Trimerization of Monocyanate Ester in Nanopores

Article abstract of DOI:10.1021/jp912235c

The effects of nanoconfinement on the reaction kinetics and properties of a monocyanate ester and the resulting cyanurate trimer are studied using differential scanning calorimetry (DSC). On the basis of both dynamic heating scans and isothermal reaction

Full text of DOI:10.1021/jp912235c

J. Phys. Chem. B 2010, 114, 7727–7734
7727
Trimerization of Monocyanate Ester in Nanopores
Yung P. Koh and Sindee L. Simon*
Department of Chemical Engineering, Texas Tech UniVersity, Lubbock, Texas 79409
ReceiVed: December 29, 2009; ReVised Manuscript ReceiVed: February 27, 2010
The effects of nanoconfinement on the reaction kinetics and properties of a monocyanate ester and the resulting
cyanurate trimer are studied using differential scanning calorimetry (DSC). On the basis of both dynamic
heating scans and isothermal reaction studies, the reaction rate is found to increase with decreasing nanopore
size without a change in reaction mechanism. Both the monocyanate ester reactant and cyanurate product
show reduced glass transition temperatures (Tgs) as compared to the bulk; the Tg depression increases with
conversion and is more pronounced for the fully reacted product, suggesting that molecular stiffness influences
the magnitude of nanoconfinement effects. Our results are consistent with the accelerated reaction and the Tg
depression found previously for the nanoconfined difunctional cyanate ester, supporting the supposition that
intracyclization is not the origin of these effects.
Introduction
network structure results. However, a monomer intracyclization
side reaction can occur in this system,20,21 and if it occurred
The properties of materials confined to the nanoscale dimen-
sions differ from the bulk, depending on the confinement system,
material studied, and the measurement technique.1-3 Among the
properties examined in nanoconfinement studies, many have
focused on the changes in the glass transition temperature (Tg),
since the glass temperature is one of the most important
properties of a material, dictating, for example, application
temperature range. It is generally accepted that the glass
transition temperature at the nanoscale is depressed relative to
the bulk unless strong interactions between the confined material
and the confinement medium are present. Potential explanations
include intrinsic size effects1-6 and enhanced mobility at the
surface7-13 coupled with a larger surface-to-volume ratio with
decreasing confinement size; however, more systematic studies
are still required to explain the large range of seemingly
contradictory results in the literature.
Nanoconfinement not only results in a change in Tg and
associated dynamics, but it can also result in changes in
reactivity. Recently, Huck14 showed the possibility of using
nanoconfinement as a synthetic tool to obtain desirable reactiv-
ity, selectivity, or yield through modification of the local
chemical and conformational environment. Indeed, self-as-
sembled monolayers, in which molecules are confined to a
monolayer on surfaces, showed 3 orders of magnitude slower
reaction rate than that of bulk reaction of alkaline hydrolysis
of N-hydroxysuccinide ester due to steric crowding at the
surface.15 On the other hand, nanoscale energetic materials, such
as thermites, lead to faster burning rates relative to the bulk
and, thus, improved performance. The enhanced reactivity of
nanoscale thermites is presumably due to enhanced heat and
mass transfer by the proximity of molecules and larger interfacial
area at the nanoscale.16,17
with greater probability under nanoconfinement, the side reaction
could lead to both the enhanced reactivity and depressed Tg
observed relative to the unconfined bulk reaction.19 It was argued
that the probability of monomer intracyclization did not change,
as evidenced by the fact that the Tg versus conversion relation-
ship and the gel point did not change under nanoconfinement.18,19
To further corroborate this conclusion, here we examine reaction
of a monofunctional cyanate ester under nanoconfinement, since
the monofunctional nature of the reactant precludes monomer
intracyclization. Hence, the purpose of this study is to investigate
the effects of nanoconfinement on the reaction kinetics and glass
transition temperature of monofunctional cyanate confined in
the nanopores of controlled pore glasses. In particular, we
examine the behavior in silanized hydrophobic nanopores in
this work and compare the results to those found for difunctional
cyanate ester under the same confinement.
