Reactions at solid-liquid interfaces. The mechanism and kinetics of the fluorination of 2,4-dinitrochlorobenzene using solid potassium fluoride in dimethylformamide

Article abstract of DOI:10.1021/jp012612r

The halogen exchange reaction of 2,4-dichloronitrobenzene with potassium fluoride in dimethylformamide containing tetrabutylammonium salts has been studied employing an electrochemical detection methodology based upon the use of square wave voltammetry to follow the loss of reactant and the formation of the product and intermediates. The results obtained show that the kinetics of loss of parent material behave on one hand as a dissolution-rate-controlled process and on the other as a homogeneous chemical process. Initially homogeneous reaction dominates the observed kinetics as the presaturated solution is stripped of fluoride ion; at longer time, the observed kinetics are controlled by the rate of KF dissolution. Modeling the system using a fully implicit finite difference method with Richtmyer modification (FIRM algorithm) yielded a mean value for the homogeneous rate constant for the formation of 2,4-dinitrofluorobenzene by reaction of 2,4-dichloronitrobenzene with fluoride ion in DMF at 85 ?°C of 640 ?± 250 mol^-1 cm³ s^-1 and a mean value for the saturation concentration of fluoride ion of (6.5 ?± 0.5) ?? 10^-6 mol cm^-3. Ultrasound was found not to significantly enhance the rate of the reaction in the intensity range studied. Furthermore, the utility of microelectrodes for obtaining simple quantifiable voltammetric responses from compounds of which the macroelectrode responses are complicated by chemical followup steps is demonstrated. Ultrasonically induced mixing has been shown to facilitate reproducible microelectrode responses in intrinsically heterogeneous systems.

Full text of DOI:10.1021/jp012612r

12534
J. Phys. Chem. B 2001, 105, 12534-12546
Reactions at Solid-Liquid Interfaces. The Mechanism and Kinetics of the Fluorination of
2,4-Dinitrochlorobenzene Using Solid Potassium Fluoride in Dimethylformamide
Gavin Macfie, Benjamin A. Brookes, and Richard G. Compton*
Physical and Theoretical Chemistry Laboratory, Oxford UniVersity, Oxford OX1 3QZ, U.K.
ReceiVed: July 11, 2001
The halogen exchange reaction of 2,4-dichloronitrobenzene with potassium fluoride in dimethylformamide
containing tetrabutylammonium salts has been studied employing an electrochemical detection methodology
based upon the use of square wave voltammetry to follow the loss of reactant and the formation of the
product and intermediates. The results obtained show that the kinetics of loss of parent material behave on
one hand as a dissolution-rate-controlled process and on the other as a homogeneous chemical process. Initially
homogeneous reaction dominates the observed kinetics as the presaturated solution is stripped of fluoride
ion; at longer time, the observed kinetics are controlled by the rate of KF dissolution. Modeling the system
using a fully implicit finite difference method with Richtmyer modification (FIRM algorithm) yielded a mean
value for the homogeneous rate constant for the formation of 2,4-dinitrofluorobenzene by reaction of 2,4-
dichloronitrobenzene with fluoride ion in DMF at 85 °C of 640 ( 250 mol-1 cm3 s-1 and a mean value for
the saturation concentration of fluoride ion of (6.5 ( 0.5) × 10-6 mol cm-3. Ultrasound was found not to
significantly enhance the rate of the reaction in the intensity range studied. Furthermore, the utility of
microelectrodes for obtaining simple quantifiable voltammetric responses from compounds of which the
macroelectrode responses are complicated by chemical followup steps is demonstrated. Ultrasonically induced
mixing has been shown to facilitate reproducible microelectrode responses in intrinsically heterogeneous
systems.
1. Introduction
SCHEME 1
Halogen exchange (HALEX) reactions, in which a chlorinated
aromatic molecule undergoes substitution of chlorine for fluorine
under phase-transfer catalysis (PTC) conditions, are widely used
in many areas, including the pharmaceutical, agrochemical, and
dyestuff industries.1 Despite the wealth of fluorination agents
that have been developed,1 the use of alkali metal fluorides
remains widespread with solid potassium fluoride (KF) giving
the best compromise between cost and reactivity, CsF being
both more reactive and more expensive and LiF and NaF being
completely unreactive.2 Considerable effort has been devoted
to developing pretreatments that increase the area of KF
available for reaction; these include spray-drying,3 freeze-
drying,4 recrystallization from methanol,5 and the use of various
materials including alumina6 and calcium fluoride7 as supports.
Recently, polymers have also been used as supports for
fluorinating agents.8 Tetraalkylammonium salts are commonly
used as phase-transfer catalysts; however, tetrabutylammonium
fluoride (TBAF) and tetramethylammonium fluoride (TMAF)
are also effective in promoting fluorodenitration reactions, in
which a nitro group undergoes substitution by fluoride.9,10
One of the most extensively studied phase-transfer-catalyzed
solid-liquid HALEX reactions is the chlorination of n-hexyl
bromide by alkali metal chlorides in toluene with tetrabutylam-
moniun bromide as the phase-transfer catalyst.11-13 It has been
concluded that a ternary complex involving the solid ionophore,
the alkyl halide, and the phase-transfer catalyst is fundamental
to the mechanism.
Phase-transfer-catalyzed HALEX reactions of chlorinated
nitrobenzenes are less-well-understood. The reaction of 2,4-
dichloronitrobenzene (2,4-DCNB) in DMF under PTC condi-
tions2,5,14 has been studied carefully by several authors, but
nevertheless, the mechanism of the reaction remains open. In
particular, two mechanistic variations can be envisaged. First,
the organic molecule reacts at the solid surface2,5 in a truly
interfacial manner. Second, the KF may dissolve and the
fluorination take place homogeneously. Within the second limit,
two further possibilities exist as to whether the dissolution or
the homogeneous reaction is rate-limiting.
This complete mechanistic uncertainty prompted us to study
the HALEX reaction of a chloronitrobenzene with solid KF
under PTC conditions (Scheme 1). Specifically, the reaction of
2,4-dinitrochlorobenzene (2,4-DNCB) with potassium fluoride
in dimethylformamide was selected for study. Because of the
mesomeric effect of the para nitro group in the plane of the
aromatic ring, this substrate is much more activated to nucleo-
philic aromatic substitution than 2,4-DCNB, in which the
mesomeric effect of the nitro group is mitigated by the steric
effects of an ortho chlorine. Hence, relatively low temperatures
can be used to study the reaction. The product of this fluorination
reaction, 2,4-dinitrofluorobenzene (2,4-DNFB), is known as
Sanger’s reagent and has long been used as a reagent for labeling
terminal amino acid groups.15
* To whom correspondence should be addressed. Tel: 0044(0)-
186527540. Fax: 0044(0)1865275410. E-mail: richard.compton@
chemistry.ox.ac.uk.
10.1021/jp012612r CCC: $20.00 © 2001 American Chemical Society
Published on Web 11/22/2001

