Kinetics of NH3 Desorption and Diffusion on Pt: Implications for the Ostwald Process.

Kine ics o NH3Deso p ion and Diffusion on P : Implica ions o he
Os wald P ocess
Dmi iy Bo odin, Igo Rahino , Oihana Galpa so o, Jan Finge hu , Michael Schwa ze , Kai Golib zuch,
Geo gios Skoula akis, Daniel J. Aue bach, Alexande Kand a senka, Di k Schwa ze ,
Theo anis N. Ki sopoulos,*and Alec M. Wod ke*
Ci e This: J. Am. Chem. Soc. 2021, 143, 18305−18316
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sıSuppo ing In o ma ion
ABSTRACT: We epo accu a e ime- esol ed measu emen s o
NH3deso p ion om P (111) and P (332) and use hese esul s o
de e mine elemen a y a e cons an s o deso p ion om s eps,
om (111) e ace si es and o diffusion on (111) e aces.
Modeling he ex ac ed a e cons an s wi h ansi ion s a e heo y,
we find ha con en ional models o pa i ion unc ions, which
ely on uncoupled deg ees o eedom (DOFs), a e no able o
ep oduce he expe imen al obse a ions. The esul s can be
ep oduced using a mo e sophis ica ed pa i ion unc ion, which
couples DOFs ha a e mos sensi i e o NH3 ansla ion pa allel o
he su ace; his app oach yields accu a e alues o he NH3
binding ene gy o P (111) (1.13 ±0.02 eV) and he diffusion
ba ie (0.71 ±0.04 eV). In addi ion, we de e mine NH3
’s binding
ene gy p e e ence o s eps o e e aces on P (0.23 ±0.03 eV). The a io o he diffusion ba ie o deso p ion ene gy is ∼0.65, in
iola ion o he so-called 12% ule. Using ou de i ed diffusion/deso p ion a es, we explain why es ablished a e models o he
Os wald p ocess inco ec ly p edic low selec i i y and yields o NO unde ypical eac o ope a ing condi ions. Ou esul s sugges
ha mean-field kine ics models ha e limi ed applicabili y o modeling he Os wald p ocess.
1. INTRODUCTION
The Os wald p ocess is a c i ically impo an s epping s one o
indus ial p oduc ion o a ificial e ilize s, con e ing
ammonia (NH3) o ni ic acid (HNO3) in he p esence o
oxygen and wa e . The key o i s success is he efficien
oxida ion o NH3 o ni ic oxide (NO) on a P ca alys . In
indus y, he Os wald p ocess is conduc ed a empe a u es o
1050−1250 K and o al p essu es be ween 1 and 12 ba wi h
an ammonia o ai a io o 1:10.
1
To ini ia e he oxida ion,
NH3adso bs wi h high p obabili y o he majo i y e ace si e
and mus hen diffuse o low-coo dina ion s ep si es, whe e i is
able o eac wi h oxygen.
2−8
Thus, he compe i ion be ween
deso p ion and diffusion and he equilib ium be ween
adso p ion a s ep and e ace si es a e c i ical ac o s in
de e mining eac ion p obabili y; ye he compe i ion be ween
NH3deso p ion and diffusion on P has ne e been
in es iga ed. The e is no e en an expe imen al consensus
conce ning such a basic pa ame e as he binding ene gy o
NH3a P (111). Molecula beam elaxa ion spec ome y
(MBRS)
9
yielded a binding ene gy o 0.68 eV, whe eas analysis
o collision-induced deso p ion (CID) expe imen s
10
led o a
alue o 1.1 eV. Lase -induced deso p ion (LID)
11
s udies
sugges a binding ene gy o ∼0.8 eV, consis en wi h esul s
ob ained wi h empe a u e-p og ammed deso p ion
(TPD).
12,13
Analysis o TPD da a also e eals a weakening
NH3−P bond wi h inc easing NH3co e age and con adic s
he expec a ion one migh in e om MBRS, conduc ed a low
co e ages, and CID, conduc ed a high co e ages. Ob iously,
he unce ain y among he expe imen al de e mina ions o he
binding ene gy p ecludes any se ious compa ison wi h heo y.
This is p esumably he eason why he NH3binding ene gy a
P (111), despi e i s impo ance, is s ill missing om
expe imen al benchma k ables.
14
Fu he mo e, eal ca alys s
exhibi a di e si y o ac i e si es, including s eps and kinks, and
he ela i e binding s eng hs o molecules o diffe en si es can
de e mine he eac an ’s abili y o compe e wi h o he
molecules o occupy he ac i e si e(s). Sadly, no eliable si e-
specific binding ene gies o NH3on P ha e ye been epo ed.
The lack o eliable quan i a i e in o ma ion conce ning
NH3/P in e ac ions led o su oga e empi ically op imized
models, which un o una ely lack uni e sali y and ans-
Recei ed: Sep embe 1, 2021
Published: Oc obe 21, 2021
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e abili y. Ne e heless, he Os wald p ocess has been modeled
using ansi ion s a e heo y (TST) and densi y unc ional
heo y (DFT) o calcula e he ele an a e pa ame e s on
single c ys al model ca alys s like P (111),
2,15
P (100),
16
and
P (211)
2,4,17
ha a e hen used o elucida e he op imum
p ocess condi ions. Such models ha e a ely been alida ed by
compa ison o expe imen , o which he e a e ew. One o he
bes known models, equen ly used in eac o simula ions o
he Os wald p ocess, was de eloped by K aehne and Bae ns
18
(KB). The KB kine ics model elies on a mechanism de i ed
om DFT calcula ions on P (111) by Offe mans e al.
15
and
op imizing he a e pa ame e s o achie e ag eemen wi h he
expe imen al a es o NH3oxida ion on polyc ys alline P a 1
mba and 600 K. Expe imen al obse a ions could only be
explained assuming ha adso bed NH3(NH3*) and O*
occupy diffe en binding si es. These si es we e assigned o
hose ound on P (111) single c ys alson op o NH3*and
cc hollow o O*and NO*.
18
O he s uc u al ea u es like
s eps, which a e known o be mo e eac i e han e aces,
2,6,7
we e no conside ed. Scheue e al. poin ed ou ha he KB
mechanism lacks quan i a i e ans e abili y o he ammonia
slip
19
egime, whe e NH3 eac s wi h O2, o ming p edom-
inan ly N2and H2O. The lack o ans e abili y is likely due o
he use o a e cons an s, which do no eflec he co ec
elemen a y p ocesses. Fo example, he KB mechanism
includes a 0.65 eV adso p ion ba ie o NO on P , in
con adic ion o ou cu en unde s anding ha NO−P
adso p ion is ba ie less.
20,21
Beyond his, he a e pa ame e s
used o desc ibe NH3deso p ion in he KB model include an
unphysically low p e ac o in he A henius exp ession,
sugges ing he en opy o P -adso bed NH3is highe han
ha o he gas-phase molecule. Clea ly, he e is a p essing need
o eliable in o ma ion on si e-specific binding ene gies and
en opies o NH3and o he molecules on P su aces.
In his wo k, we epo elemen a y he mal a e cons an s o
NH3deso p ion om and diffusion on P (111) and P (332) a
su ace empe a u es 430 ≤T≤620 K, de i ed om kine ic
da a ob ained wi h he eloci y- esol ed kine ics me hod.
