No abstract

Poly(alkylene dicarboxylate)s constitute a family of biodegradable polymers with increasing interest for both commodity and speciality applications. Most of these polymers can be prepared from biobased diols and dicarboxylic acids such as 1,4-butanediol, succinic acid and carbohydrates. This review provides a current status report concerning synthesis, biodegradation and applications of a series of polymers that cover a wide range of properties, namely, materials from elastomeric to rigid characteristics that are suitable for applications such as hydrogels, soft tissue engineering, drug delivery systems and liquid crystals. Finally, the incorporation of aromatic units and α-amino acids is considered since stiffness of molecular chains and intermolecular interactions can be drastically changed. In fact, poly(ester amide)s derived from naturally occurring amino acids offer great possibilities as biodegradable materials for biomedical applications which are also extensively discussed.

Three different tetraphenylalanine (FFFF) based peptides that differ at the N‐ and C‐termini have been synthesized by using standard procedures to study their ability to form different nanoassemblies under a variety of conditions. The FFFF peptide assembles into nanotubes that show more structural imperfections at the surface than those formed by the diphenylalanine (FF) peptide under the same conditions. Periodic DFT calculations (M06L functional) were used to propose a model that consists of three FFFF molecules defining a ring through head‐to‐tail NH3+⋅⋅⋅−OOC interactions, which in turn stack to produce deformed channels with internal diameters between 12 and 16 Å. Depending on the experimental conditions used for the peptide incubation, N‐fluorenylmethoxycarbonyl (Fmoc) protected FFFF self‐assembles into a variety of polymorphs: ultra‐thin nanoplates, fibrils, and star‐like submicrometric aggregates. DFT calculations indicate that Fmoc‐FFFF prefers a parallel rather than an antiparallel β‐sheet assembly. Finally, coexisting multiple assemblies (up to three) were observed for Fmoc‐FFFF‐OBzl (OBzl = benzyl ester), which incorporates aromatic protecting groups at the two peptide terminals. This unusual and noticeable feature is attributed to the fact that the assemblies obtained by combining the Fmoc and OBzl groups contained in the peptide are isoenergetic.

Hydrogels based on polysaccharide and protein natural polymers are of great interest in biomedical applications and more specifically for tissue regeneration and drug delivery. Cellulose, chitosan (a chitin derivative), and collagen are probably the most important components since they are the most abundant natural polymers on earth (cellulose and chitin) and in the human body (collagen). Peptides also merit attention because their self-assembling properties mimic the proteins that are present in the extracellular matrix. The present review is mainly focused on explaining the recent advances on hydrogels derived from the indicated polymers or their combinations. Attention has also been paid to the development of hydrogels for innovative biomedical uses. Therefore, smart materials displaying stimuli responsiveness and having shape memory properties are considered. The use of micro-and nanogels for drug delivery applications is also discussed, as well as the high potential of protein-based hydrogels in the production of bioactive matrices with recognition ability (molecular imprinting). Finally, mention is also given to the development of 3D bioprinting technologies.

Abstract. We consider the isoperimetric problem in planar sectors with density r p , and with density a > 1 inside the unit disk and 1 outside. We characterize solutions as a function of sector angle. We also solve the isoperimetric problem in R n with density r p , p < 0.