Effects of Void Environment and Acid Strength on Alkene Oligomerization Selectivity

12 Pages·2016·3.37 MB·English

ResearchArticle
pubs.acs.org/acscatalysis
ff
E ects of Void Environment and Acid Strength on Alkene
Oligomerization Selectivity
Michele L. Sarazen,† Eric Doskocil,‡ and Enrique Iglesia*,†
†
DepartmentofChemicalandBiomolecularEngineering,UniversityofCalifornia,Berkeley,Berkeley,California94720,UnitedStates
‡
BP Products North America Inc., 150 West Warrenville Rd., Naperville, Illinois 60563, United States
*
S Supporting Information
ABSTRACT: Theeffectsofchannelconnectivity,voidenviron-
ment, and acid strength on the relative rates of oligomerization,
β-scission, and isomerization reactions during light alkene
conversion (ethene, propene, isobutene; 2−400 kPa alkene;
473−533 K) were examined on microporous (TON, MFI,
MOR, BEA, FAU) andmesoporous (amorphous silica−alumina
(SiAl), MCM-41, Keggin POM) Brønsted acids with a broad
range of confining voids and acid strength. Skeletal and
regioisomers equilibrate under all conditions of pressure and
conversionandonallcatalysts,irrespectiveoftheiracidstrength,
void size, or framework connectivity, consistent with rapid
hydride and methyl shifts of alkoxides intermediates and with their fast adsorption−desorption steps. Such equilibration is
evident from detailed chemical speciation of the products and also from intramolecular isotopic scrambling in all oligomers
formed from 2-13C-propene on TON, MFI, SiAl, and POM clusters. Previous claims of kinetic control of skeletal isomers in
oligomerization catalysis through shape-selective effects conferred by void environments may have used inaccurate tabulated
thermodynamics,asweshowinthisstudy.Thevoidenvironment,however,influencesthesizedistributionofthechainsformed
in these acid-catalyzed alkene reactions. One-dimensional microporous aluminosilicates predominantly form true oligomers,
those expected from dimerization andsubsequent oligomerization events for a given reactant alkene; such chains are preserved
becausetheycannotgrowtosizesthatwouldinhibittheirdiffusionthroughessentiallycylindricalchannelsintheseframeworks.
Amorphous SiAl and colloidal silica-supported POM clusters contain acid sites of very different strength; both exhibit size
variations across the void space, but at length scales much larger than molecular diameters, thus preserving true oligomers by
allowingthemtoegressthevoidbeforeβ-scissionevents.Mesoporousacidsofverydifferentstrength(POM,SiAl)givesimilar
trueisomerselectivities,asalsoobservedonMFIstructureswithdifferentheteroatoms(X-MFI,whereX=Al,Ga,Fe,B),which
also differ in acid strength; this insensitivity reflects oligomerization and β-scission reactions that involve similar ion-pair
transition states and therefore depend similarly on the stability of the conjugate anion. Three-dimensional microporous
frameworks contain voids larger than their interconnecting paths, an inherent consequence of intersecting channels and cage−
windowstructures.Asaresult,oligomerscanreachsizesthatrestricttheirdiffusionthroughtheinterconnections,untilβ-scission
events form smaller and faster diffusing chains. These undulations are of molecular dimensions and their magnitude, which is
definedhereastheratioofthelargestscaletothesmallestscalealongintracrystaldiffusionpaths,determinestheextenttowhich
oligomerization−scission cycles contribute to the sizedistribution ofproducts. These contributions are evident in the extent to
which chain size and the number of 13C atoms in each molecule formed from 2-13C-propene approach their binomial
distributions, as they do on microporous acids with significant undulations. The general nature of these conclusions is evident
from the similar effects of void shape and connectivity and of acid strength on selectivity for ethene, propene, and isobutene
reactants.
KEYWORDS: oligomerization, β-scission, skeletal isomerization, zeolites, Brønsted acid catalysis
1. INTRODUCTION differentC−Cbondlocationsinthetwodirections;thermody-
namic trends favor C−C bond formation over cleavage for
TheoligomerizationofalkenesonsolidBrønstedacidsprovides
an effective strategy to form new C−C bonds from small smalleralkenesandathigherpressuresandlowertemperatures.
hydrocarbons.1−4 These processes become attractive as such Solid acids also catalyze concurrent hydrogen transfer and
cyclization reactions, as well as skeletal and double-bond
small molecules are excluded from fuels, because of vapor
pressurerestrictions,andassmallalkenesbecomeavailablefrom
biomass-derivedoxygenates.Solidacids,suchastheacidformsof Received: July27, 2016
zeolites, catalyze these reactions.5 Oligomerization occurs in Revised: September2, 2016
parallelwithitsreversereaction(β-scissioninalkenes),albeitat
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isomerizationreactionsthatleadtoisomersdifferentfromthose becauseofhowsuchstructuralfeaturesinfluencethediffusionof
initiallyformedinoligomerizationevents.6−10Therelativerates the largest products that can form within the local confining
ofthesedifferentreactionsareinfluencedbythechannelsizein environment. The design of such features into the local
microporoussolidacids,whichallowselectivediffusionofcertain environment around protons thus becomes pertinent for the
reactants and products and the potential preference for some chain length distribution in oligomerization products, but are
transition states over others based on their size.11 Previous inconsequentialfortheirskeletalstructureorthelocationoftheir
studies on zeolites (predominantly MFI frameworks) have double bonds; these molecular features are set by the
shown that chain growth selectivity depends sensitively on equilibrationofthegaseousalkeneisomers,whichisaconclusion
temperatureandresidencetime,bothofwhichhaveatendency that required the systematic reconsideration of previously
to favor secondary reactions of the primary oligomers formed. reportedformationGibbsfreeenergiesforhexeneisomers.