22
We
find ha he kine ic aces o he deso p ion a e o NH3 om
a P (111) su ace do no ollow fi s -o de kine ics bu a e
ins ead biexponen ial. This is a ibu ed o he excep ionally
high diffusion ba ie o NH3on he (111) e ace ha slows
down he diffusion ac oss he e aces owa d he s eps:
molecules ha deso b om he e ace p io o eaching he
s eps comp ise he as componen o he biexponen ial,
whe eas molecules ha make con ac wi h he s eps comp ise
he slow componen . We globally fi deso p ion da a om
P (111)s ep densi y 0.4 ±0.2% monolaye (ML)and
P (332)s ep densi y 16.7%MLusing a kine ics model ha
includes NH3*deso p ion om e aces and s eps, hopping
ac oss e aces and hopping om s eps o e aces. F om he
de i ed a e cons an s, we can accu a ely compu e he
deso p ion a e o NH3 om P su aces as well as he
popula ion o s ep and e ace si es as a unc ion o s ep
densi y, p essu e, and empe a u e.
The high quali y o he kine ic da a o e a wide ange o
empe a u es p o ides a g ea deal o in o ma ion h ough
applica ion o TST, bu he mos common implemen a ions o
TST epo ed so a canno ep oduce ou esul s. This
p oblem is sol ed by de eloping a semiempi ical pa i ion
unc ion o adso bed ammonia ha includes he coupling
be ween se e al modes ha ac i ely pa icipa e in diffusion.
Using his o m o TST, we ob ain an excellen fi o he
measu ed a e cons an s as well as NH3
’s binding ene gy on
e aces o P (111) (1.13 ±0.02 eV), he diffusion ba ie
be ween binding si es o P (111) (0.71 ±0.04 eV), and he
deg ee o ene ge ic s abiliza ion o NH3a s eps compa ed o
e aces (0.23 ±0.03 eV). These esul s a e in good ag eemen
wi h DFT calcula ions ha we also epo he e. No e he
diffusion ba ie o his sys em is ∼65% o he binding ene gy,
a s ong iola ion o he so-called 12% ule,
23,24
pos ula ing
ha diffusion ba ie cons i u es a a he small ac ion o a
binding ene gy. Clea ly, he 12% ule should be used wi h
cau ion.
We also used DFT calcula ions o in es iga e he co e age
dependence o he NH3deso p ion a e; ou esul s a e able o
ep oduce p e iously epo ed TPD expe imen s ca ied ou
o NH3/P (111),
12
conduc ed a much lowe su ace
empe a u es. This success o ou app oach o e such a wide
empe a u e ange jus ifies modeling ca alys NH3co e ages a
high empe a u es and p essu es ypical o Os wald ca alysis
eac o s. Ou model p edic s NH3co e ages below ∼10%,
whe eas es ablished eac o models p edic ully co e ed
ca alys s a all condi ions ele an o he Os wald p ocess.
We belie e his explains why some o he es ablished eac o
models end o o e es ima e he deg ee o NH3slippage a
p ocess- ele an condi ions.
18
Finally, we find ha he de i ed
deso p ion and diffusion a es om his wo k sugges ha he
mean-field app oxima ion, equen ly employed o model
eac ion a es, is no app op ia e o desc ip ion o NH3
eac i i y on P unde indus ially ele an condi ions.
2. RESULTS
The eloci y- esol ed kine ics echnique has been desc ibed in
de ail elsewhe e.
22,25,26
Compa ed o o he kine ics me hods
applied o su ace p ocesses, i has he ad an age o p o iding
ime- esol ed deso p ion flux di ec ly, as NH3
’s eloci y- and
angle- esol ed densi y is ob ained as a unc ion o i s su ace
esidence ime using ion imaging. B iefly, NH3is deposi ed a a
P su ace o known empe a u e using a sho (∼35 μs)
molecula beam pulse o ini ia e he he mal deso p ion
p ocess. The flux o deso bing ammonia (∝d[NH3*]/d )is
ob ained as a unc ion o esidence ime by scanning he delay
be ween he molecula beam pulse and an ioniza ion lase
pulse. The beam-lase delay is easily con e ed o su ace
esidence ime h ough knowledge o he molecule’s speed.
Toge he his yields he kine ic ace, defined as he flux o
ammonia lea ing he su ace e sus esidence ime. A each
alue o ime, eloci y- esol ed kine ics p o ides no only he
kine ic ace bu also, in addi ion, he speed and angula
dis ibu ions o he deso bing ammonia molecules. See sec ion
5.1 o u he de ails o he me hods used o hese
measu emen s.
We ob ained he speed dis ibu ions o NH3deso p ion
om bo h P (111) and (332) a se e al su ace empe a u es,
TS(Suppo ing In o ma ion (SI), sec ion S1). We fi hese o
Maxwell−Bol zmann dis ibu ions, ex ac ing an effec i e
ansla ional empe a u e o he deso bing molecules, T .
Fo expe imen s wi h P (332), T was ound o be equal o TS;
whe eas, o P (111) T was less han TS. Based on de ailed
balance,
27
hese esul s immedia ely indica e ha NH3
adso p ion o P has no ac i a ion ba ie and, he e o e, ha
he binding ene gy is equal o he deso p ion ene gy.
Fu he mo e, we also ob ain he shape o he s icking
p obabili y cu e as a unc ion o kine ic ene gy S(E ), and
by assuming S(E =0) obe1,
28
we ob ain he absolu e
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quan i y S(E ). This is used o ob ain he he mal s icking
p obabili y ⟨S0⟩(T) be ween 0 and 2000 K, which is shown in
sec ion S2 in he SI. A p e ious epo a a single empe a u e
9
ag ees well wi h ou esul s.
We also ob ained kine ic aces o NH3deso p ion om
P (111) and P (332), which a e shown on a loga i hmic scale
a nine su ace empe a u es in Figu e 1. The sha p, ea ly ime
(fi s 0.1 ms) ea u e is a esidual NH3backg ound om he
di ec ly sca e ed beam. I is independen o su ace empe -
a u e and exhibi s a na ow angula dis ibu ion peaking close
o he specula angle. The dominan con ibu ion o he
obse ed signal is empe a u e-dependen and a ises om
he mally deso bing NH3. I has a b oad angula dis ibu ion
(∼cos(θ)), whe e θis he angle wi h espec o he su ace
no mal. The NH3deso p ion a e om P (332) ollows fi s -
o de kine ics as expec ed o a simple deso p ion p ocess;
howe e , NH3deso bing om P (111) wi h 0.4 ±0.2% s eps
is biexponen ial, wi h a as (majo ) and a slow (mino )
componen . We epea ed he deso p ion expe imen s a a
P (111) su ace wi h ewe s eps and ound ha he slow
componen could be e en u he educed (see sec ion S3 in
he SI). No ice ha , when compa ed a he same empe a u e,
he majo componen o P (111) da a is as e han deso p ion
om P (332). This indica es ha NH3has an inc eased
esidence ime on highly s epped su aces.
Figu e 2 shows schema ically he ene gy landscape and key
elemen a y p ocesses, wi h hei a e cons an s, o a kine ics
model capable o desc ibing NH3diffusion and deso p ion a
P su aces as a unc ion o s ep densi y. The model is one-
dimensional desc ibing diffusion pe pendicula o s eps only.
Each a e cons an is pa ame ized in an A henius o m. The
sho ime beha io o he kine ic ace, ep esen ing he di ec
sca e ing, is modeled wi h a empe a u e-independen model
based on he a i al ime dis ibu ion o he NH3a he su ace.
