Hard-spheres with dipoles and quadrupoles

Fig. 13. Values of h"°(r) for hard spheres with dipoles and quadrupoles at p = 0.8 and H = Q = 1.0. The dots are MC results (N=256, R(. =3.4rf), and the solid, dashed, and dash-dot curves represent the QHNC, LHNC, and MSA, respectively, for a spherically truncated potential. (Results from Ref. 59.)...

Hard Spheres with Dipoles and Quadrupoles. The LHNC, QHNC, and mean spherical approximations have been solved for fluids of hard spheres with both dipole and quadrupole moments. Theoretical results for spherically truncated potentials have been compared with Monte Carlo (SC)... 

Hard Spheres with Dipoles and Quadrupoles. LHNC and MSA results for fluids of hard spheres with dipoles and quadrupoles are shown in Fig. 20. In both approximations e decreases with increasing quadrupole moment. The LHNC results are particularly dramatic, since the dipolar hard-sphere or Q = 0 value is very large to begin with. As discussed in Section III.B.3, the QHNC approximation is not very satisfactory for dipole-quadrupole systems, since solutions are not found for some values of ju and Q. When solutions can be obtained, however, the QHNC e also decreases sharply with quadrupole moment. 

Dielectric Constant Results for Fluids of Hard Spheres with Dipoles and Quadrupoles at p —0.8... 

S.L. Camie and G.N. Patey, Fluids of polarizable hard spheres with dipoles and tetrahedral quadrupoles. Integral equation results with application to liquid water, Mol. Phys., 47 (1982) 1129-1151. 

One other aspect of nonprimitive electric double layer theories which is particularly relevant to the inner Stern region are the models for the water molecule and the ions. The simplest models for a water molecule and an ion are a hard-sphere point dipole and point charge, respectively. A more realistic model of the hard-sphere water molecule would include quadrupoles and octupoles and also polarizability. However the hard-sphere property is best avoided and replaced, for example, by a Lennard-Jones potential. An alternative to a multipolar water model are three point charge sites associated with the atoms within the water molecule. 

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