A detailed computational study of the potential of mean force between a pair of spherical particles dissolved in a homopolymer melt has been performed using microscopic liquid state theory. The role of particle-to-monomer diameter ratio, degree of polymerization, strength and spatial range of monomer-particle attractions, and direct interfiller attractions has been established. Beyond the small particle regime, the potential of mean force scales linearly with the particle-to-monomer diameter ratio. This simple scaling allows the construction of master curves and the quantification of material specific aspects independent of the filler-to-monomer diameter ratio. For hard-sphere fillers, four general categories of polymer-mediated organization are found: contact aggregation due to depletion attraction, segment level tight particle bridging, steric stabilization due to thermodynamically stable "bound polymer layers", and "tele-bridging" where distinct adsorbed layers coexist with longer range bridging. The conditions on the strength and spatial range of monomer-particle attractive interactions that define these different modes of organization have been established. Direct interparticle van der Waals attractions favor contact aggregation and thus compete with the rich polymer-mediated behavior. As the direct attractions increase in strength, the globally stable noncontact bridging configuration is gradually destabilized and replaced by contact aggregation as the most favored state of packing. However, bridging states often remain as metastable local minima. Steric stabilization systems are much less affected by direct interfiller attractions due to the thermodynamic stability of distinct bound polymer layers. This suggests design rules for achieving good particle dispersion. In addition, the interesting possibility is raised that sterically stabilized nanofillers may crystallize in a homopolymer matrix at relatively low volume fractions. Our results have implications for nonequilibrium phenomena such as gelation or filler network formation and kinetic stabilization via large repulsive barriers, which are qualitatively discussed.

Freeze-fracture transmission electron microscopy study of the nanoscale structure of the so-called "twist-bend" nematic phase of the cyanobiphenyl (CB) dimer molecule CB(CH 2 ) 7 CB reveals stripe-textured fracture planes that indicate fluid layers periodically arrayed in the bulk with a spacing of d ∼ 8.3 nm. Fluidity and a rigorously maintained spacing result in long-range-ordered 3D focal conic domains. Absence of a lamellar X-ray reflection at wavevector q ∼ 2π/d or its harmonics in synchrotron-based scattering experiments indicates that this periodic structure is achieved with no detectable associated modulation of the electron density, and thus has nematic rather than smectic molecular ordering. A search for periodic ordering with d ∼ in CB(CH 2 ) 7 CB using atomistic molecular dynamic computer simulation yields an equilibrium heliconical ground state, exhibiting nematic twist and bend, of the sort first proposed by Meyer, and envisioned in systems of bent molecules by Dozov and Memmer. We measure the director cone angle to be θ TB ∼ 25°a nd the full pitch of the director helix to be p TB ∼ 8.3 nm, a very small value indicating the strong coupling of molecular bend to director bend. R ecently there has been growing interest in the liquid crystal (LC) phase behavior of achiral dimer molecules, such as cyanobiphenyl-(CH 2 ) n -cyanobiphenyl (CBnCB), shown for n = 7 in Fig. 1 A (1, 2). This arises from the observation of a transition in these mesogens from a typical nematic (N) to a lower-temperature (NX) phase, also apparently nematic, which exhibits a variety of unusual characteristics (3-10). These include: (i) textural features in depolarized transmission light microscopy (DTLM) similar to those found in fluid, lamellar smectic phases but with no X-ray scattering to indicate lamellar ordering of molecules (8); (ii) a variety of other completely unfamiliar DTLM textures (6), including the spontaneous appearance of director field deformation and evidence for small Frank elastic constants (3); (iii) evidence for the chiral molecular organization on the NMR timescale (4), and in macroscopic conglomerate domains in electrooptic experiments on monodomain textures (9); (iv) distinctive odd/even effects in the linker length n, including, in particular, that i-iii are found only in the n-odd homologs (6).These observations, combined with the fact that the all-trans conformations of the n-odd homologous dimers are distinctly bent (Fig. 1B), have led to the notion that the NX is a "twistbend" (TB) phase, sketched in Fig. 1C, a nematic having a conically helixed ground state of the sort originally proposed by Meyer as the result of the spontaneous appearance of bend flexoelectric polarization (11). More recently Dozov proposed such a ground state as a spontaneously chiral conglomerate domain stabilized by molecular bend (12), and Memmer obtained such structures in computer simulations of systems of bent GayBerne dimers (13). This ground-state helix can be written for CB7CB in terms of a half-molecular director n(z), ...

The microscopic polymer reference interaction site model theory of polymer nanocomposites composed of flexible chains and spherical nanoparticles has been employed to study second virial coefficients and spinodal demixing over a wide range of interfacial chemistry, chain length, and particle size conditions. For hard fillers, two distinct phase separation behaviors, separated by a miscibility window, are generically predicted. One demixing curve occurs at relatively low monomer-particle attraction strength and corresponds to a very abrupt transition from an entropic depletion attraction-induced phase separated state to an enthalpically stabilized miscible fluid. The homogeneous mixture arises via a steric stabilization mechanism associated with the formation of thin, thermodynamically stable bound polymer layers around fillers. The second demixing transition occurs at relatively high monomer-particle adsorption energy and is inferred to involve the formation of an equilibrium physical network phase with local bridging of particles by polymers. This spinodal is sensitive to both particlemonomer diameter ratio and the spatial range of the interfacial attraction. The miscibility window narrows, and can ultimately disappear, with increasing polymer chain length, direct van der Waals attractions between fillers, and/or particle-monomer size asymmetry ratio. The implications of our results for the design of well-dispersed thermodynamically stable polymer nanocomposites, and the formation of nonequilibrium gels, are discussed.