Mechanistic details of acid-catalyzed reactions and their role in the selective synthesis of triptane and isobutane from dimethyl ether

Article abstract of DOI:10.1016/j.jcat.2010.11.004

We report here kinetic and isotopic evidence for the elementary steps involved in dimethyl ether (DME) homologation and for their role in the preferential synthesis of 2,2,3-trimethylbutane (triptane) and isobutane. Rates of methylation of alkenes and of hydrogen transfer, isomerization and β-scission reactions of the corresponding alkoxides formed along the homologation path to triptane were measured using mixtures of ¹³C-labeled dimethyl ether (¹³C-DME) and unlabeled alkenes on H-BEA. DME-derived C₁ species react with these alkenes to form linear butyls from propene, isopentyls from n-butenes, 2,3-dimethylbutyls from isopentenes, and triptyls from 2,3-dimethylbutenes; these kinetic preferences reflect the selective formation of the more highly substituted carbenium ions and the retention of a four-carbon backbone along the path to triptane. Hydrogen transfer reactions terminate chains as alkanes; chain termination probabilities are low for species along the preferred methylation path, but reach a maximum at triptyl species, because tertiary carbenium ions involved in hydrogen transfer are much more stable than those with primary character required for triptene methylation. Alkenes and alkanes act as hydrogen donors and form unsaturated species as precursors to hexamethylbenzene, which forms to provide the hydrogen required for the DME-to-alkanes stoichiometry. Weak allylic C-H bonds in isoalkenes are particularly effective hydrogen donors, as shown by the higher termination probabilities and ¹²C content in hexamethylbenzene as ¹²C-2-methyl-2-butene and ¹²C-2,3-dimethyl-2-butene pressures increased in mixtures with ¹³C-DME. The resulting dienes and trienes can then undergo Diels-Alder cyclizations to form arenes as stable by-products. Isomerization and β-scission reactions of the alkoxides preferentially formed in methylation of alkenes are much slower than hydrogen transfer or methylation rates, thus preventing molecular disruptions along the path to triptane. Methylation at less preferred positions leads to species with lower termination probabilities, which tend to grow to C₈₊ molecules; these larger alkoxides undergo facile β-scission to form tert-butoxides that desorb preferentially as isobutane via hydrogen transfer; such pathways resolve methylation "missteps" by recycling the carbon atoms in such chains to the early stages of the homologation chain and account for the prevalence of isobutane among DME homologation products. These findings were motivated by an inquiry into the products formed via C₁ homologation, but they provide rigorous insights about how the structure and stability of carbenium ions specifically influence the rates of methylation, hydrogen transfer, β-scission, and isomerization reactions catalyzed by solid acids.

Full text of DOI:10.1016/j.jcat.2010.11.004

Journal of Catalysis 277 (2011) 173–195
Contents lists available at ScienceDirect
Journal of Catalysis
journal homepage: www.elsevier.com/locate/jcat
Mechanistic details of acid-catalyzed reactions and their role in the selective
synthesis of triptane and isobutane from dimethyl ether
⇑
Dante A. Simonetti, John H. Ahn, Enrique Iglesia
Department of Chemical Engineering, University of California at Berkeley, Berkeley, CA 94720, USA
a r t i c l e i n f o
a b s t r a c t
Article history:
We report here kinetic and isotopic evidence for the elementary steps involved in dimethyl ether (DME)
homologation and for their role in the preferential synthesis of 2,2,3-trimethylbutane (triptane) and iso-
butane. Rates of methylation of alkenes and of hydrogen transfer, isomerization and b-scission reactions
of the corresponding alkoxides formed along the homologation path to triptane were measured using
Received 14 August 2010
Revised 26 October 2010
Accepted 10 November 2010
Available online 18 December 2010
1
3
13
1
mixtures of C-labeled dimethyl ether ( C-DME) and unlabeled alkenes on H-BEA. DME-derived C spe-
cies react with these alkenes to form linear butyls from propene, isopentyls from n-butenes, 2,3-dim-
ethylbutyls from isopentenes, and triptyls from 2,3-dimethylbutenes; these kinetic preferences reflect
the selective formation of the more highly substituted carbenium ions and the retention of a four-carbon
backbone along the path to triptane. Hydrogen transfer reactions terminate chains as alkanes; chain ter-
mination probabilities are low for species along the preferred methylation path, but reach a maximum at
triptyl species, because tertiary carbenium ions involved in hydrogen transfer are much more stable than
those with primary character required for triptene methylation. Alkenes and alkanes act as hydrogen
donors and form unsaturated species as precursors to hexamethylbenzene, which forms to provide the
hydrogen required for the DME-to-alkanes stoichiometry. Weak allylic C–H bonds in isoalkenes are par-
Keywords:
Carbenium ion
Dimethyl ether
Isomeric alkanes
Solid acid catalysis
Transportation fuels
12
ticularly effective hydrogen donors, as shown by the higher termination probabilities and C content in
1
2
12
hexamethylbenzene as C-2-methyl-2-butene and C-2,3-dimethyl-2-butene pressures increased in
mixtures with 1 C-DME. The resulting dienes and trienes can then undergo Diels–Alder cyclizations to
form arenes as stable by-products. Isomerization and b-scission reactions of the alkoxides preferentially
formed in methylation of alkenes are much slower than hydrogen transfer or methylation rates, thus pre-
venting molecular disruptions along the path to triptane. Methylation at less preferred positions leads to
species with lower termination probabilities, which tend to grow to C8+ molecules; these larger alkoxides
undergo facile b-scission to form tert-butoxides that desorb preferentially as isobutane via hydrogen
transfer; such pathways resolve methylation ‘‘missteps’’ by recycling the carbon atoms in such chains
to the early stages of the homologation chain and account for the prevalence of isobutane among DME
3
homologation products. These findings were motivated by an inquiry into the products formed via C
1
homologation, but they provide rigorous insights about how the structure and stability of carbenium ions
specifically influence the rates of methylation, hydrogen transfer, b-scission, and isomerization reactions
catalyzed by solid acids.
Ó 2010 Elsevier Inc. All rights reserved.
1
. Introduction
[3–7]. These systems are strongly inhibited by the water formed in
dehydration and homologation reactions and appear to catalyze
The conversion of CH
carbons provides a potential route to transportation fuels from C
intermediates produced from synthesis gas derived from diverse
natural gas, coal, or biomass sources [1,2]. 2,2,3-Trimethylbutane
triptane; 112 research octane number) forms with high selectivity
3
OH and dimethyl ether (DME) to hydro-
only a few methanol turnovers [3–5]. Acid zeolites also convert
DME and methanol selectively to isobutane and triptane at modest
temperatures (400–500 K) and pressures (60–250 kPa) in continu-
ous gas-phase flow systems with moderate deactivation and a sig-
nificant number of catalytic turnovers (>10 mol of C per Al after
20 ks on stream) [8,9]. H-BEA was chosen for this study because
1
(
from methanol at modest temperatures (ꢀ450 K) via carbenium
ꢁ1
ion transition states using Zn or In iodide in aqueous batch systems
it showed the highest productivity (740
tane selectivity (21% selectivity to C species and 72% selectivity
to triptyls within C ), and stability (0.04 ks first-order deactiva-
lmol (s mol Al) ), trip-
7
ꢁ1
7
⇑
Corresponding author. Fax: +1 510 642 4778.
E-mail address: iglesia@berkeley.edu (E. Iglesia).
tion rate constant) among the large-pore zeolites studied (H-
MOR, H-USY, H-BEA) [9]; zeolites with smaller 8-MR and 10-MR
0
021-9517/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved.
doi:10.1016/j.jcat.2010.11.004

1
74
D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
structures (H-FER, H-MFI) gave lower rates [9], apparently as a re-
sult of steric constraints on diffusion rates or transition states. DME
(5–40 mg; 180–250 lm particles) held in place by a fritted VCR
gasket and quartz wool.
preferentially formed C
4
and C
7
hydrocarbons (each with ꢀ30%
Temperatures were measured with a type-K thermocouple
placed at the external reactor wall and held constant using a Wat-
low controller (Series 96) and a resistive heater. All samples were
selectivity); isobutyl species (isobutene and isobutane, 90%; –tyl
suffix is used here and elsewhere to denote alkanes and alkenes
with a given backbone structure) and triptyl species (triptene
ꢁ1
heated to reaction temperature (at 0.8 K s ) in flowing He
3
ꢁ1
and triptane; 80%) were the predominant isomers within the C
and C fractions, respectively [9], in spite of the strong thermody-
namic preference for other isomers [10]. The most abundant
isomers within C (isopentane and isopentenes) and C (2,3-
4
(0.083 cm s ) before introducing reactant mixtures. The chemical
and isotopic composition of the reactor effluent was determined by
gas chromatography using flame ionization and mass selective
detectors (HP 5890/HP 5972), each connected to a capillary column
7
5
6
dimethylbutane and 2,3-dimethylbutenes) products also contain
the linear four-carbon backbone structure characteristic of triptane
(HP-1, methyl silicone, 50 m ꢂ 0.32 mm ꢂ 1.05
lm film). Isotopo-
logue distributions were determined from mass fragmentation
[
9].
Here, we provide kinetic and isotopic evidence for chain growth
patterns using deconvolution methods reported previously [8,12].
and termination pathways that selectively form triptane and iso-
butane from DME reactants. We use competitive reactions be-
2
.2. Determination of individual rates of methylation, hydrogen
transfer, isomerization, and b-scission from isotopic tracer studies
1
3
13
tween
C-labeled dimethyl ether ( C-DME) and unlabeled
alkenes of varying size and shape to measure individual rates of
methylation, hydrogen transfer, isomerization, and b-scission reac-
tions and develop a quantitative description of the mechanistic de-
tails of chain growth during DME homologation to triptane on solid
acid catalysts. The remarkable specificity for triptane and isobu-
tane reflects (i) a preference for methylation at positions that
preserve a four-carbon backbone, (ii) slow isomerization and b-
scission reactions of these four-carbon backbones, which would
divert chains from the path to triptane, (iii) fast isomerization
and b-scission of chains that grow beyond triptane to form isobu-
tane and isobutene, thus returning part of these longer chains to
the homologation reaction manifold, and (iv) the high hydrogen
transfer rates to tert-butoxide and 2,3,3-trimethyl sec-butoxide
compared with methylation of isobutene and triptene because of
the more stable carbenium ion transition states for hydrogen
transfer relative to methylation. These mechanistic features are
shown to reflect pathways mediated by ion-pairs at late transition
states ubiquitous in acid catalysis instead of any specific spatial
constraints imposed by the zeolite BEA structure; indeed, the pref-
The rate of hydrogen transfer for homologation intermediates of
a given size (n) and structure (RHT,n) was determined from the rate
of formation of the unlabeled alkane corresponding to the added
unlabeled alkene. These rates were determined from:
R
Cn ꢂ j
R
HT;n
¼
ð1Þ
n
in which RCn is the total rate (on a carbon basis) of formation of al-
kanes of the same size and structure as the co-fed alkene, j is the
fraction of these alkanes that are unlabeled, and n is the number
of carbons in the co-fed alkene. The rates of b-scission (Rbs,n) of
DME homologation intermediates were determined from the rates
of formation of unlabeled products (alkenes and alkanes) of b-scis-
sion of co-fed unlabeled alkenes. Skeletal backbone rearrangement
rates (RIs,n) were determined from the rate of appearance of unla-
beled isomers (alkene and alkane) with shorter and longer back-
bones than the co-fed alkene. These rates were calculated using
Eqs. (2) and (3), in which j and n are defined as in Eq. (1), RCm<n is
the total rate of formation (on a carbon basis) of species from b-scis-
sion of the co-fed alkene, and RCnꢁIs is the total rate of formation (on
a carbon basis) of skeletal alkane and alkene isomers of the co-fed
alkene:
4 7
erential formation of C and C products, and of isobutane and
triptane as their respective preferred isomers are observed on all
large-pore zeolites examined [9] and also on mesoporous hetero-
polyacids and silica–alumina [11]. Thus, the conclusions presented
here, derived from an inquiry into the unique selectivity to isobu-
R
Cm<n ꢂ j
R
bs;n
Is;n
¼
¼
ð2Þ
ð3Þ
tane and triptane from acid-catalyzed conversion of C
1
species,
n
R
CnꢁIs ꢂ j
provide guidance about the effects of molecular structure and of
carbenium ion stability on acid catalysis in general.
R
n
The rates of methyl shift (RMS,n) isomerization (without concomitant
changes in backbone chain length) were determined using the same
method as for RIs,n, except that the rate of unlabeled isomers (alkene
and alkane) with methyl groups located at different positions along
2
. Experimental methods
2.1. Catalyst, reactants, and kinetic and isotopic tracer studies
the backbone than the co-fed alkene was used in place of RCnꢁIs
.
The acid form of BEA zeolite was prepared by heating NH
4
-BEA
12
13
Methylation of C-alkene with C-DME forms molecules con-
ꢁ1
(
1
Si/Al = 12.5, Zeolyst [8]) to 773 K (at 0.02 K s ) and holding for
12
13
taining C- and C-atoms, but hydrogen transfer, isomerization,
3
ꢁ1 ꢁ1
0 h in flowing, dry air (1.7 cm s
g
, zero grade, Praxair). Reac-
12
and b-scission of the alkoxides derived from C-alkenes form only
13
O13CH
tant mixtures consisted of CH
C-DME) and unlabeled alkenes ( C-alkenes). These alkenes in-
3
3
(99%, ISOTEC; denoted as
unlabeled molecules; the rate of formation of such unlabeled mol-
ecules represents the combined rates of these three reactions. The
position and rate of methylation (RMe,n) of each added alkene can
be determined from the rate of formation of all molecules contain-
1
3
12
cluded propene (99%, Sigma Aldrich), 1-butene (99%, Scott Spe-
cialty Gases), trans-2-butene (99%, Sigma Aldrich), isobutene
99%, Matheson), 2-methyl-2-butene (99%, Sigma Aldrich), 2-pent-
enes (mixture of cis and trans isomers, 98%, Sigma Aldrich), 2,3-di-
methyl-2-butene (98%, Acros Organics), 2-methyl-2-pentene (98%,
Fluka), 2,3,3-trimethyl-1-butene (triptene; 98%, Sigma Aldrich),
(
12
12
ing at least one C-atom, except for those containing only C-
atoms:
P
ð
R
i
ꢂ XÞ
i
2
,4-trimethyl-2-pentene (99%, ChemSampCo), and 3,4,4-tri-
R
Me;n
¼
ꢁ RHT;n ꢁ RIs;n ꢁ RMS;n ꢁ Rbs;n
:
ð4Þ
n
methyl-2-pentene (99%, ChemSampCo). Reactant streams consist-
13
ing of
.7 kPa) of one of these alkenes were mixed with He (99.999%,
Praxair) and introduced into a stainless steel tubular reactor
6.4 mm outer diameter) containing the H-BEA catalyst
C-DME (75–84 kPa) with small concentrations (0.5–
i
In this equation, R is the total rate (on a carbon basis) of formation
1
2
3
of molecules with i-carbons, X is the C-atomic fraction in each
molecule (determined from isotopologue distributions), and n is
the number of carbons in the co-fed alkene.
(

