Polymerization kinetics of adamantane-based dicyanate ester and thermal properties of resulting polymer

Article abstract of DOI:10.1016/j.reactfunctpolym.2021.104956

The kinetics of liquid-state polymerization of adamantane-based dicyanate ester has been studied for the first time by means of conventional and temperature-modulated DSC. It has been detected that the later stages of polymerization undergo a transition from kinetic- to diffusion-controlled regime. Detailed analysis of the polymerization kinetics in the reaction-controlled regime has revealed that the process rate can be well described in the frameworks of the presently proposed autocatalytic quasi-one-step model. The proposed model eliminates arbitrarily guessing the value for the initial conversion that provides a reasonable alternative to the broadly used truncated Sestak-Berggren model. The adamantane-based dicyanate ester polymerization product demonstrates markedly higher thermal stability and glass transition temperature compared to those of dicyanate esters with flexible hydrocarbon bridging units. The obtained experimental results confirm our hypothesis about the influence of the rigidity of cyanate ester molecule on its reactivity and thermal properties of the corresponding polymer product.

Full text of DOI:10.1016/j.reactfunctpolym.2021.104956

Reactive and Functional Polymers 165 (2021) 104956
Contents lists available at ScienceDirect
Reactive and Functional Polymers
journal homepage: www.elsevier.com/locate/react
Perspective Article
Polymerization kinetics of adamantane-based dicyanate ester and thermal
properties of resulting polymer
,
Andrey Galukhina *, Roman Nosova, Guzel Taimovaa, Ilya Nikolaeva, Daut Islamovb,
,c,**
Sergey Vyazovkina
a Alexander Butlerov Institute of Chemistry, Kazan Federal University, 18 Kremlevskaya Street, 420008 Kazan, Russian Federation
b Arbuzov Institute of Organic and Physical Chemistry, FRC Kazan Scientific Center, Russian Academy of Sciences, 8 Arbuzov street, Kazan 420088, Russian Federation
c Department of Chemistry, University of Alabama at Birmingham, 901 S. 14th Street, Birmingham, AL 35294, USA
A B S T R A C T
The kinetics of liquid-state polymerization of adamantane-based dicyanate ester has been studied for the first time by means of conventional and temperature-
modulated DSC. It has been detected that the later stages of polymerization undergo a transition from kinetic- to diffusion-controlled regime. Detailed analysis of
the polymerization kinetics in the reaction-controlled regime has revealed that the process rate can be well described in the frameworks of the presently proposed
autocatalytic quasi-one-step model. The proposed model eliminates arbitrarily guessing the value for the initial conversion that provides a reasonable alternative to
the broadly used truncated Sestak-Berggren model. The adamantane-based dicyanate ester polymerization product demonstrates markedly higher thermal stability
and glass transition temperature compared to those of dicyanate esters with flexible hydrocarbon bridging units. The obtained experimental results confirm our
hypothesis about the influence of the rigidity of cyanate ester molecule on its reactivity and thermal properties of the corresponding polymer product.
1. Introduction
the group and may either increase or diminish thermal stability [13,14].
The introduction of adamantane groups into polymer structure is of
special interest because of their rigidity and high thermodynamic sta-
bility. Being introduced into the main chain or as side group, ada-
mantane increases thermal stability of the polymeric material [15,16].
Finding general relationships between the structure of a monomer
and its reactivity is a difficult task because of numerous possible
mechanisms of polymerization process (cationic, anionic, radical, co-
ordination, etc). For example, electron-withdrawing groups accelerate
anionic-polymerization of vinyl monomers, but inhibit its cationic
polymerization [17,18]. Also, the process may switch from a kinetic- to
diffusion-controlled regime during the polymerization progress that
further complicates the task. However, since this switch is usually
observed near the glass transition temperature of the reaction mixture
one can expect that the structural factors decreasing the segmental
mobility (i.e., those increasing Tg) should promote an earlier transition
of the reaction kinetics to diffusion-controlled regime during polymer-
ization. This idea is illustrated schematically in Fig. 1, where two
High-performance thermosets based on cyanate resins play an
important role in the electronic, military, and aerospace industries
because the resulting materials possess unique mechanical, thermal, and
dielectric properties [1–4]. Their irreplaceable practical utility promotes
fundamental studies of intrinsic relationships between the structure of
cyanate esters and their reactivity, as well as properties of the final
polymeric materials. Such studies are essential for directed design of
thermosets with desired properties [3,5–7]. The thermal stability and
glass transition temperature are the most important thermal properties
that determine possible areas and conditions of the application of
thermosets.
