Time-resolved photoacoustic calorimetry as a tool to determine rate constants of hydrogen-abstraction reactions

Article abstract of DOI:10.1002/kin.20173

The hydrogen-abstraction reaction from phenol by tert-butoxyl radical was used to test time-resolved photoacoustic calorimetry (TR-PAC) as a method to obtain kinetic data. Absolute rate constants for this reaction were determined in benzene and in the 298-312 K temperature range, using a temperature- controlled photoacoustic calorimeter, yielding an average value of 3.5 × 10⁸ M^-1 s^-1. This is in good agreement with the literature results obtained by laser flash photolysis (LFP). Kinetic solvent effects (KSE) in the same reaction were also studied using acetonitrile, carbon tetrachloride, and ethyl acetate as solvents. The results obtained by TR-PAC are close to those derived by LFP (using the cumyloxyl radical as the abstracting species) and follow the expected trend based on the KSE.

Full text of DOI:10.1002/kin.20173

Time-Resolved
Photoacoustic Calorimetry
as a Tool to Determine Rate
Constants of
Hydrogen-Abstraction
Reactions
2
1
1
PAULO M. NUNES, CATARINA F. CORREIA, RUI M. BORGES DOS SANTOS,
1
´
˜
JOSE A. MARTINHO SIMOES
1Departamento de Qu ı´ mica e Bioqu ı´ mica, Faculdade de Ci eˆ ncias, Universidade de Lisboa, 1749-016 Lisboa, Portugal
2Centro de Biomedicina Molecular e Estrutural, Universidade do Algarve, Campus de Gambelas, 8005-139 Faro, Portugal
Received 1 July 2005; revised 12 October 2005; accepted 9 December 2005
DOI 10.1002/kin.20173
Published online in Wiley InterScience (www.interscience.wiley.com).
ABSTRACT: The hydrogen-abstraction reaction from phenol by tert-butoxyl radical was used
to test time-resolved photoacoustic calorimetry (TR-PAC) as a method to obtain kinetic data.
Absolute rate constants for this reaction were determined in benzene and in the 298–312 K tem-
perature range, using a temperature-controlled photoacoustic calorimeter, yielding an average
8
−1 −1
s . This is in good agreement with the literature results obtained by
value of 3.5 × 10 M
laser flash photolysis (LFP). Kinetic solvent effects (KSE) in the same reaction were also stud-
ied using acetonitrile, carbon tetrachloride, and ethyl acetate as solvents. The results obtained
by TR-PAC are close to those derived by LFP (using the cumyloxyl radical as the abstracting
species) and follow the expected trend based on the KSE. ꢀC 2006 Wiley Periodicals, Inc. Int J
Chem Kinet 38: 357–363, 2006
INTRODUCTION
to probe the thermochemistry of reactions involving
short-lived species and to extract photochemical infor-
mation (quantum yields and decay lifetimes) [1–25].
TR-PAC has also been applied to determine rate con-
stants of photoinitiated processes [6,17].
In spite of being a recent technique, time-resolved pho-
toacoustic calorimetry (TR-PAC) has been widely used
The reaction of tert-butoxyl radical with phenol can
be used as a test for both classical (nonresolved or
static) photoacoustic calorimetry (PAC) and TR-PAC
Correspondence to: Paulo M. Nunes; e-mail: panunes@fc.ul.pt.
Contract grant sponsor: Funda c¸ a˜ o para a Ci eˆ ncia e a Tecnologia
FCT), Portugal.
Contract grant numbers: SFRH/BD/6519/2001, SFRH/BPD/
1465/2002.
c 2006 Wiley Periodicals, Inc.
(
[22,26]. The thermochemical study of this reaction
1
ꢀ
yields the phenol O H bond dissociation enthalpy

358
NUNES ET AL.
in solution, which can then be compared with liter-
ature data, obtained from independent photoacoustic
calorimetry studies and from other experimental and
computational techniques [27–30]. Although TR-PAC
can also provide kinetic information for the hydrogen-
abstraction reaction, to our knowledge, this technique
has not been used for that purpose. We therefore set out
to demonstrate that TR-PAC can afford reliable kinetic
data for hydrogen-abstraction reactions.
