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

摘要

The meanhyphen;square endhyphen;tohyphen;end distance lang;R2rang; of linear, very long polyethylene molecules in solutions is calculated under the assumptions that (i) the internal rotational angle thgr; about skeletal bonds measured from thetransposition may take only the three discrete values, thgr;T, thgr;G, and thgr;Gprime;corresponding to thetrans(T),gauche(G), and anothergauche(Gprime;) conformations, (ii) theGandGprime; conformations are less stable than theTconformation by a statistical weight sgr;, (iii) theGGprime; andGprime;Gconformations 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 theTconformation are also calculated. Typical numerical computations are carried out by setting the bond angle equal to the tetrahedral angle and thgr;T=0 and thgr;G=mdash;thgr;Gprime;=120deg;. For equal values of sgr;, values of lang;R2rang;/nb2obtained are, as has been expected, remarkably larger than those calculated under the assumption of the independent rotation. Herenis the number of skeletal bonds andbis the bond length. Comparison at 140deg;C of theoretical values ofdln lang;R2rang;/dTwith the experimental value recently reported by Flory and his collaborators shows that the energy of theGandGprime; conformations exceeds that of theTconformation by about 820 cal/mole if the entropy difference is assumed to be zero. The corresponding value of lang;R2rang;/nb2at 140deg;C is found to be about 8.0. Effects on lang;R2rang;/nb2of small changes in bond angle and thgr;G, and of small fluctuations of thgr; about thgr;T, thgr;G, and thgr;Gprime;are examined. Detailed discussions are given on validities of various assumptions made in defining the present physical model.