The influence of the polymer structure on the thermal properties of
polymers is generally well studied. It is known that introduction of rigid
fragments into the main polymer chain increases both thermal stability
and glass transition temperature (Tg) of the corresponding polymers [8].
The presence of polar side groups or groups capable of forming hydrogen
bonds tends to decrease the segmental mobility of polymer chains and
thus results in higher glass transition temperatures of the corresponding
polymers [9–12]. The effect of aforementioned groups on thermal sta-
bility of polymers is more complex and depends on particular nature of
monomers of similar reactivity (similar
different Tg’s (both for monomers and polymers) have significantly
different points of intersection of the corresponding -T and Tg- curves.
It is seen that polymerization of a monomer that gives rise to a polymer
α-T curves), but with markedly
α
α
* Corresponding author.
** Corresponding author at: Department of Chemistry, University of Alabama at Birmingham, 901 S. 14th Street, Birmingham, AL 35294, USA.
E-mail addresses: and_galuhin@mail.ru (A. Galukhin), vyazovkin@uab.edu (S. Vyazovkin).
https://doi.org/10.1016/j.reactfunctpolym.2021.104956
Received 27 February 2021; Received in revised form 11 May 2021; Accepted 2 June 2021
Available online 10 June 2021
1381-5148/© 2021 Elsevier B.V. All rights reserved.

A. Galukhin et al.
Reactive and Functional Polymers 165 (2021) 104956
(>99.5%, EKOS-1), hydrochloric acid (>35%, Component-Reagent),
Na2SO3 (anhydrous, > 99%, Chimmed), Na2SO4 (anhydrous, > 99.5%,
Chimmed), SiO2 (60 Å, 0.04–0.063 mm, Machery-Nagel), P2O5 (>98%,
Vekton), and isopropanol (99.8%, REACHEM) were purchased and used
as received. Acetone (>98%, TatChemProduct) was purchased and
additionally distilled over P2O5.
Target dicyanate ester 4 was obtained according to the synthetic
procedure presented in Fig. 2.
1,3-dibromoadamantane 2 and 1,3-bis(4-hydroxyphenyl)adaman-
tane 3 were synthesized according to known synthetic protocols
[22,23].
Synthesis of 1,3-bis(4-cyanatophenyl)adamantane 4. 1,3-bis(4-
hydroxyphenyl)adamantane 3 (2.0 g, 6 mmol), cyanogen bromide
(2.7 g, 25 mmol), and 30 mL of acetone were added to a round bottom
flask with a magnetic stirrer. The reaction mixture was cooled to ꢀ 20◦С,
and then triethylamine (3.5 mL, 25 mmol) was added dropwise. The
synthesis was carried out for an hour under continuous stirring and
cooling. Then solvent was removed from reaction mixture under
reduced pressure and obtained residue was dissolved in dichloro-
methane and washed several times with deionized water. Obtained
organic solution was dried over anhydrous Na2SO4 and target compound
was separated by column chromatography (dichloromethane as an
eluent). The resulting product 4 was purified by recrystallization from
the mixture of CH2Cl2 and hexane. The final yield of pure product was
1.8 g (81%). Mp: 122 ◦C. 1H NMR, CDCl3-d1, δ (ppm): 1.83 (s, -CH2-,
2H), 1.97–2.00 (m, -CH2-, 8H), 2.38 (s, -CH-, 2H), 7.27 (d, ArH, 4H, J =
8.4 Hz), 7.47 (d, ArH, 4H, J = 8.4 Hz). 13C NMR, δ (ppm): 29.32, 35.47,
37.22, 42.11, 49.02, 108.98, 115.02, 126.98, 149.19, 150.97. Crystal
Data. C24H22N2O2, Mr = 370.43, triclinic, P-1 (No. 2), a = 7.3404(3) Å,
Fig. 1. Schematic illustration of the effect of the polymer Tg value on the
reactivity of a monomer. Dashed lines represent variation of Tg with conversion
(α), solid lines represent α-T plots obtained at the heating rate β. Circles show
intersection points of the corresponding α-T and Tg-α curves.
