Dipolar hard-sphere particles

FIGURE 8.18 Phase diagram of dipolar hard-sphere particles in the (dipole moment strength y, packing fraction Tj) representation. The circles denote points where the phase boundary was determined and the gray areas denote coexistence regions (where tie lines are vertical). (From Hynninen AP and Dijkstra M. 2005. Physical Review Letters 94 138303. With permission.)... 

The solution detennines c(r) inside the hard core from which g(r) outside this core is obtained via the Omstein-Zemike relation. For hard spheres, the approximation is identical to tire PY approximation. Analytic solutions have been obtained for hard spheres, charged hard spheres, dipolar hard spheres and for particles interacting witli the Yukawa potential. The MS approximation for point charges (charged hard spheres in the limit of zero size) yields the Debye-Fluckel limiting law distribution fiinction. 

Finally, C tld /,.[ = cdd = c Jm is the Fourier transform of the replica-replica direct correlation function (blocking function), and the connected function is defined as usual by cc = cdd — cdd, and similarly for hc. Let us recall that the replicated particles are the dipolar hard spheres, i.e. the annealed fluid in the partly quenched mixture. 

MRF results for dipolar hard spheres at p = 0.8 have been reported by Adams and by Levesque, et al. Adams has carried out a 500-particle = 3.85d) MRF calculation at =2.75 assuming that c=50 in the re-action-field expression (3.47). The MRF results (Figs. 9 and 10) lie below the LHNC and QHNC results for an infinite system, but well above the SC... 

Fries, P. H. and G. N. Patey. 1985. The solution of the hypemetted-chain approximation for fluids of nonspherical particles—A general-method with application to dipolar hard-spheres. Journal of Chemical Physics. 82, 429. 

Ferroelectric fluid phases have also been observed in simulations of disk-shaped particles with embedded dipole moments along the symmetry axis [ 147,148] (see Sect. 4) and in a dipolar hard sphere model carrying two parallel dipole moments displaced equally from the sphere centre [ 149]. In the latter model antiferroelectric arrangement of the particles is, however, equally preferred at sufficiently large separations (0.3a) of the two dipole moments. 

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... 

---