Eq. (2).
Em − ꢀobs H
ꢀrV
ꢀ
r H =
+
(2)
ꢁ
r
χ
In this equation, ꢁr represents the reaction quantum
yield. The correction term includes the reaction volume
change, ꢀrV , and the adiabatic expansion coefficient
of the solution, ꢁ. Since the calorimetric solutions are
usually very dilute, the adiabatic expansion coefficient
of the solvent is used as a substitute for the solution
value (see, however, section Instrumental Setup and
Experimental Procedure).
Equation (1) is the basis of classical photoacoustic
calorimetry or nontime-resolved PAC. Its application is
valid only when the process generating the photoacous-
tic signal is much faster than the transducer response
EXPERIMENTAL
Materials
Benzene (Aldrich), acetonitrile (Aldrich), carbon tetra-
chloride (Bio-Lab), and ethyl acetate (Lab-Scan)
were of HPLC grade and used as received. Di-tert-
butylperoxide (Aldrich) was purified according to the
literature procedure [31]. Phenol (Aldrich, ≥99%) was
sublimed in vacuum and kept under nitrogen prior
to use. ortho-Hydroxybenzophenone (Aldrich) was
recrystallized twice from an ethanol–water mixture.
[2]. This is the time constraint of classical PAC, and can
be written as τ ꢁ 1/ν, where τ represents the lifetime
of the process and ν is the characteristic frequency of
the microphone. In only this case will the time-profile
of the photoacoustic wave depend exclusively on the in-
strumental response, and not on the rate of the process,
allowing the direct correspondence between its ampli-
tude S and the observed heat fraction φobs. On the other
hand, processes that are much slower than the trans-
ducer response (τ ꢂ 1/ν) will give rise to virtually no
signal. In the intermediate regime (τ ≈ 1/ν), each pro-
cess with a different rate will originate a unique wave-
form. For instance, in a system where one or more of
such processes occur, the signal obtained will be a con-
voluted waveform that will appear phase shifted and re-
duced in amplitude due to the presence of components
corresponding to slower reactions. Using a deconvolu-
tionanalysisforthetimedependenceofthesignal S, the
magnitude of each of the signal-inducing events as well
as their lifetimes will be obtained [35]. This is the basis
of time-resolved photoacoustic calorimetry (TR-PAC).
The analysis involves the normalization of the photoa-
coustic waveform for its respective absorbance (1 − T)
and incident laser energy E, as indicated in Eq. (1).
Extraction of the observed heat fraction, φobs,i , and the
lifetime, τi , for each process is then accomplished by
the deconvolution of the waveform, facilitated by the
use of commercially available software [36].
Photoacoustic Calorimetry
Theory of Photoacoustic Calorimetry. The theoreti-
cal basis of photoacoustic calorimetry has been widely
discussed [1,12,26,32], but a small digest is provided
here. The PAC technique involves the measurement of
an acoustic wave generated by a sudden volume change
that occurs when a laser pulse strikes a solution con-
taining the reactants and initiates a chemical reaction.
The resulting photoacoustic signal, S, can be recorded
by a sensitive microphone such as an ultrasonic trans-
ducer. Equation (1) defines this signal as directly pro-
portional to the solution transmittance, T , the incident
laser energy, E, and the observed fraction of photon
energy released as heat, φobs. K is a calibration con-
stant, dependent on the instrumental specifications and
geometry, and on the thermoelastic properties of the
solution.
S = Kφobs(1 − T )E
(1)
When φobs is multiplied by the molar photon en-
ergy (Em = NAhꢀ), the observed enthalpic change,
Reaction enthalpies for each process are then cal-
culated as before [32]. For instance, considering
a two-step sequential reaction, the enthalpy of the
first step (photochemical) is given by Eq. (2) with
ꢀobs H = ꢀobs H1, calculated from the amplitude φobs,1
obtained from the deconvolution, and ꢀrV = ꢀrV1.