having higher Tg is more likely to encounter vitrification at earlier stages
of the reaction progress.
In all, we hypothesize that incorporation of adamantane into the
structure of cyanate resin as a rigid bridging fragment should increase
the glass transition temperature and thermal stability of the resulting
polymer. Also we expect that the reactivity of the monomer should be
affected by vitrification as described above. To explore this hypothesis
we have synthesized adamantane-based dicyanate ester, which is sub-
jected to thermal polymerization. We have studied the obtained mono-
mer reactivity by both conventional and temperature-modulated DSC
under nonisothermal conditions and parameterized its polymerization
kinetics with the aid of isoconversional methodology [19]. We have also
applied thermogravimetry to test the thermal stability of the polymeri-
zation product and compared it with that of the polymers produced from
commercially available dicyanate esters of similar structure. It should be
noted that although adamantane-based cyanate esters are known since
the middle of the last decade [20,21] the kinetics of their polymerization
has never been studied before.
b = 10.5239(6) Å, c = 12.9183(6) Å,
α
= 107.619(4)◦, β = 104.129(4)◦,
γ = 93.734(4)◦, V = 911.86(8) Å3, T = 100.0(2) K, Z = 2, Z’ = 1,
μ(Cu
Kα) = 0.686, 10,248 reflections measured, 3681 unique (Rint = 0.0297)
which were used in all calculations. The final wR2 was 0.1182 (all data)
and R1 was 0.0409 (I > 2(I)). CCDC number 2065109.
2.2. Methods
2.2.1. Methods for the determination of the structure and purity of target
monomer
Data set for single crystal of the monomer was collected on a Rigaku
XtaLab Synergy S instrument with a HyPix detector and a PhotonJet
microfocus X-ray tube using Cu Kα (1.54184 Å) radiation at low tem-
perature. Images were indexed and integrated using the CrysAlisPro
data reduction package. Data were corrected for systematic errors and
absorption using the ABSPACK module: numerical absorption correction
based on Gaussian integration over a multifaceted crystal model and
empirical absorption correction based on spherical harmonics according
to the point group symmetry using equivalent reflections. The GRAL
module was used for analysis of systematic absences and space group
determination. The structure was solved by direct methods using
SHELXT and refined by the full-matrix least-squares on F2 using SHELXL
[24,25]. Non‑hydrogen atoms were refined anisotropically. The
hydrogen atoms were inserted at the calculated positions and refined as
2. Experimental section
2.1. Materials
Iron powder (≥99%, Sigma-Aldrich), bromine (99.6%, Acros Or-
ganics), adamantane (>99%, Sigma-Aldrich), triethylamine (>99%,
Sigma-Aldrich), cyanogen bromide (97%, Acros Organics), phenol
(99.5%, Acros Organics), ethanol (95%, RFK), trichloromethane
(>99.5%, EKOS-1), dichloromethane (>99.5%, EKOS-1), hexane
Fig. 2. Scheme of synthesis of target dicyanate ester.