Here,weaddresstheunderpinningdescriptorsfortheeffectsof
theshape,size,andconnectivityoftheconfiningvoidsandofthe 2. EXPERIMENTALMETHODS
acid strength and the intracrystalline density of protons on 2.1. Measurements of Alkene Chain Growth Selectiv-
selectivity. ity. MFI, TON, MOR, BEA, FAU, MCM-41, and amorphous
These descriptors are specifically examined for ethene, silica−alumina (SiAl) samples were obtained from commercial
propene, and isobutene (C , where n = 2, 3, 4; pressure (P), sources (as described in Table 1). All zeolites were exchanged
n
2−400 kPa; temperature (T), 473−533 K) oligomerization
reactions in the context of the relative rates of oligomerization Table1.FrameworkStructure,Source,Si/AlRatio,and
and of secondary isomerization and β-scission reactions of the ProtonCountsfortheSolidAcidsUsedinThisStudy
primary alkenes formed. The data reported here, taken at very
low conversions, preclude the effects of deactivation, which acid source Si/Alratioa H+/Al(H+/u.c.)ratio
occurs predominantly through the binding of larger oligomers, BEA Zeolyst 11.8 0.40(2.0)b
formedviasubsequentalkeneadditionstepstogrowingchains. MFI Zeolyst 16.6 0.65(3.6)b
Thedetailedchemicalspeciationoftheisomersformedandthe MFI Zeolyst 29.2 0.78(2.5)b
rate of intramolecular scrambling of 13C atoms within the MFI Zeolyst 43.8 1.0(2.1)b
oligomers derived from 2-13C-propene show that frequent MFI Zeolyst 173 0.64(0.36)b
readsorption and hydride and methyl shifts within primary MFI Sud-Chemie 14 0.71(4.3)b
isomer products lead to skeletal isomers, regioisomers, and MFI Tri-Cat 25 0.35(1.3)b
stereoisomers at concentrations solely determined by their MOR Zeolyst 10 0.86(2.9)b
interconversion thermodynamics, even at very low reactant TON BP 39 0.55(0.36)b
conversions.Consequently,isomerdistributionswithinchainsof TON BP 49 0.50(0.26)b
a given size are similar on all solid acids, despite their large TON BP 24 0.38(0.40)b
differencesinreactivity,voidstructure,protondensity,andacid FAU Engelhard 7.5 0.37(8.5)b
strength. Such distributions are not dependent on conversion, silica−alumina Sigma−Aldrich 5.5 0.25c
residence time, or reactant pressures for all alkenes. These Al-MCM-41 Sigma−Aldrich 39 0.3c
findings illustrate the preeminence of thermodynamics in acid source Si/Tratioa H+/Tratiob
determining isomer selectivities in the products formed via Ga-MFI BP 45 0.86(1.8)
alkeneoligomerizationcatalysis. B-MFI BP 43 0.77(1.7)
Thisstudyshowsthatone-dimensional(1D)zeolites(TON, Fe-MFI ref14 61 0.85(1.3)
MOR)andmesoporousacids,suchasAl-MCM-41,amorphous POMcontenton POMsurfacedensity protons
silica−alumina (SiAl) and silica-supported polyoxometalates silica(wt%) (POMnm−2) (H+/POM)c
(POM), preserve the chain length of oligomerization products H3PW12O40 5 0.03 2.5
by allowing the unobstructed diffusion of any chains that can H4SiW12O40 5 0.03 1.9
form within their channels and voids. In contrast, three- aFrom elementalanalysis (ICP-OES; Galbraith Laboratories). bFrom
dimensional (3D) zeolites (MFI, BEA, FAU), with void decomposition of NH4+ exchanged sample. cFrom 2,6-di-tert-
structuresthatexhibitubiquitousundulationscreatedbychannel butylpyridine titration.
intersections(MFI,BEA)orcage−windowframeworks(FAU),
allowthelocalformationofoligomerslargerthantheintervening withNH cations,usingproceduresdescribedelsewhere.12The
4
passages,thusrequiringβ-scissioneventsforthefacileegressof number of protons in each sample was measured from the
products.Theselectivitytotrueoligomerswasnotdependenton amountofNH evolveduponheatingNH +-exchangedsamples.
3 4
acidstrength,irrespectiveofwhetheractiveprotonsresidewithin Transmissionelectronmicroscopy(TEM)imagesweretakenon
mesoporous voids (POM, MCM-41/SiAl) or in MFI micro- a Philips/FEI Tecnai 12 microscope operated at 120 kV for
porous channels (X-MFI, where X = Al, Ga, Fe, B). The acid crystalsizeestimatesbysuspendingthesamplesinethanoland
strength of these solids influences the addition of alkenes to dispersing them onto ultrathin carbon/holey carbon films
alkoxide oligomersandtheβ-scission ofthelarger alkoxidesto supported on 400 mesh Cu grids (Ted Pella, Inc.). Keggin
the same extent, because these reactions involve ion-pair POMclustersweredispersedontoamorphoussilica(Cab-O-Sil
transition states with similar charges at their cationic organic HS-5; 310 m2 g−1; pore volume, 1.5 cm3 g−1). The number of
moiety and the acid’s conjugate anion. In fact, these reactions protons in Keggin POM clusters and mesoporous aluminosili-
merelyrepresenttwooppositedirectionsofthesameelementary cates (MCM-41, SiAl) was determined from the amount of a
step,albeitwiththepossibilitythatdifferentC−Careformedand noncoordinating titrant (2,6-di-tert-butylpyridine) required to
cleavedinthetwodirections. fullysuppressratesduring2-methylpentaneisomerization13and
These findings indicate that oligomerization selectivities are propene oligomerization reactions, respectively; the proton
dependentonthesize,shape,andconnectivityoftheframework, densitiesinallsamplesarelistedinTable1.Solidacidpowders
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were pelleted, crushed, and sieved to retain 180−250 μm sampling valve and transferred through heated lines (>373 K)
aggregatesbeforeuseincatalyticexperiments. into a gas chromatograph equipped with flame ionization and
Oligomerization rates and selectivities were measured in a mass spectrometric detectors (Agilent, Models 7890 A and
tubularreactor(316stainless-steel,12mmI.D.)withplug-flow 5975C), each connected to a capillary column (HP-1, methyl
hydrodynamics.Temperatureswerecontrolledusingaresistively silicone, 50 m × 0.32 mm × 1.05 μm film) to determine the
heated furnace, and the system pressure was set by a chemicalandisotopiccompositionofthereactorcontents.
