Colligative properties of solutions: II. Vanishing concentrations

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dc.creatorAlexander, Kenneth
dc.creatorBiskup, Marek
dc.creatorChayes, Lincoln
dc.date2004-07-16
dc.date2005-01-09
dc.date.accessioned2026-07-07T06:18:06Z
dc.date.available2026-07-07T06:18:06Z
dc.descriptionWe continue our study of colligative properties of solutions initiated in math-ph/0407034. We focus on the situations where, in a system of linear size $L$, the concentration and the chemical potential scale like $c=ξ/L$ and $h=b/L$, respectively. We find that there exists a critical value $\xit$ such that no phase separation occurs for $ξ\le\xit$ while, for $ξ>\xit$, the two phases of the solvent coexist for an interval of values of $b$. Moreover, phase separation begins abruptly in the sense that a macroscopic fraction of the system suddenly freezes (or melts) forming a crystal (or droplet) of the complementary phase when $b$ reaches a critical value. For certain values of system parameters, under ``frozen'' boundary conditions, phase separation also ends abruptly in the sense that the equilibrium droplet grows continuously with increasing $b$ and then suddenly jumps in size to subsume the entire system. Our findings indicate that the onset of freezing-point depression is in fact a surface phenomenon.
dc.description27 pages, 1 fig; see also math-ph/0407034 (both to appear in JSP)
dc.identifierhttps://arxiv.org/abs/math-ph/0407035
dc.identifierhttp://arxiv.org/abs/math-ph/0407035
dc.identifierJ. Statist. Phys. 119 (2005), no. 3-4, 509-537
dc.identifierdoi:10.1007/s10955-005-3017-1
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/94623
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subjectProbability
dc.subjectChemical Physics
dc.subject82B05; 82B20; 60F10
dc.titleColligative properties of solutions: II. Vanishing concentrations
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