Methane water radial distribution

An analysis of the structure of the dilute aqueous solution of methane was also developed in terms of quasicomponent distribution functions and stereographic views of significant molecular structures. The coordination number of methane in this system was calculated on the basis of 5.38, fixed at the first minimum In the methane-water radial distribution function. A plot of the mole fraction of methane molecules x (K) vs. their corresponding water coordination number is given in Figure 7. 

Figure 6. Calculated methane-water radial distribution g(Rj ui. center of mass separation R from Monte Carlo computer simulation for the dilute aqueous solution of methane at T = 25°C...

As in the molecular dynamic calculations, MC calculations for water structures were first tested against experimental values. Beveridge and coworkers (Swaminathan et al., 1978) and Owicki and Scheraga (1977) obtained acceptable comparison of their calculations against experimental values for the oxygen-oxygen radial distribution function for both water and methane dissolved 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 conclude that the proximal radial distribution function (Fig. 1.11) provides an effective deblurring of this interfacial profile (Fig. 1.9), and the deblurred structure is similar to that structure known from small molecule hydration results. The subtle differences of the ( ) for carbon-(water)hydrogen exhibited in Fig. 1.11 suggest how the thermodynamic properties of this interface, fully addressed, can differ from those obtained by simple analogy from a small molecular solute like methane such distinctions should be kept in mind together to form a correct physical understanding of these systems. 

An important step in understanding the local structure around a nonpolar solute in water was made by Jorgensen et al. Using Monte Carlo simulations based on an intermolecular potential, which contained Lennard-Jones and Coulomb contributions, they determined the number of water molecules in the first hydration layer (located between the first maximum and the first minimum of the radial distribution function) around a nonpolar solute in water. This number (20.3 for methane, 23 for ethane, etc.) was surprisingly large compared with the coordination numbers in cold water and ice (4.4 and 4, respectively). These results provided evidence that major changes occur in the water structure around a nonpolar solute and that the perturbed structure is similar to that of the water—methane clathrates, ... 

One of the typical minimized clusters 1 (methane) 10 (waters) is presented in Figure la,b. They show that the methane molecule is enclosed in a cavity formed by water molecules. The two spheres centered on a methane molecule, with radii of 3.6 and 5.35 A, correspond to the first maximum and the first minimum in the radial distribution function goo = goo(roc) in dilute mixtures of methane in water. It is worth noting that... 

Figure 1. Optimized methane (l) water (10) cluster, (a) The front view, (b) The view from the right. The two circles in Figure 1 correspond to the first maximum (3.6 A) and first minimum (5.35 A) of the radial distribution function goc = goc(roc).

Global velocity distribution behind flame front. Upward propagation in 5.15% methane/air mixture, (a) vector map, (b) and (c) scalar maps of axial and radial velocity components, respectively. Spots are caused by condensation of water vapor on the glass walls. 

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