Comment on"Elucidating the Mechanism of Nucleation near the Gas-Liquid Spinodal"

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In a recent Letter [1], Bhimalapuram, Chakrabarty and Bagchi (BCB) study the phase transformation mechanism of the Lennard-Jones fluid and the non-conserved Ising model. They compute the free energy as a function of the size of the largest droplet of the stable phase. In apparent contradiction to classical nucleation theory (CNT), they find that in both systems the free energy develops a minimum at subcritical cluster sizes. In this Comment we argue that this minimum is specific to the chosen order parameter, and that the observed behavior is in fact consistent with CNT. CNT states that the free energy F(N) ... continued below

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Maibaum, Lutz & Maibaum, Lutz June 18, 2008.

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In a recent Letter [1], Bhimalapuram, Chakrabarty and Bagchi (BCB) study the phase transformation mechanism of the Lennard-Jones fluid and the non-conserved Ising model. They compute the free energy as a function of the size of the largest droplet of the stable phase. In apparent contradiction to classical nucleation theory (CNT), they find that in both systems the free energy develops a minimum at subcritical cluster sizes. In this Comment we argue that this minimum is specific to the chosen order parameter, and that the observed behavior is in fact consistent with CNT. CNT states that the free energy F(N) of a single cluster of size N is a concave function with a maximum at the critical nucleus size N{sub c}. BCB, on the other hand, calculate the probability distribution of N*, the size of the largest cluster in the system, and compute the free energy {beta}F*(N*) = -ln P(N*), where {beta} = 1/k{sub B}T. This order parameter does not measure the size of a single cluster. Instead, when sampling small values of N*, one measures the statistical weight of configurations in which all clusters are at most N* in size. Hence a free energy penalty is incurred when one constrains N* to values smaller than the largest average cluster in the simulation volume V. It is this penalty that causes the sudden increase of F* as N* {yields} 0 and the minimum at intermediate values of N*. We now illustrate how F(N) can be calculated from simulations. Our argument is intuitive but not exact, a formal derivation that yields an equivalent result can be found in Ref. 2. We choose the Ising model for concreteness. We aim to compute the probability that a given cluster has size N, where we imagine the center of the cluster to be fixed at site i. To simplify the calculation we consider clusters that overlap with site i, and correct for the N-fold translational degeneracy in a second step.

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  • Journal Name: Physical Review Letters

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  • Report No.: LBNL-527E
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 936102
  • Archival Resource Key: ark:/67531/metadc897908

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  • June 18, 2008

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  • Sept. 27, 2016, 1:39 a.m.

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  • Oct. 3, 2016, 1:39 p.m.

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Maibaum, Lutz & Maibaum, Lutz. Comment on"Elucidating the Mechanism of Nucleation near the Gas-Liquid Spinodal", article, June 18, 2008; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc897908/: accessed December 13, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.