The effect of a Gaussian distribution of chain-lengths on the phase-behaviour of a model system of rod-like macromolecules in solution

The calculations of Flory and co-workers for the formation and composition of isotropic, bi-phasic and anisotropic systems composed of rod-like macromolecules in solution have been extended to include a Gaussian distribution of rod-lengths. The critical concentrations for the beginning and end of the bi-phasic range $\text{v}{}^{\mathrm{<mtext>o</mtext><mtext>1</mtext>}}{}_{\mathrm{p}}$ and $\text{v}{}^{\mathrm{<mtext>o</mtext><mtext>7</mtext>}}{}_{\mathrm{p}}$ respectively, the volume fraction of anisotropic phase Φ_A, the compositions and average molecular weights of isotropic and anisotropic phases, and the order parameter S of the anisotropic phase are calculated as a function of polymer concentration v^o_p for rod-length x_o in the range 30 to 70 and for a Gaussian distribution half-width $\text{Δ}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ in the range 10 to 70. The extent of the bi-phasic range and the composition of the two components is found to be strongly dependent on the breadth of the distribution and average rod-length. The applicability of the calculations to data for poly(alkylisocyanates) in solution is briefly considered.