backpressure regulator (Tempresco). NH +-zeolites and meso- 13C-labeled propene (2-13C-propene, 99 at.% 13C, Sigma−
4
porous aluminosilicates were treated in 5% O in helium (83.3 Aldrich) was used as the reactant with helium as the balance
2
cm3g−1s−1,Praxair)byheatingto818K(atarateof0.025Ks−1) (99.999%,Praxair).Catalysts(TON,MFI,SiAl,andHSiW)were
and holding for 3 h to convert NH + cations to H+ and then treated as described in Section 2.1 before exposure to 2-13C-
4
cooledtoreactiontemperature.SupportedKegginPOMclusters propene. Isotopologue distributions of the products were
intheirH-formweretreatedinflowinghelium(50cm3g−1s−1; determined using previously reported matrix deconvolution
99.999%,Praxair)byheatingtoreactiontemperature(503K;at methods.18 The labeled reactant was used to determine the
0.083Ks−1). originsoftheproductsformed(oligomerizationvssubsequentβ-
Ethene (99.9%, Praxair), propene (99.9%, Praxair), and scission) and, morespecifically,thenumberoftimesaproduct
isobutene(99.9%,Praxair)wereintroducedintoaheliumstream has traversed an oligomerization−cracking cycle.17 These
(99.999%,Praxair),usingelectronicmassflowcontrollersatthe distributions consist of a unimodal component superimposed
molarratesrequiredtoachievethedesiredpressures.Thereactor with a component that approaches a binomial distribution; the
effluentwastransferredthroughheatedlines(>373K)toagas products were separated into the carbon fraction of molecules
chromatograph (Agilent, Model 6890). Reactant and product thatcontributetoeitherthebinomialorunimodaldistribution,
concentrations were measured by flame ionization detection which were attributed to contributions from β-scission and
afterchromatographicseparation(methylsiliconeAgilentHP-1 oligomerization, respectively. The fraction of a given isotopo-
column, 50 m × 0.32 mm × 1.05 μm); the elution order of logueinspeciesjwithlcarbonatomsthathasi13Catomswas
productswasdeterminedfrominjectionstoagaschromatograph describedbytheexpression
fittedwiththesamecolumntype,butwithflameionizationand
⎡ ⎛ ⎞⎤
mass spectrometric detectors (Agilent, Models 7890 A and [l13C] =⎢χU +(1−χ)⎜ l! (⟨f ⟩)i(1−⟨f ⟩)l−i⎟⎥
5975C)andcomparedtoknownretentiontimesofhydrocarbon i j ⎣ j j j ⎝(l−i)!i! 13C 13C ⎠⎦
mixtures on similar columns.15,16 Oligomerization rates were
(3)
normalizedbythenumberofprotonsineachsample;selectivities
werecalculatedonapercarbonbasis. where the first term of the sum (χU) corresponds to the
j j
2.2.CalculatingtheSelectivitytoTrueOligomersfrom unimodal contribution with carbon fraction χ and the second
j
Measured Product Distributions. The chain length of the term reflects the contribution from the part of the distribution
products formed from an alkene with n carbons reflects the that becomes increasingly binomial with increasing (1 − χ)
j
relativecontributionofC−Cbondformation(oligomerization) values. Here, U is a unimodal component at the expected
i
and cleavage (β-scission). Product distributions become numberof13Cinthespeciesj(e.g.,twolabelsforanyC isomer)
6
increasingly binomial after many sequential β-scission and and⟨f13C⟩isthemean13Cfractioninspeciesj,ascalculatedbyeq
oligomerization events. An underlying binomial distribution 4:
was used to the describe those molecules with chain lengths
differentfromthoseoftrueoligomers(C ,C ,...)andthenused [l13C]
to predict the molar concentration of pnrod2uncts made from β- ⟨f13C⟩j = l j j (4)
scissionwithchainlengthsthatwerethesameastrueoligomers
(seeeq1): The value of χ was determined by regressing the measured
j
isotopologue distribution to the functional form of eq 3. The
[Cm·n] = [Cm·n,t] − [Cm·n,b] (1) calculatedχ valueisnumericallythesameasthetrueoligomer
j
where[Cm·n,t]isthetotalmolarconcentrationofproductwithm· scehleemctiicvaitlysppeacriaemsej,teinrs(teeaqd2o)f,abvuetraigtinisgsopveecrifitchetoenetaicrehpdriostdinucctt
tnhceamrboolnasrfcoornmceedntfrraotmionaorefascpteacniteswwithithnmca·rnbocanrsbaonnds[pCremd·ni,cb]teids slate.
from an underlying binomial distribution fit to products of Thelabeledreactantwasalsousedtodeterminetheextentof
isomerizationwithinproductswiththesamenumberofCatoms.
intermediate length (i.e., not C , C ,...). The molar concen-
trationsofoligomerswithm·ncanrbon2snthathavenotundergone Isomerization causesintramolecular scramblingof13C,because
βse-lseccistsivioitnyp(a[rCamm·ne]t)erwthearteisudseefidnetdobcyaltchuelafotelloawitnrgueexporliegsosmioner: cthyactlorpersoupltylincarbboetnhiuismomioenritzraatnisointioannsdtaitnetsrammeodlieacteulmaretehxyclhsahnifgtes
amongCatoms.Theamountof13ClabelateachCpositionina
∑ [C ] given chemical isomer molecule was determined from the
χ = m=1 m·n
n ∑l=1[Cl,t] (2) isseoptaorpaitcionconotfenttheofisiotsmmerass.sRfraapgimdeinnttsraamftoerleccuhlraormsactroagmrabplihnigc
2.3. Mechanistic Provenance of Oligomerization would give the same 13C fraction at each C-position, as
Products and Their Intramolecular 13-C Scrambling in prescribed by eq 4. An isotopic scrambling conversion (σ) is
Oligomerization Products of 2-13C-Propene. Kinetic and definedhereineq5asaresidualsumofsquares:
isotopic tracer experiments were carried out in a glass batch
reactor,17 the contents of which were recirculated using an oil- σ = 1 − ∑kk==l1(fk − ⟨f13C⟩)2
free graphite gear micropump (GA V23, Micropump). Gas ∑k=l(f − ⟨f ⟩)2
samples were extracted from the recirculating stream using a l=1 expected 13C (5)
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wheref isthemeasured13Cfractionatpositionk,f isthe were neither 0nor1(see Figure S3 inthe SI)whenestimated
k expected
13C fraction at each position expected without intramolecular usingreportedthermodynamicdata19,20andthedeviationfrom1
fsrcarcatmiobnlinogffoarfeualclyhdscisrtaimncbtlecdhemmioclaelciusolem, ewrh,aicnhd⟨isf13Ce⟩quisatlhaet13aCll d47id3n−o5t3i3mKp,rouvsiensgydstaetmafartoicmalrlyefw2i0th;steeemFpigeruarteuSre4(inovtehreaSrIa)n.Sguecohf
positions. This expected location is used to normalize the data varied broadly among literature sources that used group
residualsumofsquares.Forexample,ahexeneisomerformedvia additivitycorrections,insomecases,byasmuchas15kJ/mol(at
2-13C-propeneoligomerizationwouldleadto13Catomsatthe2 503K;K valuesweretabulatedfromsuchdatainFigureS15in
eq
and4positionsand12Catomsattheotherfourpositions.Values theSI;ΔG valuesweretabulatedfromFigureS5intheSI).
