Comprehensive study of isobutane selective oxidation over group i and II phosphomolybdates: Structural and kinetic factors

Catal Lett (2011) 141:1767–1785

DOI 10.1007/s10562-011-0715-y

Comprehensive Study of Isobutane Selective Oxidation Over

Group I and II Phosphomolybdates: Structural and Kinetic

Factors

•

Shane Kendel Trevor Brown

Received: 4 August 2011 / Accepted: 26 September 2011 / Published online: 12 October 2011

Ó Springer Science+Business Media, LLC 2011

Abstract Various phosphomolybdates were synthesized

using cations from Groups 1 and 2 of the periodic table.

These compounds were of the form M_xH_3-xn[PMo₁₂O₄₀],

with n being the cationic charge (?1 or ?2). XRD analysis

shows pure phosphomolybdic acid has a triclinic structure.

A body centered cubic (BCC) structure gradually develops

with addition of Group 1 cations, and the triclinic phase is

completely replaced by the BCC phase once metal cations

could be ascertained, despite investigation into correlations

using several different models.

Keywords Kinetics ꢀ Selective oxidation ꢀ Methacrolein ꢀ

Heteropoly compounds ꢀ Phosphomolybdates

1 Introduction

3

˚

occupy a volume greater than 9–11 A per phosphomo-

lybdate anion. The Group 2 compounds do not form a cubic

phase, however the triclinic phase distorts once cationic

Heteropoly compounds are useful for a large range of

reactions, including alkylations, dehydrogenations, dehy-

drations and selective oxidations [1]. The unique structural

aspects of the substrates heavily inﬂuences their activity

and selectivity. There are three structural components of

heteropoly compounds [2]:

3

volume is greater about 5 or 6 A and appears to become

˚

somewhat amorphous. Isobutane selective oxidation over

the compounds yielded methacrolein (primary product),

3-methyl-2-oxetanone (lactone), acetic acid, propene,

methacrylic acid, carbon dioxide and water as products.

Propene was formed over the Group 1 compounds exclu-

sively and methacrylic acid formation was observed with

BaH[PMo₁₂O₄₀] only. Products form via two distinct pro-

cesses: Category 1 product has an exponential proﬁle and

coverage is consistent with a Langmuir model, Category 2

formations are consistent with desorptions from within the

bulk of the substrates. Methacrolein forms via both Cate-

gory 1 and 2 processes, whilst all other products are formed

by Category 2 exclusively. A rigorous kinetic analysis

yielded accurate activation parameters. Category 1 meth-

acrolein formation apparent activation energies ranged

from 34.7 1.3 to 119 4 kJ mol^-1. Category 2 forma-

tions ranged from 34.3 0.4 to 726 172 kJ mol^-1. No

relationship between activity and composition or structure

(i) Primary structure: The heteropolyanion or polyoxo-

anion molecule

(ii) Secondary structure: The arrangement of the primary

structure, together with counter cations and other

molecules such as water

(iii) Tertiary structure: The way in which the secondary

structure assembles itself into solid particles

Understanding the difference between the primary and

secondary structures is essential in order to understand the

reaction processes involved with these compounds [3]. The

secondary structure is usually regular, though reactant

molecules are able to absorb deep into the bulk of the solid

and facilitates bulk-type catalysis. As a consequence, the

secondary structure is the most important aspect in deter-

mining the catalytic activity of heteropoly compounds.

Heteropoly compounds have both microporous and meso-

porous character, but do not exhibit extensive macropo-

rosity. The small pores of heteropoly compounds generally

result in low surface areas [4, 5]. XRD studies have

S. Kendel (&) ꢀ T. Brown

School of Science and Technology, University of New England,

Armidale, NSW 2351, Australia

e-mail: shane.kendell@gmail.com

123

1768

S. Kendel, T. Brown

identiﬁed several phases, including triclinic, primitive and

body-centered cubic [6–14]. The degree of hydration

heavily inﬂuences unit cell dimensions, whereby complete

phase changes can occur [15]. The fully substituted

magnesium, calcium, strontium and barium salts (Mg_1.5

[PMo₁₂O₄₀], Ca_1.5[PMo₁₂O₄₀], Sr_1.5[PMo₁₂O₄₀] and Ba_1.5

[PMo₁₂O₄₀]), have been prepared and analyzed by

McGarvey and Moffat [16]. The publication reported that

the XRD data of the divalent compounds was ‘‘largely

featureless’’. Silviani and Burns [12] have also investigated

the diffraction spectra of the alkaline earth phosphomo-

lybdates and observed only a cubic structure without evi-

dence of any amorphous or other phases (including

triclinic).

analytic methods whilst the temperature is increased linearly

with respect to time. Large temperature ﬂuctuations associ-

ated with exothermic adsorption processes can be avoided by

establishing equilibrium at low temperatures, whereby

negligible reaction occurs. TPRS allows the investigation of

a wide range of temperatures in a short period of time and is

ideally suited to the determination of kinetic parameters.

TPRS may also be used to monitor desorptions. This tech-

nique has been employed by Kendell et al. to elucidate

accurate kinetic parameters for isobutane selective oxidation

over phosphomolybdic acid and different cationic substi-

tuted derivatives [22–24]. This paper presents the structural

affects of Group 1 and 2 cation addition the phosphomo-

lybdate structure and how this impacts on the selective oxi-

dation of isobutane into various products, but principally

methacrolein formation.

Heteropoly compounds such as phosphomolybdates are

unique in that they are able to absorb molecules into the

catalyst bulk, allowing a three-dimensional reaction ﬁeld

[17]. This process is favored by catalysts that contain

counter cations with a small radius to charge ratio, e.g.

2 Experimental

?

Na^?, Cu^2?and H^?rather than Cs^?and NH₄[2]. Het-

eropoly compounds resemble liquids in the way they

absorb such large amounts of gaseous species [18]. This

ability of heteropoly substrates to absorb molecules into the

bulk allows reactions to proceed with surface area-inde-

pendent kinetics, that is, surface area does not impact on

the reaction rates [17].

2.1 Sample Preparation

Isobutane and argon were obtained from BOC gases and

used without further puriﬁcation. Metal substituted phos-

phomolybdates were prepared by addition of metal car-

bonates to a solution of phosphomolybdic acid, then drying

to a solid. The phosphomolybdic acid and other reagents

were obtained from Aldrich and used without puriﬁcation;

analysis determined that the phosphomolybdic acid was

hydrated with 29 waters per Keggin unit. A typical prep-

aration for Li₂H[PMo₁₂O₄₀] follows: 10.3196 g of phos-

phomolybdic acid was dissolved in *40 mL of water with

stirring. 0.3273 g of Li₂CO₃was added with continued

stirring (evolution of carbon dioxide). The solution was

heated to about 60 °C with stirring until thick slurry was

produced. Drying was completed by placing in an oven at

120 °C overnight. Solid Li₂H[PMo₁₂O₄₀] was ground and

stored in preparation for TPRS experiments.

About 2.7 million tonnes of methyl methacrylate was

produced world-wide, in 2009 [19], with 85% manufac-

tured via the acetone cyanohydrin (ACH) process [20].

This process uses hydrogen cyanide as a feedstock and

forms ACH as an intermediate, both of which are highly

toxic, and ammonium hydrogen sulfate is coproduced in

large quantities, which is contaminated with organics and

has to be pyrolyzed or disposed of in spoil banks. Supply

shortage of hydrogen cyanide also affects this production

method [21]. These deleterious factors have prompted

research into environmentally responsible alternatives, and

new commercial processes for methyl methacrylate have

been developed [21] and include the two step catalytic

oxidation of isobutene into methacrylic acid, the methacr-

ylonitrile (MAN) method, the BASF route, modiﬁed ACH

process (Mitsubishi Chemical Co. Inc.), and the direct

oxidative esteriﬁcation of methacrolein (Asahi Chemical

Co. Inc.). Phosphomolybdic acid has been shown to be

effective for the selective oxidation of isobutane into

methacrolein, and substitution of the protons with copper

or lanthanide cations has improved oxidation performance

[22–24]. Therefore formation of methacrolein from the

oxidation of isobutane by phospomolybdic acid derivatives

may be a viable catalytic solution to the ACH process.

Temperature-programmed reaction spectroscopy (TPRS)

is a widely used method for analyzing chemical reactions.

Essentially it is the monitoring of reaction processes by

Group 1 compounds were of the form M_xH_3-x[PMo₁₂

O₄₀], where M = Li, Na, K, Rb or Cs, and x = 1, 2 and 3,

and also 2.5 for Cs; the Group 2 compounds were of the

form M_xH_3-2x[PMo₁₂O₄₀], where M = Mg, Ca, Sr or Ba,

and x = 0.5, 1 and 1.5.

2.2 X-Ray Diffraction (XRD)

The phosphomolybdates were analyzed via XRD using the

facilities at James Cook University, Australia. Powdered

XRD measurements were performed on a D5000 Diffrac-

tometer, equipped with a copper anode X-ray tube. The

radiation used for the analysis consisted of Cu Ka X-rays

with a wavelength of 154.06 pm. Samples were systemat-

ically scanned with 2h angles ranging from 1.3° to 65.3°,

123

Comprehensive Study of Isobutane Selective Oxidation

1769

using 0.02° increments. Past investigations have demon-

strated that the XRD data of phosphomolybdic acid is

modiﬁed depending upon extent of hydration [6, 15]. For

this reason, all samples were uniformly calcined at 300 °C

for 4 h, prior to being sent off for analysis.

precaution; indeed, kinetic investigation into the Group 1

and 2 salts has shown no evidence of degradation with the

later experiments with ca. 500 °C maximums (vide infra).

