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Inferring bulk self-assembly properties from simulations of small systems with multiple constituent species and small systems in the grand canonical ensemble
In this paper we generalize a methodology [T. E. Ouldridge, A. A. Louis, and
J. P. K. Doye, J. Phys.: Condens. Matter {\bf 22}, 104102 (2010)] for dealing
with the inference of bulk properties from small simulations of self-assembling
systems of characteristic finite size. In particular, schemes for extrapolating
the results of simulations of a single self-assembling object to the bulk limit
are established in three cases: for assembly involving multiple particle
species, for systems with one species localized in space and for simulations in
the grand canonical ensemble. Furthermore, methodologies are introduced for
evaluating the accuracy of these extrapolations. Example systems demonstrate
that differences in cluster concentrations between simulations of a single
self-assembling structure and bulk studies of the same model under identical
conditions can be large, and that convergence on bulk results as system size is
increased can be slow and non-trivial.Comment: Accepted by J. Chem. Phy
The mechanism of thickness selection in the Sadler-Gilmer model of polymer crystallization
Recent work on the mechanism of polymer crystallization has led to a proposal
for the mechanism of thickness selection which differs from those proposed by
the surface nucleation theory of Lauritzen and Hoffman and the entropic barrier
model of Sadler and Gilmer. This has motivated us to reexamine the model used
by Sadler and Gilmer. We again find a fixed-point attractor which describes the
dynamical convergence of the crystal thickness to a value just larger than the
minimum stable thickness, l_min. This convergence arises from the combined
effect of two constraints on the length of stems in a layer: it is unfavourable
for a stem to be shorter than l_min and for a stem to overhang the edge of the
previous layer. The relationship between this new mechanism and the explanation
given by Sadler and Gilmer in terms of an entropic barrier is discussed. We
also examine the behaviour of the Sadler-Gilmer model when an energetic
contribution from chain folds is included.Comment: 15 pages, 13 figures, revte
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