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temperature, and due to its requiring less space, the Constraint Index for a given
zeolitic material decreases with increasing temperature. However, Macedonia
and Maginn [81] recently used Monte Carlo integration methods employing
a classical molecular mechanics force field to predict values for the Constraint
Indices of 12 different zeolites. These authors concluded that it is not necessary
to invoke such a change in mechanism to explain decreasing Constraint Indices
with increasing temperature. Their calculations indicated that the impact of
confinement on the bimolecular transition state decreases with increasing tem-
perature, effecting a decrease of the Constraint Index. This was said to be caused
by a competition between energetic confinement effects that dominate at lower
temperatures and entropic effects that become dominant at high temperature.
As to the nature of the shape selectivity effects, Haag et al. [82] demon-
strated in a most impressive study with H-ZSM-5 samples of equal concen-
tration of acidic sites but different crystal sizes (0.05 to 2.7 µm) that nei-
ther the measurable rate of cracking of n-hexane nor that of the bulkier
3-methylpentane depend on the length of the intracrystalline diffusion paths.
From this finding, the selectivity effects encountered in the competitive
cracking of n-hexane and 3-methylpentane have to be interpreted in terms
of intrinsic chemical effects (i.e., restricted transition state shape selectiv-
ity) rather than by mass transport effects. Haag et al. [82] suggested that the
rate-controlling step in the chain-type mechanism of acid-catalyzed alkane
cracking via carbocations is the chain-propagating hydride transfer between
a cracked alkylcarbenium ion and a feed molecule, requiring significantly
more space for the transition state if the feed alkane is branched, the net effect
being a significant inhibition of cracking of 3-methylpentane. The simula-
tions performed by Macedonia and Maginn [81] indicated, however, that for
zeolites, the pores of which are too small to accommodate the bimolecular
transition state, such as ZSM-23 (MTT) and ferrierite (FER), the monomolec-
ular mechanism dominates, with the measured Constraint Index attributed
to reactant shape selectivity. Only for zeolites, the pores of which are large
enough for the bimolecular transition state but small enough for confinement
effects, the bimolecular reaction was predominant, and the selectivity was
based on restricted transition state shape selectivity.
132 Y. Traa et al.
Recently, Baeck et al. [32] demonstrated that the Constraint Index is useful
for probing subtle changes of the pore size as effected by CVD. The Con-
straint Index determined on zeolite Mg-ZSM-22 (TON) increased from about
9.9 to about 13.3 after 3 h of deposition of tetraethyl orthosilicate, reflecting
the decrease of the pore opening by CVD.
In conclusion, with the Constraint Index, the idea of probing the pore
width by catalytic test reactions was introduced into zeolite science. It no
doubt fostered the search for alternative and improved catalytic test reactions.
In spite of its shortcomings enumerated above, the Constraint Index test has
been widely used, and ample data is available in the literature.
4.2.2
Isomerization and Disproportionation of m-Xylene
On acidic catalysts, m-xylene can undergo isomerization into o- andp-xylene
and disproportionation (or transalkylation) into toluene and 1,2,3-, 1,2,4- or
1,3,5-trimethylbenzene (cf. Fig. 7). While it is obvious that disproportiona-
tion is necessarily a reaction involving a bimolecular transition state, there
is some ambiguity as to whether the acid-catalyzed isomerization of xylenes
proceeds via a monomolecular or a bimolecular pathway [83, 84].
The use of m-xylene conversion for the characterization of the effective
pore width of zeolites was first proposed by Gnep et al. [85]. These authors
identified three selectivity criteria that may furnish valuable information on
the effective pore width: (i) the relative rates of formation of o- andp-xylene,
(ii) the ratio of rates of disproportionation and isomerization and (iii) the dis-
tribution of the trimethylbenzene isomers formed in the disproportionation
reaction.
Criterion (i) is based on the finding that, in the absence of shape selectivity,
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