Jeg. Lipson, STUDIES ON FLUIDS AND THEIR MIXTURES USING THE BORN-GREEN-YVON-INTEGRAL-EQUATION TECHNIQUE, Macromolecular theory and simulations, 7(2), 1998, pp. 263-282
We have developed the Born-Green-Yvon (BGY) integral equation theory f
or investigating the equilibrium properties of fluids and their mixtur
es both on the lattice and in the continuum. Using the continuum theor
y we have studied hard sphere fluids over a range in density having ch
ain lengths between one and fifty sites. We have also investigated the
collapse transition of a square well chain and a square well ring, ea
ch having up to four hundred sites, and have predicted the theta tempe
rature for these systems. Turning to the case of a dilute (hard-sphere
) solution we have been able to show the effect of solvation on a hard
sphere chain, and captured the dependence of this effect on the ratio
of hard sphere diameters of the solvent and chain segments. In all th
e continuum studies we have found good to excellent agreement with sim
ulation results. We have also derived a lattice BGY theory which, whil
e less sophisticated than the continuum version, has the advantage of
producing simple closed-form expressions for thermodynamic properties
of interest. This theory is capable of exhibiting the full range of mi
scibility behaviour observed experimentally, including upper and lower
critical solution temperatures and closed-loop phase diagrams. We fin
d that the theory does an excellent job of fitting to different kinds
of experimental data and, making use of the parameters derived from fi
ts to pure component data alone, we have been able to predict properti
es ranging from pure fluid vapour pressures and critical temperatures
to changes in the volume and enthalpy on mixing as well as coexistence
curves for solutions.