Reactions at Solid-Liquid Interfaces
J. Phys. Chem. B, Vol. 105, No. 50, 2001 12535
Previous kinetic investigations of HALEX reactions have
relied upon analyzing samples withdrawn from the reaction
vessel by methods such as gas chromatography. However, we
have employed a unique real-time electrochemical detection
methodology based upon the use of square wave voltammetry,16
a versatile electrochemical technique, which gives a peaked
response. The deconvolution of the responses due to all of the
voltammetrically visible components allows the evolution in
time of each of their concentrations so permits clear and
unambiguous mechanistic insight. The results presented show
that the kinetics of the HALEX reaction studied are mixed, the
site of reaction being in solution but the reaction occurring at
a rate influenced by the kinetics of fluoride dissolution. The
application of microelectrode techniques is fundamental to the
method because, by virtue of their reduced diffusional time scale,
they may outrun the kinetics of any chemical step following
electrochemical transformation. Purely electrochemical current
responses are thus obtainable. Chemical processes following the
electrochemical step may complicate the observed current
response at a macroelectrode. In heterogeneous systems, it has
been shown that microelectrode responses reflect the concentra-
tions of solution species local to the electrode.17-20 These local
concentrations may differ significantly from the bulk concentra-
tions in the same system. We demonstrate that ultrasonically
induced mixing facilitates the measurement of a microelectrode
response that accurately reflects bulk concentration in the
intrinsically heterogeneous system studied.
That ultrasound can enhance the rate of solid-liquid hetero-
geneous reactions operating under conditions of phase-transfer
catalysis is well-known;21 examples include N-alkylation of
amines in water,22 synthesis of benzyl sulfide from benzyl
chloride and sodium sulfide in nonaqueous solvents,23 and the
Michael reaction of ethyl malonate to chalcone in toluene.24
The chemical effects of ultrasound are generally seen in single
electron-transfer reactions involving the formation free radi-
cals;25 however, where an ionic mechanism is followed,
ultrasonically induced rate enhancements are generally due to
mechanical effects, most notably increased mass transport across
the solid-liquid interface through a diffusion layer thinned by
acoustic streaming effects.25 Cavitational effects can also
influence rate in solid-liquid systems through several mecha-
nisms: microstreaming of solvent jets can lead to fragmentation
of solid particles, increasing the area available for reaction;2
products and intermediates can be swept away rapidly from the
solid surface, thus renewing the surface for reaction.25
(Oxford Instruments, Oxford, U.K.). In all experiments, the
counter electrode was a Pt coil and the reference electrode was
a Ag wire pseudoreference. All three electrodes were immersed
directly into the solution being studied.
Power ultrasound of frequency 20 kHz was provided by a
Heat Systems Ultrasonics (Farmingdale, NY) W-380 ultrasonic
horn of diameter 13 mm. The horn tip was insulated via a
polytetrafluoroethylene ring and a Delrin screw connection. The
power output of the transducer has been calorimetrically
calibrated for each experimental configuration.27
The procedure used to gather kinetic data was as follows. A
five-necked 100 mL flask was oven-dried at 150 °C and cooled
under an argon (Pureshield, BOC) purge. The counter and
pseudoreference electrodes were fitted to the flask. The sup-
porting electrolyte (TBABF4) and KF were then added prior to
introduction of 50 mL of DMF through transfer lines under
nitrogen pressure. The solution was then degassed for 10 min
with argon. Upon conclusion of degassing the solution, the
ultrasonic horn was inserted through the central fifth neck;
Parafilm was used to seal the neck, while a flow of argon over
the solution ensured that no oxygen contacted the solution. The
solution was sonicated using an ultrasound power of 50 W cm-2
for 10 min to “activate” the KF. Sonication using intensities
between 20 and 200 W cm-2 has been shown to reduce the
average particle size2 of spray-dried KF from 100 to 30 µm.
Temperature control was most important, and care was taken
to ensure that all experiments were carried out at 85 ( 1 °C.
Three regimes were studied; in the first, in which magnetic
stirring was used to maintain the KF in suspension, water heated
to 85 ( 1 °C was circulated by pump from a waterbath to a
plastic beaker surrounding the cell. The two other regimes, in
which ultrasound intensities of 25 and 50 W cm-2 were
employed, required circulation of water at 76 and 65 °C,
respectively, to maintain the solution temperature at 85 ( 1
°C.
Once the solution temperature had stabilized in the presence
of the required stirring or ultrasonic agitation, a platinum
microdisk electrode was inserted and 1 mL of a freshly prepared
stock solution of 2,4-DNCB in DMF was charged using an
Eppendorf pipet to give a final concentration of 10 mM.
Simultaneously with the DNCB addition a data acquisition
program was initiated to gather square wave voltammetry
(SWV) traces at predetermined intervals for the duration of the
experiment. The SWV data were analyzed using the nonlinear
curve fitting function of Microcal Origin (Microcal Software
Inc., Northampton, MA) to yield reaction profiles. The com-
posite experimental traces were fitted using a simplex28 routine
to fit multiple Gaussian peaks of known width at half-height
and peak-to-peak separation.
2. Experimental Section
Tetrabutylammonium tetrafluoroborate (TBABF4, purum,
H2O < 2%), decamethyl ferrocene (dmFc), and N,N-dimethyl-
formamide (DMF, puriss., H2O e 0.01%) were obtained from
Fluka. Spray-dried potassium fluoride (KF), 2,4-dinitrochlo-
robenzene (2,4-DNCB, 99+%,), and 2,4-dinitrofluorobenzene
(2,4-DNFB, 99%) were obtained from Aldrich. All materials
were used as supplied with the exception of KF, which was
oven-dried at 120 °C for 2 h at atmospheric pressure.
Voltammetry was performed using an Autolab computer-
controlled PGSTAT 20 potentiostat (Ecochemie, Utrecht, Neth-
erlands). Platinum disk electrodes of diameter 7 mm and 25
µm were used for the preliminary voltammetry, while kinetic
measurements were performed using only the 25 µm platinum
disk. Working electrodes were polished sequentially with
aqueous slurries of alumina of particle size 3.0, 1.0, and 0.3
µm (Kemet) prior to use.26 Rotating disk measurements were
carried out using a standard rotating disk electrode rotator
The information gained from the deconvolution of the SWV
data was complemented by UV-vis absorption spectra recorded
using a Unicam UV2 Series UV-vis spectrophotometer (Uni-
cam, Cambridge, U.K.). Samples for analysis were withdrawn
from the reaction mixture, cooled to room temperature, and
diluted by a factor of 100 with DMF containing 0.1 M TBABF4
prior to measurement in a quartz cell of path length 1.0 cm. A
background of DMF containing 0.1 M TBABF4 was employed.
Care was taken not to include any KF particles in the aliquot.
3. Results
3.1. Preliminary Voltammetry. The electrochemical behav-
iors of the starting material, 2,4-DNCB, and product, 2,4-DNFB,
of the HALEX reaction were investigated at 25 ( 1 °C to select
a voltammetric technique capable of providing a reliable

