Unifying Concepts in Electro- And Thermocatalysis toward Hydrogen Peroxide Production

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Unifying Concepts in Electro- and Thermocatalysis toward

Hydrogen Peroxide Production

Jason S. Adams,^§Matthew L. Kromer,^§Joaquí n Rodr í guez-L ó pez,* and David W. Flaherty*

Cite This: J. Am. Chem. Soc. 2021, 143, 7940 −7957

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ABSTRACT: We examine relationships between H₂O₂and H₂O

formation on metal nanoparticles by the electrochemical oxygen

reduction reaction (ORR) and the thermochemical direct synthesis

of H₂O₂. The similar mechanisms of such reactions suggest that

these catalysts should exhibit similar reaction rates and selectivities

at equivalent electrochemical potentials (μ_i), determined by

̅

reactant activities, electrode potential, and temperature. We

quantitatively compare the kinetic parameters for 12 nanoparticle

catalysts obtained in a thermocatalytic ﬁxed-bed reactor and a ring−

disk electrode cell. Koutecky−Levich and Butler−Volmer analyses

yield electrochemical rate constants and transfer coeﬃcients, which

informed mixed-potential models that treat each nanoparticle as a

short-circuited electrochemical cell. These models require that the

hydrogen oxidation reaction (HOR) and ORR occur at equal rates to conserve the charge on nanoparticles. These kinetic

relationships predict that nanoparticle catalysts operate at potentials that depend on reactant activities (H₂, O₂), H₂O₂selectivity,

and rate constants for the HOR and ORR, as conﬁrmed by measurements of the operating potential during the direct synthesis of

H₂O₂. The selectivities and rates of H₂O₂formation during thermocatalysis and electrocatalysis correlate across all catalysts when

operating at equivalent μ_ivalues. This analysis provides quantitative relationships that guide the optimization of H₂O₂formation

̅

rates and selectivities. Catalysts achieve the greatest H₂O₂selectivities when they operate at high H atom coverages, low

temperatures, and potentials that maximize electron transfer toward stable OOH* and H₂O₂* while preventing excessive occupation

of O−O antibonding states that lead to H₂O formation. These ﬁndings guide the design and operation of catalysts that maximize

H₂O₂formation, and these concepts may inform other liquid-phase chemistries.

adsorbed intermediate).⁸⁻¹⁰Wilson et al. proposed that the

1. INTRODUCTION

solvent mediates the reduction of O₂into H₂O₂and H₂O

through proton−electron transfer (PET) steps that resemble

the electrochemical ORR.¹¹Speciﬁcally, that work suggested

that H₂O heterolytically oxidizes H* to generate protons (H⁺)

and electrons (e⁻), which transfer to O₂* and O₂*-derived

intermediates bound to the same nanoparticle. Recent work

corroborates the involvement of PET steps in these reactions

through a combination of detailed rate measurements and ab

initio calculations.¹²From an electrochemical perspective,

these coupled heterolytic oxidation and reduction reactions

resemble a short-circuited hydrogen fuel cell, in which a single

metal nanoparticle cocatalyzes the hydrogen oxidation reaction

Interest in H₂O₂production has grown in recent years because

this oxidant may supersede the use of chlorine in selective

oxidations, disinfection, and bleaching applications, which

would reduce the formation of environmentally hazardous

chlorinated wastes.¹⁻⁴Traditionally, industries manufacture

H₂O₂through the anthraquinone autoxidation process, but

two emerging methods include the thermocatalytic direct

synthesis reaction (H₂+ O₂→ H₂O₂) and the electrocatalytic

two-electron oxygen reduction reaction (2H⁺+ 2e⁻+ O₂→

H₂O₂). Metal nanoparticles can catalyze both reactions in

aqueous solutions in either neutral or acidic media (pH ≤7),

but rates for both pathways increase with the activity of

protons (i.e., the rates are greater at low pH).^5,6The

electrochemical literature agrees that the oxygen reduction

reaction (ORR) occurs through heterolytic proton-coupled

electron transfer.⁷Researchers of the direct synthesis of H₂O₂

have not reached a consensus on the mechanism for

thermocatalytic H₂O₂formation. Most studies of direct

synthesis propose homolytic surface reaction mechanisms

that involve chemisorption of H₂and O₂to a metal surface and

sequential addition of H* to O₂* (where * denotes an

Received: December 30, 2020

Published: May 21, 2021

https://doi.org/10.1021/jacs.0c13399

J. Am. Chem. Soc. 2021, 143, 7940−7957

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Figure 1. (a) The proposed series of elementary steps for H₂O₂and H₂O formation during direct synthesis on metal nanoparticles, which

decouples the electrochemical hydrogen oxidation and oxygen reduction reactions proposed in the electrocatalytic literature. (b) A visual

representation of the proposed mechanism for the simultaneous occurrence of the HOR and ORR on a single catalytic nanoparticle.

(HOR) at rates that balance the quantity of H⁺and e⁻

required for the ORR.

reﬂect the rate of reaction on the catalyst. As the value of ϕ

decreases (i.e., is made more negative), the electrode provides

a greater driving force to provide electrons to the catalyst for

Faradaic reactions, which lowers the apparent activation

barriers to reduce oxygen.¹⁵For direct synthesis, however,

investigators have manipulated reaction rates by changing the

temperature (T) or chemical potential (μ_j), adjusted by

hydrogen and oxygen pressures ([H₂], [O₂]).^11,13,16

Figure 1 shows the series of elementary steps for the

thermocatalytic reduction of O₂, which includes adsorption,

desorption, and heterolytic processes, also found in the

electrocatalytic HOR (steps 1−3) and ORR (steps 4−13).¹³

This scheme predicts a fundamental connection between the

direct synthesis reaction and the HOR and ORR. Further, the

similarities between these mechanisms imply that a given

catalyst (e.g., carbon-supported metal nanoparticles) should

provide identical rates and selectivities in thermocatalytic and

electrocatalytic reactors at equivalent electrochemical poten-

Therefore, researchers can control the electrochemical

potential (μ_j) through an inﬁnite number of combinations of

̅

ϕ, T, and [j]. This understanding provides opportunities to

examine the processes depicted in Figure 1 through established

methods and analyses used within the thermocatalysis and

electrocatalysis communities and, in doing so, connect these

disciplines. Oxygen reduction and hydrogen oxidation

reactions provide an excellent foundation to examine these

concepts, because the reaction network involves only two

reactants (H₂, O₂) and two products (H₂O, H₂O₂), and their

reaction rates are readily measured. If these reactions are

inherently linked, as is hypothesized, then the vast literature on

the ORR and HOR would inform catalyst design and reaction

engineering principles for the direct synthesis of H₂O₂. These

insights would also enable the translation of high-throughput

catalyst synthesis and screening methods developed within the

electrochemical community to develop high-performance

materials for thermocatalytic H₂O₂formation.¹⁷

tials (μ_i). In other words, the rates and selectivities of H₂O₂

̅

formation are controlled by either adjusting the chemical

potential (μ_j) of the reactant species (j) or applying an

electrical potential (ϕ) from an electrode to achieve a given

value for μ_i:¹⁴

̅

μ = μ_j+ z_jFϕ

̅

j

(1)

Here, z_jis the charge of species j and F is Faraday’s constant. In

comparison, the chemical potential (μ_j) takes the functional

form¹⁴

i

j

y

z

∂G

∂n_j

μ =

= μ_j⁰+ RT ln [j]

j

z

k

{

T,P,n_j

(2)

Here, we explore the similarities and diﬀerences between

electrocatalysis and thermocatalysis through the reduction of

O₂and the oxidation of H₂. First, Koutecky−Levich and

Butler−Volmer analyses were used to extract intrinsic rate

constants (k⁰) and transfer coeﬃcients (α) for the ORR and

HOR across a library of 12 Pd- and Pt-based bimetallic

catalysts. Two models, each with distinct assumptions and

inequivalent levels of molecular detail, were evaluated using

measured kinetic parameters (k⁰and α). These models predict

the steady-state operating potential of catalytic nanoparticles

where G represents the Gibbs free energy of the system, n_jis

the total number of species j, μ⁰_jis the standard state chemical

potential of species j, R is the universal gas constant, T is the

temperature (K), and [j] is the thermodynamic activity of

species j.

In both thermocatalytic and electrocatalytic systems, values

of μ_jprovide one method to control reaction rates. For the

̅

ORR, investigators have deposited catalytic materials onto an

electrode surface and characterized the electrode potential (ϕ)

required to drive the reaction. Here, the measured currents

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passivated for 1 h by exposure to a ﬂowing mixture of 2 kPa of O₂, 10

kPa of N₂, and 89 kPa of He (100 cm³min⁻¹; Airgas, 99.999%).

The incipient wetness impregnation involved the addition of 15

cm³of a 5−60 mM HAuCl₄solution in DI water, which was added

dropwise to 10 g of the Vulcan XC-72 support. Speciﬁcally, HAuCl₄

was added to the Vulcan XC-72 to yield 0.25%, 0.75%, and 3 wt %

loadings of metal on the support. The incipiently wet support was ﬁrst

washed with 300 cm³of a 30 wt % aqueous NH₄OH solution with the

intent to precipitate Au(OH)₃in the pores of the support. The

material was then washed with 300 cm³of deionized water to remove

trace ions and vacuum-ﬁltered overnight at 298 K. The precursor

material was later heated to 393 at 10 K min⁻¹and held at 393 K for 4

h in a ﬂowing mixture of 20 of kPa H₂and 81 kPa of He (100 cm³

min⁻¹; Airgas, 99.999%) to produce metallic nanoparticles.

The electroless deposition involved the addition of Pt and Pd salts

onto the Au materials discussed above. The PdAu₆₀and PtAu₆₀

materials were synthesized from the 3 wt % Au material, whereas the

PtAu₁₅and PtAu₅catalysts were prepared from the 0.75 and 0.25 wt

% Au materials, respectively. Here, 4 g of the carbon-supported Au

was added to 140 mL of deionized H₂O and stirred at 500 rpm in a

ﬂask under a ﬂowing mixture of 20 kPa of H₂and 81 kPa of He (100

cm³min⁻¹; Airgas, 99.999%). For the PdAu₆₀and PtAu₆₀materials,

the solution was initially heated to 343 K, while the PtAu₁₅and PtAu₅

materials were stirred at 298 K. After stirring for 30 min, 10 cm³of

aqueous 1 mM Pd (NO₃)₂or (NH₃)₄Pt(NO₃)₂was added dropwise

to the solution to form the PdAu and PtAu alloys. The PdAu₆₀and

PtAu₆₀materials were maintained at 343 K for 3 h, while the PtAu₁₅

and PtAu₅materials were heated from room temperature to 343 K

and held at that temperature for 3 h. The resulting catalyst slurries

were then cooled to ambient temperature and vacuum-ﬁltered at 298

K overnight.

(treated as electrode surfaces) during the ostensibly

thermocatalytic production of H₂O₂. The ﬁrst model builds

upon the Butler−Volmer equation and assumes that each

catalytic nanoparticle simultaneously performs the HOR and

the ORR at equal potentials and with reaction rates

constrained by mass and charge conservation. The second

model expresses steady-state rates for O₂reduction and H₂

oxidation, which depend on the rate constants of elementary

reactions and the coverages of reactive species on the

nanoparticle surface (Figure 1). Overall, the coupled

heterolytic reactions between hydrogen and oxygen-derived

intermediates lead to diﬀerences in operating potentials that

reﬂect diﬀerences between the charge transfer coeﬃcients and

barriers for their respective kinetically relevant steps. Insight

from these models reveals the parameters that aﬀect O₂

reduction rates and selectivities (e.g., toward H₂O₂) in both

thermal and electrocatalytic reactors. Notably, this analysis

shows that the diﬀerent hydrogen and oxygen activities can

lead to the formation of selective surface structures (e.g., β-

PdH_x) that do not form under typical electrochemical ORR

measurements. Similarly, each catalyst displays potential-

dependent H₂O₂selectivities in electrochemical measurements,

for which their maxima are often inaccessible at the H₂and O₂

pressures used during thermocatalytic measurements.

Electrode measurements of Au, PdAu, and PtAu materials

show similar ORR kinetic parameters, while the Pt and Pd

materials show much greater HOR rates (PtAu > PdAu ≫

Au). Analogous thermocatalytic measurements show similar

H₂O₂selectivities at equivalent values of ϕ, but the presence of

Pt or Pd results in signiﬁcantly greater steady-state reaction

rates (PtAu > PdAu ≫ Au). These observations suggest that

heterolytic hydrogen oxidation rates determine the rate of

electron transfer within the thermochemical system. From

these observations, it is not surprising that H₂O₂selectivities

measured under thermochemical and electrochemical con-

ditions agree closely when catalyst nanoparticles operate at

identical electrode potentials (ϕ) and similar coverages of

reactive species. Overall, these ﬁndings establish tangible

connections between principles common within the heteroge-

neous catalysis and electrocatalysis communities, provide

reaction engineering strategies to maximize selectivities toward

H₂O₂, and suggest that electrochemical techniques may enable

the screening of catalysts for thermocatalytic reactions.

