Dipolar soft-sphere particles

FIGU RE 8.19 Phase diagram of dipolar soft-sphere particles with Yukawa parameters kdipole moment strength y, packing fraction T]) representation. The circles denote points where the phase boundary was determined and the gray area denotes the coexistence region (where tie lines are vertical). The upper horizontal axis gives an estimate of the root-mean-square external electric Field (see text for details). (From Hynninen AP and Dijkstra M. 2005. Physical Review Letters 94 138303. With permission.)... 

Increasing the dipole coupling shifts the transition densities to lower densities. For instance, in dipolar soft spheres (256 particles) magnetic ordering sets in at a density p pa 0.85 for 7, 4 [103], p pa 0.65 for X 6.25 [102,103] and p pa 0.55 - 0.60 at A, 9 [102,103]. Transition densities are similar in DHS [113,135], but are much higher in Stockmayer fluids where a ferroelectric transition exists only for A, > 4 [127,136] at densities generally larger than the liquid densities at 1-g coexistence. MC simulations by Gao and... 

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... 

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