Assembly of hard spheres in a cylinder: a computational and experimental study

Abstract

Hard spheres are an important benchmark of our understanding of natural and synthetic systems. In this work, colloidal experiments and Monte Carlo simulations examine the equilibrium and out-of-equilibrium assembly of hard spheres of diameter σ within cylinders of diameter σ≤D≤ 2.82σ. Although phase transitions formally do not exist in such systems, marked structural crossovers can nonetheless be observed. Over this range of D, we find in simulations that structural crossovers echo the structural changes in the sequence of densest packings. We also observe that the out-of-equilibrium self-assembly depends on the compression rate. Slow compression approximates equilibrium results, while fast compression can skip intermediate structures. Crossovers for which no continuous line-slip exists are found to be dynamically unfavorable, which is the main source of this difference. Results from colloidal sedimentation experiments at low diffusion rate are found to be consistent with the results of fast compressions, as long as appropriate boundary conditions are used.

Correlation lengths in quasi-one-dimensional systems via transfer matrices

“…The latter clearly shows complex oscillation behaviour which increases the uncertainty of estimate of ξ∆x. [38]. The system is gas-like at P * x = 5, displays zig-zag order at P * x = 25, and exhibits significant helicity at P * x = 45. with the onset of helicity.…”

“…Once the correlation function has been computed, ξ y can also be obtained by fitting ln g y (|i, j|) = −|i − j|/ξ y + constant. The above numerical approach was first validated by successfully comparing the resulting equation of state with those of previous simulations [34,38] (not shown). We also compared the NN and the NNN calculations of ξ y in 2D and ξ r in 3D systems with each other and with previous results [40].…”

Corrected Article: Simulation and observation of line-slip structures in columnar structures of soft spheres [Phys. Rev. E 96, 012610 (2017)]

“…Considering that our original study of hard-sphere arrangements in a cylinder was motivated as a packing problem [14], it may have seemed plausible that the structures described above would only be of importance close to the incompressible athermal limit. Recently, however, these original findings have been found to be relevant in the self-assembly of hard spheres in cylindrical channels [30]. Remarkably, it is found that at finite temperature and pressure, both uniform and line-slip arrangements can be observed: a steadily increasing pressure can induce transitions between structures, while at a high compression rate some arrangements are found to be dynamically inaccessible [30]; these results are illustrated in terms of a phase diagram that bears a resemblance to the results presented here.…”

Supercharging enables organized assembly of synthetic biomolecules

“…Given that both natural proteins 3-8 and synthetic colloids [18][19][20][21][22][23][24][25][26][27][28][29] have been shown to readily assemble into symmetric, higher order structures, we anticipate that our SuPrA strategy can now be generalized to create synthetic, scalable…”

“…Notably, while some GFP variants, including the parent protein originally found in Aeqorea Victoria dimerize, the native dimer structure fits poorly into the electron density maps of the protomer, suggesting that the architecture of the protomer is completely novel. 54 The formation of SuPrA protomers appears to be largely independent of the placement of charges, suggesting that oppositely supercharging protein variants may generally drive formation into 'stacked' or brick-like structures whose overall form is determined by symmetric interactions.Given that both natural proteins 3-8 and synthetic colloids [18][19][20][21][22][23][24][25][26][27][28][29] have been shown to readily assemble into symmetric, higher order structures, we anticipate that our SuPrA strategy can now be generalized to create synthetic, scalableAll rights reserved. No reuse allowed without permission.…”