Second Virial Coefficient of Isotactic Oligo- and Poly(methyl methacrylate)s. Effects of Chain Stiffness and Chain Ends

Abstract

The second virial coefficient A 2 was determined for isotactic poly(methyl methacrylate) (i-PMMA) over a wide range of weight-average molecular weight M w from 7.89 x 10 2 to 1.93 x 10 6 in acetone at 25.0 °C, for M w ≥ 1.55 x 10 6 in chloroform at 25.0 °C and in nitroethane at 30.0 °C, and for M w = 6.88 x 10 5 in acetonitrile at 35.0, 45.0, and 55.0 °C. (Some of the data had already been obtained in the previous work.) It is shown that the observed dependence of A 2 on M w in the oligomer region may be quantitatively explained by the Yamakawa theory that takes account of the effect of chain ends. The values of the effective excess binary-cluster integrals β 1 and β 2 associated with the chain end beads are then found to be 66 and 360 A 3 , respectively, in acetone at 25.0 °C by taking the repeat unit as a single bead. The analysis shows that the effect of chain ends remains even for relatively large M w in the good solvent as in the cases of atactic polystyrene (a-PS) and atactic poly(methyl methacrylate) (a-PMMA). The results for the true interpenetration function Ψ in A 2 without the effect of chain ends indicate that the two-parameter theory breaks down completely, as found previously for a-PS and a-PMMA ; the observed Ψ as a function of the cubed gyration-radius expansion factor α s 3 depends separately on M w and on the reduced excluded-volume strength λB. It is found that the values of Ψ for i-PMMA are appreciably smaller than thsoe for a-PMMA in the same solvent, i.e., for the same value of the binary-cluster integral β, while the former values almost coincide with the latter for the same λB. The Yamakawa theory that takes account of the effects of chain stiffness and local chain conformation on the basis of the helical wormlike chain may explain satisfactorily the observed behavior of Ψ and also the remarkable difference in it between i-PMMA and a-PMMA, the effects appearing in Ψ through both λB and the mean-square radius of gyration (S 2 ).