Rui Duarte

Hydration of cellulose/silica hybrids assessed by sorption isotherms.

The hydration of cellulose/silica hybrids (CSH) containing 13, 35, and 46% (w/w) silica synthesized in situ by a mild sol-gel aqueous process was studied employing sorption isotherms and surface energy measurements. Water sorption is governed by two simultaneous equilibria at the silica-vapor and cellulose-vapor interfaces due to the presence of cellulose regions covered and uncovered with silica as confirmed by X-ray scattering analysis. The important contribution of a water impermeable cellulose-silica interface to the surface properties of CSH is highlighted. CSH exhibit type II isotherms in the temperature range 15-40 degrees C, more appropriately described by the Guggenheim-Anderson-de Boer (GAB) model than by the Brunauer-Emmett-Teller (BET) model. Specific surface areas calculated using both models (S(BET) and S(GAB)) increase linearly with the amount of silica influencing the higher moisture content of CSH for the same water activity. However, the presence of silica reduces the strength of interaction between monolayer water molecules and the CSH surface as revealed by the net isosteric heat of sorption (35 kJ/mol for cellulosic pulp and 26 kJ/mol for CSH with 35% silica). Silica confers a higher surface energy to CSH contributing to its polar component and surface wettability (contact angle with water) when compared to cellulosic pulp. The average diameter of cellulose microfibrils and the interfacial cellulose-silica areas are assessed on the basis of the analysis of sorption isotherms.

Hyperplane arrangements between Shi and Ish

Abstract We introduce a new family of hyperplane arrangements in dimension n ≥ 3 that includes both the Shi arrangement and the Ish arrangement. We prove that all the members of this family have the same number of regions — the connected components of the complement of the union of the hyperplanes — which can be bijectively labeled with the Pak-Stanley labelling. In addition, we characterise the Pak-Stanley labels of the regions of this family of hyperplane arrangements.

Between Shi and Ish

Abstract We introduce a new family of hyperplane arrangements in dimension n ≥ 3 that includes both the Shi arrangement and the Ish arrangement. We prove that all the members of a given subfamily have the same number of regions – the connected components of the complement of the union of the hyperplanes – which can be bijectively labeled with the Pak–Stanley labeling. In addition, we show that, in the cases of the Shi and the Ish arrangements, the number of labels with reverse centers of a given length is equal, and conjecture that the same happens with all of the members of the family.

Regular pseudo-oriented maps and hypermaps of low genus

Pseudo-orientable maps were introduced by Wilson in 1976 to describe non-orientable regular maps for which it is possible to assign an orientation to each vertex in such a way that adjacent vertices have opposite orientations. This property extends naturally to non-orientable and orientable hypermaps. In this paper we classify the regular pseudo-oriented maps and hypermaps of characteristic ? ? - 3 . With the help of GAP (The GAP group, 2014) and its library of small groups, we extend the classification down to characteristic ? = - 16 (Tables?7-19 in the Appendix).