2

A. Galukhin et al.
Reactive and Functional Polymers 165 (2021) 104956
Fig. 3. Single-crystal X-ray crystallographic structure of synthesized tricyanate ester 4 (H atoms – light grey, C atoms – dark grey, N atoms – blue, O atoms – red). –
(A). Crystal packing of dicyanate ester view along a axes – (B). (For interpretation of the references to colour in this figure legend, the reader is referred to the web
version of this article.)
riding atoms. The figures were generated using Mercury 4.1 program
[26]. Crystals of the target cyanate ester were obtained by crystallization
from the mixture of CH2Cl2 and hexane. The HPLC analysis was carried
out with a Dionex Ultimate 3000 chromatograph equipped with a UV
detector (254 nm) and Dionex Acclaim 120 chromatographic column
function:
n
n
∑ ∑
J[Eα, Ti(tα) ]
[
]
Ψ(Eα) =
(1)
J Eα, Tj(tα)
i=1 j∕=i
where
(C18-bonded silica, 5 μm, 120 Å, 4.6 × 250 mm). Mixture of 85% of
[
]
∫
acetonitrile and 15% of deionized water (by volume) was used as an
eluent at a flow rate of 1 mL minꢀ 1. The 1H and 13C NMR experiments
were carried on a Bruker AVANCE III NMR spectrometer operating at
600.13 MHz. IR spectra were recorded with Bruker Vertex 70 FTIR
spectrometer.
tα
ꢀ Eα
J[Eα, Ti(tα) ] ≡
exp
dt
(2)
RTi(t)
tα
ꢀ ∆
α
and n is the number of the temperature programs. The trapezoid rule
was employed to compute the integral. The COBYLA non-gradient
method from the NLopt library was utilized to determine a minimum
of Eq. (1). The uncertainties in the Eα values were evaluated according to
procedure described elsewhere [31].
2.2.2. Thermal analysis
Calorimetric measurements were carried out using a heat flux DSC
3+ (Mettler-Toledo). Indium and zinc standards were used to perform
temperature, heat flow, and tau-lag calibrations. The experiments were
performed in the atmosphere of argon flow (80 mL minꢀ 1) at the heating
The preexponential factor values were estimated by substituting the
values of Eα into the equation of the compensation effect
rates of 2.0, 4.0, 6.0, 8.0 and 10.0 ◦C minꢀ 1 in 40
μ
L aluminum pans
lnAα = a + bEα
(3)
sealed in argon atmosphere as well. Because moisture could potentially
affect polymerization, before sealing the monomer samples placed in 40
The parameters a and b were determined by fitting the pairs of lnAi
and Ei into Eq. (3). The respective pairs were found by substituting the
μ
L aluminum pans were kept in a vacuum desiccator containing a beaker
reaction models fi(
α
), into the linear form of the basic rate equation:
filled with P2O5 for 1 day to remove traces of water before measure-
ments. The mass of the cyanate ester sample for each run was ~1 mg. For
temperature modulated DSC (TMDSC), the samples were heated from 25
to 400 ◦C at the heating rate of 1 ◦C minꢀ 1 superimposed with stochastic
temperature pulses of 0.5 ◦C amplitude and pulse time that ranged from
15 to 30 s. For the glass transition measurements 10 mg of cyanate ester
(
)
d
dt
α
Ei
RT
ln
ꢀ ln[fi(
α
) ] = lnAi ꢀ
(4)
For each reaction model, lnAi and Ei values were evaluated respec-
tively from the slope and intercept of the linear plot of left-hand side of
Eq. (4) vs the reciprocal temperature. Five pairs of lnAi and Ei were
evaluated by the model
monomer in 40 μL aluminum pans were polymerized directly in DSC
instrument (25 to 400 ◦C at the heating rate of 4 ◦C minꢀ 1) and then
studied by TMDSC. Thermogravimetric analysis was carried out with
Netzsch STA 449 F1 Jupiter thermal analyzer. The sample of ~10 mg
n
f(α
) = αm(1 ꢀ
α
)
(5)
was heated from 40 to 1000 ◦C under argon flow of 75 mL minꢀ 1
.
with five different combinations of m and n (m = 1, n = 1; m = 0.5, n = 1;
m = 1, n = 0.5; m = 2, n = 1, m = 1, n = 2). This model was selected
because of its ability to imitate the autocatalytic reaction kinetics, which
3. Computations
is typical of cyanate esters polymerization [3]. In addition, this f(α)
model is a part of a more complex reaction model by Kamal [32] that has
been used successfully for describing the kinetics of cyanate ester
polymerization [33,34].
