SynopsisIt is shown that the long periods L in slow-cooled polyethylene materials obey the general law L = Lo + ar,.,, where rw is the weight average dimension of the coil before crystallization, and Lo is a parameter of the order of I,, the crystalline core thickness, which increases as the cooling rate V decreases. a is a parameter independent of M and V but decreasing with the number of long-chain branches per molecule. The two terms in the above relation are, respectively, the contributions of crystalline and amorphous layers. For cooling rates from soO°C/min to 0.2OC/min, it is shown that the temperature T, of crystallization is constant; hence the change of morphology (long period, crystalline core thickness, crystallinity) cannot be explained by supercooling. The increase in long period and crystallite thickness in slow-cooled materials with decreasing cooling rate is interpreted in terms of annealing of the crystallized materials between the crystallization temperature T, and the secondary transition temperature Tat. Crystallization proceeds by a two-step process of solidfication and annealing. During the annealing stage, the mobility of the chains in the crystalline phase is due to defecty the kinetics of thickening is then governed by the mobility (or nucleation) of the defects appearing above Tat. In the proposed model of crystallization, the assumption that the energy of activation is proportional to T,, explains the observed laws L = 1, = log ta, where the annealing time t,, is equal to (T, -T,,)/V. The model applies also to polymers crystallized from the melt and subsequently annealed. 0 1989 John Wiley & Sons, Inc. CCC 0098-1273/89/061349-25$04.00 1350 RAULT AND ROBELIN-SOUFFACHE second term (a being a constant) represents the contribution of the amorphous phase of thickness I , .In part I4 the long periods L,, deduced from the correlation function and' L, from paracrystalline analysis were compared with the Bragg long spacing L. Similar correlations are found for the linear polymers polyethylene (PE), polytetrahydrofuran, polypropylene quenched from the melt, and for poly(ethy1ene terephthalate) crystallized from the glassy state. It is well known that the values of L,, and L, are found to be smaller than L , and this is due to the disorder of the lamellar arrangement. L,,, and L , are mostly proportional to the first moment of the distribution function of the long period, whereas L is proportional to a higher moment.In polydisperse PE the correlations between the solid and melt states are given by