EFFECT OF POLYDISPERSITY ON THE ISOTROPIC-NEMATIC PHASE-TRANSITION OF RIGID RODS

The effect of polydispersity on the isotropic-nematic phase transition of rigid rods is analyzed in terms of a second-order perturbation theory, in which the width a of an arbitrary number fraction is used as a perturbation parameter. These results show that the isotropic-nematic phase transition takes place at the isotropic density n(I), where n(I) ($) over bar L(N)(2)D=4.189(1+2.128 sigma(2)), and the nematic density nh, where n(N) ($) over bar L(N)(2)D=5.336(1+1.655 sigma(2)), with D and ($) over bar L(N) being the diameter and the number-averaged length of rods in the nematic phase. At the transition density, the weight- and number-averaged orientation order parameters have the values S-W=0.7922+1.1333 sigma(2) and S-L=0.7922+0.816 sigma(2); the ratio between the number-averaged length of rods in the isotropic phase, ($) over bar L(I), and that in the nematic phase, ($) over bar L(N), is ($) over bar L(I)/($) over bar L(N)=1-1.844 sigma(2). These perturbation results are compared with the numerical solution of the equilibrium conditions for the isotropic-nematic transition of rods obeying two modeled number fraction distributions.