eq
ofσof0and1correspondtounscrambledandfullyscrambled Intermediatevaluesofηthatdonotvarywithresidencetime
molecules,respectively. or reactant pressure must reflect either (i) a specific kinetic
The absence of significant intramolecular scrambling during preferenceforagivenisomerdistributionformeddirectlyfrom
ionizationanddetectioninthemassspectrometerchamberwas the oligomerization transition state (TS) and the absence of
determined by introducing 1-13C-hexane and its alkene secondary readsorption and isomerization reactions or (ii) full
analogues,formedviadehydrogenationof1-13C-hexaneonPt/ equilibration among isomers but inaccurate thermodynamic
Al O intothespectrometerchamber.ThePt/Al O sample(1.5 data. The first possibility seems implausible in view of the
wt2%)313 wasused in the recirculating reactor to2de3hydrogenate equilibratednatureofadsorption−desorptionprocessofalkene
1-13C-hexaneintoanequilibratedmixtureofalkeneregioisomers reactants and the facile nature of hydride and methyl shifts on
at573K(0.4kPa1-13C-hexane). solid acids;13 this explanation is also at odds with the similar
2.4. Thermodynamics of Hexene Isomer Interconver- distributions observed on solid acids with very different acid
sions.Theapproachtoequilibrium(η)fortheformationofeach strengthandconfiningenvironments(seeFigureS6intheSI).
C chemical isomer (j) from 2-methyl-2-pentene (2M2P), These arguments, taken together with the aforementioned
6
chosenhereasreference,isgivenby inconsistencies amongreported thermodynamic data, led us to
reconsider the accuracy of tabulated free energies and, instead,
( Cj ) usetheisomerdistributionsmeasuredonamesoporoussample
η = C2M2P (SiAl)athighfractionalpropeneconversions(0.30)asthebasis
K for the isomer equilibrium calculations on all other solid acids.
2M2P↔j (6)
Theequilibratednatureofallregioisomerswithineach2-MP,3-
Here, K2M2P↔j is the equilibrium constant for 2-methyl-2- MP,andn-HskeletalgrouponTON,MFI,andSiAlisevident
pentene conversion to the hexene isomer j, present at a fromtheirηvaluesobtainedinthismanner(seeFigure1);these
concentrationC.Thevaluesoftheequilibriumconstants were
j
calculated from high conversion data obtained from the
recirculating batch reactor (described in Section 3.1). These
valueswerecomparedwithliteraturevalues19,20andwithvalues
obtainedusingcorrectedgroupadditivitymethods.21Previously
tabulatedGibbsfreeenergiesforisomerformationvariedamong
thesesources,byasmuchas15kJ/mol(at503K)insomecases,
leading to widely different η values, depending on the source
used. All equilibrated isomers of a given length (η values near
unity at all conversions) were treated as a kinetic lump in all
subsequent kinetic analyses, in accordance with the chemical
speciationandisotopicscramblingdatashownhere.
3. RESULTSANDDISCUSSION
3.1.HydrideandMethylShiftsReactionsinAlkoxides
Formed Via C H Oligomerization. Hydride and methyl
3 6
shifts in bound alkoxides lead to a mixture of skeletal and Figure1.Approachtoequilibriumfortheformationofhexeneisomers
regioisomers within each chemical species of a given carbon from 2-methyl-2-pentene on TON (black), MFI (white), and SiAl
numberderivedfromthesealkoxides.Theobservedisomersare (gray)[503K,<0.05C3H6conversion,60kPa].Isomersareseparated
according to their backbone structures 2-methylpentene (2-MP), 3-
grouped here according to their backbone skeletons: 2-
methylpentene (3-MP), linear (n-H) and 2,3-dimethylbutene (2,3-
methylpentenes (2-MP), 3-methylpentenes (3-MP), linear
DMB).DataforBEAandHSiWarefoundinFigureS2intheSI).
hexenes (n-H) and 2,3-dimethylbutenes (2,3-DMB). 2,2-
Dimethylbutenes were not detected because quaternary C
atoms form via skeletal isomerization through unstable ηvaluesarenearunity,evenatpropenefractionalconversionsof
carbenium-ion transition states with significant primary charac- <0.05 and all temperatures, pressures, and conversions. We
ter.13Theconcentrationsofeachchemicalisomer(relativeto2- concludefromthesedatathathydrideandmethylshiftsarefast
methyl-2-pentene(2M2P))didnotvarywithC H conversion inC oligomersandthattheconcentrationofallisomerswitha
3 6 6
as it changed with residence time (see Figure S1 in the given carbon number is dependent only on their thermody-
SupportingInformation(SI)),exceptfor2,3-DMB,whichisone namics properties as gaseous species, even at very low
of the slowest diffusing skeletal isomers, in TON, which is the conversions and modest temperatures (see Figure 1, 503 K).
catalyst with the smallest channels; these concentration ratios These η values were near unity for 2-MP, 3-MP, and n-H
alsodidnotvarywithchangesinreactantpressure(25−400kPa backbones on all solid acids examined here (BEA and HSiW
C H in Figure S2 in the SI). However, these invariant shown in Figure S7 in the SI) at all propene fractional
3 6
approaches to equilibrium parameters (η, eq 1) for all isomers conversions (0.02−0.8; Figure S8 in the SI) and all alkene
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pressures(2−500kPaC H );similarconclusionsarereachedfor
3 6
C and C chains, which is indicative of their significant
4 5
isomerizationaftertheyformviasecondaryβ-scissionofprimary
(C )orsecondary(C ,C ,...)oligomerizationproducts(forC ,
6 9 12 5
seeFiguresS9andS10intheSI).
Isomers with 2,3-DMB backbones are also present at near-
equilibriumlevelsonallsolidacids,exceptTON;thisappearsto
reflectthesmall1D10-MRchannelsinTON(0.46nm×0.57
nm),22 which can inhibit the formation or the diffusion of
moleculeswith“bulkier”backbones.Indeed,moleculardynamics
simulations show that n-heptane diffuses much faster than 2-
methylhexane or 3-methylhexane in TON (10-fold larger
diffusivities at 600 K).23 These 2,3-DMB isomers approach
their equilibrium concentrations on TON as the H+ densities
increase(0.10and0.32ηvaluesfor2,3-DM1Bfor0.26H+/u.c.