2.2. Catalyst Characterization. The average diameters of

carbon-supported nanoparticles were estimated from the particle

size distributions obtained by transmission electron microscopy

(TEM). The distribution of nanoparticle diameters was measured by

bright-ﬁeld TEM imaging (JEOL, 2010 LaB₆) of more than 100

particles. Each sample was prepared by grinding the catalyst to a ﬁne

powder (<200 mesh), which was dusted onto a Cu holey-carbon

TEM grid (200 mesh, Ted Pella Inc.). The surface area normalized

average cluster diameter (⟨d_TEM⟩) for each catalyst was calculated

using eq 3

∑ n_id_i³

i

⟨d_TEM⟩ =

∑ n_id_i²

(3)

i

where n_iis the number of nanoparticles with the diameter d_i. Figure 2

shows a representative TEM image of the 9 nm Pd nanoparticles on

Vulcan XC-72. This image includes an inset histogram of the particle

size distribution, and TEM images for the other nanoparticle catalysts

are shown in Figure S1 and discussed in section S1 in the Supporting

Information. The metal content of each sample was measured by

inductively coupled plasma optical emission spectroscopy (Perki-

nElmer, Optima 2000DV) and energy dispersive X-ray ﬂuorescence

(Shimadzu, EDX-7000). The characterization results for all prepared

catalysts are shown in Table S1.

2.3. Steady-State Thermocatalytic Reaction Rate Measure-

ments. All steady-state H₂O₂and H₂O formation rates were

measured in a continuous-ﬂow trickle-bed reactor (48 cm length, 1

cm inner diameter) housed within a stainless-steel cooling jacket

(Figure S2 and Section S2 in the Supporting Information). The

reactor was loaded with 0.15−1 g of catalyst, which was held between

plugs of glass wool (∼10 mg), each supported by borosilicate glass

rods (8 mm diameter). These rods were secured between silver-

coated fritted VCR gaskets (Swagelok, SS-4-VCR-2-60M), which

were also used to seal the reactor. The temperature was controlled

across the reactor by ﬂowing aqueous ethylene glycol (50% volume;

Fisher Scientiﬁc E178, 99.8%) through the cooling jacket from a

recirculating temperature bath (Cole-Parmer Polystat). The temper-

ature of the catalyst bed was monitored directly using a K-type

thermocouple contained within the cooling jacket and in ﬁrm contact

2. EXPERIMENTAL METHODS

2.1. Catalyst Preparation. Catalytic nanoparticles were formed

upon activated carbon (Vulcan XC-72, pellets, Cabot Corporation) by

strong electrostatic adsorption (Pd, PdNi, PdZn, PdCu, PdCo, Pt,

PtCo, or PdPt),¹¹incipient wetness impregnation (Au),¹⁸and

electroless deposition methodologies (PdAu₆₀, PtAu₆₀, PtAu₁₅,

PtAu₅). Strong electrostatic adsorption involved the addition of

Vulcan XC-72 (5 g) to 270 cm³of deionized (DI) water (17.8 MΩ

cm), to which 30 cm³of 14.5 M NH₄OH (Macron, 30 wt %) was

added to increase the pH to a value of ∼11. The metal nitrate

precursors were dissolved in 30 cm³of DI water and then added to

the catalyst slurry. The Vulcan XC-72 was added to a mass of metal

nitrate that would provide a 1 wt % loading of metal on the support

(details are provided in Section S1 of SI). These mixtures were stirred

intermittently for 12 h and then decanted, after which the solids were

ﬁltered and then dried at 333 K in a vacuum oven for 12 h. The dried

materials were later heated to 973 K at 10 K min⁻¹and then held at

973 K for 4 h in a ﬂowing mixture of 20 kPa of H₂and 81 kPa of He

(100 cm³min⁻¹; Airgas, 99.999%) with the intent to reduce the

adsorbed metal precursors and form metallic nanoparticles. After

reduction, each sample was cooled to ambient temperature and

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exponential reduction in the number of active sites with time.¹⁹These

corrections were determined by returning to the initial conditions for

each reaction to more accurately assess the rate of deactivation.

2.4. Electrocatalytic Reaction Rate Measurements. All

electrochemical parameters for the ORR and HOR (i.e., H₂O₂

formation rates and hydrogen oxidation rates) were measured using

a CHI 760 bipotentiostat (CH Instruments). Rotating ring−disk

electrode (RRDE) measurements were performed using a Pine ASR

electrode rotator (Pine Research) using a 5.0 mm glassy-carbon disk

insert to support the catalyst and a Pt-ring assembly (OD = 7.50 mm,

ID = 6.50 mm, Pine Research) for H₂O₂disk-generation/ring-

collection experiments. This setup is schematically shown in Figure

S3. The carbon-supported catalysts were suspended in a solution of

5.0 mg of catalyst, 1.0 mL of of DI water (Elga, 18 MΩ cm), and 0.6

mL of ethanol. A 10.0 μL portion of this slurry was drop-cast onto the

5.0 mm glassy-carbon disk and dried with an infrared lamp for ∼1 h.

Once the disk was dry, 5.0 μL of a 1 wt % Naﬁon solution

(C₇HF₁₃O₅S·C₂F₄in a mixture of lower aliphatic alcohols and water,

Sigma-Aldrich) was drop-cast onto the modiﬁed electrode to prevent

detachment of the catalyst during measurements.

Past studies on the impact of Naﬁon on ORR electrocatalysis on Pt

have shown mixed results, ranging from no eﬀect on the Tafel slope or

exchange current²⁰to a ∼2× enhancement in the speciﬁc and mass

activities of Pt after removing Naﬁon from the formulation.²¹High

loadings of Naﬁon likely aﬀect the rates of mass transfer and ohmic

resistance;²⁰however, such eﬀects should not convolute the results

presented here, as all materials were prepared using the same loading

of Naﬁon and the rates are corrected for mass transfer eﬀects using a

Koutecky−Levich analysis (vide infra). Thus, the Naﬁon may present

some experimental error in comparison to the Naﬁon-free samples

used in the thermochemical rate determination (section 2.3). Still, the

use of Naﬁon is common in the electrochemical literature and is

necessary to preserve the mechanical integrity of the samples across

the breadth of compositions and rotation rates explored herein.

All RRDE experiments were carried out in 0.1 M sodium

perchlorate (NaClO₄, Sigma-Aldrich, 98+%) as the supporting

electrolyte with a carbon counter electrode (Alfa Aesar, 99.9995%

purity). This medium was chosen to replicate the neutral unbuﬀered

solution used in thermocatalytic experiments as closely as possible

(see above). An Ag/AgCl reference electrode (3.5 M KCl, CH

Instruments) was used in all measurements, with the electrode placed

in contact with the solution via a 0.1 M sodium perchlorate agar/agar

salt bridge used to prevent chloride contamination to the solution.

Unless otherwise stated, all electrode potentials were corrected

relative to a normal hydrogen electrode (NHE) with a unit activity of

hydronium ([H₃O⁺] = 1) and are reported hereafter as V vs NHE.

Experimentally acquired voltammograms and open-circuit potenti-

ometry measurements were adjusted by 205 mV to correct the Ag/

AgCl (KCl 3.5 M) scale and adjusted by an additional 414 mV to

correct between a pH of 7 to a pH of 0.

Measurements of the ORR were conducted in 0.1 M sodium

perchlorate aqueous solutions sparged with O₂gas (101 kPa, Airgas,

99.999%). For disk-generation and ring-collection experiments, the

disk potential was scanned over the range +0.7 to −0.6 V vs NHE,

while the ring was held constant at 1.2 V vs NHE to carry out the

mass-transfer-limited oxidation of H₂O₂. The collection eﬃciency

(CE) of the ring−disk was determined to be ∼25%, and this value

determined the yield of H₂O₂using equation S5.8 (section S5 in the

Supporting Information). Measurements of the HOR were conducted

in 0.1 M sodium perchlorate aqueous solutions sparged with H₂gas

(101 kPa, Airgas, 99.999%) at electrode potentials between −0.2 and

+0.6 V vs NHE. These measurements were repeated at multiple

rotation rates of between 50 and 1250 rpm to evaluate the resulting

voltammograms using a Koutecky−Levich analysis,¹⁴in which

electrocatalytic rate constants were measured as a function of

electrode potential and used to calculate intrinsic rate constants and

charge transfer coeﬃcients for the HOR and ORR (vide infra).

Complementary measurements of CO stripping were performed on

Pt/C materials, which were used to renormalize electrochemical rate

constants by the total moles of surface atoms. Such experiments were

Figure 2. Representative TEM image of 37 nm Pd nanoparticles

supported on Vulcan XC-72 with an inset histogram of the particle

size distribution. More than 100 particles were measured to calculate

the value of ⟨d_TEM⟩, which is the surface-area-averaged diameter.

Figure S1a −l shows similar images and histograms for the other

materials studied.

with the stainless-steel wall surrounding the catalyst bed. H₂and O₂

compositions in the reactor were controlled by ﬂowing certiﬁed gas

mixtures (25% H₂/N₂and 5% O₂/N₂, Airgas, 99.999%) through

digital mass-ﬂow controllers (Bronkhorst, F-211CV). Warning:

pressurized mixtures of H₂and O₂are explosive when the two

components exceed a mole fraction of 0.05. Before it contacted the

catalyst, the gaseous reactant stream contacted the DI water (>17.8

MΩ cm) that served as the solvent and was delivered by an HPLC

pump (SSI, LS class). The pressure of the resultant gas−liquid

mixture was maintained by a back-pressure regulator (Equilibar, LF)

and controlled by an electronic pressure regulator (Equilibar, GP1).

The upstream pressure of the reactor was monitored using a digital

pressure transducer (Omega, PXM409-USBH).

Sampling and analysis of the liquid and gaseous eﬄuent streams

were automated and operated continuously. The reactor eﬄuent

entered a gas−liquid separator (GLS), from which the gas stream

ﬂowed to a gas chromatograph (Agilent, 7890B) equipped with a

capillary column (Vici, Molecular Sieve 5 Å, 30 m × 0.53 mm × 20

μm) and a thermal conductivity detector that used Ar gas (Airgas,

99.999%) as a reference. The liquid fraction was drained from the

GLS at 10 min intervals by an electronic valve (ALSCO Inc.,

LEV025PL) and ﬂowed into an electronic two-position valve (Vici

Valco, 10 port EPC10W), which injected 1 cm³of the liquid eﬄuent

and 1 cm³of a colorimetric titrant (12 mM neocuproine (Sigma-

Aldrich, > 99%), 8.3 mM CuSO₄(Fisher Scientiﬁc, > 98.6%), 25/75

(v/v) ethanol/deionized water mixture (Decon Laboratories, >

99.9%)) into test tubes held in an automated fraction collector

(Biorad, 2110). Each tube was analyzed by a UV−vis spectropho-

tometer (Spectronic, 20 Genesys) at a wavelength of 454 nm to

measure the H₂O₂concentration using a corresponding calibration

curve. All experiments were conducted at a liquid ﬂow rate of 35 cm³

min⁻¹to avoid external mass transfer limitations.¹⁶

Measured formation rates are normalized by the total moles of

either Pd or Pt within each sample. The number of reactive surface

atoms (or active sites) was not estimated because the structure and

dispersion of the nanoparticles were uncertain. Similarly, the

distribution of elements within individual bimetallic nanoparticles

was unclear. Moreover, these factors likely change across the range of

reaction conditions examined. For pressure dependence and

activation enthalpy measurements, reported rates were corrected by

accounting for deactivation, assuming that these changes arise from an

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performed by dosing CO over the sample followed by potentiometric

measurements to oxidize the adsorbed CO species (section S10 in the

Supporting Information). These voltammograms were subtracted

from a reference voltammogram on the same material at the same

potentials (∼0.6−0.9 V vs NHE), and the integration of this peak

yields a Faradaic current, proportional to the number of surface atoms

on the catalyst.

an electron to the nanoparticle, leading to a more negative

electrode potential.

Potentiometry at open circuit (i.e., at zero current) allows us

to probe charge transfer reactions from the HOR or ORR on

the catalyst without perturbing their steady-state reaction rates.

