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Carbon honeycombs (CHs) are new carbon cellular structures, very promising in many respects, in particular, for high-capacity storage of various materials, especially in gaseous and liquid forms. In this study, we report a strong uptake of carbon dioxide kept inside carbon honeycomb matrices up to temperatures about three times higher as compared with CO2 desorption at ≈ 90 K from flat solid surfaces in vacuum where we conduct our high-energy electron diffraction experiments. Desorption of CO2 from CH matrices upon heating exhibits non-monotone behavior, which is ascribed to carbon dioxide release from CH channels of different sizes. It is shown that modeling of CO2 uptake, storage, and redistribution in the thin CH channels of certain types and orientations upon heating can explain experimental observations. [ABSTRACT FROM AUTHOR]

A new synthesized carbon honeycomb allotrope reported previously, built from graphene nanoribbons connected by sp3-bonded carbon junction lines, forms a family of cellular structures with high porosity and sorption capacity. In this work we first propose a complete set of possible honeycomb structures of different wall chiralities both the armchair and zigzag types, including considered earlier only theoretically, for the structural analysis of such structures by means of the high-energy electron diffraction method. The "completeness" of the model set made it possible to obtain nearly perfect coincidence of the experimental and calculated diffraction intensities. The contribution of graphite fragments and random structures, also involved in the analysis, turned out to be zero. Only a limited number of honeycomb structures of different types almost ideally describes the experiment. Thus we conclude that polydomain structures corresponding to a set of basic models formed in this investigation rather than formations dominated by random structures. The samples under study have demonstrated the unique cellular stability since were stored in vacuum ∼4.5 months before the reported measurements. Along with the original results the history of the carbon honeycomb cellular structures is briefly presented. [ABSTRACT FROM AUTHOR]

We study the problem of determination of conditions for the existence of solutions to weakly nonlinear periodic boundary-value problems for systems of ordinary differential equations with switchings and construct these solutions. The critical case where the equation for generating amplitudes of weakly nonlinear periodic boundary-value problem with switchings does not turn into the identity is analyzed. We improve the classification of critical and noncritical cases and construct an iterative algorithm for finding solutions of the weakly nonlinear periodic boundary-value problem with switchings in the critical case on the basis of the generalized Newton–Kantorovich theorem. We investigate the case of a nonlinear equation whose dimension does not coincide with the dimension of the unknown in the case where the rank of Jacobian of the nonlinear equation is complete. As an example of application of the constructed iterative scheme based on the generalized Newton–Kantorovich theorem, we obtain approximations to the solutions of periodic boundary-value problem for the mathematical model of nonisothermal chemical reaction. To check the accuracy of the obtained approximations, we evaluate the discrepancies in the original equation. We establish an estimate for the length of the range of a small parameter, where the iterative procedure aimed at the construction of solutions to the weakly nonlinear periodic boundary-value problem with switchings in the mathematical model of nonisothermal chemical reaction is convergent. To this end, we use the conditions of convergence, in particular, the requirement of contraction for the operator used to obtain the required solution of the original problem under the assumption of applicability of the generalized Newton–Kantorovich theorem. [ABSTRACT FROM AUTHOR]