(0.017fractionalconversion)and0.36H+/u.c.(0.011fractional
conversion), respectively) and as conversion increases with
increasing residence time (0.22 to 0.93 for 0.01 and 0.42
fractionalconversionon0.36H+/u.c.TON)(detailsaregivenin
FiguresS8andS11intheSI).Thesesitedensityandconversion
effectsfor2,3-DMBisomerssuggestthattheirlowerηvaluesare
likelytoreflecttheirlocalequilibrationwithinTONcrystalsand
the slower diffusion of these bulkier isomers through such
crystals. These diffusional hurdles are consistent with fast
isotopic scrambling within 2,3-DMB isomers (Section 3.2),
which indicates that chemical equilibrium is indeed locally
attainedduringpropeneoligomerization. Figure2.13Cisotopologuedistributionsfortheparentandthepentyl,
3.2. Isotopic Evidence for Fast Methyl Shifts in butyl,andpropylfragmentionsof2M2PwasformedonTON[0.08
Oligomers Formed from 2-13C-Propene. Methyl shifts C3H6 fractional conversion, 2 kPa 2-13C-propene, 503 K]. Average
numberof13Catomsandfractionalamountpercarbonareshowninthe
cause intramolecular exchange of C atoms among backbone
brackets,respectivelyforeachion.Theexpectedbinomialdistribution
locations;theirratescanbeinferredfromtheextentofwhichthe forthetotal13Ccontentofeachionisindicatedbylightgraybars.
locations of the two 13C atoms in C oligomers formed from
6
2-13C-propene have shifted from their expected positions. An
oligomerization eventthat forms 2MP backbones, for instance,
wouldplacethesetwo13Catomsatpositions2and4alongthe
backbone, but the cyclopropyl carbenium ions that mediate
methylshifts(andtherequiredconcertedH-shifts)wouldcause
to intramolecular scrambling.13,24 Ultimately, very fast intra-
molecular methyl andhydride shifts would formisotopologues
with the same 13C content at all locations throughout each
chemicalspecies.
Figure 2 shows the isotopologue distributions and 13C
contents (total and per carbon) in the parent ion and in the
pentyl,butyl,andpropylfragmentionsderivedfromthe2M2P
isomer formed via C H oligomerization on TON (8%
3 6
conversion, 2 kPa 2-13C-propene, 0.36 H+/u.c., 503 K). The
two13Catomsin2M2ParedistributeduniformlyamongallsixC Figure 3. 13C atom locations for the initial skeletal and regioisomers
atoms (0.29−0.37 13C fraction; Figure 3, center) within productformed(2M2P)andforarepresentativespeciesformedfrom
experimentalaccuracy.Uniformintramolecular13Cdistributions eachtypeofisomerizationevent(trans-4M2P,trans-2-H,trans-3M2P,
werealsoevidentinrepresentativeisomersexaminedfromeach 23DM2B) on TON [0.08 C3H6 fractional conversion, 2 kPa 2-13C-
propene,503K].Thetwodotson2M2Pindicatethelabelpositionsif
skeletalbackbone: t-4M2P(formedfrom2M2PviaH-shift), t-
noscramblinghadoccurred.Thedottedsectionsindicatefragmentsthat
2H (via chain lengthening), t-3M2P (via methyl shift), and
cannotbedistinguishedbecauseofsymmetryandforwhichonlytheir
23DM2B (via branching) (see Figure 3). The 13C-content in combined13Ccontentcanbemeasuredfromtheanalysisofthemass
each C atom cannot be individually determined for some fragmentationpatterns.
groupingsofCatoms(denotedbytheovalsinFigure3),butthe
combined isotopic content in each grouping is consistent with
fastintramolecularscrambling.Isotopicscramblingconversions also indicate that the observed deviations from chemical
(σ, eq 5) are near unity at all conversions for all the skeletal equilibrium for the bulkier 2,3-DMB isomers on TON (see
isomersandregioisomersformedfrom2-13C-propeneonTON, Figures1,aswellasFiguresS3andS4)mustreflectdiffusional
MFI,SiAl,andHSiW(0.02−0.8fractionalconversion,2kPa,503 constraintsinsteadofintrinsickinetichurdles.
K; see Figure 4), consistent with fast skeletal and double-bond The observed rapid intramolecular scrambling did not occur
isomerizationonallsolidacids.Theseisotopicdatademonstrate within the mass spectrometer chamber during ionization and
the local attainment of chemical equilibrium at acid sites; they detection. The introduction of 1-13C-hexane or its alkene
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3.3. Discerning Origins and Fate of Products Formed
via Oligomerization and Secondary β-Scission Events.
Propeneoligomerizationforms“trueisomers”withlnumberof
Catoms(l=m·n;C =,C =,C =,...forn=3);theseisomerscan
6 9 12
undergo secondary β-scission to form chains of intermediate
chain length (l ≠ m·n; C =, C =, C =, C =,... for n = 3) (see
4 5 7 8
Scheme 1). Figure 5 shows the fraction of the C atoms in the
Scheme1.C H Oligomerization−CrackingReaction
3 6 a
NetworkonSolidAcids
Figure4.Isotopicscramblingconversion(σ;eq6)forhexeneisomers
(◆)2M2P,(*)trans-4M2P,(●)trans-2-H,(■)trans-3M2P,and(▲)
2,3-DM2BonTON,SiAl,MFI,andHSiW[2kPa2-13C-propene,503
K].
aC*representsalkoxidesoflcarbonsthatareequilibratedwiththeir
analogues(formedviadehydrogenationof1-13C-hexaneonPt/ l
gas-phase concentrations by K, and k is the rate constant for
Al2O3;0.35fractionalconversion;0.4kPa1-13C-hexane;573K) oligomerization. l oligo
led to pentyl and butyl fragments with isotopic contents
consistentwithunscrambled1-13C-hexaneand1-13C-t-3-hexene convertedpropenethatappearaschainswithlCatoms(503K,
molecules (0.51−0.56; see Table S1 in the SI), indicating that 60kPaC H )atlowreactantfractionalconversions(<0.05)on
neither alkanes nor alkenes significantly isomerize during TON, M3OR6, SiAl, and SiO -supported H PW O (HPW)
2 3 12 40
ionization. The very small deviations from the expected values (Figures5a−d)andonBEA,MFI,andFAU(seeFigures5e−g).
