Relaxation in supercooled liquids above their glass transition and below the onset temperature of ''slow'' dynamics involves the correlated motion of neighboring particles. This correlated motion results in the appearance of spatially heterogeneous dynamics or ''dynamical heterogeneity.'' Traditional two-point time-dependent density correlation functions, while providing information about the transient ''caging'' of particles on cooling, are unable to provide sufficiently detailed information about correlated motion and dynamical heterogeneity. Here, we study a four-point, time-dependent density correlation function g 4 (r,t) and corresponding ''structure factor'' S 4 (q,t) which measure the spatial correlations between the local liquid density at two points in space, each at two different times, and so are sensitive to dynamical heterogeneity. We study g 4 (r,t) and S 4 (q,t) via molecular dynamics simulations of a binary Lennard-Jones mixture approaching the mode coupling temperature from above. We find that the correlations between particles measured by g 4 (r,t) and S 4 (q,t) become increasingly pronounced on cooling. The corresponding dynamical correlation length 4 (t) extracted from the small-q behavior of S 4 (q,t) provides an estimate of the range of correlated particle motion. We find that 4 (t) has a maximum as a function of time t, and that the value of the maximum of 4 (t) increases steadily from less than one particle diameter to a value exceeding nine particle diameters in the temperature range approaching the mode coupling temperature from above. At the maximum, 4 (t) and the ␣ relaxation time ␣ are related by a power law. We also examine the individual contributions to g 4 (r,t), S 4 (q,t), and 4 (t), as well as the corresponding order parameter Q(t) and generalized susceptibility 4 (t), arising from the self and distinct contributions to Q(t). These contributions elucidate key differences between domains of localized and delocalized particles.

Tooth enamel comprises parallel microscale and nanoscale ceramic columns or prisms interlaced with a soft protein matrix. This structural motif is unusually consistent across all species from all geological eras. Such invariability-especially when juxtaposed with the diversity of other tissues-suggests the existence of a functional basis. Here we performed ex vivo replication of enamel-inspired columnar nanocomposites by sequential growth of zinc oxide nanowire carpets followed by layer-by-layer deposition of a polymeric matrix around these. We show that the mechanical properties of these nanocomposites, including hardness, are comparable to those of enamel despite the nanocomposites having a smaller hard-phase content. Our abiotic enamels have viscoelastic figures of merit (VFOM) and weight-adjusted VFOM that are similar to, or higher than, those of natural tooth enamels-we achieve values that exceed the traditional materials limits of 0.6 and 0.8, respectively. VFOM values describe resistance to vibrational damage, and our columnar composites demonstrate that light-weight materials of unusually high resistance to structural damage from shocks, environmental vibrations and oscillatory stress can be made using biomimetic design. The previously inaccessible combinations of high stiffness, damping and light weight that we achieve in these layer-by-layer composites are attributed to efficient energy dissipation in the interfacial portion of the organic phase. The in vivo contribution of this interfacial portion to macroscale deformations along the tooth's normal is maximized when the architecture is columnar, suggesting an evolutionary advantage of the columnar motif in the enamel of living species. We expect our findings to apply to all columnar composites and to lead to the development of high-performance load-bearing materials.

The dynamical characteristics of ring and linear polyethylene (PE) molecules in the melt have been studied by employing atomistic molecular dynamics simulations for linear PEs with carbon atom numbers N up to 500 and rings with N up to 1500. The single-chain dynamic structure factors S(q,t) from entangled linear PE melt chains, which show strong deviations from the Rouse predictions, exhibit quantitative agreement with experimental results. Ring PE melt chains also show a transition from the Rouse-type to entangled dynamics, as indicated by the characteristics of S(q,t) and mean-square monomer displacements g 1 (t). For entangled ring PE melts, we observe g 1 (t) ∼ t 0.35 and the chain-length dependence of diffusion coefficients D N µ N -1.9 , very similar to entangled linear chains. Moreover, the diffusion coefficients D N remain larger for the entangled rings than the corresponding entangled linear chains, due to about a 3-fold larger chain length for entanglement. Since rings do not reptate, our results point toward other important dynamical modes, based on mutual relaxations of neighboring chains, for entangled polymers in general.

