Local Steric Hindrances and Conformations of Linear Polymer Molecules in Solutions. III. Polyethylene

Abstract

The mean-square end-to-end distance 〈R2〉 of linear, very long polyethylene molecules in solutions is calculated under the assumptions that (i) the internal rotational angle θ about skeletal bonds measured from the trans position may take only the three discrete values, θT, θG, and θG′ corresponding to the trans (T), gauche (G), and another gauche (G′) conformations, (ii) the G and G′ conformations are less stable than the T conformation by a statistical weight σ, (iii) the GG′ and G′G conformations for two consecutive bonds are inaccessible because of steric hindrances, and (iv) all interactions among the rotations about more than two consecutive skeletal bonds are negligible. Molecular averages such as the fraction of bonds being in the T conformation are also calculated. Typical numerical computations are carried out by setting the bond angle equal to the tetrahedral angle and θT=0 and θG=—θG′=120°. For equal values of σ, values of 〈R2〉/nb2 obtained are, as has been expected, remarkably larger than those calculated under the assumption of the independent rotation. Here n is the number of skeletal bonds and b is the bond length. Comparison at 140°C of theoretical values of d ln 〈R2〉/dT with the experimental value recently reported by Flory and his collaborators shows that the energy of the G and G′ conformations exceeds that of the T conformation by about 820 cal/mole if the entropy difference is assumed to be zero. The corresponding value of 〈R2〉/nb2 at 140°C is found to be about 8.0. Effects on 〈R2〉/nb2 of small changes in bond angle and θG, and of small fluctuations of θ about θT, θG, and θG′ are examined. Detailed discussions are given on validities of various assumptions made in defining the present physical model.