Polymer, Vol.43, No.24, 6609-6626, 2002
Role of entanglement in crystalline polymers 1. Basic theory
When stacked lamellar crystals are formed in melts, entanglements are trapped and condensed in amorphous domains (a-domains); this makes the free energy of the a-domains increase and inhibits crystallization, thus, determines the crystalline structure of the system. Based on the local-knot (LK) model of entanglement proposed by Iwata and Edwards, the entanglement state of the system is described by three parameters, condensation ratio chi, trapping ratio xi and average number (ν) over bar of LKs trapped per stem in the a-domains. It is shown that crystallinity w(c), average lamellar thickness (L) over bar (c) and average a-domain thickness (L) over bar (a) are written in terms of chi, xi and (ν) over bar alone; this means that structure of stacked lamellar crystals is determined by entanglement. Particularly, the microscopic structure is determined by how LKs are partitioned in the stems of the a-domains. The equilibrium amorphous ratio in the limit M --> infinity (which is called 'limiting equilibrium amorphous ratio (w) over cap (infinity)(a)') is a universal function of a reduced degree of supercooling, tau = (N(c)Deltah(m)/k(B)T(m)(0))DeltaT/T, where Deltah(m) is the enthalpy of fusion and N-c is the critical chain length of the entanglement transition; this means that (w) over cap (infinity)(a)(tau) is independent of polymer species, thermal history or morphological properties of the system. Based on this result, a method is proposed to determine trapping ratio 6 experimentally. Magnitudes as well as T- and M-dependence of w(c), (l) over bar (c) and (l) over bar (a) predicted by the theory agree reasonably with experiments. It is shown that the topological free energy of entanglement accumulated in the a-domains plays an important role in the melting phenomena: For example, folding surface energy sigma(e) changes largely from that estimated by the usual Thompson-Gibbs equation, and the abnormal increase of sigma(e), with increasing M in stacked lamellar crystals, the phenomenon found by Schultz and Manderkern, is explained by the accumulated topological energy. Mechanism of trapping LKs in the crystallization process is discussed in detail.
Keywords:role of entanglement in crystalline polymers;topological theory of crystalline polymers;local-knot model