Methodology
Materials. The monofunctional cyanate ester used in this
study is 4-cumylphenol cyanate ester, obtained from Oakwood
Products and used as received. Its molecular weight is 237.3
g/mol. Three 4-cumylphenol cyanate esters react by trimerization
of the three OCN groups to form a cyanurate trimer with
molecular weight of 711.9 g/mol. The chemical structure of the
monofunctional cyanate ester reactant and the resulting trim-
erization product are shown in Figure 1.
Controlled pore glass (CPG), produced by Millipore, is used
as a nanoconfinement matrix. Four different pore sizes of CPGs
are employed, ranging from 8.1 to 122.1 nm. The detailed
specifications of each CPG are listed in Table 1, as provided
by the manufacturer. The native CPG is made from borosilicate
glass and inherently contains hydroxyl groups on its surface.
Cleaning with nitric acid was followed by a silanization
treatment to replace the hydrophilic hydroxyl groups with
hydrophobic trimethylsilyl groups following the procedure of
Jackson and McKenna22 using hexamethyldisilazane (Sigma-
Aldrich). The silanization treatment has been reported to result
Recently, Li and Simon18,19 found that nanopore confinement
increased the reaction rate of bisphenol M dicyanate ester by a
factor of 20 in 11.5 nm hydrophobic pores without a change in
the kinetic rate law. In this reaction, three cyanate ester
functional groups react to form a triazine ring, and since the
reactant is difunctional, a three-dimensional thermosetting
* Corresponding author. E-mail: sindee.simon@ttu.edu.
10.1021/jp912235c  2010 American Chemical Society
Published on Web 05/24/2010

7728 J. Phys. Chem. B, Vol. 114, No. 23, 2010
Koh and Simon
DSC Measurements. A Perkin-Elmer Pyris 1 differential
scanning calorimeter (DSC) was used with an intracooler
maintained at -80 °C for Tg measurements when Tg was above
-30 °C; a liquid nitrogen cooling system maintained at -150
°C was used when Tg was below -30 °C. For the intracooler
system, measurements were made in a nitrogen atmosphere,
whereas for the liquid nitrogen system, a helium atmosphere
was employed due to helium’s better thermal conductivity at
low temperatures.
Samples were prepared by first putting ∼2-6 mg of CPG in
a hermetic DSC pan, followed by placing monocyanate ester
on top of the CPG. The CPGs are all underfilled, and the pore
fullness ranges from 70% to 90%, as calculated from pore
volume and monocyanate ester loading volume, the latter of
which ranged from 2 to 4 mg. We found that the Tg and heat of
reaction were independent of both the degree of pore fullness
and the sample size; similar results have been reported for a
dicyanate ester in silanized pores18 and for Tg of hydrogen-
bonding liquids in silanized pores.24 All samples were prepared
under a nitrogen blanket to minimize adsorption of adventitious
water. Although the monocyanate ester is a liquid at ambient
conditions and is imbibed into the CPG in a few minutes by
capillary forces,22 to ensure the complete imbibement, we waited
at least 2 h between sample preparation and DSC measurement.
A similar procedure was used to imbibe the fully reacted trimer
into 13 nm pores, except imbibement was accomplished at 160
°C for two weeks, as already mentioned.
The effects of nanoconfinement on the reactivity and proper-
ties were examined by measuring the limiting fictive temperature
(Tf′) and the residual heat of reaction after isothermal reaction
for times ranging from 0 to 4.2 days at 141 °C. As the reaction
proceeds, the fictive temperature increases from that of reactant
to that of the product, and the residual heat of reaction decreases
from the total heat of reaction to zero residual heat at the end
of reaction. The limiting fictive temperature is determined at
10 K/min after cooling at 30 K/min from the intersection of
the extrapolated liquid and glass enthalpy lines obtained from
integration of the heat flow following the method of Moynihan
et al.25 Although the glass transition temperature is correctly
measured only on cooling from the equilibrium state,26 its value
at a given rate (ꢀ) can be approximated by the limiting fictive
temperature measured on heating after cooling at the same rate
ꢀ.26-28 Hence, we refer to Tf′ equivalently as Tg in this study.
