Unperturbed dimensions of polyethylene chain molecules

The energies of the various rotational states around the CC bonds of a polyethylene chain are calculated with the aid of a selected function for the HH interactions and the known functions for the distortion of bond angles and the torsional potential. The HH function selected is the only one which reproduces the experimentally known energy difference of 800 cal./mole between the trans (t) and gauche (g L or g R ) states of normal butane and the value of 500 cal./mole for the same difference in higher normal alkanes. The calculated energies are used to derive the reduced unperturbed mean square end‐to‐end distance 〈r 〉/n l 2 , as a function of temperature (n = number of CC bonds of length l ). The influences of first and higher neighbouring bond correlation upon the three main rotational states (t, g L , and g R ) of polyethylene, as well as the rotation by about 8° of trans states, adjoining a gauche state, are taken into account by means of an extension of an existing matrix method. At 100°C. 〈r 〉/n l 2 and dln 〈r 〉/dT are found to be 10 ± 1 and −0.68·10 −3 , respectively. From the calculations it follows that the polyethylene chain can be considered as a kinked, irregularly helical structure. The irregularly helical parts consist of about 12 CC bonds, which are either irregular combinations of g L and t states or of g R and t states.