12536 J. Phys. Chem. B, Vol. 105, No. 50, 2001
Macfie et al.
Figure 1. Cyclic voltammograms of 1.16 mM 2,4-DNCB with respect
to 0.97 mM dmFc (a) and 1.25 mM 2,4-DNFB with respect to 0.98
mM dmFc (b) in DMF/0.1 M TBABF4 recorded at a 7 mm diameter
Pt disk with a Pt coil counter electrode and a Ag pseudoreference
electrode at 25 °C.
Figure 2. Cyclic voltammograms of 1.16 mM 2,4-DNCB with respect
to 0.97 mM dmFc in DMF/0.1 M TBABF4 recorded at a 7 mm diameter
Pt disk with a Pt coil counter electrode and a Ag pseudoreference
electrode at 25 °C: potential scan rates 500 (a); 50 (b); 5 mV s-1 (c).
measurement of their solution concentrations. Solutions in the
concentration range of 1-10 mM of 2,4-DNCB or 2,4-DNFB
were prepared in DMF/0.1 M TBABF4 with or without the
addition of 1 mM dmFc. The latter served to “calibrate” the
pseudoreference electrode employed. First-scan cyclic voltam-
mograms were recorded using a voltage scan rate of 500 mV
s-1 in the potential range of +0.2 to -2.0 V vs Ag at a 7 mm
diameter Pt disk electrode. Steady-state cyclic voltammograms,
obtained after the first scan, were then measured using voltage
scan rates of 5-500 mV s-1 in the potential range of +0.2 to
-1.2 V vs Ag at a 7 mm diameter Pt disk electrode. Cyclic
voltammograms were then registered at a 25 µm Pt micro-
electrode using potential scan rates in the range of 200-0.5 V
s-1. Additionally, steady-state voltammograms were measured
at a 25 µm Pt microelectrode using a potential scan rate of
10 mV s-1
.
The macroelectrode voltammograms (Figure 1) resulting from
potential scans in the range of +0.2 to -2.0 V vs Ag showed
significant complexity, showing two consecutive reduction and
oxidation waves but with additional peaks. 2,4-DCNB gave
reduction peaks at -0.89 (shoulder), -0.99, -1.37, -1.52, and
-1.69 V and oxidation peaks at -1.49 (shoulder), -1.22, and
-0.73 V vs Ag pseudoreference. 2,4-DNFB exhibited reduction
peaks at -0.93, -1.08, -1.35, and -1.57 V and oxidation peaks
at -1.44, -1.20, and -0.78 V vs Ag pseudoreference. In both
cases, dmFc gave a reduction peak at -0.06 V and an oxidation
peak at +0.02 V. The voltammograms resulting from potential
scans in the range of +0.2 to -1.2 V vs Ag featured only the
first reduction wave for both 2,4-DNCB and 2,4-DNFB (Figures
2 and 3). The ratio of the forward and backward peaks for both
compounds was found to increase with decreasing scan rate.
The microelectrode voltammograms (Figures 4 and 5), however,
exhibited forward and backward peak height ratios equal to 1.00
( 0.05, indicating the formation of a stable radical anion capable
of undergoing complete reoxidation to the parent. A steady-
state response was observed at low scan rates indicating that
the lower time scale of diffusion outruns the kinetics of the
followup reaction, which caused an increase in the height of
the first reduction waves in the corresponding macroelectrode
experiments. The half-wave potentials of 2,4-DNCB and 2,4-
DNFB in DMF/0.1 M TBABF4 were determined to be -0.77
Figure 3. Cyclic voltammograms of 1.25 mM 2,4-DNFB with respect
to 0.98 mM dmFc in DMF/0.1 M TBABF4 recorded at a 7 mm diameter
Pt disk with a Pt coil counter electrode and a Ag pseudoreference
electrode at 25 °C: potential scan rates 500 (a); 50 (b); 5 mV s-1 (c).
and -0.83 V vs the dmFc|dmFc+ redox couple, respectively,
at 25 ( 1 °C.
The electrochemical behavior of 2,4-DNCB and 2,4-DNFB
in DMF/0.1 M TBABF4 has recently been investigated29 and
shown to be mechanistically complex. At voltage scan rates
above 20 V s-1, 2,4-DNCB exhibited behavior analogous to
that of 1,3-dinitrobenzene, that of two consecutive reversible
one-electron reductions with half-wave potentials of -0.88 and
-1.34 V vs SCE indicating formation of a stable radical dianion.
Below 20 V s-1, new reduction peaks at -1.51 and -1.63 V
vs SCE and a new oxidation peak at +0.68 V vs SCE were
observed. Additionally, the height of the first wave was found
to increase to more than one electron per mole. The authors

Reactions at Solid-Liquid Interfaces
J. Phys. Chem. B, Vol. 105, No. 50, 2001 12537
oxidation peak was observed at +0.71 V vs SCE, and the height
of the first reduction wave was found to increase. In this case,
the explanation involves dimerization of the radical anion from
the first reduction wave to form a Meisenheimer complex, which
is reduced at -0.87 and -1.06 V vs SCE; this explains the
increase in the first reduction wave. At potentials corresponding
to the second wave, the reduction wave for the undimerized
2,4-DNFB radical anion and two small reduction waves resulting
from two successive one-electron reductions from the product
formed by the loss of the fluoride anions from the doubly
reduced Meisenheimer complex were observed.
Excellent agreement exists between the data presented here
and that presented by Gallardo et al., noting that the reference
electrode employed in the latter study was an SCE, whereas a
Ag wire pseudoreference was used in this work. In the case of
2,4-DNCB, Gallardo found peaks corresponding to the first and
second reduction waves at -0.94 and -1.34 V and peaks
corresponding to the reduction of TNBP at -1.41 and -1.63
V; this current study found peaks corresponding to the first and
second reduction waves at -0.99 and -1.37 V and peaks
corresponding to the reduction of TNBP at -1.52 and -1.69
V; the presence of the additional shoulder at -0.87 V, which
does not appear in the former study, can be accounted for by
the fact that it is steady-state data rather than first-scan data
and as such will contain some 1,3-dinitrobenzene, the reduction
potential of which is given in ref 29 as -0.82 V. In the case of
2,4-DNFB, Gallardo found peaks corresponding to the first
reduction wave at -0.79, peaks corresponding to the reduction
of the Meisenheimer complex at -0.87 and -1.06 V, and peaks
corresponding to the reduction of the singly and doubly
defluorinated Meisenheimer complex at -1.35 and -1.56 V.
This current study found a peak corresponding to a composite
of the first reduction wave of 2,4-DNFB and the first reduction
wave of the Meisenheimer complex at -0.93 V, a peak
corresponding to the second reduction waves of the Meisenhe-
imer complex at -1.08, and peaks corresponding to the
reduction of the singly and doubly defluorinated Meisenheimer
complex at -1.35 and -1.57 V.
Figure 4. Cyclic voltammograms of 10.08 mM 2,4-DNCB in DMF/
0.1 M TBABF4 recorded at a 25 µm diameter Pt disk with a Pt coil
counter electrode and a Ag pseudoreference electrode at 25 °C at
potential scan rates of 150-0.5 V s-1
.
Last and importantly, comparison of the microelectrode data
presented in this current study with the macroelectrode data
presented in ref 29 demonstrates the utility of microelectrode
techniques for the voltammetric study of systems in which
chemical reaction follows an electrochemical step, because the
shorter time scale of the experiment ensures that the electro-
chemical transformation can be reversed prior to the chemical
step at lower scan rates than in the corresponding macroelectrode
experiment. Thus, purely electrochemical voltammetric re-
sponses can be obtained in the case of both 2,4-DNCB and 2,4-
DNFB by limiting the potential scan range and employing
microelectrode techniques.
3.2. Determination of Diffusion Coefficients. Diffusion
coefficients were first determined with microelectrode30 tech-
niques and subsequently confirmed by rotating disk methods.
From solutions of 2,4-DNCB and 2,4-DNFB with concentrations
of 10.02 and 10.25 mM, respectively, linear sweep voltammo-
grams were recorded at a 12.5 µm Pt disk electrode using a
potential scan rate of 10 mV s-1. The steady-state limiting
currents thus obtained are presented in Figure 6 and were treated
using the equation for the diffusion-limited current at a
microelectrode16
Figure 5. Cyclic voltammograms of 10.02 mM 2,4-DNFB in DMF/
0.1 M TBABF4 recorded at a 25 µm diameter Pt disk with a Pt coil
counter electrode and a Ag pseudoreference electrode at 25 °C at
potential scan rates of 200-0.5 V s-1
.
attributed the new reduction peaks to the reduction of 2,2′,4,4′-
tetranitrobiphenyl (TNBP) formed through dimerization of the
1,3-dinitrobenzene radical that results from cleavage of the
chlorine from 2,4-DNCB. Addition of water to the solution
prevented the appearance of the TNBP peaks, indicating that
hydrogen abstraction is the preferred pathway for the 1,3-
dinitrobenzene radical, TNBP being formed only after all of
the protons in the solution have been consumed. The electro-
chemical behavior of 2,4-DNFB was also found to depend on
voltage scan rate with two consecutive reversible one-electron
reductions indicating formation of a stable radical dianion. At
scan rates less than 1 V s-1, two additional reduction peaks
were observed at -1.35 and -1.56 V vs SCE, an additional
Ilim ) 4nFrDcbulk
(3.1)
to obtain diffusion coefficients. In the above equation Ilim is
the limiting current, n is the number of electrons transferred, F