Many polymeric materials crystallize when cooled below their melting temperature. Although progress has been made in our understanding of the crystallization process through both experimental and theoretical efforts, these studies have focused mainly on the crystal nucleation and growth mechanism, where critical nuclei are formed from a metastable state during the first stages of crystallization, leading ultimately to the growth of crystal domains. Attention has also been given to the structure during the precrystallization (induction period). A pretransition state occurring before crystallization has been characterized as an unstable phase separation initiated by density and orientational fluctuations. These fluctuations are caused by an increase in the average length of rigid trans segments along the polymer backbone during the induction period. These observations are consistent with the theory proposed in ref. 14 on the isotropic-to-nematic transition of polymer liquid crystals, that is, the parallel ordering of polymers is caused by an increase in chain rigidity. Here we use large-scale computer simulations to investigate melts of polymers in the early ordering stages (induction period) before crystallization. In the ordered domains we identify growing dense regions similar to smectic liquid crystals. Our simulations reveal a 'coexistence period' in the ordering before crystallization, where nucleation and growth mechanisms coexist with a phase-separation mechanism.

We present a calculation of a fourth-order, time-dependent density correlation function that measures higher-order spatiotemporall correlations of the density of a liquid. From molecular dynamics simulations of a glass-forming Lennard-Jones liquid, we find that the characteristic length scale of this function has a maximum as a function of time which increases steadily beyond the characteristic length of the static pair correlation function g(r) in the temperature range approaching the mode coupling temperature from above.

We have found weak long-range antiferromagnetic order in the quasi-two-dimensional insulating oxide KCr 3 ͑OD͒ 6 ͑SO 4 ͒ 2 which contains Cr 3ϩ Sϭ3/2 ions on a kagomé lattice. In a sample with Ϸ76% occupancy of the chromium sites the ordered moment is 1.1(3) B per chromium ion which is only one-third of the Néel value g B Sϭ3 B . The magnetic unit cell equals the chemical unit cell, a situation which is favored by interplane interactions. Gapless quantum spin fluctuations (⌬/k B Ͻ0.25 K) with a bandwidth of 60 K ӷT N ϭ1.6 K are the dominant contribution to the spin correlation function S(Q,) in the ordered phase.

Recently, we demonstrated via large-scale molecular dynamics simulations a "coexistence period" in polymer melt ordering before crystallization, where nucleation and growth mechanisms coexist with a phase-separation mechanism [Gee et al., Nat. Mater. 5, 39 (2006)]. Here, we present an extension of this work, where we analyze the directional displacements as a measure of the mobility of monomers as they order during crystallization over more than 100 ns of simulation time. It is found that the polymer melt, after quenching, rapidly separates into many ordered hexagonal domains separated by amorphous regions, where surprisingly, the magnitude of the monomer's displacement in the ordered state, parallel to the domain axial direction, is similar to its magnitude in the melt. The monomer displacements in the domain's lateral direction are found to decrease during the time of the simulation. The ordered hexagonal domains do not align into uniform lamellar structures during the timescales of our simulations.

Molecular dynamics simulations of bulk melts of poly(dimethylsiloxane) (PDMS) are utilized to study chain conformation and ordering under constant stress uniaxial extension at room temperature. We find that large extensions induce chain ordering in the direction of applied stress. During the extension, we also find that voids are created via a cavitation mechanism. At the end of our simulations, by visual inspection, we distinguish cavity, fibril, and amorphous regions that coexist together. The surrounding material about the formed cavities is fibril-like, while the remaining material remains amorphous. We also estimate the surface energy of the cavity. The cavity size continually increases in the dimension of applied stress but saturates in the lateral dimensions, most likely due to the finite size of the system. Despite chain orientation and ordering in the direction of applied stress, crystallization is absent in the time and stress range of our simulation. This study represents a baseline for the future study of mechanical properties of PDMS melts enriched with fillers under stress.