D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
175
Chain termination probabilities (b):
These experiments show how molecular structures and carbe-
nium ion stabilities dictate the rates of chain growth and termina-
R
HT;n
tion during the homologation of
1
C species derived from
b ¼ R
Me;n þ RHT;n
ð5Þ
equilibrated methanol-DME reactants [8] via the chain growth
pathways shown in Scheme 2. These experiments also show more
generally how molecular structures determine the rates of the car-
benium-ion-mediated pathways ubiquitously involved in acid
catalysis [45].
are defined as the ratio of the rate of hydrogen transfer to the sum
of the rates of methylation and hydrogen transfer (the less revers-
ible termination step). The probabilities of skeletal isomerization
C
(cSk), b-scission (c ), and methyl shift (cMS) are defined by analogy
with Eq. (5), with the rates of chain lengthening or shortening (RIs,n),
b-scission (Rbs,n), or methyl shift (RMS,n) in the numerator (Eqs. (6)–
4
3.1. Selective methylation of propene to form linear C species
(
8)):
Propene can be methylated at the terminal carbon atom to form
linear C species or at the central carbon atom to form isobutyl spe-
4
R
Is;n
13
12
cSk ¼ R
cC ¼ R
ð6Þ
ð7Þ
ð8Þ
cies. Co-reactions of C-DME (84 kPa) and C-propene (2 kPa)
were used to probe the preferential methylation position in pro-
pene and whether propene methylation accounts for the high iso-
butane selectivites prevalent in DME homologation catalysis on
acid zeolites [8,9].
Me;n þ RHT;n
R
bs;n
Me;n þ RHT;n
R
MS;n
cMS ¼ R
Me;n þ RHT;n
The selectivity to linear C
4
chains (n-butane and n-butenes) and
to singly labeled C isotopologues formed by a single methylation
4
1
3
12
with C-DME/ C-propene mixtures decreased with increasing
reactor residence time (Fig. 1), indicating that these molecules
form as primary products via deprotonation or hydrogen transfer
3
. Results and discussion
1
2
12C-alkenes co-fed with 13
of sec-butoxide species derived from C-propene reactions with
C-DME are methylated to larger spe-
1
3
C-DME. The trans-2-butene isotopologues consisted predomi-
cies [3,4,9,13–24] or protonated to alkoxides [25–28], which can
undergo hydrogen transfer [4,9,29–35], isomerization [30,36–39],
or b-scission [40–44] via the pathways shown in Scheme 1. Thus,
nantly of singly labeled species, with a minority binomial compo-
nent containing more highly labeled isotopologues (dashed curve;
Fig. 2a). We chose trans-2-butene as the representative linear C
4
1
3
C-DME reactions with 12C-alkene isomers of varying size along
alkene, because it shows the same isotopic distribution as n-bu-
tane, but is present at higher concentrations than n-butane and
the other n-butene isomers. At all residence times, singly labeled
trans-2-butene molecules are ꢀ10 times more abundant than
the chain growth path to triptane were used to probe the rate
and position of methylation of alkenes, as well as the rates of
hydrogen transfer, isomerization, and b-scission of alkoxides
formed in DME homologation reactions. These experiments were
conducted at 473 K, because such conditions lead to significant
1
3
2
-butenes with two or more C-atoms (Fig. 2a), indicating that lin-
ꢁ
1
ear C
pene with C-DME. In contrast, selectivities to isobutyl species
and to their singly labeled isotopologues) increased with increas-
4
species predominantly form via a single methylation of pro-
rates of triptane formation (3.8
tivities to triptane and isobutane (21% selectivity to C
bons with 72% selectivity to triptyls in C and 42% selectivity to
hydrocarbons with 94% selectivity to isobutyls in C ) [9]. Unla-
alkenes lacking the four-carbon backbone in trip-
l
mol (s mol Al) ) and high selec-
1
3
7
hydrocar-
(
7
ing residence time (Fig. 1); thus, we conclude that isobutane and
isobutene form via secondary b-scission of larger chains. Indeed,
isobutane molecules show a binomial isotopologue distribution
C
4
4
1
2
12
beled
5 7
C – C
tane, and thus not involved as precursors to triptane, were used
to show how deviations from the four-carbon backbone lead
to chain growth beyond C
the products of these reactions. The facile b-scission paths of C
molecules and their selective formation of isobutyl species
were confirmed by
trimethyl-2-pentene, the isomeric octene preferentially formed
by methylation of triptene [9].
(Fig. 2b), also consistent with b-scission reactions of larger iso-
meric chains containing C-atoms from both DME and propene as
the predominant route to isobutane products.
7
molecules and to fast b-scission of
8
The prevalence of singly labeled isotopologues in n-butyl (but
not isobutyl) species and their higher selectivity at shorter resi-
dence times show that methylation of propene occurs preferen-
tially at the terminal carbon to form linear instead of branched
butoxides that desorb via deprotonation or hydrogen transfer as
linear butenes or butane, respectively. Preferential methylation at
the terminal carbon in propene reflects the higher stability of their
secondary butyl carbenium ion transition state in sec-butoxide for-
mation compared with the primary cations involved in the transi-
tion state for the formation of tert-butoxides via methylation at the
internal carbons in propene (as shown in Scheme 3). We conclude
that isobutane (and isobutene) does not form via propene methyl-
13
12
C-DME co-homologation with
C-3,4,4-
C
, C
C alkanes
n
n-y
y
species
Hydrogen
Transfer
β-scission
(R
)
HT,n
(R
)
bs,n
4
ation, which forms linear C species instead. The predominant for-
*
Cn
*Cn+1
mation of binomial isobutane isotopologues (Fig. 2b) shows that
isobutane predominantly forms via secondary b-scission of larger
chains, after extensive skeletal rearrangements that scrambled
Isomerization
RIs,n
(
)
13
C-atoms along the backbone of these larger chains.
Methylation
The selective formation of n-butyl species in the methylation of
propene is consistent with cluster calculations of reactions of co-
adsorbed propene with methanol [21,46], which show smaller bar-
riers for methylation at terminal than internal C-atoms in propene.
These studies suggest that the stability imparted upon methylation
transition states by the formation of the most substituted carbe-
nium ions dictates that methylation occurs preferentially at the
(
RMe,n
)
C isomers
n
C alkenes
n
Scheme 1. Reaction pathways for alkenes and alkoxides formed as intermediates
along dimethyl ether homologation pathways. Reactions denoted with solid lines
occur faster than those denoted with dashed lines.

1
76
D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
*
HT
*
*
*
*
*
*
*
“
CH3”
“CH3”
“CH3”
“CH3”
“CH3”
Me
…
Is
“CH
”
3
3
“CH ”
*
*
*
C
Scheme 2. Chain growth sequence for dimethyl ether homologation (starting with propene for simplicity). The asterisk indicates the position of alkoxide attachment to the
surface. HT, Me, Is, and C labels represent hydrogen transfer, methylation, isomerization, and cracking reactions, respectively. ‘‘CH
derived from dimethyl ether.
3
’’ represents surface methylating species
transfer between a gas-phase hydride donor and an alkoxide form
transition states that resemble the carbenium ion formed by
detachment of alkoxide through cleavage of C–O bond with the
zeolite framework [30,33]. Therefore, the low termination proba-
35
30
25
20
15
10
5
0
Total nC
4
3
bility for C species reflects the greater stability of the butyl carbe-
nium ion transition state formed in methylation of propene (with
its positive charge stabilized over two secondary C-atoms) com-
pared with the propyl carbenium ion transition state formed by
breaking the C–O bond in sec-propoxide during hydrogen transfer
Total isobutyl
[
30] (Scheme 3). As in the case of the methylation and hydrogen
transfer steps examined in the next sections, the stability of the
cationic transition states involved dictates the preferred routes
along the path to triptane. In this case, such considerations favor
the selective methylation of propene at its terminal carbon to form
linear C species over methylation to form isobutyl species or irre-
4
versible termination by hydrogen transfer to sec-propoxide to form
Singly-labeled nC
4
CarbonSlecvity(%)
Singly-labeled isobutyl
propane.
0
50
Residence Time
s mol Al [mol inlet gas] )
100
150
200
3.2. Methylation, termination, isomerization, and b-scission of C
4
species derived from butenes
-
1
(
The rates of methylation, hydrogen transfer, isomerization, and
b-scission of linear and branched C molecules were measured
from individual experiments in which unlabeled isobutene, 1-bu-
tene, or trans-2-butene were introduced as reactants with 13C-
DME (Table 1a). The isotopologue distributions of isopentane and
isobutane molecules formed from these reactants are shown in
Fig. 1. Selectivity (% carbon basis) to linear C
4
species and isobutyl species as a
ꢁ
1
4
function of reactor residence time (s mol Al [mol inlet gas] ) for reactions between
13
C-labeled dimethyl ether (84 kPa) and unlabeled propene (2 kPa) at 473 K on H-
BEA (Si/Al = 12.5). Total carbon conversions were less than 5%.
less substituted C-atom in C@C bonds of alkenes [21,46]. Methyla-
tion transition states, however, distribute the positive charge be-
tween the two C-atoms in the alkene C@C bond; as a result,
methylation activation barriers decrease as the combined number
of alkyl substituents on the two C-atoms in C@C bond increases
Fig. 3. These alkenes can undergo methylation to form C
that ultimately desorb via deprotonation as C alkenes (and meth-
ylate again) or as C alkanes via hydrogen transfer. Butoxides can
also undergo b-scission or isomerization before methylation or
5
alkoxides
5
5
hydrogen transfer; the rates of formation of unlabeled skeletal C
4
1
3
12
[
21,46]. In later sections, we show that the rate and position of
isomers and of unlabeled C
1
–C
3
species from C-DME/
C
4
alkene
methylation for alkenes are indeed consistent with this qualitative
guidance.
reactants reflect the respective rates of isomerization and b-scis-
sion of butoxides derived from C alkenes. These rates were used
to determine the termination, b-scission, and isomerization proba-
4
13C-DME (78 kPa) and 12
C-propene (0.5 kPa) reactions were
used to measure the rates of methylation of propene (to form lin-
ear C species) and hydrogen transfer to propoxide species formed
by protonation of propene (to form propane). The termination
probability (Eq. (5)) for C species (b = 0.013; Table 1) indicates
bilities (listed in Table 1b and defined in Eqs. (5)–(7)).
Co-reactions of C-DME (78 kPa) with C-1-butene or 12C-
trans-2-butene (0.5 kPa) were used to measure the rates of acid-
catalyzed intramolecular hydride shifts, which move the alkoxide
linkage to the surface and the location of the double bond within
the alkene as it deprotonates. The trans and cis isomers of 2-butene
were formed in equilibrium ratios (2.0–2.4 vs. 2.0 equilibrium
1
3
12
4
3
that propene undergoes methylation much faster than propoxide
formation and irreversible termination by hydrogen transfer. The-
oretical studies using DFT methods have shown that hydrogen

D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
177
Residence time (RT)
(
s mol Al [mol inlet gas] -1
)
(
a) 1.0
1.0
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
1
3
1
3
1
3
C fraction total = 0.22
13
C fraction total = 0.20
3
C fraction total = 0.08
C fraction binomial = 0.10
1
1
3
C fraction binomial = 0.18
C fraction binomial = 0.16
0.8
0.6
0.4
0.2
0.0
RT = 5.5
RT = 44
RT = 88
M
l
e
f
r
a
c
t
i
o
n
M
e
r
c
i
n
Mlefraction
0
1
2
3
4
0
1
2
13
3
4
0
1
132
3
4
1
3
Number C atoms
Number C atoms
Number C atoms
Residence time (RT)
s mol Al [mol inlet gas] -1)
(
(
b) 0.5
0.5
0.4
0.3
0.2
0.1
0.0
0.5
0.4
0.3
0.2
0.1
0.0
1
3
13
C fraction total = 0.18
C fraction binomial = 0.18
13
C fraction total = 0.35
13
C fraction total = 0.30
C fraction binomial = 0.41
1
3
13
C fraction binomial = 0.44
0.4
0.3
0.2
0.1
0.0
RT = 5.5
RT = 44
RT = 88
n
o
ti
rca
lef
o
M
Mlefraction
Melfraction
0
1
2
3
4
0
1
132
3
4
0
1
2
3
4
1
3
13
Number C atoms
Number C atoms
Number C atoms
Fig. 2. Isotopologue distributions and C-atomic fractions of (a) trans-2-butene and (b) isobutane molecules produced from reactions between 13C-labeled dimethyl ether
13
84 kPa) and 12C-propene (2 kPa) at 473 K on H-BEA at residence times of 5.5 (left), 44 (middle), and 88 (right) s mol Al [mol inlet gas] and propene conversions of 13% (left),
ꢁ1
(
6
13
3% (middle), and 73% (right). Total carbon conversions (DME and propene) were less than 5%. The dashed markers indicate the binomial distribution expected for the C-
fraction in the binomial portion present in each particular chemical species [8].
value at 473 K [10]; Table 1) and termination (b), skeletal isomer-
5
the terminal C-atom of 1-butene to form branched or linear C spe-
cies, respectively. Co-reactions of C-DME with all C-linear bu-
1
2
13
12
ization (
-butene (b = 0.08,
b = 0.10, Sk = 0.02,
cSk), and b-scission (
c
C
) probabilities were similar for C-
12
1
c
c
Sk = 0.02,
c
C
= 0.05) and C-trans-2-butene
tenes at 473 K gave much higher rates of formation of isopentyl
13
ꢁ1
(
c
C
= 0.04) reactions with C-DME (Table 1),
species (isopentane and isopentenes; 18–21
lmol [mol Al s]
;
as expected from the fast equilibration of their double-bond posi-
tion. These data indicate that linear C species (sec-butoxide and
-butoxide) exist at equilibrium on acid sites and the gas-phase
Table 1) than of linear pentyl species (n-pentane and n-pentenes;
0.76–0.91 lmol [mol Al s] ; Table 1), indicating that methylation
occurs preferentially at internal C-atoms of 2-butenes instead of
the terminal C-atom in 1-butene (Scheme 4). The isopentane and
isopentene molecules are mostly singly labeled (Fig. 3a), indicating
ꢁ1
4
1
thermodynamics are ultimately established by subsequent read-
sorption and hydride shift during reactions of 13C-DME and C-
linear butenes. We conclude that protonation–deprotonation
events and intervening hydride shift isomerization occur much
faster than methylation, hydrogen transfer, isomerization, and b-
scission steps during DME homologation on acid sites even at the
low temperatures of these reactions.
12
5
that branched C products predominantly form via methylation
of linear butenes at methylene positions. Previous studies have
proposed that transition states for methylation of 2-butene and
1-butene resemble tert-pentyl and n-pentyl carbenium ions,
respectively, with charge delocalized over both of the C-atoms in
the alkene double bond [21,46]. These studies also indicate that
methylation at the internal C-atom in 1-butene does not occur,
Methylation of linear butenes, and subsequent deprotonation or
hydrogen transfer, can occur at internal C-atoms of 2-butenes or at

