The electronic structure of mono and bilayers of colloidal 2H‐MoS2 nanosheets synthesized by wet‐chemistry using potential‐modulated absorption spectroscopy (EMAS), differential pulse voltammetry, and electrochemical gating measurements is investigated. The energetic positions of the conduction and valence band edges of the direct and indirect bandgap are reported and observe strong bandgap renormalization effects, charge screening of the exciton, as well as intrinsic n‐doping of the as‐synthesized material. Two distinct transitions in the spectral regime associated with the C exciton are found, which overlap into a broad signal upon filling the conduction band. In contrast to oxidation, the reduction of the nanosheets is largely reversible, enabling potential applications for reductive electrocatalysis. This work demonstrates that EMAS is a highly sensitive tool for determining the electronic structure of thin films with a few nanometer thicknesses and that colloidal chemistry affords high‐quality transition metal dichalcogenide nanosheets with an electronic structure comparable to that of exfoliated samples.

We introduce a nonlinear, one-dimensional bending-twisting model for an inextensible bi-rod that is composed of a nematic liquid crystal elastomer. The model combines an elastic energy that is quadratic in curvature and torsion with a Frank-Oseen energy for the liquid crystal elastomer. Moreover, the model features a nematic-elastic coupling that relates the crystalline orientation with a spontaneous bending-twisting term. We show that the model can be derived as a Γ-limit from three-dimensional nonlinear elasticity. Moreover, we introduce a numerical scheme to compute critical points of the bending-twisting model via a discrete gradient flow. We present various numerical simulations that illustrate the rich mechanical behavior predicted by the model. The numerical experiments reveal good stability and approximation properties of the method.

Using rate-independent evolutions as a framework for elastoplasticity, an a posteriori bound for the error introduced by time stepping is established. A time adaptive algorithm is devised and tested in comparison to a method with constant time steps. Experiments show that a significant error reduction can be obtained using variable time steps.2010 Mathematics Subject Classification. Primary: 65N12, 74C05.