We use pe iodic bounda y condi ions and make he model
applicable o diffe en s ep densi ies by a ying he numbe o
e ace si es sepa a ing he s eps. Using his diffusion−
deso p ion kine ics model (see sec ion S4.2 o he SI o
de ails), we fi he measu ed deso p ion a es om P (111)
and P (332) simul aneously a all empe a u es (see sec ion
S4.3 o he SI o de ails). The fi , shown as dashed (−−) and
dash-do ed (−·−) lines in Figu e 1, is excellen . The six
independen ly de i ed A henius a e pa ame e s and hei
unce ain ies a e p esen ed in Table 1.
Using he alues o Table 1,wesimula edhowNH
3
deso p ion would look in he absence o s eps (blue do ed
Figu e 1. Kine ic aces o NH3deso bing om P (111) (+) and
P (332) (×) o su ace empe a u es be ween 463 and 583 K. The
s ep densi y o he P (111) is 0.4 ±0.2%ML and o P (332) is 16.7%
ML. The ligh blue dashed (−−) and dash-do ed (−·−) lines show
he global fi o he expe imen al kine ic da a o P (111) and
P (332), espec i ely. The shaded egions indica e he model
unce ain y associa ed wi h he s ep densi y o he P (111) su ace.
The blue do ed line (···) indica es he model’s p edic ion o NH3
deso p ion a e om a s ep- ee (ideal) P (111) su ace.
Figu e 2. Schema ic o e iew o he elemen a y p ocesses (g ay)
included and ene gy pa ame e s (black) ex ac ed om he
deso p ion−diffusion kine ics model. S eps and e aces a e indica ed
by he le e S and T, espec i ely. The NH3binding ene gy a (111)
e aces o P is E0,d
T= 1.13 ±0.02 eV, he si e- o-si e hopping ba ie
is E0,h
T= 0.71 ±0.04 eV, and he ene gy p e e ence o s eps is ΔEST =
0.23 ±0.03 eV. Following a simila s a egy as desc ibed in e 20,we
include fi e elemen a y p ocesses wi h fi s -o de a e cons an s: (1)
hopping be ween adjacen e ace si es, kh
T; (2) hopping om e ace
o s ep si es, which is assumed o be he same as kh
T; (3) hopping om
s ep o e ace si es, kh
S; (4) deso p ion om e ace si es kd
T; and (5)
deso p ion om s ep si es, kd
S. We no e ha kd
Sdesc ibing p ocess (5)
is no an independen a e cons an , kd
S=kd
Tkh
S/kh
T; see sec ion S4.1 o
he SI.
Table 1. Ra e Cons an s o Deso p ion and Diffusion o
Ammonia on Pla inum
a
,
b
elemen a y a e cons an s fi ed pa ame e s fi esul s
kd
T(T)Ea,d
T/eV 1.09 ±0.02
log10(Ad
T/s−1) 14.8 ±0.2
kh
S(T)ΔEST/eV
c
0.23 ±0.03
log10(Ah
S/s−1) 13.7 ±0.6
kh
T(T)Ea,h
T/eV 0.73 ±0.04
log10(Ah
T/s−1) 13.6 ±0.4
de i ed quan i ies
kd
S(T)=kd
Tkh
S/kh
TEa,d
S/eV 1.32 ±0.04
log10(Ad
S/s−1) 14.9 ±0.6
DT(T)
d
log10(D0
T/cm2s−1)−1.9 ±0.4
a
Resul s we e ob ained om he global fi o he kine ics model o
expe imen al deso p ion a es om P (111) and P (332).
b
The
elemen a y a e cons an s a e pa ame ized acco ding o he A henius
equa ion: k(T)=Aexp(−Ea/kBT).
c
Ea,h
S=Ea,h
T+ΔEST. Since Ah
S≈Ah
T,
he diffe ence o ac i a ion ene gies ΔEST is nea ly equal o he
diffe ence o binding ene gies ΔE0, ST.
d
=−
i
k
j
j
jy
{
z
z
z
D
TD( ) exp E
kT
T0
Ta,h
T
B,
whe e D0
Tis de i ed om Ah
T ollowing e 29.
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18307
lines (···)inFigu e 1). This shows ha he as componen o
he biexponen ial decay eflec s di ec deso p ion om e ace
si es. In ligh o he ela i ely la ge s ep s abiliza ion ene gy
ΔEST also shown in Table 1, i becomes clea why deso p ion
om P (332) is slowe han he as componen o deso p ion
om P (111). Table 1 also shows he compu ed p e ac o o
he e ace diffusion cons an DT(T) de i ed om he hopping
a e cons an kh
T(T) ollowing e 29 as well as he a e cons an
o di ec deso p ion om s eps kd
S(T), which is de i ed om
he o he a e cons an s. No ice ha he A henius p e ac o
o e ace deso p ion and di ec s ep deso p ion a e nea ly
equal; ha is, he en opy o he NH3is nea ly he same o
hese wo binding si es. This is a s iking esul and means ha
he ammonia molecule is highly localized a e ace si es, a
conclusion ha is consis en wi h he la ge ac i a ion ene gy
ound o e ace hopping Ea,h
T= 0.73 ±0.04 eV.
Combining kine ic da a wi h DFT pa ame ized TST can be
highly use ul. Thus, we pe o med a a ie y o DFT
calcula ions using he Pe dew−Bu ke−E nze ho (PBE)
exchange-co ela ion unc ional.
30
Ou expe imen s a e
ele an o he ze o-co e age limi ; hence, we elied mos
hea ily on DFT calcula ions ca ied ou using a pe iodic 4 ×4
uni cell. We find ha he on- op si e is he mos s able binding
si e o NH3*a P (111) wi h a (ze o-poin ene gy co ec ed)
binding ene gy o 0.86 eV a 0.06 ML. In addi ion, we
pe o med calcula ions wi h 2−4NH
3*molecules placed in
he cell o p oduce co e ages om 0.12 o 0.25 ML. We
calcula ed he NH3*binding ene gy a P (111) in each case
and find i o dec eases linea ly wi h inc easing co e age wi h a
slope o α=−1.61 eV/ML. Based on his finding, we
de e mine a ze o-co e age binding ene gy o 0.95 eV (see
sec ion S5 o he SI). Simila ly, we calcula e he binding ene gy
a P (332) and, by compa ison o P (111), find ha he s ep
s abiliza ion is 0.30 eV.
In addi ion o he binding ene gy calcula ions, we pe o med
analysis o he minimum ene gy pa hway o hopping be ween
on- op binding si es o P (111). We use he climbing image
nudged elas ic band (CI-NEB) me hod
31
o loca e he TS ha
we ound a he b idge si e. We ob ain a ze o-poin ene gy
co ec ed hopping ba ie o 0.70 eV (0.52 eV) o he 4 ×4(2
×2) supe cell. We also pe o med calcula ions o he ha monic
equencies a he on- op mos s able binding si e and o he
ansi ion s a es ound a he b idge si e (see Table 2).
3. FURTHER ANALYSIS AND DISCUSSION
3.1. Two App oaches o he Adso ba e Pa i ion
Func ion. In his sec ion, we analyze he de i ed he mal a e
cons an s in e ms o ansi ion s a e heo y. This allows us o
de i e undamen al quan i ies such as he deso p ion ene gy
and he diffusion ba ie heigh . We elabo a e de ailed
exp essions o he adso ba e pa i ion unc ion in wo ways.
