Mechanical Bonds and Topological Effects in Radical Dimer Stabilization

While mechanical bonding stabilizes tetrathiafulvalene (TTF) radical dimers, the question arises: what role does topology play in catenanes containing TTF units? Here, we report how topology, together with mechanical bonding, in isomeric [3]- and doubly interlocked [2]catenanes controls the formation of TTF radical dimers within their structural frameworks, including a ring-in-ring complex (formed between an organoplatinum square and a {2+2} macrocyclic polyether containing two 1,5-dioxynaphthalene (DNP) and two TTF units) that is topologically isomeric with the doubly interlocked [2]catenane. The separate TTF units in the two {1+1} macrocycles (each containing also one DNP unit) of the isomeric [3]catenane exhibit slightly different redox properties compared with those in the {2+2} macrocycle present in the [2]catenane, while comparison with its topological isomer reveals substantially different redox behavior. Although the stabilities of the mixed-valence (TTF2)^(•+) dimers are similar in the two catenanes, the radical cationic (TTF^(•+))_2 dimer in the [2]catenane occurs only fleetingly compared with its prominent existence in the [3]catenane, while both dimers are absent altogether in the ring-in-ring complex. The electrochemical behavior of these three radically configurable isomers demonstrates that a fundamental relationship exists between topology and redox properties

Comparison of Capillary Flow Porometry (CFP) and Liquid Extrusion Porometry (LEP) Techniques for the Characterization of Porous and Face Mask Membranes

This work aims to study the characterization of several membrane filters by using capillary flow porometry (CFP) and liquid extrusion porometry (LEP) to obtain their pore size distributions (PSD) and mean pore diameters (davg). Three polymeric membranes of different materials namely, polyethylene (PET), cellulose nitrate (CN), and FM (face mask), and one inorganic (namely, alumina Al2O3) from ultrafiltration (UF)/microfiltration (MF) and particle separation were analyzed using a pressure constant fluid/liquid extrusion porometer, developed at institute de la filtration et techniques séparatives (IFTS). Several porosimetric fluids have been used to wet and penetrate into the porous/fiber structure. The results show the accuracy of the setup on characterizing membranes in the UF/MF range by CFP, with reasonable agreement with nominal data of the filters. Additionally, LEP extension of the equipment obtained good agreement with nominal data and the CFP results, while filters presenting a microstructure of highly interconnected pores (face mask) resulted in clear differences in terms of resulting PSD and average sizes when CFP and LEP results are compared

Conway’s Question: The Chase for Completeness

We study various degrees of completeness for a Tychonoff space X. One of them plays a central role, namely X is called a Conway space if X is sequentially closed in its Stone–Čech compactification β X (a prominent example of Conway spaces is provided by Dieudonné complete spaces). The Conway spaces constitute a bireflective subcategory Conw of the category Tych of Tychonoff spaces. Replacing sequential closure by the general notion of a closure operator C, we introduce analogously the subcategory Conw C of C-Conway spaces, that turns out to be again a bireflective subcategory of Tych. We show that every bireflective subcategory of Tych can be presented in this way by building a Galois connection between bireflective subcategories of Tych and closure operators of Top finer than the Kuratowski closure. Other levels of completeness are considered for the (underlying topological spaces of) topological groups. A topological group G is sequentially complete if it is sequentially closed in its Raĭkov completion . The sequential completeness for topological groups is stronger than Conway’s property, although they coincide in some classes of topological groups, for example: free (Abelian) topological groups, pseudocompact groups, etc