12538 J. Phys. Chem. B, Vol. 105, No. 50, 2001
Macfie et al.
Figure 7. Square wave voltammograms for 9.33 mM 2,4-DNCB in
DMF/0.1 M TBABF4 (solid), composite signal obtained after addition
of 2,4-DNFB to give a concentration of 10.24 mM (dots), and 2,4-
DNFB signal obtained by subtracting the 2,4-DNCB signal from the
composite (dashes) recorded at a 25 µm diameter Pt disk with a Pt
coil counter electrode and a Ag pseudoreference electrode at 88 °C:
square wave amplitude 50 mV; frequency 50 Hz; step potential 5 mV.
Figure 6. Steady-state microelectrode voltammograms of 10.02 mM
2,4-DNCB (a) and 10.25 mM 2,4-DNFB (b) in DMF/0.1 M TBABF4
recorded on a 25 µm diameter Pt disk with a Pt coil counter electrode
and a Ag pseudoreference electrode at 25 °C at a potential scan rate of
10 mV s-1
.
is the Faraday constant, r is the electrode radius, D is the
diffusion coefficient, and cbulk is the bulk concentration. To
ensure accuracy, the area of the electrode was determined
electrochemically with a compound of known diffusion coef-
ficient. The diffusion coefficients of both 2,4-DNCB and 2,4-
DFNB were thus measured to be (0.9 ( 0.1) × 10-5 cm2 s-1 at
25 ( 1 °C.
To confirm these measurements, solutions of 2,4-DNCB and
2,4-DNFB with concentrations of1.16 and 1.25 mM, respec-
tively, were prepared, and steady-state hydrodynamic voltam-
mograms were recorded at a 7 mm Pt disk electrode rotating at
frequencies between 1 and 36 Hz. A voltage scan rate of 50
mV s-1 was used. The limiting currents thus obtained were
analyzed using the Levich equation for a rotating disk electrode31
-0.8 V vs Ag, the range in which the first reduction takes place
for both compounds without any electrode deactivation. Both
the resolution and the sensitivity are greatly enhanced in SWV
with respect to dc methods.33 A solution of 9.33 mM 2,4-DNCB
was prepared in DMF/0.1 M TBABF4 and heated to 88 °C with
ultrasound. SWV traces were recorded at a 12.5 µm Pt disk
electrode. The SWV pulse used had an amplitude of 50 mV, a
step potential of 5 mV, and a frequency of 50 Hz. A quantity
of pure 2,4-DNFB was then added by Eppendorf pipet to give
a solution concentration of 10.24 mM, and SWV traces were
recorded using the parameters detailed above. The 2,4-DNCB
signal was subtracted to give the contribution of 2,4-DNFB to
the mixture.
The results are presented in Figure 7; the peaks are substan-
tially overlayed, but when the individual component peaks are
resolved by subtracting the 2,4-DNCB signal from the composite
signal obtained after 2,4-DNFB addition, it can be seen that
both compounds give symmetrical, well-defined peaks. The
position of the 2,4-DNCB peak is -0.505 V vs Ag and that of
2,4-DNFB is -0.560 V, giving a peak-to-peak separation of
65 mV. Curve-fitting shows that at 88 ( 1 °C both peaks have
a width at half-height (W1/2) of 0.125 V.
3.4. Reaction Profiling via Square Wave Voltammetry.
In systems containing both 2,4-DNCB and KF in which the
HALEX fluorination was occurring, a large number of SWV
traces were gathered over the course of 2 h according to the
procedure outlined in the Experimental Section. Experiments
were carried out at 85 °C first in insonated conditions, in which
the KF was kept in suspension by ultrasound of intensity 25 W
cm-2. At the start of each experiment, immediately after the
addition of the 2,4-DNCB stock solution, the voltammetric
response was that of the starting material, 2,4-DNCB. As time
progressed, the peak reduced in height while broadening at the
negative side. As the reaction progressed further, broadening
was also observed at the positive side of the parent peak. A
further effect, which occurred at longer time, was the appearance
of a peak at more negative potential than the parent or the 2,4-
Ilim ) 0.62nFAcbulkD2/3ν -1/6ω1/2
(3.2)
to obtain diffusion coefficients. In the above equation, Ilim is
the limiting current, n is the number of electrons transferred, F
is the Faraday constant, A is the electrode area, cbulk is the bulk
concentration, D is the diffusion coefficient, ν is the kinemetic
viscosity of the solvent, and ω is the frequency of rotation. In
the case of 2,4-DNFB, a straight-line limiting current vs
(frequency)1/2 plot was obtained; from this, a value of (0.9 (
0.1) × 10-5 cm2 s-1 was inferred for the diffusion coefficient.
In the case of 2,4-DNCB, the limiting current vs (frequency)1/2
plot showed deviation from linearity at low frequencies,
indicating a coupled chemical step implicated in measurements
at the macroelectrode, and this precluded any inference of the
diffusion coefficient.
The two independent measures of the diffusion coefficient
of 2,4-DNFB are in excellent agreement. The value obtained
for the diffusion coefficient of 2,4-DNCB by the microelectrode
method is in excellent agreement with that calculated using the
Wilke-Chang equation,32 (1.0 ( 0.1) × 10-5 cm2 s-1
.
3.3. Square Wave Voltammetry. Square wave voltammetry
(SWV) was used to obtain a peaked voltammetric response for
both 2,4-DNCB and 2,4-DNFB in the potential range of 0 to

