Hierarchy of anomalies in the two-dimensional Mercedes-Benz model of water

Abstract

We investigate by Monte Carlo simulations density, diffusion and structural anomalies of the simple two dimensional Mercedes-Benz (MB) model of water, which is a very simple toy model for explaining the origin of water properties. MB water molecules are modeled as two-dimensional Lennard-Jones disks, with three orientation-dependent hydrogen-bonding arms, arranged as in the MB logo. The model is in a way also variance of silica-like models. Beside the know thermodynamic anomaly for the model we also found diffusion and structural anomalies and map out the cascade of density, structural, pair entropy and diffusivity anomalies for MB model. The orientational order parameters with three and six fold symmetry were determined and maximum for each observed. The anomalies occur in hierarchy order which is slight variation of hierarchy order in real water. The diffusion anomaly region is the innermost in the hierarchy while for water is density anomaly region.

The physics of empty liquids: from patchy particles to water

“…Despite the short-range nature of the attractive interaction, the molecularly enforced tetrahedral geometry suffices in creating a network that can compare with the geometries revealed by neutron experiments, offering the possibility to shed light on the intimate nature of the anomalous behavior. The Mercedes-Benz models [63,64] and the mW model [65,66] also belong to the class of coarse grained potentials. The appeal of coarse grained potentials is motivated by their high computational efficiency compared to atomistic models, allowing to considerably extend length and time-scales of simulations making it possible, for example, to study rare events like homogeneous nucleation in direct simulations [67][68][69].…”

Simple Model of Liquid Water Dynamics

“…In cold water, the bond-breaking is mostly of H-bonds; in hotter water, the steeper slope of D ( T ) comes from the lower barrier to breaking Lennard-Jones water–water contacts. See different contributions of different populations in the SI …”

“…See different contributions of different populations in the SI. 38 Figure 5 compares the pressure dependence, D = D(p), predicted versus experiments, for different temperatures. Higher-temperature water (green curves) is much like a normal Lennard-Jones liquid�the effect of pressure is mainly to squeeze molecules together, reducing their water's diffusion speed.…”

The physics of Empty Liquids: from Patchy particles to Water

“…Despite the shortrange nature of the attractive interaction, the molecularly enforced tetrahedral geometry suffices in creating a network that can compare with the geometries revealed by neutron experiments, offering the possibility to shed light on the intimate nature of the anomalous behavior. The Mercedes-Benz models [61,62] and the mW model [63,64] also belong to the class of coarse grained potentials. The appeal of coarse grained potentials is motivated by their high computational efficiency compared to atomistic models, allowing to considerably extend length and time-scales of simulations making it possible, for example, to study rare events like homogeneous nucleation in direct simulations [65,66].…”