Design of Complex Solid‐Solution Electrocatalysts by Correlating Configuration, Adsorption Energy Distribution Patterns, and Activity Curves

Abstract Complex solid‐solution electrocatalysts (also referred to as high‐entropy alloy) are gaining increasing interest owing to their promising properties which were only recently discovered. With the capability of forming complex single‐phase solid solutions from five or more constituents, they offer unique capabilities of fine‐tuning adsorption energies. However, the elemental complexity within the crystal structure and its effect on electrocatalytic properties is poorly understood. We discuss how addition or replacement of elements affect the adsorption energy distribution pattern and how this impacts the shape and activity of catalytic response curves. We highlight the implications of these conceptual findings on improved screening of new catalyst configurations and illustrate this strategy based on the discovery and experimental evaluation of several highly active complex solid solution nanoparticle catalysts for the oxygen reduction reaction in alkaline media.


Introduction
Despite remarkable achievements in designing novel electrocatalysts, [1] state-of-the-art catalysts are still often based on noble metals.T his is especially important for complex multi electron-proton transfer reactions,s uch as the oxygen reduction reaction (ORR) and the oxygen evolution reaction (OER), in which scaling relations play an important role and novel approaches are required for ab reakthrough. [2] High entropy alloys (HEAs) forming ac omplex solid solution (CSS) in the form of nanoparticles (NPs) have recently been discovered as an ew class of electrocatalysts. [3] We propose the use of the term CSS instead of HEA when referring to electrocatalysis,s ince the additional refinement of atomic arrangement is the foundation of the unprecedented properties,a sn ot all "HEAs" are indeed stabilized by high entropy.T he unique interaction of many neighboring elements directly next to each other is the basis of an immense possible number of different active sites,which cover awide range of adsorption energies. [4] Optimization of the composition allows for increasing the number of active sites with favorable adsorption energy for the reaction of interest, and thus,t he optimal choice of elements and their respective ratio can generate very active catalysts as long as aC SS phase is formed. Thes uccessful use of CSSs as electrocatalysts for several reactions,s uch as ammonia synthesis, [5] CO oxidation, [6] CO 2 reduction, [7] the ORR, [6,8] hydrogen evolution reaction (HER), [9][10][11] or the OER [9,11,12] was shown confirming universal applicability.H owever,t he complex underlying working principles are still widely unknown with al ack of ac onceptual framework. Hence,i ndepth understanding is required to tailor new catalysts for specific reactions.A djusting of the activity of ORR catalysts was shown experimentally by tailoring the CSS composition, [8] astrategy which could be rationalized by atheoretical study of the adsorption energy distribution pattern (AEDP) [4] and its implication on the specific electrochemical behavior. [3] However,itwas not yet shown which effect different AEDPs have on activity curves and which effects are expected for addition or replacement of elements within the CSS phase.
Herein, we elucidate these fundamental concepts and discuss which information about the AEDP can be gained simply by analyzing the experimental activity curves.W e highlight how this can significantly enhance the discovery of active catalysts and show experimental results for ORR catalysts where these concepts are tested. Thus,w er eveal intrinsically active CSS catalysts,w hich can be further optimized for their implementation in catalyst films.

Results and Discussion
Deriving the Shape of Intrinsic Activity Curves Ther andom arrangement of five or more elements in as ingle-phase solid solution yields ac ontinuous and unique AEDP,which was recently theoretically derived by Batchelor et al. [4] Considering on-top adsorption of reaction intermediates,there are as many adsorption peaks as there are elements in the CSS,with all active site motifs with one specific element in the active site center forming one of those peaks.W hen two-or three atoms form the active sites,t he number of possible centers and thus the number of adsorption peaks increases even more.T op ostulate the measured electrochemical response of such ad istribution pattern, we simplified the model by reducing the number of active sites within one adsorption peak to 7, while preserving the shape of the distribution pattern (Scheme 1a). In this hypothetical example,t he optimal binding energy is at higher binding energies relative to the peak, implying that active site 7has the highest activity,f ollowed by active site 5u ntil finally active site 6 follows with the least favorable binding energy.P lotting the kinetic activity curves while considering that active site 1 yields the highest current (since it represents the highest number of active sites in the original distribution pattern), seven individual curves are obtained, which sum up to the overall measured curve (Scheme 1b). Forasymmetrical peak shape,a ll deviations from average activity cancel out and ac onsistent exponentially increasing overall curve is obtained, even though it consists of avast number of active site contributions of different activity.F or irregular peak shapes, the absence of ac ounteracting active site of same intensity, but opposite distance to the average position induces am arginal distortion, which slightly affects the linearity in Tafel plots even if the kinetic region is analyzed. Additionally, the peak distribution, whether it is narrow or broad, affects the "slope" of the polarization curve in the same way as the transfer coefficient in the Butler-Volmer equation does (Scheme 1c,d). Accordingly,T afel analysis should be reconsidered for CSS catalysts and its interpretation extended to include variations in peak distribution. It should be noted that the inflection point is not affected.