Kendell et al. have conducted IR analyses on similar

phosphomolybdates before and after TPRS and the

structure was preserved [22].

2.3 Experimental Apparatus and Technique for TPRS

Prior to each experiment the reactant feed stream was

ﬂowed for ca. 2 h. This allowed for a steady-state to be

established. The ﬁrst four experiments were then conducted

whilst maintaining this steady-state ﬂow. The ﬁfth exper-

iments differed: the steady-state regime is established in

the hour or so preceding, however 20 min prior to com-

mencement of the ﬁfth experiments, the reactant ﬂow was

turned off and the cell was evacuated for 20 min. This

allowed for elimination of gas-phase isobutane, and the

products formed during TPRS were from reaction of

adsorbed isobutane only. Aside from this, the temperature

ramp and data acquisition process remained the same as the

previous four experiments.

A low-pressure steady-state apparatus has been con-

structed in order to analyze reactions using the TPRS

technique. This apparatus has been described previously

[22–24]. Brieﬂy, reactions were conducted in a Pyrex

Knudsen cell reactor, which contained approximately

1.5 g (accurately weighed) of the solid samples. Prior to

initiating experiments, samples were pretreated under

vacuum in the Knudsen cell at 200 °C for about 24 h to

remove the majority of water, and residual carbonates. A

reactant feed-stream of an equimolar mixture of isobutane

and argon was used (oxygen was not included in the feed

stream, instead oxidations were facilitated by lattice

oxygen in the substrate, consistent with a Mars-van

Krevelen mechanism [25]). The feed stream is ﬂowed into

the Knudsen cell reactor, with the ﬂow restricted to less

than 10¹⁵molecules per second and reactor pressure

maintained between 7-10 Pa; this ensured a molecular

ﬂow regime in which gas-phase collisions were mini-

mized and secondary reactions prevented [24]. Oxidation

products, argon and unreacted isobutane exited the

Knudsen cell through an aperture and passed directly into

a quadrupole mass spectrometer. The theory of hetero-

geneous reactions in a Knudsen cell have been detailed

previously [24, 26].

3 Results and Discussion

3.1 XRD Analysis

The XRD investigation showed that all the phosphomo-

lybdates exhibit a crystalline structure, however there is a

wide variation amongst the X-ray spectra, and hence

variation in the unit cells and lattices. The structure of

phosphomolybdic acid consists of a triclinic phase, as

previously discussed by Langpape et al. [6]. Past investi-

gations have demonstrated that the XRD data of phos-

phomolybdic acid is modiﬁed depending upon extent of

hydration [6, 15]. For this reason, all samples were uni-

formly calcined at 300 °C for 4 h, prior to being sent off

for analysis. The powdered XRD pattern for phosphomo-

lybdic acid is given in Fig. 1a. Pure phosphomolybdic acid

exists in a triclinic phase. The maximum peak shown in

The reactor was enclosed in a temperature-program-

mable furnace. Each sample was subjected to ﬁve tem-

perature-programmed experiments. The ﬁrst experiments

with each phosphomolybdate tend to yield poor quality

data due to the occupation of active sites by water and

other molecules [24], therefore these initial runs function

as an additional pretreatment procedure. TPRS for each

compound was conducted from 100 °C to a maximum

of 400 °C (for the ﬁrst experiment) or 500 °C (for the

subsequent four experiments), at a heating rate of

5 °C min^-1. Decomposition of phosphomolybdic acid

occurs at temperatures above 400 °C [11, 27–29], so the

lower maximum temperature for the initial TPRS exper-

iment allowed for elimination of water and other mole-

cules from the phosphomolybdates, whilst ensuring

thermal degradation of the Keggin framework does not

occur before useful selective oxidation data can be

obtained. It should be noted however, the addition of

cations to the phosphomolybdate anion enhances thermal

stability signiﬁcantly [12, 30–32], so the termination

of the ﬁrst experiment at 400 °C is a conservative

ꢀ

Fig. 1a occurs at 2h = 9.06 and corresponds to the ð011Þ

lattice plane.

The extent of hydration signiﬁcantly affects the XRD

patterns. Previous work by Langpape et al. has been pub-

lished which shows the XRD data for phosphomolybdic

acid and cesium phosphomolybdates with varying degrees

of hydration [6]. Comparison of the diffraction pattern of

phosphomolybdic acid (calcined at 300 °C for 4 h) with

the work from Langpape et al. suggests that the extent of

hydration of the pure acid is 13 water molecules per

Keggin unit, and therefore the acid used for the X-ray work

in this study is assumed to be H₃[PMo₁₂O₄₀]ꢀ13H₂O. It

should be noted, however, that the 300 °C calcinations

render the samples completely anhydrous and that the 13

water molecules per H₃[PMo₁₂O₄₀] are the result of

123

1770

S. Kendel, T. Brown

Fig. 1 XRD spectra for pure

phosphomolybdic acid (a) and

the lithium (b), sodium (c),

potassium (d), rubidium (e) and

cesium (f) phosphomolybdate

series

300

200

100

600

400

200

b

-

a

(011)

Li₃[PMo₁₂O₄₀

]

H₃[PMo₁₂O₄₀

]

Li₂H[PMo₁₂O₄₀

]

LiH₂[PMo₁₂O₄₀

]

0

10

20

30

40

0

10

20

30

40

2 theta (degrees)

600

Na₃[PMo₁₂O₄₀]

K₃[PMo₁₂O₄₀]

c

d

400

200

0

400

200

K₂H[PMo₁₂O₄₀

]

Na₂H[PMo₁₂O₄₀]

NaH₂[PMo₁₂O₄₀]

KH₂[PMo₁₂O₄₀

]

0

10

20

30

40

10

20

30

2 theta (degrees)

800

600

400

200

0

600

f

e

Cs₃[PMo₁₂O₄₀

]

Rb₃[PMo₁₂O₄₀

]

400

200

0

Cs_2.5H_0.5[PMo₁₂O₄₀

]

Rb₂H[PMo₁₂O₄₀

]

Cs₂H[PMo₁₂O₄₀

]

RbH₂[PMo₁₂O₄₀

]

CsH₂[PMo₁₂O₄₀

]

10

20

30

0

10

20

30

40

2 theta (degrees)

ꢀ

rehydration of the sample prior to analysis. Moreover,

the ﬁrst TPRS removes any rehydration water that results

from handling the samples, hence all kinetically relevant

TPRS experiments are conducted on anhydrous phospho-

molybdates.

effects, as compared to the pure acid. The large ð011Þ peak

from the triclinic phase becomes distorted with the ﬁrst

replacement of a proton with a lithium cation. The peak

partially separates with the second substitution and ﬁnally

forms two distinct peaks with Li₃[PMo₁₂O₄₀] (Fig. 1b).

This is evidence of another phase being present along with

the triclinic phase.

3.1.1 Group 1 Phosphomolybdates

Sodium addition to the phosphomolybdate framework

results in X-ray spectra that are very different to that of the

pure acid, and these are given in Fig. 1c. The lower

substituted NaH₂[PMo₁₂O₄₀] and Na₂H[PMo₁₂O₄₀] com-

pounds display peaks that are not clearly deﬁned, which is

Substitution of the protons by the alkali cations causes a

change in the spectra dependent upon the cation used and

the extent of replacement. The addition of lithium to the

phosphomolybdate anion causes signiﬁcant structural

123

Comprehensive Study of Isobutane Selective Oxidation

1771

likely due to the presence of the triclinic phase. The fully

substituted Na₃[PMo₁₂O₄₀] salt, however, shows clearly

resolvable XRD peaks. This is due to the presence of

a body centered cubic phase. Several peaks of the

Na₃[PMo₁₂O₄₀] diffraction pattern, given in Fig. 1c, have

been labeled with the Miller indices associated with the

cubic structure.

alongside the cubic phase, albeit in small measure. Black

et al. has shown that XRD data is heavily dependent upon

the extent of hydration [15]. The potassium phosphomo-

lybdates investigated by Black et al. [15] were calcined at

400 °C, whereas those analyzed in this work were prepared

at 300 °C. However, past about 150 °C all water of

hydration should be removed so the discrepancy is most

likely attributed to rehydration of our sample prior to

analysis.

The addition of potassium to the phosphomolybdate

structure is associated with the appearance of the body

centered cubic phase. The body centered cubic character

is apparent in the KH₂[PMo₁₂O₄₀] diffraction pattern,

however the peaks are complicated. In comparison, K₂H

[PMo₁₂O₄₀] and K₃[PMo₁₂O₄₀] display well resolved

spectra, consistent with body centered cubic structures, and

there is little evidence of another phase being present.

Figure 1d shows a comparison of the three potassium

compound spectra. Clearly seen for the KH₂[PMo₁₂O₄₀]

pattern, are peaks at about 11° and 27° on the 2h axis.

These correspond to peaks in the K₂H[PMo₁₂O₄₀] and

K₃[PMo₁₂O₄₀] spectra. This demonstrates that a partial

body centered cubic phase is established with the mono-

substituted potassium salt, however, another phase is

responsible for the poorly resolved pattern.

