  We address questions posed by experiments which show that most small-chain
alcohols reduce the miscibility transition temperature when added to giant
plasma membrane vesicles, but increase that temperature when added to giant
unilamellar vesicles. In both systems the change in temperature depends
non-monotonically on the length of the alcohol chain. To emphasize the roles
played by the internal entropies of the components, we model them as linear
polymers. We show that, within Flory-Huggins theory, the addition of alcohol
causes an increase or decrease of the transition temperature depending upon the
competition of two effects. One is the dilution of the solvent interactions
caused by the introduction of solute, which tends to lower the temperature. The
other is the preference of the solute for one phase or the other, which tends
to raise the temperature. The magnitude of this term depends on the entropies
of all components. Lastly we provide a reasonable explanation for the behavior
of the transition temperature with alcohol chain length observed in experiment.