The enthalpy of the second step (thermal) is calculated
from Eq. (3). Although only the first step is light ini-
tiated, the yield of the sequential step is dependent on
ꢀ
obs H = φobs Em, is obtained. However, this quantity
consists of a thermal contribution, due to the enthalpy
of the reaction, and a reaction volume contribution, due
to the differences between the partial molar volumes of
the reactants and products [33]. The latter leads to the
introduction of a correction factor when calculating the
reaction enthalpy through an energy balance [26,34],

TIME-RESOLVED PHOTOACOUSTIC CALORIMETRY
359
the quantum yield.
[22,26]. Briefly, solutions of ca. 0.33 M of di-tert-
butylperoxide andphenolin the adequate concentration
−
ꢀobs H2
ꢀrV2
(see Table I), kept in a thermostatic bath, were purged
ꢀ
r H2 =
+
(3)
ꢁ
r
ꢁ
using solvent-saturated argon and were flowed through
a quartz flow cell (Hellma 174-QS). Phenol concentra-
tions were determined using a Beer–Lambert plot. The
solutions were photolyzed with pulses from a nitrogen
laser (PTI PL 2300, 337.1 nm, pulse width 800 ps).
The incident laser energy was varied by using neutral
density filters (ca. 5–30 ꢂJ/pulse at the cell, flux <40
Kinetic data may be obtained from each process
lifetime, τi . The inverse of this quantity, 1/τi , is the
observed rate constant of that process, kobs,i . Again,
considering a two-step sequential reaction, where the
first step is a very fast absorption of light generating A,
and the second one consists of a bimolecular reaction
of A with another molecule B,
−
2
J m ). Each pulse induced a volume change in solu-
tion, producing an acoustic wave that was detected by a
piezoelectric transducer (Panametrics V101, 0.5 MHz)
in contact with the bottom of the cell. The signals
were amplified (Panametrics 5662) and measured by a
digital oscilloscope (Tektronix 2430A). The signal-to-
noise ratio was improved by averaging 32 acquisitions.
A pyroelectric probe (Gentec ED-100A) was placed
after the quartz cell to measure the emerging laser
beam intensity. The probe signal was amplified (Gentec
EDX-1) with a 100-fold gain and stored in an energy
meter (Gentec EM-1). Each data point, at each of four
different incident laser energies used, was determined
five times. To check for multiphoton effects, the aver-
age signal was plotted against the laser energy (excel-
lent linear correlations, r > 0.9995, with zero intercept
have always been observed). The apparatus was cali-
brated by carrying out a photoacoustic run using an op-
tically matched (within typically 6% absorbance units
at 337.1 nm) solution of ortho-hydroxybenzophenone
A(sln) + B(sln) → Products(sln)
the correspondent rate law is
(4)
d[A]
−
= k2[A][B]
(5)
dt
Assuming that the concentration of B is constant during
this process lifetime, reaction (4) may be viewed as a
pseudo-unimolecular step, and Eq. (5) may be rewritten
as
d[A]
−
= kobs,2[A]
(6)
dt
The integrated rate law for the decay of A will be
ꢀ
ꢁ
−
t
[
A](t) = [A] exp(−kobs,2t) = [A] exp
(7)
0
0
τ2
(photoacousticcalibrant)inthesamesolventusedinthe
experiment (this solution does not include the peroxide
but also contains phenol, with the same concentration
as in the experiment; see below). The above photoa-
coustic calibrant dissipates all of the absorbed energy
as heat (φobs = 1) [1]. For each run (experiment or cali-
bration), fourdatapointswerecollected, corresponding
to the four different laser intensities obtained using the
neutral density filters. The resulting waveforms from
each data point were recorded for subsequent math-
ematical analysis, affording two waveforms for each
point, sample and calibration (again containing the
with
1
kobs,2 =
= k2[B]
(8)
τ2
The slope of the plot of kobs,2 versus [B] will afford
the second-order rate constant, k2.
Instrumental Setup and Experimental Procedure.
