Combining in situ FTIR spectroscopy, BTEM analysis, bulk density measurements and DFT for two Diels-Alder reactions. A general approach for partial molar volume and reaction volume analyses

Article abstract of DOI:10.1039/c3ra47057a

Two organic reactions, namely the reaction of cyclopentadiene (CPD) and dimethyl acetylene dicarboxylate (DMAD) and the dimerization reaction of CPD were conducted in toluene at 298.1 K at atmospheric pressure and measured by in situ FTIR spectroscopy. Band-target entropy minimization (BTEM) analyses were employed for obtaining the pure component spectra of the solutes and their corresponding concentrations. The solute concentrations and the bulk density data were used to evaluate the partial molar volumes of the solute constituents. The partial molar volumes evaluated from this multi-component approach were in good agreement with those determined from independent binary solution measurements. The corresponding volumes of reaction for the CPD + DMAD and dimerization CPD + CPD reactions were determined to be -37 ± 3 cm ³ mol^-1 and -31 ± 2 cm³ mol ^-1, respectively. For completeness, DFT calculations were performed and used to rationalize the vibration modes corresponding to the BTEM spectral estimates as well as to provide predictions of the molar volumes of the solutes. The present study demonstrates the usefulness of a combined spectroscopic, signal processing, bulk density measurement and DFT approach to the determination of partial molar volumes and volumes of reaction directly from the multi-component reactive systems. This journal is the Partner Organisations 2014.

Full text of DOI:10.1039/c3ra47057a

RSC Advances
View Article Online
View Journal | View Issue
PAPER
Combining in situ FTIR spectroscopy, BTEM
analysis, bulk density measurements and DFT for
two Diels–Alder reactions. A general approach for
partial molar volume and reaction volume
analyses†
Cite this: RSC Adv., 2014, 4, 22194
A. Martin Tjahjono,* Gao Feng, Martin Wijaya Hermanto, Foo Cechao
and Marc Garland*
Two organic reactions, namely the reaction of cyclopentadiene (CPD) and dimethyl acetylene dicarboxylate
(DMAD) and the dimerization reaction of CPD were conducted in toluene at 298.1 K at atmospheric
pressure and measured by in situ FTIR spectroscopy. Band-target entropy minimization (BTEM) analyses
were employed for obtaining the pure component spectra of the solutes and their corresponding
concentrations. The solute concentrations and the bulk density data were used to evaluate the partial
molar volumes of the solute constituents. The partial molar volumes evaluated from this multi-
component approach were in good agreement with those determined from independent binary solution
measurements. The corresponding volumes of reaction for the CPD + DMAD and dimerization CPD +
3
ꢀ1
3
ꢀ1
CPD reactions were determined to be ꢀ37 ꢁ 3 cm mol and ꢀ31 ꢁ 2 cm mol , respectively. For
completeness, DFT calculations were performed and used to rationalize the vibration modes
corresponding to the BTEM spectral estimates as well as to provide predictions of the molar volumes of
the solutes. The present study demonstrates the usefulness of a combined spectroscopic, signal
processing, bulk density measurement and DFT approach to the determination of partial molar volumes
and volumes of reaction directly from the multi-component reactive systems.
Received 26th November 2013
Accepted 6th May 2014
DOI: 10.1039/c3ra47057a
www.rsc.org/advances
The volume of reaction can be experimentally determined in
three different ways, namely (i) from the pressure dependence
Introduction
8
The partial molar volume (PMV) has been a subject of interest in of the equilibrium constant, (ii) from direct measurement of the
1
–7
both theoretical and experimental studies for decades. As one volume change of reactants and products employing dilatom-
of the most investigated physico-chemical properties, PMV etry, and (iii) from the measurements of partial molar volumes
gives information on the molecular size or space occupied by a of all reactants and products. The latter is typically determined
solute molecule and facilitates better understanding of solute from independent binary solutions at temperature 298.1 K and
behavior in solution i.e. solute–solute and solute–solvent atmospheric pressure.
interactions.
Recently, due to signicant progress in advanced in situ
PMV has also been used to analyze the effect of pressure on spectroscopic techniques and automated bulk-uid property
chemical reactions. Many classes of organic, inorganic and measurements, new opportunities arise especially for the
organometallic reactions are pressure dependent and therefore physico-chemical characterization of multi-component reac-
8
–10
11,12
exhibit non-zero volumes of reaction.
In some reactions, the tive systems.
For example, in situ spectroscopic measure-
3
volume of reaction can be very large (on the order of 30–50 cm
mol ) and hence such reactions are very sensitive to pressure.
ments allow the accurate evaluation of the solute
concentrations even under reaction conditions. When this
ꢀ
1
8
In practical terms, understanding of the volume of reaction can quantitative information is combined with bulk physico-
allow optimization in yields and/or selectivity patterns.
chemical measurements, the individual solute physico-chem-
ical properties can be readily determined. In situ measure-
ments also offer some practical advantages as no sampling is
required and no separation/purication is needed to charac-
terize the physico-chemical properties of the reactive species.
Indeed, such an approach using FTIR spectroscopy and
density measurements has been applied to a very fast, almost
Institute of Chemical and Engineering Sciences, 1 Pesek Rd, Jurong Island, Singapore
6
†
1
27833. E-mail: marc_garland@ices.a-star.edu.sg
Electronic supplementary information (ESI) available. See DOI:
0.1039/c3ra47057a
22194 | RSC Adv., 2014, 4, 22194–22204
This journal is © The Royal Society of Chemistry 2014