(0.50) are in agreement with the slow rates of such intra- Theproductsformedarepredominantlyalkenes,withonlytrace
molecular rearrangements reported for linear octenes during concentrationsofsmallalkanes(n≤6;<2.5%Catoms),which
ionization and detection in mass spectrometers.25 The intra-
formviaH-transferfromlargeralkenestoalkoxides(seeScheme
molecular scrambling occurring in the reactor is also evident
1) together with dienes and cycloalkenes coproducts that
fromthefactthatproductsthatcanonlybemadefromβ-scission
become detectable only at higher propene conversions (see
exhibitabinomialnumberofcarbons,whichreflectstheywere
FigureS13intheSI;<0.2%Catomsofproducts).
formed from intramolecularly scrambled larger molecules (see The different carbon number distributions observed on
FigureS12intheSI). different solid acids (Figure 5) can be expressed in terms of
These data, taken together with the equilibrium isomer therelativeratesofC−Cbondformationandcleavageevents.β-
distributions derived from chemical speciation, are consistent
Scission can occur for an alkene with l C atoms with a rate
withfastinterconversionsamongisomersunderallconditionsof
propene oligomerization. Such equilibration reflects the cβo-sncsitsasniotnk,β,lb;ecchaauinseswoifththfeewuenrstthaabnlesixcaCrbaetnoimumsdioonnsotinuvnodlevregdo,
thermodynamicsofgaseousalkeneisomers;itprovidesevidence
which is consistent with the absence of ethene or methane in
for the very rapid communication between alkenes and surface
protonsviaadsorption−desorptionsteps,evenattheveryshort products(Figure5)andtheinformationprovidedbyref27.
residence times that lead to differential propene conversions. Oligomerization steps that form true oligomers include the
Such equilibrated adsorption−desorption processes for prod- additionofpropenetoanyalkoxidederivedfromanalkeneofa
lengthcorrespondingtothoseofatrueoligomer(l=m·n).For
ucts,aswellaspropenereactants,alsoshowthatneitherreactant
example,theratioofB-scissiontoformationratesforC alkenes
adsorptionnorproductdesorptioncanbethekineticallyrelevant 6
isgivenby
steps in oligomerization catalytic sequences. This rapid intra-
molecularequilibrationamongskeletalanddouble-bondalkene
r k K P
isomers, even for the 2,3-DMB isomer backbones that did not β,6 = β,6 6 6
attainfullchemicalequilibriumonTON(seeFigures3and4), roligo,6 koligo,3K3(P3)2 (7)
precludesanydeterminationofindividualratesofformation of
each isomer from oligomerization transition states. The whereK istheequilibriumconstantforalkoxideformationwithl
l
prevalence andprevious useof inaccurate thermodynamic data Catoms,k istherateconstantforformationofC oligomers,
oligo,3 6
may have led to equivocal claims of kinetic and even shape and P is the pressure of an alkene with l C atoms. In order to
l
selectivities in previous studies.2,26 Any deviations from the accountforallproducts,eq7mustbesummedoverallcarbon
thermodynamic distribution of gaseous alkene isomers in numbers(eq8):
oligomerizationinsteadreflectdiffusionalconstraintsforspecific
isomers.Theequilibratednatureofallisomersofchainswitha r ∑ k KP
given number of C atoms allows their rigorous lumping as a β = l=6 β,l l l
r ∑ k K PP
singlechemicalspeciesinallrateandselectivityexpressions. oligo m=1 oligo,m 3m 3 3m (8)
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r
β
χ = 1 −
r
oligo (9)
This χ parameter gives the fraction of all C atoms in the
convertedreactantsthatremainastrueoligomersbyexitingthe
catalyst bed before a β-scission event (Section 2.2). The
secondary nature of β-scission events leads to χ values that
decrease as the propene conversion increases (Figure 6).
Figure6.Trueoligomerselectivity(χ;eq2)forCH oligomerizationas
3 6
afunctionofpropenefractionalconversionfor(a)zeolites((◆)TON,
(●) MOR, (■) BEA, (▲) MFI and (*) FAU) and (b) mesoporous
acids((■)MCM-41,(●)SiAl,(◆)HPW,and(▲)HSiW)[at60kPa,
503K;dashedlinesservetoguidetheeye].
However,theχvaluesincreaseasthepropenepressureincreases
forsamplesthatdonothaveχvaluesofunity,consistentwitheqs
7−9(conversionrange0.02−0.04;seeFigureS14intheSI).
The formation of C and C products from propene (and
4 5
others with l ≠ m·3 C atoms) provide direct evidence of the
occurrence of β-scission events. However, β-scission in larger
speciescanalsoformproductsofthesamelengthasoligomers,
an occurrence for which we account by fitting a binomial
distribution to the intermediate C-length products and then
subtractingit(Section2.2;seeFigure7).Thecontributionfrom
this distribution is much greater in 3-D zeolites (MFI, BEA,
FAU) than other acids (Figures 5 and 7) and it becomes
increasinglybinomialwithincreasingconversion,indicatingthat
fewer of the observed oligomers are, in fact, “true oligomers”.
The use of 2-13C-propene can also rigorously quantify the
fraction of “true oligomers” in the products. The intervening
intramolecular13Cscramblingthatoccurswitholigomerization-
β-scissionevents(Section3.2)leadstoabinomialdistributionin
thenumberof13Catomsinaproductformedfromcleavingofa
fully intramolecularly scrambled species. For example, each C
6
formed from 2-13C-propene dimerization contains two 13C
atoms(Figure8a;e.g.,2M2PonTONatlowconversions(dark
gray)).IsotopologuesofC isomerswithmoreandlessthantwo
6
13Catomsstarttoappearasconversionincreases(forbothTON
andMFI;seelightgraybarsinFigures8aand8b).Theshiftfrom
Figure5.Carbonselectivitiesforchainsinlnumberofcarbonatoms a unimodal to a binomial distribution suggest that fewer “true
formed in C H oligomerization reactions (propene fractional
3 6 oligomers” leave the catalyst bed intact, while an increasing
conversions are given in parentheses: (a) TON (0.005), (b) MOR
number form via β-scission of larger oligomers as conversion
(0.009),(c)SiAl(0.005),(d)HPW(0.003),(e)BEA(0.004),(f)MFI
(0.009),and(g)FAU(0.003)[503K,60kPa]. increaseswithincreasingresidencetime.Thisisconsistentwith
the observed binomial isotopologue distributions of products
that can be made only via β-scission (C = and C =; see Figure
4 5
wherek istherateconstantforoligomerizationstepmwith S12).
oligo,m
propene and oligomer with 3m C atoms. The true oligomer TheisotopologuedistributionsshowninFigure8indicatethat
selectivityparameter(χ)(eq2)isrelatedtotheratioofratesin thefractionof2M2Pisomersthatleavebeforeβ-scission(χ ;
2M2P
eq8bytheexpression see eq 3) is smaller on MFI than TON. In fact, both chemical
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3.4. Selectivity of Oligomerization to β-Scission on
Solid Acids with Different Frameworks. The effects of
frameworkstructureontherelativeratesofoligomerizationand
β-scission, described by the χ values for each solid acid, were
examinedforabroadrangeofaluminosilicateframeworks.The
data in Figure 6 suggest that 1D zeolites, with channels of
uniform cross section, and mesoporous solids, with channels
significantly larger than the oligomers formed, lead to higher χ
values than 3D zeolites at all conversions; 3D zeolites exhibit
fluctuationsincross-sectionalchannelareasthatmoleculesmust
traverseastheyformanddiffusethroughthevoidstructure.