1
78
D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
Eq. (4) (Section 2.2) is used to determine the total methylation
Hydrogen Transfer
1
3
5
rate of linear butenes by C-DME, which includes the C species
13
that methylate further to form longer chains with more C-atoms
that can undergo b-scission after intramolecular rearrangements.
Linear C
zation, and b-scission before the corresponding butenes methylate
to branched C products. The rates of these reactions are deter-
mined here from the rates of formation of unlabeled n-butane,
unlabeled isobutyl species, and unlabeled C –C species, respec-
4
species can undergo hydrogen transfer, skeletal isomeri-
+
5
1
3
1
3
12
tively, from C-DME/ C-linear butene reactants. The correspond-
ing termination, isomerization, and b-scission probabilities for
*
*
Methylation
linear C
Eqs. (5)–(7)).
The data obtained from 13C-DME/12C-linear butene reactants
data showed that methylation of linear alkenes (with
species) occurs faster than steps involving
hydrogen transfer (b = 0.08–0.10; Table 1), isomerization
Sk = 0.02; Table 1), or b-scission ( = 0.04–0.05; Table 1) of
butoxide species. These low probabilities of termination (b), isom-
erization ( Sk), and b-scission ( ) allow the preferential growth of
linear C species to isopentane and isopentene, instead of terminat-
ing chains as n-butane or altering their linear C backbone via
4
species are then calculated, in turn, from these rates
(
C
4
1
3
δ
+
C-DME-derived C
1
δ+
(c
c
C
CH
3
c
c
C
X
4
4
isomerization or b-scission. The observed preference for methyla-
tion of linear butenes over hydrogen transfer, skeletal isomeriza-
tion, or b-scission of butoxides reflects the greater stability of the
tert-pentyl carbenium ions involved in methylation at central car-
bons in 2-butene (with charge delocalized over secondary and ter-
tiary C-atoms) relative to the transition states with only secondary
carbenium ions required to cleave C–O bonds in hydrogen transfer
to adsorbed linear butoxides [4,9,29–35] or the carbenium ions
with primary character required for their skeletal isomerization
[30,36–39] or b-scission [40–44] (Scheme 4).
*
Scheme 3. Reaction pathways for C
3
species (propene and propoxide) in acid-
catalyzed dimethyl ether homologation pathways. Methylation of propene occurs
faster than hydrogen transfer to propoxide. Methylation of propene to isobutane
does not occur because of the formation of a primary carbenium ion.
Table 1
ꢁ
(a) Rates (
l
mol [mol Al s] 1) of methylation, hydrogen transfer, skeletal isomeriza-
tion, b-scission, and formation of isopentyl (Riso-C5) and normal pentyl (Rnormal-C5
species and (b) trans/cis-2-butene ratios, termination (b), skeletal isomerization ( Sk),
) probabilities for reactions of C-labeled dimethyl ether (78 kPa)
)
The small measured skeletal isomerization probabilities (
Sk
c ;
c
Table 1) also show that the high observed isobutane selectivities
1
3
and b-scission (
c
C
13
12
(
observed previously [9] and in the C-DME/ C-alkene studies
and unlabeled propene, trans-2-butene, 1-butene, or isobutene (0.5 kPa) at 473 K on
presented herein [8]) must reflect b-scission of larger chains in-
stead of n-butoxide skeletal isomerization, which occurs infre-
quently before sequential chain growth of linear butenes. The
H-BEA (Si/Al = 12.5). Reactions conducted at a space velocity of 0.024 mol inlet gas
ꢁ
1
[
mol Al s] . Total carbon conversions (DME and alkene) were less than 5%, and
alkene conversions were 97% of propene, 97% of isobutene, 85% of 1-butene, and 34%
of trans-2-butene.
13
binomial isobutane isotopologue distributions formed from C-
1
2
Co-feed alkene
DME/ C-linear butene mixtures (Fig. 3b) contain small contribu-
1
3
tions from unlabeled molecules (0.05) and C contents higher than
in isopentane (0.49 vs. 0.25), consistent with their formation via
b-scission of larger chains formed by subsequent methylation with
Propene trans-2-Butene 1-Butene Isobutene
(
a)
Methylation
37
0.5
–
–
–
53
68
33
38
1
3
Hydrogen transfer
Skeletal isomerization
b-scission
5.8
1.4
2.2
18
5.9
0.9
3.5
21
C-DME after extensive intramolecular carbon scrambling. Isobu-
tane does not form by isomerization or hydrogen transfer to butox-
0.4
3.5
9.5
12
ide species derived from protonation of
C-linear butenes
R
R
iso-C5
a
(c
Sk = 0.02) or via isopentane cracking ( = 0.002; Table 2; dis-
c
C
normal-C5
–
0.91
0.76
–
cussed in Section 3.3.5).
(
b)
Co-reactions of 13C-DME (78 kPa) and 12C-isobutene (0.5 kPa)
trans/cis-2-Butene ratio
–
2.4
2.0
2.3
were used to probe reaction pathways of isobutene, whether
formed directly from DME or via b-scission of larger chains during
homologation reactions and to contrast the reactivity of branched
and linear butenes. Isobutene can be methylated by DME at its ter-
minal C-atom to form isopentyl molecules or at its tertiary C-atom
to form neopentane after hydrogen transfer. Isopentyl species form
b
0.01
–
–
0.10
0.02
0.04
0.08
0.02
0.05
0.54
0.006
0.05
c
c
Sk
C
a
Rate of neopentane formation below detection limit of gas-chromatograph
3
ꢁ1
(
1.4 ꢂ 10ꢁ
lmol [mol Al s] ).
ꢁ1
at much higher rates (9.5
lmol [mol Al s] ; Table 1) than neopen-
ꢁ3
ꢁ1
consistent with the required involvement of tert-pentyl carbenium
ions with primary character [21]. The selective formation of iso-
pentyl species confirms the preference for transition states that
can delocalize charge over tertiary and secondary C-atoms
tane (below the detection limit of 10
l
mol [mol Al s] ) from
C-DME/ C-isobutene mixtures, consistent with the exclusive
methylation at the terminal carbon in isobutene (Scheme 4). The
1
3
12
1
3
12
isopentane isotopologues formed from
C-DME/ C-isobutene
(
Scheme 4). This preference for isopentyl cations also leads to the
reactants (Fig. 3c) consisted mostly of singly labeled species
(0.63 mole fraction), consistent with their predominant formation
via single C-DME methylation events. The selective methylation
at isobutene terminal carbons reflects the greater stability of its
tert-pentyl carbenium ion transition state compared with the
primary carbenium ion and terminal alkoxides involved in the
smaller barriers of methylation of 2-butenes than 1-butenes
derived from theoretical treatments [21]. Kinetic preferences based
on double-bond location become undetectable by experiment
because of the rapid interconversion among linear butene isomers
in the time scale of methylation turnovers.
1
3

D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
179
a) 1.0
(b)
1.0
(
13
13
C fraction = 0.25
C fraction = 0.49
0.8
0.6
0.4
0.2
0.0
0.8
0.6
0.4
0.2
0.0
M
e
F
a
t
o
MleFraction
0
1
2
3
4
5
0
1
2
3
4
1
3
13
Number C atoms
Number C atoms
1.0
0.8
0.6
0.4
0.2
0.0
(
c) 1.0
(d)
1
3
C fraction = 0.34
13
C fraction = 0.20
0.8
0.6
0.4
0.2
0.0
M
e
F
a
t
o
MleFraction
0
1
2
3
4
5
0
1
2
3
4
1
3
13
Number C atoms
Number C atoms
Fig. 3. Isotopologue distributions and C-atomic fractions for (a) isopentane and (b) isobutane molecules produced from co-reaction of 13C-labeled dimethyl ether (78 kPa)
1
3
with 1 C-linear butene (0.5 kPa) and (c) isopentane and (d) isobutane molecules produced from co-reaction of C-labeled dimethyl ether (78 kPa) with C-isobutene
(
2
13
12
ꢁ
1
0.5 kPa). Reactions conducted at 473 K on H-BEA (Si/Al = 12.5) at space velocity of 0.025 mol inlet gas [mol Al s] with >90% alkene conversion and less than 5% total carbon
conversion (DME and alkene).
formation of the neopentyl precursors to neopentane, consistent
with theoretical estimates, indicating that the methyl group is
preferentially placed at the less substituted C-atom in the C@C
bond of an alkene [21]. The presence of isotopologues other than
singly labeled isopentane (Fig. 3a and c) indicates that some iso-
pentane molecules are produced from growing chains that undergo
b-scission reactions, thus returning the alkenes formed to the
methylation pathways leading to isopentane and larger alkanes.
Comparison of the rates of methylation of butene isomers and
hydrogen transfer to their respective alkoxides (and their respec-
tive b values) allows consideration of how the structure of these
molecules and the stability of the respective carbenium ion transi-
tion states lead to a preference for chain growth for butyl species
and for termination in the case of isobutyl species. Unlabeled
isobutane is the predominant isotopologue formed from
and tert-pentyl carbenium ion transition states required for hydro-
gen transfer to tert-butoxide [30,33] and for methylation of isobu-
tene [21] (Scheme 4), respectively. In contrast to isobutyl species,
sec-butoxides undergo hydrogen transfer at much lower rates than
ꢁ1
n-butenes methylate (5.8 vs. 53–68 lmol [mol Al s] ; Table 1)
because hydrogen transfer involves secondary n-butyl carbenium
ions in transition states, while methylation proceeds via more sta-
ble tert-pentyl carbenium ions with tertiary character. These rates
4
of methylation and hydrogen transfer for C species result in higher
termination probabilities (b) in reactions of isobutene than linear
butenes (0.54 vs. 0.08–0.10; Table 2), which reflect the more stable
transition state for hydrogen transfer to tert-butoxides than to
sec-butoxides as a result of the tertiary carbenium ions involved
in hydrogen transfer to branched alkoxides [30,33] (Scheme 4).
These b values also suggest that methylation of primary–tertiary
C@C bonds in isobutene would involve a less stable transition state
than methylation of secondary–secondary C@C bonds in 2-butene,
because the former bonds retain some positive charge at a primary
C-atom in its transition state [21,24] (Scheme 4).
1
3
12
C-DME/ C-isobutene mixtures (0.68 mole fraction; Fig. 3d), indi-
cating that tert-butoxide species formed via protonation of isobu-
tene undergo rapid hydrogen transfer to form isobutane. The
similar rates of hydrogen transfer to tert-butoxide (38
l
l
mol
mol
ꢁ1
[
[
mol Al s] ; Table 1) and methylation of isobutene (33
mol Al s] ; Table 1) reflect the similar stabilities of tert-butyl
4
We conclude from these b values that linear C species preferen-
ꢁ1
tially grow to form branched C chains (via n-butene methylation),
5

1
80
D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
(a)
Hydrogen Transfer
*
CH3
β
-scission
+
+
*
δ+
*
δ+
Methylation
C
H
3
+
*
δ+
δ+
Methylation
CH
3
*
Isomerization
(b)
Hydrogen Transfer
*CH3
β-scission
+
+
*
δ+
CH
δ+
Methylation
*
*
3
+
*
Isomerization
β
-scission of C8+
…
Scheme 4. Reaction pathways for (a) n-butyl species (n-butenes and sec-butoxide) and (b) isobutyl species (isobutene and tert-butoxide) in acid-catalyzed dimethyl ether
homologation pathways. Methylation of n-butene to isopentyl species occurs faster than hydrogen transfer to sec-butoxide. Methylation of isobutene to isopentyl species
occurs slower than hydrogen transfer to tert-butoxide. Isomerization and b-scission of both sec-butoxide and tert-butoxide occur much more slowly than hydrogen transfer to
these alkoxides and methylation of their alkenes.
while isobutyl species predominantly terminate as isobutane
via hydrogen transfer to tert-butoxide). We also find that branched
facile hydrogen transfer to tert-butoxides that would prevail
from the alternate methylation of propene at its internal carbon
atom.
(
species give higher termination probabilities than their linear iso-
mers, because their tertiary C-atoms form more stable cationic tran-
sition states for hydrogen transfer. These b values also show that the
preferential formation of linear butenes from propene avoids
premature chain termination during methylation reactions via the
3 4
Schemes 3 and 4 show the reaction pathways for C and C spe-
cies during homologation of DME (or methanol) on Brønsted acid
sites. The formation of stable cationic transition states dictates
the selective methylation at the terminal C-atom in propene to