The pa i ion unc ion is no mally conside ed a p oduc o
pa i ion unc ions o he indi idual deg ees o eedom
(DOFs). We show he e ha his uncoupled TST app oach ails
o ep oduce ou expe imen al esul s. We hen in oduce a
pa i ion unc ion which makes a be e accoun ing o he s a e
coun when some o he DOFs a e coupled (coupled TST).
Coupled modes a e iden ified h ough DFT calcula ions o
NH3
’s minimum ene gy pa hway o hopping whe e we find
ha hinde ed ansla ion and us a ed o a ional modes a e
ac i ely pa icipa ing in he si e- o-si e exchange. This is
eflec ed by an inc ease o su ace−molecule dis ance and
il ing o NH3
’s symme y axis along he minimum ene gy
pa hway. Also he associa ed ib a ional equencies dec ease
a he ansi ion s a e o hopping by a ac o o 2 o 3 (see
Table 2), eflec ing hei impo ance o accu a e desc ip ion o
he adso ba e en opy. This app oach allows us o explain he
empe a u e dependence o he a e cons an s p ecisely o e
he en i e empe a u e ange. This hen p o ides he mos
accu a e ene gy ba ie s o NH3si e- o-si e hopping and
deso p ion om P (111) p esen ly a ailable.
The gene al exp ession o he TST a e cons an o
deso p ion o diffusion is
=−
⧧i
k
j
j
j
j
j
y
{
z
z
z
z
z
kT kT
h
Q
Q
E
kT
() exp
TST B
ad
0
B(1)
whe e Qad is he pa i ion unc ions o he ammonia adso ba e,
Q⧧is he pa i ion unc ion o he ansi ion s a e, and E0is
he ze o-poin ene gy co ec ed ba ie heigh . Highly accu a e
e alua ion o Qad is o en unnecessa y in analyzing su ace
deso p ion a e da a as he unce ain y in he expe imen al
p e ac o o en exceeds an o de o magni ude
32
o in many
cases is no measu ed a all.
8
When analyzing high-quali y
kine ic da a as ob ained wi h eloci y- esol ed kine ics, Qad
becomes a sensi i e p obe o he NH3/P in e ac ions.
Inapp op ia e app oxima ions lead o de ec able de ia ions
om he measu ed deso p ion a es. In he ollowing, we
demons a e he deficiencies o uncoupled TST and he
ad an ages o coupled TST o he compu a ion o Qad.
The fi s app oach, uncoupled TST (uTST), uses a
sophis ica ed and es ablished app oach. He e, we base i on
he app oxima ion o a hinde ed ansla o ,
33
which is
conside ed as one o he mo e accu a e ways o compu e
Qad.
34
He e, he pa i ion unc ions o Tx,ya e desc ibed using
a model po en ial, pa ame ized using DFT-calcula ed
hinde ed ansla ional equencies (see Table 2) and he
Table 2. Resul s o DFT Calcula ions Pe o med o This
Wo k: Ha monic F equencies o NH3*a he Mos S able
Binding Si e (On-Top) and on he T ansi ion S a e (TS) o
Hopping (B idge) Ob ained om a 4 ×4[2×2 ] Supe cell
Using he PBE Exchange-Co ela ion Func ional
a
mode calcula ed ha monic equencies/cm−1
i( gas) desc ip ion on- op TS o hopping
(b idge)
1(3a) asym. s e ch 3483.1 [3484.4] 3546.7 [3550.5]
2(3b) asym. s e ch 3481.5 [3482.8] 3540.1 [3545.6]
3(1) sym. s e ch 3356.8 [3342.7] 3400.6 [3397.4]
4(4a) asym. bending 1572.5 [1551.3] 1583.3 [1586.8]
5(4b) asym. bending 1571.5 [1549.7] 1581.3 [1577.9]
umb (2) umb ella mode 1142.0 [1055.2] 930.0 [856.2]
ee C3-axis
o a ion -[-] -[-]
Rx us a ed o a ion 672.7 [636.3] 325.8 [131.3]
Ry us a ed o a ion 672.4 [636.3] 269.9 [109.5]
Tzhinde ed
ansla ion 357.8 [338.3] 127.5 [ 45.9 ]
Txhinde ed
ansla ion 122.8 [109.5] 190.9i[176.4i]
Tyhinde ed
ansla ion 119.9 [109.5] 68.2 [-]
a
The imagina y equency in Txa he TS eme ges om he
degene acy wi h he hopping coo dina e. In his wo k we numbe ed
he in e nal modes o adso bed NH3 om high o low equency. The
con en ional nomencla u e om gas-phase ib a ional spec oscopy is
p o ided in pa en heses o con enience.
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expe imen ally de i ed e ace hopping ba ie s (see sec ion
3.3). The hinde ed ansla ional pa i ion unc ion exploi s an
es ablished in e pola ion scheme, ensu ing i s p ope beha io
a low and high empe a u es.
21,33,35
We ea NH3 o a ion
a ound i s symme y axis as a ee o a ion, jus ified by ou
DFT esul s and in ag eemen wi h p e ious heo e ical
wo k.
36
The emaining DOFs a e desc ibed by ha monic
oscilla o s. Fo uTST, we use DFT-calcula ed equencies o
NH3bound a i s mos s able binding si e (see Table 2),
consis en wi h how his app oach is con en ionally applied
( o u he de ails, see sec ion S6.1 o he SI).
The uTST assumes ha all DOFs a e decoupled, making Qad
a p oduc o he pa i ion unc ions o each DOF sensi i e only
o he s uc u e o he molecule a he on- op binding si e.
Howe e , when NH3*mig a es o e a diffusion ba ie , i s
binding s eng h a he su ace weakens, and consequen ly, he
ib a ional modes, especially hose ha s ongly influence he
o ien ed molecule−su ace binding (Rx,y,Tz, and umb), so en
subs an ially (see Table 2). Since hese modes ha e low
equencies, u he equency educ ion has a la ge impac on
he he mally accessible densi y o s a es.
To accoun o his effec , we de eloped a second app oach,
dubbed he ea e as he coupled TST (cTST) model. B iefly,
cTST allows ansla ion pa allel o he su ace o explici ly
so en se e al o ammonia’s ib a ional equencies. This
p ecludes a p oduc o m o Qad. Ins ead, we cons uc a
pa i ion unc ion whe e he ib a ional equencies o se e al
modes ( umb,Rx,Ry, and, Tz) a y along he minimum ene gy
pa hway o si e- o-si e hopping. This app oach desc ibes mo e
ai h ully he bond so ening induced by he mo ion owa d he
diffusion ba ie . O he DOFs a e desc ibed as in uTST model.
The cons uc ion o Qad o he cTST is desc ibed in de ail in
he SI sec ion S6.2. In he nex sec ion, we apply uTST and
cTST o he desc ip ion o deso p ion and hopping a es o
NH3a P (111).
3.2. Analysis o he Deso p ion Ra e Cons an s Using
TST. To ob ain deso p ion a e cons an s om TST, we mus
compu e Q⧧. The mode n o mula ion o TST p esc ibes a
di iding plane ha sepa a es eac an s om p oduc s such ha
e e y ajec o y ha o igina es in he eac an egion o
configu a ion space and e ol es o he p oduc egion mus
pass h ough he di iding plane a leas once. The choice o he
posi ion o he di iding plane can influence he p obabili y o
ec ossing, which in oduces a ec ossing e o o he TST a e.
Fo NH3deso p ion om P , i is con enien o place he
di iding plane a om he su ace, whe e he gas-phase NH3
molecule becomes he ansi ion s a e. This choice o he
ansi ion s a e is con enien , as he he mal s icking coefficien
⟨S0⟩(TS) ob ained abo e se es as he exac ec ossing
co ec ion.