Since there are multiple adsorption peaks for CSSs,e ach will contribute one exponentially increasing current curve of different activity depending on the position of the peak maximum relative to the optimal binding energy.H ence,i n principle the number of "current waves" adding up equals the number of elements in the CSS,with the intensity affected by the molar ratio and the activity governed by the relative position of the respective peak maximum regarding optimal binding energies.M ass-transport effects may limit the visibility of lower active "current waves". Forr eactions with rather low mass-transport limits,s uch as the ORR, it gets more likely to only see the most active wave.However,when the composition is not optimized and the distance and intensity of the two or even three most active peaks regarding optimal binding energies is rather similar, the combined contributions can be observed.

Effect of Configuration Alteration
Theeffect of adding or replacing elements within the CSS phase is schematically depicted in Scheme 1, based on the previously discussed AEDP-activity curve correlation. Foran elemental catalyst, only one fixed and distinct binding energy exists if only the most active of the few facets such as (111) is considered, [13] which yields an exponentially increasing activity curve based on the position relative to the optimal binding energy.A th igher overpotentials,i tt ransitions to ap lateau either due to active-site limitation or more likely due to masstransport limitation yielding ap lateau current for hemispherical diffusion towards single NPs. [14] ForC SSs,c atalytic curves can attain many shapes since the distances between the current wave segments are directly correlated to the distances of the peak maxima within the AEDP.I nt his scheme,o nly equiatomic compositions are considered and the active-sitelimited plateau currents for each wave segment are set to the same value.F or optimized compositions,t he altered peak intensities have adirect influence on the current intensities of the respective waves,that is,awell-pronounced peak close to the optimal binding energy will yield aw ave segment at low overpotentials with high currents,w hich represents the ideal result for optimization of CSS catalysts.H owever,t he complexity of the interaction between neighboring elements prevents simple predictions of the AEDP and hence the activity.O ne would need to either calculate the AEDP for Scheme 1. a) Simplified scheme to illustrate active site distribution within one adsorption peak. Active sites of similar activity are grouped together and summarized as one site, whose intensity depends on the amount of similar sites. b) Visualized intrinsic current response in the kinetic region of these grouped active sites, considering their activity as well as the intensity.F or symmetrical distribution, the overall current response representing one peak still follows aconsistent exponential increase,f ollowed by ap lateau current once active site limitation is reached. The activity is governed by the positiono fthe peak maximum regardingoptimal binding energies. c) Visualizationo f two different scenarios of anarrow and abroad distribution of an adsorptionp eak. d) Respectivec hange of the "slope" in the overall current response as highlighted in (b) with regard of the peak distribution shown in (c). Whereas the inflection point is not affected, areversed deviationa tlower or higher currents is obtained. An exponential increase as predicted by the Butler-Volmer equation is still preserved for symmetricp eak shapes.
each configuration (which elements constitute the CSS) with consecutive optimization of composition (molar ratio of elements in aCSS) and/or measure each catalyst individually in as creening process.S ince each change in composition impacts activity,s creening of the whole composition range would be required with the related challenge of time and effort. However,m odulation in composition mainly affects the intensity with only minor shifts in adsorption energy of each peak. [4] Thus,o ne important conclusion of the concepts discussed is the possibility to significantly reduce the effort of ascreening process by evaluating equiatomic alloys and assess the intrinsic activity of the most active current wave.B ythis approach, promising configurations can be identified and the number of catalysts,w hich have to be experimentally investigated, can be significantly reduced. In as econd step, optimization of the composition can be performed, now also including the current magnitude of the most active wave segment.
