Molecularly defined (L)‐lactic acid oligomers and polymers: Synthesis and characterization

The synthesis of (L )‐lactide oligomers from dimer to 64mer via an exponential growth strategy is described. By careful selection of orthogonal protective groups, the synthesis were conducted using a t‐butyldimethylsilyl (TBDMS) ether as the protective group of the hydroxyl group and benzyl (Bn) ester as the protective group of the carboxylic acid group. The yields of both the deprotection steps and coupling reactions using 1,3‐dicyclohexylcarbodiimide or 1‐[3‐(dimethylamino)propyl]‐3‐ethylcarbodiimide hydrochloride were high (70–100%) and the absence of a requirement for conducting the majority of reactions under an inert atmosphere permitted a robust and efficient synthetic strategy to be developed. This allowed monodisperse dimer, tetramer, octamer, 16mer, 32mer, and 64mer materials to be prepared in gram quantities and fully characterized using mass spectrometry and size exclusion chromatography. Evaluation of the thermal and physical properties using thermogravimetric analysis, differential scanning calorimetry, and small angle X‐ray scattering demonstrated a close correlation between the molecular structure of the well‐defined Poly(lactide) oligomers and their physical properties. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5977–5990, 2008     

Equivalents of the finitary non-deterministic inductive definitions

We present statements equivalent to some fragments of the principle of non-deterministic inductive definitions (NID) by van den Berg (2013), working in a weak subsystem of constructive set theory CZF. We show that several statements in constructive topology which were initially proved using NID are equivalent to the elementary and finitary NIDs. We also show that the finitary NID is equivalent to its binary fragment and that the elementary NID is equivalent to a variant of NID based on the notion of biclosed subset. Our result suggests that proving these statements in constructive topology requires genuine extensions of CZF with the elementary or finitary NID.