The effect of temperature jumps during polymer crystallization

Temperature changes during the growth of lamellar polymer crystals give rise to steps on the surface of the crystals. It has recently been suggested that these steps could provide important insights into the mechanism of polymer crystallization. In particular, a characterization of the profiles of these steps might reveal the fixed-point attractor that underlies a recently proposed crystallization mechanism. Here we examine this hypothesis by performing simulations of such temperature jumps using the Sadler-Gilmer model. We find that for this model the step profiles do reveal the fixed-point attractor. However, for temperature decreases they also reflect the rounding of the crystal edge that occurs in this model and for temperature increases they also reflect the fluctuations in the thickness present in the crystal. We discuss the implications of these results for the interpretation of experimental step profiles.Comment: 8 pages, 7 figures, revte

Large effect of polydispersity on defect concentrations in colloidal crystals

We compute the equilibrium concentration of stacking faults and point defects in polydisperse hard-sphere crystals. We find that, while the concentration of stacking faults remains similar to that of monodisperse hard sphere crystals, the concentration of vacancies decreases by about a factor two. Most strikingly, the concentration of interstitials in the maximally polydisperse crystal may be some six orders of magnitude larger than in a monodisperse crystal. We show that this dramatic increase in interstitial concentration is due to the increased probability of finding small particles and that the small-particle tail of the particle size distribution is crucial for the interstitial concentration in a colloidal crystal.Comment: 6 pages, 4 figure

Large difference in the elastic properties of fcc and hcp hard-sphere crystals

We report a numerical calculation of the elastic constants of the fcc and hcp crystal phases of monodisperse hard-sphere colloids. Surprisingly, some of these elastic constants are very different (up to 20%), even though the free energy, pressure and bulk compressibility of the two crystal structures are very nearly equal. As a consequence, a moderate deformation of a hard-sphere crystal may make the hcp phase more stable than the fcc phase. This finding has implications for the design of patterned templates to grow colloidal hcp crystals. We also find that, below close packing, there is a small, but significant, difference between the distances between hexagonal layers (c/a ratios) of fcc and hcp crystals.Comment: 4 pages, 4 figures, accepted for publication in Physical Review Letter

A Lattice-Boltzmann method for the simulation of transport phenomena in charged colloids

We present a new simulation scheme based on the Lattice-Boltzmann method to simulate the dynamics of charged colloids in an electrolyte. In our model we describe the electrostatics on the level of a Poisson-Boltzmann equation and the hydrodynamics of the fluid by the linearized Navier-Stokes equations. We verify our simulation scheme by means of a Chapman-Enskog expansion. Our method is applied to the calculation of the reduced sedimentation velocity U/U_0 for a cubic array of charged spheres in an electrolyte. We show that we recover the analytical solution first derived by Booth (F. Booth, J. Chem. Phys. 22, 1956 (1954)) for a weakly charged, isolated sphere in an unbounded electrolyte. The present method makes it possible to go beyond the Booth theory, and we discuss the dependence of the sedimentation velocity on the charge of the spheres. Finally we compare our results to experimental data.Comment: 18 pages, 5 figures, to appear in Phys. Rev.

Point Defects in Hard Sphere Crystals

We report numerical calculations of the concentration of interstitials in hard-sphere crystals. We find that, in a three-dimensional fcc hard-sphere crystal at the melting point, the concentration of interstitials is 2 * 10^-8. This is some three orders of magnitude lower than the concentration of vacancies. A simple, analytical estimate yields a value that is in fair agreement with the numerical results.Comment: 12 pages, 2 figures; Submitted to J. Phys. Chem.