Reactions at Solid-Liquid Interfaces
J. Phys. Chem. B, Vol. 105, No. 50, 2001 12539
time, was the appearance of a peak at more negative potential
than the parent or the 2,4-DNFB peak. The appearance of this
peak was accompanied by a reduction in the height of the
composite peak comprising the voltammetric responses of the
parent, 2,4-DNFB, and the third peak.
A series of representative experimental SWV traces obtained
at various time intervals from the same solution are shown in
Figure 9. The features discussed above are illustrated; the solid
line represents the experimental data, the dashed line represents
the fit of the experimental data obtained by deconvolution, and
the dotted lines represent the individual responses that make
up the fit. By measuring the height of the individual component
peaks, the relative contributions of the corresponding species
to the voltammetric response could be assessed as a function
of time, allowing the construction of a “reaction profile”, a
representative example of which is depicted in Figure 10.
Valuable mechanistic insights can be obtained through the
careful interpretation of these reaction profiles, to which we
return below.
3.5. Variation of Substrate Concentration. An experiment
was performed to probe the effect of 2,4-DNCB concentration
on the observed reaction profile during ultrasonic irradiation at
intensity 25 W cm-2; apart from the reduced substrate concen-
tration, the conditions were as described above. The amount of
KF added was 2 g. The general form of the reaction profile
obtained was analogous to that depicted in Figure 10. The 2,4-
DNCB disappearance data is shown in Figure 11 along with
that obtained using the higher substrate concentration of 10 mM.
Initially, the consumption is fast with over 95% of the substrate
being consumed in the first 1500 s of the reaction. Little
consumption was observed subsequently. The “titration” effect
observed in this experiment provides a rough estimate of the
initial fluoride ion concentration as will be discussed more fully
in the discussion section.
Figure 8. Fitting of a square wave voltammogram simulated according
to the procedure in ref 34 (dots) with a Gaussian peak (solid): R2 )
0.99981.
DNFB peak. The appearance of this peak was accompanied by
a reduction in the height of the composite peak comprising the
voltammetric responses of the parent, 2,4-DNFB, and the third
peak. These processes are illustrated in Figure 9.
The data thus obtained were analyzed by deconvolution to
resolve the contributions of the individual components, allowing
the generation of reaction profiles. Four experiments were
carried out in which the amount of KF added was increased
from 1 to 8 g. This approach was then applied to a more
intensely sonicated system employing ultrasound at 50 W cm-2
and finally to a “silent” system in which the KF was kept in
suspension by mechanical agitation provided by a magnetic
stirrer bar.
3.4.1. Characteristics and Modeling of the SWV Response
and Reaction Profiles. We next consider the evolution of the
SWV response at a typical HALEX reaction. At the start of
each experiment, immediately after the addition of the 2,4-
DNCB stock solution, the voltammetric response was that of
the starting material, 2,4-DNCB and the data approximated to
a high degree of accuracy with a single Gaussian peak of W1/2
) 0.125 V. Figure 8 shows a SWV peak simulated according
to the procedure detailed in ref 34 and the corresponding
Gaussian fit (R2 ) 0.999 81). As time progressed, the peak
reduced in height while broadening at the negative side,
indicating that the 2,4-DNCB initially present was being
converted into another species with a more negative reduction
potential. It was found that the best fit was obtained with two
peaks of W1/2 ) 0.125 V separated by 65 mV.
As the reaction progressed further, the experimental SWV
response could no longer be fitted with these two peaks and
the addition of a further peak, this time positive in potential
from the parent compound, was required to obtain a good fit.
Because the peak width of a Nernstian SWV peak is determined
only by the amplitude of the square wave and the temperature,35
a new peak also of width 0.125 V was required. Initially, the
potential of this peak was allowed to “float” during the iterative
process; the best fit across the entire range of time-resolved
experimental composite traces was found to be given when this
third peak was located 120 mV positive in potential from the
parent compound. A further effect, which occurred at longer
3.6. Sonication of Solutions of 2,4-DNCB and 2,4-DNFB
in the Absence of KF. Solutions at a concentration of 10 mM
of both 2,4-DNCB and 2,4-DNFB were prepared in DMF/0.1
M TBABF4. The solutions were degassed with argon prior to
sonication using an intensity of 50 W cm-2 for a period of 2 h
during which the temperature was maintained at 85 ( 1 °C by
circulation of hot water. SWV traces were recorded every 15
min. The measured response was found to be unchanged in both
cases, suggesting that neither the substrate employed or the
intended product are susceptible to sonochemically induced
reaction pathways in the reaction medium employed.
3.7. Sonication of 2,4-DNFB in the Presence of KF. Two
grams of solid KF was added to a solution of 0.1 M TBABF4
in DMF; the solution was sonicated using an intensity of 50 W
cm-2 for 10 min. The ultrasound intensity was then reduced to
25 W cm-2, and a quantity of 2,4-DNFB liquid was added by
pipet to give a solution concentration of 10.0 mM. The solution
was sonicated for 2 h, and SWV traces were gathered at regular
intervals throughout.
Some broadening was observed on the positive side of the
peak, and over time the height of the 2,4-DNFB peak was
reduced by half, accompanied by the growth of a peak more
negative in potential. The likely identity of this peak and the
processes underlying its appearance are discussed below.
3.8 UV-Vis Data. Immediately upon addition of 2,4-DNCB
stock solution to the presonicated suspension of KF in DMF/
0.1 M TBABF4, a color change was observed from clear to
yellow. This yellow deepened to orange/red within 3-5 min
of substrate addition; some further color change was discernible

12540 J. Phys. Chem. B, Vol. 105, No. 50, 2001
Macfie et al.
Figure 9. Square wave voltammograms obtained during the course of a typical HALEX reaction of 10 mM 2,4-DNCB with 2 g of KF in DMF
0.1 M/TBABF4 at 85 °C: experimental data (solid); fit (dashed); contributions of individual components (dots). An ultrasound intensity of 50 W
cm-2 was employed.
Figure 11. Decline of the current response for 2,4-DNCB during
HALEX reaction with 2 g of KF in DMF 0.1 M/TBABF4 at 85 °C. An
ultrasound intensity of 25 W cm-2 was employed. Starting concentra-
tions of 2,4-DNCB were 3 mM (O) and 10 mM (0).
Figure 10. Reaction profile for the HALEX reaction of 10 mM 2,4-
DNCB with 2 g of KF in DMF 0.1 M/TBABF4 at 85 °C obtained
through deconvolution of experimental SWV signal into individual
components. An ultrasound intensity of 50 W cm-2 was employed:
(a) 2,4-DNCB; (b) 2,4-DNFB; (c) “component 3”; (d) “component 4”.
The observed absorption bands are consistent with the
formation of the Meisenheimer complex [F-2,4-DNCB]- as
reported by Clark,36 who observed absorption bands at 374 and
430 nm when solutions of 2,4-DNCB in various solvents were
exposed to both homogeneous and heterogeneous sources of
fluoride ion. This intermediate is shown, together with some of
its major valence bond structures, in Scheme 2. From the data
presented in ref 36, the extinction coefficient of [F-2,4-DNCB]-
was estimated as 87 500 M-1 cm-1, allowing the solution
concentration of [F-2,4-DNCB]- to be calculated from the
by eye. To assess qualitatively this effect, samples were
withdrawn from the reaction liquor at regular intervals and their
absorption spectra were recorded after appropriate dilution. The
effect of varying the added mass of KF was investigated in a
series of experiments in which the higher ultrasound intensity
of 50 W cm-2 was employed. Two absorption maxima of
approximately equal height were observed at wavelengths of
375 and 430 nm, and the height of both peaks increased with
time.

