Effective Landau theory of ferronematics

Abstract

An effective Landau-like description of ferronematics, i.e., suspensions of magnetic colloidal particles in a nematic liquid crystal (NLC), is developed in terms of the corresponding magnetization and nematic director fields. The study is based on a microscopic model and on classical density functional theory. Ferronematics are susceptible to weak magnetic fields and they can exhibit a ferromagnetic phase, which has been predicted several decades ago and has recently been found experimentally. Within the proposed effective Landau theory of ferronematics, one has quantitative access, e.g., to the coupling between the magnetization of the magnetic colloids and the nematic director of the NLC. On mesoscopic length scales, this generates complex response patterns.

A ferronematic slab in external magnetic fields

“…Thereby energy is gained by accomplishing alignment at the expense of the entropic contribution due to the denser packing which is proportional to r log r, where r is the local number density of the colloids (see ref. 15). Segregation is neglected in Section III; nonetheless, we do not expect segregation to influence our results qualitatively (see Section IV).…”

“…as a function of the component of the external magnetic field B along the x-axis for the particular choice of the coupling constant g = 240 (which corresponds to a value of the microscopic coupling constant c E 0.035 15 ) and of the wall anchoring strength W wall = 3.1 Â 10 À5 J m À2 ; this choice of parameters is reasonable in the context of available experimental data (see ref. 10, 11 and 15).…”

“…The authors of ref. 10 proposed a phenomenological expression thereof which is formulated in terms of the magnetization M and the nematic director n. A similar expression was derived analytically starting from a microscopic description of the system: 15 f ðM; nÞ ¼ a 2 jMj 2 À 1 2 gm 0 ðM Á nÞ 2 À M Á B…”

“…where m 0 = 4p  10 À7 N A À2 is the permeability of vacuum, a 4 0 is a constant which depends on the properties of both the nematic medium and the colloids (for an explicit form, see ref. 15), g Z 0 measures the coupling between the magnetization and the nematic director, and B = Be x is the external magnetic field. Note that here g is independent of the magnetization M, i.e., eqn (1) describes the coupling between M and n to the lowest order in M. Both a and g are functions of the microscopic coupling constant c := WR/K, where W is the anchoring strength measuring the interaction energy of the NLC per surface area of a single colloid, R is the radius of a colloidal particle modeled as a thin disc (i.e., a disc whose thickness is much smaller than its radius, such that the interaction of the rim with the NLC medium can be disregarded), and K is the elastic constant of the NLC within the one-elasticconstant approximation.…”

“…10. In our previous study 15 we derived the dependence of the coupling parameter g on the microscopic coupling c, which in turn depends on the particle size. Obtaining the critical field as a function of g allows us to relate it to the size of the colloids and therefore one can potentially tune the value of the critical field by tuning the mean of the size distribution of the particles used.…”