View Article Online
Paper
RSC Advances
Table 1 Summary of the experimental runs performed in the study.
a
Mole fractions of the reactants are given in parentheses
Reaction
Exp. run Mass of solvent (g) CPD (g)
DMAD (g)
CPD + DMAD 1
40.331
41.560
40.348
37.576
39.559
43.119
0.795 (0.026) 1.083 (0.016)
1.223 (0.039) 0.819 (0.012)
1.016 (0.033) 0.793 (0.012)
1.458 (0.051) —
1.609 (0.053) —
1.601 (0.049) —
2
3
Fig. 1 Reaction of cyclopentadiene (CPD) and dimethyl acetylene
dicarboxylate (DMAD) to produce the adduct, dimethyl bicyclo[2.2.1]-
CPD + CPD
4
5
6
2,5-heptadiene-2,3-dicarboxylate.
a
Note: higher CPD concentrations were used in the dimerization
reaction due to slow conversion.
puried and separated from its stabilizer by passing it through a
column consisting of silica gel. The pure DCPD dimer was used
in independent binary experiments in order to obtain a refer-
ence value for its partial molar volume at innite dilution.
The purity of the reactant CPD monomer as well as the
puried DCPD dimer were checked by H NMR aer dissolution
3
in CDCl (Bruker Avance 400 MHz, equipped with a 5 mm TBI
probe with z gradient, running a standard Bruker supplied
pulse sequence). The integration of the proton resonances
provided lower bounds for the purity of freshly cracking CP
monomer (>99%) and puried DCPD dimer (>98.5%).
Fig. 2 Dimerization reaction of cyclopentadiene (CPD).
1
instantaneous reaction in order to determine partial molar
1
3
volumes and volume of reaction.
In the present contribution, FTIR spectroscopic measure-
ments and automated density measurements are applied to two
organic reactions namely (i) the reaction of cyclopentadiene
(
(
CPD) and dimethyl acetylene dicarboxylate (DMAD) (Fig. 1) and
ii) the dimerization reaction of CPD (Fig. 2).
Both the CPD and DMAD reaction and dimerization of CPD
were carried out three times. The reactions were performed in
dilute toluene at temperature 298.1 K and pressure circa 0.103
MPa (under dry nitrogen). The amount of solvent and solute
used for reactions was determined using a balance (Metter
These reactions were selected for this study as they belong to
a broader class of pericyclic reactions, which typically exhibit
large volume of reaction. Both reactions were performed in
toluene and investigated at temperature 298.1 K and atmo-
spheric pressure. The FTIR spectroscopic data combined with
BTEM analysis provided the pure component spectra of the
reactive solutes and these were compared to the DFT predicted
spectra. In addition, the pure component spectra together with
mass balances allowed the determination of the instantaneous
concentrations during reaction. The latter were then combined
with the bulk density to evaluate the partial molar volumes of
the constituents and the corresponding reaction volumes. In
this study, DFT calculations were also used to provide predic-
tions for the molar volumes of the reactive solutes.
ꢀ
4
Toledo, AB204-S) with a precision of ꢁ10 g. The difference in
the masses of the syringes before and aer the injection was
taken as the mass of the substance injected into the reactor.
Experimental details concerning the amount of solvent and
solutes used for various runs are summarized in Table 1.
Equipment
The reactions were performed under dry nitrogen at a pressure
of circa 0.103 MPa (Keller, LEO 1) in a 50 mL jacketed glass
reactor equipped with a magnetic stirrer. The temperature in
the reactor was maintained isothermal at 298.1 K (using Poly-
science model 9106 circulator, temperature stability ꢁ0.05 K).
The uid was pumped in a closed loop system from the reactor
through the pump (Masterex® L/S, programmable digital
Experimental section
Materials
The solvent toluene (Sigma Aldrich, CHROMASOLV® for HPLC, drive) to the density meter (Anton Paar, DMA 5000, accuracy of
ꢀ6
ꢀ1
9
9.9%) was dried over activated molecular sieves type 4 A˚ 10 g mL ), to the ow-through cell situated in the infrared
(
(
Aldrich). The reactant dimethyl acetylene dicarboxylate, DMAD spectrometer (Bruker, Equinox 55), then recycled back to the
ꢀ1
Aldrich, 99%) from freshly opened bottles was used without reactor. The ow-rate of the pump was set to circa 12 mL min
Density measurements were necessarily performed under
CPD was obtained by cracking dicyclopentadiene dimer, DCPD static or non-ow condition in order to reduce measurement
.
further purication. The reactant cyclopentadiene monomer,
(
Fluka, purum, >95%). The CPD monomer was subsequently error. In this regard, an in-house soware was developed using
ꢂ
kept under argon and stored at a temperature of circa ꢀ70 C to Visual Basic .NET to synchronize the density meter measure-
prevent its dimerization. Before its usage, the CPD monomer ment and pump on/off switching time. Briey, the pump was
was checked by NMR to ensure its purity (i.e. negligible amount initially switched on for a predetermined period of time (i.e. 4
of dimer formed). In addition, the crude DCPD dimer was minutes) to circulate the uid, and then it was switched off
This journal is © The Royal Society of Chemistry 2014
RSC Adv., 2014, 4, 22194–22204 | 22195

