Liquid part of the phase diagram and percolation line for two-dimensional Mercedes-Benz water

Ben Naim's four-arm model with density anomaly: Theory and computer simulations

Molecular dynamics, Wertheim's integral equation theory (IET), and thermodynamics perturbation theory (TPT) were used to study the thermodynamics and structure of particles interacting through angle-dependent potential. The particles are modeled as two-dimensional Lennard-Jones disks with four hydrogen bonding arms arranged symmetrically. The model was introduced by Ben-Naim and we call it the BN4 model. The BN4 model exhibits density anomaly and other anomalous properties similar to those in water and in the Mercedes-Benz (MB) model. The IET is based on the orientationally averaged version of the Ornstein-Zernike equation and correctly predicts the pair correlation function of the model at high temperatures. Both TPT and IET are in semiquantitative agreement with the simulation values of the molar volume, isothermal compressibility, thermal expansion coefficient, and heat capacity.

Simple rose model of water in constant electric field

A simple two-dimensional statistical mechanical water model, called the rose model, was used in this work. We studied how a homogeneous constant electric field affects the properties of water. The rose model is a very simple model that helps explain the anomalous properties of water. Rose water molecules are represented as two-dimensional Lennard-Jones disks with potentials for orientation-dependent pairwise interactions mimicking formations of hydrogen bonds. The original model is modified by addition of charges for interaction with the electric field. We studied what kind of influence the electric field strength has on the model's properties. To determine the structure and thermodynamics of the rose model under the influence of the electric field we used Monte Carlo simulations. Under the influence of a weak electric field the anomalous properties and phase transitions of the water do not change. On the other hand, the strong fields shift the phase transition points as well as the position of the density maximum.

The electric field changes the anomalous properties of the Mercedes Benz water model

The influence of a homogeneous constant electric field on water properties was assessed. We used a simple two-dimensional statistical mechanical model called the Mercedes-Benz (MB) model of water in the study. The MB water molecules are two-dimensional disks with Gaussian arms that mimic the formation of hydrogen bonds. The model is modified with added charges for interaction with the electric field. The influence of the strength of the electric field on the water's properties was studied using Monte Carlo simulations. The structure and thermodynamics of the water were determined as a function of the strength of the electric field. We observed that the properties and phase transitions of the water in the low strength electric field does not change. In contrast, the high strength electric field shifts boiling and melting points as well as the position of the density maxima. After further increasing the strength of the electric field the density anomaly disappears.

Monte Carlo simulations of simple two dimensional water-alcohol mixtures

Simple alcohols such as methanol and ethanol, are organic chemicals that can be used to store energy, which can be used as an alternative to fossil fuels. Each alcohol has at least one hydroxyl group attached to a carbon atom of an alkyl group. They can be considered as organic derivatives of water in which one of the hydrogen atoms is replaced by an alkyl group. In this work, we determined the thermodynamic and structural properties of two dimensional water-alcohol mixtures using the Monte Carlo method. We used two-dimensional Mercedes-Benz (MB) model for water and MB based models for lower alcohols. The structural and thermodynamic properties of the mixtures were studied by Monte Carlo simulations in the isothermal-isobaric ensemble. We show that 2D models display similar trends in the density maxima as in real water-alcohol mixtures. With increasing content of alcohols, the temperature of maxima increases and upon further increase starts to decrease and at high concentrations, the density maxima disappears.

Statistical-mechanical liquid theories reproduce anomalous thermodynamic properties of explicit two-dimensional water models

We have developed an analytical theory for a simple model of liquid water. We apply Wertheim's thermodynamic perturbation theory (TPT) and integral equation theory (IET) for associative liquids to the rose model, which is among the simplest models of water. The particles interact through rose potentials for orientation dependent pairwise interactions. Modifying both the shape and range of a three-petal rose function, we construct an efficient and dynamical mimic of the two-dimensional (2D) Mercedes-Benz (MB) water model. The particles in 2D MB are 2D Lennard-Jones disks with three hydrogen bonding arms arranged symmetrically, resembling the Mercedes-Benz logo. Both models qualitatively predict both the anomalous properties of pure water and the anomalous solvation thermodynamics of nonpolar molecules. The IET is based on the orientationally averaged version of the Ornstein-Zernike equation. This is one of the main approximations in the present work. IET correctly predicts the pair correlation functions at high temperatures. Both TPT and IET are in semi-quantitative agreement with the Monte Carlo values of the molar volume, isothermal compressibility, thermal expansion coefficient, and heat capacity. A major advantage of these theories is that they require orders of magnitude less computer time than the Monte Carlo simulations.

Simple two-dimensional models of alcohols

Alcohols are organic compounds characterized by one or more hydroxyl groups attached to a carbon atom of an alkyl group. They can be considered as organic derivatives of water in which one of the hydrogen atoms is replaced by an alkyl group. In this work, the Mercedes-Benz model of water is used to design simple two-dimensional (2D) models of lower alcohols. The structural and thermodynamic properties of the constructed simple models are studied by conducting Monte Carlo simulations in the isothermal-isobaric ensemble. We show that 2D models display similar trends in structuring and thermodynamics as in experiments. The present work on the smallest amphiphilc organic solutes provides a simple testing ground to study the competition between polar and non-polar effects within the molecule and physical properties.

Isothermal-isobaric algorithm to study the effects of rotational degrees of freedom-Benz water model

We have developed isothermal-isobaric algorithm for non-equilibrium Monte Carlo simulations. As first we have shown that the new method correctly predict density by comparing it to the density determined in canonical Monte Carlo simulations through the virial pressure. The new method was then used to study the effect of translational and rotational degrees of freedom on the structural and thermodynamic properties of the simple Mercedes-Benz water model. By holding one of the temperatures constant and varying the other one, we investigated how the position of the density maxima changes. We have observed that upon increase of rotational temperature the fluid become more Lennard-Jones like and the density maxima disappears.

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

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 a variance of silica-like models. Beside the known 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 one observed. The anomalies occur in hierarchy order, which is a slight variation of the hierarchy order in real water. The diffusion anomaly region is the innermost in the hierarchy while for water it is the density anomaly region.

Modelling water with simple Mercedes-Benz models

The structures and properties of biomolecules like proteins, nucleic acids, and membranes depend on water. Water is also very important in industry. Overall, water is unusual substance with more than 70 anomalous properties. The understanding of water is advancing significantly due to theoretical and computational modeling. There are different kind of models, models with fine-scale properties and increasing structural detail with increasing computational expense and simple models which focus on global properties of water like thermodynamics, phase diagram and are less computational expensive. Simplified models give a better understanding of water in ways that complement more complex models. Here, we review a simple model, the two dimensional Mercedes-Benz (MB) model of water. We present results by Monte Carlo simulations for anomalies and phase diagram and application of various theoretical methods.