The residual heat of reaction is used to calculate the conversion
as a function of reaction time:
Figure 1. The trimerization reaction of 4-cumylphenol cyanate ester
to produce its cyanurate product.
TABLE 1: Specifications of Controlled Pore Glasses
mean
pore
pore
diameter
distribution
(%)b
specific
pore
specific
surface
product
name
diameter
volume
(nm)a
(cm3/g)a
area (m2/g)c
CPG00080
CPG00130
CPG00500
CPG01200
8.1
13.0
50.0
9.0
7.4
3.7
3.7
0.49
0.68
1.10
1.73
197.0
130.0
50.9
122.1
31.2
a Determined by mercury intrusion method. b Analyzed by
ultrasonic sieving method. c Measured by nitrogen adsorption
method.
in negligible changes in pore diameter and pore size distribu-
tion.23 The silanized CPGs were stored in a desiccator before
use.
The borosilicate CPG is expected to be insoluble in the
monocyanate ester and the resulting cyanurate product. Backing
up this assertion that organic liquids do not leach material out
of the CPG, the melting point depression of benzene in 8.1 nm
CPG nanopores, silanized with hexamethyldisilazane, was
measured 10 min after initial imbibement and as a function of
time after imbibement for times up to 1 week. The melting point
depression, measured in slightly overfilled pores by the differ-
ence in the onset of melting between benzene in the pores and
the bulk material external to the pores, was found to be constant
at 16.10 ( 0.03 K in 8.1 nm pores for times from 10 min up to
1 week. The results indicate that the CPG nanopores are a stable
matrix for nanoconfinement of organic liquids.
In addition to the preparation and reaction of the monocyanate
ester samples in all of the sizes of nanopores, we also reacted
monocyanate ester in the bulk unconfined state and then imbibed
the cyanurate product in 13 nm pores to examine whether the
Tg depression depended on reaction conditions. The imbibement
of the cyanurate was monitored for two weeks at 160 °C by
measuring Tg as a function of imbibement time; complete
imbibement was accomplished in 1 week. As shown later, the
Tg depression is the same within the error of the measurements
for the nanoconfined cyanurate, regardless of whether it was
synthesized in the pores or synthesized in the bulk and then
imbibed in the pores.
∆HT - ∆Hr
x )
(1)
∆HT
where ∆HT is the total heat of reaction of an initially unreacted
monocyanate ester and ∆Hr is the residual heat for a partially
reacted sample at a given reaction time.
Two types of experiments were performed. In the first, termed
method 1, an initially unreacted sample was scanned to 141
°C, partially reacted at 141 °C for a prespecified time, cooled,
and then rescanned to 141 °C to obtain Tg for the given reaction
time. Further reaction at 141 °C was then accomplished,
followed by cooling and rescanning to 141 °C to obtain Tg at a
longer reaction time. This cycle was continued until complete
reaction was reached. In this way, one sample was used to obtain
Tg versus reaction time data, reducing errors associated with
multiple samples. The reaction temperature of 141 °C was
chosen such that the trimerization reaction of the bulk was not

Trimerization of Monocyanate Ester in Nanopores
J. Phys. Chem. B, Vol. 114, No. 23, 2010 7729
TABLE 2: Total Heat of Reaction and Onset Temperature
of the Reactant under Nanoscale Constraints at Different
Sizes
D (nm)
∞
122.1
50.0
13.0
8.1
∆H (kJ/mol) 104.1 ( 1.3 105.0 ( 3.1 104.1 ( 5.4 103.4 ( 4.1 102.5 ( 3.5
Tonset (°C) 277.4 ( 6.6 235.4 ( 3.4 232.6 ( 1.2 202.6 ( 3.1 192.3 ( 1.3
The low-temperature shoulder of the exotherm in Figure 2
becomes more pronounced as nanopore size decreases, and for
material confined to 8 nm pores, the shoulder is quite distinct.