Reactions at Solid-Liquid Interfaces
J. Phys. Chem. B, Vol. 105, No. 50, 2001 12541
in solution; hence, the second, slower phase of consumption
was not observed.
4.3. Modeling the Disappearance of 2,4-DNCB. To examine
the effect of coupled homogeneous and heterogeneous kinetics
on the reaction profile, the following rate equations were
considered: The first describes consumption of 2,4-DNCB by
homogeneous reaction with fluoride according to the second-
order rate constant khom
.
dA
dt
) -khomAB
(4.1)
where A is the concentration of 2,4-DNCB and B is the
concentration of fluoride ion. The second describes consumption
of fluoride ion by the homogeneous reaction above and
production of fluoride ion by dissolution of KF, a process
described by the Noyes-Whitney equation,37
dB
dt
) -khomAB + KL(Bsat - B)
(4.2)
where Bsat is the saturation concentration of fluoride ion and
KL is an effective mass transport coefficient defined as
Figure 12. Concentration of the fluoro-Meisenheimer complex of 10
mM 2,4-DNCB present in solution as determined by UV-vis spec-
troscopy during the HALEX reaction of 2,4-DNCB with varying
amounts of KF in DMF/0.1 M TBABF4 at 85 °C. An ultrasound
intensity of 50 W cm-2 was employed.
kLa
V
Da
δV
KL )
)
(4.3)
where kL is the mass transport coefficient, a is the surface area
of dissolving solid, V is the volume of the solution, D is the
diffusion coefficient, and δ is the diffusion layer thickness. We
desire a solution for A(t) and B(t), the time-dependent concen-
trations of F- and 2,4-DNCB, respectively, given eqs 4.1 and
4.2 above. We choose a fully implicit finite difference method
with Richtmyer modification (FIRM algorithm) as reported by
Feldberg38,39 to solve the defined problem.
SCHEME 2
The approximate solutions for A(t) and B(t) at times tm will
be labeled Am and Bm. Also, because the flux of A and B is
dominated by the second-order decay process (dA/dt and dB/dt
are greatest at t ) 0), we use a time function, tm, where the
time step increases geometrically to increase simulation speed:
absorption at 375 nm. Thus, Figure 12 shows the time evolution
of [F-2,4-DNCB]- concentration in the presence of various
quantities of KF; the concentration increases with time up to a
value of 1.4 mM.
4. Discussion
∆tm ) ∆t0γm-1 ) tm - tm-1
m ) 1, 2,..., M
(4.4)
4.1 Explanation of Approach. In the kinetic treatment that
follows, we confine our discussion to 2,4-DNCB disappearance
because it is the consumption of 2,4-DNCB in the heterogeneous
reaction that is of interest in determining the nature of the
interfacial mechanism in operation. While the voltammetric
response indicates the formation of products other than the
intended halogen exchange product, the isolation of these
products is beyond the scope of the current investigation. The
likely identity of these species is discussed below. We initially
limit our discussion to the reaction profiles obtained with an
The mathematical derivation of this method is treated rigorously
by Feldberg et al.39 in previous literature. The time derivative
of A is evaluated with the Richtmyer modification as
a2,A
b2,A + R1Am+1
(∂tm/∂j)m+1/2
dA
dt m+1/2
≈
)
(4.5)
(
)
(∂tm/∂j)m+1/2
where
j)jlevel
ultrasound intensity of 25 W cm-2
.
a2,A
)
)
RjAm+2-j
∑
4.2. Implications of the Observed DNCB Disappearance
Behavior. In all experiments employing 10 mM of substrate,
the main feature of the reaction profile is an initial rapid
disappearance of 2,4-DNCB over the first few hundred seconds
followed by a far slower decrease at longer time. However, when
the lower starting concentration of substrate of 3.0 mM was
employed, all material was consumed rapidly (Figure 11),
suggesting that the observed behavior could be accounted for
by an initial phase of reaction with preexisting homogeneous
fluoride anion followed by a phase in which the only available
mechanism for 2,4-DNCB disappearance is reaction with
fluoride ion following dissolution of solid KF. In the 3.0 mM
experiment, all of the substrate reacted with fluoride ion already
j)1
j)jlevel
b2,A
RjAm+2-j
∑
j)2
and Rj are a set of Richtmyer coefficients, specific to the number
of concentration values used in the approximation, jlevel. The
differential (∂tm/∂j)m+1/2 for our chosen expanding time function
is
∆t ln(γ)γm+1/2
(∂tm/∂j)m+1/2 ) -
(4.6)
γ - 1

12542 J. Phys. Chem. B, Vol. 105, No. 50, 2001
Substitution of eq 4.3 into eq 4.4 yields
dB dA
Macfie et al.
TABLE 1: Results of Simulation for the HALEX Reaction
of 10 mM 2,4-DNCB with 2 g of KF in DMF/0.1 M TBABF4
at 85 °Ca
)
+ KL(Bsat - B)
(4.7)
khom, mol-1
dt
dt
[KF], g
cm3 s-1
KL, s-1
Bsat, mM
MAD, mM
The fully implicit discretized form of eqs 4.1 and 4.5 become
1
2
5
8
385
830
566
776
2.50 × 10-5 5.99 × 10-6 5.61 × 10-7
3.45 × 10-5 6.40 × 10-6 5.93 × 10-7
7.30 × 10-5 6.63 × 10-6 3.96 × 10-7
9.55 × 10-5 6.93 × 10-6 2.95 × 10-7
b2,A + R1A
m+1 ) -khomAm+1Bm+1
(4.8)
(4.9)
(∂tm/∂j)m+1/2
a An ultrasound intensity of 25 W cm-2 was employed.
and
calculated values of the concentration solution A(t) at the
experimental time point ti. In practice, linear interpolation was
used to determine the value of Atheory(ti) given ti and a vector of
solutions, Am. The algorithm used to search the three-
dimensional variable space for a minimum in MAD was the
downhill simplex method.28 This algorithm uses a selection of
transformations on an n-dimensional simplex formed from n +
b2,B + R1Bm+1 b2,A + R1A
)
m+1 + KL(Bsat - Bm+1
)
(∂tm/∂j)m+1/2
(∂tm/∂j)m+1/2
Substituting the isolated solution for Bm+1 from eq 4.7
R1Am+1 + b2,A
Bm+1 ) -
(4.10)
1 search vectors (kfi, KL , Bsati, i ) 1,..., n + 1). When the
i
khom(∂tm/∂j)m+1/2Am+1
fractional difference between the highest and lowest function
values of the simplex drops below a predefined tolerance ftol,
the search vector yielding the lowest function value is considered
optimum and the algorithm terminates. It is best to restart the
algorithm at this position to verify that the minimum is global
and not local.
4.5.2. Results. Initial results were gathered for the four
experiments in which sonication at a level of 25 W cm-2 was
employed. The initial concentration of 2,4-DNCB was 10 mM,
and the weights of added KF were 1, 2, 5, and 8 g.
into eq 4.8 results in a solvable quadratic equation in Am+1
.
0 ) Am+12(-R1) + Am+1 b2,B - b2,A - KL(∂tm/∂j)m+1/2Bsat
-
(
R1(R1 + KL(∂tm/∂j)m+1/2
)
-
)
khom(∂tm/∂j)m+1/2
b2,A
(R1 + KL(∂tm/∂j)m+1/2) (4.11)
khom(∂tm/∂j)m+1/2
The optimum values found by the simplex method are
tabulated in Table 1, while plots of the corresponding fit between
experimental and theoretical data are shown Figure 13. As can
be seen from the data, optimized Bsat and khom values are
consistent across experiments. The mean value for the homo-
geneous rate constant for the reaction of 2,4-DNCB with fluoride
ion is 640 ( 250 mol-1 cm3 s-1, and the mean value for the
saturation concentration of fluoride ion is (6.5 ( 0.5) × 10-6
Equations 4.10 and 4.11 specify an iterative method for the
solutions Am+1 and Bm+1. The startup protocol involves setting
A0 ) A-1 ) A-2 ... ) A2-j and B0 ) B-1 ) B-2 ... ) B2-j
.
level
level
The use of an expanding time step, several Richtmyer levels,
and fully implicit formulation of the problem allows an iterative
solution of high accuracy to be computed quickly on contem-
porary computers. This allows the analysis of the experimental
data to be achieved with an appropriate multidimensional
function minimization algorithm, rather than a working (hyper)-
surface interpolation method.40,41
mol cm-3
.
The consistency of the homogeneous rate constants provides
strong evidence that homogeneous reaction with preexisting
fluoride ion is the initial mechanism for 2,4-DNCB disappear-
ance. Furthermore, this mechanism is in operation across the
entire range of solid-liquid compositions studied.
4.4. Computation. The data analysis (Simplex method) and
visualization were written for and performed using IDL 5.042
on a Silicon Graphics Indigo 2 workstation. The solution to
eqs 4.10 and 4.11 was written in C++ as an external program,
which was then called from IDL using the SPAWN function.
The values obtained for the saturated fluoride ion concentra-
tion are independent of the amount of solid KF initially present.
This provides compelling evidence that the 10 min presonication
period does indeed saturate the solution with fluoride ion and
that the method employed gives a consistent and accurate
indirect measure of the solution fluoride concentration.
The KL values exhibit a linear trend with added KF (Figure
14). KL is a composite of the mass-transfer coefficient and the
ratio of the KF surface area to reactor volume. Because the value
of the mass-transfer coefficient is determined by the operative
convective regime and the diffusion coefficient of the species
being transferred, it would be expected to be constant for a given
chemical species and ultrasound intensity. The surface area of
KF available for dissolution is directly proportional to the mass
of KF; hence, the observed linear increase in rate with increasing
solid-liquid ratio demonstrates that the reaction rate is dis-
solution-rate-limited at long time, although, of course, the site
of the chemical reaction remains homogeneous.
In all simulations, the following parameters were used: jlevel
)
.
6; γ ) 1.005; ∆t0 ) 4.0 s; M ) 500; B0 ) 10-5, ftol ) 10-4
4.5 Analysis. 4.5.1. Method. Inspection of the kinetic eqs
4.1 and 4.2 shows that the solutions, A(t) and B(t), are functions
of the variables, khom, KL, B0, A0, and Bsat. The experimental
setup demands that A0 takes a known value. Also to simplify
the system, by setting B0 ) Bsat, which is a reasonable
assumption because all solutions were sonicated for 10 min at
reaction temperature prior to substrate addition, we reduce the
multidimensional search to three variables. The search involves
locating the global minimum in the error between experimental
and numerically calculated values of A(t). The error calculated
as the mean absolute deviation (MAD) is formally defined as
n
1
MAD )
|Aexp(ti) - Atheory(ti)|
(4.12)
∑
4.6. Ultrasound Effects. The above discussion clearly
demonstrates the physical meaning of the observed concentration
profiles in terms of coupled homogeneous and heterogeneous
kinetics, showing how the experimental data could be accounted
ni ) 1
where n is the number of points in the experimental data set
and Aexp(ti) and Atheory(ti) are the experimentally and theoretically

