al.,
Science 277, 1078 (1997).
gel
2. Morphologies from a structural
model
3. DDA calculation of extinction
cross section
sol
T
Ind. particles
Experiment
gel
sol
melting
transition
Gel-sol
transition
near melting
transition
R. Jin, et. al, J. Am. Chem. Soc. 125, 1643 (2003).