Ferrofluid aggregation in chains under the influence of a magnetic field

The theory of particle association in flexible chains in dilute ferrofluids is generalized to the case of an arbitrarily strengthened magnetic field. The chain distribution in dynamic equilibrium is obtained on the basis of free energy minimization method under the neglect of interchain interaction. The chain partition function is calculated analytically with the help of the rotation matrix technique under the condition when the interparticle dipole-dipole interaction between the nearest neighboring ferroparticles in each chain is taken into account. At weak fields, the chain distribution and the initial susceptibility are shown to be dependent on the value of the correlation coefficient describing the zero field mutual orientational correlations between the magnetic moments of two neighboring ferroparticles in a chain. The internal chain orientational correlations and the field dependent chain lengthening result in higher magnetization of the aggregated ferrofluid in comparison with the Langevin magnetization.