[4] Phase Separation in Pure Component DPPC Lipid Bilayers A lipid bilayer can be treated thermodynamically as a 2D object, and so the work done on the system is no longer W=pdV. The work done on a lipid bilayer is W=dA, where is the surface tension and A is the total area of the bilayer. The fundamental equation for this system is then written as: dU=TdS+dA+dN where N represents the total number of lipid molecules. Notice how has taken the place of P in the usual representation of the internal energy. The pure component DPPC lipid bilayer has a melting temperature of 315K. This melting temperature represents the temperature where a condensed gel phase is in equilibrium with a liquid-crystalline (LC) phase of higher area per molecule. At a temperature below 315K, the bilayer is in a stable equilibrium state as the pure gel phase, and at a temperature above 315K the bilayer is in a stable equilibrium state as a pure LC phase. a.) What are the criteria for phase equilibrium in this system? The Helmholtz free energy for the two phases at 315K can be modeled by the following expressions as a function of area A (in units of Angstroms squared) and number of molecules N ( A0 is a constant equal to 1 Angstrom squared): Fgel/kT=0.5A02NA248A0A+1133.51NFlc/kT=0.25A02NA232A0A+1005.51N b.) Plot F/NkT as a function of area per molecule (A/N) for the pure component DPPC bilayer at 315K in the following range 40