Reactions at Solid-Liquid Interfaces
J. Phys. Chem. B, Vol. 105, No. 50, 2001 12543
Figure 13. Comparison of experimentally measured (O) and modeled (solid line) 2,4-DNCB concentration profiles for the HALEX reaction of 10
mM 2,4-DNCB with varying amounts of KF in DMF/0.1 M TBABF4 at 85 °C. The modeled fluoride ion concentration is also shown (dotted line).
An ultrasound intensity of 25 W cm-2 was employed. Amounts of KF were (a) 1 g, (b) 2 g, (c) 5 g, and (d) 8 g.
for in all cases using the same homogeneous rate constant and
the saturated fluoride ion concentration while allowing the KL
term to vary. The KL term was found to scale linearly with the
mass of KF added to the system (Figure 14), implying that a
dissolution rate constant could be estimated using eq 4.3;
however, in practice, the actual surface area of KF is unknown.
When the higher ultrasound intensity of 50 W cm-2 was utilized,
the results were in good agreement with those obtained using
promoting the dissolution of KF, a conclusion which may at
first seem counterintuitive and at odds with a previous study in
which the flux of material from an insonated disk of solid
material was found to increase slightly with increasing ultra-
sound intensity.43 It is, however, readily explicable when the
experimental configuration is carefully considered. The primary
function of the ultrasonic irradiation in this current study is to
keep the KF particles suspended; they circulate around the
reaction vessel and as such are only exposed periodically to
the regime of high-intensity cavitation and consequent micro-
jetting, which occurs only immediately adjacent to the horn tip.
Hence, mass transport from the solid surface to bulk solution
occurs not through the intensely thinned diffusion layer of a
directly insonated disk but through a much larger diffusion layer,
primarily enforced by the shear forces exerted by the particle
as it moves through the solution and through bulk convection.
the lower ultrasound intensity of 25 W cm-2
.
Two conclusions can be drawn from comparison of the 2,4-
DNCB disappearance profiles obtained using different levels
of ultrasonic irradiation: First, as demonstrated by the agreement
between the data obtained using 50 W cm-2 and that obtained
using 25 W cm-2, there is no significant effect of ultrasound in
accelerating the disappearance of 2,4-DNCB. From this it
follows that there is no significant effect of ultrasound in

