Sodium pair potential

The resultant pair potentials for sodium, magnesium, and aluminium are illustrated in Fig. 6.9 using Ashcroft empty-core pseudopotentials. We see that all three metals are characterized by a repulsive hard-core contribution, Q>i(R) (short-dashed curve), an attractive nearest-neighbour contribution, 2( ) (long-dashed curve), and an oscillatory long-range contribution, 3(R) (dotted curve). The appropriate values of the inter-atomic potential parameters A , oc , k , and k are listed in Table 6.4. We observe that the total pair potentials reflect the characteristic behaviour of the more accurate ab initio pair potentials in Fig. 6.7 that were evaluated using non-local pseudopotentials. We should note, however, that the values taken for the Ashcroft empty-core radii for Na, Mg, and Al, namely Rc = 1.66, 1.39, and... 

Table 6.4 Pair potential parameters for sodium, magnesium, and aluminium at their equilibrium volumes. (From Pettifor and Ward...

Fig. 6.10 The phase shift, cc3, of the long-range contribution to the pair potential for sodium, magnesium, and aluminium as a function of their relative atomic volume, / ). (AfterWard (1985).)...

Fig. 6.12 The structure map, (Z, a3), that is predicted using the long-range pair potential,

Figure 17. Contributions to the ion-ion pair potential as a function of distance apart, r, of two ions i and j, radii n and rj the contributions correspond to the terms in equation (21) for sodium chloride in water with Ay — 400J mol-1.

Figure 11 shows the g(r) for two emulsion samples. The emulsion samples had the same composition, except one had sucrose ester (0.1 wt%) as the watersoluble siufactant and the other had sucrose oleate (0.1 wt%). The fat content was 40 wt%, the protein (sodium caseinate) was 4 wt%, and the water content was 56 wt%. The RDF shows that the corresponding effective pair potential of interaction between fat particles is also oscillatory. The periodicity of the curve is nearly the size of the particles. The structure factor S((t) for these samples is shown in Fig. 12. The first peak height of the structure factor of the sucrose oleate sample is higher, indicating that the addition of sucrose oleate facilitates the fat-particle structure formation. Thus, the fat-particle structure in the sucrose oleate sample is much...

Fig. 7.11. Pair potentials for metallic sodium (Shyu and Gaspari (1967))...

Figure 6 shows the potential of mean force (PMF) between a sodium ion and a chloride ion in water, at infinite dilution of the two ions, obtained from classical atomistic simulations [75]. The first minimum of the potential corresponds to the contact ion pair (CIP) distance, the second minimum corresponds to the solvent-shared ion pair (SIP) distance, and the third minimum to the solvent-separated ion pair (2SIP) distance. Figure 7a shows an example of a SIP in aqueous NaCl [75]. The infinite dilute potential of mean force in Fig. 6 can be used as an effective pah-potential in implicit solvent simulations. The osmotic coefficient (j) (ps) = nilpJc- T (with n the osmotic pressure and ps the salt number density) can be obtained through the virial route. For the case of a binary mixture of components i and j and pairwise additive, density-independent pair potentials, the virial equation can be expressed as... 

H. Inoue, A. Masuno, T. Watanabe, Modeling of the structure of sodium borosilicate glasses using pair potentials. J. Phys. Chem. B 116,12325-12331 (2012)... 

Michielsen J, Woerlee P, van de Graaf F, Ketelaar JAA (1975) Pair potential for alkali metal halides with rock salt crystal stmcture. Molecular dynamics calculations on sodium chloride and lithium iodide. J Chem Soc Faraday Trans 2(71) 1730-1740... 

Liu, W. B. Wood, R. H. Doren, D. J., Hydration free energy and potential of mean force for a model of the sodium chloride ion pair in supercritical water with ab initio solute-solvent interactions, 7. Chem. Phys. 2003,118, 2837-2844... 

In most instances, the group IA metals form +1 ions, but this is not always the case. Because of the low ionization potential of sodium, an unusual situation exists with regard to forming Na+ and Na ion pairs. If we consider the reaction... 

Figure 4.20.A shows a more recent cell reported by Cobben et al. It consists of three Perspex blocks, of which two (A) are identical and the third (B) different. Part A is a Perspex block (1) furnished with two pairs of resilient hooks (3) for electrical contact. With the aid of a spring, the hooks press at the surface of the sensor contact pads (4), the back side of which rests on the Perspex siuface, so the sensor gate is positioned in the centre of the block, which is marked by an engraved cross as in the above-described wall-jet cell. Part B is a prismatic Perspex block (2) (85 x 24 x 10 mm ) into which a Z-shaped flow channel of 0.5 mm diameter is drilled. Each of the wedges of the Z reaches the outside of the block. The Z-shaped flow-cell thus built has a zero dead volume. As a result, the solution volume held between the two CHEMFETs is very small (3 pL). The cell is sealed by gently pushing block A to B with a lever. The inherent plasticity of the PVC membrane ensures water-tight closure of the cell. The closeness between the two electrodes enables differential measurements with no interference from the liquid junction potential. The differential signal provided by a potassium-selective and a sodium-selective CHEMFET exhibits a Nemstian behaviour and is selective towards potassium in the presence of a (fixed) excess concentration of sodium. The combined use of a highly lead-selective CHEMFET and a potassium-selective CHEMFET in this type of cell also provides excellent results.

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