The effect of flexibility on the phase diagram of simple molecular models

In this paper the effect of molecular flexibility on the phase diagram is studied. Three groups of models are used; a pearl-necklace model, a linear tangent hard sphere model and a hybrid model consisting of a rigid section and a flexible section. Each of these models are built up from hard sphere interaction sites. Calculations of the virial coefficients show significant differences between each of the models. In spite of this the equation of state is hardly affected by flexibility in the medium density range. However, at higher densities flexible and linear rigid chains display significant differences; the former having only fluid and solid phases whereas the the rigid model also forms mesophases (nematic and smectic A). The introduction of flexibility into a rigid model has the effect of moving the onset of liquid crystal formation to higher densities. Flexibility is also seen to stabilize the smectic phase at the expense of the nematic phase. Critical properties have been obtained from Wertheim's thermodynamic perturbation theory (TPT1) in the limit of infinitely long chains. Zero number density of chains, zero mass density and pressure and finite non-zero values of the critical temperature and compressibility factor are predicted at the critical point. For very long chains the critical temperature (i.e. the Θ temperature) is seen to be the Boyle temperature. From Wertheim's theory it is possible to analytically determine the temperature Θ for square well chains.