Other, more recent analyzes have been reported by Hu

and Burns [34] and Langpape et al. [6] with cesium

derivatives, of varying compositions of the form Cs_xH_3-x

[PMo₁₂O₄₀]. These have shown that for x \ 2, two distinct

phases are observed in XRD patterns, while for x C 2 only

the cubic phase is detectable. These ﬁndings agree with the

results obtained by Black et al. [15] and with those reported

above. Further investigation by Langpape et al. [6] has

shown evidence that for cesium phosphomolybdates with

substitution greater than or equal to two cesium atoms per

Keggin unit, there exists Cs₃[PMo₁₂O₄₀] particles thinly

coated by pure H₃[PMo₁₂O₄₀]. This ﬁnding is supported

by related work conducted on cesium phosphotungstates

by Misono, where he has shown that particles of

Cs₃[PW₁₂O₄₀] form with H₃[PW₁₂O₄₀] ﬁlling the inter-

stices of the Cs₃[PW₁₂O₄₀] crystallites [2]. For cesium salts

with two or more cesium atoms per Keggin unit, the

coating of pure acid on the fully substituted cesium phos-

phomolybdate particles may not be detected by XRD,

hence only the body centered cubic phase may be apparent

for these salts. This effect is most likely responsible for

Black et al. [15] observing exclusive cubic phases in the

potassium salts with two or more potassium cations per

Keggin unit. Rubidium is between potassium and cesium in

the periodic table, and therefore it intuitively follows that

the structural trends of the phosphomolybdates made from

this alkali metal are consistent with the results for the

potassium and cesium derivatives.

All rubidium and cesium compounds exhibit a body

centered cubic phase, as shown in Fig. 1e and f, respec-

tively. However, these ﬁgures demonstrate that there is still

a signiﬁcant contribution from another phase for the mono-

substituted rubidium and cesium salts; RbH₂[PMo₁₂O₄₀]

has three peaks below 2h = 10° and CsH₂[PMo₁₂O₄₀]

exhibits a large spike at 2h = 9^o.

3.1.2 Factors Affecting Structure of Group 1

Phosphomolybdates

A previous study by Black et al. has identiﬁed the presence

of multiple phases for the potassium phosphomolybdates

[15] and Christian and Whittingham have observed the

presence of multiple cubic structures [33]. The catalysts

investigated were of the form K_xH_3-x[PMo₁₂O₄₀], where

x = 0, 0.5, 1, 1.5, 2, 2.5, 2.75 and 3. This study showed

that diffraction patterns of catalysts with intermediate

composition (0.5 B x B 2.0) consist of more than one

phase, while the heavier substituted (2.0 B x B 3.0) cata-

lysts possess the K₃[PMo₁₂O₄₀] phase exclusively.

Figure 1d shows that the mono-substituted potassium salt

(KH₂[PMo₁₂O₄₀]) has a mixture of cubic and another

phase, whereas the doubly- and triply-substituted com-

pounds (K₂H[PMo₁₂O₄₀] and K₃[PMo₁₂O₄₀]) essentially

exhibit only the body centered cubic structure. A close

examination of Fig. 1d, however, identiﬁes two small

peaks below 2h = 10^ofor the K₂H[PMo₁₂O₄₀] compound

that are not consistent with a body centered cubic structure.

These peaks are evidence that another phase is present

Table 1 shows a comparison of the effective ionic radii

[35] of the different Group 1 cations, all radii refer to the

cation in a six coordination state. The coordination state is

likely higher than six, however there is no structural data to

indicate the exact coordination number. Also shown in this

table are the volumes for one, two or three cations of each

species. Volumes were determined using the spherical

volume relationship V = (4/3)pr³n, where r refers to the

ionic radius and n is the number of cations. These values

refer to the Group 1 cation volume contribution to a par-

ticular phosphomolybdate, e.g. the rubidium cations from

3

˚

Rb₂H[PMo₁₂O₄₀] contribute a volume of 29.4 A . The bold

volumes indicate the phosphomolybdates that display a

resolvable body centered cubic structure. As this table

shows, the cubic character is associated with those phos-

phomolybdates possessing a Group 1 cationic volume

123

1772

S. Kendel, T. Brown

3

˚

greater than or equal to 11.0 A (Group 1 volume contri-

bution for KH₂[PMo₁₂O₄₀]). The greatest cationic volume

previous XRD analyzes on phosphomolybdic acid [6] with

the peak positions at around 8.2° and 9.2° being indicative

3

without cubic character is 8.89 A (Na₂H[PMo₁₂O₄₀]).

˚

ꢀ

of the respective ð110Þ and ð011Þ planes of a triclinic

Therefore it may be inferred that the minimum Group 1

cationic volume required to induce a cubic phase is

3

between 9 and 11 A . Because the coordination number is

phase. These peaks are visible for all the magnesium

derivatives, but the Mg_1.5[PMo₁₂O₄₀] displays a weaker

ð110Þ contribution than the other salts. There are however,

peaks in the spectra that are not accounted for by triclinic

phases and so there are other phases present, although no

evidence of a cubic phase is observed for the magnesium

phosphomolybdates. The calcium compounds also exhibit

XRD spectra consistent with the presence of triclinic

˚

likely greater than six, these volumes are not exact, but

instead give an approximation of the cationic volume

required to form the cubic phase. In any case, the volumes

can be used to make a relative comparison of Group 1

cations. Other factors may determine predisposition of

phosphomolybdates toward cubic character as a whole,

however this relationship holds well for the Group 1

species.

ꢀ

phases, especially the presence of the ð011Þ plane. The

contribution from the ð110Þ plane (*2h = 8.3°) is prom-

inent for Ca_0.5H₂[PMo₁₂O₄₀], however it is quite weak for

CaH[PMo₁₂O₄₀] and undetectable in the Ca_1.5[PMo₁₂O₄₀]

pattern (Fig. 2b). As with the magnesium spectra, there

exists an indeterminable phase along with the triclinic

component, and no cubic structure is observed. Figure 2c

displays the diffraction patterns of the strontium phos-

phomolybdates. The strontium compounds maintain the

3.1.3 Unit Cell Dimensions

Shown in Table 2 are unit cell dimensions as determined in

this work and from previous publications. These values

differ from those obtained in this work, however the gen-

eral trends are the same, with the exception of Langpape

et al. reporting a larger unit cell for Cs₃[PMo₁₂O₄₀] than for

Cs_2.5H_0.5[PMo₁₂O₄₀]. The generally larger unit cell

dimensions are probably due to differing extents of

hydration. The samples were calcined at 350 °C for 5 h by

Langpape et al. [6], at 300 °C for 6 h by Hu and Burns [34]

and at 300 °C for 4 h for this work. Unit cell dimensions

for non-cubic phases observed from the XRD data were

unable to be determined.

ꢀ

ð011Þ plane, while the ð110Þ lattice only appears with

Sr_0.5H₂[PMo₁₂O₄₀]. The pattern for the fully substituted

salt, Sr_1.5[PMo₁₂O₄₀], appears to become disordered and

may reﬂect the development of signiﬁcant amorphous

character. As with the previous Group 2 phosphomolyb-

dates, there is no discernable cubic phase associated with

the strontium derivatives, and phases other than triclinic

contribute to the diffraction data. The barium phospho-

molybdates, like the previous Group 2 phosphomolybdates,

ꢀ

exhibit the characteristic ð011Þ plane, as shown in Fig. 2d.

3.1.4 Group 2 Phosphomolybdates

The ð110Þ lattice plane is non-existent in the heavier

substituted BaH[PMo₁₂O₄₀] and Ba_1.5[PMo₁₂O₄₀] com-

pounds and is barely resolvable with Ba_0.5H₂[PMo₁₂O₄₀].

The spectra of BaH[PMo₁₂O₄₀], and Ba_1.5[PMo₁₂O₄₀] in

particular, are disordered and may reﬂect a substantial

amorphous component in these solids. As with the other

Group 2 phosphomolybdates, there is more than the tri-

clinic phase associated with each of the barium containing

solids, and a cubic phase is not present.

The XRD patterns for the Group 2 phosphomolybdates are

quite different from their Group 1 analogues. There is no

evidence of a cubic phase with any of the divalent cation

derivatives, instead the triclinic phase associated with the

Group 1 compounds is maintained. XRD data for the

magnesium compounds analyzed in this work is given in

Fig. 2a. The location of the peaks correlates closely to

Table 1 Comparison of effective ionic radii and volumes for the Group 1 cations used for the synthesis of the phosphomolybdates in this work

3

Effective ionic volume (A )

˚

Effective ionic radius (A)

˚

Cation

Single cation

Double cation

Triple cation

Li^?

Na^?

K^?

Rb^?

Cs^?

