Phase transitions in DNA-linked nanoparticle assemblies: a decorated-lattice model

We use decorated-lattice models to explore the phase behavior of two types of DNA-linked colloidal mixtures: systems with identical nanoparticles functionalized with two different DNA strands (mixture Aab) and mixtures involving two types of particles each one functionalized with a different DNA strand (mixture Aa-Ab). The model allows us to derive the properties of the mixtures from the well-known behavior of underlying spin-n Ising models with temperature and activity dependent effective interactions. The predicted evolution of the dissolution profiles for the colloidal assemblies as a function of temperature and number of single DNA strands on a nanoparticle M is in qualitative agreement with that observed in real systems. According to our model, the temperature at which the assemblies dissolve can be expected to increase with increasing M only for concentrations of colloids below a certain threshold. For more concentrated solutions, the dissolution temperature is a decreasing function of M. Linker-mediated interactions between Aa and Ab particles in the Aa-Ab mixture render the phase separation involving disordered aggregates metastable with respect to a phase transition between a solvent-rich and an ordered phase. The stability of the DNA-linked assembly is enhanced by the ordering of the colloidal network and the ordered aggregates dissolve at higher temperatures. Our results may explain the contrasting evolution of the dissolution temperatures with increasing probe size in Aab and Aa-Ab mixtures as observed experimentally.