Dynamics and Statics of DNA-Programmable Nanoparticle Self-Assembly and Crystallization

DNA linker mediated self-assembly is emerging as a very general strategy for designing new materials. In this Letter, we characterize both the dynamics and thermodynamics of nanoparticle-DNA self-assembly by molecular dynamics simulations from a new coarse-grained model. We establish the general phase diagram and discuss the stability of a previously overlooked crystalline phase (D-bcc). We also characterize universal properties about the dynamics of crystallization. We point out the connection to $f$-star polymer systems and discuss the implications for ongoing experiments as well as for the general field of DNA mediated self-assembly.

Figure 1

Coarse-grained model of ssDNA-GNP. $n_s$ and $n_l$ are the coarse-grained number of spacer and linker beads, respectively. $r$ is the number of ssDNA attached to each GNP. $R$ is the radius of a GNP, and $T$ is the average end-to-end distance of the ssDNA. The structure of the ssDNA linker, which allows hybridizations, is modeled with central beads (CT), the complementary basis, and flanking beads (FL).

Figure 2

Hybridizations per nanoparticle ($r=20-35$, $\eta =1.0$, and $N_{\mathrm{GNP}}=54$) for $T$ in (0.8, 2.3). The inset shows the fraction of hybridizations that live up to a time $t$, $f(H)$ for different temperatures ($r=20$).

Figure 3

Random system of GNPs at $T=1.4$ quenched to $T=1.2$ as a function of time. (a) Mean-square displacement. (b) Fraction of solid GNPs. (c) Number of clusters ($r=25$, $N_{\mathrm{GNP}}=54$, and $\eta =1.0$). sc $A$ and sc $B$ stand for simple cubic of $A$ and $B$ GNPs, respectively.

Figure 4

Instantaneous structures of points $M$, $P$, and $Q$ in Fig. 3. (Left) Pair distribution function between GNPs. The vertical lines correspond to the bcc positions $(\frac{a}{2},\frac{a}{2},\frac{a}{2})$, $(a,0,0)$, $(a,a,0)$, etc. (Right) Static structure factor, where dotted vertical lines correspond to the bcc-lattice Bragg peaks. The Debye-Waller factor (DW) Eq. (2) is shown.

Figure 5

Equilibrated snapshots of (a) D-bcc and (b) CsCl-bcc, with $A$ (blue) and $B$ (red) GNPs and hybridizations (black) (other colors from Fig. 1).

Figure 6

Top: Phase diagram $r$ vs $\eta$ for ${\epsilon }_{\mathrm{bp}}=0$ ($f$-star polymers) and ${\epsilon }_{\mathrm{bp}}=10$. The dotted line on the left is the location of bcc for hard spheres. Bottom: Phase diagram for $r$ vs temperature ($\eta =1.0$). Phase boundaries are approximate. The $f$-stars are from Ref. 23 and the experimental line from Ref. 7, shifted as discussed in the text. Snapshots include the reconstructed bcc lattice from the $S(\overrightarrow{q})$.

Figure 7

Interparticle distance $d_p$ vs $\eta$, where $d_p=a_{\mathrm{bcc}}-2R$. Experimental results are from Ref. 4.