D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
181
Table 2
l
mol [mol Al s] 1) of methylation, hydrogen transfer, skeletal isomerization, b-scission, and methylation at internal C-atoms (Rinternal C-atoms) and terminal C-atoms
ꢁ
(
(
a) Rates (
13
R
terminal C-atoms) and (b) 2-/1-alkene ratios and termination (b), skeletal isomerization (cSk), methyl shift isomerization (cMS), and b-scission (c ) probabilities for reactions of C-
C
labeled dimethyl ether (78 kPa) and 0.5 kPa of unlabeled 2-methyl-2-butene (2M2B), 2-pentene (2P), 2,3-dimethyl-2-butene (23DM2B), 2-methyl-2-pentene (2M2P), triptene,
,4-dimethyl-2-pentene (24DM2P), or 3,4,4-trimethyl-2-pentene (344TM2P) at 473 K on H-BEA (Si/Al = 12.5). Reactions conducted at space velocity of 0.024 mol inlet gas
2
ꢁ
1
[
mol Al s] with >90% alkene conversion and less than 5% total carbon conversion (DME and alkene).
Co-feed alkene
2
M2B
2P
23DM2B
2M2P
Triptene
24DM2P
344TM2P
(
a)
Methylation
56
21
59
3.9
0.25
0.66
13
70
66
13
0.2
0.8
18
–
33
48
0.91
0.77
–
91
17
2.0
1.9
5.0
–
25
0.02
–
Hydrogen Transfer
Skeletal Isomerization
b-scission Cracking
7.4
0.73
1.0
45
5.0
0.16
0.22
46
a
d
b
e
c
0.02c
–
R
R
internal C-atoms
30
d
e
c
terminal C-atoms
8.0
–
0.19
(
2
b
c
c
c
b)
-/1-Alkene ratio
3.4f
–
1.3g
0.10
0.009
0.013
–
–
–
–
–
0.27
0.002
0.003
–
0.06
0.004
0.005
–
0.16
0.002
0.010
0.03
0.59
0.011
0.009
–
0.17
0.018
0.018
0.04
0.001
–
1.3
–
Sk
C
MS
a
b
c
d
e
f
2
,3-Dimethylbutyl species.
Triptyl species.
Total rate of formation of trimethylpentyl isomers.
Methylpentyl species and 2,2-dimethylbutyl species.
Dimethyl-pentyl species.
Ratio of 2-methyl-2-butene to the sum of 2-methyl-1-butene and 3-methyl-1-butene.
Ratio of 2,3-dimethyl-2-butene to 2,3-dimethyl-1-butene.
g
form linear butyl chains (Fig. 2a) and internal C-atoms in linear bu-
tenes to form isopentyl species (Fig. 3a). These methylation trends
preserve the four-carbon backbone also present in triptane
cies as isobutane (b = 0.54; Table 1) after they form via b-scission
of larger chains, but a fraction of these isobutyl species are incor-
porated into the chain growth path and ultimately appear as trip-
tane via selective methylation of isobutene to isopentyl species (as
shown in Fig. 3c and Scheme 4).
(Scheme 2) and account for the early steps in its preferential for-
mation in DME and methanol homologation. We conclude that
the relative stabilities of ion-pairs at methylation transition states
lead to the selective formation of n-butyl species from propene and
isopentyl species from n-butenes at rates faster than those of the
intervening isomerization, b-scission, or hydrogen transfer of the
respective alkoxides (as shown by the termination, isomerization,
and b-scission probabilities in Table 1). The relative transition state
stabilities for hydrogen transfer to tert-butoxide and methylation
of isobutene leads to the preferential termination of isobutyl spe-
3.3. Propagation, termination, isomerization, and b-scission of C
5 7
–C
species
Next, we examine the isotopologue distributions of Cn+1 (Fig. 4)
13
12
and C
alkenes and the chain termination, isomerization, and b-scission
probabilities (Table 2) of C –C molecules involved as intermediates
4
(Fig. 5) products formed from C-DME reactions with
n
C -
5
7
1.0
0.8
0.6
0.4
0.2
0.0
(b)1.0 13
(c) 1.0
(
a)
13
C fraction = 0.37
C fraction = 0.15
13
C fraction = 0.25
0.8
0.8
0.6
0.4
0.6
0.4
M
l
e
F
r
a
c
t
i
o
n
M
e
F
a
t
o
MleFraction
0.2
0.0
0.2
0.0
0
1
2
3
4
5
6
0
1
2
3
4
5
6
0
1
2
3
13
4
5
6
13
13
Number C atoms
Number C atoms
Number C atoms
Fig. 4. Isotopologue distributions and C-atomic fractions of (a) 2,3-dimethylbutane molecules and (b) 2-methylpentane molecules produced from co-reaction of 13C-labeled
1
3
1
2
13
12
dimethyl ether (78 kPa) with C-2-methyl-2-butene (0.5 kPa) and (c) triptane molecules produced from co-reaction of C-labeled dimethyl ether (78 kPa) with C-2,3-
dimethyl-2-butene (0.5 kPa). We use the 85 amu fragment of triptane as a surrogate for the parent ion, because the former appears in much higher concentrations in the mass
ꢁ
1
spectrometer than the latter. Reactions conducted at 473 K on H-BEA (Si/Al = 12.5) at space velocity of 0.025 mol inlet gas [mol Al s] with >90% alkene conversion and less
than 5% total carbon conversion (DME and alkene).

1
82
D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
(
a) 1.0
(b) 1.0
(c) 1.0
13
1
3
C fraction = 0.35
13
C fraction = 0.50
C fraction = 0.25
0.8
0.6
0.4
0.2
0.0
0.8
0.6
0.4
0.2
0.0
0.8
0.6
0.4
M
l
e
F
r
a
c
t
i
o
n
M
e
F
a
t
o
MleFraction
0.2
0.0
0
1
2
3
4
0
1
2
13
3
4
0
1
2
13
3
4
13
Number C atoms
Number C atoms
Number C atoms
(
d) 1.0
(e) 1.0
(f)1.0
1
3
13
13
C fraction = 0.46
C fraction = 0.35
C fraction = 0.25
0.8
0.6
0.4
0.2
0.0
0.8
0.8
0.6
0.4
0.6
0.4
M
l
e
F
r
a
c
t
i
o
n
M
e
F
a
i
n
MleFraction
0.2
0.0
0.2
0.0
0
1
2
3
4
0
1
2
3
4
0
1
2
3
4
1
3
13
13
Number C atoms
Number C atoms
Number C atoms
Fig. 5. Isotopologue distributions and C-atomic fractions of isobutane (a–c) and trans-2-butene (d–f) molecules produced from co-reaction of 13C-labeled dimethyl ether
1
3
1
2
12
12
(
78 kPa) with 0.5 kPa of C-2-methyl-2-butene (panels a and d), C-2,3-dimethyl-2-butene (panels b and e), and C-triptene (panels c and f). Reactions conducted at 473 K
ꢁ
1
on H-BEA (Si/Al = 12.5) and at a space velocity of 0.025 mol inlet gas [mol Al s] with >90% alkene conversion and less than 5% total carbon conversion (DME and alkene).
along the chain growth path to triptane. Specifically, 13C-DME
78 kPa) reactions with unlabeled 2-methyl-2-butene, 2,3-di-
3-methyl-1-butene isomers was similar to that expected at equi-
librium (3.4 vs. 3.6 [10]; Table 2) as a result of fast intramolecular
hydride shift reactions. This equilibrated mixture of isopentenes
(
methyl-2-butene, or triptene (0.5 kPa) were used to probe how the
stability of carbenium ion transition states in methylation reactions
tends to preserve a linear four-carbon backbone along the chain
growth path and ultimately form 2,3,3-trimethyl sec-butoxide; such
species desorb via fast hydrogen transfer to form triptane before sig-
nificant methylation of its triptene desorption products to form C8+
chains. We also examine rates of methylation, termination, isomer-
ization, and b-scission (Table 2) for molecules that do not form along
the methylation route to triptane (from 13C-DME (78 kPa) reactions
with 2-pentene, 2-methyl-2-pentene, and 2,4-dimethyl-2-pentene)
to probe the reactivity of alkene molecules lacking the four-carbon
backbone present in triptane.
1
3
can undergo methylation by C-DME and subsequent deprotona-
tion or hydrogen transfer (Scheme 5) at the secondary C-atom of
2-methyl-2-butene to form 2,3-dimethylbutyl species (2,3-
dimethylbutane and 2,3-dimethylbutenes), at terminal C-atoms
of 2-methyl-1-butene and 3-methyl-1-butene to form methyl-pen-
tyl isomers (2-methylpentane, 3-methylpentane, 2-methylpent-
enes, 3-methylpentenes, and 4-methylpentenes), and at the
tertiary C-atom of 2-methyl-2-butene to form 2,2-dimethylbutyl
isomers (2,2-dimethylbutane and 4,4-dimethyl-1-butene).
The rate of formation of 2,3-dimethylbutyl species from
1
3
12
mixtures of
[
C-DME with
mol Al s] ; Table 2) is significantly larger than the combined
rates of formation of methyl-pentyl and 2,2-dimethylbutyl spe-
C-2-methyl-2-butene (4.9 lmol
ꢁ
1
3.3.1. Methylation of isopentenes, linear pentenes, 2,3-
ꢁ1
dimethylbutenes, methylpentenes, triptene, and dimethyl-pentenes
cies (0.9 lmol [mol Al s] ; Table 2), indicating that methylation
1
3
12
Reactions of C-DME with C-2-methyl-2-butene give the
rates and position of methylation of isopentene intermediates
shown in the previous section to form preferentially in
methylation reactions of n-butenes and isobutene. The ratio of
occurs preferentially at the secondary C-atom in 2-methyl-2-bu-
tene instead of at the terminal or the tertiary C-atom of the other
isopentene isomers (Scheme 5). Isotopologues of 2,3-dimethylbu-
tane (and all 2,3-dimethylbutenes) predominantly consist of sin-
gly labeled species (0.77 mole fraction; Fig. 4a), indicating that
2
-methyl-2-butene to the sum of the 2-methyl-1-butene and

D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
183
(a)
Hydrogen Transfer
*
+
*
CH3
*
+
β
-scission
+
*
δ+
δ+
*
Methylation
C
H
3
*
+
*
δ+
δ+
*
δ+
*
CH
3
δ+
Isomerization
Methylation
CH
3
(b)
Hydrogen Transfer
*
+
*
CH3
+
*
β
-scission
+
*
*
δ+
*
δ+
CH
3
Methylation
+
*
Isomerization
Scheme 5. Reaction pathways for (a) isopentyl species (isopentenes and 2-methyl sec-butoxide) and (b) n-pentyl species (n-pentenes and sec-pentoxide) in acid-catalyzed
dimethyl ether homologation pathways. Methylation of isopentene to 2,3-dimethylbutyl species occurs faster than hydrogen transfer to 2-methyl sec-butoxide. Methylation
of n-pentenes to methyl-pentyl species occurs faster than hydrogen transfer to sec-pentoxide. Isomerization and b-scission of both sec-pentoxide and 2-methyl sec-butoxide
occur much more slowly than hydrogen transfer to these alkoxides and methylation of their alkenes.
most of them form via a single methylation of 2-methyl-2-butene
at its secondary carbon. In contrast, isotopologues of 2-methyl-
pentanes (and methyl-pentenes) form only after significant intra-
molecular rearrangements of larger chains that then undergo b-
scission and subsequent methylation events. The preference for
methylation of the tertiary–secondary C@C bond of 2-methyl-2-
butene to form 2,3-dimethyl sec-butoxide reflects the greater
stability of carbenium ion transition states with their charge at
1
3
pentane (and of all methyl-pentyl species) formed from C-
DME/1 C-2-methyl-2-butene mixtures show
2
a much broader
13
distribution (Fig. 4b) and a much larger C content than 2,3-
dimethylbutane (0.37 vs. 0.15). These data indicate that methyl-

1
84
D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
(a)
Hydrogen Transfer
*
+
*
CH3
-scission
*
+
β
+
*
*
δ+
δ+
C
H
Methylation
3
+
δ+
δ+
*
CH
3
*
Isomerization
Methylation
(b)
Hydrogen Transfer
*
*
+
+
*
β
-scission
+
*
δ+
*
δ+
C
H
Methylation
3
+
δ
+
*
δ+
CH
3
*
Isomerization
Methylation
Scheme 6. Reaction pathways for (a) 2,3-dimethylbutyl species (2,3-dimethylbutenes and 2,3-dimethyl sec-butoxide) and (b) methyl-pentyl species (methyl-pentenes and
-methyl sec-pentoxide) in acid-catalyzed dimethyl ether homologation pathways. Methylation of 2,3-dimethylbutenes to triptyl species occurs faster than hydrogen transfer
2
to 2,3-dimethyl sec-butoxide. Methylation of methyl-pentenes to dimethyl-pentyl species occurs faster than hydrogen transfer to 2-methyl sec-pentoxide. Isomerization and
b-scission of both 2,3-dimethyl sec-butoxide and 2-methyl sec-pentoxide occur much more slowly than hydrogen transfer to these alkoxides and methylation of their alkenes.
tertiary and secondary C-atoms [21], compared with those re-
quired for methylation of the primary–tertiary or primary–sec-
ondary C@C bonds in 2-methyl-1-butene or 3-methyl-1-butene,
respectively, which retain some charge at a primary C-atom
Reactions of 13C-DME with 12C-2,3-dimethyl-2-butene allow
estimates of the rate and position of methylation of the 2,3-dimeth-
ylbutenes that preferentially form by methylation of isopentenes.
Fast intramolecular hydride shifts lead to ratios of 2,3-dimethyl-
2-butene to 2,3-dimethyl-1-butene at near equilibrium values (1.3
(Scheme 5).

D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
185
(a)
Hydrogen Transfer
+
*
*
*
CH3
+
β
-scission
+
δ
+
*
H
C
3
*
δ
+
Methylation
+
*
Isomerization
(b)
Hydrogen Transfer
*
β
-scission
+
+
*
δ+
δ+
*
Methylation
C
H
3
+
*
Isomerization
Scheme 7. Reaction pathways for (a) triptyl species (triptene and 2,3,3-trimethyl sec-butoxide) and (b) dimethyl-pentyl species (dimethyl-pentenes and 2,4-dimethyl sec-
pentoxide) in acid-catalyzed dimethyl ether homologation pathways. Methylation of triptene to 3,4,4-trimethyl sec-pentoxide occurs much more slowly than hydrogen
transfer to 2,3,3-trimethyl sec-butoxide. Methylation of methyl-pentenes to 2,3,4-trimethyl sec-pentoxide occurs faster than hydrogen transfer to 2,4-dimethyl sec-pentoxide.
Isomerization and b-scission of both 2,3,3-trimethyl sec-butoxide and 2,4-dimethyl sec-pentoxide occur much more slowly than hydrogen transfer to these alkoxides and
methylation of their alkenes.
vs. 1.5 [10]; Table 2). This equilibrated mixture of 2,3-dimethylbut-
enes can grow via methylation at internal tertiary carbons to form
triptyls (triptane and triptene) or at terminal carbon atoms to form
terminal C-atoms in 2,3-dimethyl-1-butene (Scheme 6). The
predominant triptane isotopologues are singly labeled (Fig. 4c),
consistent with their formation via a single methylation of 2,3-dim-
ethylbutenes. This methylation position again preserves the four-
carbon backbone, as in the case of the preferential methylation
routes for n-butenes and isopentenes (Schemes 4 and 5). These data
show that chain growth in acid-catalyzed homologation reactions
2
,3-dimethyl-pentyls (2,3-dimethylpentane, 2,3-dimethylpent-
1
3
enes, and 3,4-dimethylpentenes). Triptyls form from C-DME/
1
2
C-2,3-dimethyl-2-butene reactants much faster (49
l
l
mol
mol
ꢁ
1
[
[
mol Al s]
; Table 2) than 2,3-dimethyl-pentyls (1.5
ꢁ1
mol Al s] ; Table 2), indicating that methylation occurs preferen-
involvesthestep-wiseadditionof C
1
species(derivedfrommethanol
tially at internal C-atoms in 2,3-dimethyl-2-butene instead of
and DME) to alkene intermediates at positions that selectively form