0.76

1.02

1.38

1.52

1.67

1.84

4.45

11.0

14.7

19.5

3.68

8.89

22.0

29.4

39.0

5.52

13.3

33.0

44.1

58.5

The single, double and triple cation columns refer to the respective effective volumes occupied by one, two or three cations. The bold volumes

correspond to the phosphomolybdates exhibiting a resolvable body centered cubic structure. Effective ionic radii data obtained from previous

work by Shannon [35]

123

Comprehensive Study of Isobutane Selective Oxidation

1773

larger cation substitution diminishing the intensity of the

Table 2 Unit cell dimensions for those Group 1 catalysts possessing

the body centered cubic phase

ð110Þ peak, however this seems to have little impact on the

´

˚

ꢀ

ð011Þ peak. A similar phenomenon has been observed with

Compound

a (A)

other heteropoly compounds and the contribution of the

ð110Þ is thought to be related to the micropore volume of

the solids [8, 9, 13]. The larger cations also appear to

introduce disorder and possibly amorphousness. Table 3

shows the relationship between volume of the divalent

cations and absence of the ð110Þ peak. The effective ionic

radii data was obtained from previous work by Shannon

[35] and each of the values is for the cation in a six

coordination state. The bold volumes in Table 3 show the

volumes of those phosphomolybdates which do not

possess the ð110Þ plane. This corresponds to compounds

This work

Hu and Burns Langpape

et al. [6]

[34]

Na₃[PMo₁₂O₄₀

]

11.882 (2)

11.476 (4)

11.568 (10)

11.571 (7)

11.632 (7)

11.681 (11)

11.642 (6)

11.671 (20)

11.763 (11)

11.829 (4)

11.810 (3)

11.936 (1)

–

KH₂[PMo₁₂O₄₀

K₂H[PMo₁₂O₄₀

]

–

]

–

K₃[PMo₁₂O₄₀

]

11.5975 (2)

–

RbH₂[PMo₁₂O₄₀

Rb₂H[PMo₁₂O₄₀

]

–

]

–

Rb₃[PMo₁₂O₄₀

]

11.6687 (5)

–

CsH₂[PMo₁₂O₄₀

Cs₂H[PMo₁₂O₄₀

]

–

11.819 (8)

11.820 (7)

11.825 (5)

11.828 (6)

3

˚

]

–

with Group 2 cation volumes of 6.28 A (representing

Cs_2.5H_0.5[PMo₁₂O₄₀

]

–

Ca_1.5[PMo₁₂O₄₀]) or greater. The lowest alkaline cation

volume contribution that would result in absence of

Cs₃[PMo₁₂O₄₀

]

11.8412 (9)

3

˚

the ð110Þ plane is somewhere between 5 and 6 A

(Ba_0.5H₂[PMo₁₂o₄₀] and Ca_1.5[PMo₁₂O₄₀]). As in the case

of the Group 1 cations the volumes are not absolute, but

they approximate the required volume and may be used for

relative comparisons.

3.1.5 Discussion of Group 2 Phosphomolybdate

XRD Data

Clearly resolvable triclinic phases are present for the Group

2 phosphomolybdates, with characteristic peaks given by

The fully substituted magnesium, calcium, strontium and

barium salts (Mg_1.5[PMo₁₂O₄₀], Ca_1.5[PMo₁₂O₄₀], Sr_1.5

[PMo₁₂O₄₀] and Ba_1.5[PMo₁₂O₄₀]), have been prepared and

ꢀ

the ð110Þ and ð011Þ lattice planes. There is a trend with

Fig. 2 XRD patterns for the

magnesium (a), calcium (b),

strontium (c) and barium

(d) phosphomolybdates

analyzed in this work

1200

900

600

300

0

1200

a

b

Mg_1.5[PMo₁₂O₄₀

]

Ca_1.5[PMo₁₂O₄₀]

CaH[PMo₁₂O₄₀]

900

600

300

0

MgH[PMo₁₂O₄₀

(110)

-

(011)

Ca_0.5H₂[PMo₁₂O₄₀]

Mg_0.5H₂[PMo₁₂O₄₀

]

0

10

20

30

40

0

10

20

30

40

2 theta (degrees)

1200

900

600

300

0

1200

900

600

300

0

d

c

Sr_1.5[PMo₁₂O₄₀]

Ba_1.5[PMo₁₂O₄₀]

BaH[PMo₁₂O₄₀]

SrH[PMo₁₂O₄₀]

Ba_0.5H₂[PMo₁₂O₄₀]

Sr_0.5H₂[PMo₁₂O₄₀]

0

10

20

30

40

0

10

20

30

40

2 theta (degrees)

123

1774

S. Kendel, T. Brown

analyzed by McGarvey and Moffat [16]. The publication

reported that the XRD data of the divalent compounds was

‘‘largely featureless’’. These authors concluded that the

preparation methods they employed did not result in alkaline

earth phosphomolybdates, but rather a mixture of phospho-

molybdic acid and a divalent salt. This is likely to be due to

the use of hydroxides in the synthetic method, which raise the

preparatory solution pH; the Keggin structure is only stable

at pH values less than 1.5 [36] and is rapidly and completely

destroyed at a pH value of 4 [37]. The phosphomolybdates in

this work were not prepared using alkaline earth hydroxides

and therefore the triclinic XRD patterns are observed.

Silviani and Burns [12] have also investigated the dif-

fraction spectra of the alkaline earth phosphomolybdates.

In contrast to the results presented here, Silviani and Burns

[12] observed only a cubic structure without evidence of

any amorphous or other phases (including triclinic). The

synthesis of the compounds was analogous to the method

used in this thesis, so it is unlikely that a synthetic anomaly

is responsible for the different X-ray spectra. A signiﬁcant

difference lies in the way the samples were prepared prior

to analysis; Silviani and Burns [12] did not calcine the

solids in any way and tried to prevent samples from losing

water, whereas the compounds in this work were taken to

300 °C for 4 h. The different sample pre-treatments cause

vastly different hydration extents and as outlined previ-

ously [15]. This is associated with very different XRD

spectra and may explain the discrepancy between this work

and that published by Silviani and Burns [12].

water. However propene forms over some of the Group 1

salts (but not over Group 2 compounds) and methacrylic

acid is also seen over a single Group 2 phosphomolybdate:

BaH[PMo₁₂O₄₀]. It has been shown that lactone is a pre-

cursor to methacrylic acid, and the lactone is prevented

from rearranging into methacrylic acid due to the unique

low-pressure, steady-state, molecular ﬂow conditions used

in TPRS [38]. Interestingly, the cesium series of phos-

phomolybdates were the compounds that did not produce

any lactone or acetic acid, and only minimal CO₂, but were

very active toward methacrolein formation. Therefore

cesium addition has yields highly selective oxidation sub-

strates. Carbon dioxide and water are not products of

interest and it can be difﬁcult to quantify their quantities,

hence they have been excluded from further analysis.

3.2.1 Distributions

Two types of distributions were identiﬁed, designated as

Category 1 and Category 2:

Category 1: Distributions where formation increases

with increasing temperature, in a manner consistent with

an exponential product evolution and are only observed

whilst gas-phase isobutane is present.

Category 2: Proﬁles that consist of several rises, falls

and inﬂections (although sometimes a single peak is

observed), usually overlapping and only resolvable into

individual peaks by extensive modeling using Gaussian

curves; this type of distribution is observed with or

without gas-phase isobutane ﬂowing over the substrate.

3.2 Products from TPRS

Products observed from the reaction of isobutane with

phosphomolybdic acid using this technique were methac-

rolein, 3-methyl-2-oxetanone (lactone), acetic acid, carbon

dioxide and water; these selective oxidation products for

isobutane over phosphomolybdic acid have been previ-

ously reported by Kendell and coworkers [23, 24]. Products

observed over the Group 1 and 2 phosphomolybdates are

also methacrolein, lactone, acetic acid, carbon dioxide and

3.2.2 Resolution of Category 2 Peaks

The Category 2 proﬁles are complicated, but nonetheless

they are experimentally reproducible and form consis-

tently. It is assumed that the convoluted nature of the

Category 2 product formation is due to the concurrent

desorption of product from different distinct active sites

within the phosphomolybdate, with each site exhibiting

Table 3 Comparison of effective ionic radii and volumes for the Group 2 cations used for the synthesis of the phosphomolybdates in this work

3

Effective ionic volume (A )

˚

Effective ionic radius (A)

˚

Cation

0.5 cation

1 cation

1.5 cation

Mg^2?

Ca^2?

Sr^2?

0.72

1.00

1.18

1.35

0.78

2.09

3.44

5.15

1.56

4.19

6.88

10.3

2.35

6.28

10.3

15.5

Ba^2?

The 0.5, 1 and 1.5 cation columns refer to the respective effective volumes occupied by 0.5, 1 and 1.5 cations. The bold volumes correspond to

the phosphomolybdates that do not exhibit a resolvable ð110Þ triclinic lattice plane. Effective ionic radii data obtained from previous work by

Shannon [35]

123

Comprehensive Study of Isobutane Selective Oxidation

1775

50

40

30

20

10

0

unique kinetic parameters. Previous researchers have sim-

ulated temperature-programmed desorption using Gaussian

curves and used these to determine thermodynamic

parameters [39–42]. The mass spectral intensities in this

work, I_P, are a function of temperature, T. I_Pis simulated

by the following Gaussian expression [23, 43]:

Experimental

A Simulation

B Simulation

A+B Simulation

!

2

ꢁðT ꢁ pÞ

2w²

I_P¼ h exp

ð1Þ

The parameters h and p determine respective peak

height and position, while w alters the peak width. Usually,

multiple Gaussian curves are required to adequately

simulate the experimental data, with parameters for each

curve optimized via a non-linear least squares analysis of

their summation.

100

200

300

400

500

T (^oC)

Fig. 4 Lactone experimental data for isobutane oxidation over

Mg_1.5[PMo₁₂O₄₀]. The experimental data is simulated by applying

two separate distinct Gaussian distributions

Methacrolein forms via Category 1 and 2 processes, with

all other products forming as Category 2 distributions.

Figure 3 shows the smooth exponential rise associated with

Category 1 methacrolein formation over the KH₂[PMo₁₂O₄₀]

salt. Figure 4islactoneformationoverMg_1.5[PMo₁₂O₄₀];the

experimental data has been simulated by two Gaussian

distributions.

peaks, four lactone desorptions, three acetic acid desorp-

tions and no propene desorptions.