Our photoacoustic calorimeter setup and experimen-
tal procedure have been described in detail elsewhere
Table I Rate Constants for Hydrogen Atom Abstraction from Phenol by tert-Butoxyl Radical in Benzene at Different
Temperatures
T (K)a
k0 (× 10 s
4
−1 b
)
k2 (× 10 M
8
−1 −1 b
s )
[PhOH] (mM)
2
2
1
.31–5.73
.13–8.51
.19–8.00
298.2 ± 0.6
304.1 ± 0.3
311.8 ± 0.4
298–312
7.9 ± 11.5
31.8 ± 10.8
10.9 ± 8.3
4.0 ± 0.3
3.0 ± 0.2
3.5 ± 0.2
3.5 ± 0.6
Average
a
Reported temperatures are averages of the temperatures determined in the five experiments. Errors indicated are standard deviations.
b
Errors indicated are standard deviations for the fitting parameters of Eq. (11), except for the average value, where the error is twice the
standard deviation of the mean.

360
NUNES ET AL.
phenol in the same concentration as in sample). After
the normalization of the waveforms explained in sec-
tion Theory of Photoacoustic Calorimetry, the analysis
for each point involves the subtraction of the solvent
signal from both the sample and calibration waveforms,
and then their deconvolution using the software Sound
Analysis by Quantum Northwest [36].
Subtraction of the solvent signal can be important
because a significant background signal (from the sol-
vent and/or substrate) may affect the deconvolution of
the waveforms, which in essence depends on a fitting
procedure (in extreme cases, it can even render the fit-
ting impossible). However, in the solutions used in the
present work, the background signal was negligible, so
this step was not necessary. This has been previously
verified by the agreement between the results obtained
before and after the subtraction of the solvent signal
Thermo Haake EK20 cryostat was circulated through
all heat exchangers.
The temperature was measured both at the inlet and
outlet of the quartz flow cell. This was achieved by fit-
ting the cell with Y-shaped glass adapters. The calori-
metric solution flowed through one of the arms, and
a Teflon-encapsulated thermistor (Omega 44104) was
placed inside the other (closed) arm, filled with sili-
con oil to improve the thermal conductivity. The ther-
mistors were previously calibrated in the temperature
range of 273.4–333.3 K against a quartz thermome-
ter (Hewlett-Packard 2804A). The thermistor’s resis-
tance was measured in a four-wire configuration using
a Hewlett-Packard 34970A multimeter equipped with a
Hewlett-Packard 34901A data acquisition/switch unit.
Temperature determination accuracy is better than
0.05 K.
[22].
Another important issue regards the need to use sub-
strate (phenol, in this case) in the calibration solution.
The resemblance of the thermoelastic properties of the
calibration solution and the sample solution, namely
their adiabatic expansion coefficients χ (Eq. (3)), is an
essential requirement of the PAC technique. Since the
solutions used are normally very dilute, it is generally
assumed that both will have χ equal to that of the pure
solvent. For instance, in methanol, this assumption is
notvalid[37]. However, usingbenzene, iso-octane, car-
bontetrachloride, andacetonitrileassolvents, theshape
and time of arrival of the photoacoustic waveform is
the same for calibration and experiment, and increas-
ing the amount of peroxide in the sample solution does
not noticeably affect the time of arrival of the photoa-
coustic waveform. This evidence seems to corroborate
the above assumption. Moreover, and which is a more
rigorous test, a plot of the photoacoustic signal versus
the amount of peroxide added during the experiment
remains linear even beyond 12% (v/v) of peroxide in
solution [38]. In our experimental conditions only 6%
RESULTS AND DISCUSSION
The general strategy for determining the reaction rates
in hydrogen abstraction from phenol is illustrated in
Scheme 1. Photolysis of di-tert-butylperoxide gener-
ates two tert-butoxyl radicals (reaction (9)) that will
abstract a hydrogen atom from phenol, yielding the
phenoxy radical (reaction (10)).
The first reaction is, in practical terms, instanta-
neous, affording lifetimes τ that reflect instrumental
1
response, namely the characteristic frequency of the
microphone, 0.5 MHz. The lifetime for the second
step, τ , however, is related to the second-order rate
2
constant, k . Under our experimental conditions, the
2
phenol concentration in each run can be regarded as
constant. Therefore, the decay of the tert-butoxyl radi-
cal follows the kinetics described in the section Theory
of Photoacoustic Calorimetry and the rate constant
of the hydrogen-abstraction reaction can therefore be
extracted by plotting 1/τ against the phenol concentra-
2
(v/v) was used.
tion in the calorimetric solution, according to Eq. (8).