1
86
D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
Scheme 7
Scheme 7
+
+
*
*
*
*
+
+
+
*
*
*
Scheme 8. b-Scission pathways for trimethylpentoxides that form from methylation of triptene and 2,4-dimethyl-2-pentene. b-Scission of 3,4,4-trimethyl sec-pentoxide and
2
,4,4-trimethyl sec-pentoxide occurs more rapid than b-scission of 2,3,4-trimethyl sec-pentoxide.
the four-carbon backbone and then preserve it along the path to
triptane shown in Scheme 2. This selective C addition occurs
2,2,3- and 2,2,4-Trimethylpentane isomers were also unde-
1
3
12
1
tected among the products formed from
C-DME/ C-2,4-di-
because methylation of alkenes occurs at positions for which the
required transition state involves the most stable carbenium ion.
Such pathways lead to the formation of highly branched products,
which involve transition states with more highly substituted carbe-
nium ions than those involved in the formation of less branched
isomers.
methyl-2-pentene reactants. The combined rates of formation of
2,3,4-trimethylpentane and 2,3,3-trimethylpentane in this case
ꢁ1
(5.7
formation rate (20
ylpentane selectivity within C
methyl-2-pentene (relative to
l
mol [mol Al s] ; Table 3) accounted for ꢀ30% of the total
ꢁ1
C
8
lmol [mol Al s] ). The higher 2,3,4-trimeth-
1
3
12
8
species from C-DME/ C-2,4-di-
1
3
12
C-DME/ C-triptene reactants)
13C-DME reactions with unlabeled 2-pentenes (mixture of cis
and trans isomers) or 2-methyl-2-pentene were used to examine
indicates that dimethyl-pentenes are methylated at internal C-
atoms (or internal alkenes) to form 2,3,4-trimethylpentyl isomers
that undergo slower b-scission reactions than 2,2,3- and 2,2,4-
trimethylpentyl isomers (Schemes 7 and 8).
5 6
the rate and position of methylation for C –C molecules that do
not preferentially form along the DME homologation route to trip-
tane. The rate of formation of methyl-pentyl species (2-methylpen-
tane, 3-methylpentane, 2-methylpentenes, 3-methylpentenes, and
8
These data indicate that triptene is methylated to C isomers
that undergo rapid b-scission before hydrogen transfer, reflecting
the formation of stable tertiary transition states in b-scission reac-
tions of 2,2,3- and 2,4,4-trimethyl sec-pentoxides [40–44] formed
via triptene methylation and subsequent methyl shifts (Schemes
7 and 8). 2,3,4- and 2,3,3-Trimethylpentanes are much more abun-
dant among octane isomers than 2,2,4- and 2,2,3-trimethylpen-
tanes, because the latter give more favorable b-scission transition
states and are rapidly depleted via such reactions [40,41,44]. This
4
-methylpentenes) is higher for 2-pentene than for 2-methyl-2-
ꢁ1
butene (13 vs. 8.0 lmol [mol Al s] ), and the rate of formation
of dimethyl-pentyl species (2,3-dimethylpentane, 2,3-dimethyl-
pentenes, and 3,4-dimethylpentenes) from 2-methyl-2-pentene
was also larger than from 2,3-dimethyl-2-butene (18 vs. 5.0
l
mol
al-
ꢁ1
[
5 6
mol Al s] ). These data show that methylation of C and C
kenes without the four-carbon backbone leading to triptane occurs
selectively at internal C-atoms (or internal alkenes) to form larger
homologs that also lack the required four-carbon backbone
8
rapid b-scission of C species and its role in returning the frag-
ments of larger molecules to the chain growth path and in the for-
mation of isobutane are discussed in detail in Section 3.4.
(
Schemes 5b and 6b). We show below (Section 3.3.3) that hydro-
gen transfer to these alkoxides is slower than methylation of the
corresponding alkenes, causing them to grow beyond C chains.
C-DME reactions with C-triptene or C-2,4-dimethyl-2-
pentene were used to examine the rate and position of methylation
of these two C alkene isomers to form C molecules. 2,2,3-Trim-
7
1
3
12
12
Table 3
Termination probabilities (b) and C-fractions within hexamethyl benzene (13C-
1
3
13
13
7
8
HMB) and Cn+1 alkane (
Cn+1) molecules for reactions between C-labeled dimethyl
ethylpentane (formed via methylation of triptene at its terminal
C-atom; Scheme 7) and 2,2,4-trimethylpentane (formed via meth-
ylation of triptene followed by methyl shifts; Scheme 8) were not
ether (78 kPa) and unlabeled 2-methyl-2-butene (2M2B) or 2,3-dimetyl-2-butene
(23DM2B) at 473 K on H-BEA. Reactions carried out between 2% and 7% total carbon
conversions (DME and alkene) with >90% conversion of alkenes.
1
3
12
ꢁ3
detected in
C-DME reactions with
C-triptene (<10
lmol
Co-feed alkene
ꢁ
1
[
mol Al s] ). The combined rates of formation of 2,3,4-trimethyl-
M2Ba
2M2Bb
23DM2Ba
23DM2Bb
2
pentane and 2,3,3-trimethylpentane (the other isomers formed
by methyl shifts along the 2,2,3-trimethylpentane backbone) from
b
0.27
0.15
0.75
0.48
0.14
0.52
0.10
0.27
0.20
0.44
13
c
c
0.26d
d
C
n+1
1
3
12
ꢁ1
C-DME reactions with
C-triptene (0.19
products (0.92
mol Al s] ). These low trimethylpentane formation rates suggest
l
mol [mol Al s]
;
13C-HMB
0.72
Table 2) account for ꢀ20% of all
C
8
lmol
a
b
c
ꢁ1
0
.5 kPa alkene and at space velocity of 0.024 mol inlet gas [mol Al s]
.7 kPa alkene and at a space velocity of 0.006 mol inlet gas [mol Al s]
C-fraction within 2,3-dimethylbutane molecules.
C-fraction within triptane molecules.
.
ꢁ1
[
ꢁ1
3
.
that trimethyl-pentoxides undergo rapid isomerization and
b-scission prior to hydrogen transfer.
13
13
d

D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
187
These 13C-DME/12C-alkene reaction data also allow accurate
estimates of the total rates of methylation for each of the C –C al-
transfer to tert-butoxide and 2-methyl sec-butoxide compared
with sec-butoxide and sec-pentoxide (33 vs. 5.8 and 21 vs. 3.9 mol
[mol Al s] ; Tables 1 and 2). These hydrogen transfer rates and
trends indicate that alkoxides with tertiary carbon centers form
more stable tertiary carbenium ions upon cleavage of their C–O
bonds than linear alkoxides with similar carbon number.
3
7
l
ꢁ1
kenes used (Tables 1 and 2); such methylation events include mol-
ecules that formed via multiple methylation events and even
possible subsequent or intervening b-scission (Eq. (4)). The meth-
ylation rates for alkenes that contain only terminal C@C bond iso-
ꢁ
1
mers, such as propene (37
l
mol [mol Al s] ), isobutene (33
l
l
mol
We note, however, that hydrogen transfer rates for 2,3-di-
methyl sec-butoxide are not much larger than for sec-butoxide
ꢁ1
ꢁ1
[
mol Al s] ), and triptene (34
mol [mol Al s] ) are smaller than
ꢁ
1
for alkenes that can form internal C@C bonds, such as n-butenes
(7.4 vs. 5.8
methyl sec-pentoxide (13
l
mol [mol Al s] ) and actually smaller than for 2-
ꢁ
1
ꢁ1
ꢁ1
(
53–68
l
mol [mol Al s] ), isopentenes (56
l
mol [mol Al s] ),
l
mol [mol Al s] ; Table 2) in spite of
ꢁ
1
and 2,3-dimethylbutenes (70
l
mol [mol Al s] ). These trends re-
the tertiary character in the hydrogen transfer transition state for
2,3-dimethyl sec-butoxide. This appears to reflect the high rates
of 2,3-dimethyl-2-butene methylation (Table 2), which deplete it
along the catalyst bed, with a consequent decrease in 2,3-dimethyl
sec-butoxide concentrations available for hydrogen transfer. We
flect the greater stability of the more highly substituted methyla-
tion transition states of internal alkenes that avoid the
involvement of terminal carbons, which form carbenium ions with
primary character [21,46].
In general, the rates and selectivities (shown in the supporting
information) derived from 13C-DME/ C-alkene experiments are
consistent with two general features of methylation of alkenes
also note that the rates of hydrogen transfer of tert-butoxide
12
ꢁ1
(33
(38
l
mol [mol Al s] ; Table 1) and 2,3,3-trimethyl sec-butoxide
ꢁ1
lmol [mol Al s] ; Table 2) are larger than for 2-methyl
by C
1
species derived from methanol or DME: (i) C
1
species add
sec-butoxide, 2,3-dimethyl sec-butoxide, and 2,4-dimethyl sec-
pentoxide (21, 7.4, and 17 lmol [mol Al s] ; Table 2), in spite of
ꢁ
1
at the less substituted C-atom in the alkene C@C bond so as to pre-
serve the more highly substituted C center (and the more stable
carbenium ion at the transition state) and (ii) methylation is faster
for molecules that can form internal alkenes (n-butenes, isopent-
enes, and 2,3-dimethylbutenes) than for molecules that can form
only terminal alkanes (propene, isobutene, and triptene), because
internal alkenes preclude the need to form carbenium ions with
primary character in methylation transition states. As a result, high
triptyl selectivities in acid-catalyzed DME homologation merely re-
flect the stability of ion-pairs at methylation transition states,
which favor methylation positions that form molecules with
four-carbon backbones and the higher methylation rates for triptyl
precursors (n-butene, 2-methyl-2-butene, and 2,3-dimethyl-2-bu-
tene) than for triptene. It also reflects the high termination proba-
bilities via hydrogen transfer to alkoxides with tertiary carbon
atoms, as we discuss next.
the presence of tertiary carbenium ions in all of their hydrogen
transfer transition states. These trends suggest that low methyla-
tion rates of isobutene and triptene (compared with isopentenes,
2,3-dimethylbutenes, and 2,4-dimethylpentenes; Tables 1 and 2)
lead to large intracrystalline concentrations and thus higher sur-
face concentrations of the corresponding alkoxides and higher
rates of hydrogen transfer compared to other alkoxides that also
form tertiary carbenium ion transition states in hydrogen transfer.
Intracrystalline alkene gradients and their high reactivity and con-
versions make accurate estimates of hydrogen transfer rates diffi-
cult. In what follows, we circumvent such difficulties by
comparing termination probabilities (b), which contain ratios of
methylation and hydrogen transfer rates, which are both propor-
tional to alkene concentrations and thus unaffected by alkene gra-
dients that depend on the size and reactivity of individual alkenes.
Table 2 shows b values for molecules formed in DME homologa-
tion reactions. Triptyl (b = 0.59; Table 2) and isobutyl (b = 0.54;
Table 2) species exhibit much higher termination probabilities
3.3.2. Hydrogen transfer to alkoxides derived from C
5 7
–C alkenes
In this section, we address the effect of co-fed alkene size on
hydrogen transfer rates (Table 2a) to provide evidence for the role
of alkoxide structure on hydrogen transfer rates and its conse-
quences for chain termination probabilities and for selective trip-
tane formation. We also show how the relative magnitude of
methylation and hydride transfer rates (reflected in termination
probabilities shown in Table 2b) of highly branched species com-
3 6
compared with C –C species that form along the chain growth
path to triptane (0.01, 0.10, 0.27, and 0.10 for propyl, n-butyl, iso-
pentyl, and 2,3-dimethylbutyl species, respectively; Tables 1 and
2). The high b values for isobutyl and triptyl species reflect the fast
hydrogen transfer to their respective alkoxides, which involve ter-
tiary carbenium ion transition states (Schemes 4b and 7a). The cor-
responding low rates of methylation of isobutene and triptene,
which involve species with significant charge at primary carbons,
also contribute to the high b values for isobutyl and triptyl species
(Schemes 4b and 7a) and to the predominance of triptane and iso-
butane as DME homologation products (Fig. 1 in [9] and Figs. S1–S2
in the supporting information).
1
bine to lead to their selective formation during C homologation
reactions involving methylation of alkenes and hydrogen transfer
to the resulting alkoxides to form the respective alkanes.
Alkenes introduced with 13C-DME protonate to form alkoxides
that desorb either via deprotonation or hydrogen transfer in
reactions concurrent with the methylation of such alkenes via
reactions with adsorbed DME-derived C
1
species. The relative rates
Low b values for propyl, n-butyl, isopentyl, and 2,3-dimethylbu-
tyl species indicate that methylation of their alkenes is much faster
than hydrogen transfer to their respective alkoxides. Preferential
chain growth can arise from low hydrogen transfer rates (hydrogen
transfer to propoxide; Table 1), high methylation rates (methyla-
tion of 2,3-dimethylbutenes; Table 2), or both (hydrogen transfer
to sec-butoxide and methylation of n-butenes; Table 1). Propene
methylation is slow (relative to larger alkenes) because, as in the
case of isobutene and triptene, it contains only terminal C@C
of methylation of alkenes and of hydrogen transfer to their
respective alkoxides determine the probability that these growth
pathways will be interrupted by the formation of less reactive
alkanes. The rates of formation of the unlabeled alkane correspond-
ing to the co-fed alkene gives accurate estimate rates of hydrogen
transfer and termination probabilities (b; Eq. (5)) for C
formed during DME and methanol homologation on solid acids.
Hydrogen transfer rates to alkoxides derived from C –C
kenes along the chain growth path to triptane (21, 7.4, and
5 7
–C species
5
7
al-
bonds; however, C
3
species preferentially methylate because
ꢁ
1
4
9
l
mol [mol Al s] for 2-methyl sec-butoxide, 2,3-dimethyl sec-
hydrogen transfer to sec-propoxides (requiring secondary carbe-
nium ions) is slower than methylation of propene (and also slower
than hydrogen transfer to larger alkoxides) (Section 3.1; Scheme 3).
In contrast, 2,3-dimethyl sec-butoxides form tertiary carbenium
ions during hydrogen transfer, but the fast methylation of 2,3-di-
methyl-2-butene (a tetra-substituted alkene) leads to low chain
butoxide, and 2,3,3-trimethyl sec-butoxide, respectively; Table 2)
ꢁ1
are much larger than for propoxide (0.5
l
mol [mol Al s] , Table 1)
ꢁ1
and n-butoxide (5.8
lmol [mol Al s] ; Table 1). The higher hydro-
gen transfer rates to branched alkoxides relative to the correspond-
ing linear alkoxide is also reflected in the higher rates of hydrogen