12544 J. Phys. Chem. B, Vol. 105, No. 50, 2001
Macfie et al.
is desired to obtain meaningful and representative measurements
using microelectrode techniques.
Recent investigations into the mechanism of heterogeneous
HALEX reactions have focused on the fluorination of 2,4-
dichloronitrobenzene using solid KF and have yielded contra-
dictory conclusions. We now consider this contradiction in the
light of the results of our current investigation into 2,4-DNCB.
Study of the reaction using a dispersed powder reactor14 over a
wide concentration range found that the observed rate could be
homogeneous-reaction-rate-limited, dissolution-rate-limited, or
operating in a mixed kinetic regime in which both processes
have an influence on the observed rate. An expression was
derived that was identical to that resulting from our own
treatment under the assumption of steady-state conditions (dB/
dt ) 0):
VBsat
q )
(4.13)
1
V
kLa
+
khom
A
where q is the observed rate in mol s-1 and V is the reactor
volume. Importantly, this current study applies also to non-
steady-state conditions and provides an indirect measurement
of the time-dependent actual fluoride concentration.
Figure 14. Simulated effective mass transfer coefficient, KL, for the
dissolution of KF into DMF/0.1 M TBABF4 at 85 °C as a function of
the initial mass of KF. An ultrasound intensity of 25 W cm-2 was
employed.
Other studies have concluded that the fluorination of 2,4-
dichloronitrobenzene using solid KF is a true surface reaction,
the rate of which is limited by the formation of a surface
complex. Smyth5 considers both the phase-transfer mechanism,
in which the reaction occurs homogeneously following dissolu-
tion of KF, and the interfacial mechanism, in which the rate-
determining step is a complex formed on the solid surface; the
phase-transfer mechanism in this case is dismissed because of
the calculation of a large Hammett reaction constant (F ) +6.4)
and the observation that the rate of disappearance of the starting
material is proportional to the stirring speed. The fluorination
of 2,4-dichloronitrobenzene proceeds via two competing mech-
anisms; ortho- followed by para-substitution is favored, but para-
followed by ortho-substitution is a competing pathway to the
difluorinated product (Scheme 3). Langlois et al.2 consider the
observed relative rates of ortho- and para-substitution in both
the first and second fluorination step (k11/k12 and k22/k21,
respectively) and the fact that they depend on the source of the
KF before concluding that homogeneous reaction must be ruled
out, favoring instead the mechanism proposed by Sasson44 for
the heterogeneous fluorination of n-octyl chloride, in which the
reaction proceeds in a border phase at the solid-liquid interface
consisting mostly of solvent but with a higher concentration of
phase-transfer catalyst than that found in bulk solution.
The results of our current study provide compelling evidence
for homogeneous reaction following dissolution of KF; indeed,
it is even possible to discern the point at which kinetic control
switches from homogeneous reaction to dissolution-rate-limited
reaction and hence to provide an elegant extension of the
treatment presented in ref 14. It should however be noted that
the results of Smyth and Langlois are not necessarily inconsistent
with those presented here, because the observation that reaction
rate is proportional to stirring speed does not necessarily imply
that the reaction is occurring at an interface; a homogeneous
reaction limited by dissolution rate of one or more reactants
would display the same behavior. The observation of the large
Hammett reaction constant shows that the rate is strongly
influenced by substituent effects; this was interpreted as proof
that KF dissolution was not the rate-determining step; however,
a large Hammett reaction constant is exactly what would be
SCHEME 3
Hence, there is no significant effect of ultrasound intensity on
solid dissolution rates in a dispersed system.
The second conclusion that can be drawn is a more general
conclusion relating to the applicability of microelectrode detec-
tion techniques to heterogeneous systems. By virtue of their
small size, microelectrodes sample a very small volume of
solution. In truly homogeneous solutions, this yields a true
measure of bulk solution concentration. In heterogeneous
systems, however, the composition of the small volume sampled,
and hence the current response, may differ substantially depend-
ing on the precise location of the electrode. Microelectrodes
have been successfully applied to the in situ measurement of
trace elements in sediment porewater,17 local oxygen concentra-
tions in clay soils18 and biofilms,19 and mixing-induced hetero-
geneities in continuously stirred tank reactors.20 In an intrinsi-
cally heterogeneous system, such as the subject of this current
study, the observed microelectrode response is strongly de-
pendent on the solution conditions local to the electrode, as is
clearly demonstrated by the highly scattered and nonsystematic
results obtained in the mechanically stirred case. Indeed, that
systematic and reproducible results were obtained in the
experiments in which ultrasonically induced mixing was em-
ployed is a strong argument for the application of power
ultrasound to intrinsically heterogeneous systems in which it

Reactions at Solid-Liquid Interfaces
J. Phys. Chem. B, Vol. 105, No. 50, 2001 12545
plausible as a fluorinated nitroalkane would be expected to have
a more positive reduction potential than the fluorinated nitroaro-
matic from which it was formed. We speculate that the fourth
peak, centered around -0.7 V vs Ag, is the product of this
fluorodenitration reaction, 3,4-difluoronitrobenzene (D). There
are no data in the literature concerning the reduction potential
of this compound, but it might reasonably be expected to be
more negative in potential than the monofluorinated compound
from which it was formed. The only species unaccounted for
in the proposed scheme is the Meisenheimer complex [F-2,4-
DNCB]-, which we suggest might likely be voltammetrically
invisible in the potential scan range studied.
5. Conclusions
The HALEX reaction of 2,4-dichloronitrobenzene with potas-
sium fluoride in the presence of tetrabutylammonium salts in
dimethylformamide has been studied employing an electro-
chemical detection methodology based upon the use of square
wave voltammetry. The problem of overlapping signals was
resolved by curve fitting. The results presented show that the
kinetics of the HALEX reaction studied exhibit diverse kinetic
behavior under different conditions, behaving on one hand as a
dissolution-rate-controlled process and on the other as a
homogeneous chemical process. The experiment presented here
is unusual in that both regimes are visible in the same
experiment: initially homogeneous reaction dominates the
observed kinetics as the presaturated solution is stripped of
fluoride ion; at longer time, the observed kinetics are controlled
by the rate of KF dissolution. Ultrasound was found not to
significantly enhance the rate of the reaction in the intensity
range studied.
The theory used to interpret the experimental results is in
principle applicable to all chemical systems involving mixed
kinetic regimes. Furthermore, the utility of microelectrodes for
obtaining simple quantifiable voltammetric responses from
compounds of which the macroelectrode responses are com-
plicated by chemical followup steps has been demonstrated.
Ultrasonically induced mixing has been shown to facilitate
reproducible microelectrode responses in intrinsically hetero-
geneous systems.
Figure 15. Proposed scheme for the fluorination of 2,4-dinitrochlo-
robenzene. The voltammetrically visible species are denoted A, B, C,
and D.
anticipated when the reaction occurs homogeneously following
KF dissolution. Furthermore, perusal of the data presented in
ref 2 shows that the ratios k11/k12 and k22/k21 vary with the source
of KF and the presence of phase-transfer catalysts. However,
the variation is surprisingly small (k11/k12 ) 2.9 (SD ) 0.5)
and k22/k21 ) 1.0 (SD ) 0.5) (n ) 10)) and hence probably
argues in favor of the homogeneous-reaction hypothesis.
The observation by UV-vis spectroscopy of the Meisenhe-
imer complex [F-2,4-DNCB]- in solution adds yet more weight
to the hypothesis of homogeneous reaction. If any ternary
complex was formed on the surface between the tetrabutylam-
monium cation, the substrate, and the ionic solid, it would
remain there until the fluorinated product was formed, rather
than desorbing as an intermediate complex. This observation is
highly relevant as it confirms that the reaction does indeed
proceed via a two-step mechanism with a Meisenheimer
intermediate; it has been postulated that 2,4-DNCB may react
with other nucleophiles via a multistep mechanism within the
solvent cage that has as its first step a single electron transfer
between the reactants.45
From the analysis above, it is clear that the mechanistic
interrogation of systems in which the overall kinetics are
determined by both dissolution and homogeneous reaction, such
as the heterogeneous HALEX reaction considered here, presents
a significant challenge. This is because the same system can
exhibit diverse kinetic behavior under different conditions,
behaving on one hand as a dissolution-rate-controlled process
and on the other as a homogeneous chemical process as
described in ref 14. The experiment presented here is unusual
in that both regimes are visible in the same experiment: initially,
homogeneous reaction dominates the observed kinetics as the
presaturated solution is stripped of fluoride ion; at longer time,
the observed kinetics are controlled by the rate of KF dissolution.
4.7. Assignment of SWV Peaks. Although only the 2,4-
DNCB data have been used in the analysis for reasons stated
above, the appearance and position of the other peaks can be
rationalized according to the scheme presented in Figure 15.
The initial peak can unquestionably be assigned to 2,4-DNCB
(A), and the fact that the disappearance of this peak is
accompanied by the growth of a peak at a potential correspond-
ing to 2,4-DNFB (B) makes the assignment of this peak definite.
Furthermore, we speculate that the third peak, occurring 120
mV positive in potential of 2,4-DNCB could be attributed to
the Meisenheimer intermediate of a second fluorination step (C),
in this case a fluorodenitration as described by Clark.6 This is
Acknowledgment. We thank the EPSRC for support for
G.M. and B.A.B. and Avecia for funding through a CASE
studentship for G.M.
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