37
Fu he mo e, Q⧧is easily compu ed using
abula ed gas-phase ib a ional equencies and o a ional
cons an s. We ca ied ou his p ocedu e in a simila way o
a ecen epo o NO deso p ion om Pd;
21
also, see sec ion
S6.3 o he SI.
We may hen w i e down a highly accu a e o mula o he
expe imen ally de i ed deso p ion a e cons an s:
=⟨ ⟩kT S Tk T() () ()
d0TST (2)
Using eq 2, we op imized E0 o fi he cTST and uTST model
o he expe imen ally de i ed e ace deso p ion a e
cons an s ed ci cles wi h e o ba s and solid ed line in
Figu e 3a. The ed line is he e ace deso p ion a e cons an
ha we ex ac om he global kine ics model fi (see also
Table 1). Complemen a y o he global fi esul s, we analyze
Figu e 3. (a) NH3deso p ion a e cons an s om P (111) e ace ob ained om global kine ics model fi ( ed line) and om indi idual fi s o he
kine ic aces ( ed ci cles wi h e o ba s; see sec ion S7 o he SI). The ed line is no he A henius fi o he ci cles. Te ace deso p ion a e
cons an s a e compa ed o he uTST (blue do ed) and cTST (blue dashed) models. The fi s -o de deso p ion a e cons an s om P (332) (black
c osses wi h e o ba s) and he co esponding A henius fi (solid black line) a e compa ed wi h a model assuming ha deso p ion happens
di ec ly om s eps (kd
S om Table 1, o ange dash-do ed line) and a model ha desc ibes deso p ion as a “ e ace-assis ed”p ocess including
deso p ion om e aces and s eps (eq 4, g een dash-do -do ed line). (b,c) Compa ison o expe imen ally de i ed A henius ac i a ion ene gy and
p e ac o o e ace deso p ion om P (111) and A henius pa ame e s p edic ed based on uTST (do ed blue line) and cTST (blue dashed line)
models a 530 K (a e age empe a u e o p esen expe imen s). The ed a ows wi h e o ba s esul om global fi o diffusion−deso p ion
kine ics model o expe imen al da a (see SI sec ion S4.3) and a e ep esen ed by he ed line in panel (a). The ed his og ams a e pa ame e
dis ibu ions eme ging om A henius fi (no shown o cla i y) o ed ci cles o panel (a). (d,e) Compa ison o he A henius pa ame e ob ained
om fi s -o de deso p ion a e cons an s om P (332) o a e pa ame e s based on di ec -s ep and “ e ace-assis ed”deso p ion model a 530 K.
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he as decay o each NH3kine ic ace om P (111) ha we
assigned o eflec he e aces’deso p ion (see Figu e 1) and
de i e he ed ci cles om Figu e 3a; see sec ion S7 o he SI
o de ails. The cTST (uTST) yields he blue dashed (do ed)
line in Figu e 3a wi h E0,d
T= 1.13 ±0.02 (1.17) eV. Figu e 3b,c
offe s a clea compa ison o he cTST and uTST models o he
de i ed A henius a e pa ame e s, which accu a ely ep esen
he expe imen al a e cons an s. He e, he ed a ow wi h he
e o ba ep esen s he expe imen al unce ain y o he
A henius ac i a ion ene gy (Figu e 3b) and A henius
p e ac o (Figu e 3c) o e ace deso p ion ob ained om
he global kine ics model fi o he expe imen al da a, see
sec ion S4.3 o he SI o de ails. Complemen ing his, he ed
his og ams display he unce ain y o he e ace deso p ion
A henius a e pa ame e s ha we de i e om an A henius fi
(omi ed in Figu e 3a o cla i y) o he ed ci cles om Figu e
3a. Bo h a e pa ame e s a e accu a ely ep oduced by he
cTST model (blue dashed e ical line), while he uTST model
(blue do ed e ical line) clea ly ails. Specifically, he uTST
p edic s an adso ba e en opy ha is oo low, and hus he
esul ing p e ac o is oo high (Figu e 3c). The ac i a ion
ene gy is hen o ced o be a ificially high o compensa e o
his e o in he p e ac o (Figu e 3b).
Based on his analysis, we ecommend he esul s o he
cTST model (E0,d
T= 1.13 ±0.02 eV) o u u e use as he
ammonia deso p ion ene gy on P (111). This alue ag ees
wi h esul s om CID
10
(1.1 ±0.1 eV), al hough he e o ba
o ha wo k was a ou side chemical accu acy. Resul s om
LID (0.8 eV) a e clea ly incompa ible wi h he p esen wo k.
11
This is likely due o he ac ha hose expe imen s we e done
a ela i ely high co e ages. Despi e wo king a low co e ages,
p e ious MBRS esul s (0.68 eV) a e also incompa ible wi h
ou esul s. The alue o E0,d
T ound wi h eloci y- esol ed
kine ics is in poo ag eemen wi h DFT calcula ions when a
PBE exchange-co ela ion unc ional is used0.95 eVsee
sec ion S5 o he SI. P e ious wo k wi h he PW91 unc ional
38
yielded a alue o ∼1.0 eV, which ag ees only sligh ly be e
wi h he p esen esul s, confi ming simila i ies be ween he
PBE and he PW91 unc ionals.
14
In he global fi o he kine ics model, we ha e also de i ed
ΔEST, he ac i a ion ene gy diffe ence be ween deso p ion o
NH3a s eps and e aces o P . As hese wo p ocesses exhibi
nea ly he same p e ac o , he diffe ence o ac i a ion ene gies
can be se equal o he diffe ence in binding ene gies, ΔE0,ST =
0.23 ±0.03 eV. This compa es well o p e ious TPD wo k
(∼0.2 eV)
8
and ou DFT calcula ions, which p edic an ene gy
p e e ence a s eps o 0.3 eV. These esul s also ha e
implica ions o he mechanism o deso p ion om s eps. In
Figu e 3a, we compa e a model ha nai ely assumes
deso p ion om a s epped su ace, like P (332), ha occu s
di ec ly ha is, diffusion om s eps o e aces is
unimpo an . This clea ly ails o cap u e he expe imen al
obse a ions (o ange lines in Figu e 3a,d,e). This sugges s a
mo e in ica e s ep deso p ion mechanism, whe e bo h s eps
and e aces play a ole. This is discussed u he in sec ion
3.5.1.
3.3. Analysis o he Hopping Ra e Cons an s Using
TST. We also used he cTST and uTST models o desc ibe
NH3si e- o-si e hopping on P (111). He e, we equi e he
pa i ion unc ion o he hopping TS. To compu e ha , we
app oxima e all bu wo DOFs as simple ha monic oscilla o s
(wi h equencies om Table 2). The excep ions a e he NH3*
o a ion a ound i s symme y axis, which is again assumed o
be a ee o a ion, and Ty, which is ea ed as desc ibed in
sec ion S6.4 o he SI. No e ha ansla ion along xd ops ou ,
as his is he hopping coo dina e. We fi s ca y ou his
calcula ion using he DFT-de i ed and ze o-poin ene gy
co ec ed hopping ba ie o 0.70 eV p esen ed abo e. The
modeled cTST and uTST hopping a e cons an s a P (111)
a e shown as blue dashed and blue do ed lines o Figu e 4,
espec i ely, and a e compa ed o he expe imen ally de i ed
hopping a e cons an (black solid line).
