Nanoporous Gold: From Structure Evolution to Functional Properties in Catalysis and Electrochemistry

Nanoporous gold (NPG) is characterized by a bicontinuous network of nanometer-sized metallic struts and interconnected pores formed spontaneously by oxidative dissolution of the less noble element from gold alloys. The resulting material exhibits decent catalytic activity for low-temperature, aerobic total as well as partial oxidation reactions, the oxidative coupling of methanol to methyl formate being the prototypical example. This review not only provides a critical discussion of ways to tune the morphology and composition of this material and its implication for catalysis and electrocatalysis, but will also exemplarily review the current mechanistic understanding of the partial oxidation of methanol using information from quantum chemical studies, model studies on single-crystal surfaces, gas phase catalysis, aerobic liquid phase oxidation, and electrocatalysis. In this respect, a particular focus will be on mechanistic aspects not well understood, yet. Apart from the mechanistic aspects of catalysis, best practice examples with respect to material preparation and characterization will be discussed. These can improve the reproducibility of the materials property such as the catalytic activity and selectivity as well as the scope of reactions being identified as the main challenges for a broader application of NPG in target-oriented organic synthesis.


SI-1 Relations between Different Measures for the Ligament Size of Nanoporous Gold
Section 3 in the main text of this review introduces the following measures for the ligament size of nanoporous gold (NPG):  , an average of the diameter of ligaments, measured along their waist, typically obtained by evaluating scanning electron micrographs  , an average of the diameter of ligaments, measured by granulometry  , the characteristic spacing between the centers of neighboring ligaments, as embodied in the first maximum of the microstructure autocorrelation function  , the diameter of an equivalent cylindrical ligament with the same volume-specific surface area as the sample The considerations below explore how those various measures are interrelated in NPG.
To start out, will be linked to , exploiting the finding that the microstructure of that material is well represented by the leveled-wave model, as presented in section 3.1. The model is generated as a superposition of plane waves with identical wavelength, λ, but different directions of the wave vector, of magnitude and with random phase shifts. The resulting random field is then binarized ("leveled"), using the threshold value ξ for discriminating between solid and pore phase. The solid fraction, φ, and the threshold value are interlinked by 1 ξ = √2 erf (2φ − 1).
For the leveled wave model, one finds that 1 = 1.23 = 1.23 , and for the volume-specific (per volume of the solid phase) surface area, α , The specific surface area is linked to by α = . (S5) The numerical constant 1.23 in Eq. (S3) is related to the conversion between reciprocal space (wave number , wavelength λ) and autocorrelated real space (mean distance between ligaments). According to the Debye scattering equation, 2,3 and except for a constant pre-factor and a constant background scattering, the structure factor for a set of randomly oriented objects with a characteristic near-neighbor spacing and with otherwise random positioning (for instance, a gas of diatomic molecules) is . Numerically, its first maximum is found at the wavenumber Contrary to and , no analytic solution is known for of the leveled-wave model. Analyzing the results of numerical 3D image analysis of leveled-wave model renderings, one finds that, approximately and for 0.2 < φ < 0.5, satisfies 1 = (0.53 φ + 0.41).
We are interested in the relative magnitude of those three measures for size, and in conversion factors. With this in mind, we chose one of the three measures as the reference one. Here, somewhat arbitrarily, is chosen for that role. We then obtain = .
( . . ) Those results are displayed in Figure 11 of the main text.
Next, it will be explored how the ligament size parameter relates to the aforementioned parameters. Recall that is a measure for the mean diameter of ligaments, measured at their smallest cross-section. Out of the set of parameters under inspection here, one can therefore expect to to have the smallest numerical value for any given sample of NPG. Comparing definitions, one finds that is conceptually more closely related to than to the remaining parameters: both, and , are based on measuring diameters. They are distinguished inasmuch as also considers the thicker regions near the nodes, were ligaments meet, and that larger regions carry more weight in the averaging for . 4,5 The commonalities suggest that provides the most obvious reference to which values of are to be compared. One expects to be not too dissimilar from , but systematically smaller, see the reasoning above.
As the basis for the above-mentioned comparison, one requires -for one and the same sample or set of samples -experimental data for and for any one of the three remaining parameters discussed above. The literature does not provide an ultimately satisfactory database in this respect. We here analyze a single data set, from the PhD thesis work of Nadiia Mameka at Hamburg University of Technology. 6 Samples in that work were prepared and conditioned as outlined in section 2.3 of the main document of this review. Table 4.1 in ref 6 shows all required microstructural parameters, along with from scanning electron microscopy and with determined by electrochemical capacitance measurements in 1 mol L -1 HClO4. The relevant data from that table is reproduced here as the first 4 columns in Table S1. One can readily use the composition data to evaluate the mass density and, accounting for the solid fraction, the volumespecific surface area . Equation (S5) then leads to , and Eq. (S10) provides . That data is shown as columns 5-7 in Table S1. Table S1. Experimental microstructure data for 4 independent samples of nanoporous gold. The bottommost 4 rows show the 4 samples, and the leftmost 4 columns (residual silver fraction , solid fraction φ, mass-specific surface area α , scanning-electron-microscope based ligament size ) are from  Figure S1. Implication of the data in reference 18 for the comparison between scanning-electron-microscopy-based ligament size, , and the granulometry-based ligament size, , in a small set of samples with solid fraction φ around 0.3. A) and B) plots with linear axes in different scaling; C) plot with double logarithmic axis. Circles and error bars refer to experimental data. Green line is best fit of straight line through the origin. Gray lines and shaded regions indicate a symmetric confidence band containing all data points. Figure S1 explores the correlation between the data for expects and for as displayed in Table S1. In view of the extremely slim database, only the simplest model can be tested in a meaningful way. That is here a linear scaling, independent of the solid fraction, in other words ( , φ) = . The green lines in the figure panels represent the straight line of best fit through the origin on a linear scale. The gray lines represent a symmetric confidence band including all data points. That data can be represented numerically by The various representations in Figure S1 communicate clearly that the data provides only a weak confirmation of the linear scaling. Therefore, the scaling factor and its confidence interval, as derived from fitting the data set, must be viewed as a tentative result. Additional experiments are needed as a basis for a reliable conclusion on the scaling between and other measures for the characteristic microstructural length scale of NPG. The result, as it stands, however confirms the expectation, based on the definitions of the various size parameters, that provides a particularly small numerical value compared to the remaining measures, likely about twice smaller than the granulometry ligament size. Figure S2. The various size measures (as identified in the legend and explained in the text) for characteristic length scales of the leveled-wave model as a representation of nanoporous gold. Each measure has been scaled with the characteristic wavelength, λ, used in constructing the model microstructure. Data for must be viewed as tentative, see discussion in the main text. Figure S2 summarizes the findings for the various size measures in a graph where each measure has been scaled with the characteristic wavelength λ. Furthermore, Figure 11 in section 3.5 of the main document shows the same data but with the sizes scaled with . The compilations again advertise the large differences in the numerical values of the differently defined size measures. It is emphasized that the differences, in themselves, do not represent "error" or other inconsistency between the measures. It is simply a consequence of their different definitions. There is, however, a large uncertainty in how to convert between the SEM ligament size and the remaining sizes. That relation calls for a dedicated experimental study, which is not covered by literature so far.

