AN APPROACH TO THE FORMATION AND GROWTH OF NEW PHASES WITH APPLICATION TO POLYMER CRYSTALLIZATION - EFFECT OF FINITE-SIZE, METASTABILITY, AND OSTWALD RULE OF STAGES

This article aims to link the mainstream subject of chain-folded polym er crystallization with the rather speciality field of extended-chain crystallization, the latter typified by the crystallization of polyeth ylene (PE) under pressure. Issues of wider generality are also raised for crystal growth, and beyond for phase transformations. The underlyi ng new experimental material comprises the prominent role of metastabl e phases, specifically the mobile hexagonal phase in polyethylene whic h can arise in preference to the orthorhombic phase in the phase regim e where the latter is the stable regime, and the recognition of ''thic kening growth'' as a primary growth process, as opposed to the traditi onally considered secondary process of thickening. The scheme relies o n considerations of crystal size as a thermodynamic variable, namely o n melting-point depression, which is, in general, different for differ ent polymorphs. It is shown that under specifiable conditions phase st abilities can invert with size; that is a phase which is metastable fo r infinite size can become the stable phase when the crystal is suffic iently small. As applied to crystal growth, it follows that a crystal can appear and grow in a phase that is different from that in its stat e of ultimate stability, maintaining this in a metastable form when it may or may not transform into the ultimate stable state in the course of growth according to circumstances. For polymers this intermediate initial state is one with high-chain mobility capable of ''thickening growth'' which in turn ceases (or slows down) upon transformation, whe n and if such occurs, thus ''locking in'' a finite lamellar thickness. The complete situation can be represented by a P, T, 1/l(l = crystal thickness) phase-stability diagram which, coupled with kinetic conside rations, embodies all recognized modes of crystallization including ch ain-folded and extended-chain type ones. The task that remains is to a ssess which applies under given conditions of P and T A numerical asse ssment of the most widely explored case of crystallization of PE under atmospheric pressure indicates that there is a strong likelihood (cri tically dependent on the choice of input parameters) that crystallizat ion may proceed via a metastable, mobile, hexagonal phase, which is tr ansiently stable at the smallest size where the crystal first appears, with potentially profound consequences for the current picture of suc h crystallization. Crystallization of PE from solution, however, would , by such computations, proceed directly into the final stage of stabi lity, upholding the validity of the existing treatments of chain-folde d crystallization. The above treatment, in its wider applicability, pr ovides a previously unsuspected thermodynamic foundation of Ostwald's rule of stages by stating that phase transformation will always start with the phase (polymorph) which is stable down to the smallest size, irrespective of whether this is stable or metastable when fully grown. In the case where the phase transformation is nucleation controlled, a ready connection between the kinetic and thermodynamic consideration s presents itself, including previously invoked kinetic explanations o f the stage rule. To justify the statement that the crystal size can c ontrol the transformation between two polymorphs, a recent result on 1 -4-poly-trans-butadiene is invoked. Furthermore, phase-stability condi tions for wedge-shaped geometries are considered, as raised by current experimental material on PE. It is found that inversion of phase stab ilities (as compared to the conditions pertaining for parallel-sided s ystems) can arise, with consequences for our scheme of polymer crystal lization and with wider implications for phase transformations in tape ring spaces in general. In addition, in two of the Appendices two them es of overall generality (arising from present considerations for poly mers) are developed analytically; namely, the competition of nucleatio n-controlled phase growth of polymorphs as a function of input paramet ers, and the effect of phase size on the triple point in phase diagram s. The latter case leads, inter alia to the recognition of previously unsuspected singularities, with consequences which are yet to be asses sed.