Search Results (9 total)

We consider the escape of a flexible, self-avoiding polymer chain out of a confined geometry. By means of simulations, we demonstrate that the translocation time can be described by a simple scaling law that exhibits a nonlinear dependence on the degree of polymerization and that is sensitive to the nature of the confining geometry. These results contradict earlier predictions but are in agreement with recently confirmed geometry-dependent expressions for the free energy of confinement.

The original Thomson problem of “spherical crystallography” seeks the ground state of electron shells interacting via the Coulomb potential; however one can also study crystalline ground states of particles interacting with other potentials. We focus here on long-range power-law interactions of the form 1∕r^γ (0<γ<2), with the classic Thomson problem given by γ=1. At large R∕a, where R is the sphere radius and a is the particle spacing, the problem can be reformulated as a continuum elastic model that depends on the Young’s modulus of particles packed in the plane and the universal (independent of the pair potential) geometrical interactions between disclination defects. The energy of the continuum model can be expressed as an expansion in powers of the total number of particles, M∼(R∕a)², with coefficients explicitly related to both geometric and potential-dependent terms. For icosahedral configurations of 12 five-fold disclinations, the first nontrivial coefficient of the expansion agrees with explicit numerical evaluation for discrete particle arrangements to four significant digits; the discrepancy in the fifth digit arises from a contribution to the energy that is sensitive to the particular icosadeltahedral configuration and that is neglected in the continuum calculation. In the limit of a very large number of particles, an instability toward grain boundaries can be understood in terms of a “Debye-Huckel” solution, where dislocations have continuous Burgers’ vector “charges.” Discrete dislocations in grain boundaries for intermediate particle numbers are discussed as well.

We present a numerical study of colloidal crystal growth on finite templates. Specifically, we consider planar, crystalline templates with the structure of the 100, 110, and 100 faces of a fcc crystal. We explore how the size of the induced crystallites depends on template area, lattice spacing and degree of supersaturation. We find that thermal fluctuations of the templating particles around their average positions have a strong effect on the size of the crystallites that grow epitaxially. If the fluctuations exceed the Lindemann criterion, the templates cease to function as a crystallization seed. We find that our numerical results are well described by a suitably modified version of classical nucleation theory.

We used optical tweezers to measure the force-extension curve for the formation of tubes from giant vesicles. We show that a significant force barrier exists for the formation of tubes, which increases linearly with the radius of the area on which the pulling force is exerted. The tubes form through a first-order transition with accompanying hysteresis. We confirm these results with Monte Carlo simulations and theoretical calculations. Whether membrane tubes can be formed in, for example, biological cells, thus depends on the details of how forces are applied.

We report simulations of crystal nucleation in binary mixtures of hard spherical colloids with a size ratio of 1∶10. The stable crystal phase of this system can be either dense or expanded. We find that, in the vicinity of the solid-solid critical point where the crystallites are highly compressible, small crystal nuclei are less dense than large nuclei. This phenomenon cannot be accounted for by either classical nucleation theory or by the Gibbsian droplet model. We argue that the observed behavior is due to the surface stress of the crystal nuclei. The observed effect highlights a general deficiency of the most frequently used thermodynamic theories for crystal nucleation. Surface stress should lead to an experimentally observable expansion of crystal nuclei of colloids with short-ranged attraction and of globular proteins.

We attack the generalized Thomson problem, i.e., determining the ground state energy and configuration of many particles interacting via an arbitrary repulsive pairwise potential on a sphere via a continuum mapping onto a universal long range interaction between angular disclination defects parametrized by the elastic (Young) modulus Y of the underlying lattice and the core energy E_core of an isolated disclination. Predictions from the continuum theory for the ground state energy agree with numerical simulations of long range power law interactions of the form 1/r^γ (0<γ<2) to four significant figures. The generality of our approach is illustrated by a study of grain boundary proliferation for tilted crystalline order and square lattices on the sphere.

The formation of vortex loops (global cosmic strings) in an O(2) linear sigma model in three spatial dimensions is analyzed numerically. For over-damped Langevin dynamics we find that defect production is suppressed by an interaction between correlated domains that reduces the effective spatial variation of the phase of the order field. The degree of suppression is sensitive to the quench rate. A detailed description of the numerical methods used to analyze the model is also reported.

We determine the Poisson ratio of self-avoiding fixed-connectivity membranes, modeled as impenetrable plaquettes, to be σ  =  -0.37(6), in statistical agreement with the Poisson ratio of phantom fixed-connectivity membranes σ  =  -0.32(4). Together with the equality of critical exponents, this result implies a unique universality class for fixed-connectivity membranes. Our findings thus establish that physical fixed-connectivity membranes provide a wide class of auxetic (negative Poisson ratio) materials with significant potential applications in materials science.