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 Work Supported by NSF DMR and DMR Calculations carried out using facilities of the Ohio Supercomputer Center

1. Introduction

DNA/Au nanoparticle colloids and linking strands Linker DNA R. Jin, et. al, J. Am. Chem. Soc. 125, 1643 (2003). R. Elghanian, et. al., Science 277, 1078 (1997). Linker DNA

Recent Experiments Particle-size dependence of Melting Measured Melting Curves R.Elghanian, et. al., Science 277, 1078 (1997). C.-H. Kiang, Physica A 321, 164 (2003). Particle diameter DNA only DNA/Au DNA only

R. Jin, et. al, J. Am. Chem. Soc. 125, 1643 (2003). Recent Experiments: Rebound Effect

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 nanocompositesIncreased magnification image 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 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 Model the system as simply as possible 3. Calculation of Extinction Cross Section o Discrete Dipole Approximation (Draine & Flatau, 1994) o Dilute cluster limit o Reaction limited cluster aggregation model

Two State Model We treat p as static probability. : Concentration of duplex : Total concentration of DNA probability that DNA pair remains hybidized is 1. DNA hybridization

“multiple DNA per bond” effect p p =1-(1-p) n eff n Particle-size dependence of avg. no of DNA per bond Temperature dependence of Peff = Prob. that pair of Au particles have > 1 DNA links Particle diameter 1. DNA hybridization

My strategy for explaining the results in experiments 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 Model the system as simply as possible 3. Calculation of Extinction Cross Section o Discrete Dipole Approximation (Draine & Flatau, 1994) o Dilute cluster limit o Reaction limited cluster aggregation model

1. Prepare the low-T config. Schematics of melting for a regular square lattice 2. Cut bonds with prob. 1-p 3. Place the connected clusters into larger box with random position and random orientation.

p=0.95 p=0.50 p=0.0 p=0.25>p c Our model: melting of a regular simple cubic cluster Bond percolation threshold p=0.15<p c

My strategy for explaining the results in experiments 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 Model the system as simply as possible 3. Calculation of Extinction Cross Section o Discrete Dipole Approximation (Draine & Flatau, 1994) o Dilute cluster limit o Reaction limited cluster aggregation model

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)

DNA only DNA/Au DNA only Theory vs. Experiment D Temperature dependence of extinction cross section at 520nm Theory Experiment DNA only (higher concentration)

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

Radius of gyration RLCA case 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 N MC= MC =70000 N MC =7000 RLCA

6. Summary

DNA/Au nanocomposite system R. Jin, et. al, J. Am. Chem. Soc. 125, 1643 (2003). R. Elghanian, et. al., Science 277, 1078 (1997). Linker DNA 1. Expected phase diagram 2. Morphologies from a structural model 3. DDA calculation of extinction cross section gel sol Ind. particles Gel-sol transition melting transition T0 gelsol near melting transition Gel-sol transition melting transition Experiment