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. Author manuscript; available in PMC: 2010 Mar 26.
Published in final edited form as: J Phys Chem B. 2009 Mar 26;113(12):3957–3971. doi: 10.1021/jp808412x

Figure 4.

Figure 4

The tie-line fields of two-phase coexistence regions have a ruled surface parameterization containing a tie-line field function for specifying how the slopes of tie-lines vary across the field. A) The ruled surface parameterizations of the coexistence curve configurations represented in Figure 2B. The u chord-length parameter specifies the Lo phase composition on the Lo phase boundary (directrix) and the v chord-length parameter specifies the Ld phase composition on the Ld phase boundary (directrix). By definition, the boundary conditions v(0) = 0 and v(1) = 1 ensure that the start point of the Lo directrix connects to the start point of the Ld directrix. B) The ruled surface parameterization of the closed Lo + Ld coexistence region in the SPM/DOPC/Chol lipid system. Also shown is the total coexistence curve parameter b that specifies the location of the critical points (black squares) on the coexistence curve. C) (1) Possible (solid lines) and not possible (dashed line) functional forms for the tie-line field function v(u) of the ruled surface parameterization. (2) The tie-line field function used in our TLF method plotted with different values of the variable parameter c.