Mercedes-Benz Research Articles

F-Cell World Drive 2011: Are Tactical Medicine Principles Applicable to a Civilian Scenario?

In 2011, a Mercedes Benz (MB) conducted the F-Cell World Drive tour around the globe in 125 days. While crossing Asia from Shanghai (China) to Helsinki (Finland) by car, en route medical care was provided by embedded emergency physicians. The designated route crossed four different countries, multiple climate zones, and challenging road conditions. There was only limited information provided about hospitals and emergency medical services within different host nations in the planning phase, so we adopted tactical medical principles for mission planning and execution, as we were facing remote conditions and limitations to equipment, staffing, and patient transport.

Receptacle Model of Salting-In by Tetramethylammonium Ions

Water is a poor solvent for nonpolar solutes. Water containing ions is an even poorer solvent. According to standard terminology, the tendency of salts to precipitate oils from water is called salting-out. However, interestingly, some salt ions, such as tetramethylammonium (TMA), cause instead the salting-in of hydrophobic solutes. Even more puzzling, there is a systematic dependence on solute size. TMA causes the salting-out of small hydrophobes and the salting-in of larger nonpolar solutes. We study these effects using NPT Monte Carlo simulations of the Mercedes-Benz (MB) + dipole model of water, which was previously shown to account for hydrophobic effects and ion solubilities in water. The present model gives a structural interpretation for the thermodynamics of salting-in. The TMA structure allows deep penetration by a first shell of waters, the dipoles of which interact electrostatically with the ion. This first water shell sets up a second water shell that is shaped to act as a receptacle that binds the nonpolar solute. In this way, a nonpolar solute can actually bind more tightly to the TMA ion than to another hydrophobe, leading to the increased solubility and salting-in. Such structuring may also explain why molecular ions do not follow the same charge density series as atomic ions do.

Theory for the three-dimensional Mercedes-Benz model of water

The two-dimensional Mercedes-Benz (MB) model of water has been widely studied, both by Monte Carlo simulations and by integral equation methods. Here, we study the three-dimensional (3D) MB model. We treat water as spheres that interact through Lennard-Jones potentials and through a tetrahedral Gaussian hydrogen bonding function. As the "right answer," we perform isothermal-isobaric Monte Carlo simulations on the 3D MB model for different pressures and temperatures. The purpose of this work is to develop and test Wertheim's Ornstein-Zernike integral equation and thermodynamic perturbation theories. The two analytical approaches are orders of magnitude more efficient than the Monte Carlo simulations. The ultimate goal is to find statistical mechanical theories that can efficiently predict the properties of orientationally complex molecules, such as water. Also, here, the 3D MB model simply serves as a useful workbench for testing such analytical approaches. For hot water, the analytical theories give accurate agreement with the computer simulations. For cold water, the agreement is not as good. Nevertheless, these approaches are qualitatively consistent with energies, volumes, heat capacities, compressibilities, and thermal expansion coefficients versus temperature and pressure. Such analytical approaches offer a promising route to a better understanding of water and also the aqueous solvation.

Theory for the solvation of nonpolar solutes in water

We recently developed an angle-dependent Wertheim integral equation theory (IET) of the Mercedes-Benz (MB) model of pure water [Silverstein et al., J. Am. Chem. Soc. 120, 3166 (1998)]. Our approach treats explicitly the coupled orientational constraints within water molecules. The analytical theory offers the advantage of being less computationally expensive than Monte Carlo simulations by two orders of magnitude. Here we apply the angle-dependent IET to studying the hydrophobic effect, the transfer of a nonpolar solute into MB water. We find that the theory reproduces the Monte Carlo results qualitatively for cold water and quantitatively for hot water.

Confined Water: A Mercedes-Benz Model Study

We study water that is confined within small geometric spaces. We use the Mercedes-Benz (MB) model of water, in NVT and muVT Monte Carlo computer simulations. For MB water molecules between two planes separated by a distance d, we explore the structures, hydrogen bond networks, and thermodynamics as a function of d, temperature T, and water chemical potential mu. We find that squeezing the planes close enough together leads to a vaporization of waters out of the cavity. This vaporization transition has a corresponding peak in the heat capacity of the water. We also find that, in small pores, hydrogen bonding is not isotropic but, rather, it preferentially forms chains along the axis of the cavity. This may be relevant for fast proton transport in pores. Our simulations show oscillations in the forces between the inert plates, due to water structure, even for plate separations of 5-10 water diameters, consistent with experiments by Israelachvili et al. [Nature 1983, 306, 249]. Finally, we find that confinement affects water's heat capacity, consistent with recent experiments of Tombari et al. on Vycor nanopores [J. Chem. Phys. 2005, 122, 104712].