We examine the effects of such undulations in a more
systematic manner by using the ratio of the pore limiting
diameter (PLD) to the largest cavity diameter (LCD) for each
zeoliteframework28asasuitableandquantitativedescriptor.We
turn to this undulation parameter (Ω) as a metric because
channel size, by itself, cannot account for the much greater
contributionofβ-scissiononMFIandFAUthanonTONand
MOR,despitethefactthatTONandMFI(10-MRzeolites)and
FAU and MOR (12-MR zeolites) share similar connecting
apertures. Zeolites with voids larger than the channels
connecting such voids give PLD/LCD (Ω) ratios smaller than
unity(MFI(3D,10-MRchannels),FAU(3Dcageswith12-MR
windows), and BEA (3D, 12-MR channels); Figure 9). 1D
Figure7.CarbonselectivityforCH oligomerizationonMFIandTON
3 6
ateitherlowCH fractionalconversion(0.012and0.03,respectively;
3 6
top) or high CH fractional conversion (0.45 and 0.49, respectively;
3 6
bottom) with nonoligomer products fit to a binomial distribution
(dashedline)[503K,60kPa].TheamountofreactantCH shownis
3 6
calculatedfromthebinomialdistribution.
Figure 9. Largest cavity diameter plotted against the pore limiting
diameter(PLD)forvariouszeolites.Thedashedlinerepresentsaunity
ratio.
zeolites (here, TON (10-MR) and MOR (12-MR with 8-MR
Figure8.Comparingisotopologuedistributionfor2-methyl-2-pentene sidepockets)),andmesoporousMCM-41giveΩvaluesofunity,
on (a) TON at low fractional conversion (0.03; dark gray) and high
becausetheylackundulationsintheirchannels.SiAlandtheSiO
fractionalconversion(0.49;lightgray)andon(b)MFIatlow(0.01; 2
darkgray)andhighfractionalconversion(0.45;lightgray)[2kPa2-13C- silicasupportforthePOMclustersconsistofcolloidalaggregates
propene,503K]. with evident cross-sectional changes in their voids, but their
dimensions(2.4nm)arelargerthanthoseofthelargestchains
thatarelikelytoforminoligomerizationreactions.
MFI contains intersecting sinusoidal and straight channels
speciation and isotopic labeling experiments show that MFI (0.51−0.56 nm) that create a large void (0.7 nm).22,28,29 Such
samples give smaller χ values and more binomial-like chain large voids can accommodate larger transition states, such as
lengthdistributions(seeFigures5−8)thanTONsamplesatall those required for subsequent addition of alkenes to C
6
propene conversions and pressures. The sections that follow alkoxides, than their intervening connecting channels and
addressthemechanisticunderpinningsforthesedifferencesand apertures. The larger oligomers thus formed must egress the
also extend the effects of void structure to other reactants and void structure through these smaller intervening channels. The
zeoliteframeworks,whilealsoaddressingtheroleofacidstrength concomitant diffusional hurdles cause the retention of these
indeterminingoligomerizationselectivity. oligomerswithinMFIcrystals(andtheother3Dzeolites),until
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smaller molecules form via β-scission events. The cylindrical
channels in TON, in contrast, cannot grow chains larger than
those able to egress from the void structure. The absence of
intersections, andofthelargervoids orcagelike structures that
suchintersectionsform,leadstoχvaluesnearunity,asobserved
previouslywithoutadefinitemechanisticinterpretation.30Thus,
theΩparameter,definedhereasthePLD/LCDratio,represents
a more appropriate description than the specific respective
dimensionsoftheaperturesorcagesintheseporoussolids.
Highχvalueswerealsoobservedon1DMORzeolites(Figure
10) and on all mesoporous samples (Figure 6), despite their
Figure11.Trueoligomerselectivityparameterfor2M2P(χ ;eq3),
2M2P
asafunctionofpropenefractionalconversionon(◆)TON,(▲)MFI,
(●) SiAl,and (■)HSiW[2 kPa2-13C-propene, 503 K;dashedlines
servetoguidetheeye].Theratioofporelimitingdiameter/largestcavity
diameter(Ω;PLD/LCD)isgivenforzeolitesamples.
indicate that the products have not gone through the cycle
severaltimesandthemajorityofβ-scissionresultsinC andC
4 5
products,whichisconsistentwithFigure7.
3.5. Effects of Acid Strength and Site Density on the
Selectivity ofβ-Scission to Oligomerization. Microporous
andmesoporous aluminosilicates provide diverse voidenviron-
Figure 10. True oligomer selectivity parameter (χ) for C H
3 6 mentsbutacidsitesofsimilarstrength.31KegginPOMclusters,
oligomerization,asafunctionofporelimitingdiameter/largest cavity
in contrast, are solid acids of greater strength than
diameter(PLD/LCD),forTON(0.005fractionalconversion),MOR
(0.009), MCM-41 (0.005), BEA (0.004), MFI (0.009), and FAU aluminosilicates (exhibiting deprotonation energies (DPE) of
(0.003)[503K,60kPa,dashedlinesservetoguidetheeye]. 1085 kJ mol−1 for H3PW12O40 vs 1190−1222 kJ mol−1 for
aluminosilicates).14,32Figures6band12showthatχvaluesare
unaffected by acid strength on all solid acids with mesoporous
much larger channels and voids. These similar selectivities
indicate that the size of the voids do not directly influence the voids(H3PW12O40,H4SiW12O40,MCM-41,SiAl).Acidstrength
extentofβ-scission.Instead,β-scissionisonlyrequiredtooccur influences therateofaddition ofalkenesto alkoxide oligomers
whenarestrictionalongthediffusionalpathselectivelyblocksthe and that of β-scission events in larger alkoxides to the same
diffusionoflargeroligomers,whichcanformonlyinvoidslarge extent. Both reactions involve full ion -pairs at their respective
enoughtoaccommodatethetransitionstatesofsubsequentC−
C bond formations. True oligomer selectivity parameters (χ)
decrease as Ω values decrease and become much smaller than
unityforall3Dzeolites(MFI,BEA,FAU;seeFigure10).Such
trendsreflecttheabilityoflargervoidstoformlargeroligomers
thatmustundergoβ-scissiontoallowtheirfacileegressassmaller
chains through the smaller channels that connect such larger
voids.Thesetrendsbecomemuchstrongerasthedifferencein
sizebetweenthevoidandthesubsequentchannel,whichcauses
feweroligomerstoegressintact.