Because the adsorption of water can also result in the shoulder
of the exotherm,30,31 the heating rate dependence of the shape
of the exotherm was examined in Figure 3 for the bulk and
nanoconfined sample in 13 nm CPG. The low-temperature
shoulder of the exotherm appears as the heating rate decreases
not only for the 13 nm CPG confined sample but also for the
bulk. Since care was taken to prepare all samples under a
nitrogen blanket to avoid adventitious water and since there is
no expectation of adventitious water in the bulk samples, the
shoulder of the exotherm in Figure 2 is suggested to reflect the
complex trimerization reaction mechanism, which involves
multiple steps. However, although the shape of the exotherm is
a function of the scan rate, the heats of reactions are independent
of the heating rate within experimental error. Also shown in
Figure 3, the activation energy calculated from the shift in the
exotherms with heating rate using the isoconversion method32
Figure 2. DSC heating scans of initially unreacted monocyanate ester
at 10 K/min heating rate for the bulk and samples in nanopores of
diameter D as indicated.
too slow (i.e., the reaction was completed within 5 days), while
at the same time, the reaction under the smallest nanopore
constraint was not too fast (i.e., the reaction took a minimum
of several hours). In the second type of experiment, termed
method 2, both Tg and the residual heat of reaction were obtained
after reaction for reaction times ranging from 0 to 4.2 days.
This second experiment, in which a different sample was used
for each reaction time, provided the relationship between Tg
and conversion x, as well as a serving as a check on our primary
methodology.
The DSC temperature was calibrated with n-octane, gallium,
and indium at 10 K/min on heating. The isothermal calibration,
which is relevant for the isothermal reaction temperature, was
performed at 0.1 K/min, which was found in other work29 to
be equivalent to performing an isothermal calibration. The heat
flow of the DSC was calibrated with indium. Separate calibra-
tions were performed for two types of cooling systems used.
Results
Dynamic Scans of Initially Unreacted Monocyanate Ester.
The reaction exotherms of initially unreacted monocyanate ester
in both bulk and nanoconfined states are shown in Figure 2.
The DSC heating scans were performed at the heating rate of
10 K/min. As the nanopore size decreases, the exotherm moves
to lower temperatures, indicating that the trimerization of
monocyanate ester is accelerated with decreasing nanopore size.
The reaction onset temperature, determined by the intersection
of the baseline with a line drawn tangent to the steepest part of
the primary exotherm on the low-temperature side, is a measure
of reactivity and shifts to lower temperatures under nanocon-
finement. Although the reaction rate is enhanced at the nano-
scale, the total exotherm area or heat of reaction (per mol
reactant) is the same for the bulk and nanoconfined samples,
within the measurement error of 1.3% for the bulk and as high
as 3.9% for the nanoconfined samples, indicating that the overall
reaction mechanism is unchanged and that the reaction goes to
completion at the nanoscale. Both the reaction onset temperature
and the total heat of reaction as a function of nanopore size are
tabulated in Table 2. The reaction onset temperatures for the
bulk and nanoconfined difunctional cyanate ester polycyanurate
system similarly decrease with decreasing nanopore size, and
the heat of reaction for the difunctional system is similarly
independent of confinement size, with a value of 111.6 ( 4.3
J/mol OCN,18 similar to that measured here.
Figure 3. DSC heating scans of initially unreacted monocyanate ester
at different heating rates, ꢀ, for the bulk and samples in 13 nm
nanopores. The heat flow (y axis) is scaled by ꢀref/ꢀ, where ꢀref is 10
K/min.

7730 J. Phys. Chem. B, Vol. 114, No. 23, 2010
Koh and Simon
Figure 5. Square root of the fractional heat capacity change at Tg1 vs
reciprocal pore radius. The open symbol is the cyanurate trimer reacted
in the bulk unconfined state and then imbibed in 13 nm nanopores.
Assuming the two-layer model of core plus surface layer, shown
schematically, the thickness of the latter is obtained from the slope.
unconfined state and then imbibed in 13 nm nanopores. The
value of Tg1 is 17.6 °C and the value of Tg2 is 41.2 °C, within
2 and 4 °C, respectively, of the values obtained for the material
synthesized in the 13 nm nanopores. Hence, the depression in
Tg and the presence of Tg2 is not influenced by reaction under
nanoconfinement, but rather appears to be a result of the
confinement of the glass-former itself.