1
88
D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
termination probabilities (Scheme 6). n-Butyl species show low b
values because the internal C@C bonds of n-butenes undergo rapid
methylation (via tert-pentyl carbenium ions), while sec-butoxides
undergo slow hydrogen transfer (via secondary carbenium ions)
as shown in Scheme 4a. High b values reflect fast hydrogen transfer
substituted alkenes and tertiary alkoxides (Scheme 6). In contrast
with methyl-pentyl and 2,3-dimethylbutyl species, isopentyl and
triptyl species (discussed in previous and latter paragraphs, respec-
tively) do not share these properties with their less branched iso-
mers (n-pentyls and dimethyl-pentyls) and consequently exhibit
higher b values.
(
tertiary alkoxides) and slow methylation (terminal alkene); con-
versely, low termination probabilities reflect stable transition
states for methylation of alkenes with alkyl substituents at both
C-atoms in the C@C bond (n-butenes, 2-methyl-2-butene, and
The reactions of 13C-DME with 12C-2,4-dimethyl-2-pentene
were used to explore backbone structure effects on b values for
C
7
species. The ability of dimethyl-pentenes to form internal
alkenes compared with triptene (which can only form a terminal
alkene) leads to their higher rates of methylation (91 vs. 33 mol
2
,3-dimethyl-2-butene) and/or secondary carbenium ions in
hydrogen transfer steps (sec-propoxide and sec-butoxide). High
triptane selectivities (Fig. S1 in the supporting information) result,
in turn, from chain growth intermediates (propyl, n-butyl, isopen-
tyl, and 2,3-dimethylbutyl species) with low termination probabil-
ities and with a sharp increase in termination probability at
triptyls.
l
ꢁ1
[mol Al s] ; Table 2), which leads in turn to lower hydrogen trans-
fer rates because of rapid depletion of dimethyl-pentenes and the
corresponding alkoxide along the catalyst bed. As a result, di-
methyl-pentyl species exhibit smaller rates of hydrogen transfer
ꢁ1
than triptyls (17 vs. 48 lmol [mol Al s] ; Table 2), even though
The guiding principles responsible for acid-catalyzed synthesis
of triptane via C homologation and relating molecular properties,
1
both 2,3,3-trimethyl sec-pentoxide and 2,4-dimethyl sec-pentoxide
form tertiary carbenium ions at their hydrogen transfer transition
states (Scheme 7). These rates give, in turn, smaller b values for di-
methyl-pentyl (0.17; Table 2) than triptyl (0.59; Table 2) species.
We conclude that high triptyl selectivities among C products re-
7
flect not only their favored formation via alkene methylation
events (Section 3.3.1), but also their higher termination probabili-
carbenium ion transition state stabilities, and chain termination
probabilities also apply to other molecules, such as those lacking
13
the four-carbon backbone of triptane. C-DME reactions with
1
2
12
12
C-2-pentenes, C-2-methyl-2-pentene, and C-2,4-dimethyl-2-
pentene were carried out to determine b values for these species
and contrast them with their more highly branched isomers and
to confirm the effects of backbone structure on chain termination
probabilities. The rate of hydrogen transfer to sec-pentoxide is
7
ties compared with less highly branched C isomers.
The reaction pathways depicted in Scheme 2 and the termina-
tion probabilities for all species and intermediates involved (Tables
1 and 2) account for the remarkable isobutane and tiptane selectiv-
ities found in DME homologation on Brønsted acid sites. Triptyl
and isobutyl species are preferentially detected among products
because of their slow methylation (only terminal C@C bonds)
and the fast hydrogen transfer to their tertiary alkoxides. Methyl-
ation positions dictated by the stability of the cationic transition
states involved lead to the retention of the four-carbon backbone
in triptane, but these species (n-butyl, isopentyl, and 2,3-dim-
ethylbutyl) contain internal C@C bonds and methylate rapidly via
highly substituted carbenium ions that cause them to terminate
infrequently until they form triptane. Isobutane does not form
via primary DME homologation pathways, but appears as a
predominant product because of its preferential formation via b-
scission of C8+ chains and the fast hydrogen transfer rates of tert-
butoxide species formed by isobutene protonation. Intermediates
that form via methylation of alkenes at less preferred positions
ꢀ
5 five times smaller than for 2-methyl sec-pentoxide (3.9 vs.
ꢁ1
21 lmol [mol Al s] ; Table 2), because the transition state for
hydrogen transfer to latter (tertiary carbenium ion; Scheme 5a)
is more stable than that of the former (secondary carbenium ion;
Scheme 5b). The rate of methylation of n-pentenes, however,
ꢁ1
resembles that for isopentenes (59 vs. 56 lmol [mol Al s] ;
Table 2), in spite of the difference in substitution along the back-
bone. As a result, b values are much smaller for n-pentyl than for
isopentyl species (0.06 vs 0.27; Table 2), predominantly because
of the effects of substitution on hydrogen transfer rates. We find
that b values for species of a given carbon number are higher for
the branched isomer compared to the linear isomer, because the
effect of branching on transition state stability is greater for hydro-
gen transfer to their alkoxides than for methylation of the corre-
sponding alkene.
The small b value for n-pentyl species indicates that their meth-
ylation to isohexyl species (Section 3.3.1; Scheme 6b) is faster than
termination of sec-pentoxides to n-pentane causing them to prefer-
entially grow, albeit not along the path to triptane. In what follows,
we show that methy-pentyl species also rapidly methylate to di-
7
forms species that methylate beyond C molecules, because they
can form C@C bonds at non-terminal positions and/or lack the ter-
tiary carbons required for fast hydrogen transfer to form less reac-
tive alkanes.
methyl-pentyl species and then onto C
8
chains, which undergo
Hydrogen transfer involves the removal of a hydride ion from
gas-phase molecules (alkanes or alkenes) to bound alkoxides
[4,9,29–35]. The reactivity of the gas-phase donor depends on its
C–H bond strength; as a result, branched alkanes and alkenes
(and in particular unsaturated species with allylic C–H bonds)
are more effective than linear molecules with C–H bonds only at
primary or secondary carbons. These donors transform into more
unsaturated species upon hydrogen transfer and can subsequently
cyclize to stable arenes, such as hexamethylbenzene (HMB)
[47,48], which are required to satisfy the overall stoichiometry of
DME or methanol conversion to alkanes (according to Eq. (9))
[4,9,17]:
subsequent isomerization and b-scission reactions to form isobutyl
species that rapidly terminate as isobutane via hydrogen transfer
to tert-butoxide. We conclude that the formation of n-pentyl spe-
cies (and other molecules without the four-carbon backbone) do
not decrease the triptane fraction within C
grow beyond C and return some of their carbon atoms to chain
growth pathways via b-scission reactions.
7
products, because they
7
1
3
C-DME reactions with 12C-2-methyl-2-pentene are used next
to extend these conclusions about the effects of structure on b val-
ues to reactions of C species. Both methyl-pentenes and 2,3-dim-
ethylbutenes form highly substituted alkenes and, as a result,
6
ꢁ1
methylate at similar rates (66 and 70
lmol [mol Al s] ; Table 2).
2
-Methyl sec-pentoxide and 2,3-dimethyl sec-butoxide also show
½3n þ 12ꢃCH
3
OCH
3
! 6C
n
H
2nþ2
þ
2C
6
ðCH
3
Þ
þ ½3n þ 12ꢃH
2
O :
6
ꢁ1
Dimethyl Ether
Alkanes
Hexamethylꢁbenzene
Water
similar hydrogen transfer rates (13 vs. 7.4 lmol [mol Al s] ;
Table 2), consistent with the involvement of tertiary carbenium
ions at hydrogen transfer transition states for the respective alkox-
ides. As a result, methyl-pentyl and 2,3-dimethylbutyl species have
similar termination probabilities (0.16 vs. 0.10; Table 2) reflecting
their similar structure and their respective ability to form highly
ð9Þ
In the next section, we examine the effect of alkene concentration in
C-DME/ C-alkene reactants on b values and C-fractions in HMB
(Table 3) to address the molecular properties required of hydrogen
1
3
12
13

D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
189
donors and their role in the rejection of carbon via the formation of
stable unsaturated HMB molecules.
homogeneous or acid-mediated Diels–Alder reactions to form are-
nes through intermolecular pathways that eliminate the need for
intramolecular ring closure steps [47,48,51–59].
3.3.3. Hydrogen transfer to C
5 7
–C alkoxides from prevalent gas-phase
hydrocarbons
3.3.4. Isomerization of alkoxides derived from C
5 7
–C alkenes
Alkanes, alkenes, and even more unsaturated species can act as
hydrogen donors during DME homologation catalysis; their contri-
butions depend on their relative abundance and their reactivity,
which depends on their C–H bond strength and their ability to
accommodate a positive charge as they transfer a hydride to ad-
sorbed alkoxides and ultimately become the bound alkoxide them-
selves. The heterolytic dissociation energies of C–H bonds (to form
an organic cation and a hydride) [49,50] indicate that tertiary
C
5
–C alkoxides along the chain growth path to triptane (2-
7
methyl sec-butoxide, 2,3-dimethyl sec-butoxide, and 2,3,3-tri-
methyl sec-butoxide) can undergo skeletal isomerization and, in
doing so, disrupt their backbone structure before methylation oc-
curs. In this section, we address the isomerization reactivity of alk-
oxides present as bound products of methylation steps along the
chain growth path to triptane using measurements of the chemical
13
and isotopic composition of products (Table 2) formed in C-DME
reactions with C-alkenes.
ꢁ
12
allylic C–H bonds in alkenes are able to donate an H more effec-
tively than primary allylic C–H bonds in alkenes or tertiary C–H
bonds of alkanes, making such species the most effective molecules
among the H-donor pool available during DME homologation and
the likely precursors to polymethylated arenes that provide the
carbon rejection route in DME homologation on solid acids.
2-Methyl sec-butoxide skeletal isomerization rates were mea-
13
sured from the formation rates of unlabeled n-pentane from C-
1
2
DME/ C-2-methyl-2-butene mixtures. In the case of 2,3-dimethyl
sec-butoxide and 2,3,3-trimethyl sec-butoxide isomerization, rates
were measured from the formation rates of unlabeled 2-methyl-
Reactions of C-DME with C-2-methyl-2-butene and 12C-2,3-
dimethyl-2-butene at different inlet pressures (0.5 and 3.7 kPa)
were conducted to probe the effects of alkenes on hydrogen
transfer and the composition of HMB molecules formed as
homologation by-products. The b values for isopentyl and 2,3-
dimethylbutyl species increased from 0.27 to 0.48 and 0.10 to
1
3
12
pentane and 3-methylpentane from C-DME/ C-2,3-dimethyl-2-
butene and of unlabeled 2,3-dimethylpentane and 2,4-dimethyl-
13
12
1
3
12
pentane from
C-DME/ C-triptene, respectively. The ratio of
skeletal isomerization rates to combined rates of methylation
and hydrogen transfer is reported here as the skeletal isomeriza-
tion probability (
dimethylbutyl, and triptyl species (0.002–0.011; Table 2) indicate
that the skeletal isomerization rates for these C –C alkoxides are
cSk; Eq. (6)). Low values of cSk for isopentyl, 2,3-
0
0
.27, respectively (Table 3), as the alkene pressure increased from
.5 to 3.7 kPa. These effects of alkene pressure on b indicate that
5
7
alkenes influence hydrogen transfer rates more strongly than
methylation rates, even though both rates are expected to depend
linearly on alkene pressures [24,30–33], suggesting that alkenes
act as more effective H-donors than the pool of molecules that car-
ry out such reactions during DME homologation without added al-
kenes. Hydrogen transfer from these alkenes to the prevalent
alkoxides can lead to the formation of stable tertiary allylic cations
and to conjugated dienes upon deprotonation of the unsaturated
alkoxide analogs of these cations. Furthermore, the carbenium
ion transition states involved in hydrogen transfer from 2,3-dim-
ethylbutenes and isopentenes are likely to be more stable than
those involved in hydrogen transfer from the prevalent tertiary al-
kanes (isobutane, triptane, isopentane, and 2,3-dimethylbutane).
We conclude from the strong effects of 2,3-dimethyl-2-butene
and 2-methyl-2-butene pressure on termination probabilities that
alkenes with tertiary allylic H-atoms serve as preferred hydrogen
donors because of their weak C–H bonds and stable carbenium
ions; the unsaturated products of their hydrogen transfer reactions
serve as intermediates in the formation of dienes and arenes re-
quired to balance the stoichiometry of DME conversion to alkanes.
much smaller than the rates of hydrogen transfer to their respec-
tive alkoxides and methylation of their respective alkenes. The val-
ues of cSk are much smaller than unity for all relevant species,
indicating that backbone rearrangements occur infrequently along
chain growth to triptane, because the skeletal isomerization of the
relevant alkoxides involve the formation of primary and secondary
cyclopropyl carbenium ion transition states [30,36–39] that are
much less stable than the tertiary cationic transition states in-
volved in methylation of the respective alkenes and hydrogen
transfer to the respective alkoxides (as shown in Schemes 5–7).
The higher isomerization probabilities of 2,3-dimethylbutyl
(0.009) and triptyl species (0.011) compared with isopentyl species
(0.002) reflects the involvement of more stable secondary carbe-
nium ions (Schemes 6 and 7); however, even for these alkoxides,
isomerization remains a minority reaction path compared with
methylation and hydrogen transfer. Therefore, molecules with
four-carbon backbones are kinetically protected against deviations
from their path to triptane because of the nature of their cationic
transition states relative to those involved in the methylation
and hydrogen transfer steps responsible for the growth and termi-
nation of chains.
13
The effects of alkene pressure on the C-atomic fraction within
13
HMB molecules formed in C-DME reactions in the presence of
Acid-catalyzed isomerization also occurs when methyl groups
in alkoxides shift along their backbone; the detection of these
1
2
C-2-methyl-2-butene or 12C-2,3-dimethyl-2-butene can be used
1
3
12
13
to probe the probable precursors of polymethylated arenes. The
pathways from
C-DME/ C-2,3-dimethyl-2-butene and
C-
1
3
13
12
12
C-fraction in HMB molecules formed from
C-DME/ C-2-
DME/ C-trans-2-butene reactants requires that we identify the
location of DME-derived C-atoms within triptane and isopentane
products formed via single methylation events of
methyl-2-butene and C-trans-2-butene, respectively, because
methyl shift isomerization in isopentyl and triptyl species does
not change their molecular identity.
methyl-2-butene and 13C-DME/ C-2,3-dimethyl-2-butene reac-
tants decreased from 0.75 to 0.52 and 0.72 to 0.44 (Table 3),
respectively, as each alkene inlet pressure increased from 0.5 to
12
13
12
C-2,3-di-
1
2
1
3
3
.7 kPa. The C-fraction in HMB decreased with increasing alkene
pressure to a greater extent than in 2,3-dimethylbutane formed
1
3
12
13
from C-DME/ C-2-methyl-2-butene (0.15–0.14; Table 3) or in
The C-fractions within the tert-butyl and iso-propyl mass frag-
1
3
12
13
12
triptane from C-DME/ C-2,3-dimethyl-2-butene (0.26–0.20; Ta-
ble 3). These data indicate that the co-fed alkene is more effectively
converted to HMB via hydrogen transfer cyclization reactions than
to larger alkanes via methylation reactions. We conclude from
these data that alkenes are effective hydrogen donors involved in
chain termination via hydrogen transfer. In doing so, these alkenes
convert to more unsaturated species with even weaker allylic C–H
bonds in diene and triene structures, which can then cyclize via
ments of the triptane molecules formed from C-DME/ C-2,3-di-
methyl-2-butene reactants were 0.199 and 0.203, respectively.
These values are slightly higher than those expected for fast and
equilibrated methyl shift along the backbone of singly labeled trip-
tane molecules (0.15 and 0.13 for tert-butyl and iso-propyl, respec-
tively) as a result of contributions from more highly labeled
1
3
triptane molecules to these C-fractions. The ratio (tert-butyl to
iso-propyl) of these experimental fractions (0.98) is slightly smaller

