The one-orbital model for manganites with cooperative phonons and superexchange coupling JAF is investigated via large-scale Monte Carlo simulations. The results for two orbitals are also briefly discussed. Focusing on the electron density n=0.75, a regime of competition between ferromagnetic metallic and charge-ordered (CO) insulating states is identified. In the vicinity of the associated bicritical point, colossal magnetoresistance (CMR) effects are observed. The CMR is associated with the development of short-distance correlations among polarons, above the spin ordering temperatures, resembling the charge arrangement of the low-temperature CO state.

Introduction. The dynamics of polymer chains are now generally very well understood in the pioneering frameworks of the Rouse model for short chains, and the reptation model for longer chains. [1][2][3][4][5] While these theories yield well-known expressions for the variation of the diffusivity D and viscosity η with the chain length N, an open question is the chain length at which one crosses over from Rouse-like behavior to reptation. This length, termed the entanglement length, N e , is relatively easy to estimate experimentally, but has been hard to access in a simulation due to the fact that, up until recently, there was no satisfactory definition of an entanglement. 6,7 In numerical studies, most estimates of the entanglement length involve conducting simulations and examining dynamic quantities, such as the frequency dependent storage modulus. Extensive work has been done by Kremer and Grest 8 to identify the onset of chain entanglement, with somewhat mixed results. Examination of the chain length dependence of chain diffusion yields a cross over from the Rouse scaling (N -1 ) to reptation scaling (N -2 ) behavior in the vicinity of chains of length 35. In contrast, estimates of storage modulus from nonequilibrium molecular dynamics simulations yield an entanglement chain length in the vicinity of 80.We approach this problem with the tools of equilibrium molecular dynamics (MD). 9 Equilibrium stress fluctuations which result naturally from these simulations directly provide estimates of the viscosity through the Green-Kubo equation, as suggested by Smith et al. 10 The storage and loss modulus are also computed from the stress autocorrelation function, and the hints of a plateau are seen in the storage modulus. The plateau is the strongest indication of onset of reptation dynamics, and is seen for chain lengths of 80 and higher. Estimates of the entanglement length N e , provide a number closer to 30, consistent with the first estimate provided by Kremer and Grest.Simulation Model and Methods. The MD simulation employs a standard chain model. Interaction between nonbonded monomers are described by a shifted, purely repulsive Lennard-Jones (LJ) potential: U(r) ) 4 [(σ/r) 12 -(σ/r) 6 ] + for r < 2 1/6 σ, and U(r) ) 0 for r > 2 1/6 σ. Adjacent bonded monomers interact via a stiff FENE potential, in the form of V FENE ) -k(R 0 2 /2) ln(1

Equilibrium molecular dynamics simulations on amorphous polymers filled with solid nanoparticles show that mechanical reinforcement results from the formation of a long-lived transient polymer−particle network only over a narrow range of parameter space. In these cases it is necessary that (i) the interfacial zone occupy significantly less volume than the bulk region and (ii) particle−polymer interactions must be strong enough that the relaxation time for the small fraction of adsorbed monomers is much longer than that characterizing the neat polymer. In all other cases, reinforcement will appear to be particle driven since there is no clear demarcation between the adsorbed segments and the bulk polymer. However, the apparent size of the particle will be larger because of the adsorbed segments. Both reinforcement mechanisms occur for systems that do not easily equilibrate, leading us to stress the importance of starting states and processing history which is reminiscent of glassy systems.

Polyatomic density functional theory was used to model tridecane chains near a hard wall under melt conditions. Polymer reference interaction site model (PRISM) liquid state theory provided the bulk structure input for the density functional. The density profile, the fractional distribution of sites, and the variation of the end-to-end separation of the chains as a function of distance from wall contact were calculated, and excellent agreement with the results of full multichain simulation was found.

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