On the applicability of the classical nucleation theory in an Ising system

Shneidman, Vitaly A.; Jackson, K. A.; Beatty, Kirk M.

doi:10.1063/1.479985

Cited by 77 publications

(56 citation statements)

References 59 publications

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“…Because a non-square droplet cannot be accommodated perfectly on a square lattice, it is also useful to consider the orientationally-averaged effective droplet surface tension σ eff (T ) derived by Shneidman et al [25]:…”

Section: Results: 2d Simulationsmentioning

confidence: 99%

Patterning a surface so as to speed nucleation from solution

Hedges

Whitelam

2012

Soft Matter

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Motivated by the question of how to pattern a surface in order to best speed nucleation from solution, we build on the work of Page and Sear [Phys. Rev. Lett. 97, 65701 (2006)] and calculate rates and free energy profiles for nucleation in the 3d Ising model in the presence of cuboidal pores. Pores of well-chosen aspect ratio can dramatically speed nucleation relative to a planar surface made of the same material, while badly-chosen pores provide no such enhancement. For a given pore, the maximum nucleation rate is achieved when one of its two horizontal dimensions attains a critical length, largely irrespective of the other dimension (provided that the latter is large enough). This observation implies that patterning a surface in a raster-like fashion is a better strategy for speeding nucleation than e.g. scoring long grooves in it.

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Section: Results: 2d Simulationsmentioning

confidence: 99%

Patterning a surface so as to speed nucleation from solution

Hedges

Whitelam

2012

Soft Matter

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“…Nucleation pathway of Ising model in three-dimensional lattice has also been studied using transition path sampling approach [27]. In addition, Ising model has been frequently used to test the validity of classical nucleation theory (CNT) [28][29][30][31][32]. However, all these studies are limited to regular lattices in Euclidean space.…”

Section: Introductionmentioning

confidence: 99%

Nucleation in scale-free networks

et al. 2011

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We have studied nucleation dynamics of the Ising model in scale-free networks with degree distribution P (k) ∼ k −γ by using forward flux sampling method, focusing on how the network topology would influence the nucleation rate and pathway. For homogeneous nucleation, the new phase clusters grow from those nodes with smaller degree, while the cluster sizes follow a power-law distribution. Interestingly, we find that the nucleation rate RHom decays exponentially with the network size N , and accordingly the critical nucleus size increases linearly with N , implying that homogeneous nucleation is not relevant in the thermodynamic limit. These observations are robust to the change of γ and also present in random networks. In addition, we have also studied the dynamics of heterogeneous nucleation, wherein w impurities are initially added, either to randomly selected nodes or to targeted ones with largest degrees. We find that targeted impurities can enhance the nucleation rate RHet much more sharply than random ones. Moreover, ln(RHet/RHom) scales as w γ−2/γ−1 and w for targeted and random impurities, respectively. A simple mean field analysis is also present to qualitatively illustrate above simulation results.PACS numbers: 89.75. Hc, 05.50.+q

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“…The Arp 2/3 protein complex imitates the shape of an unfavorable intermediate of the spontaneous actin nucleation process [22]. In contrast, in two-and three-dimensional systems-condensation of a gas [31], crystallization [30], or in the Ising model [45]-classical nucleation theory [56,11] predicts that a barrier to nucleation exists because clusters have unfavorable energies proportional to the surface area of the cluster (possibly due to interfacial tension or pressure differences with respect to the surrounding solution), and favorable energies proportional to the volume of the cluster. Because volume grows more quickly than surface area as clusters grow larger, a supersaturated regime exists where small clusters tend to melt, but above a critical size, cluster growth rather than melting is favored.…”

Section: Stages Of An Assembly Reaction During An Anneal Are Separatementioning

confidence: 99%

Programmable Control of Nucleation for Algorithmic Self-Assembly

Schulman¹,

Winfree²

2010

SIAM J. Comput.

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Abstract. Algorithmic self-assembly, a generalization of crystal growth processes, has been proposed as a mechanism for autonomous DNA computation and for bottom-up fabrication of complex nanostructures. A "program" for growing a desired structure consists of a set of molecular "tiles" designed to have specific binding interactions. A key challenge to making algorithmic self-assembly practical is designing tile set programs that make assembly robust to errors that occur during initiation and growth. One method for the controlled initiation of assembly, often seen in biology, is the use of a seed or catalyst molecule that reduces an otherwise large kinetic barrier to nucleation. Here we show how to program algorithmic self-assembly similarly, such that seeded assembly proceeds quickly but there is an arbitrarily large kinetic barrier to unseeded growth. We demonstrate this technique by introducing a family of tile sets for which we rigorously prove that, under the right physical conditions, linearly increasing the size of the tile set exponentially reduces the rate of spurious nucleation. Simulations of these "zig-zag" tile sets suggest that under plausible experimental conditions, it is possible to grow large seeded crystals in just a few hours such that less than 1 percent of crystals are spuriously nucleated. Simulation results also suggest that zig-zag tile sets could be used for detection of single DNA strands. Together with prior work showing that tile sets can be made robust to errors during properly initiated growth, this work demonstrates that growth of objects via algorithmic self-assembly can proceed both efficiently and with an arbitrarily low error rate, even in a model where local growth rules are probabilistic.

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On the applicability of the classical nucleation theory in an Ising system

Cited by 77 publications

References 59 publications

Patterning a surface so as to speed nucleation from solution

Patterning a surface so as to speed nucleation from solution

Nucleation in scale-free networks

Programmable Control of Nucleation for Algorithmic Self-Assembly

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