View Article Online
RSC Advances
Paper
(consolidation of exp. runs 1–3 and 4–6). The data were then
analyzed in two spectral regions, namely a wide spectral region
ꢀ
1
with wavenumber range of 1000–3500 cm and a narrower
ꢀ
1
region with wavenumber range of 1300–2000 cm . The wide
spectral region was analyzed for qualitative purpose, namely to
obtain pure component spectra exhibiting a wide variety of
vibrations. In contrast, the spectral data analysis in the narrow
region was performed in order to obtain more accurate quan-
titative information. For each region, Singular Value Decom-
position (SVD) and thereaer Band-target Entropy
14–16
Minimization (BTEM) analysis
were performed in order to
reconstruct the underlying pure component spectra of the
reactive species. These reconstructed spectra were then
compared to the corresponding DFT predicted spectra.
Fig. 3 Experimental setup for simultaneous on-line FTIR spectros-
copy and automated density measurements.
Concentration of the reactive species
Quantitative spectral analysis was performed with data from the
narrow spectral region with wavenumber range of 1300–2000
ꢀ
1
cm . The raw reaction spectra were preprocessed to exclude
the spectral contributions from the moisture and to correct the
while the density meter was signalled to measure. To ensure
that the density meter was able to complete the measurement,
the period of non-ow condition was set to be 6 minutes. Aer
each density measurement, the soware logged the measured
density value and its corresponding measured time. The uid
was re-circulated by switching on the pump for circa 2 minutes
before subsequent density measurement was taken (note:
recirculation time in the system was circa 60 s). In this setup,
the density measurements of the solution were able to be
collected automatically circa every 8 minutes.
17
slight baseline shi. The matrix of preprocessed spectra will
be denoted as A. Subsequently, a dimensionless approach using
18
solvent as internal standard was applied to the preprocessed
spectra to eliminate the inuence of any changes in reaction
volume and in cell path length. It should be noted that this
special spectral data treatment is necessary since the change of
volume due to reaction is non-negligible in the present systems.
Based on the Lambert–Beer–Bouguer law (LBBL) model, the
dimensionless data Ai
std
ꢀ1
can be related to the preprocessed
Mid-infrared spectra in the range 1000–3500 cm and with
ꢀ1
absorbance data A as shown in eqn (1), where V is the reaction
volume, l is the optical path length, s is number of species, aij is
molar absorptivity, n is total number of moles of species s, and i
j
is wavenumber.
resolution of 4 cm were collected automatically every 2 min for
the reaction CPD + DMAD and every 4 min for dimerization
reaction. Co-added scans of 32 spectra were measured in order to
ensure good signal-to-noise ratios. The CaF2 single crystal
windows used (Korth Monokristalle, Kiel, Germany) had dimen-
sions of 20 mm diameter by 2 mm thickness. Two sets of Viton
gaskets provided sealing and Teon spacers (25 mm) were used
between the windows. The general experimental setup for simul-
taneous spectra and density measurements using on-line FTIR
spectroscopy coupled with the density meter is shown in Fig. 3.
i
s
X
ꢀ
ꢁ
V
l
dml
¼ Ai
A
i
¼
a
ij
n
j
(1)
j¼1
The variables V and l can be eliminated by using internal
standard absorbance Au , of a reference species (i.e. solvent) at a
std
Due to the inherent acquisition times, the FTIR spectroscopic reference wavenumber u as shown in eqn (2). The substitution
measurements and the density measurements occurred on two of eqn (2) into eqn (1) results in eqn (3).
different time-scales. In particular, the FTIR spectra could be
std
u
V
l
a
n
std
std
acquired rather rapidly (circa every 2 or 4 minutes), whereas, due
to temperature stability issues the density measurements were
acquired at a slower rate (8 minutes). In order to synchronize the
time series between both spectroscopic and density data, the
density data were t to a polynomial function. This function was
subsequently used to obtain the densities of solution associated
with the spectral acquisition time.
¼
(2)
(3)
A
u
std
Xꢂ
s
ꢃ
a
n
std
std
dml
u
Ai
¼
A
i
¼
aijn
j
A
u
j¼1
The moles of the standard (solvent) nstd is known in each
experimental run and the internal standard absorbance A
std
u
is
calculable from the peak height of the solvent at a selected
reference wavenumber u. The quantity au (molar absorptivity
of the standard) can be set equal to 1 as it is merely a scalable
Numerical section
Spectral data analysis – pure component spectra
std
The infrared spectra for each reaction system were consolidated constant (note: its effect will be lumped in the scaling elements
to provide two absorbance reaction data matrices sꢃs which will be determined below).
d
22196 | RSC Adv., 2014, 4, 22194–22204
This journal is © The Royal Society of Chemistry 2014

