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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, straight phi, 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) proportional to straight phi(-1/2), H(C2) proportional to straight phi(-1/4), and H(C3) proportional to (straight phi(gamma)/G2)exp(piG/straight phi((gamma/2))), where gamma=0.39 and G=0.29 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.

Field-induced phase behavior of a confined monodisperse ferrofluid emulsion was studied using optical microscopy, light transmission, and static light scattering techniques. Upon application of magnetic field, randomly-dispersed magnetic emulsion droplets form solid structures at λ = 1.5, where λ is defined as the ratio of the dipole–dipole interaction energy to the thermal energy at room temperature. The new solid phase consists of either single droplet chains, columns, or worm-like clusters, depending on the volume fraction, cell thickness and rate of field application. For the column phase, an equilibrium structure of equally-sized and spaced columns was observed. Our measurements taken for cell thickness 5µ m ≤ L ≤ 500µ m and volume fraction 0.04 show the column spacing to be reasonably described by d = 1.49L0.34.

A ferrofluid emulsion goes through gas — solid phase transition when an external magnetic field is applied. The solid structures are observed as either column, bent-wall, or labyrinthine patterns. The appearance of these different patterns depend upon the rate of the field applied, thickness of the sample cell along the field direction, and the volume fraction of the emulsion droplets used. Using optical microscopy, formed patterns are recorded and analyzed in which a “phase” diagram of the structural transition from column to bent-wall is measured.

Two field-induced phase transition regimes are found in a ferrofluid emulsion system, which are defined by three critical fields, Hc1<HC2<Hc3. The first regime, which starts at Hc1 and finishes at Hc2, is the transition from a gas to induced Nematic liquid crystal phase. In the second regime, or Hc2<H<Hc3, induced Nematic liquid crystal transits to columnar solid structure. A phase diagram is drawn and is explained well by a scaling calculation, which gives Hc1~Φ−1/2, Hc2~Φ−1/4, and Hc3~Φγ exp (πG/Φγ/2), where Φ is the volume fraction, γ=0.172 and G=1.44.