Enantioselective catalytic lithiation using a chiral binaphthyl derivative as electron carrier

The lithiation, of the secondary chloride 2, catalyzed by binaphthyl derivatives, i.e. BINAM 4, BINOL 5, BINAP 6, H8-BINAP 7, Tol-BINAP 8, 2,2’-bis(pyrrolidin-1-yl)-1,1’-binaphthalene 9, and 2,2’-dimethyl-1,1’-binaphthalene 11, in the presence of different ketones has been studied, yielding the corresponding alcohol derivatives 3 and 12-16 in moderate to good yields. Binaphthyl derivative 11 has revealed to be very active as catalyst in the lithiation process at room temperature, and has allowed the preparation of the alcohol derivatives with enantioselectivities up to 50%.

Nano-biocomposite films with modified cellulose nanocrystals and synthesized silver nanoparticles

Ternary nano-biocomposite films based on poly(lactic acid) (PLA) with modified cellulose nanocrystals (s-CNC) and synthesized silver nanoparticles (Ag) have been prepared and characterized. The functionalization of the CNC surface with an acid phosphate ester of ethoxylated nonylphenol favoured its dispersion in the PLA matrix. The positive effects of the addition of cellulose and silver on the PLA barrier properties were confirmed by reductions in the water permeability (WVP) and oxygen transmission rate (OTR) of the films tested. The migration level of all nano-biocomposites in contact with food simulants were below the permitted limits in both non-polar and polar simulants. PLA nano-biocomposites showed a significant antibacterial activity influenced by the Ag content, while composting tests showed that the materials were visibly disintegrated after 15 days with the ternary systems showing the highest rate of disintegration under composting conditions.

Developing pre-service teachers’ noticing of students’ understanding of the derivative concept

This research study examines the development of the ability of pre-service teachers to notice signs of students’ understanding of the derivative concept. It analyses preservice teachers’ interpretations of written solutions to problems involving the derivative concept before and after participating in a teacher training module. The results indicate that the development of this skill is linked to pre-service teachers’ progressive understanding of the mathematical elements that students use to solve problems. We have used these results to make some suggestions for teacher training programmes.

Combined effects of cellulose nanocrystals and silver nanoparticles on the barrier and migration properties of PLA nano-biocomposites

Poly(lactic acid) (PLA)-based high performance nano-biocomposites were prepared to be used in active food packaging. Pristine (CNC) and surfactant modified cellulose nanocrystals (s-CNC) with silver (Ag) nanoparticles were used as the matrix modifiers. Binary and ternary systems were prepared. Morphological investigations revealed the good distribution of silver nanoparticles in PLA ternary systems. The combination of s-CNC and Ag nanoparticles increased the barrier effect of the produced films while the results of overall migration for the PLA nano-biocomposites revealed that none of the samples exceeded the overall migration limit, since results were well below 60 mg kg−1 of simulant.

Surface modification of cellulose nanocrystals by grafting with poly(lactic acid)

The use of biopolymers obtained from renewable resources is currently growing and they have found unique applications as matrices and/or nanofillers in ‘green’ nanocomposites. Grafting of polymer chains to the surface of cellulose nanofillers was also studied to promote the dispersion of cellulose nanocrystals in hydrophobic polymer matrices. The aim of this study was to modify the surface of cellulose nanocrystals by grafting from L-lactide by ring-opening polymerization in order to improve the compatibility of nanocrystals and hydrophobic polymer matrices. The effectiveness of the grafting was evidenced by the long-term stability of a suspension of poly(lactic acid)-grafted cellulose nanocrystals in chloroform, by the presence of the carbonyl peak in modified samples determined by Fourier transform infrared spectroscopy and by the modification in C1s contributions observed by X-ray photoelectron spectroscopy. No modification in nanocrystal shape was observed in birefringence studies and transmission electron microscopy.

Students’ understanding of the function-derivative relationship when learning economic concepts

The aim of this study is to characterise students’ understanding of the function-derivative relationship when learning economic concepts. To this end, we use a fuzzy metric (Chang 1968) to identify the development of economic concept understanding that is defined by the function-derivative relationship. The results indicate that the understanding of these economic concepts is linked to students’ capacity to perform conversions and treatments between the algebraic and graphic registers of the function-derivative relationship when extracting the economic meaning of concavity/convexity in graphs of functions using the second derivative.

Sensitivity Analysis in Convex Optimization through the Circatangent Derivative

The main goal of this paper is to analyse the sensitivity of a vector convex optimization problem according to variations in the right-hand side. We measure the quantitative behavior of a certain set of Pareto optimal points characterized to become minimum when the objective function is composed with a positive function. Its behavior is analysed quantitatively using the circatangent derivative for set-valued maps. Particularly, it is shown that the sensitivity is closely related to a Lagrange multiplier solution of a dual program.