View Article Online
Paper
RSC Advances
X
dml
N
Vi
In matrix form, the dimensionless absorbance data Akꢃn can
be rewritten as in eqn (4) and related to n , aˆ
and d the
o
solv
V
m
¼ xsolv
V
þ
x
i
(7)
kꢃs sꢃn
sꢃs
soluteꢀi
moles of the species-s, the normalized pure component
absorptivities (from BTEM) and the scaling elements, respec-
tively. The subscripts k and v denote the number of spectra in
one experimental run and the number of data channels asso-
ciated with the spectroscopic wavenumber range, respectively.
It can be noted that the scaling elements are needed to relate
the real magnitude of the pure component absorptivities and its
normalized pure component absorptivities.
Since the molar volume of the solvent is calculable from
solvent mass and solvent density, eqn (7) can be re-arranged to
eqn (8). The partial molar volumes at innite dilution of the
N
i
ꢀ
reactive solutes–i V
were determined using multivariate
regression.
X
N
Vi
o
solv
V
m
ꢀ xsolv
V
¼
x
i
(8)
soluteꢀi
dml
A
kꢃv ¼ nkꢃs
d
sꢃs aˆ sꢃv
(4)
DFT calculations
The DFT calculations were performed with Gaussian 09 version
A.02. The reactive species CPD, DMAD, adduct and dimer
Moles of the species can be estimated from (eqn (5)) where
aˆ sꢃn is the pseudo inverse matrix of aˆ sꢃn. Proper scaling
]
+
19
[
DCPD were modelled and calculations were carried out in order
to obtain the fully optimized geometries and the corresponding
(5) predicted infrared spectra. As well, the molar volumes can be
estimated based on the van der Waals surface of the mole-
elements d must be evaluated in order to evaluate the moles.
sꢃs
dml
+
ꢀ1
)
n
kꢃs ¼ Akꢃv[ aˆ sꢃv] (dsꢃs
Since the reaction was carried out in a closed system, various
20
cules. B3LYP functional and cc-pVTZ basis set was used by
mass balances apply. This condition is accordingly used as
taking into account the dielectric constants of the solvent
toluene. All the DFT calculations were carried out at temperature
constraints to evaluate the scaling elements (diagonal d ). The
sꢃs
following mole balance constraints were used in this study.
In the reaction CPD + DMAD, only three major reactive
species are considered, namely CPD, DMAD, and adduct. Based
on its reaction stoichiometry, the summation of moles of CPD
and adduct and the summation of moles of DMAD and adduct
at any reaction time are equal to the initial moles of CPD and
DMAD, respectively.
In the dimerization reaction of CPD, only two reactive
species are involved, namely CPD and DCPD. Based on its
reaction stoichiometry, the summation of moles of CPD and
twice the moles of DCPD at any reaction time are equal to the
initial moles of CPD.
2
98 K. SCRF model IEFPCM was used to account for the solvent
effect in the geometric optimization and the subsequent infrared
spectral prediction while SCRF model IPCM was used in the
molar volume calculations. The present infrared spectral calcu-
lation takes a similar computational approach as previously used
to predict the infrared spectrum of CPD, namely, (a) frequencies
are reported directly as provided by the DFT calculations (with
chosen functional and basis set) without recourse to scaling
21
(correcting for systematic shis using a known reference
compound) and (b) graphical spectra are generated using the
above mentioned frequencies as well as line widths consistent
with the average experimentally observed line widths.
Using a least square minimization procedure, the scaling
elements (diagonal dsꢃs) of the reactive species (note: 3
elements for CPD + DMAD reaction and 2 elements for dimer- Results and discussion
ization reaction) were evaluated. The resulted scaling elements
were subsequently used to calculate the moles of the corre-
sponding species as a function of time using eqn (5).
Reaction of CPD and DMAD
The reaction between CPD and DMAD (see Fig. 1) was carried
out in toluene at temperature 298.1 K. Three reaction runs were
performed with different reactant ratios (see Table 1). The
reaction was monitored simultaneously using FTIR spectros-
copy and density meter. From all 3 reaction runs, a total of 595
in situ FTIR reaction spectra were recorded. From the spectro-
scopic measurements, several spectral changes were observed
during reactions and some major changes occurring in the
Total molar volume and partial molar volume
The primary quantities used in this study for modeling
purposes are the total molar volume and mole fractions. The
total molar volume V is obtained using eqn (6), where n, M, r
m
and x are mole, molar mass, density of solution and mole
fraction, respectively. Subscripts solv. and i refer to the solvent
and the solutes.
ꢀ1
wavenumber range of 1300–1800 cm are shown in Fig. 4.
ꢀ
1
The major bands of CPD at 1365 cm and DMAD at 1731
X
X
ꢀ1
cm are shown decreasing with time. Further inspection shows
n
solv
M
solv
þ
n
i
M
i
x
solv
M
solv
þ
i i
x M
ꢀ
1
that the band of limiting reactant DMAD at 1731 cm
soluteꢀi
soluteꢀi
V
m
¼
! ¼
(6)
ꢄ
ꢀ1
X
r
decreases more rapidly than the band of CPD at 1365 cm . The
bands at 1322, 1628, and 1717 cm which are seen increasing
r nsolv
þ
n
i
M
i
ꢀ1
soluteꢀi
with time correspond to the vibrations of the adduct. A rather
ꢀ
1
distinct spectral change is noted at circa 1435 cm . Although
In dilute solution the total molar volume can be related to this band is decreasing with time, it does not appear to be
o
ꢀ1
ꢀ1
the molar volume of the solvent Vsolv and the partial molar strictly correlated with the bands at 1365 cm and 1727 cm
.
N
i
11
ꢀ
volumes at innite dilution of the solutes–i V
using eqn (7).
This observation indicates that there could be some overlapping
This journal is © The Royal Society of Chemistry 2014
RSC Adv., 2014, 4, 22194–22204 | 22197

View Article Online
RSC Advances
Paper
Spectral analysis
A wide range spectral deconvolution of reactive species in the
ꢀ
1
wavenumber range of 1000–3500 cm was performed using
BTEM. This analysis was used in order to conrm the identity of
species present. The reconstructed pure component spectra of
the reactants DMAD and CPD as well as the product in the wide
spectral range are presented in Fig. 6 and 7, respectively. These
spectra are also compared with the corresponding DFT pre-
dicted spectra.
In Fig. 6(a), the BTEM reconstructed spectrum of DMAD is
shown to be in good agreement with the DFT predicted spec-
ꢀ
1
ꢀ1
trum. The strong bands at 1263 cm and 1731 cm and
ꢀ
1
ꢀ1
Fig. 4 Ten representative infrared reaction spectra of the reaction medium bands at 1042 cm and 1435 cm are in excellent
between CPD and DMAD for the first 6 hours (time progression is
shown from red to blue). The spectrum of the solvent toluene is
indicated by the dashed line.
22
agreement with the bands reported in the literature. Based on
the DFT calculations, these four bands are associated with the
bands present at this position between the reactants and the
product.
The reaction progress was also monitored by the density
meter. The density changes observed during the three experi-
mental runs are shown in Fig. 5. It can be noted that the initial
density values and the reaction rates are very sensitive to the
initial reactant concentrations. More specically, the second
and third reaction runs have low initial densities due to the
higher concentration of CPD (lowest density component) used.
During the automated density measurements, a few outlier
density data were generated (see the omitted points in Fig. 5).
This is primarily due to the occasional formation of bubbles in
the density cell. These outliers were easily identied and
accordingly excluded in the analyses.
Fig. 5 The density monitoring of reaction between CPD and DMAD Fig. 6 The BTEM and DFT infrared spectra of (a) DMAD and (b) CPD in
carried out in three experimental runs (exp. run 1 – C; exp. run 2 – ;; toluene. Artifact arising due to strong absorption of the solvent toluene
ꢀ1
exp. run 3 – -).
at wavenumber 1496 cm is noted.
22198 | RSC Adv., 2014, 4, 22194–22204
This journal is © The Royal Society of Chemistry 2014