The recommendations of the ICTAC Kinetic Committee were fol-
lowed to evaluate the activation energy and preexponential factor de-
pendencies [27]. The extent of conversion, α, values were determined as
The experimentally estimated values of Eα and Aα have been used to
establish the integral reaction model in the numerical form:
∑
the partial areas of the DSC peaks associated with polymerization of the
cyanate ester. The effective activation energy, Eα, was evaluated as a
function of conversion with the aid of the flexible integral isoconver-
sional method of Vyazovkin [28–30]. The method allows one to elimi-
g(α
) =
AαJ[Eα, Ti(tα) ]
(6)
α
nate a systematic error in Eα when it varies with
α. The error is
eliminated via flexible integration that assumes the constancy of Eα
within a very narrow integration range, Δ . The value of Δ was taken as
0.01. Within each Δ , Eα is determined by finding a minimum of the
4. Results and discussion
The structure of the synthesized monomer was confirmed by single
α
α
α
3

A. Galukhin et al.
Reactive and Functional Polymers 165 (2021) 104956
Fig. 4. Scheme of cyclotrimerization of cyanate ester.
Fig. 6. Heat flow curves for cyanate ester polymerization (numbers denote
heating rates in ◦C minꢀ 1).
90 kJ per 1 mol of OCN groups, which agrees well with the known re-
action heat values for dicyanate esters (80–110 kJ per 1 mol of OCN
groups) [2].
To quantify the reactivity of the synthesized cyanate ester DSC data
were treated by isoconversional kinetic analysis. The isoconversional
values of the activation energy Eα and preexponential factor Aα for
polymerization process are displayed in Fig. 7. Fig. 7A shows that
polymerization of cyanate ester demonstrates insignificant variation of
Fig. 5. Non-reversing heat flow and heat capacity curves for cyanate ester
polymerization measured at 1 ◦C minꢀ 1 with stochastic modulation.
crystal X-ray diffraction analysis, which suggests the absence of both
intra- and intermolecular interactions between cyanate groups (Fig. 3).
Polymerization of cyanate esters produces significant amounts of
heat due to the formation of highly stable aromatic 1,3,5-triazine frag-
ments as cross-links (Fig. 4). Thus, the reaction progress is conveniently
followed by DSC.
the activation energy with conversion in a range of 0.10–0.75 of
α
(variation of Eα does not exceed 10% of average Eα in that range of
conversions), which equals to 93 ± 3 kJ molꢀ 1. The subsequent rise of
the activation energy to 114 kJ molꢀ 1 is likely related to the transition of
the polymerization kinetics to a diffusion-controlled regime. The pre-
exponential factor values demonstrate similar variation (Fig. 7B) with
average lnAα value of 15.7 ± 0.6 in the same aforementioned conversion
range.
The kinetics of cross-linking polymerization, especially at later stages
of the process can be complicated by a transition from a kinetic- to
diffusion-controlled regime [19]. This transition occurs when rising
viscosity of the reaction mixture slows down translational motion of the
polymer chains so that the characteristic time of diffusion exceeds the
characteristic time of the reaction. This phenomenon is usually associ-
ated with vitrification of the forming polymer, which is observed when
its glass transition temperature rises above the temperature of the
reacting system (Fig. 1). Because vitrification decelerates dramatically
the polymerization process, its occurrence is an unequivocal sign of the
process transitioning into a diffusion-controlled regime.
The constancy of the activation energy at conversions below 0.75
signifies that polymerization process is controlled by a single reaction
step, which is uncommon for non-catalyzed polymerization of cyanate
esters. Because the process occurs via a complex mechanism involving
the formation of several intermediates [5], one should rather expect to
encounter a variation in the effective activation energy with conversion,
as observed in previous work [34,36]. The kinetics of cyanate esters
polymerization is usually described by a reaction model that involves
two steps (eq. (7)), one of which has auto-catalytic nature [6,33,37–43],
however attempts to describe the kinetics of polymerization as a single
nth-order [44] or auto-catalytic [45] reaction have also been reported.
