Fluids, dipolar

The second group of images is located at positions defined by E)q. (6.60) and dipole moments /i = /, . Consider now N dipoles in the basic cell and replicate this cell in directions parallel to the walls. Then the total configurational potential energy can be written as (see Appendix F.3.3.2) 

Finally, using essentially the same arguments as for the charged system, we can show that (see Appendix F.3.3.2) 

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Patey G N, Levesque D and Weis J J 1982 On the theory and computer simulation of dipolar fluids Mol. Phys. 45 733-46... 

Gray C G, Sainger Y S, Joslin C G, Cummings P T and Goldman S 1986 Computer simulation of dipolar fluids. Dependence of the dielectric constant on system size a comparative study of Ewald sum and reaction field approaches J. Chem. Phys. 85 1502-4... 

The behavior of simple and molecular ions at the electrolyte/electrode interface is at the core of many electrochemical processes. The complexity of the interactions demands the introduction of simplifying assumptions. In the classical double layer models due to Helmholtz [120], Gouy and Chapman [121,122], and Stern [123], and in most analytic studies, the molecular nature of the solvent has been neglected altogether, or it has been described in a very approximate way, e.g. as a simple dipolar fluid. Computer simulations... 

The structure formation in an ER fluid was simulated [99]. The characteristic parameter is the ratio of the Brownian force to the dipolar force. Over a wide range of this ratio there is rapid chain formation followed by aggregation of chains into thick columns with a body-centered tetragonal structure observed. Above a threshold of the intensity of an external ahgn-ing field, condensation of the particles happens [100]. This effect has also been studied for MR fluids [101]. The rheological behavior of ER fluids [102] depends on the structure formed chainlike, shear-string, or liquid. Coexistence in dipolar fluids in a field [103], for a Stockmayer fluid in an applied field [104], and the structure of soft-sphere dipolar fluids were investigated [105], and ferroelectric phases were found [106]. An island of vapor-liquid coexistence was found for dipolar hard spherocylinders [107]. It exists between a phase where the particles form chains of dipoles in a nose-to-tail... 

Weis,J.-J. and Levesque, D. Simple Dipolar Fluids as Generic Models for Soft Matter. Vol. 185, pp. 163-225. 

Lee, Rasaiah, and Hubbard presented one of the first molecular dynamic studies of the effect of an external field on the properties of a dipolar fluid between charged walls. They simulated a film of 206 Stock-mayer fluid molecules (a Lennard-Jones core in which a point dipole is imbedded) between two flat walls under the influence of external electric fields of intensities ranging from 0 to 4 V/nm. We summarize their results here because they can be used as a reference point for the more complicated case of water. 

The high population of ion pairs near criticality motivated Shelley and Patey [250] to compare the RPM coexistence curve with that of a dipolar fluid. It is now known that a critical point does not develop in a system of dipolar hard spheres [251]. However, ion pairs resemble dumbbell molecules comprising two hard spheres at contact with opposite charges at their centers. Shelley and Patey found that the coexistence curves of these charged dumbbells are indeed very similar in shape and location to the RPM coexistence curve, but very different from the coexistence curve of dipolar dumbbells with a point dipole at the tangency of the hard-sphere contact. 

This formula in an equivalent form (with Xg> instead of Xg because a magnetic moment diffusion inside an isotropic particle was considered) had been obtained in Section III.A.3 as Eq. (4.96). Besides that, similar formulas, with xg indeed, are well known in the theory of rotary Brownian diffusion in dipolar fluids [69]. 

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