3.2.3 Detection of Methacrylic Acid

Tables 4 and 5 show the products formed over the

Group 1 and 2 phosphomolybdates respectively. The

abbreviations MA, LAC, AA, PE and MAA designate

methacrolein, lactone, acetic acid, propene and methacryic

acid respectively. The ‘‘MA Cat. 1’’ column indicates with

a Y if Category 1 methacrolein formation was observed

and a dash if not. The columns to the right of this detail

how many Category 2 desorption peaks are associated with

each species; e.g. for selective oxidation of isobutane over

LiH₂[PMo₁₂O₄₀], Category 1 methacrolein was observed

and there were four Category 2 methacrolein desorption

Methacrylic acid has been shown to form from the oxida-

tion of isobutane over heteropoly compounds such as

phosphomolybdates [7, 44–50]. Typically, methacrylic

acid is not formed for isobutane selective oxidation with

the low-pressure TPRS system employed in this study

[22–24]. This is because the molecular ﬂow conditions

Table 4 Products associated with the anaerobic oxidation of isobu-

tane over phosphomolybdates containing metals from Group 1 of the

periodic table

Catalyst

MA Cat. 1 MA Cat. 2 LAC AA PE

LiH₂[PMo₁₂O₄₀

Li₂H[PMo₁₂O₄₀

]

Y

–

4

7

1

4

5

4

7

6

–

5

2

5

–

2

4

6

1

4

5

–

6

4

3

4

3

–

3

4

–

6

–

5

4

–

5

3

–

6

–

60

50

40

30

Li₃[PMo₁₂O₄₀

]

–

NaH₂[PMo₁₂O₄₀

Na₂H[PMo₁₂O₄₀

]

–

]

–

Na₃[PMo₁₂O₄₀

]

–

KH₂[PMo₁₂O₄₀

K₂H[PMo₁₂O₄₀

]

Y

–

]

20

Methacrolein

K₃[PMo₁₂O₄₀

]

–

RbH₂[PMo₁₂O₄₀

Rb₂H[PMo₁₂O₄₀

]

–

10

0

]

Y

–

Rb₃[PMo₁₂O₄₀

]

CsH₂[PMo₁₂O₄₀

Cs₂H[PMo₁₂O₄₀

]

Y

100

200

300

T (^oC)

400

500

]

Cs_2.5H_0.5[PMo₁₂O₄₀

]

Fig. 3 Methacrolein production from isobutane anaerobic oxidation

over KH₂[PMo₁₂O₄₀

Cs₃[PMo₁₂O₄₀

]

123

1776

S. Kendel, T. Brown

also been used extensively in past investigations [24, 43].

A complete derivation of the theory surrounding the

application of Langmuir distributions to the coverage cor-

responding to low-pressure, molecular ﬂow conditions has

been detailed previously [24]; a good ﬁrst approximation to

the reactant fractional coverage for Category 1 (h₁) is given

by the following relationship:

Table 5 Products associated with the anaerobic oxidation of isobu-

tane over phosphomolybdates containing metals from Group 2 of the

periodic table

Catalyst

MA Cat. 1 MA Cat. 2 LAC AA MAA

Mg_0.5H₂[PMo₁₂O₄₀

]

Y

–

4

5

4

5

4

7

4

5

6

7

6

5

2

5

3

6

4

5

3

6

5

–

5

–

4

–

6

5

–

6

5

7

–

1

–

MgH[PMo₁₂O₄₀

Mg_1.5[PMo₁₂O₄₀

Ca_0.5H₂[PMo₁₂O₄₀

CaH[PMo₁₂O₄₀

Ca_1.5[PMo₁₂O₄₀

Sr_0.5H₂[PMo₁₂O₄₀

SrH[PMo₁₂O₄₀

Sr_1.5[PMo₁₂O₄₀

Ba_0.5H₂[PMo₁₂O₄₀

BaH[PMo₁₂O₄₀

Ba_1.5[PMo₁₂O₄₀

]

I_R=a_R

]

h₁¼

ð2Þ

1 þ I_R=a_Rþ I_P=a_P

]

Here, I_Rand I_Pdenote the reactant and product mass

spectral intensities. The spectral intensities are related to

ﬂow rate, in molecules s^-1, by a_Rand a_P. Figure 6 shows

]

Y

–

]

the coverage for the Category

1

distribution of

]

Y

–

methacrolein over Ba_0.5H₂[PMo₁₂O₄₀]. The coverage

changes less than 5% during the course of an experiment.

]

–

3.3.2 Category 2 Coverage

minimize molecule collisions and thus prevent secondary

reactions. Previous work by Nguyen et al. has shown that

lactone is the precursor to methacrylic acid formation, with

the rearrangement catalyzed by water and acid [38].

Suprisingly, methacrylic acid was detected over the

BaH[PMo₁₂O₄₀] compound. Observation of this species

coincided with rise and fall of a lactone peak, with the

lactone and methacrylic acid forming in parallel, as shown

in Fig. 5, and indicates that some of the lactone is being

converted to methacrylic acid. There are actually six lac-

tone desorption peaks associated with the lactone forma-

tion over BaH[PMo₁₂O₄₀], with only the second site being

associated with the rearrangement. It is not clear why a

single barium substitution facilitates methacrylic acid for-

mation, or why the acid forms in conjunction with the

second lactone desorption site only. However, since it has

been shown by Nguyen et al. [38] that water and acid

catalyze the rearrangement of the lactone into the acid, it

may be inferred that the particular site responsible for this

rearrangement has water and acid in close proximity.

The Category 2 distributions are a summation of bell-

shaped desorptions, as resolved by Gaussian curves. Unlike

the Category 1 methacrolein formation, these products rise

and concomitantly fall during TPRS. Aside from the

intrinsic Arrhenius parameters and temperature, the rate of

desorption is determined by the coverage of the desorbing

species. At the commencement of TPRS, desorption

products are not detected and it is assumed that the frac-

tional coverage at each desorption site is 100%. Likewise,

at the completion of TPRS the product formation is neg-

ligible and it is supposed that all species have desorbed and

the coverage is zero. The Langmuir adsorption isotherm

fails to adequately describe the coverage of Category 2

distributions; however the fractional coverage may be

40

LAC

30

3.3 Coverage Considerations

20

The vastly different ways in which Category 1 and 2

products form is due to the way in which isobutane inter-

acts with the phosphomolybdate substrate. Accordingly,

these two distributions require signiﬁcantly dissimilar

coverage models to explain product formation.

MAA

10

0

100

150

200

250

300

3.3.1 Category 1 Coverage

T (^oC)

The exponential rise associated with the Category 1 dis-

tribution is modeled using a Langmuir distribution. This

model accurately simulates the experimental data and has

Fig. 5 Gaussian simulations for methacrylic acid formation and the

second lactone peak, from isobutane anaerobic oxidation with

BaH[PMo₁₂O₄₀

]

123

Comprehensive Study of Isobutane Selective Oxidation

1777

determined by considering the desorption of the products.

Integration of the Gaussian curves yields a fractional

desorption function, u, but antiderivatives for these func-

tions do not exist, so instead the fractional desorption

function is determined by the following summation:

Arrhenius-type expression and has been derived previously

[24]:

ꢀ

ꢁ

E_app

RT

n

ln I_P¼ ꢁ

þ ðm þ nÞ ln h þ ln ba_PA_appNðactÞ

ð5Þ

This relationship is applicable to the formation of

Category 1 products and Category 2 desorption species,

whereby the respective h₁or h₂coverage terms are used for

h in Eq. 4. Here, E_appand A_appare the respective apparent

activation energy and pre-exponential factor, for Category

1 product formation or Category 2 desorptions. The

reaction order is given by n, and the parameter m is

introduced to correct for any anomalies due to errors in the

coverage model or deactivation of the substrate. b is the

heating rate and a_Prelates the mass spectral intensity to

the ﬂux of product molecules. N(act) is the number of

active sites available for reaction.

X

1

u ¼

I_P

ð3Þ

N

Here N is the total sum of the mass spectral

measurements (I_P) and is used to normalize the

summation. The fractional coverage of the Category 2

products is then given by:

X

1

h₂¼ 1 ꢁ u_P¼ 1 ꢁ

I_P

ð4Þ

N

Figure 7 shows the product proﬁles (bottom peaks) and

coverage functions (top sigmoid curves) for the two lactone

distributions observed over Mg_1.5[PMo₁₂O₄₀]. The

coverage functions represent isobutane coverage at each

active site for lactone formation. It is important to

understand that the coverage terms here represent the

coverage of isobutane for each individual active site, rather

than considering the isobutane coverage as a whole. This is

essential to accurately interpreting the kinetics of each

individual product. The coverage changes from unity to

essentially zero throughout the TPRS experiment for each

Category 2 distribution.

A multiple linear regression analysis is performed with

ln I_Pas the Y-input, and 1/RT and ln h as the X-inputs; this

yields slopes of -E_appand (m ? n), and an intercept of

ln(ba_PA_appN(act)ⁿ). In practice it can be difﬁcult to ascer-

tain the exact number of active sites available for reaction,

particularly where multiple sites are operating indepen-

dently of each other, so the parameters that constitute the

intercept are collectively labeled as A. However, the

phosphomolybdates are all derived from phosphomolybdic

acid, and hence would have comparable numbers of active

sites. Aside from N(act), all other parameters for the

intercept are equivalent. Therefore A may be used to make

a qualitative relative comparison of the pre-exponential

values of the different substrates, rather than in a strictly

quantitative manner.

3.4 Kinetic Investigation

A method of simulating of experimental data using low-

pressure TPRS technique has been developed [24, 26, 51].

