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 selfassembled materials, beyond the range of phenomena accessible with ordinary molecular fluids.DNA nanotechnology | limited valence colloids | critical behavior I n recent years, a strong effort has been devoted to introduce a new generation of micro-and nanocolloids interacting via strongly anisotropic forces. Anisotropic interactions can simply arise from a nonspherical particle shape or from more sophisticated physical and/or chemical patterning of the particle surface (1-7). An alternative strategy to produce complex nanoparticles is to exploit the self-assembly of DNA oligomers. The rational design of the DNA sequences enables guiding the association of multiple DNA strands into a rich variety of nanosized objects, such as geometrical figures, hollow capsules, and nanomachines, as well as more complex meso-and macroscopic structures (8-13). The selectivity of DNA binding can also be exploited to control the mutual interactions between the structures (14, 15), whereas the spontaneous assembly of DNA sequences enables producing large ensembles of particles. These properties make DNA a powerful tool to explore fundamental phenomena of soft matter and statistical physics, as indicated by previous studies of liquid-crystalline ordering and phase separations in solutions of short DNA oligomers (16-18). Here we exploit DNA self-assembly to experimentally address the phase behavior of particles interacting with specific valence, strength, and selectivity.Colloidal particles with controlled valence are the next step toward the realization of new colloidal materials and phases dependent on the presence of a small number of bonds (1-7). Theoretical and numerical studies (19) predict that a solution of low-valence particles should exhibit phase coexistence-the colloidal analog of the vapor-liquid coexistence in simple liquidsbut only at v...

DNA is acquiring a primary role in material development, self-assembling by design into complex supramolecular aggregates, the building block of a new-materials world. Using DNA nanoconstructs to translate sophisticated theoretical intuitions into experimental realizations by closely matching idealized models of colloidal particles is a much less explored avenue. Here we experimentally show that an appropriate selection of competing interactions enciphered in multiple DNA sequences results into the successful design of a one-pot DNA hydrogel that melts both on heating and on cooling. The relaxation time, measured by light scattering, slows down dramatically in a limited window of temperatures. The phase diagram displays a peculiar re-entrant shape, the hallmark of the competition between different bonding patterns. Our study shows that it is possible to rationally design biocompatible bulk materials with unconventional phase diagrams and tuneable properties by encoding into DNA sequences both the particle shape and the physics of the collective response.

Kinetic arrest in colloidal dispersions with isotropic attractive interactions usually occurs through the destabilization of the homogeneous phase and the formation of a non-equilibrium network of jammed particles. Theory and simulations predict that a different route to gelation should become available when the valence of each colloidal particle is suitably reduced. Under these conditions, gelation should be achievable through a reversible sequence of equilibrium states. Here we report the reversible dynamic arrest of a dispersion of DNA-based nanoparticles with anisotropic interactions and a coordination number equal to four. As the temperature is decreased, the relaxation time for density fluctuations slows down by about five orders of magnitude, following an Arrhenius scaling in the entire experimentally accessible temperature window. The system is in thermodynamic equilibrium at all temperatures. Gelation in our system mimics the dynamic arrest of networking atomic strong glass formers such as silica, for which it could thus provide a suitable colloidal model.

We evaluate, by means of molecular dynamics simulations employing a realistic DNA coarsegrained model, the phase behaviour and the structural and dynamic properties of tetravalent DNA nanostars, i.e. nanoconstructs completely made of DNA. We find that, as the system is cooled down, tetramers undergo a gas-liquid phase separation in a region of concentrations which, if the difference in salt concentration is taken into account, is comparable with the recently measured experimental phase diagram [S. Biffi et al, Proc. Natl. Acad. Sci, 110, 15633 (2013)]. We also present a meanfield free energy for modelling the phase diagram based on the bonding contribution derived by Wertheim in his studies of associating liquids. Combined with mass-action law expressions appropriate for DNA binding and a numerically evaluated reference free energy, the resulting free energy qualitatively reproduces the numerical data. Finally, we report information on the nanostar structure, e.g. geometry and flexibility of the single tetramer and of the collective behaviour, providing a useful reference for future small angle scattering experiments, for all investigated temperatures and concentrations.

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DNA oligomers with properly designed sequences self-assemble into well defined constructs. Here, we exploit this methodology to produce bulk quantities of tetravalent DNA nanostars (each one composed of 196 nucleotides) and to explore the structural signatures of their aggregation process. We report small-angle neutron scattering experiments focused on the evaluation of both the form factor and the temperature evolution of the scattered intensity at a nanostar concentration where the system forms a tetravalent equilibrium gel. We also perform molecular dynamics simulations of one isolated tetramer to evaluate the form factor numerically, without resorting to any approximate shape. The numerical form factor is found to be in very good agreement with the experimental one. Simulations predict an essentially temperature-independent form factor, offering the possibility to extract the effective structure factor and its evolution during the equilibrium gelation.

Self-assembling DNA-nanostars are ideal candidates to explore equilibrium gelation in systems composed of limited-valence particles. We present here a light scattering study of the dynamics in a trivalent DNA-nanostars equilibrium gel and of its dependence on ionic strength and concentration. Reversible bonds between different nanostars, whose formation is sensitively dependent on temperature, concentration and ionic strength, are provided by complementary DNA sticky ends. We find that the decay of the density correlations is described by a two-step relaxation process characterised by: i) a slow time scale that varies over nearly four orders of magnitude in a temperature window of less than 30 degrees; ii) an increase of the amplitude (the so-called non-ergodicity factor) of the slow relaxation. The slow process follows an Arrhenius law with temperature. We observe that the activation enthalpy does not depend on the ionic strength and that the dependence of the relaxation time on the ionic strength can be rationalized in terms of the free-energy cost of forming a sticky-end duplex. Finally, we observe that dynamics is insensitive to nanostar concentration, in full agreement with the predicted behaviour in equilibrium gels.

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