To check whether vitrification occurs during the polymerization we
have performed temperature modulated DSC measurements (TMDSC).
The technique permits separation of the reversing (vitrification) and
non-reversing (chemical reaction) contributions to the measured total
heat flow [35]. Since the liquid and glass states possess different heat
capacities, vitrification manifests itself as a step change in the measured
value of the heat capacity. As seen from Fig. 5, such a step is clearly
observed in the quasistatic heat capacity, Cp,0 determined from the
reversing heat flow component of the TMDSC measurement. The mid-
point of the heat capacity step is found at 273 ◦C, which corresponds
to conversion of 0.95. Thus, one can expect that the kinetics of poly-
merization of the present monomer may demonstrate a transition to a
diffusion-controlled regime in the later stages of the process.
d
dt
α
n
n
= k1αm(1 ꢀ
α
) + k2(1 ꢀ
α
)
(7)
However it should be noted that the occurrence of single-step ki-
netics is not the only reason of constant activation energy. The latter
would be constant when a process involves two or more steps having the
same (or reasonably close) values of the activation energy. To make eq.
(7) more convenient for description of such situation let us factor out (1
ꢀ
α
)n and k1, and replace k2/k1 by B:
d
dt
α
n
= k1(B + αm)(1 ꢀ
α
) ,
(8)
The kinetics of polymerization process was studied by conventional
DSC. Heat flow curves for polymerization of the cyanate ester at
different heating rates are presented in Fig. 6. Average heat of poly-
merization is 480 ± 20 J gꢀ 1 or 180 ± 8 kJ molꢀ 1. This corresponds to
The rate equation of a similar form (with m = 1, n = 1 or 2, and B as a
constant) was semi-empirically derived by Simon and Gillham [6,41] for
mono- and dicyanate esters polymerization. In these studies, the
4

A. Galukhin et al.
Reactive and Functional Polymers 165 (2021) 104956
Fig. 7. Dependencies of activation energy (A, left panel) and preexponential factor (B, right panel) as a function of conversion for polymerization of cyanate ester.
constant B was linked to the amount of impurities, which catalyze re-
action initially. Of course, eq. (8), as derived here, is quite different not
only because it contains the exponents m and n, but also because it as-
signs entirely different meaning to the parameter B. In general, eq. (8)
can be reduced to four different cases:
[
]
E1ꢀ E2
RT.
1. E1 ∕= E2, A1 ∕= A2, then B = A exp
A12
[
]
E1ꢀ E2
2. E1 ∕= E2, A1 ≈ A2, then B ≈ exp
RT
3. E1 ≈ E2, A1 ∕= A2, then B ≈ A
2
4. E1 ≈ E2, A1 ≈ A2, then B ≈ A11
The first and second cases (E1 ∕= E2) result in B being a function of
temperature, whereas third and fourth cases (E1 ≈ E2) provide constant
B values. Thus, both eqs. (7) and (8) can be used for description of
polymerization of cyanate esters involving one or two steps. For the sake
of clarity, we propose to use eq. (7) explicitly involving two kinetic
triplets for the processes with variable activation energy, whereas eq. (8)
involving one kinetic triplet for the processes demonstrating constant or
insignificantly variable activation energy. The reaction model in the rate
eq. (8) presented by the function:
Fig. 8. Experimental g(α) data for polymerization of dicyanate ester.
n
f(α
) = (B + αm)(1 ꢀ
α
)
(9)
Table 1
Estimated kinetic parameters for polymerization of dicyanate ester 4.
where B is a constant, can be considered as a reasonable alternative to
the autocatalytic model expressed by eq. (5) (aka the truncated Sestak-
Berggren or expanded Prout-Tompkins model), widely used for
description of autocatalytic processes. An alternative is needed because
eq. (5) cannot be used for kinetic simulations without making an illog-
Fit to
E1/kJ
ln(A1/
m
n
B
ln(A2/
molꢀ 1
sꢀ 1
)
sꢀ 1
)
Eq. (10)
–
–
1.16 ±
0.01
1.15 ±
0.01
0.024 ±
0.001
0.09 ±
0.02
–
Eq. (8)
(way
1)
*93 ± 3
15.5 ±
1.3 ±
0.1
0.9 ±
0.1
**13.1
ical assumption that a reaction has to start at a nonzero value of
α [46].