Considering the examples in Scheme 2, replacing or adding elements induces,t odate unpredictable,s hifts of all individual adsorption peaks within the AEDP and theoretical or experimental evaluation of the changes is necessary.Incase of the six-element alloy CSS #6_2 (Scheme 2, bottom right), aclose overlap of the three most active peaks yields acatalytic curve in which all three wave segments are hardly separated. Thef ive-element CSS #5_2 with replaced elements (Scheme 2, top right) shows an altered AEDP in which the third most active peak is shifted towards unfavorable binding energies and only two wave segments are visible within the considered potential regime.T he CSS which is most active which has the best peak closest to the optimum is the sixelement CSS #6_1 (Scheme 2, middle). Thus,i ti sn ot yet possible to predict the effect of adding or replacing elements and both can have positive and negative effects.However,the shape of the catalytic curve in the kinetic region provides direct information about the AEDP,that is,the separation of the wave segments is adirect measure of the separation of the peaks in the AEDP and the activity of these waves is directly linked to the position of the peaks.

Experimental Verification
Fore xperimental evaluation of these concepts,i ti s favorable to have am eans to measure the intrinsic activity of CSS catalysts in the absence of any matrix effects,such as mass loading, conductivity,p orosity,o rt he influences of binders,w hich may mask relevant information. [15] Therefore, we followed our previously suggested approach of potentialassisted immobilization of NPs at etched carbon nanoelectrodes, [8] which yields sub monolayer,w ell-separated coverage of isolated NPs.A dditionally,d ue to the increased hemispherical diffusion, the kinetic region is enlarged and the hypothesized wave segment pattern can be observed within abroader potential regime.
All NP suspensions were synthesized by combinatorial cosputtering [16]   from the physical vapor deposition technique and the absence of any surfactants or stabilizer,w hile having good control over the composition of the NPs with narrow size distributions.The elemental compositions for the sputtered alloys are shown in Table 1b ased on EDX data, which were obtained for the sputtered thin films located next to the ionic-liquid (IL) cavities on the substrate wafer. With the exception of Ag, all the elements are present in close to the aspired equiatomic ratio.S ince all the samples are prepared in the same way utilizing the same IL, NP sizes are expected to be in the range from 2t o5nm with an arrow size distribution. [8] Hence,t he changes in activity curves can be solely assigned to the changes in elemental configurations and thus,t he altered intrinsic properties of the active sites.Before immobilization of the CSS NPs,the blank electrode was cycled until astable response was obtained and this current was subtracted from the current after immobilization of NPs to obtain the electrode-corrected current, which solely represents the NP response. [17] It is important to note that the carbon electrode is not completely inert and its much lower activity gets compensated by its much higher accessible surface area in comparison to the NPs,which have avery low loading.Hence, there will be no plateau current but alocal maximum, which eventually transitions into an overshooting peak if not interrupted before by the subsequent current wave segment. However,w hen the 2nd current wave is following directly after the first as ar esult of the similar position of the respective adsorption peaks,the 2nd current increase can still be observed before the complete decline of the first wave. Thus,the qualitative peak separation within the AEDP can be extracted by analysis of the electrode-corrected curve pattern, that is,the adsorption peak separation is directly correlated to the current wave separation.
In the case of non-noble metal alloys,itisalso important to consider that some surface atoms,for example,Crand Mn in the Cantor alloy,a re probably oxidized. [18] Hence,achallenging refinement of the theoretical model would be required, that is,h ow the active sites are structured in such cases.T ou nderstand its effect on catalytic properties is important for future studies.H owever,t he distribution in adsorption peaks is derived from the presence of aCSS,which is still preserved and the general shape of the distribution pattern is presumably preserved, but reduced to those peaks, which refer to non-oxidized elements.I nF igure 1a,t hree individual electrode-corrected CrMnFe-CoNi curves obtained from different electrodes are shown. Owing to statistical differences in mass loading, the current intensities are different. However,t he potential regions for each wave segment are consistent as highlighted with the colored regions.E ach wave segment represents one adsorption peak in the AEDP and thus,aqualitative representation of the related AEDP can be derived (black distribution pattern). With four visible current waves,f our peaks can be plotted within the considered potential window and the position of the fifth peak remains unknown, but it is at even higher distance to the optimum (transparent peak at undefined position to the left).
