As the clay±clay repulsion becomes stronger, however, the phase diagram is dominated by the new ªplastic solidº (or ªhouse-of-cardsº) structure. Here, the disks exhibit three-dimensional positional ordering, but no orientational ordering. [2] This phase should exhibit the dynamic properties of a solid or a gel (unlike the liquid-like isotropic and nematic phases). At larger volume fractions, orientational ordering must take place, and we observe a plastic solid±columnar (PS±Col) transition. This transition is similar to the one found by Brown et al. [16,17] in their studies of plate-like particles of nickel hydroxide. (In their studies, a repulsive potential was induced by electrostatic interactions; we expect that the polymer-induced entropic repulsion should produce similar effects for the polymer/clay systems.)
In order to study the sensitivity of the phase diagram to variations in the concentration of end-functionalized chains, we repeated both the SCF and DFT calculations for U = 0.01. The only difference between the two cases was that the threshold value for favorable intermixing between the polymers and sheets shifted from e = ±4.5 (for U = 0.05) to approximately ±6 (for U = 0.01). Correspondingly, the phase diagram shifted downward for the U = 0.01 example; the overall features of the diagram remain the same as the U = 0.05 case. This result is to be expected since the amount of available end-functionalized chains in the melt is decreased and thus, higher values of e are needed to promote the adsorption of these species.
In summary, we investigated the phase behavior of a mixture containing organically modified clay, non-functionalized polymers and a small volume fraction of end-functionalized chains. The parameter e characterizes the interaction between the terminal functional group and the surface. For small negative e, the system is completely immiscible. As the sticker/surface attraction is increased, the system exhibits isotropic and nematic morphologies at relatively low clay volume fractions (u £ 0.12). The latter structures correspond to thermodynamically stable, exfoliated composites. Finally, when the surface/ sticker attraction is increased even further, the system exhibits a plastic solid morphology at low u, and a columnar phase at very high u. The plastic solid phase probably indicates the formation of a gel-like network structure where the adjacent plates are oriented at right angles between each other, and the overall orientation is isotropic. [2] The proposed technique can be applied to describe the equilibrium phase behavior of other model nanocomposite or polymer/colloid systems. The resulting phase diagrams can be used as guidelines for the development of new composites with thermodynamically stable morphologies.