Good linear correlations were observed using phe-
nol concentrations ranging from 1 to 9 mM and ben-
zene as solvent, at three different temperatures (Fig. 1),
leading to the results displayed in Table I. No temper-
Temperature Control. The quartz flow cell and piezo-
electric transducer were placed inside a thermally insu-
lated box (290 × 150 × 130 mm) containing two metal
heat exchangers. Small holes in the transparent, 8 mm
thick, polymethacrylate box walls were drilled in the
laserpath and to allow the connections of the transducer
cable, the pyroelectric probe, the thermistor cables (see
below), and the sample flow tubes. The heat exchangers
were attached to the box walls parallel to the laser path.
Another heat exchanger was used to heat the sample
flow tube, to ensure a rapid temperature stabilization
inside the cell. Liquid from a thermostatic bath con-
trolled with a Haake D8 temperature controller and a
ature effect on k is observed in our results, in keeping
2
with the low-activation energy for this reaction: a value
hꢀ
r
t-BuOOBu-t(sln) → 2 t-BuO (sln) φobs,1, τ1 (9)
r
PhOH (sln) + t-BuO (sln) →
r
PhO (sln) + t-BuOH (sln) φobs,2, τ2
(10)
Scheme 1

TIME-RESOLVED PHOTOACOUSTIC CALORIMETRY
361
signal. Indeed, the intercepts of the plot shown in Fig. 1
have large uncertainties (Table I).
It has been pointed out in the literature that the ki-
netics of hydrogen atom abstraction reactions in some
molecules are subject to solvent effects. This has been
explained by making three assumptions: the substrate
molecule, XH, could act as a hydrogen-bond donor to
a solvent molecule, S; the extent of the equilibrium
for the formation of XH–S complex is essentially in-
dependent of the surrounding medium; and the hydro-
gen atom in the XH–S complex cannot be directly ab-
r
stracted by the abstractor radical, Y , i.e., the XH–S
r
complex must be dissociated before reaction with Y
can occur [40]. These assumptions explain why the
kinetic solvent effect is observed in phenols, pheny-
lamines, and tert-butyl hydroperoxide but not in cyclo-
hexane, where the substrate cannot act as a hydrogen-
bond donor. They also explain why kinetic solvent
r
effect is independent of Y , as its magnitude should
be determined by the strength of XH–S interaction
[
40–42].
To investigate the kinetic solvent effect on reaction
10) (Scheme 1), we have determined the rate constants
(
in three other solvents (carbon tetrachloride, acetoni-
trile, and ethyl acetate). The results are presented in
Table II.
It has been suggested that rate constants for hydro-
gen abstractions follow the empirical correlation [40]:
ꢂ
ꢃ
ꢂ
ꢃ
Figure 1 Variation of 1/τ2 for the hydrogen atom abstrac-
tion from phenol by tert-butoxyl radical in benzene at three
different temperatures with phenol concentration.
log ks
(M
−1
s
−1
) = log k
0
(M
−1 −1
s
)
r
r
XH/Y
XH/Y
H
2
H
2
−
8.3α β
(12)
H
where β is the solvent hydrogen bond basicity [43],
2
of 11.7 kJ mol 1 was obtained in a toluene and di-
tert-butylperoxide (1:1, v/v) mixture in the 213–295 K
range [39]. Therefore, we select as our value in benzene
−
H
α is the hydrogen bond acidity for the molecule XH
2
0
r
[44], k
is the rate constant for the same reac-
XH/Y
H
s
r
tion in a hydrocarbon where β = 0, and k
is
2
XH/Y
8
−1 −1
s at 305 K. This is in good
(
3.5 ± 0.6) × 10 M
the rate constant for a hydrogen-abstraction reaction
in a hydrogen-acceptor solvent (S). This equation fits
a considerable range of kinetic data obtained by LFP
for hydrogen-abstraction reactions. It translates quan-
titatively the three assumptions mentioned before: the
hydrogen-bond donor ability of the substrate, XH, cor-
8
−1 −1
agreement with the literature value, 3.3 × 10 M
s
at 295 K, obtained from laser flash photolysis (LFP)
experiments [39].