In the next step,weinvestigated the effect of replacement or addition of one element on the wave segment structure and thus,ashift of the individual peaks in the qualitative AEDP. In addition to altered inter-elemental interactions,changes in oxidation probabilities can also affect the AEDP in the case of transition-metal CSS catalysts and knowledge about the oxidation properties of each element can help to differentiate between both effects.Upon addition of Mo,Nb, or Cu, aclear local current maximum is observed with consecutive transition to an overshooting peak at different scales because of different mass loadings.T his behavior indicates splitting of the two most active current waves (since overshooting is observed for the theoretical presence of ap lateau [17] )a nd thus,s plitting of the first two adsorption peaks as well. However,i nstead of levelling off to zero current, the second adsorption peak causes as econd current increase at higher overpotentials visible as the next current wave.Replacement of Ni by Vhas asimilar effect, yet the second wave segment is not visible in the potential regime considered. Another possible conclusion is av ery close overlap of those two waves,y ielding only one combined current wave of higher intensity.A ddition of Ag is not supposed to maintain ah omogeneous CSS phase because of the large difference in atomic size [19] and tends to have strong effects on the crystal structure with achange in average coordination number. [20] It was further observed that such HEAs can have strong inhomogeneous fluctuations in the elemental distribution with local aggregations. [21] Theo bserved current progression also exhibits the decline of the first current wave,w hich is, however, followed by the second current wave before the local maximum is reached. This pattern suggests ac loser  MnFeCoNi [8] 23 27 23 27 CrFeCoNi [8] 25 27 23 25 CrMnCoNi [8] 28 22 23 27 CrMnFeNi [8] 27 24 24 25 CrMnFeCo [8] 27 23 27 23

Angewandte Chemie
Research Articles position of the first two adsorption peaks within the AEDP. Thes ame observation is obtained for the two CSSs with complete replacement of all five elements (Figure 1b). TiNbMoTaW shows three visible wave segments,w hich all migrate into the following one,w hereas TiVZrNbTas hows two,w hich are more separated. Forsimplicity,all the derived qualitative AEDP only show adsorption peaks,w hich are shifted towards the strongbinding side compared to optimal adsorption energy.H owever,only the absolute distance to the volcano maximum can be predicted, but not the direction since as hift in either direction causes the same decrease in activity.H ence,w e point out that other solutions of the derived AEDP also exist, where one,afew,orall peaks are at the same distance,but on opposite sides of the volcano optimum.

Comparison of Most Active Current Waves
To allow for comparison of the intrinsic activity of different catalysts,normalization of electrode-corrected catalytic curves by the first plateau current was performed (Figure 2a). [17] This approach is intended to compensate for different amounts of immobilized particles.I nt he specific case of CSS catalysts,t his method allows for comparison of the first wave segment of each catalyst (Figure 2b)a nd thus, the most active adsorption peaks within the AEDP.Hence,it exactly offers the aspired information for the proposed first step.B yf inding the elemental configurations with promising AEDPs with suitable position of the most active peak, promising catalyst candidates can be selected and used for further composition optimization.
