Physics – Mathematical Physics
Scientific paper
2004-07-16
J. Statist. Phys. 119 (2005), no. 3-4, 509-537
Physics
Mathematical Physics
27 pages, 1 fig; see also math-ph/0407034 (both to appear in JSP)
Scientific paper
10.1007/s10955-005-3017-1
We 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 $c=\xi/L$ and $h=b/L$, respectively. We find that there exists a critical value $\xit$ such that no phase separation occurs for $\xi\le\xit$ while, for $\xi>\xit$, 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.
Alexander Kenneth
Biskup Marek
Chayes Lincoln
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