0.1
This problem is aggravated by the fact that the resulting simulations are
affected significantly by the specific choice of this initial nonzero value
Eq. (8)
(way
2)
*93 ± 3
15.2 ±
0.8 ±
0.7 ±
*0.024 ±
**11.5
of
α. The proposed model (eq. (9)) does not have this problem that
0.2
0.1
0.1
0.001
provides an important advantage over autocatalytic model expressed by
eq. (5). It should be noted, that the constant B in the proposed model
being a ratio of preexponential factors of two competing reactions with
similar activation energies indicates how many times the nth-order re-
action rate constant exceeds the autocatalytic reaction rate constant. In
case of B ≤ 0.1 or B ≥ 10, the contribution of one of the reactions to the
effective reaction rate constant is less than 10%, which is close to the
error of its calculation, therefore such reactions might be considered as a
quasi-one-step processes.
Symbol * denotes values used as constants during fitting; Symbol ** denotes the
lnA2 values estmated from the values of B and lnA1
eq. (6) to the integral form of eq. (9) as follows:
α
∫
d
α
g(α
) =
(10)
n
(B + αm)(1 ꢀ
α)
0
To show the ability of the proposed model (eq. (9)) to describe
The results of the fit are presented in Fig. 8. It is seen that the pro-
posed model allows for a good quality fit. The estimated values of B, m,
experimental data we have fitted the numerical g(α) data obtained via
5

A. Galukhin et al.
Reactive and Functional Polymers 165 (2021) 104956
Fig. 10. Comparison of the experimental polymerization rate curves (triangles)
with the ones estimated with (solid line) and without (dashed line) account of
diffusion control.
Fig. 9. The diffusion factor fd(α) values averaged over all heating rates (di-
amonds) calculated with kinetic parameters from Table 1 (second line) and the
best fit by eq. (12) (dashed line).
values at the corresponding
α values. As expected, the values of fd(α)
and n are shown in Table 1. The results indicate that the m and n values
are close to 1 and from the value of B we can conclude that A2 is about 40
times larger than A1.
stay close to unity up to conversion of 0.75 then drop quickly to
~0.3–0.4 after the reaction swithes to diffusion-control regime (Fig. 9).
Fournier et al. proposed the following empirical equation [47] to
describe a dependence of diffusion factor on conversion:
Alternatively, we have used the rate data for
α < 0.75 to fit to eq. (8)
to estimate the parameters of the kinetically-controlled polymerization.
This has been done in two different ways (denoted in Table 1 as “way 1”
and “way 2”). First, the fitting has been performed by using A1, m, n, and
B as the fit parameters. Second, only A1, m, and n have been used as the
fit parameters, while keeping B as a constant determined by fitting eq.
(10). In both cases, k1 in eq. (8) has been replaced with the Arrhenius
equation, in which the E1 value taken as a constant (93 ± 3 kJ molꢀ 1), as
determined by the advanced isoconversional method. The resulting
values of the obtained kinetic parameters are presented in Table 1
(uncertainties are given in as the standard deviations). Using B as a fit
parameter yields about 4 times larger value than the one determined
from eq. (10). However, the parameters m and n remain close to 1. When
using B obtained from fitting eq. (10), the parameters m and n drop to
smaller values. Yet, the value of lnA1 remains practically the same in
both cases. Combining the A1 and B values, it is also possible to estimate
the lnA2 values, which differ by less than 2 units on the natural log scale
(Table 1). More precisely, the respective A2 values differ by about 5
times. To sum up, all the obtained fitting parameters seem reasonably
consistent with each other regardless of the way used for fitting. Since
fitted B parameter values are below 0.1 regardless of fitting procedure,
the polymerization in reaction-controlled regime might be considered as
a quasi-one-step processes according to the aforementioned reasons.
