Diffusion of Nanoparticles in Liquid Crystalline Systems

Nicholas Abbot, Juan de Pablo

Figure 1: A) x-y projection of the trace of a functionalized gold nanoparticle suspended in 5CB determined by particle tracking and dark-field microscopy, and B) corresponding displacemetn distribution extracted from that trace. C) Representative configurations from simulations of nanoparticles in nematic liquid crystal for parallel anchoring (top) and homeotropic anchirong (bottom). D) Trace of nanoparticle from MD simulations of system shown in C) (units of particle diameter).

A central property of a nanoparticle suspended in an isotropic solvent is its diffusion coefficient, which has traditionally been used to estimate the particle diameter or, when the diameter is known, to estimate the solvent's viscosity. The situation is more complex when the nanoparticle is suspended in a nematic liquid crystal. Experimental data for diffusion coefficients in such systems are not available, and it is unclear whether the so-called Stokes-Einstein relation that relates diffusivity to size and viscosity in isotropic fluids actually holds at all. Perhaps more importantly, it is not known whether the nature of the anchoring of the liquid crystal at the particles' surface is the same as that encountered on flat substrates, or whether it is influenced by curvature.

To address such questions, we have undertaken darkfield microscopy experiments and have shown that such a technique can be used to track the trajectories of chemically-functionalized gold nanoparticles in nematic liquid crystals (LCs), thus leading to measurements of the diffusion coefficients of the nanoparticles in the LCs (see Figure 1). These measurements reveal that the diffusion coefficients of the nanoparticles dispersed in the LC are strongly dependent on the surface chemistry of the nanoparticles. Because the changes in surface chemistry are measured to have negligible influence on the diffusion coefficients of the same nanoparticles dispersed in isotropic solvents, we conclude that surface chemistry-induced changes in the local order of LCs underlie the behavior of the diffusion coefficients of the nanoparticles in the LC. Surface chemistry-dependent ordering of the LCs near the surfaces of the nanoparticles was also found to influence diffusion coefficients measured when the LC was heated above the bulk nematic-to-isotropic transition temperature. These experimental measurements have been placed into the context of past theoretical predictions regarding the impact of local ordering of LCs on diffusion coefficients. Our experimental observations are consistent with those of detailed molecular dynamics simulations in which the anchoring at the particles' surface can be varied systematically (see Figure 1). The results that emerged from our studies have provided important new insights into the mobility of nanoparticles in LCs, and have suggested new approaches based on measurements of nanoparticle dynamics that yield previously unavailable information on the ordering of LCs near nanoparticles.