EFFECT OF CHAIN TRANSPORT IN THE SECONDARY SURFACE NUCLEATION BASED FLUX THEORY AND IN THE LAURITZEN-HOFFMAN CRYSTAL-GROWTH RATE FORMALISM

A previous study (Snyder, C. R.; Marand, H.; Mansfield, M. L. Macromol ecules 1996, 29, 7508) by the authors suggested that, within the conte xt of the Lauritzen-Hoffman secondary surface nucleation theory, the a pportionment factor for the free energy of crystallization (psi(LH)) a nd the retardation factor due to transport of chain segments (beta(LH) ) may differ for placement of the first vs all subsequent stems. In th is manuscript, we investigate the consequences of this treatment on th e crystal growth rate of polyethylene in regimes I, II, and III. It ha s been impossible so far to find an analytical solution for the second ary nucleation rate, i, and the average lamellar thickness, [1], when the apportionment and the retardation factors for the first stem (psi' and beta') are treated as being different from those used for all sub sequent stems (psi and beta). It is shown in this work that approximat e solutions, which cover most conditions, can be obtained by assuming two extreme cases. In the first case, it is assumed that the rate cons tant for initial stern removal (B-1) is larger than tile difference be tween the rate constants for subsequent stem placement and removal (A - B); i.e. A - B much less than B-1. Such an approximation leads to th e conclusion that the crystal growth rate in regimes I and II is only dependent upon the retardation factor for subsequent stem placement. I n the second case, it is demonstrated that if (A - B) much greater tha n B-1, the resulting flux equation is valid over most other circumstan ces where the first assumption (B-1 much greater than A - B) does not hold. This leads to the conclusion that the crystal growth rate in reg ime I is only dependent upon the path followed for initial stern place ment whereas in regime II it is dependent upon both the initial and su bsequent stem placement paths. Conversely, it is shown, without any as sumption regarding the relative magnitudes of beta' and beta, that in regime III the crystal growth rate is dependent upon the path of initi al stem placement and independent of the path of subsequent stem place ment. Under these conditions, the molecular weight dependency of the c rystal growth rate in regimes I and II vs III may differ substantially . Finally, some remarks are given on the consequences of this approach for the crystallization of other polymers at larger undercoolings tha n encountered for poly(ethylene).