View Article Online
Paper
RSC Advances
ꢀ
1
1
717, 1739 cm are consistent with those predicted spectral
bands. Based on the DFT calculations, the bands at 1293, 1322,
ꢀ
1
and 1434 cm correspond to C–O stretching, C–C stretching,
and CH symmetric bending, respectively. Bands at 1561 and
3
ꢀ
1
1
628 cm correspond to the C]C stretching and bands at 1717
ꢀ
1
and 1739 cm correspond to the C]O stretching. The bands in
the region of 2800–3200 cm
ꢀ1
are associated with the CH
stretching vibrations.
BTEM analysis was also attempted to identify and reconstruct
the pure component spectra of other species, in particular the
dimer DCPD which could be formed due to slow dimerization of
CPD in the solution. The analysis was restricted to the spectral
datasets which were collected during the rst 3 hours of reaction.
BTEM analysis could not identify and reconstruct the pure
spectrum of the dimer DCPD from the data in this short reaction
time. This indicates that the formed dimer DCPD, if any, should
be in very small amount and therefore can be neglected.
Quantitative spectral analysis
Fig. 7 The pure component infrared spectra of the adduct recon- The reaction spectra in the narrower wavenumber range of
ꢀ1
structed using BTEM (bottom) and predicted from DFT calculations 1300–2000 cm , which covers numerous strong vibrations
(
2
top). Inset: comparison spectra in the wavenumber range of 1280–
arising from the reactive species (see Fig. 4) were chosen for
quantitative analysis. BTEM analysis was re-utilized to recon-
struct the underlying pure component spectra of the three
reactive species from the reaction spectra. The resulting pure
component spectra are presented in Fig. 8(a).
ꢀ1
000 cm . Artifact arising due to strong absorption of the solvent
ꢀ1
toluene at wavenumber 1496 cm is noted.
vibrations of C–C–O stretching, C]O stretching, C–O–C
stretching and CH bending, respectively. Some weak bands
3
Subsequently, using the dimensionless approach detailed in
Numerical section, the moles and hence the mole fractions of
the three reactive species were determined. In this procedure,
the solvent toluene was selected as an internal standard, with its
ꢀ
1
appearing in the range of 2800–3100 cm correspond to some
C–H stretching vibrational modes.
In Fig. 6(b), the BTEM reconstructed spectrum of CPD is
compared to the corresponding DFT predicted spectrum. This
spectrum is also compared with the spectral bands of liquid
CPD reported in the literature. The strong band at 1365 cm
and medium weak to medium bands at 1089, 1238, 1292, 1590,
1
agreement with those bands reported in literature.
DFT calculations, it is possible to assign that the strong band at
1
bands at 1089 and 1292 cm correspond to CH bending modes
and the band at 1238 cm corresponds to the CH
mode. Bands at 1590 and 1626 cm are related to the combi-
ꢀ1
peak height at 1496 cm taken as the reference. The mole
fractions of each reactive species resulting from this quantita-
tive spectral analysis are shown in Fig. 8(b).
23
ꢀ1
As will be noted (vide infra), that the dimerization product
DCPD was directly identiable in the independent dimerization
experiments and detectable in the CPD + DMAD reaction at
longer reaction times i.e. greater than circa 3 hours. Therefore,
for the partial molar volume evaluation, analysis will be
restricted to short reaction times i.e. less than 2 hours.
ꢀ1
626, 2734, 2884, 2900, 3043, 3075, 3105 cm are in excellent
23,24
From the
ꢀ
1
365 cm to the CH2 scissoring vibration mode. Similarly,
ꢀ1
ꢀ1
2
wagging
ꢀ
1
Partial molar volumes of reactive species
nation vibrations of CH bending and C]C stretching. The The measured densities and the mole fractions of the constit-
ꢀ
1
bands in the region of 2700–3100 cm are associated with the uents in the solution were used to calculate the total molar
CH stretching vibrations.
volume of the solution using eqn (6). The partial molar volumes
The pure component spectrum of the adduct reconstructed at innite dilution of each individual solute were subsequently
using BTEM is presented in Fig. 7. The spectrum of the adduct determined from the total molar volume and the mole fractions
is much more complex than either of the reactants. This is of individual reactive species using eqn (8).
expected as the adduct has more atoms and lower symmetry.
The DFT predicted spectrum is also shown in Fig. 7.
In this study, the results from three experimental runs (exp.
runs 1–3) were evaluated simultaneously in order to provide
Although there are some discrepancies in relative intensities, some compositional as well as volumetric variations for the
the DFT predicted spectrum is still useful to conrm the iden- reactants and the adduct. The partial molar volumes at innite
tity of the adduct as the predicted frequencies are fairly dilution of the reactive species, namely DMAD, CPD and adduct
consistent with those of experimental spectrum. A closer look in obtained from eqn (8) are summarized in Table 2. These values
ꢀ
1
the ngerprint region of 1280–2000 cm (see the inset of Fig. 7) are compared to the corresponding partial molar volumes
shows a good agreement between BTEM and DFT predicted independently determined from binary solution experiments.
spectra. The ngerprint bands at 1293, 1322, 1434, 1561, 1628, The partial molar volume of the adduct can be compared to the
This journal is © The Royal Society of Chemistry 2014
RSC Adv., 2014, 4, 22194–22204 | 22199

View Article Online
RSC Advances
Paper
partial molar volume value calculated from the volume of
25
reaction taken from literature. As can be seen, the partial
molar volumes at innite dilution of the three reactive species
determined from multi-component reactive system are in good
agreement with those determined from binary solution or
calculated from literature data.
Dimerization reaction of CPD
The dimerization reaction of CPD was carried out in toluene at
temperature 298.1 K and atmospheric pressure. The reaction
was monitored simultaneously using FTIR spectroscopy and the
density meter. From the spectroscopic measurements, some
spectral changes were observed due to reaction. The spectral
ꢀ1
changes occurring in the wavenumber range of 1300–1420 cm
are shown in Fig. 9. In Fig. 9(a), the band of the reactant CPD at
ꢀ
1
1
1
365 cm
340 cm
and the band of the dimer product DCPD at
are seen decreasing and increasing with time,
ꢀ1
respectively. The very slow conversion of this reaction is
indicated by the relatively subtle spectral changes in the period
of 24 hours.
The progress of the dimerization reaction was also moni-
tored using the density meter. The density changes during the
10 hour reaction time are shown in Fig. 9(b). Since the density is
increasing almost linearly with time, it suggests that the rate of
this reaction is nearly constant within this period. This is
consistent with the limited conversion occurring during the
measurement period for this second order reaction.
Reaction spectra and wide range spectral deconvolution
The deconvoluted spectra of the reactive species in the wide
ꢀ
1
wavenumber range of 1000–3500 cm was performed using
BTEM analysis. The analysis was successfully employed to
reconstruct the underlying pure component spectra for both
monomer CPD and dimer DCPD. The BTEM pure component
infrared spectrum of monomer CPD is not shown as it is very
similar to the result presented in Fig. 6(b).
Fig. 8 (a) The BTEM pure component spectra of the reactants DMAD,
The BTEM pure component spectrum of the dimer DCPD is
presented in Fig. 10 and compared with the corresponding DFT
predicted spectrum. As seen in Fig. 10, the BTEM reconstructed
spectrum of DCPD is in good agreement with the DFT predicted
spectrum. Noteworthy is the comparison of spectra in the
ꢀ1
CPD and the adduct in the wavenumber range of 1300–2000 cm . (b)
The mole fractions of DMAD (;), CPD (C) and adduct (-) evaluated
from exp. run 1 (black), exp. run 2 (grey) and exp. run 3 (white). Note:
the mole fractions in the initial mixing period are not shown.
ꢀ
1