Theexperimental results of this study applied to the ORR in alkaline media are shown in Figure 2c.F or comparison, Pt NPs prepared with the same parameters serve as benchmark ORR catalyst. [8] Thea ctivity seems to be shifted to higher overpotentials when comparing with more conventional RDE data. This is due to the utilized approach based on isolated NPs of avery low loading.The implication of an unavoidable lower signal to noise ratio is discussed in detail in the Supporting Information. As highlighted previously, [8] the CrMnFeCoNi catalyst is significantly more active than its subsystems composed of fewer elements,w hich can be attributed to the presence of novel active sites within the CSS.T he possibility of increasing the activity by tailoring the composition with increased Mn-content supports the theoretical hypothesis regarding the adsorption-energy distribution pattern. [4] We extended the list of investigated catalysts and evaluated the effect of addition of a6 th element to the CrMnFeCoNi system. According to the model, the adsorption-energy distribution pattern should change in aw ay that now six adsorption peaks are present. Owing to interaction of an additional element, the position of each peak is altered and can hardly be predicted. We also investigated the influence of al attice distortion in the uniform elemental distribution within the CSS by addition of Ag. Its effect on intrinsic activity is as hift of the catalytic curve toward higher overpotentials implying as hift of the peak maximum in the adsorption energy diagram away from the optimal position. Thes ame effect, but less pronounced, is observed for the addition of Cu instead of Ag. Copper is the next in number element in the first transition row of the periodic table,which indicates the preservation of the CSS phase as aresult of the similar size.However,addition of Nb or Mo clearly shows an improvement in intrinsic activity.T hose two alloys reach the best performance,e ven slightly improved compared to the adjusted CrMnFeCoNi composition with enhanced Mn content and superior of the benchmark catalyst Pt even though in these alloys an equiatomic ratio is present. Replacing one element of the quinary system CrMnFeCoNi by reducing the atomic number of each element by one ("downshift" of atomic number) to obtain VCrMnFeCo results in ad ecrease in activity.W ea lso investigated the effect of complete replacement of all five elements by testing the refractory HEAs [22] TiVZrNbTaa nd TiNbMoTaW.B oth show very similar intrinsic activity of the most active current wave, which is only marginally lower compared to the nonoptimized CrMnFeCoNi system.

Conclusion
To summarize,d ue to the continuous coverage of aw ide range of adsorption energies,C SS catalysts usually possess highly active sites.T his is validated by our results,s howing ab ig gap in intrinsic activity between the binary through quaternary subsystems,and all tested alloys comprising five or more elements.W hereas the low intrinsic activity of the binary systems is consistent with the position of their elements in volcano plots,the CSS catalysts show at least an enhanced activity arising from the broad adsorption energy distribution also partially covering more favorable energies.T oreach very high activities,agood fit of the best adsorption peak maximum with the optimal binding energy as well as ah igh intensity of this peak corresponding to ahigh number of those sites is required. We showed how the presence of two current waves of similar activity indicates similar positions of the two most active adsorption peaks within the AEDP,w hereas as ingle exponential increase is an indication of aw ellseparated most active peak. Although it is to date hard to predict the position of those peaks just by the selected elements,weevaluated aselection of CSS catalysts regarding the position of the most active peak and found some very active configurations.T otransfer this high activity to catalystfilm applications where the intensity also plays an important role,o ptimization of the composition becomes very important. Since the position of the peak is presumably not strongly affected by changes in the molar ratio,t he results obtained with equiatomic compositions provide valuable information concerning promising elemental configurations.T his correlation improves the search for active CSS catalysts significantly, since experimental screening can be simplified to equiatomic samples without the need to evaluate all different compositions within each set of elements as well. Thus,c onceptual understanding of the general working principles of this new complex catalyst class is provided which is applicable to any reaction. Furthermore,i tp articularly provides am ethod to assess information about the intrinsic activity of abundant CSSs for the ORR. Exploiting these possibilities,w ed iscovered CrMnFeCoNiNb and CrMnFeCoNiMo as very promising candidates for the ORR, whose composition can be optimized to complement the suitable position of the most active peak with ah igh intensity and thus,t ransfer the high activity to up-scaled applications. Figure 2. a) Schematic current-overpotential curves of CSS catalysts forming aCSS of different configuration and mass loading. The combinedcurrent response of all the active sites within one adsorption peak of the adsorption-energy distribution pattern is represented by one "current wave". Forasimilar position of the two most active peaks regarding optimal binding energies, two "wave segments" yield the overall current response with the presence of an intermittent plateau current. b) Normalized curves of (a) respective to the plateau current (colored areas) to compare the activity of different catalysts of their respective most active adsorption peaks. c) Experimental results of ORR activity in 0.1 m KOH of selected multinary alloys immobilized at etched carbon nanoelectrodes. Normalization was performeda s described in (b). The sample order is based on the required overpotential to reach À0.5 at the normalizeds cale. "cat" = "catalyst".