Fluctuating micro-heterogeneity in water - tert-butyl alcohol mixtures and lambda-type divergence of the mean cluster size with phase transition-like multiple anomalies

Abstract

Water - tert-butyl alcohol (TBA) binary mixture exhibits a large number of thermodynamic and dynamic anomalies. These anomalies are observed at surprisingly low TBA mole fraction, with $x_{\text{TBA}} \approx 0.03 - 0.07$. We demonstrate here that the origin of the anomalies lies in the local structural changes that occur due to self-aggregation of TBA molecules. We observe a percolation transition of the TBA molecules at $x_{\text{TBA}} \approx 0.05$. We note that "islands" of TBA clusters form even below this mole fraction, while a large spanning cluster emerges above that mole fraction. At this percolation threshold, we observe a lambda-type divergence in the fluctuation of the size of the largest TBA cluster, reminiscent of a critical point. Alongside, the structure of water is also perturbed, albeit weakly, by the aggregation of TBA molecules. There is a monotonic decrease in the tetrahedral order parameter of water, while the dipole moment correlation shows a weak non-linearity. Interestingly, water molecules themselves exhibit a reverse percolation transition at higher TBA concentration, $x_{\text{TBA}} \approx 0.45$, where large spanning water clusters now break-up into small clusters. This is accompanied by significant divergence of the fluctuations in the size of largest water cluster. This second transition gives rise to another set of anomalies around. Both the percolation transitions can be regarded as manifestations of Janus effect at small molecular level.