The proper design of DNA sequences allows for the formation of well defined supramolecular units with controlled valence, f,via a consecution of self-assembling processes.This methodology has permitted the experimental realisation of a system composed by a mixture of DNA chains (B, with f=2) and DNA nanostars (NS) (f=4) in which the only relevant interaction is that between particles with different valence, thanks to the non-complementary design of the sticky-ends . The performance of these patchy-systems is strongly related to the number of patches present on particles’ surfaces  that in consequence limits the maximum number of bonds that the particles will be able to form.
In previous results, we discussed the formation of a kinetically arrested homogeneous DNA hydrogel at low-T , however, little is known about whether the sol-gel transition is mediated by the formation of a percolating network. In addition, the combination of Dynamic Light Scattering (DLS) and Small Angle Neutron Scattering (SANS), in comparison with percolation theory models and computational simulations conform a solid contribution to the sol-gel transition understading.
Recent DLS measurements revealed that it is possible to use DNA self-assembled units as a model-system to investigate in a controlled way the percolation transition and the cross-over from chemical to physical gelation, exploiting the steep temperature dependence of the DNA nucleotides interaction free-energy. By tuning the NS/B ratio according to the theoretical models of Flory and Stockmayer, we managed to bring the system at a well defined distance from percolation.
The results showed an Arrhenius dependence in a T range between 10°C and 55°C, suggesting that the relaxation time decays measured are effectively mediated by the T, which controls the lifetime of the NS-B bonds. It will be discussed that close to the percolation point, Flory-Stockmayer theories suggest the formation of NS-B clusters composed of different amounts of NS and B structures. Therefore, the associated density autocorrelation functions are characterised by a typical decay time, which is directly related to the cluster size. The emergence of a logarithmic decay in the autocorrelation functions obtained out from these DLS experiments and the power law critical exponents, associated to the fractal dimension of the cluster distribution, comes to validate these hypothesis.