(
)
S. Schneider et al.rChemical Physics Letters 308 1999 211–217
215
Ž
.
Inspection of Figs. 3 and 4 immediately reveals
that the data points follow in the logrlog plot of kiso
versus h an approximately linear dependence with
ane, he found 12.1 kJrmol hs1.00 mPa s and
Ž
.
10.1 kJrmol hs10.0 mPa s thus pointing to the
importance of the molecular structure and specific
properties of the solvent.
If one wants to compare the results obtained in
this work for the bridged compound 4 with the
many, in part apparently contradictory results for
trans-stilbene 1, one should recall that the evaluation
of the viscosity and temperature dependence of the
Ž
.
Ž
slopes around 0.3 n-hexane and 0.15 methyl-
.
cyclohexane .
Ž
.
This qualitative finding suggests a global fit of
the data by means of the generally accepted relation-
ship:
kiso sF h Pexp yE rRT
Ž .
,
3
Ž .
Ž
.
A
Ž .
isomerization rate as expressed in Eq. 3 is done by
Ž .
with the viscosity dependent term F h being ap-
using different assumptions. We have chosen to eval-
uate our data with the minimum set of free fit
parameters, i.e. temperature independent values for a
w
x
proximated by a power law 28,29 :
ya
F h sCP hrmPas
Ž .
with 0(a(1 .
4
Ž .
Ž
.
Ž
.
and EA cf. Table 1 . It is obvious that by allowing
slightly temperature dependent slopes in the single
curve fitting we would produce viscosity dependent
activation energies from isoviscous Arrhenius plots.
Thus, our fits demonstrate that in case of the bridged
compound 4 the temperature effects on a andror EA
must be so small that they do not show up at the
level of accuracy of our experiment.
The solid lines in Figs. 3 and 4 represent the result of
a global fit using the same values for a and EA for
all temperatures and viscosities. That such a global
fit is possible in good quality is astonishing in view
of the different results obtained by various groups
for the parent trans-stilbene. Previous investigations
at ambient pressure yielded slopes of a ;0.32 in
w
x
higher alkanes 16,29–33 with viscosities ranging
between 0.1 and 4 mPa s. From transient absorption
measurements at variable pressure in n-hexane,
With these assumptions, we find that the activa-
tion energy of 4 is lower by about 0.3 kJ moly1 in
methylcyclohexane than in n-hexane. This trend par-
w
x
Schroder 17 derived a temperature dependent slope
allels the finding by Schroder for trans-stilbene and
¨
¨
Ž
.
Ž
rising from as0.29 Ts298 K to as0.46 Ts
points to the importance of specific solute–solvent
interactions for the magnitude of the activation bar-
rier.
.
453 K . It must, however, be mentioned that the
scatter in Schroder’s data collected at the highest
temperatures 398 and 453 K is fairly large and
consequently the values of the slopes at higher tem-
peratures are subject to some uncertainty.
Sundstrom and Gillbro 31 probed the trans-
stilbene isomerization kinetics by picosecond tran-
sient absorption spectroscopy in longer chain n-al-
¨
Ž
.
The small reduction of the activation barrier in 4
when compared to that given by Schroder for 1
¨
Ž
.
especially in n-hexane is interesting in view of
w
x
earlier discussions which proposed that the torsion
around the single bond could facilitate isomerization
around the double bond. On the other hand, in the
derivative comprising the five-membered rings, 5,
the thermal activation barrier is lowered even more,
¨
Ž
.
kanes ns12,14,16 . Their isoviscosity plot for hs
1.64 mPa s yielded an intrinisic barrier for isomeriza-
namely to only about 6.3 kJ moly1 15–17 . Since in
contrast to the latter compound, the rate for isomer-
w
x
w
x
tion of only 10.1 kJrmol. Courtney et al. 32 found
an activation barrier of 15 kJrmol in hexane. In
w
x
contrast, Park and Waldeck 33 reported a value of
about 18 kJ moly1 as average activation energy for
Ž
.
hydrocarbon solvents 350 K-T-278 K . They
found an increase in activation energy with the length
of the alkane chain, i.e. with increasing viscosity.
The origin of the latter trend was commented as
being opposite to that expected for a solvation effect.
Table 1
Parameters derived from a global fit of the pressure dependent
rates of isomerization Figs. 3 and 4 by Eqs. 3 and 4
Ž
.
Ž . Ž .
n-hexane
0.93=1012
0.26
Methylcyclohexane
1.08=1012
0.14
y1.
Ž
C s
w
x
According to Schroder 7,17 , the activation energy
in n-hexane drops from 14.3 hs0.33 mPa s to
11.8 kJrmol hs1.15 mPa s . In methylcyclohex-
¨
a
Ž
.
.
y1
Ž
.
EA kJ mol
12.8
12.5
Ž