Global phase diagram for monomer/dimer mixtures

by 1975- Attwood, Brian Christopher

ATTWOOD, BRIAN CHRISTOPHER. Global phase diagram for monomer/dimer mixtures. (Under the direction of Carol K. Hall) The objective of this thesis is to calculate the global phase diagram predicted by the Generalized Flory Dimer equation of state for mixtures of square-well monomers and dimers. Towards that goal, we first extend the Generalized Flory Dimer (GFD) theory for hard sphere monomer/dimer mixtures to square-well monomer/dimer mixtures. Theoretical predictions for the compressibility factor as a function of volume fraction are compared to discontinuous molecular dynamic simulation results on monomer/dimer mixtures at well depth ratios 0.5 - 1.5 and dimer mole fractions 0.111 - 0.667 and on monomers/8-mer mixtures at well depth ratios 0.5 - 1.5. Agreement is found generally to be good and consistent with the agreement obtained when the GFD theory is applied to other square-well systems. Next we calculate the GFD predicted global phase diagram for square-well monomer/dimer mixtures using a brute force method. The locus of critical points in the plane is calculated for a grid of points in the plane, where is a measure of the difference between the monomer and dimer well depths and is a measure of the strength of the attraction between monomers and dimers. Initially, the locus of critical points was calculated for 360 points in a square grid between the values of -0.9 and 0.9 for both and . Additional points were calculated as necessary to gain resolution in areas where more detail was needed. The most significant features of the resulting global phase diagram are the absences of type IV and type VI behaviors. The absence of type VI behavior is not surprising because the existence of closed loop liquid-liquid immiscibility predicted by equations of state for molecules of spherical potentials is a matter of debate. The absence of type IV behavior is somewhat more unexpected because such behavior is found in most previous work on systems of spherical molecules. Although we performed extra calculations in the area in the plane where type IV behavior should be exhibited, it is possible that our search was not intense enough to find the small region where type IV behavior might exist. The phase diagram is shifted towards the negative and directions when compared to the van der Waals global phase diagram for equal diameter spherical molecules. The shift in the The shift in the direction can be attributed to the size difference between monomers and dimers. direction implies that monomer/dimer systems have a greater tendency towards liquid-liquid immiscibility in our system than in monomer/monomer systems.