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The 2D Ising model is well-formulated to address problems in adsorption thermodynamics. It is particularly well-suited to describing the adsorption isotherms predicting the surface enantiomeric excess, ees, observed during competitive co-adsorption of enantiomers onto achiral surfaces. Herein, we make the direct one-to-one correspondence between the 2D Ising model Hamiltonian and the Hamiltonian used to describe competitive enantiomer adsorption on achiral surfaces. We then demonstrate that adsorption from racemic mixtures of enantiomers and adsorption of prochiral molecules are directly analogous to the Ising model with no applied magnetic field, i.e., the enantiomeric excess on chiral surfaces can be predicted using Onsager’s solution to the 2D Ising model. The implication is that enantiomeric purity on the surface can be achieved during equilibrium exposure of prochiral compounds or racemic mixtures of enantiomers to achiral surfaces. 

Comprehensive mapping of enantiospecific surface reactivity versus the crystallographic orientation of Cu( hkl ) surfaces vicinal to Cu(111) has been conducted using a spherically shaped single crystal on which the surface normal vectors, [ hkl ], span all possible orientations lying with 14° of the [111] direction. This has allowed direct measurement on 169 different Cu( hkl ) surfaces of the two rate constants, k (hkl)i and k (hkl)e, that determine the kinetics of the vacancy-mediated, explosive decomposition of tartaric acid (TA). The initiation rate constant, k (hkl)i, quantifies the kinetics of an initiation step that creates vacancies in the adsorbed TA monolayer. The explosion rate constant, k (hkl)e, quantifies the kinetics of a vacancy-mediated explosion step that results in TA decomposition and product desorption. Enantiospecificity is revealed by the dependence of TA decomposition kinetics on the chirality of the local surface orientation. Diastereomerism is demonstrated by the fact that d -TA is more reactive than l -TA on S surfaces while l -TA is more reactive on R surfaces. The time to reach half coverage, t (hkl)1/2, during isothermal TA decomposition at 433 K allowed determination of the most enantiospecific surface orientation; Cu(754). The ideal Cu(754) surface structure consists of (111) terraces separated by monoatomic steps formed by the (100) and (110) microfacets. 

Abstract Sensing of clinically relevant biomolecules such as neurotransmitters at low concentrations can enable an early detection and treatment of a range of diseases. Several nanostructures are being explored by researchers to detect biomolecules at sensitivities beyond the picomolar range. It is recognized, however, that nanostructuring of surfaces alone is not sufficient to enhance sensor sensitivities down to the femtomolar level. In this paper, we break this barrier/limit by introducing a sensing platform that uses a multi-length-scale electrode architecture consisting of 3D printed silver micropillars decorated with graphene nanoflakes and use it to demonstrate the detection of dopamine at a limit-of-detection of 500 attomoles. The graphene provides a high surface area at nanoscale, while micropillar array accelerates the interaction of diffusing analyte molecules with the electrode at low concentrations. The hierarchical electrode architecture introduced in this work opens the possibility of detecting biomolecules at ultralow concentrations.