ngerprint region of 1000–1800 cm (see inset). The band at
ꢀ1
1340 cm as well as other weaker bands at 1023, 1132, 1160,
ꢀ1
1252, 1439 cm obtained from this study are also in excellent
Table 2 Partial molar volumes of reactants and product of CPD +
DMAD reaction in toluene at 298.1 K
23
agreement with those bands reported in literature. Based on
the DFT calculations, the bands at 1023, 1132, 1160, 1252, 1340,
1439 cm correspond to C–C stretching, C–H bending, CH2
N
i
N
i
3
ꢀ1
ꢀ1
Vꢀ
ꢁ d(Vꢀ
) (cm mol
)
twisting, C–C stretching, C–H bending, CH
respectively. The bands around 1600 cm corresponds to the
C]C stretching vibrations and bands around 2800–3100 cm
correspond to the C–H stretching vibrations.
2
scissoring,
a
Species
From reaction
From binary
literature
ꢀ1
ꢀ1
b
DMAD
CPD
Adduct
124.6 ꢁ 0.5
83.3 ꢁ 0.2
170.0 ꢁ 0.7
122.4 ꢁ 0.2
82.3 ꢁ 0.1
n/a
124.3c
82.4
172.4
d
a
From separate binary solution measurements performed in this study. Quantitative spectral analysis
b
c
d
Ref. 26, in solvent toluene. Ref. 27, in solvent toluene. Calculated
3
ꢀ1 25
N
Quantitative analysis was carried out based on the spectra in the
from volume of reaction data (ꢀ33.6 cm mol
i
) of CPD and
and Vꢀ
ꢀ
1
DMAD obtained from the present binary measurements.
wavenumber range of 1300–2000 cm . BTEM analysis was re-
22200 | RSC Adv., 2014, 4, 22194–22204
This journal is © The Royal Society of Chemistry 2014

View Article Online
Paper
RSC Advances
Fig. 10 The BTEM and DFT infrared spectrum of dimer DCPD in
toluene (inset: comparison spectra in the wavenumber range of 1000–
ꢀ
1
1
1
800 cm ). Artifacts due to absorption of solvent toluene at circa
ꢀ1
496 cm are noted.
Partial molar volumes of reactive species
The obtained densities and the mole fractions of the constitu-
ents in the solution were used to calculate the total molar
volume of the solution using eqn (6). The partial molar volumes
N
i
ꢀ
at innite dilution of each individual reactive solute V
were
subsequently determined from total molar volume and the
mole fractions of reactive species using eqn (8). The results are
shown in Table 3.
In order to validate the reproducibility of the present deter-
mination, two additional experimental runs (exp. runs 5 and 6)
were carried out. The spectroscopic and volumetric analyses
were performed in a similar manner. The results of the three
experimental runs are shown in Table 3. The results obtained
from three experimental runs are reproducible and the devia-
tions of the partial molar volumes obtained for different runs
are considered small (circa 0.1 and 1% for CPD and DCPD,
respectively).
Fig. 9 (a) Infrared reaction spectra of the dimerization reaction of CPD
in the solution (shown in the period of 24 hours). Spectrum of solvent
toluene is shown with the dashed line (b) density monitoring of
dimerization reaction.
The partial molar volumes of the CPD and DCPD obtained
directly from multi-component reactive system were also
compared to the partial molar volumes independently deter-
utilized to reconstruct the underlying pure component spectra mined from binary solution measurements as well as to the
of two reactive species from the reaction spectra. The pure literature value. As can be seen, the partial molar volumes
component spectra of the monomer CPD and dimer DCPD determined from multi-component solution are reliable as they
obtained using BTEM in the narrower region are shown in are in excellent agreement with those determined from binary
Fig. 11(a).
measurements.
Subsequently, the moles and hence the mole fractions of the
reactive species were determined using the dimensionless
approach (see Numerical section). In this calculation, the
Calculation method – molar volume of solutes
solvent toluene was chosen as an internal standard with its peak A simple procedure based on the Monte Carlo method for
ꢀ
1
height at wavenumber 1496 cm was taken as a reference. The calculating molar volume for a variety of organic molecules has
20
mole fractions of two reactive species resulted from this quan- been proposed by Wong et al. This method (now available in
titative spectral analysis are shown in Fig. 11(b).
the Gaussian soware package) was utilized in this study to
This journal is © The Royal Society of Chemistry 2014
RSC Adv., 2014, 4, 22194–22204 | 22201

