Exploring the Mechanical Behaviors of 2D Materials in Electrochemical Energy Storage Systems: Present Insights and Future Prospects

2D materials (2DM) and their heterostructures (2D + nD, n = 0,1,2,3) hold significant promise for applications in Electrochemical Energy Storage Systems (EESS), such as batteries. 2DM can serve as van der Waals (vdW) slick interface between conventional active materials (e.g., Silicon) and current collectors, modifying interfacial adhesion and preventing stress-induced fractures. Additionally, 2DM can replace traditional polymer binders (e.g., MXenes). This arrangement also underscores the critical role of interfacial mechanics between 2DM and active materials. Furthermore, 2DM can be designed to function as an electrode itself. For instance, a porous graphene network has been reported to possesses approximately five times the capacity of a traditional graphite anode. Consequently, gaining a comprehensive understanding of the mechanical properties of 2DM in EESS is paramount. However, modeling 2DM in EESS poses significant challenges due to the intricate coupling of mechanics and electrochemistry. For instance, defective graphene tends to favor adatom adsorption (e.g., Li+) during charging. In cases of strong adsorption, adatoms may not readily detach from electrodes during discharging. As a result, in such scenarios, adsorption-desorption (charge-discharge) processes govern the mechanical properties of 2DM when used as binders and current collectors. Regrettably, most existing studies on the mechanical properties of 2DM in EESS have failed to adequately address these critical issues. This perspective paper aims to provide a comprehensive overview of recent progress in the chemo-mechanics of 2DM's mechanical properties. A wide spectrum of multiscale modeling approaches, including atomistic/molecular simulations, continuum modeling, and machine learning, are discussed.Comment: 49 pages, 33 figure

Quantitative optical mapping of two-dimensional materials

The pace of two-dimensional materials (2DM) research has been greatly accelerated by the ability to identify exfoliated thicknesses down to a monolayer from their optical contrast. Since this process requires time-consuming and error-prone manual assignment to avoid false-positives from image features with similar contrast, efforts towards fast and reliable automated assignments schemes is essential. We show that by modelling the expected 2DM contrast in digitally captured images, we can automatically identify candidate regions of 2DM. More importantly, we show a computationally-light machine vision strategy for eliminating false-positives from this set of 2DM candidates through the combined use of binary thresholding, opening and closing filters, and shape-analysis from edge detection. Calculation of data pyramids for arbitrarily high-resolution optical coverage maps of two-dimensional materials produced in this way allows the real-time presentation and processing of this image data in a zoomable interface, enabling large datasets to be explored and analysed with ease. The result is that a standard optical microscope with CCD camera can be used as an analysis tool able to accurately determine the coverage, residue/contamination concentration, and layer number for a wide range of presented 2DMs

Quantum Symmetries and Strong Haagerup Inequalities

In this paper, we consider families of operators $\{x_r\}_{r \in \Lambda}$ in a tracial C$^\ast$-probability space $(\mathcal A, \phi)$, whose joint $\ast$-distribution is invariant under free complexification and the action of the hyperoctahedral quantum groups $\{H_n^+\}_{n \in \N}$. We prove a strong form of Haagerup's inequality for the non-self-adjoint operator algebra $\mathcal B$ generated by $\{x_r\}_{r \in \Lambda}$, which generalizes the strong Haagerup inequalities for $\ast$-free R-diagonal families obtained by Kemp-Speicher \cite{KeSp}. As an application of our result, we show that $\mathcal B$ always has the metric approximation property (MAP). We also apply our techniques to study the reduced C$^\ast$-algebra of the free unitary quantum group $U_n^+$. We show that the non-self-adjoint subalgebra $\mathcal B_n$ generated by the matrix elements of the fundamental corepresentation of $U_n^+$ has the MAP. Additionally, we prove a strong Haagerup inequality for $\mathcal B_n$, which improves on the estimates given by Vergnioux's property RD \cite{Ve}

Shape optimization problems on metric measure spaces

We consider shape optimization problems of the form $$\min\big\{J(\Omega)\ :\ \Omega\subset X,\ m(\Omega)\le c\big\},$$ where $X$ is a metric measure space and $J$ is a suitable shape functional. We adapt the notions of $\gamma$-convergence and weak $\gamma$-convergence to this new general abstract setting to prove the existence of an optimal domain. Several examples are pointed out and discussed.Comment: 27 pages, the final publication is available at http://www.journals.elsevier.com/journal-of-functional-analysis

Subsystem constraints in variational second order density matrix optimization: curing the dissociative behavior

A previous study of diatomic molecules revealed that variational second-order density matrix theory has serious problems in the dissociation limit when the N-representability is imposed at the level of the usual two-index (P, Q, G) or even three-index (T1, T2) conditions [H. van Aggelen et al., Phys. Chem. Chem. Phys. 11, 5558 (2009)]. Heteronuclear molecules tend to dissociate into fractionally charged atoms. In this paper we introduce a general class of N-representability conditions, called subsystem constraints, and show that they cure the dissociation problem at little additional computational cost. As a numerical example the singlet potential energy surface of BeB+ is studied. The extension to polyatomic molecules, where more subsystem choices can be identified, is also discussed.Comment: published version;added reference

Light spin-1/2 or spin-0 Dark Matter particles

We recall and precise how light spin-0 particles could be acceptable Dark Matter candidates, and extend this analysis to spin-1/2 particles. We evaluate the (rather large) annihilation cross sections required, and show how they may be induced by a new light neutral spin-1 boson U. If this one is vectorially coupled to matter particles, the (spin-1/2 or spin-0) Dark Matter annihilation cross section into e+e- automatically includes a v_dm^2 suppression factor at threshold, as desirable to avoid an excessive production of gamma rays from residual Dark Matter annihilations. We also relate Dark Matter annihilations with production cross sections in e+e- scatterings. Annihilation cross sections of spin-1/2 and spin-0 Dark Matter particles are given by exactly the same expressions. Just as for spin-0, light spin-1/2 Dark Matter particles annihilating into e+e- could be responsible for the bright 511 keV gamma ray line observed by INTEGRAL from the galactic bulge.Comment: 10 page

Extensive v2DM study of the one-dimensional Hubbard model for large lattice sizes: Exploiting translational invariance and parity

Using variational density matrix optimization with two- and three-index conditions we study the one-dimensional Hubbard model with periodic boundary conditions at various filling factors. Special attention is directed to the full exploitation of the available symmetries, more specifically the combination of translational invariance and space-inversion parity, which allows for the study of large lattice sizes. We compare the computational scaling of three different semidefinite programming algorithms with increasing lattice size, and find the boundary point method to be the most suited for this type of problem. Several physical properties, such as the two-particle correlation functions, are extracted to check the physical content of the variationally determined density matrix. It is found that the three-index conditions are needed to correctly describe the full phase diagram of the Hubbard model. We also show that even in the case of half filling, where the ground-state energy is close to the exact value, other properties such as the spin-correlation function can be flawed.Comment: 28 pages, 10 figure