Prior to simulation all data is smoothed using a 25 point

quadratic algorithm [52]. The following equation is an

3.4.1 Activity Parameters

1.01

1

Arrhenius parameters were calculated for Category 1 and

Category 2 product formations. Methacrolein is the only

product to form via a Category 1 proﬁle, whilst Category 2

products include methacrolein, lactone, acetic acid, pro-

pene (observed with Group 1 salts) and methacrylic acid

(occurring over BaH[PMo₁₂O₄₀] exclusively). The addition

of counter cations to the phosphomolybdate structure

eliminates Category 1 methacrolein deactivation, hence

when conducting a regression analysis on Category 1

methacrolein formation data, m ? n in the kinetic model

(Eq. 5) was set to unity. Table 6 displays the kinetic

parameters determined for Category 1 methacrolein over

phosphomolybdates of Groups 1 and 2 respectively.

Arrhenius data for the Category 2 distributions is expan-

sive, so rather than list all activation parameters, a range of

E_avalues for each product is given in Table 7. Unlike the

Category 1 distributions, m ? n was not unity, rather a

value of about 1.3 was universally observed. This likely

0.99

0.98

0.97

0.96

0.95

100

200

300

T (^oC)

400

500

Fig. 6 The fractional coverage of isobutane during reaction with the

Ba_0.5H₂[PMo₁₂O₄₀] compound. This ﬁgure shows coverage proceed-

ing from unity to approximately 95% during the course of a

temperature-programmed experiment

123

1778

S. Kendel, T. Brown

1.2

0.8

0.4

0

k_BT_iso

hc

x ¼

ð6Þ

The parameters k_B, h and c are Boltzmann, Planck and

speed of light constants respectively. Table 8 displays the

isokinetic temperature and transition state frequency

associated with the cesium, magnesium and calcium

compounds. The isokinetic relationship is generally

restricted to phosphomolybdates consisting of the same

45

30

15

0

cations.

A

comparison of Arrhenius plots for

phosphomolybdates with differing cations usually does

not yield a common point of intersection (isokinetic

temperature). For this reason isokinetic points for the

cesium, magnesium and calcium phosphomolybdates were

individually established. Nevertheless it is interesting to

observe that the cesium and magnesium compounds exhibit

nearly identical isokinetic temperatures and corresponding

transition state frequencies. This connotes that transition

states for methacrolein formation over these phospho-

molybdates are comparable. Vibrational frequencies for

methacrolein were determined using Gaussian 03 software,

with calculations performed at the B3LYP/6-31G level.

The computational IR frequencies were compared with the

actual IR for methacrolein and were in good agreement.

The closest frequencies to the values found in Table 8 were

*310 and 740 cm^-1. These were well outside a 10%

error margin. This may indicate that these transition state

geometries differ substantially from fully formed methac-

rolein.

200

300

400

500

T (^oC)

Fig. 7 Fractional coverage of isobutane on Mg_1.5[PMo₁₂O₄₀] (top)

and corresponding Gaussian product simulations for lactone

formation

indicates that the Category 2 products form with an overall

reaction order of 1.3. Several samples were resynthesized

and reanalyzed using TPRS and very little deviation in

kinetic results was observed.

There is great variation among the activation energies

associated with the Category 1 and 2 distributions. For

Category 1 methacrolein production, LiH₂[PMo₁₂O₄₀]

exhibits the lowest activation barrier whilst the fully

substituted cesium salt, Cs₃[PMo₁₂O₄₀], has the highest.

The Category 2 products show larger variability: the lowest

activation barrier is 34.3 0.4 kJ mol^-1(for the third

propene proﬁle over Rb₃[PMo₁₂O₄₀]) whilst the highest is

726 172 kJ mol^-1(occurring with the fourth lactone

peak over KH₂[PMo₁₂O₄₀]).

There was no isokinetic relationship observed with any

of the Category 2 product formations, e.g. lactone forming

over RbH₂[PMo₁₂O₄₀] cannot be compared to that pro-

duced over Rb₂H[PMo₁₂O₄₀] or Rb₃[PMo₁₂O₄₀]. This

intimates that each Category 2 product forms with unique

transition states, even though they belong to the same

phosphomolybdate family.

3.4.2 Isokinetic Relationship

The kinetic parameters presented in Table 6 show that an

increase in E_appcorresponds to an increase in log₁₀A for

the cesium, magnesium and calcium series. This phenom-

enon is known as the ‘‘compensation effect’’ or ‘‘isokinetic

relationship’’ or and is observed with many reactions

[53–65]. Associated with this actuality is a temperature at

which the rates of product formation are equivalent, and

this is commonly referred to as the ‘‘isokinetic tempera-

ture’’ but is also referred to as an ‘‘isocatalytic tempera-

ture’’ [57, 58, 62, 63, 65]. Figure 8 shows the Arrhenius

plots for Category 1 methacrolein formation over the var-

ious cesium salts and the isokinetic temperature. The

isokinetic temperature is related to the transition state

frequency, x, and has been derived from stochastic [60],

transition-state theory [62, 63, 66] and dynamic [58]

models:

3.5 Reaction Mechanisms

Category 1 is associated with exponential-like distributions

and occurs only with methacrolein formation whereas

Category 2 proﬁles are observed with methacrolein, lac-

tone, acetic acid, propene and methacrylic acid (carbon

dioxide and water were excluded from modeling). There-

fore Category 1 methacrolein formation is likely to occur

via a different mechanism from the Category 2 products.

None of the Category 2 methacrolein, lactone, acetic acid

and propene distributions mirror one another, and there is

no other clear relationship between the two, such as

number of peaks and temperature positions. Hence it is

likely that each has a separate reaction pathway and may

involve unique active sites. The methacrylic acid formation

displayed by the BaH[PMo₁₂O₄₀] compound matches one

123

Comprehensive Study of Isobutane Selective Oxidation

1779

existing between methacrolein and lactone, it may also be

concluded that methacrolein does not act as an intermediate

for methacrylic acid production. Therefore methacrylic

acid is proposed to form via an initial one-step oxidation of

isobutane into lactone and a subsequent rearrangement of

the lactone.

Table 6 Arrhenius parameters for Category 1 methacrolein forma-

tion via isobutane anaerobic oxidation with various Group 1 metal

phosphomolybdates

Catalyst

E_app(kJ mol^-1

)

log₁₀

A

Modeling T

Range (°C)

LiH₂[PMo₁₂O₄₀

]

34.7 (1.3)

92 (2)

4.57 (0.13) 389–478

8.0 (0.2) 428–486

6.71 (0.05) 355–437

Propene formation does not correspond to the evolution

proﬁles for carbon dioxide and no methane was observed

(therefore propene formation was not due to cracking of

isobutane). Therefore propene formation is not accompa-

nied by cracking or combustion of isobutane, instead all

carbon atoms from isobutane are used in the production of

the oleﬁn. This is supported by previous work which has

shown that heteropoly compounds are able to function as

dealkylating, alkylating or skeletal isomerisation catalysts

[1, 2, 78]. The proposed reaction mechanisms for all

observed gas-phase products are:

KH₂[PMo₁₂O₄₀

Rb₂H[PMo₁₂O₄₀

]

64.0 (1.6)

93 (5)

CsH₂[PMo₁₂O₄₀

Cs₂H[PMo₁₂O₄₀

]

9 (1)

290–372

347–417

]

72 (1)

7.5 (0.1)

Cs_2.5H_0.5[PMo₁₂O₄₀

Cs₃[PMo₁₂O₄₀

Mg_0.5H₂[PMo₁₂O₄₀

MgH[PMo₁₂O₄₀

Mg_1.5[PMo₁₂O₄₀

Ca_0.5H₂[PMo₁₂O₄₀

CaH[PMo₁₂O₄₀

Ca_1.5[PMo₁₂O₄₀

SrH[PMo₁₂O₄₀

Ba_0.5H₂[PMo₁₂O₄₀

]

106.1 (1.6)

119 (4)

9.96 (0.15) 342–444

10.9 (0.8) 370–434

6.62 (0.06) 355–468

6.3 (0.1) 412–497

]

70.9 (0.7)

67 (2)

]

88.6 (1.1)

84.5 (1.1)

88.7 (1.1)

72 (2)

7.89 (0.08) 365–466

7.90 (0.08) 402–475

8.30 (0.08) 367–453

]

Oxidation and oxidative dehydrogenation of isobutane

to form methacrolein

]

6.7 (0.1)

440–476

]

50.3 (0.7)

94.6 (0.4)

5.96 (0.05) 422–478

8.57 (0.03) 326–479

]

3[O]

+

2H₂O

ðR1Þ

O

of the lactone proﬁles, hence it is proposed that lactone is

an intermediate for methacrylic acid.

Previous studies have proposed that isobutene acts as an

intermediate for methacrolein and methacrylic acid pro-

duction [46, 50, 67–69], although other authors dispute this

claim [70–72]. Similarly, some studies indicate that

methacrolein is an intermediate in the formation of meth-

acrylic acid [45, 49, 69], while others give evidence

negating this ﬁnding [70, 72, 73]. Previous work has indeed

shown methacrolein and methacrylic acid production from

respective isobutene and methacrolein oxidations over

heteropoly compounds [20, 71, 74–77]. However, the dis-

cussion of intermediate formation rests on whether either

isobutane forms methacrolein and methacrylic acid in one-

step oxidations, or respective isobutene- and methacrolein-

like intermediary species are involved in a multi-step

pathway. The low-pressure, steady-state equipment used

for product analysis is very sensitive and the molecular

ﬂow conditions minimize secondary collisions which is

conducive to isolating intermediates. Nevertheless, isobu-

tene was not detected over any of the phosphomolybdates,

hence there is little support for isobutene acting as an

intermediate in methacrolein formation from isobutane

oxidation. Hence a conclusion from this work is that the

oxidation of isobutane into methacrolein occurs via a single

step (contemporaneous dehydrogenation and oxygen

addition).

