Effective Medium Theory of DNA-linked Gold Nanoparticle Aggregates: Effect of Aggregate Shape

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Effective Medium Theory of DNA-linked Gold Nanoparticle Aggregates: Effect of Aggregate Shape

Anne A. Lazarides, K. Lance Kelly, and George C. Schatz Department of Chemistry, Northwestern University Evanston, IL 60208-3113 ABSTRACT We present a dynamical effective medium theory (EMT) of the dielectric properties of nanoparticle aggregates formed from DNA-linked gold nanoparticles. Experimental measurements show that such aggregates have reduced UV extinction and plasmon bands that are considerably red-shifted and broadened relative to the plasmon absorption feature observed in spectra of dispersed colloid. The EMT, which can be used to reproduce the observed spectral changes, is tested by comparing aggregate spectra calculated using the EMT dielectric function with spectra from explicit coupled particle calculations, and good agreement is found. The EMT dielectric function is used as well in discrete dipole calculations to calculate extinction spectra for a variety of aggregate shapes not amenable to analytic solution, and the sensitivity of the spectra to aggregate shape is examined. We find that the spectra are only weakly sensitive to aggregate shape, and conclude that, when calculating extinction of the DNA-linked aggregates for comparison with experiment, spherical shapes can be assumed.

INTRODUCTION Recently, a DNA detection method has been developed that is based upon the distancedependent optical properties of gold nanoparticle aggregates that form in the presence of DNA linker molecules.1-4 Gold particles are functionalized with alkane-thiol-capped oligonucleotides (single-stranded DNA); complementary linker oligonucleotide (DNA) strands direct the assembly of nanoparticle networks through the forces of sequence-specific hybridization (DNA duplex formation). The optical properties of the linked nanoparticles have been shown to be a function of the size of the nanoparticles, the length of the linking duplex DNA, and the size of the nanoparticle aggregates. When nanoparticles of a size between 12 and 16 nm are linked with DNA duplexes composed of 24 oligonucleotide base pairs, aggregate formation is accompanied by a color change from red to purplish-blue (Figure 1).

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wavelength (nm) Figure 1. Extinction spectra for dispersed and DNA-linked Au nanoparticles, courtesy of the authors of ref. 3. The 13 nm particles are capped with 3’- and 5’-(alkanethiol) 12-base oligonucleotides. The aggregated colloid is formed in the presence of a 24-base oligonucleotide, each half of which is complementary to the one of the two nanoparticle-capping oligonucleotides.

In earlier work, two of us demonstrated that aggregates composed of thousands of particles may be described accurately using a coupled dipole approach in which the particles are located on a cubic lattice, and the induced polarizations are determined using complex conjugate gradient solutions of the dipole interaction equations, with Fourier methods used