Again, cTST esul s a e wi hin ∼30% o he expe imen al
alues. The uTST model p edic s a e cons an s ha a e
sys ema ically ∼2× oo la ge. We no e ha he esidual e o in
he cTST a e cons an is no necessa ily due o an e o in he
DFT ba ie heigh . Ins ead, i could be an indica ion ha a
coupled pa i ion unc ion o he ansi ion s a e is also
equi ed, some hing ha is beyond he scope o his wo k.
Coupling DOFs in he TS would inc ease TS s a e densi ies
and inc ease he hopping a e cons an , possibly leading o
be e ag eemen wi h he expe imen . The use o an
uncoupled pa i ion unc ion o he TS is also likely o be
he eason why he de ia ion o uTST om expe imen is only
a ac o o ∼2due o a compensa ion o e o s aking place in
Qad and Q⧧.
We used wo app oaches o a emp an expe imen al
de e mina ion o he hopping ba ie . In he fi s , we op imized
E0,h
Tin he cTST model o fi ou expe imen al hopping a e
cons an (black solid line o Figu e 4). This led o 0.68 eV,
which ep esen s a lowe limi . See also he ed solid line in
Figu e 4. In he second app oach, we used he DFT hopping
ba ie and de e mined he diffe ence be ween ac i a ion
ene gy and ba ie heigh o hopping, based on he cTST
model; Ea,h
T(500 K) −E0,h
T= 0.017 eV, which we sub ac ed
om he expe imen ally ob ained ac i a ion ene gy o
hopping (Ea,h
T= 0.73 ±0.04; see Table 1). Fo he es ima ion
o he ac i a ion ene gy, we used an a e age empe a u e o ou
Figu e 4. B oad black line shows he de i ed hopping a e cons an s
in he empe a u e ange o ou expe imen s. The ex apola ion o he
de i ed hopping a e cons an based on i s A henius pa ame e s is
shown as he g ay shaded egion ha indica es he unce ain y o
ex apola ion. The blue solid line is he esul o he hopping a e
cons an ha is es ima ed based on he 12% ule (eq 3) sugges ed by
Ma ikakis and co-wo ke s.
23,24
The blue dashed (do ed) line is he
esul o cTST (uTST) modeling o hopping a e cons an using
DFT-calcula ed hopping ba ie s. The ed solid line is he cTST
model using he hopping ba ie fi ed o he expe imen al a e
cons an . The esidual misma ch be ween expe imen and he cTST
model can be explained wi h unce ain ies in he assump ions o he
TS pa i ion unc ions (see ex ).
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P (111) expe imen s (500 K, which a e mos impo an o
ex ac ion o diffusion a es). This yielded an es ima e o he
hopping ene gy ba ie : E0,h
T= 0.71 ±0.04 eV, which also
compa es well wi h he DFT-de i ed hopping ba ie ob ained
wi h he PBE unc ional and he es ima ed lowe limi .
3.4. Commen abou he 12% Rule o Diffusion
Ba ie s. We no ice ha he A henius exp ession-based
p e ac o de i ed o NH3hoppingAh
T=10
13.6±0.4 s−1is
highe han alues conside ed “common”, i.e., 10<13 s−1.
Howe e , his high alue no only is in good ag eemen wi h
DFT and cTST p edic ion o 1013.3 s−1bu also is physically
easonable. When a molecule is posi ioned a a weakly bound
si e, like he TS o hopping, i s in e ac ion wi h he su ace is
weakened, and hus he molecule is mo e likely o ha e an
enhanced densi y o s a es and concomi an highe en opy.
When he hopping ba ie is e y high, he TS is ac ually
simila o a gas-phase molecule. Hence, he hopping p e ac o
will app oach he p e ac o o deso p ion, and he hopping o
he molecule can be imagined o esemble ansien o pa ial
deso p ion, which is he case o NH3on P (111). Con as ing
his o he case o a small hopping ba ie , he adso ba es’
densi y o s a es ha dly changes a he hopping ansi ion s a e
compa ed o he molecule a i s ini ial binding si e. The e o e,
he TST a e cons an can be exp essed using only he
in o ma ion abou he molecule’shinde ed ansla ional
equency, he e, ∼120 cm−1:
=−
⎯→⎯⎯⎯⎯⎯⎯⎯⎯⎯ −
−
i
k
j
j
j
j
j
y
{
z
z
z
z
z
i
k
j
j
j
j
j
y
{
z
z
z
z
z
kT kT
hQ
E
kT
E
kT
() 1exp
@500 K 10 s exp
x
B
qHO
hop,low
B
12.5 1 hop,low
B(3)
The associa ed p e ac o will be in he ange o 1012−13 s−1,
conside ed o be “ ypical”. A simila conclusion was eached by
Ma ikakis and co-wo ke s
23,24
in de eloping he so-called 12%
ule (=Ehop/Ebind) o diffusion ba ie s who a gued ha no
only is he a io o Ehop o Ebind likely o be abou 0.12 bu ha
he p e ac o s o hopping a e commonly 1012−13 s−1.
Ammonia binding o and diffusion on P (111) is an illus a i e
example, emphasizing ha one has o be cau ious wi h d awing
uni e sal conclusions abou scaling ela ions based on s able
si e binding ene gies alone, wi hou conside ing he nuances o
molecula s uc u e. In Figu e 4, we show o compa ison he
hopping a e cons an wi h ba ie es ima ed based on he 12%
ule wi h he co esponding hopping p e ac o om eq 3,
whe e he ailu e o his es ima e becomes e iden .
I had been ealized ea lie ha he choice o he adso ba e
en opy
33,34,39,40
models and inclusion o anha monic
co ec ions
41
has a subs an ial impac on he p edic ion o
he modynamic s a e unc ions ele an o he desc ip ion o
eac ion a es. Howe e , coupling o diffe en DOFs, which we
clea ly show o be impo an o NH3a P , is no mally no
conside ed. While hese p oblems could, o cou se, be sol ed
by demanding cons uc ion o a ull dimensional po en ial
ene gy su ace, i is use ul o de elop a sys ema ic hie a chy o
co ec ion schemes o p o ide an accu a e desc ip ion o
he mal eac ion a es using TST beyond he ha monic
app oxima ion. In ha spi i , he applica ion o he cTST
model, inco po a ing he coupling o in-plane coo dina es o
diffe en DOFs is a good s ep o wa d, especially as i equi es
li le mo e inpu in o ma ion om DFT han is al eady used
o he less sophis ica ed app oaches.
3.5. Implica ions o Modeling o he Os wald
P ocess. The abili y o ammonia o find i s way o s eps is
c i ical o i becoming chemically ac i a ed in he Os wald
p ocess.
2,4,5,7
In p inciple, his may happen by ei he di ec
adso p ion and deso p ion o and om s eps o by adso p ion
a e aces ollowed by diffusion o s eps in compe i ion wi h
deso p ion. The complexi y o he adso p ion/diffusion/
deso p ion o en goes unapp ecia ed. In his sec ion, we ake
up his ma e .