Two Tgs at the nanoscale are commonly reported in the
literature,18,19,22,33-38 and the origin has been explained using a
two-layer model,33 consisting of a more mobile core and less
mobile surface layer. The decreased mobility of the surface layer
can be attributed to physical (mechanical interlocking) or
chemical interactions, or both, between the nanoconfined
material and nanoconfining medium. The length scale of the
surface layer can be determined assuming that the volume of
material in a given layer is proportional to the step change of
the heat capacity for that layer, that the density of the material
does not change along the pore radius, and that the shape of
pore is cylindrical:38
Figure 4. Glass transition temperature of monocyanate ester reactant
(upper figure) and for the cyanurate trimer (lower figure) as a function
of reciprocal pore diameter, D. The open symbols are the cyanurate
trimer reacted in the bulk unconfined state and then imbibed in 13 nm
nanopores. Typical DSC traces showing the two Tgs are shown in the
insets.
is unchanged at the nanoscale, being 23.7 ( 1.5 kcal/mol at 13
nm and 23.9 ( 1.0 kcal/mol for the bulk reaction.
Tg Depression of Unreacted Monocyanate Ester and
Cyanurate Trimer. The Tg of unconfined or bulk monocyanate
ester is -60.3 ( 0.6 °C, and upon reaction, the value increases
to that of the fully reacted cyanurate product at 46.8 ( 0.6 °C,
a 100 K increase over that of the monocyanate ester. As
expected, the Tgs of nanoconfined monocyanate ester reactant
and the fully reacted cyanurate product are depressed relative
to the bulk, as shown in Figure 4a and b, respectively, as a
function of reciprocal nanopore size. Two Tgs are observed for
both reactant and product confined in all nanopores, and these
are designated Tg1 and Tg2, respectively; typical scans showing
the two Tgs in 13 nm pores are shown in the insets of the figures.
For the monocyanate ester reactant, the primary Tg (Tg1)
decreases slightly with decreasing nanopore size and is de-
pressed by 4.3 ( 1.3 K at 8.1 nm confinement, whereas the
secondary Tg (Tg2) is 18-25 K above Tg1, increasing slightly
with decreasing nanopore size, and always higher than the bulk
unconfined Tg. On the other hand, for the cyanurate product,
Tg1 decreases significantly with decreasing nanopore size and
is depressed by 31.3 ( 0.9 K in 8.1 nm pores, whereas Tg2 is
15-30 K above Tg1 and decreases slightly with decreasing pore
size. Interestingly, Tg2 of the nanoconfined cyanurate product
is lower than the Tg of the bulk cyanurate.
r2 - (r - d)2
(r - d)2
∆Cp2
∆Cp1
Vs
Vc
)
)
(2)
where ∆Cp2 is the step change of heat capacity at Tg2, ∆Cp1 is
the step change of heat capacity at Tg1, Vs is the volume of
material in the surface layer, Vc is the volume of material in
the core, r is the nanopore radius, and d is the surface layer
thickness. By rearranging eq 2, we obtain eq 3, which is used
in the calculation of the surface layer, d.
∆Cp1
d
r
) 1 -
(3)
∆C + ∆Cp2
ꢀ
p1
Hence, the surface layer thickness can be determined from the
slope of a plot of the square root of the fractional step change
of the heat capacity at Tg1 versus the reciprocal pore radius; the
result is shown in Figure 5 for unreacted monocyanate ester
and fully reacted cyanurate. The resulting thickness of the
surface layer is 1.2 nm with a standard error of fit of 0.1 nm,
which is consistent with the cooperative length scale associated
Shown also in Figure 4b, open symbols are the glass transition
temperatures of the cyanurate trimer reacted in the bulk

Trimerization of Monocyanate Ester in Nanopores
J. Phys. Chem. B, Vol. 114, No. 23, 2010 7731
Tg1∆Cp1 + Tg2∆Cp2
Tg,avg
)
(5)
∆Cp1 + ∆Cp2
The dotted line in Figure 6 is the best fit to the DeBenedetto
equation using λ as a fitting parameter, and the resulting value
of λ is 0.375 with a standard error of 0.012. A derivation of the
DeBenedetto equation,44 in which it is assumed that Tg is an
isentropic transition and that the mixture of the initial reactant
and final product is an ideal solution, relates λ to the step
changes in the heat capacities of the reactant and product, ∆Cpo
and ∆Cp∞, respectively:44
∆Cp∞
λ )
(6)
∆Cpo
Figure 6. Dimensionless Tg as a function of conversion of monocyanate
ester reacted in the bulk and in 13 nm nanopores. The solid line is the
best fit to the Debenedetto equation with the fitting parameter λ value
of 0.375.