1
90
D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
than expected from 13C-atoms located with equal probability at all
methyl groups in tert-butyl and iso-propyl groups (1.13), but nev-
ertheless consistent with fast methyl shifts along the 2,3,3-tri-
methyl sec-butoxide backbone. The absence of methyl shifts
13C-DME/12C-2-methyl-2-pentene mixtures and of unlabeled 2,3-
1
3
12
dimethylpentane from C-DME/ C-2,4-dimethyl-2-pentene reac-
tants. The rates of methyl shift along the methyl-pentyl and di-
methyl-pentyl backbones are much slower than the rates of
methylation of their respective alkenes and hydrogen transfer to
1
3
would have placed C only at the tert-butyl end as a result of
1
2
13
methylation of C-2,3-dimethyl-2-butene with C-DME. These
data show that methyl shifts along the hydrocarbon backbone of
their respective alkoxides (
and dimethyl-pentyl species, respectively; Table 2). These low
cMS values are consistent with the non-equilibrium ratios of 2-
cMS = 0.03 and 0.04 for methyl-pentyl
2
,3,3-trimethyl sec-butoxide are fast relative to hydrogen transfer
to this alkoxide and methylation of triptene, as for hydride shifts
leading to double-bond isomerization but not for isomerizations
that change the length of the hydrocarbon backbone. These marked
differences in rate between methyl shift and skeletal isomerization
reflect the more stable carbenium ion transition states required for
shifting methyls along the backbone relative to steps that lengthen
or shorten hydrocarbon backbones in alkoxides [38]. These fast
methyl shifts along the backbone of triptane form the same mole-
cule because the methyl shift occurs along the plane of symmetry
in these molecules and therefore does not affect isomer selectivi-
methylpentane to 3-methylpentane (greater than 3.0 vs. equilib-
rium value of 2.2 at 473 K [10]) and 2,4-dimethylpentane to 2,3-
dimethylpentane (greater than 1.3 vs. equilibrium value of 0.24
at 473 K [10]) formed during DME homologation (see supporting
information). These cMS values also reflect the less stable nature
of the cyclopropyl carbenium ion transition states required for
methyl shifts compared with the tertiary cationic transition states
involved in both hydrogen transfer to their alkoxides and methyl-
ation of their alkenes. The
dimethyl-pentyl chains, however, are higher than their respective
cSk values (0.002 and 0.018 for methyl-pentyl and dimethyl-pentyl
cMS values for these methyl-pentyl and
ties within C
7
hydrocarbons.
The 1 C-fractions within the iso-propyl (0.33) and ethyl (0.47)
3
species, respectively), consistent with the more stable carbenium
ion transition states required for shifting methyls along the back-
bone than those required for lengthening or shortening hydrocar-
bon backbones in alkoxides [38].
The lower rates of methyl shift along the backbones of these
five-carbon backbone molecules relative to that along the back-
bone of triptyl chains reflects the requirement of secondary alkox-
ides and carbenium ion transition states for the former compared
with tertiary species for the latter. These low rates of methyl shift
also reflect the formation of chemically distinct species with differ-
ent properties for methylation of their respective alkenes and
hydrogen transfer to their respective alkoxides. These methyl
shifts, however, are inconsequential to triptane selectivities within
1
3
mass fragments of singly labeled isopentane formed from C-
1
2
DME/ C-trans-2-butene are larger than expected for equilibrated
methyl shift along the alkoxide backbone (0.22 and 0.17 for iso-
propyl and ethyl mass fragments respectively), and their ratio
1
3
(iso-propyl to ethyl) of C-fractions (0.70) is also smaller than ex-
13
pected for fast methyl shifts (1.3). The presence of C-atoms in the
ethyl fragment indicates that methyl shift does occur along 2-
methyl sec-butoxide, because in the absence of such shifts, methyl-
1
2
13
ation of C-trans-2-butene places C-atoms exclusively on the
iso-propyl end of isopentane. The slower methyl shifts in 2-methyl
sec-butoxide compared with 2,3,3-trimethyl sec-butoxide may re-
flect the requirement for secondary alkoxides (3-methyl sec-butox-
ide) and carbenium ion transition states for isopentane instead of
the tertiary alkoxides and transition states required for methyl
shift in triptane.
C
7
species, because the reactants and products in these isomeriza-
tion steps tend to be selectively removed from the C pool by fast
7
chain growth (Sections 3.3.1–3.3.2) and subsequent b-scission
Methyl shifts in 2,3-dimethylbutane are also slower than chain
growth and termination reactions. 2,2-Dimethylbutane is the
(Sections 3.3.5 and 3.4) reactions.
C
2
6
isomer favored by thermodynamics at 473 K (2.9 ratio of
,2-dimethylbutane to 2,3-dimethylbutane [10]) and would pref-
3.3.5. b-Scission reactions of alkoxides derived from C
5 7
–C alkenes
b-Scission of C –C alkoxides along the chain growth path to
5
7
erentially form if methyl shifts were fast. The formation of 2,2-
triptane can also disrupt their linear four-carbon backbones before
methylation of the corresponding alkenes or hydrogen transfer
steps that desorb these alkoxides as alkanes. We measure here
b-scission rates of these alkoxides (Table 2a) and compare them
to rates of hydrogen transfer to the corresponding alkoxides and
methylation of alkenes formed by desorption of these alkoxides
(Table 2b) to probe the effects of chain structures on these rates
and the role b-scission reactions in the selectivity patterns ob-
served in DME homologation reactions.
1
3
12
dimethylbutane from C-DME/ C-alkene reactants, however, is
ꢁ3
ꢁ1
negligible (rates <10
lmol [mol Al s] ; Section 3.3.1 and sup-
porting information). Methyl shift isomerization of 2,3-dimethyl-
butane to 2,2-dimethylbutane requires the formation of a species
with an unfavorable quaternary carbon atom and a secondary car-
benium ion (2,2-dimethyl sec-butoxide), and thus, is unlikely to oc-
cur at rates comparable to methylation of 2,3-dimethylbutene and
hydrogen transfer to 2,3-dimethyl sec-butoxide (which involve ter-
tiary carbenium ion transition states). The methyl shift of triptyl
intermediates, which also requires formation of quaternary carbon,
occurs rapidly (in contrast to methyl shift along 2,3-dimethylbutyl
backbones) apparently because both the initial and final states are
tertiary alkoxides. This rapid methyl shift along the triptyl chains
may also occur because triptane is the first species along the meth-
ylation path that can undergo simultaneous methyl shift (during
methylation of 2,3-dimethyl-2-butene) via a cyclo-butyl carbe-
nium ion that delocalizes charge more effectively than the
cyclo-propyl cation envisioned as the 2,3-dimethyl-2-butene
methylation transition state.
The rates of b-scission of 2-methyl sec-butoxide, 2,3-dimethyl
sec-butoxide, and 2,3,3-trimethyl sec-butoxide (the C –C alkox-
5 7
ides for alkenes on the methylation path to triptane) were deter-
mined from the respective rates of formation of unlabeled
1
3
12
b-scission products in reactions of C-DME with C-2-methyl-2-
1
2
12
butene, C-2,3-dimethyl-2-butene, or C-triptene. The ratio of
the rates of b-scission of these alkoxides to the combined rates of
hydrogen transfer to these alkoxides and methylation of their
respective alkenes represents the b-scission probability (
C
c ; Eq.
(7)). The small values of for these C –C species (0.003–0.013;
c
C
5
7
Table 2) indicate that they undergo methylation and hydrogen
transfer at much higher rates than for b-scission reactions. These
low b-scission rates reflect the involvement of unstable primary
carbenium ion transition states and alkoxides for b-scission path-
ways in molecules with the four-carbon backbone structure of trip-
tane [40–44] (Schemes 5–7). Such molecules are kinetically
protected against deviations from the path to triptane via b-scis-
sion, because the structure of the alkene-derived alkoxides leads
The ratio of the rate of methyl shifts along the backbone to the
combined rates of hydrogen transfer and methylation represents
the methyl shift probability (
cMS; Eq. (8)). These values were deter-
mined for C and C species that do not form along the preferred
6
7
chain growth path to triptane and which, in contrast with triptyl
species, form chemically distinct species upon methyl shifts, from
the rate of formation of unlabeled 3-methylpentane from

D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
191
to less stable transition states for b-scission than for stable tertiary
3.4. Isobutane formation via b-scission of trimethylpentane isomers
cationic transition states involved in alkene methylation or hydro-
gen transfer to the corresponding alkoxide.
The rates of b-scission of C –C alkoxides that do not lie along
5 7
the chain growth path to triptane (sec-pentoxide, 2-methyl sec-
pentoxide, and 2,4-dimethyl sec-pentoxide) were measured from
The binomial isotopologue distributions of all isobutane mole-
cules (Fig. 2b, Fig. 3b and d, and Fig. 5a–c) formed in reactions of
C-DME with C-alkenes suggest that they form via b-scission
1
3
12
of larger molecules that have undergone sequential methylation
and intramolecular isomerization reactions. The low observed
the respective rates of formation of unlabeled C
3
–C
4
species from
1
3
12
12
13
12
C-DME mixtures with C-1-pentene, C-2-methyl-2-pentene,
8 7
rates of formation of C alkanes from C-DME/ C -alkene reac-
1
2
or C-2,4-dimethyl-2-pentene; these rates were used to deter-
mine b-scission probabilities for these species. The small values
Table 2) measured for n-pentyl (0.005) and methyl-pentyl (0.010)
species are similar to those for their more highly branched isomers
isopentyl (0.003) and 2,3-dimethylbutyl (0.013) species) and
tants (Section 3.3.1; Table 2) also indicate that methylation of trip-
tene, which occurs infrequently in view of its high termination
probability (Section 3.3.2), leads to C chains that can undergo
8
rapid b-scission and are therefore removed from the C8+ products.
We return now to this specific issue and provide evidence for the
c
C
(
(
reflect the less stable primary carbenium ion transition states
required for b-scission of sec-pentoxide and 2-methyl sec-
pentoxide compared with the tertiary carbenium ions involved as
transition states in hydrogen transfer to these alkoxides and meth-
selective formation of isobutyl species via facile b-scission of C
molecules, which form via the methylation of C alkenes with
DME-derived species. We report the rate of appearance of C-
8
7
12
1
3
12
atoms in C
4
products from C-DME reactions with
n
C -alkenes
ylation of the respective alkenes (Schemes 5b and 6b). The
c
C
value
of varying size (n = 3–8; Fig. 6) and also examine the chemical
for dimethyl-pentyl species (0.018) is slightly larger than for triptyl
species (0.009), because of the greater stability of the secondary
carbenium ion formed during b-scission pathways of C alkoxides
7
and isotopic nature of the products (Figs. 7 and 8) formed
1
3
12
from C-DME reactions in the presence of C-3,4,4-trimethyl-2-
pentene, the isomer preferentially formed by methylation of
triptene.
with five-carbon backbones compared with the primary carbenium
ions and alkoxides required for b-scission in 2,3,3-trimethyl sec-
The contribution of the co-fed alkene to the products formed in
1
3
12
butoxide (Scheme 7) [40]. This
c
C
value for dimethyl-pentyl spe-
C-DME/ C-alkene reactions can be determined from the rate of
1
2
cies, however, remains much smaller than unity, indicating that
methylation of 2,4-dimethylpentenes and hydrogen transfer to
appearance of C-atoms in each product molecule. Fig. 6 shows
12
how the rates of incorporation of the alkene-derived C-atoms
into molecules that form along the chain growth path to triptane
(as well as into isobutyl species) depend on the size of co-fed al-
kenes (involved in the preferred homologation path: propene,
trans-2-butene, 2-methyl-2-butene, 2,3-dimetyl-2-butene, trip-
tene, and 3,4,4-trimethyl-2-pentene). The alkene contributions to
the rate of formation of triptane increased monotonically with
2
,4-dimethyl sec-pentoxide occur much more frequently than
b-scission of 2,4-dimethyl sec-pentoxide.
The small Sk and values for C –C molecules along the chain
c
c
C
5
7
growth pathway to triptane preserve their four-carbon backbone, a
structural feature that leads to much more stable carbenium ion
transition states for methylation of their alkenes and hydrogen
transfer to their alkoxides than for isomerization and b-scission
increasing alkene size from propene (C
3
) to 2,3-dimethyl-2-butene
of their alkoxides. C
sary for triptane also have low
5
–C
7
molecules that lack the structure neces-
Sk and values, but such mole-
(C ) (Fig. 6a), because the number of methylation events required
to form 2,3,3-trimethyl sec-butoxide and desorb it as triptane via
6
c
c
C
cules are removed from chain growth paths via alkene
methylation to C8+ chains with facile b-scission paths. In the next
section, we show how such b-scission pathways provide a kinetic
hydrogen transfer decreases with increasing alkene size. As for
1
2
triptane products, the rate of C appearance in isobutyl and n-bu-
tyl species (alkanes and alkenes) increases monotonically with al-
kene size, consistent with larger alkenes returning their carbon
‘
‘cleansing’’ mechanism that corrects deviations from the path to
triptane.
atoms more rapidly to C
4
products than smaller homologs. The
a) 1000
(b) 1000
(
isobutyl
1
00
100
10
1
iso-C5
Triptane
n-C4
2,3-dimethylbutyl
Propene
1
0
1
2
3
4
5
6
7
8
9
10
2
3
4
5
6
7
8
9
10
Carbon atoms in co-feed alkene
Carbon atoms in co-feed alkene
1
2
Fig. 6. Rate of formation ( C-atomic basis) of (a) triptane (N), isobutyl (j), and linear C
4 5
(h) species and (b) propene (.), iso-C (ꢀ), and 2,3-dimethylbutyl (d) species for
reactions between 13C-labeled dimethyl ether (78 kPa) and 0.5 kPa unlabeled propene, trans-2-butene, 2-methyl-2-butene, 2,3-dimethyl-2-butene, triptene, or 3,4,4-
trimethyl-2-pentene at 473 K on H-BEA (Si/Al = 12.5). Reactions conducted at 473 K and space velocity of 0.025 mol inlet gas [mol Al s] with >90% alkene conversion and
less than 5% total carbon conversion (DME and alkene).
ꢁ
1

1
92
D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
1.0
0.8
0.6
0.4
0.2
0.0
1.0
1.0
0.8
0.6
0.4
0.2
0.0
(
a)
0.8
0.6
0.4
M
l
e
F
r
a
c
t
i
o
n
M
e
F
a
t
o
MleFraction
0.2
0.0
0
1
2
3
4
5
0
1
2
3
4
5
0
1
2
3
4
5
1
3
13
13
Number C atoms
Number C atoms
Number C atoms
b) 1.0
1.0
0.8
0.6
0.4
0.2
0.0
1.0
(
0
.8
.6
0.8
0.6
0.4
0.2
0.0
0
M
l
e
F
r
a
c
t
i
o
n
0.4
MelFraction
MelFraction
0
.2
.0
0
0
1
2
3
4
5
6
0
1
2
3
13
4
5
6
0
1
2
3
4
5
6
1
3
13
Number C atoms
Number C atoms
Number C atoms
1.0
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
1.0
(
c)
0.8
0.6
0.4
0.2
0.0
M
l
e
F
r
a
c
t
i
o
n
M
e
F
a
t
n
MleFraction
0
1
2
3
4
5
6
0
1
2
3
4
5
6
0
1
2
3
4
5
6
1
3
13
13
Number C atoms
Number C atoms
Number C atoms
Fig. 7. Isotopologue distributions of (a) isopentane, (b) 2,3-dimethylbutane, and (c) triptane molecules produced from reactions between 13C-labeled dimethyl ether (78 kPa)
and 0.5 kPa unlabeled trans-2-butene (left), isobutene (middle), or 3,4,4-trimethyl-2-pentene (right) at 473 K on H-BEA (Si/Al = 12.5). We use the 85 amu fragment of triptane
as a surrogate for the parent ion, because the former appears in much higher concentrations in the mass spectrometer than the latter. Reactions conducted at 473 K and space
ꢁ
1
velocity of 0.025 mol inlet gas [mol Al s] with >90% alkene conversion and less than 5% total carbon conversion (DME and alkene).
formation of unlabeled linear C
of 3,3,4-trimethyl sec-pentoxide (the octane isomer formed via
methylation of triptene as shown in Scheme 7), which forms
4
molecules reflects the b-scission
tert-butoxide and n-butene (Scheme 8). These trends reflect the
propensity for growth beyond triptane to form molecules of size
and structure conducive to facile b-scission pathways.

