We explore the potential energy landscape of structure breaking binary mixtures (SBBM) where two constituents dislike each other, yet remain macroscopically homogeneous at intermediate to high temperatures. Interestingly, we find that the origin of strong composition dependent non-ideal behaviour lies in its phase separated inherent structure. The inherent structure (IS) of SBBM exhibits bi-continuous phase as is usually formed during spinodal decomposition.We draw analogy of this correlation between non-ideality and phase separation in IS to explain observation of non-ideality in real aqueous mixtures of small amphiphilic solutes, containing both hydrophilic and hydrophobic groups. Although we have not been able to obtain IS of these liquids, we find that even at room temperature these liquids sustain formation of fluctuating, transient bicontinuous phase, with limited lifetime ($\tau \lesssim$ 20 ps). While in the model (A, B) binary mixture, the non-ideal composition dependence can be considered as a fluctuation from a phase separated state, a similar scenario is expected to be responsible for the unusually strong non-ideality in these aqueous binary mixtures.

Using polydispersity index as an additional order parameter we investigate freezing/melting transition of Lennard-Jones polydisperse systems (with Gaussian polydispersity in size), especially to gain insight into the origin of the terminal polydispersity. The average inherent structure (IS) energy and root mean square displacement (RMSD) of the solid before melting both exhibit quite similar polydispersity dependence including a discontinuity at solid-liquid transition point. Lindemann ratio, obtained from RMSD, is found to be dependent on temperature. At a given number density, there exists a value of polydispersity index (𝛿_P) above which no crystalline solid is stable. This transition value of polydispersity (termed as transition polydispersity, 𝛿_P) is found to depend strongly on temperature, a feature missed in hard sphere model systems. Additionally, for a particular temperature when number density is increased, 𝛿_P shifts to higher values. This temperature and number density dependent value of 𝛿_P saturates surprisingly to a value which is found to be nearly the same for all temperatures, known as terminal polydispersity (𝛿_TP). This value (𝛿_TP ∼ 0.11) is in excellent agreement with the experimental value of 0.12, but differs from hard sphere transition where this limiting value is only 0.048. Terminal polydispersity (𝛿_TP) thus has a quasiuniversal character. Interestingly, the bifurcation diagram obtained from non-linear integral equation theories of freezing seems to provide an explanation of the existence of unique terminal polydispersity in polydisperse systems. Global bond orientational order parameter is calculated to obtain further insights into mechanism for melting.