These measurements deﬁne the operating potential (Φ^op) at

which direct synthesis reactions occur. Figure 3 shows the

2.5. Pressurized Electrochemical Potential Measurements.

Pressurized open-circuit potentiometry and voltammetry measure-

ments were carried out on the catalytic materials in a custom-built

electrochemical cell (150 cm³) with a Teﬂon interior, as shown in

Figure S4. This experimental setup mimics the conditions of the

trickle-bed reactor during thermocatalytic reaction measurements. At

open circuit, there is no current ﬂow between the electrodes, which

allows for direct measurements of the electrode potential on metal

nanoparticles under a given condition. The leaktight cell contained

three insulated oriﬁces that accommodated a glassy-carbon working

electrode (BASi, 3.0 mm diameter), a Ag/AgCl reference electrode

connected via a salt bridge, and a carbon counter electrode that was

used for cyclic voltammetry measurements. Warning: the use of a

metallic (e.g., Pt) counter electrode was avoided to prevent explosive

gas mixtures when they are in contact with an exposed metal surface;

for similar reasons, the electrode surfaces were always kept immersed

in the electrolyte. Catalytic materials were drop-casted onto the

working electrode using 5.0 μL of the catalyst slurry described in

section 2.4. The material was dried under an infrared lamp for ∼1 h

and then coated with a 1 wt % Naﬁon solution to bind the catalyst to

the electrode surface. During measurements, the electrodes were

submerged in the cell (100 cm³of deionized H₂O, >17.8 MΩ cm),

and the liquid phase was sparged with H₂and O₂gas. Here, the H₂

and O₂compositions in the cell were controlled by ﬂowing certiﬁed

gas mixtures (25% H₂/N₂and 5% O₂/N₂, Airgas, 99.999%) through

digital mass-ﬂow controllers (Parker Porter, 601 series) at 110−180

cm³min⁻¹, and a back-pressure regulator (Andon Specialties, BP3−

1A11QCK11L) maintained the operating pressure. The potential of

the working electrode was measured using open-circuit potentiometry

while the gas pressure was modiﬁed in the range 60−400 kPa of H₂

and a constant 60 kPa of O₂. The cell was held at each pressure for

30−60 min, and the last 5 min of each period were averaged to

determine the operating potential at open circuit. For pressurized

voltammetry measurements, a supporting electrolyte (0.1 M NaClO₄)

was added to the aqueous solution, and these experiments followed a

methodology similar to that shown in section 2.4.

Figure 3. Open-circuit potentiometry measurements of operating

potentials for Pd, PdNi, PtAu₆₀, PtCo, and Pt catalysts as functions of

H₂pressure (60−400 kPa of H₂, 60 kPa of O₂, 298 K) in comparison

to the Nernstian response for the ORR and HOR paths, described by

eqs 4 and 5. Nernstian expressions were calculated using the unit

activities of H₃O⁺and H₂O species, while the ORR expression was

calculated using 0.1 mM concentrations of H₂O₂and 60 kPa of O₂to

mimic open-circuit potentiometry measurements.

operating potential for Pd, PdNi, PtAu₆₀, PtCo, and Pt

catalysts as a function of the H₂pressure (60−400 kPa) at a

constant pressure of O₂(60 kPa) at 298 K. Over this range,

PtCo shows the greatest operating potential of 0.65 V vs NHE,

which decreases to 0.40 V vs NHE as the H₂pressure is

increased. In contrast, PtAu₆₀shows a Φ^opvalue of 0.46 V vs

NHE, which decreases to the lowest observed value of 0.35 V

vs NHE. All other materials show a similar negative shift in the

operating potential within this range (0.35−0.65 V vs NHE),

as discussed in Figures S5 −S17 of section S3 in the Supporting

Information. These results suggest that each catalyst facilitates

a heterolytic reaction among hydrogen, oxygen, and water

during the direct synthesis. In the absence of a catalyst, the

glassy-carbon electrode shows a much higher Φ^opvalue of

∼0.75 V vs NHE (Figure S18) and is mostly insensitive to H₂

pressure, which agrees with the unmeasurably low HOR rates

observed on it. Overall, these results suggest that oxygen

reduction follows a similar heterolytic mechanism on metal

nanoparticles under both electrochemical and thermal

conditions.

Figure 3 demonstrates that hydrogen transfers charge to

nanoparticles, yet it is unclear how the operating potential

depends on the elementary steps depicted in Figure 1.

Therefore, we compared these values to the predicted

operating potentials of quantitative models that consider the

rates of elementary steps and the activity of the H₂and O₂

reactants. First, we examine the broadly simplifying assumption

that the reactants are in equilibrium with the ORR products

(i.e., steps 1−11 are quasi-equilibrated) by rearranging eqs 1

and 2 to derive the Nernst equations for the HOR and 2e⁻

3. RESULTS AND DISCUSSION

3.1. Eﬀects of H₂and O₂Pressures on the Electrode

Potential of Nanoparticle Catalysts. Figure 1 depicts the

mechanism for H₂O₂and H₂O formation and implies that

these electron transfer reactions should confer an electrical

potential on the metal nanoparticle catalysts during the

thermochemical reactions of H₂and O₂gases. Consequently,

the operating potential of the metal nanoparticles should

depend upon the relative rate of heterolytic hydrogen

oxidation and oxygen reduction steps, which are inﬂuenced

by diﬀerences in kinetic barriers and reactant activities ([H₂],

[O₂]). Past work shows that rates of H₂O₂and H₂O formation

on metal nanoparticles increase in proportion with the

hydrogen pressure (0−80 kPa of H₂, 60 kPa of O₂).^13,16,22

Thus, oxygen reduction rates can increase by orders of

magnitude by changing either the hydrogen chemical potential

or the electrode potential (ϕ) of the catalyst. However, these

rates do not depend on H₂pressure at higher values (100−400

kPa of H₂, 60 kPa of O₂),¹¹which suggests that hydrogen-

derived intermediates occupy most catalytic sites under these

conditions. As the coverage of hydrogen increases on the

catalyst surface, there is a higher probability that it will donate

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ORR half-reactions (section S4 in the Supporting Informa-

tion).¹⁴

mass and charge at the steady state. Since both the HOR and

the ORR involve distinct steps with barriers sensitive to the

identity and structure of the nanoparticle surface,²⁸⁻³⁰this

model indicates that the disparities in Φ^opand catalyst

performance during direct synthesis result from the diﬀerences

in ORR and HOR kinetics.

We quantitatively describe these diﬀerences with a Butler−

Volmer model to predict changes in operating potential on the

nanoparticle materials. This treatment assumes that the

apparent Gibbs free energy barrier (ΔG_app^⧧) of the reaction

decreases as the diﬀerence in Φ and Φ⁰increases for the

reaction, and the sensitivity of this change is proportional to

the charge transfer coeﬃcient (α).¹⁴This diﬀerence (also

known as overpotential) reﬂects the favorability of a reaction

on given material, and materials that present high barriers will

require greater overpotentials to achieve the same rate.

[H₃O⁺]²

[H₂][H₂O]

i

y

RT

2F

j

z

Φ⁰= Φ⁰_HOR

+

ln

j

z

2

k

{

[H₃O⁺]²

[H₂][H₂O]

i

y

z

i

y

z

j

RT

j

0

j

=

ln K

− ln

j

HOR

2

j

2F

(4)

k

{

k

{

2

i

y

[H O ][H O]

RT

2F

j

z

Φ⁰= Φ⁰_{H O}

−

ln

2

j

z

[H₃O⁺]²[O₂]

2

k

{

2

i

y

z

i

j

y

z

j

[H O ][H O]

RT

0

2

=

ln K

− ln

H₂O₂

[H₃O⁺]²[O₂]

2F

(5)

k

{

k

{

where the equilibrium potential (Φ⁰) of the HOR (H₂+ 2H₂O

⧧

ΔG_app= ΔG_int− αzF(Φ − Φ⁰)

(6)

↔ 2e⁻+ 2H₃O⁺) and the 2e⁻ORR (2e⁻+ 2H₃O⁺↔ H₂O₂+

2H₂O) depend on their standard potentials of reaction (Φ_H⁰_OR

,

where α is analogous to the symmetry factor of the Bells−

Evans−Polanyi principle, whereby the apparent barrier

depends on the position of the transition state along the

reaction coordinate of the elementary step.³¹The value of α

also depends on the reorganization energy, which accounts for

inner- and outer-sphere interactions that aﬀect the transition

state of electron transfer reactions.¹⁴The value of ΔG_app^⧧also

accounts for the intrinsic barrier of the elementary process

(ΔG_int^⧧) that the catalyst surface presents to the reactants

when the electrode potential equals the equilibrium potential.

The apparent barrier aﬀects the rate constant of the reaction

(k_app), while the rate of the reaction (r_app) depends on both

k_appand the reactant activity ([j]) at the catalyst surface, as

shown in the Eyring equation:

Φ⁰_{H O}) and the activities of reactants and products in these

2

systems ([H₂], [O₂], [H₂O], [H₃O⁺], [H₂O₂]). Here, the

standard potential is related to the equilibrium constants of

these reactions (K⁰_HOR, K_H⁰_O) at the standard state. Section S4

2

in the Supporting Information presents derivations of these

expressions and analogous equations for the formation of H₂O.

In each case, these Nernst expressions only consider the

thermodynamics of the reaction (Φ^op= Φ⁰) and neglect the

activation barriers of the HOR or ORR on the catalytic surface.

Thus, the Nernst equations of the HOR and ORR describe a

system that behaves with inﬁnitely fast reaction rates toward

these pathways.

Figure 3 shows that the materials produce operating

potentials that lie between the Nernstian predictions for the

HOR and the ORR. These observations suggest that the Φ^op

value depends on the activation barriers of these reactions and

other kinetic properties of the materials, preventing equili-

brium predictions for either the pure HOR or ORR paths.

Figure 3 also shows that the operating potential decreases with

hydrogen pressure on each catalyst, consistent with the trend

displayed by the HOR Nernst equation. Materials also show

diﬀerent slopes between the measured Φ^opvalue versus

hydrogen pressure. Thus, greater hydrogen pressures result

in a more negative operating potential on the nanoparticles,

but the eﬃciency and extent of charge transfer are sensitive to

the identity of the catalyst. Therefore, a more rigorous model is

needed to capture these subtle diﬀerences between materials.

These results were analyzed by assuming that a mixed

potential develops when anodic (e.g., HOR) and cathodic

(e.g., ORR) currents are equal on a metal surface,²³⁻²⁵which

are described as bipolar electrodes. This theory describes the

corrosion of surfaces,²³electroless deposition of metals,²⁶and

production of H₂and Cl₂(from reactions of a redox mediator

with nanoparticles).²⁷This concept, however, has not been

demonstrated for an ostensible thermocatalytic reaction of

gaseous reagents on supported catalytic nanoparticles, such as

the direct synthesis of H₂O₂. Here, the coupled HOR and

ORR reactions govern the rates and selectivities of H₂O₂

formation at a steady state in a continuous-ﬂow reactor in the

absence of an externally applied electrode potential or a

pathway to conduct electrons away from the nanoparticles.

Therefore, electron transfer rates for the HOR and ORR must

be equal upon a given nanoparticle (Figure 1b) to balance the

r_app

⧧

k_bT

h

app

= k_app[j]θ =

e^−ΔG^/RT[j]θ

[L]

(7)

where k_bis the Boltzmann constant, h is the Planck constant, θ

is the fraction of unoccupied reactive sites, and [L] is the total

available sites on an electrode or electrocatalyst that can

facilitate charge transfer to species j. By combining eqs 6 and 7,

we connect core relationships from electrochemistry and

chemical kinetics that yield the general Butler−Volmer

expression for the forward rate of reaction as a function of

the electrode potential

r_app

^⧧/RT

0

k_bT

h

int

=

e^−ΔG

e^{αzF(Φ−Φ )/RT}[j]θ

[L]

0

= k⁰e^{αzF(Φ−Φ )/RT}[j]θ

(8)

where k⁰is the intrinsic rate constant of electron transfer to

species j at the equilibrium potential. Here, the coverage of

hydrogen- and oxygen-derived species on the nanoparticle

surface increases in proportion to the reactant activity at low

surface coverages. Thus, we restate eq 8 in terms of the

electrical current on an electrode (section S5 in the Supporting

Information) and extract relationships that resemble more

traditional treatments of the HOR and ORR, reported

elsewhere.^15,32,33

i_HOR

[L]

r_HOR

[L]

= n_HORFk_H⁰_ORe^α

= −n_HOR

F

_HORF(Φ−Φ⁰_HOR

^)/RT[H₂][H₂O]θ

(9)

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i_ORR

[L]

r_ORR

[L]

= n_ORR

F

_ORRF(Φ−Φ_O⁰_RR

= n_ORRFk_O⁰_RRe^−α

^)/RT[O₂]θ

(10)

where the currents for the HOR (i_HOR) and ORR (i_ORR

)

,

depend on their respective intrinsic rate constants (k_H⁰_OR

k⁰_ORR), charge transfer coeﬃcients (α_HOR, α_ORR), and the total

number of electrons transferred (n_HOR= 2, n_ORR= 2−4).