It is noted that the DeBenedetto equation reverts to the
Gordon-Taylor equation for a binary mixture (as we have here),
and the same theoretical parameter is expected.45,46 The experi-
mental value of ∆Cp∞/∆Cpo is 0.401/0.562 ) 0.712 ( 0.016
for our system, much different from the fitted value of λ )
0.375 ( 0.012. The inconsistency between theoretical and
experimental values is a result of the ideal mixing assumption
in the theoretical derivation. Indeed, the bulk cyanurate trimer
can crystallize during the reaction and shows a broad melting
transition with an onset ranging from 115 to 130 °C (decreasing
with increasing crystallinity), indicating phase separation of the
cyanurate and monocyanate ester, that is, nonideal solution
behavior. Consequently, the fitting parameter λ is not equal to
the theoretical value. Despite this, the DeBenedetto equation
still describes the experimental data very well, as shown in
Figure 6.
The evolution of the primary Tg1 and secondary Tg2 as a
function of reaction time at the isothermal temperature of 141
°C is shown in Figure 7a and b, respectively. Tg increases from
the Tg of the initially unreacted monocyanate ester (Tg0) as the
reaction proceeds, and then Tg levels off at full conversion and
has a final value corresponding to that of the cyanurate trimer
product (Tg∞), the value of which decreases with decreasing pore
size, as already discussed in Figure 4. The consistency between
the two methodologies used to obtain data (single sample versus
multiple samples) is demonstrated by the solid and open symbols
for 13 nm and bulk data. In addition, the reproducibility of the
method 1 (single sample) results is demonstrated by the
agreement of the solid symbols and the + and × symbols for
the bulk data.
with Tg.39 The thickness of the surface layer for our nanoconfined
monofunctional cyanate ester and its cyanurate product in
controlled pore glass (CPG) is also comparable to that of
difunctional cyanate ester in silanized and native CPG (d )
0.9 nm)18,19 as well as to polystyrene/o-TP (o-terphenyl) in CPG
(d ) 1.0-2.5 nm)38 and glycerol in CPG (d ) 0.9 nm),24
although it differs from that for propylene glycol in Gelsil
nanopores (d ) 0.15 nm).40
Isothermal Reaction Kinetics. The glass transition temper-
ature is employed as a kinetic parameter to monitor the progress
of reaction as a function of reaction time in this study. Following
Tg is akin to following conversion, since Tg and conversion have
a unique one-to-one relationship18,41 given by the DeBenedetto
equation,42
Tg - Tg0
Tg∞ - Tg0
λx
*
Tg )
)
(4)
1 - (1 - λ)x
where λ is a structure-dependent parameter, T* is the dimension-
g
less glass transition temperature, Tg0 is the Tg of the unreacted
monocyanate ester, and Tg∞ is the Tg of the completely reacted
cyanurate trimer. The advantage of using Tg instead of conver-
sion to follow the reaction is that Tg is sensitive and is easily
and accurately determined.43 The error in the Tg measurement
is ∼1 K, and the change in Tg with conversion is 105 K (for
the bulk), giving an error of ∼1.0%; on the other hand, the
error in the heat of reaction is 1.3-3.9% initially, depending
on pore size, and increases as the residual heat decreases. In
addition, only one sample is needed to obtain the entire Tg versus
reaction time data (using the experimental procedure method 1
described earlier), whereas each conversion data point consumes
one sample, since after the residual heat of reaction is measured,
the sample is fully reacted.
