Aqueous solution pair distribution functions

The presence of aqueous solvent was found to have little effect upon the mean structure of the pyranoid ring in these MD simulations, with only slight deviations in the time-averaged structure away from that observed in vacuum simulations or in the crystallographic diffraction experiments ( ). However, the presence of the solute had substantial effects upon the average "structuring" of the solvent. Figure 7 displays a pair distribution function g(r), defined as (27)... 

Figure 7. Water oxygen-exocyclic methylene carbon pair distribution function, calculated from a molecular dynamics simulation of a-D-glucopyranose in aqueous solution, giving the normalized probability of finding a water oxygen atom a given distance r from the C6 carbon atom. (Reproduced from Ref. 32. Copyright 1989 American Chemical Society.)...

Figure 2. Experimental pair-distribution functions g(r) for 2 mol dm aqueous solutions of sodium chloride at room temperature and at 1 bar (lower curve) and 1000 bar (upper curve) pressures.

The use of difference methods offers a means whereby a detailed picture of ionic hydration can be obtained 22). For neutron diffraction, the first-order isotopic difference method (see Section III,A) provides information on ionic hydration in terms of a linear combination of weighted ion-water and ion-ion pair distribution functions. Since the ion-water terms dominate this combination, the first-order difference method offers a direct way of establishing the structure of the aquaion. In cases for which counterion effects are known to occur, as, for example, in aqueous solutions of Cu + or Zn +, it is necessary to proceed to a second difference to obtain, for example, gMX and thereby possess a detailed knowledge of both the aquaion-water and the aquaion-coun-terion structure. 

We start with detailed definitions of the singlet and the pair distribution functions. We then introduce the pair correlation function, a function which is the cornerstone in any molecular theory of liquids. Some of the salient features of these functions are illustrated both for one- and for multicomponent systems. Also, we introduce the concepts of the generalized molecular distribution functions. These were found useful in the application of the mixture model approach to liquid water and aqueous solutions. 

Primitive models have been very useful to resolve many of the fundamental questions related to ionic systems. The MSA in particular leads to relatively simple analytical expressions for the Helmholtz energy and pair distribution functions however, compared to experiment, a PM is limited in its ability to model electrolyte solutions at experimentally relevant conditions. Consider, for example, that an aqueous solution of NaCl of concentration 6 mol dm (a high concentration, close to the precipitation boundary for this solution) corresponds to a mole fraction of salt of just 0.1 i.e. such a solution is mostly water. Thus, we see that to estimate the density of such solutions accurately the solvent must be treated explicitly, and the same applies for many other thermodynamic properties, particularly those that are not excess properties. The success of the Triolo et approach can be attributed to the incor-... 

At this time diffraction data for ion-ion distributions in aqueous solutions of moderate concentration are beginning to become available. In aqueous NiCl2 solutions very refined neutron diffraction studies indicate that the Ni2+-Cl pair correlation function has a peak near 3.l8 under conditions in which the Cl does not penetrate the Ni(H20)g2+ unit. (J+2 ) It is reported that EXAFS studies give the same result. (1 3) While the information is most welcome it is puzzling because a geometrical calculation indicates that the closest center to center distance for the Ni2+ and a Cl that does not penetrate the hydration shell is closer to 3.98. (7)... 

The term species refers to the actual form in which a molecule or ion is present in solution. For example, iodine in aqueous solution may conceivably exist as one or more of the species I2, I, la" HIO, IO , lOJ, or as an ion pair or complex, or in the form of organic iodo compounds. Figure 6.1 shows the various forms in which metals are thought to occur in natural waters. It is operationally difficult to distinguish between dissolved and colloidally dispersed substances. Colloidal metal-ion precipitates, such as Fe(OH)3(s) or FeOOH(s) may occasionally have particle sizes smaller than 100 A—sufficiently small to pass through a membrane filter. Organic substances can assist markedly in the formation of stable colloidal dispersions. Information on the types of species encountered under different chemical conditions (types of complexes, their stabilities, and rates of formation) is a prerequisite to a better understanding of the distribution and functions of trace elements in natural waters. 

Furthermore, according to the Hong and Noolandi model, the initial distribution function for pro ons2in aqueous solution, characterized by a diffusion coefficient D 10 cm sec, is diffusing within 10 psec to form a distribution function with a half width of roughly Rjj/2, or 14 A for the given reaction parameters. This period of time is shorter by a factor of 2 than our experimental time resolution. It follows that the real physical situation as well as our time resolution allow us to detect only a diffused distribution of ion pairs distances rather than a sharp distribution. 

Because MD simulation analysis is based on particle interactions, extensive information can be obtained regarding the microscopic structnres of aqueous alkali halide solutions, including ion hydration states, hydrogen-bonding network structure, and ion pairing structure, which can be obtained from the analysis of the radial distribution function (RDF), g(f) (or pair correlation function), which describes how the atomic density varies as a function of distance from one particular atom. 

For water to form the solvent-separated pair, let l , be the minimum distance to be accommodated in the aqueous core region of the reverse micelle. From the pair correlation function between methane and the oxygen, the location of the first minima is observed (Rao et al. 2007) at a distance of Iso = 5.6 k. Fet Ir be the distance between atomic centers of the solute atoms in the solvent-separated configuration, hence the minimum distance, l , = l, + 24. For the case of methane in the solvent-separated configuration in free water, 1 = 1 k and = 18.2 A. For the contact pair, 4 = 3.95 A and the corresponding value of = 15.15 A. From the water density distributions in the reverse micelle. 

Figure 2 Ion-ion radial distribution function calculated from a 100 ps simulation of a l.O M aqueous NaCI solution. The simulation box contained 29 ion pairs and 1531 water molecules. Discontinuities at the 16 A cut-off limit are marked with an arrow...

Neutron scattering methods provide the best experimental means cnr-rently available to probe the atomic strncture of aqueous solutions. It can be proved that a formal mathematical (Fourier transformation) link can be formed between the neutron scattering pattern obtained experimentally and the pair radial distribution functions Sotfi r) of pairs of atoms a and of the system. Knowledge of these functions, either individn-ally or as combinations [G (r)] specific to a particular atom (or ion), a,... 

In this section, we discuss the correlations and effective interactions between ions in aqueous solution. For this purpose we typically look at simulation boxes with about 2000 water molecules and add between 1 and 200 salt pairs in the solution. The main output from the simulation is the radial distribution function jij (r) between the ions. In order to obtain good statistics for further analysis, long simulation runs of about 200 ns are needed. The potential of mean force (PMF) follows by Boltzmann inversion from the radial distribution function according to... 

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