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Electrochemical CO2 reduction (CO2R) is an attractive option for storing renewable electricity and for the sustainable production of valuable chemicals and fuels. In this roadmap, we review recent progress in fundamental understanding, catalyst development, and in engineering and scale-up. We discuss the outstanding challenges towards commercialization of electrochemical CO2R technology: energy efficiencies, selectivities, low current densities, and stability. We highlight the opportunities in establishing rigorous standards for benchmarking performance, advances in in operando characterization, the discovery of new materials towards high value products, the investigation of phenomena across multiple-length scales and the application of data science towards doing so. We hope that this collective perspective sparks new research activities that ultimately bring us a step closer towards establishing a low- or zero-emission carbon cycle.

Here we present an angle-resolved photoelectron spectroscopy (ARPES), x-ray absorption spec-troscopy (XAS), and density-functional theory (DFT) investigations of water and ammonia ad-sorption on graphene/Ni(111). Our results on graphene/Ni(111) reveal the existence of interface states, originating from the strong hybridization of the graphene {\pi} and spin-polarized Ni 3d valence band states. ARPES and XAS data of the H2O (NH3)/graphene/Ni(111) system give an information about the kind of interaction between adsorbed molecules and graphene on Ni(111). The presented experimental data are compared with the results obtained in the framework of the DFT approach., Comment: accepted in Nanoscale Research Letters; 16 pages, 4 figures, 2 tables

We present two models for the drying of waterborne paints, which consist of non-volatile latex particles suspended in water. One model considers the water and latex density in a layer as a function of time. Water evaporation at the surface represents the drying. This model results in a one-dimensional free boundary problem, which is solved numerically. Extensions to the model are given that describe the stiffening of the paint. A second model is a particle based dynamical simulation where latex particles form a network through which water particles move. A thin slab of the suspension in a threedimensional box is studied. Water particles escaping the slab at the surface represent the drying, progressing network formation the stiffening of the paint. Both models allow for validation with material properties as determined experimentally on real coatings.

The thermal-to-percolative crossover exponent \phi, well-known for ferromagnetic systems, is studied extensively for Edwards-Anderson spin glasses. The scaling of defect energies are determined at the bond percolation threshold p_c, using an improved algorithm. Simulations extend to system sizes above N=10^8 in dimensions d=2,...,7. The results can be related to the behavior of the transition temperature T_g (p-p_c)^\phi between the paramagnetic and the glassy regime for p-> p_c. In three dimensions, where our simulations predict \phi=1.127(5), this scaling form for T_g provides a rare experimental test of predictions arising from the equilibrium theory of low-temperature spin glasses. For dimension near and above the upper critical dimension, the results provide a new challenge to reconcile mean-field theory with finite-dimensional properties., Comment: 4 pages, added figure and other improvements, final version, related information can be found at http://www.physics.emory.edu/faculty/boettcher/

The stiffness exponents in the glass phase for lattice spin glasses in dimensions $d=3,...,6$ are determined. To this end, we consider bond-diluted lattices near the T=0 glass transition point $p^*$. This transition for discrete bond distributions occurs just above the bond percolation point $p_c$ in each dimension. Numerics suggests that both points, $p_c$ and $p^*$, seem to share the same $1/d$-expansion, at least for several leading orders, each starting with $1/(2d)$. Hence, these lattice graphs have average connectivities of $\alpha=2dp\gtrsim1$ near $p^*$ and exact graph-reduction methods become very effective in eliminating recursively all spins of connectivity $\leq3$, allowing the treatment of lattices of lengths up to L=30 and with up to $10^5-10^6$ spins. Using finite-size scaling, data for the defect energy width $\sigma(\Delta E)$ over a range of $p>p^*$ in each dimension can be combined to reach scaling regimes of about one decade in the scaling variable $L(p-p^*)^{\nu^*}$. Accordingly, unprecedented accuracy is obtained for the stiffness exponents compared to undiluted lattices ($p=1$), where scaling is far more limited. Surprisingly, scaling corrections typically are more benign for diluted lattices. We find in $d=3,...,6$ for the stiffness exponents $y_3=0.24(1)$, $y_4=0.61(2), y_5=0.88(5)$, and $y_6=1.1(1)$. The result for the upper critical dimension, $d_u=6$, suggest a mean-field value of $y_\infty=1$., Comment: 8 pages, RevTex, 15 ps-figures included (see http://www.physics.emory.edu/faculty/boettcher for related information)

A difficult and long-standing problem in mathematical physics concerns the determination of the value of $f(\infty)$ from the asymptotic series for $f(x)$ about $x\!=\!0$. In the past the approach has been to convert the asymptotic series to a sequence of Pad\'e approximants $\{P^n_n(x)\}$ and then to evaluate these approximants at $x\!=\!\infty$. Unfortunately, for most physical applications the sequence $\{P^n_n(\infty)\}$ is slowly converging and does not usually give very accurate results. In this paper we report the results of extensive numerical studies for a large class of functions $f(x)$ associated with strong-coupling lattice approximations. We conjecture that for large $n$, $P^n_n(\infty)\!\sim\!f(\infty)+B/\ln n $. A numerical fit to this asymptotic behavior gives an accurate extrapolation to the value of $f(\infty )$., Comment: plain TEX, 7 pages, 7 figures included, WASH-U-HEP-93