Influence of temperature on high molecular weight poly(lactic acid) stereocomplex formation

The influence of temperature on the formation of high molecular weight poly(lactic acid) (PLA) stereocomplex was studied by evaluation of the precipitates from dioxane solutions of PLA enantiomers (PLLA and PDLA). The racemic mixtures were characterized by Gel Permeation Chromatography, Infrared Spectroscopy, Differential Scanning Calorimetry, Scanning Electronic Microscopy, Wide-Angle X-ray Scattering and Vicat Softening Temperature. Precipitation was carried out under different solution temperatures, keeping constant the mixing ratio (XD), the molecular weight, the optical purity of both PLA enantiomers and the stirring rate. It was found that the precipitates contained only pure stereocomplex crystallites (racemic crystallites), without observing crystal phase separation between both homocrystals. The kinetics of the insoluble phase formation could be adjusted with the Avrami model, classically used for polymer crystallization in molten state. It was observed that the maximum PLA stereocomplex production rate was at about 40°C. However, more thermally stable racemic crystallites were formed at high solution temperatures. It was found that all the precipitates were sphere-like at 10 g·dl–1 at the solution temperature of 25, 40, 60 and 80°CPeer ReviewedPostprint (author's final draft

On Rayner structures

In this note, we study substructures of generalised power series fields induced by families of well-ordered subsets of the group of exponents. We characterise the set-theoretic and algebraic properties of the induced substructures in terms of conditions on the families. We extend the work of Rayner by giving both \emph{necessary} and sufficient conditions to obtain truncation closed subgroups, subrings and subfields.Comment: 11 pages, to appear in Communications in Algebr

Generalised power series determined by linear recurrence relations

In 1882, Kronecker established that a given univariate formal Laurent series over a field can be expressed as a fraction of two univariate polynomials if and only if the coefficients of the series satisfy a linear recurrence relation. We introduce the notion of generalised linear recurrence relations for power series with exponents in an arbitrary ordered abelian group, and generalise Kronecker's original result. In particular, we obtain criteria for determining whether a multivariate formal Laurent series lies in the fraction field of the corresponding polynomial ring. Moreover, we study distinguished algebraic substructures of a power series field, which are determined by generalised linear recurrence relations. In particular, we identify generalised linear recurrence relations that determine power series fields satisfying additional properties which are essential for the study of their automorphism groups.Comment: 33 pages, submitte

Automorphisms and derivations on algebras endowed with formal infinite sums

We establish a correspondence between automorphisms and derivations on certain algebras of generalised power series. In particular, we describe a Lie algebra of derivations on a field $k(\!(G)\!)$ of generalised power series, exploiting our knowledge of its group of valuation preserving automorphisms. The correspondence is given by the formal Taylor expansion of the exponential. In order to define the exponential map, we develop an appropriate notion of summability of infinite families in algebras. We show that there is a large class of algebras in which the exponential induces the above correspondence.Comment: 38 pages, 2 figure