Thelowerselectivitytoβ-scissionoveroligomerizationon1D
zeolites and mesoporous samples compared with that on 3D
zeolites, irrespective of channel size, is consistent with the
differentextenttowhichthenumberof13Catomsinoligomers
formed from 2-13C-propene approaches binomial in these
samples (see Figure 8). The randomization of the number of
13CatomsactsasadescriptorofthenumberoftimestheCatoms
in such chains must traverse an oligomerization−cracking
sequence. Figure 11 shows that χ2M2P values decrease as the Figure12.Trueoligomerselectivity(χ)forCH oligomerization,asa
conversion increases, but are higher on 1D TON and functionofdeprotonationenergy(DPE)32(gi3ven6inunitsofkJmol−1)
mesoporous acids than on MFI. The higher χ2M2P value and, formesoporoussamples:HPW,HSiW,MCM-41andSiAlatdifferent
then,macroscopicχfortheentiredistributionvalue(Figure10) fractional conversion: (◆) 0.002−0.004, (■) 0.009−0.01, and (▲)
on MFI at low conversions (0.87 versus 0.42, respectively), 0.04−0.05[503K,58kPaCH].
3 6
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transitionstates;33theirsimilarchargecausesthestabilityofthe Table2.ValuesoftheDiffusionParametersforMFIandTON
two transition states to benefit similarly from the more stable Zeolites
conjugate anions in stronger acids. This similarity renders χ
H+/u.c. Ψ(molH+nm−1)
valuesindependentofacidstrength,becauseitrepresentsaratio
of the rate constants that describe these reactions, which are MFIFramework
equallyaffectedbyacidsofdifferentstrength(eqs7−9). 4.5 7484
Such effects can also be probed using X-MFI zeolites with 3.6 9595
differentisomorphouslysubstitutedheteroatoms(X=Al3+,Ga3+, 2.5 4593
Fe3+, B3+). These samples provide a very diverse range of acid 2.1 3721
strengths within a zeolite framework that imposes diffusional 1.1 5431
constraintsthroughtheundulationsthatenhancecontributions 0.36 808
fromβ-scission.Thenumberofprotonspercrystalvolumealso TONFramework
enhances contributions of these secondary reactions. The 0.4 416
combinedeffectsaredescribedbytheThielemodulus: 0.36 622
0.26 121
k
Φ2 ∝ ψ
De (10)
where
ψ = [H+]L2 (11)
which is proportional to the site reactivity (k), the volumetric
protondensity[H+],andthesquareofthecharacteristicdiffusion
distance (in this case, the zeolite crystal radius (L)); it also is
inverselydependentonthediffusivityoftheprecursormolecule
that undergoes β-scission (D). The values of true oligomer
e
selectivities for Al-MFI with a large range of proton densities
(0.36−4.5H+/unitcell)areplottedagainstΨinFigure13,where
Figure 14. True oligomer selectivity parameter (χ) for C H
3 6
oligomerization, as a function of proton density [[H+]/unit cell] for
MFIsampleswithdifferentheteroatoms:(■)Al,(▲)Fe,(●)Ga,and
(◆)B[503K,58kPaCH,0.005−0.015fractionalconversion].
3 6
propene.Theseselectivitiesindicatethatthelargeroligomersdo
notformasmuchinthesmallchannelsofTON,comparedtothe
intersectionvoidinMFI(Figure15).However,thetrimersthat
are formed experience transport limitations egressing from the
MFIcrystalwheretheundulationofchannelstructureinducesβ-
scission,suchthatsmalleralkenescanegresswithoutrestriction.
3.6. Effects of Reactant Alkene Chain Length on
Figure 13. True oligomer selectivity parameter (χ) for C H Oligomerization Selectivity. The chain length and sub-
oligomerization,asafunctionofdiffusionparameteronAl-MFIzeol3ites6 stituentsinthereactantalkenesinfluencetheturnoverratesfor
[503K,58kPaCH,0.005−0.015fractionalconversion]. botholigomerizationandtheβ-scissionreactionsofoligomeriza-
3 6
tionproductsand,consequently,thedistributionofchainlengths
ListhecrystalsizeestimatedfromTEM(Ψvaluesaregivenin in products (eqs 7 and 8). Figure 16 shows that these
Table2).ThemonotonictrendinFigure13confirmsthat,fora distributions in the products formed from C H (Figures 16a
2 4
givenacidstrength(Al-MFI),Ψprovidesanadequatesurrogate and 16b) and i-C H (Figures 16c and 16d) reactants differ
4 8
for the Thiele modulus and increasing this value increases the markedlyonTONandMFI,asinthecaseofpropenereactants
selectivitytodiffusion-enhancedsecondaryreactions(decreases (Figure5).The1DTONframeworkTONallowstrueoligomer
χ). Acid strength affects the rate constants in eq 10 and also products (C , C and C for C H ; C for i-C H ) to egress
4 6 8 2 4 8 4 8
should affect the selectivity to the extent that stronger acids withoutsignificantβ-scission,thusleadingtoχvaluesnearunity
imposealargerdiffusivebarrier.34Therefore,themuddledeffects forbothreactants(seeFigures17aand17b).Incontrast,suchχ
inFigure14areindicativeoftheuseofanincompletedescriptor valuesaremuchsmallerforC H reactionsonMFIthanTONat
2 4
ofthecatalystpropertiesthataccountforthemagnitudeofχ. allconversions.Thechainlengthdistributionisalmostbinomial
Such diffusional enhancements of secondary reactions of (Figure 16b) for C H , as in the case of C H reactants (see
2 4 3 6
primary oligomerization products in MFI can also be inferred Figures5and7).Thesebinomialdistributionofchainlengthsare
from the effects of the diffusion parameter (Ψ) on the relative reminiscent of those reported at higher alkene conversions for
abundance of dimers (C ) and trimers (C ) formed from C −C alkenesonMFI.1,35
6 9 2 10
7068 DOI:10.1021/acscatal.6b02128
ACSCatal.2016,6,7059−7070