Efficiency of various lattices from hard ball to soft ball: Theoretical study of thermodynamic properties of dendrimer liquid crystal from atomistic simulation

Self-assembled supramolecular organic liquid crystal structures at nanoscale have potential applications in molecular electronics, photonics, and porous nanomaterials. Most of these structures are formed by aggregation of soft spherical supramolecules, which have soft coronas and overlap each other in the packing process. Our main focus here is to study the possible packing mechanisms via molecular dynamics simulations at the atomistic level. We consider the relative stability of various lattices packed by the soft dendrimer balls, first synthesized and characterized by Percec et al. (J Am. Chem. Soc. 1997, 119, 1539) with different packing methods. The dendrons, which form the soft dendrimer balls, have the character of a hard aromatic region from the point of the cone to the edge with C-12 alkane "hair". After the dendrons pack into a sphere, the core of the sphere has the hard aromatic groups, while the surface is covered with the C-12 alkane "hair". In our studies, we propose three ways to organize the hair on the balls, Smooth/Valentino balls, Sticky/Einstein balls, and Asymmetric/Punk balls, which lead to three different packing mechanisms, Slippery, Sticky, and Anisotropic, respectively. We carry out a series of molecular dynamics (MD) studies on three plausible crystal structures (A15, FCC, and BCC) as a function of density and analyze the MD based on the vibrational density of state (DoS) method to extract the enthalpy, entropy, and free energies of these systems. We find that anisotropic packed A15 is favored over FCC, BCC lattices. Our predicted X-ray intensities of the best structures are in excellent agreement with experiment. "Anisotropic ball packing" proposed here plays an intermediate role between the enthalpy-favored "disk packing" and entropy-favored "isotropic ball packing", which explains the phase transitions at different temperatures. Free energies of various lattices at different densities are essentially the same, indicating that the preferred lattice is not determined during the packing process. Both enthalpy and entropy decrease as the density increases. Free energy change with volume shows two stable phases: the condensed phase and the isolated micelle phase. The interactions between the soft dendrimer balls are found to be lattice dependent when described by a two-body potential because the soft ball self-adjusts its shape and interaction in different lattices. The shape of the free energy potential is similar to that of the "square shoulder potential". A model explaining the packing efficiency of ideal soft balls in various lattices is proposed in terms of geometrical consideration.