Crystallization of hard aspherical particles

We use numerical simulations to study the crystallization of monodisperse systems of hard aspherical particles. We find that particle shape and crystallizability can be easily related to each other when particles are characterized in terms of two simple and experimentally accessible order parameters: one based on the particle surface-to-volume ratio, and the other on the angular distribution of the perturbations away from the ideal spherical shape. We present a phase diagram obtained by exploring the crystallizability of 487 different particle shapes across the two-order-parameter spectrum. Finally, we consider the physical properties of the crystalline structures accessible to aspherical particles, and discuss limits and relevance of our results.Comment: 4 pages, 3 figures. Published in the Journal of Chemical Physics

Theoretical analysis of degradation mechanisms in the formation of morphogen gradients

Fundamental biological processes of development of tissues and organs in multicellular organisms are governed by various signaling molecules, which are called morphogens. It is known that spatial and temporal variations in the concentration profiles of signaling molecules, which are frequently referred as morphogen gradients, lead to a cell differentiation via activating specific genes in a concentration-dependent manner. It is widely accepted that the establishment of the morphogen gradients involves multiple biochemical reactions and diffusion processes. One of the critical elements in the formation of morphogen gradients is a degradation of signaling molecules. We develop a new theoretical approach that provides a comprehensive description of the degradation mechanisms. It is based on the idea that the degradation works as an effective potential that drives the signaling molecules away from the source region. Utilizing the method of first-passage processes, the dynamics of the formation of morphogen gradients for various degradation mechanisms is explicitly evaluated. It is found that linear degradation processes lead to a dynamic behavior specified by times to form the morphogen gradients that depend linearly on the distance from the source. This is because the effective potential due to the degradation is quite strong. At the same time, nonlinear degradation mechanisms yield a quadratic scaling in the morphogen gradients formation times since the effective potentials are much weaker. Physical-chemical explanations of these phenomena are presented

Phase behavior of repulsive polymer-tethered colloids

We report molecular dynamics simulations of a system of repulsive, polymer-tethered colloidal particles. We use an explicit polymer model to explore how the length and the behavior of the polymer (ideal or self-avoiding) affect the ability of the particles to organize into ordered structures when the system is compressed to moderate volume fractions. We find a variety of different phases whose origin can be explained in terms of the configurational entropy of polymers and colloids. Finally, we discuss and compare our results to those obtained for similar systems using simplified coarse-grained polymer models, and set the limits of their applicability.Comment: 7 pages, 5 figures. Published in the Journal of Chemical Physic

Unexpected relaxation dynamics of a self-avoiding polymer in cylindrical confinement

We report extensive simulations of the relaxation dynamics of a self-avoiding polymer confined inside a cylindrical pore. In particular, we concentrate on examining how confinement influences the scaling behavior of the global relaxation time of the chain, t, with the chain length N and pore diameter D. An earlier scaling analysis based on the de Gennes blob picture led to t ~ N^2D^(1/3). Our numerical effort that combines molecular dynamics and Monte Carlo simulations, however, consistently produces different t-results for N up to 2000. We argue that the previous scaling prediction is only asymptotically valid in the limit N >> D^(5/3) >> 1, which is currently inaccessible to computer simulations and, more interestingly, is also difficult to reach in experiments. Our results are thus relevant for the interpretation of recent experiments with DNA in nano- and micro-channels.Comment: 10 pages, 11 figure

Free energy of alternating two-component polymer brushes on cylindrical templates

We use computer simulations to investigate the stability of a two-component polymer brush de-mixing on a curved template into phases of different morphological properties. It has been previously shown via molecular dynamics simulations that immiscible chains having different length and anchored to a cylindrical template will phase separate into striped phases of different widths oriented perpendicularly to the cylindrical axis. We calculate free energy differences for a variety of stripe widths, and extract simple relationships between the sizes of the two polymers, N_1 and N_2, and the free energy dependence on the stripe width. We explain these relationships using simple physical arguments based upon previous theoretical work on the free energy of polymer brushes.Comment: 5 pages, 5 figures, accepted for publication in the Journal of Chemical Physic

Controlling the temperature sensitivity of DNA-mediated colloidal interactions through competing linkages

We propose a new strategy to improve the self-assembly properties of DNA-functionalised colloids. The problem that we address is that DNA-functionalised colloids typically crystallize in a narrow temperature window, if at all. The underlying reason is the extreme sensitivity of DNA-mediated interactions to temperature or other physical control parameters. We propose to widen the window for colloidal crystallization by exploiting the competition between DNA linkages with different nucleotide sequences, which results in a temperature-dependent switching of the dominant bond type. Following such a strategy, we can decrease the temperature dependence of DNA-mediated self assembly to make systems that can crystallize in a wider temperature window than is possible with existing systems of DNA functionalised colloids. We report Monte Carlo simulations that show that the proposed strategy can indeed work in practice for real systems and specific, designable DNA sequences. Depending on the length ratio of the different DNA constructs, we find that the bond switching is either energetically driven (equal length or `symmetric' DNA) or controlled by a combinatorial entropy gain (`asymmetric' DNA), which results from the large number of possible binding partners for each DNA strand. We provide specific suggestions for the DNA sequences with which these effects can be achieved experimentally