SI-2 Conversion of the Potential Scale Between Commonly Used Reference Electrodes
The papers reviewed in this article use a large variety of reference electrodes that have a thermodynamically defined electrode potential with respect to the standard hydrogen electrode (SHE). Except for statements where a direct comparison is required, we avoided recalculated electrode potentials to a single reference electrode. Instead, we provide below the potentials of commonly used reference electrodes in the field of NPG (Table S2). The SHE has by definition an electrode potential of 0.0000000 V at all temperatures. It is formed by a Pt metal in contact with gaseous hydrogen at the pressure of 100 kPa and an aqueous solution with a hydronium ion activity a(H3O + ) = 1 mol L 1 . This solution has the pH 0. A solution of HCl fulfilling this condition has approximately a concentration of 1.2 mol L 1 . If instead, the half-cell of the hydrogen electrode is prepared with an HCl solution of the concentration 1 mol L 1 , this electrode is called normal hydrogen electrode (NHE). Its use as reference point is discouraged by IUPAC. Another hydrogen electrode is called reversible hydrogen electrode (RHE). This is a Pt metal in contact with gaseous hydrogen of pressure 100 kPa and the working solution of the cell. Equation (S12) can be used to convert an electrode potential measured against SHE, ESHE, to a potential measured against RHE, ERHE, or vice versa.
The experimental advantage of using a RHE rests in the avoidance of any diffusion potentials between the inner filling solution of a reference electrode in contact to a working solution that differs in composition from the filling of the reference electrode. Conceptually, the RHE has the advantage that potentials of electrode reactions involving the transfer of protons remain constant vs RHE, but would show a pH-dependence when stated against SHE. This applies to such important reactions as hydrogen evolution reaction (HER), oxygen evolution reaction (OER), oxygen reduction reaction (ORR), methanol oxidation reaction (MOR) etc.  Frequently, the solution composition is given as concentration. For acidic solution, the pH can be conveniently be measured. For alkaline solution with pH > 12, this is more difficult due to the alkali error of common pH glass electrodes. Thus, activity coefficients have to be considered when estimating the potential of the RHE in a solution of a particular concentration of a base.
with c° = 1 mol L -1 and a° = 1 mol L -1 being the standard concentrations and standard activities.
A selection of activity coefficients from Ref 7 is compiled in Table S3. Please note, that the content of the solution is stated a molality bi, i.e., solv Amount of compound Mass of the solvent Since water as the solvent has a density close to 1 kg L -1 and additions of electrolytes changes this only by a small amount, estimations are often sufficiently accurate by assuming Of course, precision data especially for higher concentrations require a transformation of the quantities taking in account the density of the solution and using interpolation techniques. However, the correction introduced by considering an activity coefficient fc of 0.9 is +2.7 mV and for fc = 0.6 it is +13.1 mV. Thus, the correction may be comparable to other uncertainties in the electrode potential especially if a reference electrode with a diaphragm (e.g., SCE, Ag|AgCl, Hg|Hg2SO4|K2SO4(sa)) is used that is prone to the formation of liquid junction potentials. The different reference electrode potentials exhibit different dependencies on temperature, e.g., via the temperature dependence of solubility products. Therefore, the values in Table S2 are valid only for 298 K. For other temperatures, the temperature functions of the reference electrodes must be considered. They are typically available from the manufacturers. A detailed consideration of this issues goes beyond the scope of this review.
Occasionally, one needs the conversion of electrodes potential [V] measured against a reference electrode to the vacuum energy scale [eV]. According to IUPAC, 8 equation (S17) is recommended. Evac = -e  ESHE -(4.440.02) eV (S17) Apart from an offset and a different unit, the potential axes have opposing directions as illustrated in Figure S3.