Perhaps more important than the effect of nanoconfinement
on Tg∞, the Tg-versus-reaction time curves shift to shorter time
with decreasing nanopore size. Hence, the trimerization reaction
is accelerated as pore size decreases, consistent with the shift
of the exotherms to lower temperatures in the dynamic scans,
as shown in Figure 2. The bulk reaction kinetics of monofunc-
tional cyanate ester follow a first-order plus first-order auto-
catalytic reaction model,
Figure 6 shows the relationship between Tg and conversion
for the bulk unconfined sample and for the sample confined in
13 nm pores. The relationship is unchanged by the nanopore
confinement, similar to our prior results for a difunctional
cyanate ester.18 It must be noted that since two Tgs exist at the
nanoscale, the Tg value of the 13 nm nanopore is the average
glass transition temperature determined on the basis of the
primary and secondary Tg values, weighted by their correspond-
ing heat capacity changes at Tg:18
dx
dt
) k(1 - x)(x + b)
(7)
where x is conversion, t is reaction time, and k is the Arrhenius
rate constant for the first-order autocatalytic reaction. The
constant b has been related to the fraction of trace impurities
which catalyze the reaction initially.41 In addition, any differ-
ences in the activation energies of the first order and first-order

7732 J. Phys. Chem. B, Vol. 114, No. 23, 2010
Koh and Simon
Figure 8. The acceleration factor as a function of reciprocal pore
diameter for Tg1 (solid symbols) and for Tg2 (open symbols). The dashed
line is intended only as a guide to the eye.
similar for the primary Tg1 and secondary Tg2 data. The
acceleration factor increases with decreasing nanopore size, with
the reaction rate being accelerated by a factor of 21 in 8 nm
pores (as measured by Tg1).
Discussion
In this study, nanoconfinement accelerates the trimerization
reaction relative to the bulk. The enhanced reactivity at the
nanoscale has been suggested to be due to an enhanced collision
efficiency or frequency induced by the presence of the nanopore
surface,18 since the proximity of the surface results in a decreased
rate of reactants diffusing apart. Other explanations for the origin
of the acceleration include a change in reaction mechanism at
the nanoscale, the catalytic effect of the nanopore surface, or
both. However, the same heat of reaction and the same kinetic
rate expression for the bulk and the nanoconfined materials
provide evidence that the reaction mechanism is unchanged at
the nanoscale. In addition, the catalytic effect of the nanopore
surface is not considered to be the cause of the enhanced
reactivity on the basis of the same activation energy for the
bulk and nanoconfined samples and similar acceleration factors
for Tg1 and Tg2. Hence, an intrinsic size effect18 is suggested to
be the reason for the enhanced reactivity under nanoconfinement.
In addition, our result of the enhanced reactivity for the
trimerization of monofunctional cyanate ester gives proof that
the enhanced reactivity of difunctional cyanate ester under
nanoconfinement18,19 is not due to its intracyclization side
reaction, since our reactant cannot cyclize due to its monofunc-
tional nature.
Figure 7. Glass transition temperature as a function of logarithmic
reaction time in the bulk and for material confined in nanopores for
Tg1 (upper figure) and Tg2 (lower figure) at the reaction temperature of
141 °C. Solid symbols and + and × symbols represent the data obtained
by method 1 (single sample). Open symbols represent the data obtained
by method 2 (multiple samples). The solid lines are the best fit to the
reaction model. Only one Tg is observed for the bulk, and these values
are plotted in both figures.