D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
193
(
a) 1.0
(b) 1.0
13C fraction = 0.20
13C fraction binomial = 0.37
13
C fraction = 0.13
13C fraction binomial = 0.36
0.8
0.6
0.4
0.2
0.0
0.8
0.6
0.4
0.2
0.0
M
e
F
a
t
o
MleFraction
0
1
2
3
4
0
1
2
3
4
13
13
Number C atoms
Number C atoms
Fig. 8. Isotopologue distributions of (a) isobutane and (b) linear C
4
species produced from reactions between 13C-labeled dimethyl ether (78 kPa) and 12C-3,4,4-trimethyl-2-
ꢁ
1
pentene (0.5 kPa) at 473 K on H-BEA (Si/Al = 12.5). Reactions conducted at 473 K and space velocity of 0.025 mol inlet gas [mol Al s] with >90% alkene conversion and less
than 5% total carbon conversion (DME and alkene).
The rates of 12C appearance in isobutyl and linear C
species in-
sec-pentoxide (0.02
l
mol [mol Al s] ; Table 2) is more than an or-
ꢁ1
4
creased sharply for the case of added 3,4,4-trimethyl-2-pentene
relative to other added alkenes (Fig. 6a). In contrast to the rates
der of magnitude lower than those to C
DME homologation and suggests that C chains undergo b-scission
or methylation prior to terminating as C alkanes. The total rate of
3 7
–C alkoxides formed in
8
of C
4
species, the rates of formation (12C-atomic basis) of propene,
8
1
3
12
isopentane, and 2,3-dimethylbutane are similar for co-feed alkenes
of increasing size (less than a factor of 3 difference among rates;
Fig. 6b). These similar rates show that the increases in the rates
formation of C9–10 species from C-DME/ C-3,4,4-trimethyl-2-
ꢁ1
pentene reactants (0.033 lmol [mol Al s] ) is also more than an
order of magnitude lower than the rates of formation of Cn+1 spe-
1
2
ꢁ1
of formation ( C-atomic basis) of C
4
species are a result of b-scis-
cies (5.0–45
l
mol [mol Al s] ; Table 2) from C
n
-alkene co-feeds
sion of C molecules instead of an increase in the concentration of
8
that are smaller than 3,4,4-trimethyl-2-pentene, suggesting that
the C9–10 chains that form via C methylation may also undergo ra-
pid b-scission. Moreover, the b-scission probability of 3,4,4-trim-
1
2
13
12
C-atoms in the reactant inlet stream. In each C-DME/ C-alkene
8
1
2
reaction, the rate of C appearance in isobutane and isobutene was
more than an order of magnitude higher than that in n-butane and
n-butene (Fig. 6a), and the isobutene to isobutane ratio (less than
ethylpentyl species is >100 times larger than for all the smaller
C
chains (c = 1.3 vs. 0.003–0.013; Table 2). These data show that
0
.13) was much lower than the n-butene (1-butene, trans-2-bu-
tene, and cis-2-butene) to n-butane ratio (greater than 7.6). This
preference for isobutane within C hydrocarbons reflects the much
C molecules formed via methylation of triptene undergo rapid
8
b-scission well before significant methylation or hydrogen transfer
can occur, apparently as the result of stable tertiary carbenium ion
transition states for b-scission of these molecules, in contrast with
the primary alkoxides or methyl carbenium ion transition states
required for b-scission of triptane and its precursors (Schemes 4–
4
lower rates of methylation of isobutene relative to hydrogen trans-
fer to tert-butoxide (b = 0.54; Table 1) compared with the higher
rates of n-butene methylation relative to hydrogen transfer to
sec-butoxide (b = 0.08; Table 1). This higher b value explains the
8
7). These facile b-scission events of C species lead to high concen-
high selectivity to isobutane from b-scission of C
8
chains, even
trations of isobutane in DME homologation products (discussed in
the previous paragraph).
though b-scission of the octane isomers from triptene methylation
also produces n-butyl species (Scheme 8).
The isopentane, 2,3-dimethylbutane, and triptane isotopo-
Fig. 6a also shows a decrease in the rate of 12C appearance in
triptane molecules for the case of added 3,4,4-trimethyl-2-pentene
relative to other added alkenes. The rates of 12C appearance in trip-
tane (as well as isopentane and 2,3-dimethylbutane) would in-
crease for the case of added 3,4,4-trimethyl-2-pentene (relative
logues formed from C-DME/ C-3,4,4-trimethyl-2-pentene, C-
13
12
13
DME/ C-isobutene, and 13C-DME/ C-trans-2-butene reactants
consist predominantly of singly labeled, doubly labeled, and triply
labeled molecules, respectively (Fig. 7). The similarity among these
distributions indicates that
dominantly acts as source of C
1
2
12
1
2
C-3,4,4-trimethyl-2-pentene pre-
species that methylate further to
to other added alkenes, as they do for isobutane) if C
8
chains
4
cracked to smaller species that then entered chain growth to trip-
form the isotopologues of isopentane, 2,3-dimethylbutane, and
1
2
12
13
tane. The decrease in the rate of formation of triptane (on a C-ba-
sis), however, indicates that once chains methylate to
triptane that are also formed when C-butenes are added to C-
DME at the reactor inlet. Moreover, the isobutyl and linear C spe-
C
8
4
1
3
12
molecules, they undergo b-scission with the resulting species ter-
minating as isobutane at much higher probabilities than methylat-
ing to triptane. We therefore conclude that high concentrations of
isobutane from DME and methanol homologation results from fac-
cies (Fig. 8) formed from C-DME/ C-3,4,4-trimethyl-2-pentene
reactants contain a significant fraction of completely unlabeled
molecules and binomial-like distributions of more highly labeled
species (dashed markers in Fig. 8). The completely unlabeled com-
ile b-scission of C
8
molecules that form via methylation of C
7
al-
ponents of these isotopologue distributions reflect the C
4
mole-
kenes (Schemes 7 and 8).
cules produced from b-scission of species that are not
C
8
Reactions of 13C-DME (78 kPa) with 12C-3,4,4-trimethyl-2-pen-
tene (0.5 kPa) were used to measure rates of hydrogen transfer,
methylated by C-DME. The binomial portions of the distributions
in Fig. 8 resemble the isotopologue distributions of isobutyl and
13
1
3
12
methylation, and b-scission of C
8
molecules formed via methyla-
n-butyl species from C-DME/
C5–7 alkene reactions (Fig. 5),
tion of triptene. The rate of hydrogen transfer to 3,4,4-trimethyl
and thus, these molecules are likely the result of b-scission of

1
94
D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
larger chains (derived from methylation by 13C-DME of completely
unlabeled C species) that have undergone extensive intramolecu-
lar isomerization. We conclude from these data that isobutyl and
n-butyl species are formed via b-scission of C chains, although iso-
kenes, provide a useful internal kinetic standard against which
other rates can be accurately benchmarked at conditions that pre-
vent fast secondary reactions that would otherwise preclude the
rigorous mechanistic analysis of kinetic and isotopic data.
4
8
butane appears in much higher concentrations within homologa-
tion products than n-butane because of the higher termination
probability of isobutyl species compared with n-butyl species.
A confluence of kinetic preferences, at first glance seemingly
fortuitous, leads to isobutane and triptane as predominant prod-
ucts of C homologation. Methyls are added to incipient chains at
1
We also conclude that these C
4
species (particularly n-butenes be-
positions that preserve a four-carbon backbone and the chain ter-
mination probability reaches a sharp maximum at triptyls, for
which the relative stabilities of methylation and hydrogen transfer
favor the latter. When methylation occurs at less preferred posi-
cause of their much higher methylation rates compared to hydro-
gen transfer of sec-butoxide) can re-enter chain growth pathways
to triptane via methylation by DME. The isobutane molecules that
form via b-scisson of C
8
chains may also be re-incorporated into
7
tions, the resulting chains do not terminate preferentially at C ; in-
growing chains using a hydrogen transfer co-catalyst such as ada-
mantane [11,60].
stead, they form larger molecules, which undergo rapid b-scission
to form isobutane and return carbon atoms to the incipient chain
growth pathways. Isobutane becomes a preferred product, in spite
Scheme 8 shows b-scission pathways for the C
8
molecules
formed via methylation of triptene by DME (or methanol), which
would preferentially form 3,3,4-trimethyl sec-pentoxide species
based on the selective methylation position rules discussed in Sec-
tions 3.1–3.3.1. b-Scission of 3,3,4-trimethyl sec-pentoxide forms
n-butene and tert-butoxide (which gives isobutene via deprotona-
tion or isobutane via hydrogen transfer) in reactions that involve
the formation of stable tertiary carbenium ions [40]. Methyl shift
isomerization along the backbone of 3,3,4-trimethyl sec-pentoxide
leads to 2,4,4-trimethyl sec-pentoxide, which forms isobutene and
tert-butoxide in b-scission events that require tertiary carbenium
ion transition states [40]. b-Scission of 2,3,4-trimethyl sec-pentox-
ide (a tertiary alkoxide formed from methyl shift along the
backbone of 3,3,4-trimethyl sec-pentoxide and 2,4,4-trimethyl
sec-pentoxide) produces isopentene and sec-propoxide [40] (a less
stable secondary alkoxide that requires a secondary carbenium ion
transition state). Higher concentrations of 2,3,4-trimethylpentane
molecules compared to 2,2,3- and 2,2,4-trimentylpentane mole-
1
of its infrequent formation via direct C homologation pathways,
because of this recycling of kinetic ‘‘mistakes’’; tert-butoxides des-
orb as isobutane via hydrogen transfer before significant desorp-
tion as isobutene and methylation, because, as in the case of
triptyls, they form much more stable transition states for hydrogen
transfer than for methylation of isobutene. These rules, so clearly
evident here from the specific and intricate details of intermediates
and transitions states involved in homologation catalysis, apply
with equal rigor and much more broader impact to acid catalysts
in general.
4. Conclusions
Unprecedented measurement of reaction rates from competi-
1
3
12
tive reactions between C-DME and C-alkenes led to quantita-
tive description of the mechanistic details of chain growth during
DME homologation to triptane on solid acid catalysts. The relative
stabilities of carbenium ion transition states formed during meth-
ylation, hydrogen transfer, isomerization, and b-scission reactions
preferentially form molecules with linear four-carbon backbone
structures (isopentane, 2,3-dimethylbutane, and triptane). Methyl-
ation of alkenes occurs selectively to preserve the linear four-car-
bon backbones of molecules along the chain growth path to
triptane. Termination probabilities are much higher for triptyl
and isobutyl species, which terminate preferentially as alkanes
via hydrogen transfer of 2,2,3-trimethyl sec-butoxide and tert-
13
12
cules within C
ble 2) and higher rates of C appearance in C
8
products from C-DME/
C
7
-alkene reactants (Ta-
species (compared
12
4
to isopentyl species) from 13C-DME/ C-3,4,4-trimethyl-2-pentene
reactants indicate that b-scission of 2,3,4-trimethylpentyl species
is slower than b-scission of 2,2,3-trimethylpentyl and 2,2,4-trim-
ethylpentyl species, because the former requires the formation of
less stable secondary carbenium ion transition states (Scheme 8).
Thus, 2,3,4-trimethylpentyl species likely undergo methyl shift to
12
2
,2,4-trimethylpentyl species followed by more facile b-scission
events. This rapid b-scission of C molecules (as well as C isomers
8
7
3 4
butoxide, than for C , linear C , isopentyl, and 2,3-dimethylbutyl
that lack the linear four-carbon backbone of triptane (Sec-
tion 3.3.5)) provides a kinetic filtering mechanism that corrects
for chain growth mistakes (albeit with some loss of carbon to iso-
butane) that would otherwise lead to a wider product distribution
over a broader range of molecular weights.
species, which methylate preferentially along the chain growth
path. Low rates of skeletal isomerization and b-scission of these
molecules, relative to their rates of hydrogen transfer and methyl-
ation, prevent rearrangement of their linear four-carbon back-
bones. Molecules that deviate from the chain growth path to
4
triptane, via isomerization away from the linear C backbone struc-
3.5. Kinetic and isotopic probes of homologation pathways and their
ture of triptane and/or methylation to C8+ chains, are selectively re-
implications for selectivity in reactions mediated by carbenium ion
transition states
moved from chain growth paths via rapid b-scission reactions.
1
3
12
These C-DME/ C-alkene studies show that DME homologa-
tion forms triptane because growing chains undergo slow isomer-
ization or b-scission and terminate preferentially as triptane; rapid
isomerization and b-scission forms isobutane when chain growth
deviates from triptane. The remarkable isobutane and triptane
selectivity during reactions of DME on H-BEA zeolite has also been
The results presented here, although motivated by an inquiry
into the unique selectivity to isobutane and triptane from C spe-
1
cies on acids, provide significant guidance about the effects of
molecular structure and of carbenium ion stability on methylation,
hydrogen transfer, b-scission, and isomerization reaction rates. The
relative rates of these reactions, reported here with unprecedented
numerical accuracy, can be rigorously interpreted in terms of the
transition states envisioned (and suggested by theory) for methyl-
ation of alkenes, hydrogen transfer to adsorbed alkoxides, and rear-
rangements of the latter species to (i) cleave C–C bonds, (ii) change
the position of surface attachment (hydride shift) or of methyls
measured on non-zeolite solid acids (5 wt.% H
3 2
PW12O40/SiO and
SiO –Al ) [11] and reflects a chain growth mechanism character-
2
2 3
O
istic of acid catalysis, in general, that is guided by the stability of
carbenium ion transition states. The role of spatial constraints is
to provide van der Waals stabilization of the required transition
states and to alter their free energies via enthalpic or entropic
effects.
(
methyl shifts), or (iii) change the backbone length. In doing so,
methylation events, which can be monitored accurately from the
formation of singly labeled Cn+1 species from 13C-DME/12
-al-
Although relative rates will depend on spatial constraints as a
result of transition states that differ in size and van der Waals
contacts with the zeolite framework [61–64], the hierarchy of
C
n

D.A. Simonetti et al. / Journal of Catalysis 277 (2011) 173–195
195
reactivity imposed by carbenium ion stability remains pre-eminent
even within confined environments. Indeed, the unique selectivi-
ties to C and C alkanes and to their isobutane and triptane
4 7
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We acknowledge with thanks the funding for this work by BP,
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Plaisance, and Dr. Rado Raharintsalama (University of Virginia) and
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of Technology) regarding the mechanistic interpretation of the re-
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