SI-3 Voltammetry of Single Crystal Gold Electrodes
The surface voltammetry is often considered as a superposition of the contribution of the most stable, low-index crystal faces of planar Au electrodes. While this approach naturally neglects the high fraction of low-coordinated surface atoms that are typical for NPG, it provides a rough indication about the dominating facets and can capture changes of the surface structure during use of NPG electrodes. Figure S4 exemplifies such a data set in acidic perchlorate solution. The review paper 9 is recommended as an initial source showing the complex dependency of the appearance of surface voltammetry on the kind and concentration of the used electrolyte, especially the presence of anion and pH, the temperature, scan rate and the quality of the used single crystal electrodes. A more extensive collection of reference data for various electrolyte composition and single crystal faces is compiled in Table S4. Recently application in alkaline solution have gained in importance and Figure S5 provides reference voltammograms for such conditions.

SI-4 Reference Data for Underpotential Deposition/Stripping of Pb on Au Single Crystal Electrodes
Extensive experimental material for Pb UPD on Au single crystal electrodes is available from the initial period of singly crystal electrochemistry. 15,16 The experiments were conducted in 10 -3 mol L -1 PbF2 + 10 -2 mol L -1 HClO4, a system in which no specific anion adsorption is expected to interfere with the UPD process. Later, it turned out the Pb UPD on Au electrodes is quite insensitive to the presence of anions (in contrast to Cu UPD on Au). The data even agree quite well with vacuum deposition as long as the amount of vacuum deposited Pb does not exceed a monolayer. Hence water adsorption does not significantly interfere with the UPD process. The absence of surface alloying that would cause Pb to diffuse into the Au electrode and give timedependent data for the dissolution of the UPD layer is a further prerequisite for the use of Pb UPD on Au as a structure sensitive probe. Finally, the electrosorption valency is close to 2 and thus equal to the charge of the Pb 2+ ion. It does not vary significantly with the adsorption site. This is important for relating charges of the UPD process to the number of adsorbed Pb adatoms and thus to the available site of a certain structure. 16 Figure S6 to S8 show the voltammetric curves for the dissolution of a complete Pb UPD layer from the three low index single crystal Au electrodes. For Au(1 1 1) and Au(1 1 0) the deposition curves are symmmetric to the stripping curve and are not shown. Note the asymmetry for the first cycle for Au(1 0 0) in Figure S8. The superstructures of Pb on the Au substrates given in Figures  S6 to S8 were determine by low-energy electron diffraction (LEED) in vacuum.
Stepped surface representing the transition between the low-index faces shown in Figure S9 to S11. It is very clear that the assignment of on a signal from a NPG surface to only a very limited number of structural elements from low-index faces is a very strong simplification of the complexity of the UPD signals even for a well-behaved system like Pb UPD on Au.
Data in alkaline solution show similarity to those obtained in acidic solution ( Figure S12). 17 The application of such single crystal data for the analysis of polycrystalline Au electrodes and Au electrodes with small terrace size (nanoparticles and nanorods) has been exemplified 18 and is typically applied in analogous way to NPG.        a Peak potential as reported in the paper is given in gray below the value recalculated for RHE b Related to the surface area measurement if not stated otherwise. If applicable the quantity as reported in the paper is given in gray below the peak current density