By rigorously accounting for mesoscale spatial correlations in donor/acceptor surface properties, we develop a scale-spanning model for same-material tribocharging. We find that mesoscale correlations affect not only the magnitude of charge transfer but also the fluctuations-suppressing otherwise overwhelming charge-transfer variability that is not observed experimentally. We furthermore propose a generic theoretical mechanism by which the mesoscale features might emerge, which is qualitatively consistent with other proposals in the literature.

Kelvin probe force microscopy (KPFM) is a powerful tool for studying contact electrification (CE) at the nanoscale, but converting KPFM voltage maps to charge density maps is nontrivial due to long-range forces and complex system geometry. Here we present a strategy using finite-element method (FEM) simulations to determine the Green's function of the KPFM probe/insulator/ground system, which allows us to quantitatively extract surface charge. Testing our approach with synthetic data, we find that accounting for the atomic force microscope (AFM) tip, cone, and cantilever is necessary to recover a known input and that existing methods lead to gross miscalculation or even the incorrect sign of the underlying charge. Applying it to experimental data, we demonstrate its capacity to extract realistic surface charge densities and fine details from contact-charged surfaces. Our method gives a straightforward recipe to convert qualitative KPFM voltage data into quantitative charge data over a range of experimental conditions, enabling quantitative CE at the nanoscale.

Hyperuniform states are an efficient way to fill up space for disordered systems. In these states the particle distribution is disordered at the short scale but becomes increasingly uniform when looked at large scales. Hyperuniformity appears in several systems, in static or quasistatic regimes as well as close to transitions to absorbing states. Here, we show that a vibrated granular layer, close to the liquid-to-solid transition, displays dynamic hyperuniformity. Prior to the transition, patches of the solid phase form, with length scales and mean lifetimes that diverge critically at the transition point. When reducing the wavenumber, density fluctuations encounter increasingly more patches that block their propagation, resulting in a static structure factor that tends to zero for small wavenumbers at the critical point, which is a signature of hyperuniformity. A simple model demonstrates that this coupling of a density field to a highly fluctuating scalar friction field gives rise to dynamic hyperuniform states.Recently, hyperuniform systems have been identified as an efficient way to fill up space for disordered configurations. These exotic particles distributions are disordered at short distances, as liquids, and more and more uniform when looked at large scales, just as regular, ordered lattices do. Hyperuniform states have been observed in jammed granular [1, 2] and colloidal packings [3], in block-copolymer assemblies [4], in quasicrystals [5], active circle swimmers [6], and even in the patterns of photoreceptive cells in chicken eyes [7]. Recently, these states have been obtained in systems showing non-equilibrium transitions to absorbing states, were hyperuniformity is observed both in the absorbing and fluid phases, close to the transition [8][9][10]. Here, we show that a vibrated granular layer, when approaching the liquid-to-solid transition from the liquid phase, displays hyperuniform states, which are dynamically generated. A simple model demonstrates that it results from coupling density to a highly fluctuating friction field.It is possible to characterize the decay of particle correlations with distance by measuring the average number of particles N and its variance σ 2 N ≡ N 2 − N 2 in boxes of different sizes. In condensed matter, under normal conditions, correlations decay rapidly and above a certain length, σ 2 N ∝ N . This is however, not always the case. For example, in regular lattices, fluctuations take place only at the boundaries. But also in disordered systems it has been reported that for large systems σ 2 N ∝ N β /2 . When β > 2, the system is said to present giant density fluctuations and it has been observed in several dynamic non-equilibrium systems as in vibrated nematic granular layers [11] or in active matter swarms [12]. The opposite case, when β < 2, corresponds to hyperuniformity. As the system grows, number fluctuations increase slower than the usual linear behavior, σ 2 N ∝ N , and density fluctuations become suppressed at the very large wavelength limit. Indeed, another ...

Kelvin probe force microscopy (KPFM) is a powerful tool for studying contact electrification at the nanoscale, but converting KPFM voltage maps to charge density maps is non-trivial due to longrange forces and complex system geometry. Here we present a strategy using finite element method (FEM) simulations to determine the Green's function of the KPFM probe/insulator/ground system, which allows us to quantitatively extract surface charge. Testing our approach with synthetic data, we find that accounting for the AFM tip, cone and cantilever are necessary to recover a known input, and that commonly applied heuristics and approximations lead to gross miscalculation. Applying it to experimental data, we demonstrate its capacity to extract realistic surface charge densities and fine details from contact charged surfaces. Our method gives a straightforward recipe to convert qualitative KPFM voltage data into quantitative charge data over a range of experimental conditions, enabling quantitative contact electrification experiments at the nanoscale.