Macromolecules, Vol.29, No.23, 7508-7513, 1996
Lateral Substrate Completion Rate in the Lauritzen-Hoffman Secondary Surface Nucleation Theory - Nature of the Friction Coefficient
In this paper it is demonstrated that, within the context of the Lauritzen-Hoffman (LH) secondary surface nucleation theory, the nature of the friction factor governs whether or not a fraction of the total bulk free energy is apportioned to the activated state during secondary nucleation. The friction coefficient (zeta) associated with reeling the chain onto the growth front, when equated to that measured through self-diffusion studies, forces the apportionment factor (psi) to be equal to zero. On the other hand, assuming that zeta is a function of the shape of the free energy barrier allows psi to take on nonzero values. In the first instance, the "delta l catastrophe" is eliminated, whereas in the second case the "delta l catastrophe" is associated with the substrate completion process (in contrast to the classical LH theory, which associates it with the deposition of the first stem). It is shown that both occurrences are mathematical artifacts which arise because the apportionment factor is treated as being equivalent for the first and all subsequent stems, and thus two different psi’s are required. Furthermore, it is suggested that two different expressions for beta (the transport term) are required for the first versus all subsequent stems.