Water-like fluid in the presence of Lennard–Jones obstacles: predictions of an associative replica Ornstein–Zernike theory

What are the properties of water in the presence of a ‘sea’ of inert obstacles? This question arises because biological cells are highly crowded media, and it is of interest to know the properties of water inside them. It also arises for understanding water in confined molecular environments and for mixtures of water with non-polar solutes. We study two-dimensional Mercedes–Benz (MB) water that is freely mobile in a disordered, but fixed, matrix of Lennard–Jones disks. We use the associative replica Ornstein–Zernike equations supplemented by the corresponding hypernetted chain approximation, and we tested the theory using Monte Carlo simulations. We find that the structure of model water is perturbed by the presence of the obstacles. When the density of obstacles is small, the obstacles induce an increased ordering and ‘hydrogen bonding’ of the MB model molecules and increased compressibility, relative to pure fluid, in agreement with previous theoretical and experimental studies. However, interestingly, high obstacle densities reduce MB water structuring, ‘hydrogen bonding’, and compressibility, because the obstacles interfere so extensively with all the possible ways that the fluid can form good ‘hydrogen bonding’ networks.

Water-like fluid in the presence of Lennard–Jones obstacles: predictions of an associative replica Ornstein–Zernike theory

What are the properties of water in the presence of a ‘sea’ of inert obstacles? This question arises because biological cells are highly crowded media, and it is of interest to know the properties of water inside them. It also arises for understanding water in confined molecular environments and for mixtures of water with non-polar solutes. We study two-dimensional Mercedes–Benz (MB) water that is freely mobile in a disordered, but fixed, matrix of Lennard–Jones disks. We use the associative replica Ornstein–Zernike equations supplemented by the corresponding hypernetted chain approximation, and we tested the theory using Monte Carlo simulations. We find that the structure of model water is perturbed by the presence of the obstacles. When the density of obstacles is small, the obstacles induce an increased ordering and ‘hydrogen bonding’ of the MB model molecules and increased compressibility, relative to pure fluid, in agreement with previous theoretical and experimental studies. However, interestingly, high obstacle densities reduce MB water structuring, ‘hydrogen bonding’, and compressibility, because the obstacles interfere so extensively with all the possible ways that the fluid can form good ‘hydrogen bonding’ networks.

A two-dimensional model of water: Solvation of nonpolar solutes

We recently applied a Wertheim integral equation theory (IET) and a thermodynamic perturbation theory (TPT) to the Mercedes–Benz (MB) model of pure water. These analytical theories offer the advantage of being computationally less intensive than the Monte Carlo simulations by orders of magnitudes. The long-term goal of this work is to develop analytical theories of water that can handle orientation-dependent interactions and the MB model serves as a simple workbench for this development. Here we apply the IET and TPT to the hydrophobic effect, the transfer of a nonpopular solute into MB water. As before, we find that the theories reproduce the Monte Carlo results quite accurately at higher temperatures, while they predict the qualitative trends in cold water.

A two-dimensional model of water: Theory and computer simulations

We develop 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 MB model, which is among the simplest models of water. Water molecules are modeled as 2-dimensional Lennard-Jones disks with three hydrogen bonding arms arranged symmetrically, resembling the Mercedes-Benz (MB) logo. The MB model qualitatively predicts both the anomalous properties of pure water and the anomalous solvation thermodynamics of nonpolar molecules. 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 function of the model water 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.

The Mechanism of Hydrophobic Solvation Depends on Solute Radius

We model the aqueous solvation of a nonpolar solute as a function of its radius. We use a simplified statistical mechanical model of water, the Mercedes Benz (MB) model, in NPT Monte Carlo simulations. This model has previously been shown to predict qualitatively the volume anomalies of pure water and the free energy, enthalpy, entropy, heat capacity, and volume change for inserting a nonpolar solute into water. We find a very different mechanism for the aqueous solvation of large nonpolar solutes (much larger than a water) than for smaller solutes. Small solute transfer involves a large hydrophobic heat capacity; its disaffinity for cold water (room temperature or below) is due to the ordering of the neighboring waters (entropic), while its disaffinity for hot water is due to the breaking of hydrogen bonds among the neighboring waters (enthalpic). In contrast, transferring large nonpolar solutes into water involves no such large changes in heat capacity or entropy. In this regard, large nonpolar solutes are not “hydrophobic”; their solvation follows classical regular solution theory. Putting a large nonpolar surface into water breaks hydrogen bonds at all temperatures. Therefore, the traditional “iceberg” model that first-shell water structure melts out with temperature should not apply to large solutes. These results also explain why the free energy of creating an oil/water interface (75 cal Å-2 mol-1) is greater than threefold for small molecule transfers (25 cal Å-2 mol-1). A key conclusion is that hydrophobicity depends not only on the surface area of a solute but also on its shape and curvature.

A Simple Model of Water and the Hydrophobic Effect

We use a simple computational model, proposed originally by Ben-Naim, to study the anomalous properties of water and the hydrophobic effect. Water molecules are modeled as two-dimensional (2D) Lennard-Jones disks, with three orientation-dependent hydrogen-bonding arms, arranged as in the Mercedes Benz (MB) logo. Phase space is explored using NPT Monte Carlo simulations. For pure water, the MB model qualitatively predicts the density anomaly (and the related negative thermal expansion coefficient at low temperature), the minimum in the isothermal compressibility as a function of temperature, the large anomalous heat capacity, and freezing to the 2D model analogue of ice, a low-density hexagonal crystal phase. For the solvation of nonpolar solutes (disks without H bonds), the model predicts the experimental trends with temperature of the free energy, entropy, enthalpy, molar volume, and heat capacity. A unique feature of these simulations is that they provide well-converged heat capacities of transfer, an i...