Abstract
We continue our study of colligative properties of solutions initiated in ref. 1. 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 ξt such that no phase separation occurs for ξ≤ξt while, for ξ>ξt, 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.
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06 November 2023
A Correction to this paper has been published: https://doi.org/10.1007/s10955-023-03195-3
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Alexander, K.S., Biskup, M. & Chayes, L. Colligative Properties of Solutions: II. Vanishing Concentrations. J Stat Phys 119, 509–537 (2005). https://doi.org/10.1007/s10955-005-3017-1
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DOI: https://doi.org/10.1007/s10955-005-3017-1