Lactone formation from the oxidation and oxidative

dehydrogenation of isobutane

O

4[O]

+

2H₂O

O

ðR2Þ

Rearrangement of lactone into methacrylic acid

O

OH

ðR3Þ

Formation of acetic acid

O

5[O]

2

+

H₂O

OH

Considering the evidence of lactone acting as a pre-

cursor to methacrylic acid, and no clear relationship

ðR4Þ

123

1780

S. Kendel, T. Brown

Table 7 Activation energy ranges for Category 2 formations

Group 1

MA E_a(kJ mol^-1

)

LAC E_a(kJ mol^-1

)

AA E_a(kJ mol^-1

)

PE E_a(kJ mol^-1

)

MAA E_a(kJ mol^-1

)

LiH₂[PMo₁₂O₄₀

Li₂H[PMo₁₂O₄₀

]

61–78

106–242

115

122–331

80–317

276

102–123

–

72–363

–

Li₃[PMo₁₂O₄₀

]

–

NaH₂[PMo₁₂O₄₀

Na₂H[PMo₁₂O₄₀

]

54–123

64–141

55–126

58–278

54–293

85–214

70–237

–

46–200

70–242

–

]

–

56–153

Na₃[PMo₁₂O₄₀

]

–

107–123

KH₂[PMo₁₂O₄₀

K₂H[PMo₁₂O₄₀

]

128–726

78–234

84–257

57–317

156–218

103–281

–

]

89–144

–

K₃[PMo₁₂O₄₀

]

–

RbH₂[PMo₁₂O₄₀

Rb₂H[PMo₁₂O₄₀

]

119–306

–

]

–

Rb₃[PMo₁₂O₄₀

]

91–146

73–140

72–202

–

34–268

CsH₂[PMo₁₂O₄₀

Cs₂H[PMo₁₂O₄₀

]

–

]

–

Cs_2.5H_0.5[PMo₁₂O₄₀

]

–

Cs₃[PMo₁₂O₄₀

]

70–96

–

Group 2

Mg_0.5H₂[PMo₁₂O₄₀

MgH[PMo₁₂O₄₀

Mg_1.5[PMo₁₂O₄₀

Ca_0.5H₂[PMo₁₂O₄₀

CaH[PMo₁₂O₄₀

Ca_1.5[PMo₁₂O₄₀

Sr_0.5H₂[PMo₁₂O₄₀

SrH[PMo₁₂O₄₀

Sr_1.5[PMo₁₂O₄₀

Ba_0.5H₂[PMo₁₂O₄₀

BaH[PMo₁₂O₄₀

]

45–122

58–146

53–114

45 –105

50–100

41–126

82–174

65–194

39–121

81–181

43–180

57–467

58–389

52–274

104 –143

70–279

58–116

73–165

69–340

90–161

88–312

68–76

–

]

61–202

–

]

–

]

70–181

–

]

–

]

121–210

106–225

–

]

–

]

–

]

–

]

105–462

83–436

57–253

–

]

42–332

68–366

167

–

Ba_1.5[PMo₁₂O₄₀

]

8

Table 8 Isokinetic parameters obtained from the cesium, calcium

and magnesium phosphomolybdates series

CsH2

Cs2H

Cation

T_iso(K)

x (cm^-1

)

Cs2.5H0.5

Cs3

Cs^?

Mg^2?

Ca^2?

450 (5)

455 (5)

270 (5)

503 (4)

506 (4)

378 (4)

6

4

2

T

_iso= 450 5^oC

Propene production

3[O]

3

4

+

3H₂O

0.14

0.15

0.16

0.17

0.18

0.19

1000/RT (mol kJ^-1)

ðR5Þ

Complete oxidation of isobutane into carbon dioxide

Fig. 8 Arrhenius plots of the four cesium phosphomolybdates.

Shown in the ﬁgure is the isokinetic temperature; at this temperature

the rate of Category 1 methacrolein formation is equivalent

and water

123

Comprehensive Study of Isobutane Selective Oxidation

1781

migration of redox carriers (electrons and protons)

throughout the catalyst bulk. Because reaction molecules

do not migrate through the solid, Bulk-type (II) is not

related to pseudoliquid behavior. Nevertheless both Bulk-

types occur in a three dimensional reaction ﬁeld [91],

therefore surface area of the catalyst does not impact on

reaction rates [17].

13[O]

4CO₂

+

5H₂O

ðR6Þ

Category 1 methacrolein formation occurs only with

isobutane in the feed stream and the distributions are

empirically consistent with a Langmuir adsorption iso-

therm model. This suggests that reactants are adsorbing as

monolayers on the surface rather than penetrating the bulk

[92] and hence Category 1 methacrolein forms via reaction

on the surface. Therefore the Category 1 methacrolein

formation occurs either as a pure surface-type reaction with

no involvement from the bulk of the phosphomolybdates,

or a Bulk-type (II) mechanism operates whereby isobutane

adsorption and methacrolein formation are restricted to the

surface but electron and proton migration through the bulk

facilitates the reaction. Previous work on similar reactions

for the oxidative dehydrogenation of isobutyraldehyde and

isobutyric acid to yield methacrolein and methacrylic acid

respectively, have suggested that products are formed via a

Bulk-type (II) mechanism [34, 69, 93]. Surface area has

been shown to increase with respect to cesium content in

phosphomolybdic acid derivatives [6, 34, 69], although this

is not reﬂected in the Arrhenius parameters given in

Table 6. It is therefore inferred that a simple surface-type

reaction is not associated with Category 1 methacrolein

formation over the phosphomolybdates and therefore a

Bulk-type (II) process predominates.

All reactions occur concurrently, with the exception of

(R3) which is thought to occur consecutively as a rear-

rangement from lactone. In these reaction steps [O] repre-

sents oxygen atoms contained in the phosphomolybdate

anion and are known as lattice or framework oxygens. For

example, complete oxidation of isobutane requires 13[O].

These reactions occur through a Mars-van Krevelen

mechanism in which lattice oxygens are used for oxidation

and are then replaced by molecular oxygen if present in

the reactant feed stream [25, 45, 70, 72, 79–85]. Oxygen

has not been included in the reactant feed stream for this

work as it complicates both the molecular ﬂow conditions

and resolution of peak intensities, therefore the lattice

oxygens are not replenished. This should result in a

reduction of the catalyst over time, yet the low reactant

feed stream ﬂux of 10¹⁵molecules per second (of which

half is isobutane and half is argon) results in a very small

proportion of oxygen atoms being removed from the

structure during experiments and hence this effect is

insigniﬁcant. Additionally, contact times in the Knudsen

cell reactor are relatively short. Each of the proposed

reaction steps involve water evolution, which is observed

for isobutane conversion over phosphomolybdic acid and

its derivatives.

Category 2 methacrolein, lactone, acetone, propene and

methacrylic acid form with or without gas-phase isobutane

and production occurs in bell-shaped distributions typically

observed with desorption and reactant coverage proceeds

past monolayer extent. Therefore Category 2 product for-

mation is consistent with isobutane penetrating deep inside

the bulk of the phosphomolybdates, undergoing reaction

and creating products which later desorb from the surface.

These considerations suggest the establishment of a

pseudoliquid phase and Bulk-type (I) processes for the

Category 2 reaction mechanisms. The proﬁles that are

associated with the Category 2 distributions may be rep-

resentative of successive reductions of the phosphomo-

lybdate anion. For example, the lowest temperature peak

corresponds to the reduction of a phosphomolybdate anion

or region of anions. Successive product formations occur

from progressively more reduced phosphomolybdates

anions. In this way each bell-shaped distribution coincides

with reaction of isobutane with phosphomolybdate anions

of a particular oxidation state and environment. The for-

mation of different products via parallel reactions at

neighboring active sites would also affect the reduction of

3.6 Factors Inﬂuencing Activity

3.6.1 Pseudoliquid Phase, Surface and Bulk Catalysis

Heteropoly compounds have a unique ability to absorb

molecules into their bulk [86]. This phenomenon is asso-

ciated with rapid migration of reactant and products species

through the bulk in a manner which resembles liquid dif-

fusion, and hence the phase this creates is termed

‘‘pseudoliquid’’. Another characteristic of heteropoly

compounds is their ability to undergo reactions inside the

catalyst bulk as well as on the surface [17, 87–90]. The

bulk processes are categorised into two distinct variants,

labeled Bulk-types (I) and (II). Bulk-type (I) is concerned

with reactants migrating deep within the solid to undergo

reactions, with the subsequent products migrating to the

surface and desorbing. This type of reaction is due to

pseudoliquid behavior [69]. Bulk-type (II) processes con-

sist of reactants undergoing reaction on the surface of the

catalyst where the reaction is controlled by the rapid

123

1782

S. Kendel, T. Brown

the heteropolyanion, either locally or as a whole. Hence the

creation of a particular product may directly impact on

another in a complicated manner. The cesium derivatives

seem to be unique in that the only product observed is

methacrolein, though this occurs via both Category 1 and 2

processes. Perhaps cesium addition prevents isobutane

migration deep into the bulk of the solid whereby higher

oxidation products are unable to form. Work conducted by

Okuhara et al. supports this conclusion [94].

capabilities of the solids. Furthermore, the large activation

barriers experienced by some of the higher temperature

proﬁles from the Category 2 distributions may be reﬂective

of creating products from already highly reduced active

sites.