Values of Φ⁰_HORand Φ_O⁰_RRimplicitly depend on the pH of the

solution, as shown in eqs 4 and 5. Note that the apparent ORR

current considers the lumped average of the 2e⁻and 4e⁻paths.

Moreover, eqs 9 and 10 assume that the activity of hydrogen

([H₂]) and oxygen ([O₂]) on the catalyst surface equals that of

the gas phase. For ﬁtting purposes, however, we account for

the mass transfer limitations of our electrochemical system,

which we consider in the complete Butler−Volmer formalism

(section S5 and Figures S19 −S43 in the Supporting

Information).¹⁴

Applying the mixed potential model to the HOR and ORR

(i.e., i_HOR= i_ORR), we set eqs 9 and 10 equal and derive the

functional form of the operating potential of a nanoparticle.

The resulting expression uses kinetic parameters measured for

⧧

the HOR and ORR (related to ΔG_appand α for elementary

steps in Figure 1) to solve for the Φ^opof each material as a

function of the activity of hydrogen and oxygen:

α_ORRΦ_O⁰_RR+ α_HORΦ⁰_HOR

RT

Φ^op

=

−

α_ORR+ α_HOR

F(α_ORR+ α_HOR)

Figure 4. Predicted currents as a function of potential, which derive

the operating potential calculated from eq 11 using kinetics

parameters (k_H^θ_OR, k^θ_ORR, α_HOR, and α_ORR) from RRDE measurements

of the HOR and the ORR obtained independently on monometallic

(a) Pd and (b) Pt catalysts. (c) Predicted operating potentials (Φ

white shown as a function of Φ, measured at open circuit on Pd

0

i

j

y

z

n

_HORk_HOR[H ][H O]

2

j

z

ln

j

z

n_ORRk_O⁰_RR[O₂]

(11)

k

{

where RRDE methods determine values for k⁰and α for the

HOR and ORR of each catalyst (section S5, Table S2, and

Figures S19 −S43 in the Supporting Information), which can

predict Φ^opunder thermocatalytic conditions. Note that the

operating potential is constrained by the reactant activities

during direct synthesis, whereas the electrochemical techniques

independently control the electrode potential.

◆

●

▼

(black ), PdCo (red Δ), PdNi (blue ), PdZn (cyan ), PdAu

■

○

( ), PdCu (purple ▶), PdPt (yellow ⬢), Pt (green ), PtCo

▲

(orange ⬠), PtAu₆₀(black ★), PtAu₁₅(orange ), and PtAu₅

□

(purple ) nanoparticles supported on Vulcan XC-72 between 20

and 400 kPa of H₂and 60 kPa of O₂at 298 K.

Figure 4a shows HOR and ORR currents for a carbon-

supported Pd catalyst calculated as functions of electrode

potential (Φ = −0.7to +0.2 V vs NHE) at diﬀerent H₂(60−

400 kPa of H₂) and O₂(60 kPa of O₂) pressures, respectively.

The intersection of the HOR and ORR lines predicts the Φ^op

for Pd nanoparticle catalysts at each combination of H₂and O₂

pressure, which occurs when the rates of ORR and HOR are

equal. For simplicity, Figure 4a,b depicts linear Tafel slopes

(calculated from ﬁtted values of k⁰and α) over the 600 mV

window shown in Figure 4a,b. We expect reasonable

predictions across the potentials observed during open-circuit

potentiometry measurements (Φ^op= 0.35−0.65 V vs NHE)

due to overlap with the potentials used for the Tafel analysis

(Figures S19 −S43); however, nonlinearities would emerge at

the most extreme potentials.^15,34−37

Like the Nernst equation of the HOR in Figure 3, this model

predicts that Φ^opbecomes more negative as the H₂pressure

increases. These relationships (Figure 4 and eq 11) reﬂect

increasing steady-state coverages of hydrogen atoms that

transfer electrons to the nanoparticle in the presence of

oxygen. These trends are consistent with data in Figure 3, but

this model predicts the values of the Φ^opmore accurately in

comparison to the Nernstian predictions on these materials

(Figure 3). Moreover, this Butler−Volmer model reveals the

reasons for a ∼200 mV diﬀerence between values of Φ^opfor Pt

and Pd over the range of H₂pressures examined (60−400 kPa

of H₂). In Figures 4a,b, the ORR rates are similar between Pt

and Pd (Figures S19 and S20), but the HOR currents on Pt

(Figure S37) are much higher than on Pd (Figure S32) at

similar electrode potentials (i.e., Pd requires a higher

overpotential to reach the same rate). Thus, Pt more readily

oxidizes H₂and generates electrons on the nanoparticle

surface, which agrees with lower hydrogen oxidation over-

potentials on Pt materials in comparison to Pd.^38,39

Consequently, Pt shows more negative values of Φ^opand

greater operating currents (Figure 4b).

Certain catalysts, such as PdAu₆₀, show a Φ^opvalue similar

to that for Pt but react at a lower ORR current density (Figures

S10 and S16). This discrepancy results from the higher transfer

coeﬃcients of the HOR (α_HOR) and ORR (α_ORR) pathways

and the greater H₂O₂selectivity on the PdAu₆₀material in

comparison to Pt. Thus, the operating potential of a material is

a strong function of the number of electrons transmitted

(n_ORR), the intrinsic rate constants of reaction, and the charge

transfer coeﬃcients of the HOR and ORR pathways. Figure 4c

shows that the predicted Φ^opcorrelates with measured values

of Φ^op, determined by open-circuit potentiometry measure-

ments over multiple combinations of hydrogen and oxygen

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●

△

▼

Figure 5. (a) H₂O₂and (b) H₂O formation rates as a function of H₂partial pressure on Pd (black ), PdCo (red ), PdNi (blue ), PdZn (cyan

◆

■

○

▲

), PdAu (red ), PdCu (purple ▶), PdPt (yellow ⬢), Pt (green ), PtCo (orange ⬠), PtAu₆₀(black ★), PtAu₁₅(orange ), and PtAu₅

□

(purple ) nanoparticles supported on Vulcan XC-72 (20−400 kPa of H₂, 60 kPa of O₂) at 298 K. Note that the formation rates are normalized by

the total moles of Pd or Pt in each sample. Dashed lines represent ﬁts of eq 16 to measurements for each material, which assume constant values of

Φ^op.

pressures (60−400 kPa of H₂, 60 kPa of O₂). Generally, the

model agrees with the data with an R²value of 0.74, and the

discrepancies observed likely originate from slight (but

unavoidable) diﬀerences between the conditions used for

RRDE and open-circuit potentiometry measurements. Specif-

ically, the presence of electrolyte in the RRDE experiments

may indirectly inﬂuence kinetic parameters in ways that are

absent from open-circuit potentiometry measurements. More-

over, measurements of Φ^opwere necessarily conducted with

both H₂and O₂, whereas RRDE measurements were

performed with either H₂or O₂but never both. These

variations in the reaction environment likely give rise to subtle

diﬀerences in the surface coverages of reactants not reﬂected in

Tafel slopes (Figure 4a,b). Nevertheless, independent electro-

chemical measurements of HOR and ORR parameters enable

accurate predictions of the expected Φ^opvalue for a catalyst

during direct synthesis across the 12 materials, which serve as

useful tools to inform the design of catalytic materials.

Figure 1), in which water facilitates the heterolytic oxidation of

hydrogen to generate hydronium ions in solution and electrons

on adsorbed oxygen intermediates (O₂*, OH*, or OOH*).

Then, water molecules may shuttle protons to anionic oxygen

−

intermediates (O₂*, OH⁻, or OOH⁻*) to complete the

reduction of these species. Overall, the rate expressions derived

from these elementary steps accurately capture changes in both

H₂O₂and H₂O formation rates with H₂and O₂pressure upon

all catalysts examined (Sections S6 and S7 in the Supporting

Information). Notably, this mechanism aligns closely with

proposed mechanisms for the ORR.⁴²

We hypothesize that the electrocatalytic and thermocatalytic

systems should show similar selectivities toward H₂O₂if

oxygen reduction follows the same reaction pathways. Figure 5

shows steady-state H₂O₂and H₂O formation rates (and

selectivities by comparison) as functions of H₂pressure for

each material used in this study. On each catalyst, the rates

increase in proportion with the H₂pressure (<100 kPa, 60 kPa

of O₂, 298 K) before reaching a constant value at the highest

pressures (150−400 kPa of H₂, 60 kPa of O₂, 298 K). These

results agree with past observations on both bimetallic and

monometallic Pd materials^13,16and suggest that the coverage

of H atoms increases with H₂pressure before saturating the

available active sites. These rates, however, do not depend

upon the O₂pressure under these conditions^11,13,16because

oxygen-derived intermediates saturate distinct surface sites and

do not compete with hydrogen for surface sites. Each catalyst

exhibits a similar functional dependence on the pressure of

hydrogen, which suggests a similar PET mechanism facilitates

H₂O₂and H₂O formation on these materials.

Figure 1 shows a series of elementary steps that produce

H₂O₂and H₂O through PET reactions of H₂and O₂, in which

oxygen and hydrogen intermediates adsorb to distinct sites

(denoted as * and □, respectively). The dominant hydrogen

oxidation reaction mechanism on noble metals is debated in

the electrochemical literature, and some studies suggest that a

combination of the Heyrovsky (step 1), Tafel (step 2), and

Volmer steps (step 3) occurs.^15,38Similarly, it is possible for

any of these steps to be kinetically relevant, depending on what

steps present the greatest apparent barriers on a given

material.^28,43The reverse of these reactions (steps 1−3) also

occur under the reaction conditions, and their rates depend on

3.2. Relating Operating Potential to H₂Pressure

through Rate Expressions for H₂O₂and H₂O Formation.

The model presented in the previous section made a few

assumptions regarding the mechanism of H₂O₂or H₂O

formation and relied on empirically measured rate constants.

Subsequently, we endeavored to derive a molecularly detailed

model based upon the series of elementary reactions proposed

for the formation of H₂O₂and H₂O under both thermochem-

ical and electrochemical conditions. This understanding

provides insight into the relationships among operating

potential, product formation rates, and reactant activity.

Initially, we considered a homolytic reaction mechanism,

which is commonly described by Langmuir−Hinshelwood

kinetics throughout the direct synthesis literature.^22,40,41This

model, however, does not explain the role of protic solvents in

the direct synthesis reaction, since H₂O₂formation rates are

negligible in aprotic solutions. Furthermore, the Langmuir−

Hinshelwood predictions do not agree with H₂O₂formation

rates independent of oxygen pressure (50−400 kPa of O₂, 60

kPa H₂).^11,16Recent kinetic measurements and DFT

calculations indicate that oxygen reduction barriers are much

greater for homolytic surface reactions than for proton−

12,42

⧧

electron transfer (PET) steps (ΔΔE_app= 22 kJ mol⁻¹).

Therefore, we considered a PET mechanism (depicted in

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the pH and operating potential of the nanoparticle. We

compare all of these steps and their implications on the

apparent rate expressions (section S6 in the Supporting

Information) and ﬁnd that both Heyrovsky−Volmer and

Tafel−Volmer kinetics lead to rate expressions that agree with

the data in Figure 5. For simplicity, we treat the Heyrovsky−

Volmer mechanism and assume that the Heyrovsky step (step

1) is kinetically relevant, as proposed by Takanabe.¹⁵Similarly,

we assume that steps 1 and 3 are primarily irreversible (section

S6 in the Supporting Information), since these experiments

occur at neutral pH. However, these assumptions may not hold

at lower pH values or highly negative potentials. With these

approximations, the rate expression for the HOR simpliﬁes to

where the operating potential of the nanoparticle depends on

the apparent equilibrium potential (Φ⁰_5a, Φ₁⁰) and the ratios of

hydrogen oxidation (k₁⁰, α₁) versus oxygen reduction (k₅⁰_a, α_5a)

rates. Φ^opalso depends on the temperature, the selectivity of

H₂O₂(related to n_ORR), and the coverage of sites that bind

hydrogen (θ_□= f([H^□])) and oxygen (θ_*= f ([O₂*],[O*],

[OH*],[OOH*])) species. Equation 14 resembles the func-

tional form of eq 11 where α_ORR, α_HOR, k⁰_HOR, and k_O⁰_RRreﬂect

the apparent charge transfer coeﬃcients and rate constants

measured experimentally, which change with surface coverage

(θ_□, θ_*) over a given range of conditions. Overall, these

ﬁndings predict that the operating potential will decrease with

the activity of hydrogen and increase with the activity of

oxygen, which agrees with observations in Figure 4. Thus, H₂

pressure controls the value of Φ^opon nanoparticle catalysts

during the thermocatalytic ORR; however, material-dependent

parameters (e.g., k_i, α_i, and Φ⁰_i) also contribute.