View Article Online
RSC Advances
Paper
Table 3 Partial molar volumes of reactant and product of dimerization
a
reaction in toluene at 298.1 K
N
i
N
i
) (cm mol )
3
ꢀ1
Vꢀ
ꢁ d (Vꢀ
b
Species
CPD
From reaction
From binary
literature
c
82.3 ꢁ 0.1 (exp. run 4)
82.3 ꢁ 0.1
82.4
8
8
2.2 ꢁ 0.1 (exp. run 5)
2.2 ꢁ 0.1 (exp. run 6)
Ave ¼ 82.23 ꢁ 0.06
DCPD
133.4 ꢁ 0.6 (exp. run 4)
135.1 ꢁ 0.1
1
1
34.9 ꢁ 2.4 (exp. run 5)
32.1 ꢁ 2.9 (exp. run 6)
Ave ¼ 133.47 ꢁ 1.40
a
The volumetric analyses were performed using density and mole
b
fraction data taken from the rst 10 h reaction time. From separate
c
binary measurements performed in this study. Ref. 27, in solvent
toluene.
the ratio of the calculated volume and the experimental volume
ranges from 0.71 to 0.83 for a variety of organic molecules. On
the average, a ratio of 0.75 can be selected as an empirical value
which relates the calculated volume and the experimental molar
volume of many solutes. The molar volume of solutes calculated
based on this ratio are shown in Table 4 and compared to their
corresponding experimental partial molar volume values
obtained from the reaction studies.
As can be seen, the predicted molar volumes of solutes are in
relatively good agreement with the experimental values. A
greater deviation between the predicted molar volumes of
solutes and experimental partial molar volumes is noticed for
those molecules with more complex structures. For adduct and
dimer DCPD, the deviation can be up to 15% of the
Fig. 11 (a) The BTEM pure component infrared spectra of the
monomer CPD and dimer DCPD in the wavenumber range of 1300–
ꢀ
1
2
000 cm . (b) The mole fractions of CPD (C) and DCPD (;). Artifact
ꢀ1
due to absorption of solvent toluene at circa 1496 cm is noted.
estimate the molar volume of the solutes. In the present
calculation, B3LYP functional and cc-pVTZ basis set was used
and the effect of solvent as a polarisable continuum medium
was treated by employing SCRF model IPCM. Four reactive
species involved in the CPD + DMAD and dimerization reactions
namely CPD, DMAD, adduct and dimer DCPD were modeled
accordingly in the respective solvent used. The optimized
geometries of these species are given in Fig. 12.
The volumes of the solutes obtained from the calculation
method above are summarized in Table 4. As shown by the
20
previous study of Wong et al., the calculated volumes of many
solutes follow a simple empirical relationship (linear) with their
Fig. 12 Optimized geometries of various species. (a) CPD (b) DMAD
and (c) adduct (d) DCPD. The atomic assignments are: carbon (dark
corresponding experimental volumes. As shown in their study, grey), hydrogen (light grey), oxygen (red).
22202 | RSC Adv., 2014, 4, 22194–22204
This journal is © The Royal Society of Chemistry 2014

View Article Online
Paper
RSC Advances
ꢀ
1
3
ꢀ1
28
Table 4 Comparison of calculated molar volumes of solutes and their mol (ref. 25) and ꢀ36.1 cm mol (in solvent ethyl acetate)
corresponding partial molar volumes in toluene at 298.1 K
3
ꢀ1
for the CPD + DMAD reaction and ꢀ31.4 cm mol for the
29
a
3
ꢀ1
b
3
ꢀ1
Nc
i
3
ꢀ1
dimerization CPD + CPD reaction (in solvent n-butyl chloride),
Species
V
calc (cm mol
)
V
m,est (cm mol
)
Vꢀ
(cm mol )
which were obtained from high pressure reaction studies. The
present determination shows that the volume of reaction of
both CPD + DMAD and the dimerization reactions are negative.
d
CPD
61.5
95.0
146.0
61.5
82.0 (ꢀ1.6%)
126.7 (1.7%)
194.7 (14.5%)
82.0 (ꢀ0.2%)
149.1 (11.7%)
83.3
124.6
170.0
82.2
d
DMAD
d
Adduct
e
CPD
e
DCPD
111.8
133.5
Conclusions
a
b
From DFT using SCRF model IPCM.
V
m,est ¼ Vcalc/0.75, deviation to
This study demonstrates the utility of combined on-line FTIR
spectroscopy and automated density measurements to deter-
mine partial molar volume of reactive solutes as well as the
volume of reaction in the multi-component reactive system. In
this regard, BTEM spectral analyses were employed for obtain-
c
the corresponding PMV is shown in parenthesis. PMV obtained from
d
multi-component reaction system. From CPD + DMAD reaction.
e
From CPD + CPD dimerization reaction.
experimental values. This deviation is expected since the pre- ing the pure component spectra of the solutes and their corre-
dicted method employing a SCRF model only regards the sponding concentrations. The obtained solute concentrations
solvent as a dielectric continuum. This model neither accounts were combined with the bulk density data to evaluate the partial
for solvent spatial reorganization around solute molecules nor molar volumes of the solute constituents. The partial molar
accounts for any specic chemical interactions with solutes. volume values evaluated from this approach are subsequently
Despite this inadequacy to model a real solution, this predicted used to calculate the corresponding volume of reaction. The
method is still quite useful and can be considered as a viable volumes of reaction of the CPD + DMAD and dimerization
3
ꢀ1
alternative for estimating the molar volume of solutes in solu- reactions determined from this study are ꢀ37 ꢁ 3 cm mol
3
ꢀ1
tion. Detailed molecular dynamics simulations oen provide a and ꢀ31 ꢁ 2 cm mol , respectively. The DFT calculations
much more reliable and realistic approximation to molar performed in this study were useful for the assignment of the
volumes (and partial molar volumes) but this extension is structures and vibration modes corresponding to the experi-
beyond the scope of the present contribution.
mental spectral estimates as well as to provide predictions of
For completeness, it can be noted that the adduct clearly has the molar volume of the solutes. In general, the method devel-
numerous conformations in solution. Thus, in the DFT calcu- oped in this study opens a new avenue for the in situ physico-
lations, the fully optimized structure was determined for the chemical characterization in particular partial molar volumes
adduct as well as some of the more likely, energically low lying and volume of reaction from the multi-component reactive
conformations. These optimized structures are all graphically system.
presented in the ESI,† as well as their corresponding energies.
In addition, DFT with SCRF model SCI + IPCM was used to
estimate the molar volumes. The average deviation between the
Acknowledgements
estimated molar volumes for the various approaches and the This work was supported by Agency for Science, Technology and
measured partial molar volumes were (1) 27.1% using IPCM Research (A*STAR), Singapore.
alone (2) 5.9% using IPCM scaled according to the procedure of
20
Wong et al. and (3) 9.9% using SCI + IPCM. The individual
results using the latter procedure are provided in the ESI.†
Notes and references
1
P. Ruelle, A. Farina-Cuendet and U. W. Kesselring, J. Am.
Chem. Soc., 1996, 118, 1777–1784.
Calculation of volume of reaction
2 W. Zielenkiewicz and J. Poznaskia, J. Mol. Liq., 1999, 81, 37–
4
5; T. Imai, M. Kinoshita and F. Hirata, J. Chem. Phys., 2000,
The information on the individual partial molar volumes of
reactants and products obtained from the reaction studies can
be readily used to calculate the corresponding volume of reac-
tion. The volume of reaction, were subsequently determined in
this study from the difference between partial molar volumes of
products and reactants as given by eqn (9), where a and b are
112, 9469–9478.
3
4
5
S. Mizyed, P. R. Treamaine and P. E. Georghiou, J. Chem. Soc.,
Perkin Trans. 2, 2001, 3–6.
T. V. Chalikian, Annu. Rev. Biophys. Biomol. Struct., 2003, 32,
207–235.
i
i
B. Berne, J. Am. Chem. Soc., 2005, 127, 17842–17851.
the stoichiometric coefficients of the corresponding reaction.
X
X
6 G. Graziano, J. Chem. Phys., 2006, 124, 134507–134511.
7 X. Huang, C. J. Margulis, Y. Li, N. Patel, D. N. Dubins,
R. Pomes and T. V. Chalikian, J. Phys. Chem. B, 2011, 115,
N
N
D
r
V ¼
b
i
V ðproductsÞ ꢀ
a
i
V ðreactantsÞ
(9)
i
i
i
i
4856–4862.
The volume of reaction for the CPD + DMAD and CPD + CPD
8 R. Van Eldik and C. D. Hubbard, Chemistry under Extreme or
Non-Classical Conditions, John Wiley, New York, 1997.
9 R. Van Eldik, T. Asano and W. J. le Noble, Chem. Rev., 1989,
89, 549–688.
3
dimerization reactions calculated using eqn (9) are ꢀ37 ꢁ 3 cm
ꢀ
1
3
ꢀ1
mol and ꢀ31 ꢁ 2 cm mol , respectively. These values can be
3
compared favorably with the literature values of ꢀ33.6 cm
This journal is © The Royal Society of Chemistry 2014
RSC Adv., 2014, 4, 22194–22204 | 22203

