Nematic-Wetted Colloids in the Isotropic Phase: Pairwise Interaction, Biaxiality, and Defects

Abstract

We calculate the interaction between two spherical colloidal particles embedded in the isotropic phase of a nematogenic liquid. The surface of the particles induces wetting nematic coronas that mediate an elastic interaction. In the weak wetting regime, we obtain exact results for the interaction energy and the texture, showing that defects and biaxiality arise, although they are not topologically required. We evidence rich behaviors, including the possibility of reversible colloidal aggregation and dispersion. Complex anisotropic self-assembled phases might be formed in dense suspensions.Pacs numbers: 68.08.Bc, 82.70.Dd Dispersions of small particles or liquid droplets in a host fluid, namely colloidal suspensions, are a widespread and important state of matter [1]. They are long-lived metastable states, of fundamental interest from the point of view of collective interactions in complex matter. They also have considerable technological importance, e.g., in paints, coatings, foods and drugs. To prevent coagulation due to attractive van der Waals forces, usually the particles are treated in order to produce Coulombic or steric repulsive interactions. Recently, a novel source of repulsion has been reported: the elastic distortion of a liquid crystal host [2], i.e., a fluid phase with long-range orientational order of the molecules. The repulsion arises from the competition between the surface aligning property, which favors, e.g., a radial orientation of the nematic molecules, and the bulk elasticity, which favors a uniform nematic orientation [3]. This effect was shown to arise also in other anisotropic fluid hosts, e.g., lyotropic solutions of anisotropic micelles [4], and in different liquid crystal phases, e.g., cholesterics [5]. Lately, such systems were shown to form liquid or solid composite materials with unusual properties [6,7].It is well known that solid surfaces influence not only the orientation of liquid crystals, but also, in general, the degree of order of their constituent molecules. In particular, a surface can induce a wetting nematic layer even above the transition temperature at which the nematic becomes an ordinary isotropic liquid [8][9][10]. Therefore, an elastic colloidal stabilization could be achieved also above the nematic-isotropic transition. In addition, the vicinity of a phase transition may give a critical character to the stabilization mechanism and yield rich phaseseparation behaviors, as predicted in [11] for a simpler system with a scalar order-parameter.To understand these complex collective effects, it is essential to calculate the interaction between the particles precisely. An attempt, based on a quasi-planar approximation and assuming uniaxiality of the nematic tensorial order, has been proposed in Ref. [12]. Here, we give the first exact solution to the problem, including biaxiality. Our calculation, based on a multipolar expansion, is valid for weak surface ordering. We obtain numerically the texture between two spherical particles imposing normal boundary condition...

Exact calculations of the paranematic interaction energy for colloidal dispersions in the isotropic phase of a nematogenic material

“…The full-line is the exact result, numerically calculated according to Ref. [9]. The dotted-line, practically coincident with the full-line, corresponds to the asymptotic formula (8).…”

“…Two effects compete: an attraction due to the favorable overlapping of the paranematic halos and a repulsion due to the distortion of the director field. For small particles, of size comparable to the nematic-isotropic coherence length ξ, it has been predicted that repulsion may dominate and stabilize the colloidal dispersion [6,9]. (Note that latex particles as small as 50 nm have been successfully dispersed in lyotropic nematics [12].)…”

“…Besides, we point out that in the considered regime, the exact interaction is extremely well approximated by a simple analytical formula which is asymptotically exact. In recent years, a large interest has been devoted to understanding the interactions and phase behavior of colloidal particles dispersed in a nematic phase [1,2,3,4,5] or in the isotropic phase of a nematogenic compound [6,7,8,9]. In the nematic phase, colloids experience a specific elastic interaction because they induce competing distortions of the nematic director field.…”

“…It turns out that our exact calculations [9], based on a multipolar expansion for the full tensorial order-parameter Q ij , rest on the same theoretical model, and can be performed also for micron-sized particles. * Electronic address: jbf@turner.pct.espci.fr † Electronic address: galatola@ccr.jussieu.fr [7].…”

“…[8], by comparing it with the exact one, numerically calculated according to the method of Ref. [9]. For the typical values considered in Ref.…”