The α*-constant, equilibrium state and bearing netplanes in polymers, biopolymers and catalysts
Debye's idea of an 'a priori probability function' of interatomic distances in a liquid is generalised by the theory of paracrystals. In the case of a square lattice this generalised model is studied using a two-dimensional coin model. Between the nearest-neighbour separations the only correlation is with respect to their directions. The netplanes formed by nearest neighbours are 'bearing netplanes', so-called because of the bearing role they play in microparacrystals. In the expression for free enthalpy Delta G(N) a new term 3/2NA0g2 takes into account the minimum given by the alpha *-law, where N defines the number of bearing netplanes in a spatial direction, g is the nearest-neighbour-distance fluctuation and A0 the enthalpy density given by the tangential potentials. Delta G depends on the number of valence bonds within a lattice cell and therefore increases with the distance d0 between the bearing netplanes. alpha * then decreases automatically and reaches values of alpha *=0.15+or-0.05 for d00>3 AA. Even larger alpha *-values have been observed in the DuPont Kevlar fibre; this can be partly explained in terms of a non-equilibrium state. The bearing netplanes build up the surface of a microparacrystal in an equilibrium state and thus replace Wulff's rule.
Article, 1985