to reactants, are tted nonlinearly by a function of the
l 5 a 1 b* 2c*t
shape
exp(
where is the intensity, is the time, and
positive tted constants. Similarly, pro les that increase,
) (pseudo- rst-order kinetics),
l
t
a, b,
c
and are
a 2
due to products, are tted by a function of the form
b*
2c*t
c,
). The rate constants are given by and the
characteristic half-life time for the reactant TBPPI is giv-
exp(
c.
en by ln(2)/ Note that, because of baseline effects which
are not fully compensated for, as well as small errors in
a
the tting procedure, an off-set (constant ) might be pre-
sent in the product and reactant pro les, which must be
taken into account to obtain a reliable t result.
RESULTS AND DISCUSSION
FIG. 3. Raman spectra of 75 wt % TBPPI in iso-dodecane (top) and
n-hexane (bottom) recorded at T 5 25 8C and ambient pressure.
Spectra of TBPPI and n-Hexane. Figure 3 shows the
(1900 bar) conditions are reached. The time needed for
scanning and recording one spectrum is 32.2 s. Typically
a set of 40 spectra is recorded, covering a time window
of about 1200 s.
iso
Raman spectra of a 75 wt % solution of TBPPI in
-
8
n
dodecane at 25 C and ambient pressure and of pure
-
hexane. Both spectra have been baseline corrected to
compensate for broad baseline features. A comparison
The spectra recorded at different time intervals were
exported to and processed by the Labspec 2.08 program
(Dilor, S.A., France). All spectra are stored in a single
multidimensional data set with a wavenumber dimension,
a time dimension, and a spectral intensity dimension. The
data set is baseline corrected in the wavenumber dimen-
sion rst, with the application of linear local baselines
intersecting local minima. Fluorescence can lead to uc-
tuations in baseline height in the spectral dimension. The
uorescence might originate from degradated particles,
which move into the focal volume of the Raman probe
occasionally under the action of the pulsating high-pres-
sure pump. Although the baseline can be tted and sub-
tracted in the wavenumber dimension, it is very dif cult
to correct entirely because the precise shape of the base-
8
with Raman spectra recorded at 25 C and high pressure
up to 1900 bar revealed only a slight shift of most Raman
2
signals, smaller than 1 cm 1, which we will neglect here.
n
The spectra of the peroxide and the -hexane are com-
pletely different, enabling the detection of TBPPI dis-
solved in -hexane without much effort. Raman spectra
from samples of low concentration of TBPPI in -hexane
showed that, for concentrations below 2 wt %, no repro-
ducible quanti cations were obtained. Therefore, time-
resolved experiments were carried out with a 10 wt %
solution of TBPPI in -hexane at 1900 bar and 100 C.
From Fig. 3, strong bands can be identi ed due to TBPPI,
n
n
n
8
n
which do not overlap with bands due to -hexane. These
bands are located at wavenumbers 871, 801, 591, and 558
2
1
cm
.
a priori.
line is not known
The remaining uncompensated
Assignment of Peaks in the Time-Dependent Ra-
man Data Set. In Fig. 4, an entire time-dependent data
set of spectra is shown in one plot. The spectra are pre-
sented as difference spectra, created by subtracting the
nal spectrum from all other spectra. In this way the
uctuations will appear in a noise-like pattern, containing
spikes and discontinuities, superimposed on pro les of
the Raman peak intensities vs. time. Therefore, after the
baseline correction, the data set is ltered in the time
dimension, with removal of the spikes. The next step of
the data treatment is ltering in the wavenumber dimen-
sion with the application of a 9-point moving average
lter.
n
spectrum due to -hexane (the solvent) is almost com-
pletely cancelled, Raman peaks due to reactants appear
as positive peaks, and peaks due to products appear as
negative peaks. Both the negative and positive peaks be-
come weaker in this representation as time proceeds.
Note that difference traces like this cannot be analyzed
kinetically, because the intensity of all peaks is arti cially
brought to zero as the result of the subtraction procedure.
The positive peaks, due to reactants, are due to TBPPI,
as can be very easily veri ed by comparing Figs. 3 and
4. The positions of the most prominent peaks are 249,
478, 558, 592, 802, 872, 1031, 1100, 1264, and 1455
The major components of the decomposing system of
n
TBPPI dissolved in -hexane are the peroxide and the
hexane themselves and the products 2-methyl-2-propanol
t
( -butanol) and CO2 (see the Results and Discussion sec-
n
t
tion). Spectra of the peroxide, the -hexane, and the -
butanol components in the pure form are measured. Each
spectrum from the time-dependent data set is next tted
as a linear combination of these three spectra of the com-
ponents. The spectrum of CO2 contains only two very
narrow lines and is not considered in the t. From the
tting coef cients, pro les for the components are cre-
ated, and the Raman signal intensity is then essentially
represented by a tting coef cient. The pro le for the
CO2 contribution is created by integrating the intensity of
one of the two CO2 peaks for each time interval.
2
2
1
cm 1. The very strong peak at 872 cm is due to the
O–O stretching vibration of the peroxide group.2
In order to establish an assignment of peaks due to
products (negative peaks), possible steps in the decom-
position reaction TBPPI should be considered. A very
simple pathway for the decomposition of TBPPI is given
in Scheme I.
Pro les of Raman signal intensities vs. time were ex-
ported to Excel 97 (Microsoft). Pro les that decrease, due
138
Volume 55, Number 2, 2001