3.5.1. Deso p ion In ol ing Mul iple Ac i e Si es. We ha e
shown ha NH3deso p ion om P (111) is p ima ily due o
deso p ion om e aces, whe eas he deso p ion a e om
P (332) is s ongly influenced by s eps. In Figu e 3a, we show
he ex ac ed fi s -o de a e cons an s o NH3deso p ion om
P (332) (black c osses) and compa e hem o he elemen a y
a e cons an s o di ec deso p ion om s eps, kd
S(o ange
dash-do ed line)di ec deso p ion om s eps ails o explain
expe imen . This is easily unde s ood as molecules bound a
s eps can eadily hop fi s o a e ace si e, whe e deso p ion is
much as e . Simply pu , hopping om s eps o e aces wi h
subsequen deso p ion om e aces in ol es wo low ba ie
p ocesses, whe eas di ec deso p ion om s eps in ol es one
high ba ie p ocess. By assuming a s eady-s a e concen a ion
o ammonia a e aces (condi ions ha a e ensu ed o
P (332) expe imen s; see sec ion 3.5.2) and including
compe i i e deso p ion om e aces and s eps, we can de i e
he effec i e fi s -o de deso p ion a e cons an o NH3 om a
s epped su ace (see sec ion S8 o he SI o u he de ails):
μ
μ
=+ −× +
kT k k k
kk
() (1 )
e d
Sh
Sd
T
h
Td
T(4)
whe e ke (T) desc ibes he “ e ace-assis ed”deso p ion o
molecules (a low co e ages) om su aces wi h he s ep
densi y, μ, which is defined as s eps pe uni cell leng h. The
fi s e m o eq 4 is he con ibu ion o di ec deso p ion om
s eps; he second e m consis s o a p oduc be ween he
hopping a e om s eps o e aces, ollowed by he p obabili y
o deso b om e aces. Fo he de i a ion o his equa ion, we
assumed ha he o al NH3popula ion a P (332) is well
desc ibed by he popula ion a s eps. This assump ion is
jus ified, as NH3has a high ene gy p e e ence o s eps, and
en opic gain om binding a e aces is small due o a small
numbe o e aces. See he SI sec ion S8 o de ailed
de i a ion o his equa ion. The esul s o his “ e ace-
assis ed”model a e shown in Figu e 3a as he g een line, which
ag ees e y well wi h he expe imen ally de i ed fi s -o de
deso p ion a e cons an s om P (332). In addi ion, he model
ep oduces he expe imen ally de i ed ac i a ion ene gy and
p e ac o o NH3deso p ion om P (332) qui e well (see
Figu e 3d,e).
Figu e 3a shows ha deso p ion a es om an Os wald
ca alys wi h mul iple ac i e si es canno be adequa ely
desc ibed i exchange be ween s eps and e aces is no
explici ly conside ed. Howe e , e y o en, kine ics modeling o
he deso p ion p ocess does no conside mul iple binding si es
e en hough hey a e p esen a he s epped model ca alys s.
Mos commonly, single binding si es a e assumed ha ha e he
cha ac e is ic ene gies and p e ac o s ha a e associa ed wi h
he mos s able binding si e.
2,17,18
Clea ly, his app oach will
unde es ima e he a e o ac ual deso p ion, whe e he
adso ba e migh exchange be ween binding si es and lea e
he su ace h ough he less s able binding si e. In ac , such
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e o s, e en i he a e cons an s a e modeled co ec ly, may
lead o e oneous conclusions abou he efficiency o a ca alys
a he desi ed eac ion condi ions.
3.5.2. Limi ed Applicabili y o Mean-Field App oxima ion
o NH3Chemis y a P . We ha e obse ed ha he NH3
deso p ion a e om P (111) wi h a s ep densi y o 0.4 ±0.2%
has a biexponen ial beha io , eme ging om he compe i ion
be ween NH3deso p ion om e aces and i s slow diffusion
o s eps. A P (332), we obse e a single-exponen ial
deso p ion a e, indica ing ha NH3equilib a es be ween
s eps and e aces, demons a ing ha he compe i ion
be ween diffusion and deso p ion depends on he s ep densi y.
Ob iously, i will also depend on he empe a u e. Using he
de i ed elemen a y p ocess a e cons an s, we nex in es iga e
he compe i ion be ween diffusion o s eps and deso p ion
om e aces as a unc ion o he s ep densi y and empe a u e,
including condi ions ele an o Os wald p ocess.
Fo he pu pose o demons a ion, we de e mine NH3
’s
p obabili y o each a s ep a e landing a he cen e o a
e ace. To do so, we place a low ini ial concen a ion o NH3
a he cen e o he e ace and sol e he deso p ion−diffusion
a e equa ions. We se kh
S=0,“ eezing” he NH3molecule
once i eaches a s ep. A e all he NH3molecules ha e ei he
deso bed om he e ace o diffused o he s eps, we
de e mine he ac ion o molecules ha emained a s eps.
The esul s o his analysis a e shown in Figu e 5.
A low empe a u es, diffusion o s eps is as compa ed o
NH3deso p ion, and all molecules can each he s ep. A high
empe a u es, NH3is less likely o each he s eps p io o
deso p ion because he si e- o-si e hopping e en app oaches a
ime scale simila o ha o he deso p ion e en . Al hough he
p obabili y o each he s ep inc eases wi h highe s ep
densi ies, i can be clea ly seen ha a condi ions ypical o he
Os wald p ocess no all molecules landing a majo i y e ace
si es a e able o each he s ep p io o hei deso p ion. I
means ha NH3mus adso b on o e y close o a s ep si e in
o de o eac . Unde ypical Os wald condi ions, he eac an s
(NH3*and O*a s eps) a e no able o encoun e one ano he
on a ime scale as e han deso p ion, and as a consequence,
he eac an s canno be assumed o be homogeneously mixed.
This calls in ques ion he basic assump ion o he mean-field
a e equa ions commonly used o model he Os wald p ocess.
The slow hopping a es and he p e iously obse ed
p e e ence o eac ion a s eps sugges s ha kine ics modeling
o NH3chemis y a P needs o explici ly accoun o diffe en
ac i e si es and accu a ely desc ibe he exchange be ween
hem ac o s ha ha e no been conside ed in kine ics
modeling o Os wald p ocess so a . No ice ha unde
ca aly ically ele an condi ions, o he adso ba es like NO*
and O*will be p esen a he ca alys and likely dec ease NH3
’s
mobili y e en u he . These esul s sugges ha he key
eac ion in he Os wald p ocess may, in ac , be diffusion-
limi ed, con adic ing cu en models ha assume as
diffusion.
2,4,5,18
3.5.3. NH3Co e ages a a P Ca alys unde Os wald
P ocess Condi ions. Cu en kine icsmodels o NH
3
oxida ion a P lack ans e abili y o eac ion condi ions
diffe en om hose a which hey we e op imized. One
possible eason o his is ha he a e pa ame e s employed do
no desc ibe elemen a y s eps in he eac ion. Using he
expe imen ally de i ed deso p ion a es o his wo k, we can
es ima e he s a iona y NH3isos e es as a unc ion o
empe a u e and p essu e a s eps and e aces o a s epped
P ca alys a condi ions ypical o he Os wald p ocess. We
compa e hose wi h p edic ions o he KB
18
model ha is
equen ly used o Os wald p ocess eac o simula ions.
44−46
This equi es conside ing he co e age dependence o he
ammonia deso p ion ene gy and p e ac o . We use a co e age-
dependen deso p ion ba ie which we pa ame ize based on
he expe imen ally de i ed NH3binding ene gy (in he ze o-
co e age limi ) and he scaling o he binding ene gy wi h
co e age de i ed om DFT calcula ions (see sec ions S5 and
S9 o he SI). We ha e pe o med ha monic equency and
hopping ba ie calcula ions wi h DFT a 0.06 and 0.25 ML
NH3co e ages, which allows us o es ima e he co e age
dependence o he p e ac o . We assume ha he loga i hm o
he p e ac o p opo ional o he en opy diffe ence be ween
he ini ial and ansi ion s a escales linea ly wi h co e age
(see sec ion S9 o he SI o u he de ails). To es he
cons uc ed co e age-dependen deso p ion a e cons an , we
simula ed TPD spec a om P (111) and compa ed hem o
esul s om p e ious wo ks.