Fα₁(Φ^op− Φ₁⁰)

i_HOR= −2Fk₁⁰[H^□][H₂O] e

(12)

RT

where k⁰_x,Φ⁰_x, and α_xare the intrinsic rate constant, equilibrium

potential, and charge transfer coeﬃcient, respectively, for each

step x. This expression is analogous to eq 9 and suggests that

the net current of hydrogen oxidation (i_HOR) increases with the

activity of water in the solution ([H₂O]) and the coverage of

hydrogen ([H^□]) on the catalyst surface.

Functional forms of n_ORR, θ_□, and θ_*were solved and

substituted into eqs 13 and 14, which results in an expression

showing the total rate of oxygen reduction under thermoca-

talytic conditions:

α₁/(α₁+α_5a)

n_ORR

2

k₅⁰_aK₄[O₂]

i

j

y

z

r_ORR

The kinetically relevant steps of oxygen reduction involve

electron transfer to oxygen-derived species, because the

reaction rates on Pd do not depend on the isotopic label of

=

j

z

[L ]

1 + K_app,O[O₂]

2

*

k

{

the proton (e.g., k⁰/k⁰

≈ 1).^44,12Speciﬁcally, the

α

_5a/(α₁+α_5a)

0

H₂O D₂O

i

y

j k₁[H₂][H₂O] z

j

z

j

z

electrochemical literature suggests that the ﬁrst electron

transfer to O₂* (step 5a) is the kinetically relevant step for

both H₂O₂and H₂O formation on Pd and Pt materials.^42,44−46

We also assume that subsequent reduction steps are

irreversible (Figure 1), since density functional theory

(DFT) calculations indicate that each of these reactions is

exothermic with low barriers for the forward reactions.^12,42

Consequently, the reverse reactions are slow except at

operating potentials much more positive than are observed

during open-circuit potentiometry measurements.⁴⁷Thus, we

derive the apparent current expression for the ORR

j

z

1 + K_app,H[H₂]

2

k

{

_5a−Φ₁⁰)/(α_5a+α₁)RT

0

e^{Fα α (Φ}

1

5a

(15)

This equation shows that the thermocatalytic rate of the ORR

depends on expressions for both the hydrogen oxidation and

oxygen reduction reactions. Here, these terms are multiplied

by an exponential term, reﬂecting the diﬀerence in equilibrium

potentials of the HOR and ORR paths (Φ⁰_5a− Φ₁⁰). The

turnover rate of the ORR also carries an exponential

dependence upon parameters that depend on the relative

magnitude of the charge transfer coeﬃcients of the ORR and

HOR. Empirically, we observe greater values of α_ORRversus

α_HOR(Table S2), suggesting that eq 15 should simplify to

0

^op−Φ₅⁰_a)/RT

i_ORR= i_{H O}+ i_{H O}= n_ORRFk_5ae^{−α F(Φ}

5a

*

[O₂]

2

(13)

where the total ORR current (i_ORR) equals the currents

associated with the formation of H₂O₂(i_{H O}) and H₂O (i_{H O}),

α₁/α_5a

n_ORR

2

k₅⁰_aK₄[O₂]

0

i

j

y

z

i

y

r_ORR

j k₁[H₂][H₂O] z

j

z

2

≈

[L ]

1 + K_app,O[O₂]

1 + K_app,H[H₂]

which increases with the coverage of O₂* ([O₂*]) and the

operating potential of the nanoparticle. Here, the total number

of electrons transferred (n_ORR) depends on the relative rate of

the 2e⁻or 4e⁻pathways. Equation 13 reﬂects values for the

intrinsic rate constant (k₅⁰_a) and charge transfer coeﬃcient

(α_5a) of the kinetically relevant electron transfer to O₂*

(analogous to eq 10). This expression was solved explicitly

from the pseudo-steady-state coverage of each oxygen-derived

intermediate ([O*₂], [O*], [OH*], [OOH*]; Section S7 in

2

*

k

{

k

{

0

_5a−Φ₁⁰)/RT

e^{Fα (Φ}

1

(16)

This expression indicates that rates should increase in

proportion with [H₂] and should show a weak dependence

on [O₂]. Similarly, the model predicts that rates should be

independent of pressure when the surface is saturated with

hydrogen- and oxygen-derived intermediates ([H^□], [O₂*],

[O* ], [OH* ], [OOH* ]). The steady-state coverage of such

species depends on the apparent adsorption constants of

hydrogen (K_app,H) and oxygen (K_app,O), which reﬂect the

48

the Supporting Information), while Φ^oprelates to the

electron chemical potental of the metal and was calculated

by setting eqs 12 and 13 equal to each other (i.e., i_HOR= i_ORR

)

2

relative rate that surface intermediates are generated and

(α_5aΦ₅⁰_a+ α₁Φ₁⁰)

RT

F(α_5a+ α₁)

Φ^op

=

−

consumed. More speciﬁcally, K_app,Hdepends on the relative

2

(α_5a+ α₁)

rate of steps 1 and 3 (i.e., K_app,H= r₁/r₃) while K_app,Odepends

2

0

i

j

y

on numerous elementary reactions that reduce oxygen (steps

4−9, 12, and 13). Rearrangement of eq 16 yields individual

expressions for the formation of H₂O₂and H₂O:

2k [H ][H O]θ

z

1

2

0

2

□

j

z

ln

j

z

n_ORRk_5aK₄[O₂]θ

(14)

k

{

*

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r

H₂O

r_ORR

H₂O₂

+

= (S_{H O}(Φ^op) + S_{H O}(Φ^op))

2

[L ]

(17)

*

op

0

−α F(Φ −Φ )/RT

k₁⁰₂k⁰

(k₁⁰₂+ k ⁰

e

6a

op

0

−α F(Φ −Φ )/RT

13

e

)

13

S

(Φ^op) =

op

F(Φ −Φ )/RT

6a

H₂O₂

0

k₁⁰₃k⁰

e

e^−α

−α F(Φ −Φ )/RT

op

0

7

13

_6aF(Φ^op−Φ₆⁰_a)/RT

13

6a

(k₆⁰_ae^−α

+ 2k₇⁰e^{−α F(Φ −Φ )/RT}) +

6a

7

op

0

(k₁⁰₂+ k ⁰

e

)

−α F(Φ −Φ )/RT

13

(18)

13

relevant step of the HOR, which leads to slight changes in the

apparent rate constant and charge transfer coeﬃcients.

S

(Φ^op) = 1 − S

(Φ^op)

H₂O

H₂O₂

(19)

Equation 16 was ﬁt to the reaction rates shown in Figure 5

by assuming a constant value for each variable other than [H₂].

While the intrinsic rate constants (k_x⁰), charge transfer

coeﬃcients (α_x), and other terms (e.g., Φ⁰_x, n_ORR) change as

a function of the potential and the coverage of hydrogen (vide

infra), we treat these parameters as constants since we do not

have data showing the functional dependence of these values

over this range of conditions. Still, eq 16 captures the

functional change in rates shown in Figure 5, suggesting that

the proposed electrochemical reactions can reasonably

describe the trends in data for thermocatalytic systems.

Speciﬁcally, eq 16 explains why rates increase in proportion

with hydrogen pressure (eq 21) as the surface eventually

saturates with H^□(eq 22). Yet, most Pd materials showed a

considerable increase in H₂O₂selectivity at these higher

pressures of hydrogen (150−400 kPa of H₂) in comparison to

the lower pressures (20−60 kPa of H₂). Consequently, most

Pd materials showed unexpected deviations in their ﬁts of k₆⁰_a

and k⁰₇, which suggest that the rate of H₂O₂formation (k₆⁰_a)

increases relative to the rate of H₂O formation (k⁰₇) at higher

coverages of H^□. Such ﬁndings agree with the formation of the

β-PdH_xphase, which presents lower barriers to generate H₂O₂

and greater O−O dissociation barriers in comparison to

metallic Pd (vide infra).¹²Thus, eq 16 captures the functional

change in rates, but the formation of β-PdH_xconvolutes the

functions related to selectivity (eqs 18 and 19). Nevertheless,

this analysis suggests that a nanoparticle will facilitate a high

rate of H₂O₂formation if the surface presents a low barrier to

both oxidize hydrogen and reduce oxygen through the 2e⁻

route.

3.3. Comparing Catalyst Performance between

Thermocatalysis and Electrocatalysis. The H₂O₂selectiv-

ity of a metal nanoparticle material depends upon the metal

identity, the temperature, and the coverage of reactants on the

catalyst surface. The selectivity for each catalyst also reﬂects

the electrode potential under electrochemical ORR conditions

or the operating potential under direct synthesis conditions.

This selectivity is a function of the competing rates of reactions

that consume OOH* intermediates by simple electron transfer

(k⁰_6a) or dissociative electron transfer (k⁰₇, k₁⁰₃) pathways (eqs

18 and 19). Ultimately, H₂O₂selectivities reﬂect the ability of

the catalyst to cleave the O−O bond,^6,9,11,49which occurs

irreversibly under direct synthesis conditions, as shown during

the reduction of ¹⁸O₂−¹⁶O₂mixtures.⁵⁰Consequently, metals

that prevent the O−O bond rupture in dioxygen species (O₂*,

OOH*, and H₂O₂*) and provide high oxygen reduction rates

give the highest rates and selectivities for H₂O₂formation. Our

model also gives greater insight into the molecular phenomena

that dictate selectivity changes under varying reaction

conditions. Thus, we compared the selectivities of Pd and

PtAu₁₅catalysts over ranges of electrode potentials (−0.1 to

where S_H

and S_{H O}are functions of Φ^opand represent the

O₂

2

selectivities toward H₂O₂and H₂O, respectively. Here, the

H₂O₂selectivity depends on the rate that OOH* reduces to

H₂O₂(k⁰_6a, α_6a) versus the rate that OOH* (k⁰₇, α₇) or H₂O₂*

(k⁰₁₃, α₁₃) dissociate during H₂O formation. These expressions

also contain terms describing the relative rate that H₂O₂

desorbs (r₁₂) into solution versus the rate that it is reduced

to H₂O (r₁₃). Moreover, these equations quantify how

selectivities depend on the operating potential and temperature

(vide infra). These equations also suggest that the selectivities

in electrocatalytic and thermocatalytic measurements will be

equivalent if the materials operate at the same potential (Φ =

Φ^op), present similar kinetic constants, and possess identical

reactant coverages and nanoparticle phase. These expressions

also deﬁne the apparent value of n_ORRin relation to the values

of S_{H O}and S_{H O}

.

2

4

n_ORR

=

1 + S_{H O}(Φ^op)

(20)

2

Thus, eq 20 shows that the average number of electrons

transmitted during the ORR ranges from 2 to 4, depending on

whether the H₂O₂or H₂O formation pathway dominates.

When coverages of hydrogen atoms are low (i.e., [L_□] =

[□]) and the surface is saturated with oxygenates (i.e., [L_*] ≠

[*]), eq 16 takes the form

α₁/α_5a

0

i

j

y

z

r

n

_ORRk_5aK₄

H₂O₂

op

j

z

≈ S_{H O}(Φ )

(k₁⁰[H₂][H₂O])

j

z

2

[L ]

2K_app,O

2

*

k

{

_5a−Φ₁⁰))/RT

0

e^{F(α (Φ}

1

(21)

which predicts that the rate of the ORR increases in proportion

with hydrogen pressure at the lowest values of [H₂] and the

overall rate depends mostly on the Heyrovsky step. This rate

also depends on the apparent rate constant of electron transfer

to oxygen-derived species and the relative charge transfer

coeﬃcients of the HOR and ORR.

At the highest hydrogen pressures, hydrogen atoms saturate

the available surface sites (i.e., [L_□] = H^□) and eq 16

simpliﬁes to

α₃/α_5a

0

i

j

y

z

r

n

_ORRk_5aK₄

H₂O₂

op

j

z

≈ S_{H O}(Φ )

(k₃⁰[H₂O])

2

[L ]

2K_app,O

2

*

k

{

_5a−Φ₃⁰))/RT

0

e^{F(α (Φ}

3

(22)

where the rate of ORR does not depend on hydrogen pressure

and the overall rate is mostly dependent on the Volmer step.

Under such conditions, the Volmer step acts as the kinetically

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+0.6 V vs NHE), hydrogen pressures (20−400 kPa of H₂, 60

kPa of O₂), and temperatures (278−308 K), as shown in

Figure 6.

