Colloidal Nature of Cationic Calix[6]arene Aqueous Solutions

The study of the aqueous solutions of the cationic hexameric calixarene 5,11,17,23,29,35-hexakis (<i>N</i>,<i>N</i>-dimethyl-<i>N</i>-hydroxyethylammoniummethylene)-37,38,39,40,41,42-hexametoxycalix­[6]­arene hexachloride demonstrates their colloidal nature. Within the concentration range from 1 × 10^–5 to 0.01 M, this compound forms positively charged aggregates of a much larger size as compared with those of tetrameric cationic calix[4]­arene previously studied by us. The aggregation was confirmed both by DLS and TEM experiments; the last method revealed that the 10² to 10³ nm sized particles consist of smaller primary aggregates. These aggregates manifest themselves in displaying alteration of absorption spectra and marked shifts of apparent ionization constants of common acid–base indicators. These shifts resemble those registered in micellar solutions of cationic surfactants and cationic polyelectrolyte brushes. The pCl measurements also confirm the formation of calixarene aggregates. The dye associations with the calixarene are governed rather by interactions with the aggregates of the macrocycles than by expected inclusion of the guest into the hosts cavity. Hence, on using ionic calixarenes in aqueous media, not only inclusion phenomena but also micellar effects should be taken into account

Heisenberg's uncertainty principle in the PTOLEMY project : A theory update

We discuss the consequences of the quantum uncertainty on the spectrum of the electron emitted by the beta-processes of a tritium atom bound to a graphene sheet. We analyze quantitatively the issue recently raised by Cheipesh, Cheianov, and Boyarsky [Phys. Rev. D 104, 116004 (2021)], and discuss the relevant timescales and the degrees of freedom that can contribute to the intrinsic spread in the electron energy. We perform careful calculations of the potential between tritium and graphene with different coverages and geometries. With this at hand, we propose possible avenues to mitigate the effect of the quantum uncertainty

Heisenberg's uncertainty principle in the PTOLEMY project: a theory update

We discuss the consequences of the quantum uncertainty on the spectrum of the electron emitted by the beta-processes of a tritium atom bound to a graphene sheet. We analyze quantitatively the issue recently raised by Cheipesh, Cheianov, and Boyarsky [Phys. Rev. D 104, 116004 (2021)], and discuss the relevant timescales and the degrees of freedom that can contribute to the intrinsic spread in the electron energy. We perform careful calculations of the potential between tritium and graphene with different coverages and geometries. With this at hand, we propose possible avenues to mitigate the effect of the quantum uncertainty.</p