View Article Online
RSC Advances
Paper
1
0 A. Drljaca, C. D. Hubbard, R. van Eldik, T. Asano,
M. V. Basilevsky and W. J. le Noble, W. J. Chem. Rev., 1998,
M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo,
J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev,
A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski,
R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth,
P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels,
9
8, 2167–2289.
1 M. Tjahjono and M. Garland, J. Phys. Chem. B, 2007, 111,
3064–13074.
2 M. Tjahjono, D. Allian and M. Garland, J. Phys. Chem. B,
008, 112, 6448–6459.
1
1
1
1
1
1
1
1
1
1
¨
O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski and
2
D. J. Fox, Gaussian, Inc., Wallingford CT, 2009.
3 M. Tjahjono, D. Allian and M. Garland, Dalton Trans., 2006, 20 M. W. Wong, K. B. Wiberg and M. J. Frisch, J. Comput. Chem.,
2, 1505–1516. 1995, 16, 385–394.
4 E. Widjaja, C. Z. Li and M. Garland, Organometallics, 2002, 21 A. Alparone, Chem. Phys., 2006, 327, 127–136.
1
2
1, 1991–1997.
5 W. Chew, E. Widjaja and M. Garland, Organometallics, 2002,
1, 1982–1990.
6 E. Widjaja, C. Z. Li, W. Chew and M. Garland, Anal. Chem.,
003, 75, 4499–4507.
7 K. R. Beebe, R. J. Pell and M. B. Seasholtz, Chemometrics: A 23 E. Gallinella, B. Fortunato and P. J. Mirone, Mol. Spectrosc.,
Practical Guide, Wiley, New York, 1988, ch. 3. 1967, 24, 345–362.
8 W. Chew, E. Widjaja and M. Garland, Appl. Spectrosc., 2007, 24 E. Castellucci, P. Manzelli, B. Fortunato, E. Gallinella and
1, 734–746. P. Mirone, Spectrochim. Acta, Part A, 1975, 31, 451–461.
22 S. E. Stein, Infrared Spectra in NIST Chemistry WebBook, NIST
Standard Reference Database Number 69, ed. P. J. Linstrom
and W. G. Mallard, National Institute of Standards and
Technology, Gaithersburg MD, 20899, retrieved December
26, 2012, http://webbook.nist.gov.
2
2
6
9 M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, 25 C. A. Eckert, Annu. Rev. Phys. Chem., 1972, 23, 239–264.
M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, 26 G. Swieton, J. von Jouanne and H. Kelm, J. Org. Chem., 1983,
B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato,
48, 1035–1040.
X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, 27 V. D. Kiselev, A. I. Konovalov, T. Asano, E. A. Kashaeva,
J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota,
R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda,
G. G. Iskhakova, M. S. Shihab and M. D. Medvedeva, J.
Phys. Org. Chem., 2001, 14, 636–643.
O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr, 28 R. Van Eldik and C. D. Hubbard, Chemistry under Extreme or
J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd,
E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi,
Non-Classical Conditions, John Wiley, New York, 1997, p.
113.
J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, 29 C. Walling and H. Schugar, J. Am. Chem. Soc., 1963, 85, 607–
S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, 612.
22204 | RSC Adv., 2014, 4, 22194–22204
This journal is © The Royal Society of Chemistry 2014