3.3.1. Selectivity of H₂O₂Formation as a Function of

Electrode Potential. Figure 6a shows that H₂O₂selectivities of

Pd and PtAu₁₅catalysts increase exponentially to maximum

values of 60 and 90%, respectively, between electrode

potentials of 0.45−0.6 V vs NHE. At lower electrode potentials

(−0.1 to +0.3 V vs NHE), however, the selectivity of the

PtAu₁₅material gradually decreases to 50%, while the

selectivity of Pd decreases more sharply and approaches a

constant value of ∼20%. All catalysts examined present

selectivity proﬁles with similar functional forms (Figures

S44 −S56), consistent with analogous electrocatalytic measure-

ments reported elsewhere.⁴⁹The decrease in selectivities at

lower potentials suggests that the apparent free energy barrier

for H₂O₂decomposition pathways becomes comparable to the

primary H₂O₂formation pathway at the lowest potentials.

Here, both the disproportionation of H₂O₂(2H₂O₂→ O₂+

2H₂O) and the direct electroreduction of H₂O₂(step 13) may

contribute to this decrease in selectivity,^49,51but such reactions

are challenging to deconvolute. Therefore, we have considered

only the electroreduction of H₂O₂, which yields equations that

reasonably agree with the corresponding data (Figure 6a).

Below, we show the generalized form of eq 18, which applies

for any electrode potential

Figure 6. Selectivity of H₂O₂formation on PtAu₁₅and Pd

nanoparticles as a function of (a) electrode potential (−0.1 to +0.6

V vs NHE, rotating ring−disk electrode), (b) H₂and O₂pressure

(20−400 kPa of H₂, 60 kPa of O₂, 278 K, trickle-bed reactor), and (c)

inverse temperature (200 kPa of H₂, 60 kPa of O₂, 278−308 K,

trickle-bed reactor). The best ﬁt of eq 23 is shown as the dashed line

in (a).

0

−α F(Φ−Φ )/RT

k₁⁰₂k⁰

e

6a

op

0

−α F(Φ −Φ )/RT

(k₁⁰₂+ k ⁰

e

)

13

S

(Φ) =

H₂O₂

0

F(Φ−Φ )/RT

6a

−α F(Φ−Φ )/RT

k₁⁰₃k⁰

e

e^−α

0

13

6a

_6aF(Φ−Φ₆⁰_a)/RT

13

(k₆⁰_ae^−α

+ 2k₇⁰e^{−α F(Φ−Φ )/RT}) +

6a

7

0

−α F(Φ−Φ )/RT

(k₁⁰₂+ k ⁰

e

)

13

(23)

13

where the selectivity of H₂O₂formation depends on the

relative ratio of the primary 2e⁻path (step 6a) versus the

primary 4e⁻(step 7) and secondary 2e⁻(step 13) pathways

that form H₂O. Equation 23 reasonably reproduces selectivities

measured as functions of electrode potential (Figures S44 −

S56), and Table S3 displays values of the ﬁtted parameters.

This expression for S_{H O}contains a ratio for the rate of H₂O₂

Fits of k⁰_6aand k₇⁰explain why PtAu₁₅is more selective than

Pd over a broader range of electrode potentials. The greater

ratio between rate constants of the primary ORR pathways

(((k_6a/k₇)_PtAu)/(k_6a/k₇)_Pd= 4) indicate that PtAu₁₅shows a

higher intrinsic free energy barrier to form H₂O versus H₂O₂in

comparison to Pd. The high selectivities on PtAu₁₅resemble

those for PdAu alloys,^16,52on which O−O bond dissociation

pathways (k₇, k₁₃) are inhibited as Pd atoms are isolated on the

Au surface. PtAu₁₅may form similar types of monomeric or

oligomeric groupings of Pt atoms. In contrast, the surface of

monometallic Pd nanoparticles provides large ensembles of

contiguous Pd atoms with electronic structures that favor H₂O

formation.

2

decomposition to the rate of H₂O₂desorption (step 12). Here,

H₂O₂desorption rates are assumed to depend more weakly on

electrode potential, since this step does not involve charged

intermediates or an explicit electron transfer step. Con-

sequently, at low overpotentials, the rate of H₂O₂desorption

is fast, and eq 23 collapses into a sigmoidal expression. At the

greatest overpotentials, however, eq 23 predicts a sharp

decrease in selectivity that is consistent with the behavior in

Figure 6a.

Finally, this derivation implies that each catalyst possesses an

optimum electrode potential (Φ_opt) that provides the

maximum possible H₂O₂selectivity, which occurs when the

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This expression shows that changes in H₂O₂selectivity with H₂

activity reﬂect the change in selectivity with electrode potential

(derivative of eq 23) and change in operating potential with H₂

activity (derivative of eq 14). Speciﬁcally, the dependence of

selectivity on potential is a function of the charge transfer

coeﬃcients that lead to H₂O₂formation (α_6a) versus those that

lead to H₂O formation (α₇, α₁₃). In comparison, the functional

relationship of operating potential and hydrogen activity

depends upon the overall charge transfer coeﬃcients of the

ORR and HOR (α_5a, α₁). For instance, PdAu₆₀and PtCo

present similar values of α_5a(Table S2, 0.37 versus 0.30), but

PdAu₆₀presents much greater values of α₁(Table S2, 0.93

versus 0.25). Consequently, PdAu₆₀shows the smallest

decrease in operating potential (∼0.03 V, Figure S10), while

PtCo shows the greatest diﬀerence in operating potential

(∼0.25 V, Figure S7) between 60 and 400 kPa of H₂. Thus,

some metals may show a modest change in selectivity over a

broad range of hydrogen pressures if materials show little

change in their operating potential (e.g., α_5aand α₁are large).

The data in Figure 6b show trends in selectivity consistent

with the changes in operating potential determined through

open-circuit potentiometry measurements at similar pressures

(Figure 4). PtAu₁₅operates at potentials (Φ^op= 0.39−0.45 vs

NHE) coinciding with a similar change in H₂O₂selectivity

(75−90%) in Figures 6a,b, which agree with predictions from

eq 23. Pd, in contrast, operates at more positive potentials

(Φ^op= 0.51−0.61 vs NHE), which correspond to a H₂O₂

selectivityof between 16 and 25% in Figure 6a. Yet, the H₂O₂

selectivity increases from 6 to 60% between 20 and 400 kPa of

H₂, signiﬁcantly exceeding the expectations of eq 23 for these

corresponding operating potentials. Thus, the predicted

changes in selectivities over this range of hydrogen and oxygen

pressures shows better agreement for PtAu₁₅in comparison to

Pd, which suggests that intrinsic rate constants (k_6a, k₇, k₁₃)

change with reactant coverages on Pd but not on PtAu₁₅.

Again, these observations coincide with a Pd to β-PdH_xphase

transition for Pd nanoparticles, as observed by operando X-ray

absorption spectroscopy at H₂to O₂gas ratios of ∼2:1.^12,53Pt

and Pt-based bimetallics do not form hydrides under these

conditions, which explains why the changes in selectivity are

more signiﬁcant on Pd and Pd-based alloys in comparison to

the Pt- based materials (Figure 5).

derivative of eq 23 equals zero (dS_{H O}(Φ)/dΦ = 0) (Section

S8 in the Supporting Information):

2

0

i

y

z

k (α − α₁₃− α )

RT

F(α₇− α_6a)

j

7

6a

7

j

z

Φ

≈

ln

opt

k₆⁰_a× α₁₃

k

{

(α₇Φ⁰₇− α_6aΦ₆⁰_a)

α₇− α_6a

+

(24)

This relationship shows that Φ_optdepends on the diﬀerence of

the charge transfer coeﬃcients that form H₂O₂(α_6a) versus

those that form H₂O (α₇, α₁₃). This parameter also depends on

the ratio of intrinsic rate constants that primarily form H₂O

(k⁰₇) versus those that form H₂O₂(k₆⁰_a). Thus, the value of Φ_opt

represents a critical point at which the metallic density of states

overlaps with the OOH* and H₂O₂* states in a way that

maximizes electron transfer toward stable H₂O₂* species while

preventing excessive electron transfer into the O−O

antibonding states. These diﬀerences may suggest that Pt

monomers and oligomers on the surface of PtAu₁₅do not bind

dioxygen intermediates with η²adsorption modes that lead to

the signiﬁcant overlap between the d band and O−O

antibonding states on Pd. Consequently, subtle changes in

the coordination of reactants may lead to greater H₂O₂

selectivities at Φ_opton PtAu₁₅.

The results presented in this subsection suggest that Pd

performs catalysis at a suboptimal operating potential (0.51−

0.61 V vs NHE) under our tested direct synthesis conditions,

which leads to H₂O₂selectivities between 16 and 25%. Figure

6a indicates that the optimal operating potential of this Pd

material is at 0.43 V vs NHE, which leads to a selectivity as

high as 60% at this condition. PtAu₁₅, in contrast, shows values

of Φ^opbetween 0.39 and 0.45 V vs NHE, which corresponds to

H₂O₂selectivities between 76 and 86%, as shown in Figure 6a.

Therefore, PtAu₁₅operates more closely to its optimal

operating potential (0.34 V vs NHE) under direct synthesis

conditions in comparison to Pd. Thus, these results present

new opportunities to design materials that result in operating

potentials closer to the optimal potential by understanding

factors that aﬀect charge transfer coeﬃcients and rate constants

toward the HOR and ORR. Similarly, these principles may lead

to the design of reactors that facilitate oxygen reduction at this

optimum potential for H₂O₂generation.

Thus, materials may exist at similar potentials (Φ = Φ^op),

but the coverages of H^□atoms on these nanoparticles are

greater under direct synthesis conditions than under electro-

catalytic conditions because of the increased chemical potential

of hydrogen. Thus, these diﬀerences in the electrochemical

potential lead to inconsistencies between H₂O₂selectivities in

thermochemical and electrochemical systems. Speciﬁcally, the

coverage of H^□atoms ([H^□]) during direct synthesis depends

directly upon the H₂pressure (section S6 in the Supporting

Information):

3.3.2. Selectivity of H₂O₂Formation as a Function of

Hydrogen and Oxygen Activity. The H₂O₂selectivity changes

as a function of hydrogen pressure under direct synthesis

conditions. Figure 6b shows the H₂O₂selectivity of PtAu₁₅and

Pd nanoparticles (20−400 kPa of H₂, 60 kPa of O₂, 278 K).

The selectivities on PtAu₁₅increase from ∼75% toward a value

of 90% over this range of H₂pressures. In contrast, H₂O₂

selectivities on Pd vary between 6 and 9% at the lowest

pressures (20−60 kPa of H₂) before rising sharply and

becoming constant (∼60%) at the highest pressures (200−400

kPa of H₂). The change in selectivity with respect to the

thermodynamic activity of H₂is shown below, as derived in

section S9 in the Supporting Information:

k₁⁰

k₃⁰

Fα₁(Φ^op−Φ₁⁰)/RT −Fα₃(Φ^op−Φ₃⁰)/RT

[H^□] =

[H₂][□] e

e

op

(26)

i

j

y

z

op

i

j

y

z

dS

(Φ )

dS

(Φ)

2

i

j

y

z

H₂O

dΦ

d[H₂]

2

≈

∝

In contrast, electrochemical conditions produce H^□atoms by

steps associated with the hydrogen evolution reaction on the

nanoparticle surface and depend upon the applied electrode

potential:

d[H₂]

dΦ

k

{

k

{

k

{

α_6a− α₇− α₁₃

α_5a+ α₁

(25)

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Figure 7. Thermocatalytic H₂O₂selectivities and ORR rates compared to electrocatalytic selectivities and predicted ORR rates on (a, c) PdPt

■

□

▲

●

(yellow ⬢), Pt (green ), PtCo (orange ⬠), PtAu₆₀(black ★), PtAu₁₅(orange ), and PtAu₅(purple ) and (b, d) Pd (black ), PdCo (red

◆

△

▼

○

), PdNi (blue ), PdZn (cyan ), PdAu (red ), and PdCu (purple ▶) nanoparticles supported on Vulcan XC-72. The thermocatalytic

selectivity was calculated from the H₂O₂formation rate divided by the H₂consumption rate in a trickle-bed reactor (20−400 kPa of H₂, 60 kPa of

O₂) at 298 K. The electrocatalytic selectivity was calculated from the ring and disk currents of a rotating ring−disk electrode (RRDE). Selectivities

were determined at equivalent potentials (Φ = Φ^op) from open-circuit potentiometry experiments using eq 23. The rates of the ORR were

predicted from electrochemical rate constants (Table S2) using eq 16.

coverage of H^□is likely much lower on Pt materials under

similar conditions, since these materials show much greater

HOR rates in cmparison to the Pd materials (section S5 in the

Supporting Information).

k₋⁰₃

k₋⁰₁

₋₃(Φ−Φ₋⁰₃)/RT

₋₁(Φ−Φ₋⁰₁)/RT

[H^□] =

[H₂O][□] e^−Fα

e^Fα

(27)

Comparisons of these equations demonstrate that high

coverages of H^□can form by dissociative adsorption of H₂

under thermochemical conditions. Under electrochemical

conditions, however, the reduction of hydronium ions requires

electrode potentials lower than those used for the ORR,

resulting in low coverages of H^□under the conditions we

investigated.⁵⁴For example, voltammograms of Pd show that

hydrogen evolution occurs at electrode potentials below −0.1

The analysis in this section reveals an important distinction

between the thermal and electrocatalytic systems, which only

becomes apparent following these comparisons. Controlling

the hydrogen and oxygen pressure allows for greater control of

the coverage of surface species, which can lead to more

selective intrinsic rate constants than in purely electrochemical

systems. Separately, an electrode can bias the potential of a

nanoparticle toward its optimal potential (Φ_opt) to favor H₂O₂

formation over primary and secondary pathways that form

H₂O, which may not be possible under thermocatalytic

conditions. These ﬁndings imply that much greater H₂O₂

selectivities may be achieved through simultaneous control of

both the activities of H₂and O₂to optimize surface coverages

and the electrode potential to manipulate apparent rate

constants.

