Methane molecules in water

The proximal radial distribution functions for carbon-oxygen and carbon-(water)hydrogen in the example are shown in Fig. 1.11. The proximal radial distribution function for carbon-oxygen is significantly more structured than the interfacial profile (Fig. 1.9), showing a maximum value of 2. This proximal radial distribution function agrees closely with the carbon-oxygen radial distribution function for methane in water, determined from simulation of a solitary methane molecule in water. While more structured than expected from the... 

Figure 1.11 Carbon-water proximal and radial distribution functions at 300 K. The solid and dashed lines indicate the alkyl chain carbon-(water)oxygen and -(water)hydrogen proximal correlation functions, respectively, evaluated from simulations of grafted alkyl chains in contact with water. The dots indicate the methane-(water)oxygen and -(water)hydrogen radial distribution functions, respectively, evaluated from simulations of a single methane molecule in water.

We thus need perform only two simulations, L to nothing in water and L to nothing in the LR complex. The first application of this approach was to the association of two methane molecules in water, where both species (L and R) are identical. In general, L should be chosen as the smaller component. 

Figure 15.4. Potential of mean force (PMF) between two methane molecules in water. This shows a first deeper minimum corresponding to the contact geometry of the two methane molecules. Another second (less deep) minimum is also observed in the PMF, corresponding to the solvent separated minimmn. Adapted from thesis entitled Molecular dynamics simulations of hydrophobic solutes in hquid water by Andy Hsu, Institute of Atomic and Molecular Sciences, Academia Sinica. (http //w3.iams.sinica.edu.tw/lab/jlli/thesis andy/%5d.)...

Hydrophobic interactions have a complex character and are not yet fully understood. The interaction depends strongly on the size of the hydrophobic entities. For small sizes, such as two methane molecules in water, the hydrophobic interaction is small, increasing considerably for larger synthons. The hydrophobic effects become especially important for what is called the amphiphilic macrvmolecules with their van der Waals surfaces differing in character (hydrophobic/hydrophilic). The amphiphilic molecules, an example shown in Fig. 13.16, are able to self-organize, forming structures up to the nanometer scale (nanostructures). 

Figure 4.11 shows the values of 5G(cri) for various solvents. There are two prominent differences between water and non-aqueous solvents which are worthwhile noting. First, the absolute magnitude of 5G(cri) is larger in water than in the other solvents. The difference, say, at 25°C, is significant and amounts to about 0.6 kcal mol . This value is of the order of magnitude of k T at this temperature. This finding can be reformulated in terms of the ratio of probabilities. We use relation (4.3.14) for a pair of methane molecules in water and in, say, ethanol at 25 C... 

Ravishanker etal. (1982) extended the Monte Carlo simulation between two methane molecules in water-like particles. The results obtained by Ravishanker et al are quite different from those by Pangali et al., as well as those obtained by theoretical calculations by Pratt and Chandler (1977). The most striking difference is the occurrence of a second minimum at about 6 A, which corresponds to a configuration of a water-bridge between the two solutes rather than the water-separated configuration obtained by Pangali etal. (1979a,b) (Fig. 4.44). In my... 

The ratio of the average quantities can of course be computed by any of the simulation techniques based on some specific model potential for water molecules. Figure 7.20 shows one such a result obtained by Monte Carlo calculation of the potential of average force for two methane molecules in water at 25°C. 

FIGURE 7.20. Potential of average force between two methane molecules in water, obtained by Monte Carlo simulation. Redrawn with changes from Ref (1). 

Show that for two methane molecules in water, the major contribution of the van der Waals forces comes from the polar (zero-frequency) term and that Equation 2.5 for the potential reduces approximately to ... 

Figure 5 Cavity potential of mean force kT ln[e / / AA(r)l in kcal mol for two hard sphere model methane molecules in water ...

Figure 4 Mean force (a) and potential of mean force (b) between two methane molecules in water, from Smith and Haymet. The potential of mean force is calculated by thermodynamic integration (TI) of the mean force and also from the free-energy perturbation (FEP) method. TI and FEP quantities were calculated simultaneously from the same simulations, with nearly identical results. Maxima and minima in the potential of mean force correspond to separations where the mean force is zero.

Computer simulation approaches have proven very useful in enabling calculation of the association of molecules. For example, the association of two methane molecules in the gas phase would lead to a AE° (0 K) of kcal/mol, and by analog with water dimer (Table 4.3), a very positive AG° (300 K) and thus no tendency for association. In aqueous solution, one can calculate, using modern statistical mechanical simulation methods, the potential of mean force for association of two molecules, which is the free energy as a function of molecular separation in solution. Although there is some controversy about... 

TABLE 5 The Average Distance and Interaction Energy between a Water Molecule and nearest Methane Molecules in the Clusters H20-"(CH4) ... 

The Dilute Mixture of Water in Methane. When one molecule of water is surrounded by methane molecules, the molecule of water behaves like a regular nonpolar molecule (see Figure 2, where one of the typical minimized clusters 1 (water) 10 (methane) is presented). The average intermolecular distance and interaction energy between a water molecule and the nearest neighbors methane molecules in the clusters H20 "(CH4)io are listed in Table 5. 

Molecules of Water in the Vicinity of a Methane Molecule. First, one should clearly emphasize the difference between (1) the number of water molecules in the first hydration layer around a methane molecule and (2) the coordination number of a methane molecule in an infinitely dilute aqueous solution. Jorgensen et al. defined the number of water molecules in the first hydration layer around a methane molecule as the water molecules located between the spheres with radii 3.6 and 5.35 A. Hence, Jorgensen s first hydration layer contains both A and B species. However, the coordination number in a liquid is usually defined as the number of nearest touching neighbors and corresponds to A type molecules. 

Figure 3. The dependence of the interaction energy (a) and average distance (b) between a methane molecule and water molecules of type A in the clusters CH4 (H20) on the number of water molecules in the cluster n.

In this paper, the Mpller—Plesset perturbation theory was applied to clusters formed by one molecule of methane and several molecules of water, or one molecule of water and several molecules of methane. The goal was to determine the inter-molecular distances and interaction energies between a water molecule and a methane molecule in the clusters CH4 (H20) and H20 (CH4) and to compare the obtained results with available experimental data. 

The attraction between hydrocarbons or fluorocarbons in air (mainly van der Waals) increases very much when we place these molecules in water. For example, for two contacting methane molecules in free space the interaction pair potential energy is —2.5 x 10 21J, whereas in water it is —14 x 10 21J. On the other hand, experimental evidence... 

Let us consider first water and ethanol. The change in solvation Gibbs energy of a methane molecule from water to ethanol at = 10°C is... 

FIGURE 7.32. A schematic description of five methane molecules in the configuration of neopentane. All the inner hydrogens are indicated by the dotted areas. The boundaries of the excluded volume are indicated by the dashed curve (assuming a radius of 2 A for the methane and 1.4 A for the water molecule). 

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