Phase behavior and critical activated dynamics of limited-valence DNA nanostars

Abstract

Colloidal particles with directional interactions are key in the realization of new colloidal materials with possibly unconventional phase behaviors. Here we exploit DNA self-assembly to produce bulk quantities of "DNA stars" with three or four sticky terminals, mimicking molecules with controlled limited valence. Solutions of such molecules exhibit a consolution curve with an upper critical point, whose temperature and concentration decrease with the valence. Upon approaching the critical point from high temperature, the intensity of the scattered light diverges with a power law, whereas the intensity time autocorrelation functions show a surprising two-step relaxation, somehow reminiscent of glassy materials. The slow relaxation time exhibits an Arrhenius behavior with no signs of criticality, demonstrating a unique scenario where the critical slowing down of the concentration fluctuations is subordinate to the large lifetime of the DNA bonds, with relevant analogies to critical dynamics in polymer solutions. The combination of equilibrium and dynamic behavior of DNA nanostars demonstrates the potential of DNA molecules in diversifying the pathways toward collective properties and self-assembled materials, beyond the range of phenomena accessible with ordinary molecular fluids.

Keywords: DNA nanotechnology; critical behavior; limited valence colloids.

Fig. 1.

Phase behavior of DNA nanostars with valence and . (A) The and (B) nanostars are formed by the self-assembly of three and four oligomers, respectively. Arm tips terminate with one sticky overhang each. (C) Fluorescent emission from a capillary tube containing a sample of EtBr-marked nanostars photographed after the sample was centrifuged at two different T (as indicated by the green and magenta dots in E). At low-enough T (magenta-framed picture, Right), the system phase separates into DNA-rich and DNA-poor phases. (D) Above , DNA is single stranded. For , single strands hybridize, leading to the self-assembly of stable (blue frame, Left) and (orange frame, Right) nanostars. For , nanostars are independent. Below , interactions between sticky overhangs (see schematic at the bottom) promote the formation of clusters that grow progressively larger as T is lowered. (E) Experimentally determined consolution curve for nanostars with (blue dots) and (red dots). The nanostars have a markedly reduced coexistence region with respect to nanostars. The concentrations of the dense phases at low T correspond to nanostars molarities of 0.20 mM and 0.29 mM for and , respectively. As T is lowered from stable homogeneous conditions (green dot and C Left, green-framed picture) to a temperature within the consolution curve (magenta dot and C Right, magenta-framed picture) along the critical isochores (dashed gray arrows), the system phase separates into two coexisting phases whose concentration is indicated by the magenta tie line.

Fig. 2.

Pretransitional behavior of DNA nanostars along the critical isochore. (A) Scattered intensity measured as a function of T at various scattering angles. The scattering angles and the corresponding scattering vectors explored in this experiments are 30° (q = 8.15 μm⁻¹), 45° (q = 12.1 μm⁻¹), 68° (q = 17.6 μm⁻¹), 90° (q = 22.3 μm⁻¹), 101° (q = 24.3 μm⁻¹), and 152° (q = 30.6 μm⁻¹). (B) T dependence of the scattered intensity measured at 30° (full symbols) for both and systems. Dotted lines in A and B are the best fit by the Lorentzian function in Eq. 1 (dotted lines). Dashed vertical lines indicate as determined by the best fit. Scattered intensities relative to the structures have been divided by a factor of 2 to make them overlap with data at high T. (C) Field correlation functions measured at in the system for various T (symbols). Data are fitted to a sum of two stretched exponentials (lines). (D) Scattering intensity associated to the fast and slow contributions of at scattering angle . The line is the fit to the total scattering intensity already reported in B.

Fig. 3.

Dynamic behavior of and DNA nanostars along the critical isochore. (A) T dependence of the slow and fast decay times. The black line shows the expected T dependence of the diffusive τ for independent nanostars. (B) T dependence of the stretching exponent for the fast and for the slow components. (C) plotted as function of 1/T and fitted by an Arrhenius law. (D) Comparison, in a narrow T interval close to , of the extrapolated Arrhenius T dependence observed for for the DNA nanostars with the correlation times expected on the basis of the critical slowing down (SI Text).