V vs NHE (Figure S57), which is much lower than the

optimum operating potential of Pd (Φ = 0.43 V vs NHE).

pd

opt

Consequently, Pd likely exists in the metallic phase during

typical RRDE measurements. The formation of the β-PdH_x

phase occurs only at electrode potentials that are unselective

toward the formation of H₂O₂because secondary decom-

position pathways (k⁰₁₃, α₁₃) become signiﬁcant relative to the

primary formation pathways (k⁰_6a, α_6a) at these lower potentials.

Similarly, the presence of gaseous hydrogen allows Pd to form

a more selective surface structure (β-PdH_x) but at a

suboptimal potential during direct synthesis. Similarly, the

3.3.3. Selectivity of H₂O₂Formation as a Function of

Temperature. In this subsection, we consider the selectivity of

materials as a function of temperature, which gives insight into

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the apparent barriers of reaction for the H₂O₂and H₂O

formation pathways. Figure 6c shows the selectivity of Pd and

PtAu₁₅between 278 and 308 K at a constant pressure of 200

kPa of H₂and 60 kPa of O₂. PtAu₁₅shows a decrease in H₂O₂

selectivity from 87% to 57%, while the selectivity on Pd

decreases from 52% to 47% over this range. To interpret this

behavior, we diﬀerentiate the selectivity with respect to

temperature (SI section S9) and derive

in selectivity may wane at suﬃciently low temperatures. While

the selectivity of H₂O₂increases at lower temperatures, the

overall rate of H₂O₂formation decreases in both thermochem-

ical and electrochemical systems. However, an applied

electrode potential can compensate for the loss of oxygen

reduction rates, while high H₂O₂selectivities are maintained.

Thus, this analysis demonstrates a careful tradeoﬀ between

formation rates and selectivity, depending on the temperature

and the potential of the nanoparticle.

op

i

y

dS

(Φ )

3.3.4. Comparison of Rates and Selectivity of Electro-

chemical and Thermal Measurements. Using the results

from prior sections, we compare and analyze trends in H₂O₂

rates and selectivities obtained over a range of thermal and

electrochemical conditions for 12 diﬀerent compositions of Pt-

and Pd-based monometallic and bimetallic nanoparticles

supported on carbon. Figure 7a,b shows that electrochemical

and thermochemical H₂O₂selectivities on a given catalyst

correlate when they are measured at identical potentials (Φ =

Φ^op). These comparisons involve measurements obtained as a

function of H₂pressure (Figure S5) and as a function of

electrode potential (Figures S44 −S56), which are related to

one another using potentiometric measurements obtained in

mixtures of H₂and O₂gas (Figure 4 and Figures S6 −S17).

The selectivities reported in Figures 7a,b collectively show

parity across many of the studied materials (R²= 0.61). These

observations corroborate a similar reaction mechanism

between the thermocatalyic and electrocatalytic systems and

support the relationships described in the previous sections.

The Pt-based materials show a high level of parity (Figure

7a, R²= 0.94) in comparison to Pd-based materials, which

deviate more from parity (Figure 7b, R²= 0.55). These

deviations among the Pd-based materials are most signiﬁcant

at the greatest H₂pressures, which lead to high H^□coverages

and form the β-PdH_xphase.^12,53This phase does not form

readily during electrochemical measurements of the ORR,

because H^□coverages are negligible under these conditions

(vide supra). The formation of β-PdH_xlowers barriers to

generate H₂O₂(k⁰_6a) and increases O−O bond dissociation

barriers (k⁰₇, k₁⁰₃) in comparison to metallic Pd.¹²Consequently,

catalysts that contain Pd typically show greater similarities in

H₂O₂selectivities between electrochemical and thermochem-

ical conditions when the latter use lower hydrogen pressures.

In contrast, the Pt materials agree better with the parity line

over the given range of potentials, suggesting that these

materials present more similar kinetic parameters under

electrochemical and thermochemical conditions. This con-

clusion also agrees with the inability of Pt materials to form

hydrides at reactant pressures used in trickle-bed reactor

measurements.

j

H₂O

z

∝ ΔH₇^⧧− ΔH_6a^⧧+ F((α₇− α_6a)Φ^op

− (α₇Φ⁰₇− α_6aΦ₆⁰_a)) + ξ(Φ^op)

2

j

z

j

z

dT

k

{

Φ

⧧

= ΔΔH_4e‐2e

(28)

Here, the change in selectivity with temperature depends on

the diﬀerences between the apparent activation enthalpies for

the four-electron and two-electron ORR (ΔΔH_4e‑2e^⧧). This

parameter depends on the diﬀerence in the intrinsic activation

enthalpies (ΔH₇, ΔH_6a^⧧), equilibrium potentials (Φ⁰₇, Φ₆⁰_a),

⧧

and charge transfer coeﬃcients (α₇, α_6a) of the elementary

steps that form H₂O₂and H₂O from OOH*. This expression

indicates that a more negative operating potential leads to a

lower apparent reaction barrier for either ORR pathway.

Moreover, eq 14 suggests that an increase in temperature leads

to a decrease in the operating potential, indicating that these

apparent barriers should also decrease with temperature.

Therefore, eq 28 indicates that the H₂O₂selectivity should

increase if Φ^opdecreases at a constant temperature (assuming

α_6a> α₇). However, Figure 6c shows that the selectivity

decreases as the temperature increases, indicating that intrinsic

⧧

activation enthalpies (ΔH₇, ΔH_6a^⧧) dictate most of the

change in selectivity over the tested range of temperature (i.e.,

the change Φ^opwith temperature has a weak inﬂuence on

selectivity). At lower operating potentials, however, the

secondary H₂O₂decomposition pathway (step 13) becomes

more dominant, and ξ contributes to a signiﬁcant decrease in

the selectivity (Sections S4, S5 and S9 in the Supporting

Information). Therefore, the value of Φ_optcoincides with the

maximum value of ΔΔH_4e‑2e^⧧, leading to the maximum

selectivity for a material.

These interpretations of eq 28 explain the trends in Figure

6c, where we empirically measure the apparent values of

ΔΔH_4e‑2eas 40 kJ mol⁻¹on PtAu₁₅and 7 kJ mol⁻¹on Pd.

⧧

The greater value of ΔΔH_4e‑2eresults in higher selectivity on

PtAu₁₅than on Pd in Figure 6, which agrees with the ﬁts of k_6a

and k₇by eq 23. Thus, the surface structure of PtAu₁₅may

consist of monomeric Pt species that intrinsically favor the

formation of H₂O₂versus H₂O by obstructing the dissociation

of O−O bonds, while Pd consists of contiguous ensembles of

Pd that more readily dissociate these bonds. Comparisons of

the activation barriers at low and high hydrogen pressures

show that ΔΔH_4e‑2e^⧧also depends upon H₂pressure (Table S4

and Figures S59 −S70). We attribute these diﬀerences to

changes in the coverage of reactive species (e.g.,H^□), which

Figure 7c,d shows the agreement of thermochemical ORR

rates in comparison to the predictions of eq 16 on Pt- and Pd-

based materials. Generally, reactive catalysts show high

reactivity in both the electrocatalytic and thermocatalytic

systems. However, the predicted ORR rates show better

agreement with the rates measured on Pt materials than on Pd

materials. Speciﬁcally, the electrocatalytic prediction of rates is

systematically greater than those measured thermocatalytically

on Pd materials. In section S10 in the Supporting Information,

we evaluate the sources of these disparities and ﬁnd that the

overprediction of rates on Pd materials may result from

⧧

can inﬂuence intrinsic activation enthalpies (ΔH₇, ΔH_6a

)

and the operating potential (Φ^op).

H₂O₂selectivities decrease as temperatures increase on all

materials. This observation agrees with the value of eq 23 taken

at the limit of low temperature (lim_T→0S_{H O}(T) = 1) at a

diﬀerences between the apparent values of k_ORR, k_HOR, α_ORR

,

2

constant potential. However, eq 14 suggests that Φ^opincreases

and α_HORduring electrocatalysis and thermocatalysis experi-

ments. Speciﬁcally, these parameters depend strongly on the

as the temperature decreases, indicating that this improvement

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Figure 8. (a) Comparison of direct synthesis turnover rates of H₂O₂formation as a function of hydrogen pressure (20−400 kPa of H₂, 60 kPa pf

O₂, 298 K) on Au, PdAu, and PtAu materials. (b) Comparisons of current generated on a disk and ring electrode, which measures the total rate of

the ORR and the associated H₂O₂production as a function of electrode potential (−0.1 to +0.6 V vs NHE). These currents were used to calculate

(c) the H₂O₂selectivity of the materials at varying electrode potentials. (d) Comparisons between the disk current of the HOR on these materials

as a function of electrode potential (0.4−1.0 V vs NHE). Formation rates are normalized by the total moles of Pd or Pt in these samples, while rates

on monometallic Au are below the detection limit.

coverages of oxygen- and hydrogen-derived intermediates, and

nonlinearities in our Tafel analysis exacerbate these diﬀerences.

ities when kinetic parameters are determined at equivalent

electrochemical potentials.

3.4. Semiquantitative Predictions for Thermocata-

lytic Systems. In previous sections, we derived a rate

expression (eq 16) that accurately describes the changes in

H₂O₂and H₂O formation as a function of hydrogen pressure

and provided guidelines to design high-performance thermal

catalysts. Equation 16 shows that the rate of H₂O₂formation

depends mostly on the kinetic parameters of hydrogen

oxidation (k₁⁰, α₁, k₃⁰, α₃) and 2e⁻oxygen reduction (k₆⁰_a,

α_6a). Therefore, materials with a nominally similar selectivity

should show an overall higher rate of H₂O₂formation if they

present lower overpotentials to oxidize hydrogen. Figure 8

shows comparisons of H₂O₂formation rates and selectivities

on Au, PdAu₆₀, and PtAu₆₀catalysts that examine this

hypothesis.

Figure 8a shows that H₂O₂formation rates on PtAu₆₀are

twice those measured on PdAu₆₀over a range of H₂pressures

(20−400 kPa of H₂), while rates on Au are immeasurably low.

Yet, the same materials show similar oxygen reduction rates

(Figure 8b) over the examined range of electrode potentials

(−0.1 to +0.9 V vs NHE), as shown by comparable current

densities on both the ring and disk electrodes. Moreover, the

electrocatalytic H₂O₂selectivities (Figure 8c) are similar to

those measured under direct synthesis conditions at equivalent

Since eq 16 includes exponential functions of α_ORRand α_HOR

,

small changes in these values can cause the apparent rate to

change by orders of magnitude. This conclusion agrees also

with the better parity of selectivity measurements on Pt

materials versus Pd materials, which is also a strong function of

coverage. Predictions on Pt materials show reasonable

agreement, especially when the number of surface sites is

quantiﬁed with an internal standard (e.g., CO chemisorption;

Figure S71).

Overall, these disparities show that it is possible to achieve a

similar potential on a nanoparticle (Φ = Φ^op) under thermo-

and electrocatalytic conditions, but the electrochemical

potential may vary signiﬁcantly. Consequently, coverages of

reactive intermediates can diﬀer in these measurements and

result in diﬀerences in the apparent charge transfer coeﬃcients

and intrinsic rate constants. Pt-based materials seem less

sensitive to changes in reactant coverage, leading to better

agreement with the predictions of the model. On Pd-based

materials, however, diﬀerences in the coverage of hydrogen-

and oxygen-derived intermediates can alter the apparent values

of k_ORR, k_HOR, α_ORR, and α_HORduring measurements of the

HOR, ORR, and direct synthesis. Thus, this model can provide

reasonable predictions for thermocatalytic rates and selectiv-

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electrode potentials (Φ = Φ^op). These discrepancies suggest

that the kinetics of the hydrogen oxidation reaction produce

the large diﬀerences in rates observed during the thermoca-

talytic reactions of H₂and O₂.

direct synthesis conditions through independent electro-

chemical measurements of the hydrogen oxidation and oxygen

reduction reactions. Molecularly meaningful derivations show

that the operating potential depends on the relative rates of the

coupled HOR and ORR reactions on a metal nanoparticle

surface. For instance, increasing the pressure of hydrogen leads

to higher HOR rates and lower operating potentials, which

provide a greater driving force to reduce oxygen.