autocatlytic reactions are also incorporated into b. Coupling the
kinetic rate equation with the DeBenedetto equation (eq 4) yields
Tg as a function of reaction time. The solid lines shown in Figure
7 are the best fits to both the bulk and nanoconfined experimental
data. It is clear that the reaction model describes the experi-
mental results well for both the bulk and nanoconfined samples,
indicating the reaction model and overall reaction mechanism
are unchanged at the nanoscale, consistent with the unchanged
heat of reaction and unchanged activation energy, and similar
to prior results for a dicyanate ester reaction.18
The magnitude of the effects of nanoconfinement on the Tg
depression is, as mentioned in the Introduction, related to the
material, confinement method, and measurement technique. It
has recently been suggested that the effects of nanoconfinement
on Tg can be altered by modification of the molecular structure47
or addition of diluent,48,49 presumably through the changes in
chain stiffness or in the size of the cooperatively rearranging
region. Backing up the hypothesis that the magnitude of the Tg
change at fixed confinement size increases with chain stiffness,
we found in previous work18,19,50 that the Tg depression in a
dicyanate ester/polycyanurate material increases with increasing
conversion and, thus, with increasing Tg and increasing chain
stiffness. In this study, we also observe that the Tg depression
The magnitude of the reaction acceleration can be quantified
by the acceleration factor, R:
k
kbulk
R )
(8)
where k is the rate constant obtained by fitting eq 7 to the data
and kbulk is the rate constant for the bulk unconfined sample.
The R value for the bulk sample is 1.0 by definition. Figure 8
shows the resulting acceleration factor as a function of reciprocal
nanopore size. The acceleration factor of monocyanate ester is

Trimerization of Monocyanate Ester in Nanopores
J. Phys. Chem. B, Vol. 114, No. 23, 2010 7733
controlled pore glass nanopores. Changes in reaction rate and
the glass temperature are investigated as a function of pore size
using DSC. From dynamic temperature scans, the trimerization
reaction rate is found to be shifted to lower temperatures as
pore size decreases. From isothermal reaction studies, the
trimerization reaction of monocyanate ester is found to be faster
as pore size decreases with an acceleration of ∼21 relative to
the bulk reaction rate for cyanate ester in 8 nm pores (based on
Tg1). Both the monocyanate ester reactant and cyanurate product
show lower Tgs upon nanoconfinement, as compared to the bulk;
the Tg depression increases with conversion and is more
pronounced for the fully reacted product, suggesting that
molecular stiffness influences the magnitude of nanoconfinement
effects. The heat of reaction, activation energy, and reaction
kinetic model are unchanged under nanoconfinement, suggesting
that intrinsic size effects are the origin of the enhanced reactivity
for the nanopore confinement. In addition, our results of
monofunctional cyanate ester are consistent with the accelerated
reaction and the Tg depression found previously for the
nanoconfined difunctional cyanate ester, supporting the assertion
that intracyclization is not the origin for these effects, since our
monocyanate ester cannot intracyclize due to its monofunctional
nature.
Figure 9. Change in the average glass temperature from the bulk as
a function of pore diameter at different conversions, x. The dashed
lines are intended only as guides to the eye.
increases with increasing conversion. This is clearly shown in
Figure 9 by replotting the Tg depression of Figure 7 as a function
of pore diameter for different conversions, x. In Figure 9, the
average Tg was used as defined in eq 5. The change Tg in average
for the unreacted monomer (x ) 0) for a given pore size is
only 1 K, but as the reaction proceeds, the magnitude of the Tg
change increases with increasing conversion; that is, the degree
of nanoconfinement on Tg is enhanced by the reaction. The result
suggests that molecular stiffness (molecular, in this case, since
our molecules are not chains) influences the magnitude of
nanoconfinement effects.
There has been considerable discussion of the origin of the
Tg depression in nanoconfined materials.1-13,51-53 A leading
hypothesis, particularly for researchers involved in work on
polymer ultrathin films, is that higher mobility at the free surface
is responsible (or partially responsible) for the Tg depression.7-13
On the other hand, for the fully reacted cyanurate studied here,
we observed a Tg depression for both Tg1 and Tg2, with a larger
depression always observed for Tg1. If the two-layer model18,33
is correct, and we note in this regard that it is consistent with
the ∆Cp data as shown in Figure 5, the fact that Tg1 > Tg2
indicates the surface is less mobile than the core. Hence, the Tg
depression in our nanoconfined system cannot readily be
attributed to a greater mobility at the interface.
Acknowledgment. The authors gratefully acknowledge fund-
ing from the American Chemical Society Petroleum Research
Fund 45416-AC7 and funding from the Texas Higher Education
Coordinating Board Advanced Research Program.
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