The effect of rotations around all 11 single bonds in the unit cell of nylon-11 on the free energy of a disordered chain

First the reason for the 2–3 orders of magnitude difference in the Young modulus of a polymer chain in an ordered (crystalline) phase and in a macroscopic disordered sample is explained. This explanation points out: (1) that in a macroscopic sample the different chains are randomly oriented in respect to each other and (2) because of the polydispersity in the chain lengths, shorter chains will not be kept in the same position as in the crystalline phase. Consecutively, for nylon-11 a simple statistical mechanical calculation was performed for the total energy per unit cell, for the entropy term and for the free energy per unit cell in the case of free rotations around all the 11 single bonds of the unit cell. The results show a dominant role of the configurational entropy in accordance with C.F. von Weizsacker's general considerations back in 1958.