Carbonization radial structure function

Fig. 4. Experimental (target) and simulated carbon-carbon radial distribution function for an activated mesocarbon microbead adsorbent [32]. The RDFs are reported in the form 471 r fi[g(r) — 1], where p is the average carbon density and r is the carbon pair separation distance noted on the horizontal axis. The simulated RDFs for the initial and converged (dashed line) model structures are shown, with numbered peaks referenced in the text.

The average local electrostatic potential V(r)/p(r), introduced by Pohtzer [57], led Sen and coworkers [58] to conjecture that the global maximum in V(r)/p(r) defines the location of the core-valence separation in ground-state atoms. Using this criterion, one finds N values [Eq. (3.1)] of 2.065 and 2.112 e for carbon and neon, respectively, and 10.073 e for argon, which are reasonable estimates in light of what we know about the electronic shell structure. Politzer [57] also made the significant observation that V(r)/p(r) has a maximum any time the radial distribution function D(r) = Avr pir) is found to have a minimum. 

The gas-phase model would then be tested on condensed phases. In the case of the carbonate ion, the parameters can be used to examine the structure of C02(aq), C032-(aq), and HC03 (aq) as well as the structure of, for example, siderite FeC03 and nahcolite Na(HC03). For the aqueous species, the most instructive comparisons are with the results of ab initio molecular dynamics studies of solvated ions, where the radial distribution functions can be used to check the extent of solvation. Fig. 2, for... 

Typical forms of the radial distribution function are shown in Fig. 38 for a liquid of hard core and of Lennard—Jones spheres (using the Percus— Yevick approximation) [447, 449] and Fig. 44 for carbon tetrachloride [452a]. Significant departures from unity are evident over considerable distances. The successive maxima and minima in g(r) correspond to essentially contact packing, but with small-scale orientational variation and to significant voids or large-scale orientational variation in the liquid structure, respectively. Such factors influence the relative location of reactants within a solvent and make the incorporation of the potential of mean force a necessity. 

Using refined X-ray dilfraction techniques and the extraction of the radial distribution function from molecular X-ray scattering it has been possible to develop a model for a graphene layer [31]. This model is free of the difficulties mentioned above and predicts cluster sizes of between n = 3 and n — 5 for pericondensed rings (coronene, hexaperibenzo coronene) in full agreement with electron microscopic [25] and NMR [131] data which led to construction of Fig. 19. The model material [31] was a coal sample before carbonization containing, as well as the main fraction of sp2 centres, about 20% carbon atoms in aliphatic connectivity. This one-dimensional structure analysis represents a real example of the scheme displayed in Fig. 9(C). 

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... 

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. 

A general equation can be derived that describes the variation in direction of the valence electron density about the nucleus. The distortion from sphericity caused by valence electrons and lone-pair electrons is approximated by this equation, which includes a population parameter, a radial size function, and a spherical harmonic function, equivalent to various lobes (multipoles). In the analysis the core electron density of each atom is assigned a fixed quantity. For example, carbon has 2 core electrons and 4 valence electrons. Hydrogen has no core electrons but 1 valence electron. Experimental X-ray diffraction data are used to deri e the parameters that correspond to this function. The model is now more complicated, but gives a better representation of the true electron density (or so we would like to think). This method is useful for showing lone pair directionalities, and bent bonds in strained molecules. Since a larger number of diffraction data are included, the geometry of the molecular structure is probably better determined. 

Figure 5 1 Activated mesocarbon microbead RAIC model, (a) Structural representation of the converged structure. The spheres represent carbon atoms that are shown at a scale much less than their van der Waals radii for reasons of clarity, (b) C-C radial distribution functions (RDF). The experimental RDF (solid line), the simulated, converged RDF (long-dashed line), and the initial simulated RDF (dotted line) are shown. The numbers indicate the different peaks of the RDF. (Adapted from Ref. [33].)...

Figure La) Scattering function for liquid Carbon Tetrachloride together with its determination by means of molecular dynamics and Reverse Monte Carlo (RMC). With dotted lines we show the determination of the intramolecular structural parameters determined by the Bayesian method described in the text, b) Total radial distribution function for the FCC phase, together with the results of RMC.

The remainder of the paper is structured as follows. In Sect. 2, we describe our computational methods. Section 3 presents our results and discussion Sect. 3.1 presents cation radial distribution functions in the presence and absence of carbon dioxide, and Sect. 3.2 describes carbon dioxide and Na" preferred sites of adsorption. These two sections provide the rationale for the alternative scenario described in the previous paragraph and set the stage for Sect. 3.3, where we show a suggestive MD simulation of a carbon dioxide entering a blocked channel. We conclude in Sect. 4. 

The radial distribution function of polymeric carbon prepared from maleic anhydride by plasma deposition by the present authors is shown in Fig. 12 and the peak positions are listed in Table 1. The peaks are situated at 1.44 and 2.9 A, which do not match the peak position of graphite. The peak positions of carbon samples prepared at 600 C are found to be 1.4 and 2.8 A. It is clear from Fig. 12 that there is no layered structure because the region between the second and third peaks is very flat. In addition, the behavior of the radial distribution function with distance cannot be explained using other carbon models, e.g., C 1120, C 340, C 356, and C 519 suggested by Beeman et al. [46,47]. 

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