Figure 8d shows rotating disk voltammograms for the same

Au-based catalysts performing hydrogen oxidation over a

similar range of electrode potentials (−0.1 to +1.0 V vs NHE)

as the ORR measurements. These data show that PtAu₆₀

catalyzes HOR rates nearly double those of PdAu₆₀over this

range, such that the HOR overpotential of PtAu₆₀is ∼150 mV

lower than for PdAu₆₀. In comparison, the Au presents HOR

rates that are many orders of magnitude lower than those on

either material. Thus, the Pt alloy more readily oxidizes

hydrogen than the Pd alloy, while pure Au barely activates

hydrogen (k⁰_1,PtAu> k⁰_1,PdAu≫ k⁰_1,Au). Within the framework

These observations and analyses also allow the design of

high-performance oxygen reduction materials that enable high

rates and selectivity for the direct synthesis of H₂O₂from its

elements. We quantitatively described how the selectivity of

H₂O₂approaches a maximum at its optimum operating

potential (Φ_opt) during electrocatalytic measurements. In

comparison, we show how hydrogen and oxygen activities

lead to selective surfaces and catalyst structures under

thermochemical conditions, which do not occur readily in

electrochemical measurements. Thus, this analysis shows how

catalysts can access more selective states that were unrecog-

nized prior to direct comparisons between thermochemical

and electrochemical systems. This work also shows that an

increase in hydrogen oxidation rates increases the overall H₂O₂

formation rate and can bias nanoparticles toward more

selective operating potentials, as shown by comparisons of

Au, PdAu₆₀, and PtAu₆₀. Thus, ideal materials must

simultaneously present favorable barriers and charge transfer

coeﬃcients toward the 2e⁻ORR and HOR paths to obtain the

greatest rates and selectivities toward H₂O₂formation.

Therefore, this understanding informs the design of new direct

synthesis catalysts based on electrochemical studies and may

enable the economical production of H₂O₂for industrial

applications.

60

established in Sections S3.1 and S3.2 in the Supporting

Information, the greater HOR overpotentials on Au and

PdAu₆₀in comparison to PtAu₆₀lead to lower rates of H₂O₂

formation on these catalysts under thermocatalytic conditions

(eq 16). Essentially, the higher barriers of the HOR on

Pd₁Au₆₀and Au lead to larger apparent barriers to form H₂O₂

and H₂O. Such interpretations are consistent with predictions

in the literature, showing that eﬀective catalysts must readily

activate both hydrogen and oxygen to achieve high rates

toward H₂O₂.⁵⁵

This analysis also reveals that diﬀerences in HOR kinetic

parameters (k⁰₁, α₁, k₃⁰, α₃) allow PtAu₆₀to access a wider range

of operating potentials in comparison to PdAu₆₀under direct

synthesis conditions. PdAu₆₀operates between 0.39 and 0.42 V

vs NHE, while PtAu₆₀operates over a broader range of 0.35−

0.46 V vs NHE. Coincidentally, these materials operate near

PdAu₆₀

opt

PtAu₆₀

= 0.37 V vs

opt

their optimum potentials (Φ

= 0.33, Φ

These ﬁndings yield far-reaching implications for both

fundamental studies in electrocatalysis or thermocatalysis and

the technological application of catalysis. This work focuses on

oxygen reduction, but this analysis may extend to numerous

liquid-phase reactions that involve heterolytic hydrogen

transfer, such as CO₂reduction and alcohol oxidation.^3,4,56,57

The methodology outlined here also provides guidelines to

design materials and reaction conditions that increase the

selectivity and reaction rates in other systems. Speciﬁcally,

investigators may design heterogeneous catalysts using electro-

chemical methods to independently study the barriers and

charge transfer coeﬃcients of the half-reactions involved in

various redox chemistries. These measurements should also

allow the prediction of thermocatalytic behavior through a

careful analysis of electrochemical kinetic parameters. This

work presents opportunities for catalyst discovery using

electrochemical methods that are amenable to high-throughput

experimentation. Finally, the control of electrode potentials

and reactant activities may allow access to highly selective and

reactive catalyst states for desired products.

NHE) and provide similar selectivities toward H₂O₂formation

(∼50−65%). These data suggest that even higher ORR rates

and selectivities could be achieved in the direct synthesis

system if the PdAu₆₀and PdAu₆₀catalysts operated at more

negative potentials (Φ^op= 0.33−0.23, Figure 8c). Thus, a

higher HOR rate could further increase both the H₂O₂

formation rate and selectivity.

Overall, these observations on PtAu and PdAu alloys help

inform the design of catalytic materials for the direct synthesis

of H₂O₂. Speciﬁcally, catalysts should contain sites that readily

activate and oxidize hydrogen (e.g., Pd, Pt) to have an

appreciable H₂O₂formation rate under thermochemical

conditions. Our analysis also shows that the HOR reactivity

of materials can lower their operating potential, indirectly

increasing their H₂O₂selectivity by pushing it toward Φ_opt.

Similarly, these materials must selectively reduce oxygen

toward H₂O₂versus H₂O by presenting high barriers toward

the O−O bond dissociation pathways. To achieve this end,

metal nanoparticles must contain reactive moieties that bind

but do not dissociate dioxygen intermediates, such as

monomeric Pd or Pt sites within a Au substrate. Thus, high-

performance catalysts should balance 2e⁻ORR and HOR rates

so that they operate near their optimal potential and achieve

their maximum possible selectivity.

ASSOCIATED CONTENT

■

sı

* Supporting Information

The Supporting Information is available free of charge at

https://pubs.acs.org/doi/10.1021/jacs.0c13399.

4. CONCLUSIONS

Characterization of catalyst materials by TEM, EDXRF,

and ICP, open-circuit potentiometry measurements to

determine operating potentials of catalysts in a high

pressure electrochemical cell, which reﬂect thermocata-

lytic conditions, Koutcky−Levich and Tafel analysis of

In this study, we present the relationship between electro-

catalysis and thermocatalysis in aqueous oxygen reduction

chemistry. We show how to predict the operating potential,

reactivity, and H₂O₂selectivity on metal nanoparticles under

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(5) Samanta, C. Direct synthesis of hydrogen peroxide from

hydrogen and oxygen: an overview of recent developments in the

process. Appl. Catal., A 2008, 350 (2), 133−149.

electrochemical measurements of the HOR and ORR,

mathematical derivations for the Nernst equations,

hydrogen adsorption and oxidation kinetics, formation

rates of H₂O₂and H₂O formation under thermocatalytic

conditions, and H₂O₂selectivity over a broad range of

potentials, hydrogen pressures, and temperatures (PDF)

(6) Siahrostami, S.; Verdaguer-Casadevall, A.; Karamad, M.; Deiana,

D.; Malacrida, P.; Wickman, B.; Escudero-Escribano, M.; Paoli, E. A.;

Frydendal, R.; Hansen, T. W.; Chorkendorff, I.; Stephens, I. E. L.;

Rossmeisl, J. Enabling direct H₂O₂production through rational

electrocatalyst design. Nat. Mater. 2013, 12 (12), 1137−1143.

(7) Holewinski, A.; Linic, S. Elementary mechanisms in electro-

catalysis: Revisiting the ORR Tafel slope. J. Electrochem. Soc. 2012,

159 (11), H864−H870.

AUTHOR INFORMATION

Corresponding Authors

■

Joaquín Rodríguez-López − Department of Chemistry,

University of Illinois at Urbana−Champaign, Urbana,

Illinois 61801, United States; orcid.org/0000-0003-

4346-4668; Email: joaquinr@illinois.edu

David W. Flaherty − Department of Chemical and

Biomolecular Engineering, University of Illinois at

Urbana−Champaign, Urbana, Illinois 61801, United States;

orcid.org/0000-0002-0567-8481; Email: dw ﬂ hrty@

illinois.edu

(8) Ntainjua N., E.; Edwards, J. K.; Carley, A. F.; Lopez-Sanchez, J.

A.; Moulijn, J. A.; Herzing, A. A.; Kiely, C. J.; Hutchings, G. J. The

role of the support in achieving high selectivity in the direct formation

of hydrogen peroxide. Green Chem. 2008, 10 (11), 1162−1169.

(9) Ford, D. C.; Nilekar, A. U.; Xu, Y.; Mavrikakis, M. Partial and

complete reduction of O₂by hydrogen on transition metal surfaces.

Surf. Sci. 2010, 604 (19−20), 1565−1575.

(10) Rankin, R. B.; Greeley, J. Trends in selective hydrogen peroxide

production on transition metal surfaces from first principles. ACS

Catal. 2012, 2 (12), 2664−2672.

(11) Wilson, N. M.; Flaherty, D. W. Mechanism for the direct

synthesis of H₂O₂on Pd clusters: heterolytic reaction pathways at the

liquid-solid interface. J. Am. Chem. Soc. 2016, 138 (2), 574−586.

(12) Adams, J. S.; Chemburkar, A.; Priyadarshini, P.; Ricciardulli, T.;

Lu, Y.; Maliekkal, V.; Sampath, A.; Winikoff, S.; Karim, A. M.;

Neurock, M.; Flaherty, D. W. Solvent molecules form surface redox

mediators in situ and cocatalyze O2 reduction on Pd. Science 2021,

371, 626−632.

Authors

Jason S. Adams − Department of Chemical and Biomolecular

Engineering, University of Illinois at Urbana−Champaign,

Urbana, Illinois 61801, United States; orcid.org/0000-

0001-5320-200X

Matthew L. Kromer − Department of Chemistry, University of

Illinois at Urbana−Champaign, Urbana, Illinois 61801,

United States

(13) Wilson, N. M.; Schroder, J.; Priyadarshini, P.; Bregante, D. T.;

Kunz, S.; Flaherty, D. W. Direct synthesis of H₂O₂on PdZn

nanoparticles: The impact of electronic modifications and hetero-

geneity of active sites. J. Catal. 2018, 368, 261−274.

Complete contact information is available at:

https://pubs.acs.org/10.1021/jacs.0c13399

Author Contributions

(14) Bard, A. J.; Faulkner, L. R. Electrochemical Methods:

Fundamentals and Applications, 2nd ed.; Wiley: New York, 2001; pp

341−344.

^§J.S.A. and M.L.K. contributed equally to the paper.

Notes

(15) Shinagawa, T.; Garcia-Esparza, A. T.; Takanabe, K. Insight on

Tafel slopes from a microkinetic analysis of aqueous electrocatalysis

for energy conversion. Sci. Rep. 2015, 5, 13801.

The authors declare no competing ﬁnancial interest.

ACKNOWLEDGMENTS

■

(16) Wilson, N. M.; Priyadarshini, P.; Kunz, S.; Flaherty, D. W.

Direct synthesis of H₂O₂on Pd and Au_xPd₁clusters: Understanding

the effects of alloying Pd with Au. J. Catal. 2018, 357, 163−175.

(17) Fernandez, J. L.; White, J. M.; Sun, Y. M.; Tang, W. J.;

Henkelman, G.; Bard, A. J. Characterization and theory of

electrocatalysts based on scanning electrochemical microscopy

screening methods. Langmuir 2006, 22 (25), 10426−10431.

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Fernandes, J.; Ribeiro, F. R. Estimation of catalyst deactivation

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Effect of Nafion loading. J. Electrochem. Soc. 2003, 150 (11), C745.

(21) Kocha, S. S.; Zack, J. W.; Alia, S. M.; Neyerlin, K. C.; Pivovar,

B. S. Influence of Ink Composition on the Electrochemical Properties

of Pt/C Electrocatalysts. ECS Trans. 2013, 50 (2), 1475−1485.

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We acknowledge generous funding to support this work

provided by the Energy & Biosciences Institute through the

EBI-Shell program and support from the National Science

Foundation (CBET-1511819 and CCI-1740656). The authors

also acknowledge stimulating discussions with Drs. Sander Van

Bavel, Andrew Horton, and Sumit Verma of Royal Dutch Shell.

J.S.A. was supported by a National Science Foundation

Graduate Research Fellowship (DGE-1144245). Portions of

this work were carried out in part in the Materials Research

Laboratory Central Research Facilities and School of Chemical

Sciences Microanalysis Laboratory at the University of Illinois.

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J. Am. Chem. Soc. 2021, 143, 7940−7957

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Unifying Concepts in Electro- And Thermocatalysis toward Hydrogen Peroxide Production

DOI: 10.1021/jacs.0c13399

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