12
Ea lie TPD s udies
12
ound
b oad NH3deso p ion peaks, indica ing subs an ial adso ba e−
adso ba e in e ac ions, influencing he deso p ion a e. We find
ha ou model p edic s he igh empe a u e anges o he
TPD spec a and accoun s co ec ly o he co e age
dependence, which is eflec ed by he shape o he TPD
ace (see sec ion S9 o he SI).
Nex , we used he deso p ion−diffusion model o de e mine
he s eady-s a e NH3co e age a e aces and s eps a su ace
empe a u es and NH3pa ial p essu es cha ac e is ic o he
Os wald p ocess (see sec ion S9 o he SI o de ails). We
chose he highly s epped P (332) su ace as a model ca alys
o he Os wald p ocess. The esul s a e shown in Figu e 6 and
compa ed o he KB model p edic ions.
We find ha he s eady-s a e co e age o NH3is s ongly
empe a u e- and p essu e-dependen , whe eas he KB model
p edic s sa u a ed co e age unde all condi ions. Ou model
p edic s a he low NH3co e ages (blue colo in Figu e 6)
Figu e 5. P obabili y o NH3molecules ha landed in he cen e o
he e ace o each he s eps be o e deso p ion as a unc ion o s ep
densi y and ca alys empe a u e. The empe a u e anges (1050−
1250 K) and associa ed s ep densi ies o ou expe imen al (solid box)
and Os wald p ocess (dashed box) condi ions a e indica ed in he
plo . The s ep densi ies o he Os wald ca alys a e no known, bu
we conside ypical s ep/edge densi ies ound on ca aly ic nano-
pa icles
42,43
as ep esen a i e o eal ca alys s.
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o e a b oad ange o Os wald p ocess condi ions. We has en
o poin ou ha NH3co e age will be s ongly affec ed by
coadso bed O*, which can eac o emo e NH3bu also may
induce s onge ammonia binding o he su ace. S ill he
compa isons shown in Figu e 6 sugges ha i is likely ha he
commonly applied kine ics model o e p edic s he co e age o
NH3, which will lead o a highe deg ee o NH3slippage
(whe e less ni ogen ends up as NO he desi ed p oduc o
he Os wald p ocess). This is consis en wi h he ac ha he
KB model unde -p edic s he NO yield and ends o
o e es ima e he N2yield a Os wald p ocess condi ions.
18
4. SUMMARY AND CONCLUSIONS
In his wo k, we ha e in es iga ed he deso p ion kine ics o
NH3 om P (111) and P (332) be ween 430 and 620 K using
eloci y- esol ed kine ics. De ailed analysis o NH3deso p ion
kine ics using a diffusion−deso p ion kine ics model enabled
us o ex ac a e cons an s o ou elemen a y p ocesses:
di ec deso p ion om e aces and om s eps, si e- o-si e
hopping a e aces, and hopping om s eps o adjacen e ace
si es. The measu emen o a eloci y- esol ed kine ic ace
p o ides simul aneously he speed dis ibu ions o deso bing
molecules, om which we de i e NH3 he mal s icking
coefficien s o P using he p inciple o de ailed balance.
The a e cons an s o he elemen a y p ocesses o deso p ion
and diffusion ha e been u he analyzed using TST wi h DFT
inpu pa ame e s. The con en ional TST models, which
desc ibe he pa i ion unc ion o he adso ba e wi h uncoupled
DOFs, ail o ep oduce he expe imen al esul s. A co ec ion
scheme o he pa i ion unc ion is implemen ed ha allows
NH3 ib a ional equencies, associa ed wi h he molecule−
su ace in e ac ion, o so en when displaced away om he
mos s able binding si e. This app oach ai h ully ep oduces
he expe imen al kine ic da a, and we de i e accu a e
in e ac ion ene gies o NH3a P su aces, which we
summa ize in Table 3.
Ou wo k p o ides compelling e idence ha NH3diffusion
on P (111) mus pass o e a la ge ba ie , which is ∼65% o i s
binding ene gy. This is an excep ion o he so-called 12% ule.
Ins ead o elying on such simple ules, ou compa ison wi h
DFT calcula ions shows ha he minimum ene gy pa h o
diffusion appea s o be highly accu a e.
Ha ing a quan i a i ely accu a e kine ics model o ammonia
deso p ion and diffusion, we we e able o c i ically e alua e he
app oxima ions commonly employed in kine ics modeling o
he Os wald p ocess. I is known om p e ious wo k ha NH3
eac s efficien ly wi h oxygen a oms a s eps,
2,6,7
while eac ion
a e aces is less efficien . We show ha a empe a u es
ypical o he Os wald p ocess, he NH3hopping a e is close
o i s deso p ion a e, indica ing ha NH3landing a e ace
si es is unlikely o each he s eps, whe e i may eac p io o
i s deso p ion. This implies ha mean-field kine ics models
ha e limi ed applicabili y o p edic ion o NH3con e sion
a es and NO selec i i y unde Os wald p ocess condi ions.
Fu he mo e, by ca e ul analysis o NH3
’s deso p ion om
P (332), we show ha i is no possible o model he
deso p ion a e om ca alys s wi h mul iple ac i e si es by
conside ing only he di ec deso p ion om s eps, an app oach
which is ne e heless pe sis en ly employed in kine ics
modeling li e a u e.
2,17
Wi h he help o DFT calcula ions, we ex end he deso p ion
a e cons an s beyond he ze o-co e age limi o ou
expe imen , which allows us o ep oduce p e iously obse ed
TPD spec a and o es ima e NH3co e ages a Os wald
p ocess condi ions. The compa ison o ou esul s wi h a
kine ics model commonly used o eac o simula ions
p o ides a simple explana ion why es ablished models end
o o e p edic he ex en o NH3slip unde Os wald p ocess
condi ions. We showed ha his is a di ec esul o he model’s
p edic ion o high NH3co e ages, which a o he o ma ion o
N2and N2O and educe he efficiency o NO o ma ion.
In summa y, he demons a ed app oach exemplifies how
he combina ion o high-quali y kine ic da a wi h TST analysis
yields highly accu a e elemen a y s ep a e cons an s,
po en ially capable o cons uc ing mechanisms possessing
high ans e abili y wi hou elying on empi ical op imiza ion
wi hin na ow ange o expe imen al condi ions.
Figu e 6. F ac ional NH3co e ages a e aces (le ) and s eps (middle) o a P (332) model ca alys a empe a u es and NH3pa ial p essu es
ypical o he Os wald p ocess. We compa e ou esul s (le and cen e panels) o he p edic ions o he KB model ( igh panel) which assumes
one single ac i e si e o NH3. No e ha he Os wald p ocess is conduc ed a o al p essu es o ≥1 ba wi h NH3pa ial p essu es o ∼10% o he
o al p essu e.
Table 3. Mos Impo an Resul s o Ammonia In e ac ions
a P Su aces
NH3/P in e ac ion ecommended alue
(111) deso p ion ene gy E0,d
T1.13 ±0.02 eV
(111) si e- o-si e hopping ba ie E0,h
T0.71 ±0.04 eV
s ep p e e ence o e e ace ΔE0,ST 0.23 ±0.03 eV
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