It is worth mentioning that the equation used to ex-
tract kinetic data from LFP experiments includes an
additional term (k0) to account for the unimolecular
decay of tert-butoxyl radical, viz.
H
2
responds to its hydrogen bond acidity, α ; the solvent
ability to accept hydrogen bonding is represented by
H
2
H
2
H
2
its hydrogen bond basicity, β ; α and β are char-
1
acteristic of the substrate, XH, and of the solvent, S,
=
k0 + k2[PhOH]
(11)
respectively, and are independent of the nature of the
τ2
r
abstractor radical, Y .
Equation (11) leads to a nonzero intercept in the plots of
Fig. 1. However, in our TR-PAC experiments the decay
of the tert-butoxyl radical is too slow to be observed,
i.e., τ0 is far beyond the transducer response and thus
it could not possibly contribute to the photoacoustic
To test whether our TR-PAC values would follow
H
2
Eq. (12), they were plotted against β for each solvent
and compared with the rate constants for the hydrogen
abstraction from phenol with cumyloxyl radical, ob-
tained by LFP in the same solvents [42]. As shown

362
NUNES ET AL.
Table II Rate Constants for the Hydrogen-Abstraction Reactions from Phenol in Various Solvents
8
−1 −1
s )
k2 (× 10 M
T (K)a
This Workb,c
LFPd
ꢃ
H e
Solvent
2
CCl4
C6H6
MeCN
MeCOOEt
297.5 ± 0.2
298–312
6.7 ± 0.3
3.5 ± 0.6
8.6
2.8
0.058
0.075
0.05 f
0.14
0.44
0.45
297.7 ± 0.2
0.094 ± 0.004
0.11 ± 0.02
298.2 ± 0.1
a
Reported temperatures are averages of the temperatures determined in the five experiments. Errors indicated are standard deviations.
Abstraction by the tert-butoxyl radical.
Errors indicated are standard deviations of the slope in Eq. (11).
Abstraction by the cumyloxyl radical. Data from [42].
Data from [43], unless indicated otherwise.
b
c
d
e
f
Data from [40].
in Table II and Fig. 2, our results show a remarkable
are slightly smaller than those for the tert-butoxyl rad-
ical, the opposite being observed in carbon tetrachlo-
ride. This could indicate that hydrogen abstraction is
not entirely independent of the abstractor radical. An
alternative explanation, suggested by a reviewer, in-
volves a kinetic solvent effect due to the presence of
di-tert-butylperoxide, which in TR-PAC experiments
was used in higher concentration (ca. 0.3 M) than
di-cumylperoxide in LFP experiments (ca. 0.1 M).
In weak hydrogen-accepting solvents, such as CCl4,
this peroxide may act as a strong hydrogen-bond ac-
kinetic solvent effect and follow very closely the trend
previously obtained by LFP for the equivalent reac-
tion with cumyloxyl radical. Moreover, fitting our data
H
to Eq. (12) and using α = 0.596 for phenol [44], we
2
0
9
−1 −1
s and a
r
obtain k
= (1.3 ± 0.3) ×10 M
PhOH/t−BuO
slope of 7.9 ± 0.5 (close to 8.3 in Eq. (12)). When the
LFP data presented in Table II are used, we derive
0
9
−1 −1
r
k
= (1.6 ± 0.3) ×10 M
s and a slope of
PhOH/CumO
.0 ± 0.4. Our k
0
r
9
is also in good agreement
PhOH/t−BuO
with the rate constant for the hydrogen abstraction from
9
−1 −1
H
phenol in n-octane, 1.1 × 10 M
s
[40], obtained
ceptor (β = 0.33) [28] and the kinetic solvent effect
2
by LFP.
shouldbemorevisible, loweringthemeasuredratecon-
stant [28].
Table II and Fig. 2 show that the rate constants for
the hydrogen abstraction from phenol with tert-butoxyl
radical are very close to those obtained by LFP for the
cumyloxyl radical, in agreement with the assumption
mentioned above that the rate constant is independent
of the abstracting radical [40]. Although there are no
error bars associated with the LFP data, it is interest-
ing to note that the values for the cumyloxyl radical
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