A ferrofluid emulsion, subjected to a slowly increasing magnetic field, exhibits a complicated structural behavior: a gas of Brownian particles changes to columnar solid structures due to induced dipole interaction. Two transition (intermediate) structural regimes are observed: (i) randomly distributed chains and particles and (ii) distinct thin columns and randomly distributed chains and particles. Three structural transition magnetic fields are found, one marking each structural transition, from the initial to the final structural regime. A structural diagram of the structural transition magnetic fields, $H_C,$ versus particle volume fractions, φ, is constructed experimentally. Theoretical models of scaling calculations, based upon the dominant magnetic interaction in each structural regime, give the three structural transition magnetic-field relations as $H_{C1\mathrm{}}\propto {\phi }^{-1/2},$ $H_{C2\mathrm{}}\propto {\phi }^{-1/4},$ and $H_{C3\mathrm{}}\propto \left({\phi }^{\gamma }{/G}^2\right)\exp (\pi G/{\phi }^{(\gamma /2)}),$ where $\gamma =0.39\mathrm{}$ and $G=0.29\mathrm{}$ for our sample. The final end shape of columns and the relative position between columns show that the end-end repulsion between chains is important in the structural formation.

• Received 25 February 1999

DOI:https://doi.org/10.1103/PhysRevE.63.011403