M. D. Mantle et al.
dal pore size distribution (from BET and BJH analysis of ni-
trogen adsorption). As a consequence, molecules will expe-
rience many collisions with the pore walls and the measured
diffusivity, Deff, will be that of the liquid confined in the het-
erogeneous medium.
By comparing the case of 1,4-butanediol in methanol with
1,4-butanediol in methanol/water, it is clearly visible that
the log plot for this latter mixture shows a significantly
lower slope, that is, lower self-diffusivity values. This is ob-
served for both bulk liquids and liquids in catalyst particles.
Numerical values of the diffusion coefficients are reported
in Table 1. The addition of water leads to a decrease of
aTHz =aidealꢀaexperimental) deviated significantly from the value
of zero, that is, non-interacting ideal mixing. Over the entire
composition range, the positive value of aTHz indicated a de-
crease of absorption upon mixing in all alcohol/water mix-
tures (negative excess terahertz absorptions), which suggest-
ed that the introduction of a second species into an initially
pure liquid destroys the original hydrogen-bonded network
of the pure liquid, forming a new extended hydrogen-
bonded alcohol/water network, which is characterized by
slower dynamics than the original bulk liquid structure.
Moreover, it is also known that the presence of water modi-
fies the nature of the hydrogen bonds with the diol due to
its ability to act as a “bridge” between solute mole-
cules that are able to form hydrogen bonds,[29,30]
leading to the formation of larger aggregates, hence
Table 1. Numerical values of self-diffusivity and PFG interaction parameter, x, from
PFG-NMR measurements. The tortuosity of the catalyst, t, is also reported.
a slower mobility. Indeed, despite water and metha-
nol in their pure liquid state having similar diffusion
coefficients, as previously discussed, the self-diffu-
sivity of 5% mole fraction 1,4-butanediol in metha-
nol was found to be 9.2ꢂ10ꢀ10 m2 sꢀ1, whereas for
the same concentration in pure water the self-diffu-
sivity of the diol was found to be lower, with a
value of approximately 4.1ꢂ10ꢀ10 m2 sꢀ1.
Dꢂ109 [m2 sꢀ1
]
Deff ꢂ109 [m2 sꢀ1
]
x [–]
Bulk liquid
Liquid in Au/TiO2
1,4-butanediol in MeOH
1,4-butanediol in MeOH/H2O
0.92ꢁ0.01
0.48ꢁ0.01
0.54ꢁ0.01
0.28ꢁ0.01
1.7ꢁ0.04
1.7ꢁ0.04
1,4-butanediol in MeOH/base
1,4-butanediol in MeOH/H2O/base 0.41ꢁ0.01
0.71ꢁ0.02
0.27ꢁ0.01
0.15ꢁ0.01
2.6ꢁ0.07
2.7ꢁ0.07
It is therefore clear that the decrease of 1,4-buta-
nediol self-diffusivity in 1,4-butanediol/methanol
mixtures, caused by addition of water and reported
in this work, is a consequence of the changes in the
t [–]
1.9ꢁ0.05
cyclohexane
1.35ꢁ0.01
0.71ꢁ0.01
almost 50% in the diffusion rate of 1,4-butanediol within
the catalyst. The addition of base further reduces the diffu-
sion rate of 1,4-butanediol in all cases. This is expected since
the addition of the sodium methoxide salt increases the vis-
cosity of the solution. The self-diffusion coefficients of the
three components as single-component bulk liquid are: 1,4-
butanediol (1.6ꢂ10ꢀ11 m2 sꢀ1); methanol (2.2ꢂ10ꢀ9 m2 sꢀ1)
and water (2.0ꢂ10ꢀ9 m2 sꢀ1). The addition of water, diluting
the system, would intuitively lead to the conclusion that an
increase of the molecular motion of 1,4-butanediol should
be observed. Experimental results, however, clearly show a
net decrease of molecular mobility. The explanation of this
lies in the non-ideality of water/methanol mixtures, widely
reported in the literature[24–27] and in the nature of the hy-
drogen bonds involved in the different solvents.
The mutual and tracer diffusion profiles of water/metha-
nol mixtures as a function of composition show a marked
convex profile, with a minimum value,[25] which means that
when methanol is mixed with water, the diffusion of the
system is slower when compared with the pure species and
this is attributed to a higher degree of structuring in the
mixture caused by hydrogen bonding. A recent study has in-
vestigated the mixing mechanism of water/alcohol mix-
tures.[28] In this study, terahertz time domain spectroscopy
(THz-TDS) and PFG-NMR spectroscopy were used to
study the dynamics of 2-propanol/water mixtures across the
entire composition range. Self-diffusivity profiles showed a
convex profile, with a minimum in self-diffusivity. Absorp-
tion measurements in the THz frequency range showed that
the relative terahertz absorption coefficient, aTHz, (i.e.,
nature of hydrogen bonding due to water addition to the
original mixture. Values of the PFG interaction parameter,
x, that is, the ratio of the bulk liquid self-diffusivity to pore
self-diffusivity,[21] for 1,4-butanediol in both base-free mix-
tures and mixtures with base, are also reported in Table 1.
For the base-free mixtures the x-value of 1,4-butanediol was
found to be approximately 1.7 in both methanol and metha-
nol/water. This value was found to be statistically lower than
the PFG interaction parameter value of 1.9, obtained using
cyclohexane as guest molecule, which represents a good esti-
mate of the porous catalyst tortuosity, t.[31] The use of liquid
alkanes as the “optimal choice” to probe tortuosity in
porous catalysts has been validated in our recent work,
which showed that alkanes are suitable molecules to probe
structural properties of mesoporous solids, whereas the use
of functionalized molecules may yield very different values
that depend on the interactions within the porous matrix.[31]
This means that relative to the bulk liquid, 1,4-butanediol in
porous Au/TiO2 catalyst has a self-diffusion coefficient
higher than the theoretical value, the latter being the 1,4-bu-
tanediol bulk liquid self-diffusivity divided by the catalyst
tortuosity, t. This phenomenon seems to be widely observed
for viscous molecules, such as diols and glycerol, which are
capable of forming hydrogen bonds and has been reported
and discussed in our previous work.[21,31] The reason for this
enhanced diffusivity relative to the theoretical value is
thought to originate from a disruption of the extensive hy-
drogen bonding network of such molecules in mesoporous
materials,[31] although the mechanism of this is still unclear.
It is interesting to note that in the presence of the sodium
&
4
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