(178ae) Rational Design of DNA Functionalized Colloidal Particles

The ability to design particles which will spontaneously self-assemble into useful, ordered structures is one of the staple ideas in nanotechnology. DNA hybridization is now accepted as a powerful mechanism for guiding this process [1-2] because of the specificity and tunability of DNA hybridization. In brief, particles are grafted with brushes comprised of synthetic, single-stranded DNA oligomers, the sequences of which are designed to be partially self-complementary thereby creating attractive interactions between the particles.  Multiple sequences can be employed to generate multicomponent structures offering a virtually limitless number of combinations.  While there has been substantial recent progress in the self-assembly of various crystalline structures using DNA-mediated interactions, to date no rational, quantitative model for design of these particles has been developed. The large number of system parameters, such as DNA oligomer sequence and length, particle sizes and system concentrations make infeasible a trial-and-error approach.

While a thorough analysis of the self assembly behavior of same sized DNA functionalized particles has already been performed [2], the same can not be said for particles with different sizes. By including particle size ratio as an additional parameter we gain access to a much wider range of crystalline structures. In doing so we confine the phase diagrams for the behavior of same sized particles to a single cross section in our new parameter space.

The first step in generating a model for the design of these particles is determining the equilibrium phase for a given set of system parameters. The stability of a phase is found by calculating its free energy and comparing it to that of all other phases accessible to the system. By repeatedly performing these calculations for a wide range of parameters it is possible to generate phase diagrams which will provide a map of the equilibrium phase for any arbitrary point in our parameter space. The majority of our free energy calculations are done using the quasi-harmonic approximation, which was chosen for its speed [3]. To ensure the accuracy of our results we periodically make use of thermodynamic integration [4] to confirm the accuracy of the quasi-harmonic approach.

Recent experiments and simulations have shown that the final structure a system will grow is not only dependant upon its equilibrium behavior but can also be influenced by kinetic effects [2]. To study these effects we perform Brownian Dynamics simulations both with and without pre-generated crystalline seeds. Through these simulations we are able to generate predictive techniques that allow us to determine the expected disorder of a given system. With this new information we can again perform our free energy calculations and obtain a more meaningful phase diagram.

[1] R. J. Macfarlane, et al., Science, 344, 204 (2011).

[2] R.T. Scarlett, J.C. Crocker, & T. Sinno, J. Chem. Phys., 132, (2010).

[3] J. F. Lutsko, D. Wolf, & S. Yip, J. Chem. Phys., 88, 10 (1988).

[4] T. P. Straatsma, H. J. C. Berendsen, J. Chem. Phys. 89, 5876 (1988)