Pseudo Liquid-Solid Transition of Self-Assembled Spherical Aggregates

We present a molecular dynamics study into the thermotropic liquid crystalline phase behavior of taper-like dendritic polyphilic molecules. Our coarse-grained model consists of 11 spherical beads, held in a semi-flexible 'pizza slice' arrangement (Fig. 1), with a single apex beads and four interior beads defined to have self-attraction, while remaining periphery beads and cross-interactions were made softly-repulsive. In essence this choice bestows an incompatibility between the three bead types. At low temperatures, the dendrons self-organise, apex centrally, into spherical aggregates with a narrow cluster size (Fig. 2a), essentially converting into a fluid phase of supramolecular spheres of roughly the same size (Fig. 2b). At lower temperatures this psudo-fluid crystallizes into a body-centred cubic arrangement, in effect resembling a liquid-solid transition. Although the liquid crystal lattice has been reported experimentally as a unique case of self-organized supramolecular soft matter [Ungar et al. Science, 299, 1208 (2003); Zheng et al. Nature, 428, 157 (2004)] the intermediate liquid-phase is an undiscovered prediction of our model.

The liquid crystalline nature of both aggregate phases was confirmed visually, with both intra- and inter- aggregate dendron diffusion calculated. Moreover self-assembly from a quench isotropic state to the crystalline aggregate state confirmed the fluid nature of the phase, as well as elucidating the formation mechanism. Dendron cluster analysis, revealed a unimodal distribution of cluster size (Fig. 2c) in both aggregate phases, permitting a description of the aggregates as effective particles. By taking the mean position of clustered apex beads as a mapping to effective aggregate positions, aggregate radial distribution functions (Fig. 2d). Crystalline order parameters allowed further phase characterisation. Finally a Gibbs-Duhem integration was used to trace the pseudo liquid-solid coexistence curve from a point determined by thermodynamic integration.

Fig. 1 Coarse-grained model

Fig. 2. Analysis of the liquid-like mesophase composed of self-assembled aggregates (see text)