4 Summary and Conclusions

Phosphomolybdates were synthesized from cationic

exchange of phosphomolybdic acid with cations of Groups

1 and 2 of the periodic table. The Group 1 cations were

Li^?, Na^?, K^?, Rb^?and Cs^?and the Group 2 cations were

Mg^2?, Ca^2?, Sr^2?and Ba^2?. Three compounds of differing

cationic ratios were synthesized from each cation, except

for the cesium salts, of which four were made.

3.6.2 Investigation into Correlations

Previous work has shown that catalyst activity varies

markedly depending upon counter cation selection and

there is no clear relationship between the amount of

cation and activity [87]. Several attempts have been made

to link the activity of a catalyst with the physical and

chemical properties of the associated cations and these

include: ionic radius [35], ionic potential [34], electro-

negativity [95–101], enthalpy of oxide formation [99, 102,

103], electronic polarisability [95, 104, 105] and optical

basicity [106–113]. All of these parameters are listed in

Table 9. With the exception of D_fH^hfor cesium oxide and

magnesium oxide, the parameters progressively increase

or decrease down each of Groups 1 and 2. Provided the

activity and selectivity properties of the solids increased

or decreased down a particular Group, a relationship

might be established with any of the values. The Category

1 and 2 distributions presented in this thesis, and their

corresponding kinetic parameters, show no such simple

trend or obvious volcano plot. For example, the reasons

why cesium, magnesium and calcium salts display Cate-

gory 1 methacrolein formation or why some phospho-

molybdates form acetic acid, cannot be readily concluded

from the values in Table 9 (whether viewed in isolation

or in various multiplicative or divisionary combinations).

It may be that one or more of these parameters impacts

on the selectivity and activity of the phosphomolybdates,

though the contribution would be a factor only, and the

identiﬁcation of other properties is required to elucidate a

meaningful association.

XRD data from analysis of pure phosphomolybdic acid

showed the presence of a triclinic phase exclusively. Group

1 phosphomolybdates exhibit a range of structural phases.

At low cationic volumes the triclinic structure is present,

while at high volumes the body centered cubic phase pre-

dominates. The body centered cubic phase forms once the

3

˚

cationic volume exceeds about 9–11 A . Group 2 com-

pounds possess a triclinic phase, however an increase in the

cationic volume is associated with a decreasing contribu-

tion of the ð110Þ plane to the structure and an introduction

of some amorphous character. This occurs once cationic

3

˚

volume is greater than about 5–6 A .

Two distinct types of reactions were identiﬁed and

classiﬁed as either Category 1 or Category 2. Product

formation for Category 1 distributions increases with

increasing temperature, in a manner consistent with an

exponential distribution and only occurs whilst gas-phase

isobutane is present. Category 2 proﬁles consist of several

peaks (although sometimes a single peak is observed),

usually overlapping and only resolvable into individual

peaks by extensive modeling with Gaussian curves; this

type of distribution is observed with or without gas-phase

isobutane.

Products observed from the oxidation of isobutane

were methacrolein, lactone (3-methyl-2-oxetanone), acetic

acid, propene, methacrylic acid, carbon dioxide and water.

The partial and total substitution of protons with Group 1

and 2 cations resulted in a large reduction of complete

oxidation products, i.e. carbon dioxide and water; these

are difﬁcult to quantify and are of little interest, so they

were excluded from the modeling procedure. Methacro-

lein formation occurs via both Category 1 and Category 2

processes, whilst lactone, acetic acid, propene, and

methacrylic acid are exclusively Category 2 reactions.

Propene was only observed with the Group 1 compounds

Na₂H[PMo₁₂O₄₀], Na₃[PMo₁₂O₄₀] and Rb₃[PMo₁₂O₄₀],

whilst methacrylic acid production was restricted to a

Selective oxidation of isobutane conducted by Paul et al.

[44] over a similar catalyst to those used in this work, (Cs^?/

NH₄^?/H^?)₄[PMo₁₁VO₄₀], determined the reduction of the

structure exhibited an activation energy of 90.4 kJ mol^-1

.

This is comparable to the activation energies measured for

Category 1 methacrolein production over the cesium

phosphomolybdates (Table 6). This further supports the

hypothesis that Category 1 methacrolein forms via a Bulk-

type (II) mechanism. In light of this, and considering that

the oxidation of isobutane necessitates reduction of the

phosphomolybdates structure, it may be that all rates of all

product formation are determined by the reduction

123

Comprehensive Study of Isobutane Selective Oxidation

1783

Table 9 Values of ionic radius

(r_i), ionic potential (p_i),

electronegativity (v), enthalpy

of oxide formation (D_fH^h),

electronic polarisability (a) and

optical basicity (K)

˚

r_i(A) [35]

Cation

p_i(charge/r_i)*

v [95]

D_fH^h(kJ mol^-1

[102]

)

a (10^-24cm³)

[95]

K

Li^?

Na^?

K^?

Rb^?

Cs^?

Mg^2?

Ca^2?

Sr^2?

Ba^2?

0.76

1.02

1.38

1.52

1.67

0.72

1.00

1.18

1.35

1.84

4.45

11.0

14.7

19.5

2.78

2.00

1.69

1.48

0.98

0.93

0.82

0.79

1.31

1.00

0.95

0.89

-598

-414

-363

-339

-346

-602

-635

-592

-554

0.029

0.179

0.83

1.40

2.42

0.094

0.47

0.86

1.55

0.81

1.10

1.30

1.45

1.55

0.61

1.00

1.05

1.35

* Here ionic potential is deﬁned

as the ratio of cation charge to

ionic radius. All radii refer to

cation in six coordination state

single catalyst, BaH[PMo₁₂O₄₀]. The isobutane oxidation

products form in various quantities depending on cation

selection. Methacrolein was the only product obsered over

the cesium phosphomolybdates, showing that cesium

addition yields highly selective substrates.

and calcium phosphomolybdates the respective isokinetic

temperatures are 450 5, 455 5 and 270 5 °C and

the transition state frequencies are 503 4, 506 4,

378 4 cm^-1. The transition state frequencies do not

correspond to methacrolein vibrations, as calculated using

Gaussian 03 software, hence the transitions state geome-

tries are likely to be signiﬁcantly different than the fully

formed methacrolein. However, the similar methacrolein

transition state frequencies for the cesium and magnesium

compounds indicate that methacrolein forms in a compa-

rable manner over these phosphomolybdates.

Methacrolein production occurs without evidence of

isobutene-like intermediary species and most likely forms

via a one-step oxidation of isobutane. Likewise, lactone,

acetic acid, propene and carbon dioxide occur in parallel

reactions. However methacrylic acid, observed over

BaH[PMo₁₂O₄₀], mirrors a lactone formation proﬁle over

the same catalyst. This intimates that lactone is a pre-

cursor to methacrylic acid formation. Nguyen et al. have

shown that the lactone rearranges into methacrylic acid

via catalysis by water and acid [38]. It is proposed that

lactone rearranges to methacrylic acid under normal

reaction conditions of high pressures but is instead iso-

lated in this work due to the molecular ﬂow regime.

Therefore all reactions are thought to occur in parallel,

with the exception of methacrylic acid, which is created

from lactone rearrangement.

Several theories have been proposed by previous

researchers to account for activity: ionic radius, ionic

potential, electronegativity, enthalpy of oxide formation,

electronic polarisability, and optical basicity. However

none of these adequately describes the activity observed

and no clear linear or volcano relationships could be

ascertained between the Arrhenius parameters and prop-

erties of the cations. Category 1 methacrolein formation is

proposed to form via a Bulk-type (II) mechanism, where

the reaction occurs on the surface, but this is accompanied

by rapid migration of electrons and protons deep into the

bulk of the solid. Category 2 product formations of meth-

acrolein, lactone, acetic acid and propene are Bulk-type

(I) reactions, which also involve charge transfer; these

occur when the actual reactant penetrates deep into

the bulk of the solid to form products, which migrate to the

surface and desorb. Therefore, electronic properties of the

substrates likely determine reaction kinetics, rather than

geometric properties. Indeed previously work by Paul et al.

indicates that reduction of the substrate may be rate

determining [44].

All phosphomolybdates showed excellent stability and

consistent kinetic results, except for the parent acid which

experienced cumulative structural degradation over suc-

cessive experiments. Arrhenius parameters have been cal-

culated for the Category 1 and 2 distributions. The lowest

calculated activation for Category 1 methacrolein forma-

tion is 34.7 1.3 kJ mol^-1over the LiH₂[PMo₁₂O₄₀]

compound, while the highest recorded is 149 4 kJ

mol^-1for the fourth experiment over H₃[PMo₁₂O₄₀]. The

Category 2 kinetic parameters were extensive and ranged

from 34.3 0.4 kJ mol^-1(for the third propene proﬁle

over Rb₃[PMo₁₂O₄₀]) to 726 172 kJ mol^-1(occurring

with the fourth lactone peak over KH₂[PMo₁₂O₄₀]).

Salts of cesium, magnesium and calcium exhibit a

phenomenon known as the ‘‘isokinetic point’’. This refers

to the existence of a temperature at which all compounds

containing a particular cation have the same rate of Cate-

gory 1 methacrolein formation. For cesium, magnesium

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Article Doi

Comprehensive study of isobutane selective oxidation over group i and II phosphomolybdates: Structural and kinetic factors

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