Normal alkanes have a simple molecular structure, but display a surprising variety of ordered phases, including an orthorhombic crystal, followed on heating by two partially ordered rotator phases RI and RII. These phases are interesting both because of the weakly first-order transitions that separate them, and because rotator phases are implicated in the nucleation of crystals in polyethylene. To understand this interesting and technologically important phenomenon, a clear picture of the rotator phase is essential. We conducted all-atom simulations of pure C(23) and mixed C(21)-C(23) normal alkanes. Among potentials we tried, only Flexible Williams gave good agreement with the experimental sequence of phases and transition temperatures. Physical properties of the simulated phases, including lattice dimensions and transition entropy between orthorhombic and rotator RII phase are in good agreement with experiment. We define order parameters for investigating pretransitional fluctuations in RI and RII phases; we observed only very short-range correlations in these phases, but slower temperature scans may be necessary to properly investigate these weakly first-order transitions.

In efforts to produce polymeric materials with tailored physical properties, significant interest has grown around the ability to control the spatial organization of nanoparticles in polymer nanocomposites. One way to achieve controlled particle arrangement is by grafting the nanoparticle surface with polymers that are compatible with the matrix, thus manipulating the interfacial interactions between the nanoparticles and the polymer matrix. Previous work has shown that the molecular weight of the grafted polymer, both at high grafting density and low grafting density, plays a key role in dictating the effective inter-particle interactions in a polymer matrix. At high grafting density nanoparticles disperse (aggregate) if the graft molecular weight is higher (lower) than the matrix molecular weight. At low grafting density the longer grafts can better shield the nanoparticle surface from direct particle-particle contacts than the shorter grafts and lead to the dispersion of the grafted particles in the matrix. Despite the importance of graft molecular weight, and evidence of non-trivial effects of polydispersity of chains grafted on flat surfaces, most theoretical work on polymer grafted nanoparticles has only focused on monodisperse grafted chains. In this paper, we focus on how bidispersity in grafted chain lengths affects the grafted chain conformations and inter-particle interactions in an implicit solvent and in a dense homopolymer polymer matrix. We first present the effects of bidispersity on grafted chain conformations in a single polymer grafted particle using purely Monte Carlo (MC) simulations. This is followed by calculations of the potential of mean force (PMF) between two grafted particles in a polymer matrix using a self-consistent Polymer Reference Interaction Site Model theory-Monte Carlo simulation approach. Monte Carlo simulations of a single polymer grafted particle in an implicit solvent show that in the bidisperse polymer grafted particles with an equal number of short and long grafts at low to medium grafting density, the short grafts are in a more coiled up conformation (lower radius of gyration) than their monodisperse counterparts to provide a larger free volume to the longer grafts so they can gain conformational entropy. The longer grafts do not show much difference in conformation from their monodisperse counterparts at low grafting density, but at medium grafting density the longer grafts exhibit less stretched conformations (lower radius of gyration) as compared to their monodisperse counterparts. In the presence of an explicit homopolymer matrix, the longer grafts are more compressed by the matrix homopolymer chains than the short grafts. We observe that the potential of mean force between bidisperse grafted particles has features of the PMF of monodisperse grafted particles with short grafts and monodisperse grafted particles with long grafts. The value of the PMF at contact is governed by the short grafts and values at large inter-particle distances are governed by the longer gra...

Normal alkanes display multiple ordered phases, including an orthorhombic crystal (X) and two partially ordered rotator phases (RI and RII). The rotator phase transitions X-RI and RI-RII are of interest because they are weakly first-order, and because experiments suggest that crystalline polyethylene may nucleate via a metastable rotator phase. We have performed heating and cooling scans of all-atom NσT (isothermal, isostress) simulations of a pure C(23) solid. We find a sequence of phases, transition temperatures, structural and thermodynamic properties, all reasonably consistent with experiment, except that a monoclinic crystal is more stable in our simulations than the experimental orthorhombic structure. We find that the RI phase is well described as an orthorhombic crystal disordered by random ±90° rotations of molecules about their stem axis, and the RII phase can be represented as a loose hexagonal packing of parallel chain stems, which tend to orient with the in-plane projection of C-C bonds pointing between neighbors. To measure local orthorhombic, RI, or RII order, we define Potts- and Ising-like order parameters, from which global order parameters and correlation functions can be computed. We observe modest pretransitional fluctuations of local RI order in the RII phase near T(RI-RII), characteristic of this weakly first-order transition.

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Anisotropic protein interactions play a role in globular protein phase transitions, including the shape of fluid-fluid coexistence curves and the formation of hemoglobin polymer fibers in sickle cell disease. Also, the solvent has been shown to play an important role in the phase behavior of some aqueous protein solutions, through the release or trapping of water molecules upon crystallization. Both anisotropy and solvent effects have been treated separately in earlier theoretical studies. Here we propose and analyze a simple, composite model that treats both anisotropy and solvent effects. We find that this model qualitatively explains some phase behavior that has been observed in protein solutions, including normal and retrograde solubility curves and lower critical points.