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

Abstract

In a recent paper [Phys. Rev. E 61, 2831(2000], Borštnik, Stark andŽumer have studied the stability of a colloidal dispersion of micron-sized spherical particles in the isotropic phase of a nematogenic material. Close to the nematic transition, the attraction due to a surface-induced paranematic order can yield flocculation. Their calculation of the nematic-mediated interaction was based on an ansatz for the order-parameter profile. We compare it with an exact numerical calculation, showing that their results are qualitatively correct. 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. New physics arises due to the long-range character of this interaction and the induction of topological defects [1].In the isotropic phase, the surface of colloidal particles can induce a local paranematic order [10,11], giving rise to a short-range elastic interaction [6,7]. 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].) On the other hand, Borštnik, Stark andŽumer have predicted that for micron-sized particles attraction dominates [7], which allows to trigger flocculation close to the nematic transition [8].The results of Borštnik, Stark andŽumer [8] are based on a composite ansatz for the nematic director field n and for the scalar order-parameter Q, within an uniaxial hypothesis. 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

Liquid-crystal mediated nanoparticle interactions and gel formation

“…18,[34][35][36][37][38][39][40][41][42][43] The range of this interaction can be characterized by the thickness ξ W of the nematic wetting layer, which diverges as coexistence is approached. 36 The prevalence of wetting is strongly dependent on the curvature of the wet surface-prewetting behavior is expected to disappear entirely for particles with radii less than 100 nm.…”