(
[
] )
ꢀ 1 ꢀ 1,
(12)
α
ꢀ
αf
fd(
α
) = 2 1 + exp
b
where αf is the final conversion and b is an empirical parameter. The use
of empirical models, such as eq. (12), remains the most efficient way for
accounting the effect of diffusion on the crosslinking kinetics. The
application of more advanced phenomenological models is obstructed
by the need in nontrivial and extensive experimental studies to obain
such data as the diffusion rate constant and its dependence on viscosity
and temperature of the reaction medium as well as of viscosity of the
medium and its dependence on the polymerization degree and temper-
ature [49].
Eq. (12) has been fitted to the fd(α) values obtained as the ratio of the
experimental rate to the reaction-controlled rate data. The latter have
been determined by substituting the A1, m, n, and B (second line in
Table 1) into eq. (8). The αf has been set as 1 because a FTIR spectrum of
the polymerization product does not show the presence of unreacted
cyanate groups at 2265 and 2360 cmꢀ 1, i.e., polymerization can be
considered as complete. The resulting fd(α) data are presented in Fig. 9.
Fig. 10 illustrates how the rate equations with and without the
diffusion factor (i.e., eq. (8) and eq. (13)) describe the experimental data
in the whole range of conversions. Expectedly eq. (8) fails to describe the
experimental data outside of the kinetically-controlled conversion
range, whereas eq. (13) matches well the experimental plots in the
whole conversion range. The overall rate equation with account of
diffusion takes the following form:
To account for diffusion that controls the later stages (α > 0.75) of
polymerization, we have employed a simple and convenient approach,
which parameterizes the total polymerization rate as the product of
reaction-controlled reaction rate [d
α
/dt]r and conversion-dependent
diffusion factor fd(
α
) [47,48]:
(
)
(
[
] )
d
dt
α
dα
dt
= k1(1 ꢀ
α
) (B + αm
)
2
1 + exp
ꢀ 1 ꢀ 1
(13)
[
]
d
α
α ꢀ 1
0.068
n
=
fd(α
)
(11)
dt
r
It is instructive to compare the reactivity of the presently studied
fd(
α
) is close to unity when reaction proceeds in a reaction-controled
monomer containing the rigid adamantane bridging fragment with
other dicyanate esters contaning flexible hydrocarbon bridging units.
The switching of the polymerization from reaction- to diffusion-
controlled regime is of particular interest. As already mentioned, the
polymerization of presently studied dicyanate ester with rigid
regime, and decreases when it switches to diffusion control. Knowing
the parameters of the reaction-controlled process (Table 1) one can
easily calculate the corresponding reaction rate using the experimental
α
and T values in eq. (7). In accord with eq. (11) the ratio of the experi-
mental rate to the reaction controlled rate gives the diffusion factor
6

A. Galukhin et al.
Reactive and Functional Polymers 165 (2021) 104956
the presence of two peaks (448 and 540 ◦C) on derivative TG (DTG)
curve (Fig. 12). The two-step mass loss is typical for cyanate polymers
[51].
It is also informative to compare the thermal stability of the present
polymer product against above-mentioned polymers containing flexible
hydrocarbon bridging fragments. The 5% mass loss temperature of our
adamantane-based polymer is 446 ◦C, which is comparable to that of the
aforementioned polymers (439–455 ◦C) [51]. However, the maximum
mass loss rate temperature of the presently obtained polymer (540 ◦C) is
significantly higher that of the polymers obtained from the commer-
cially available monomers (468–482 ◦C) [51]. Such difference is related
to the fact that the polymers from commercial monomers lose most of
their mass during the first step of decomposition, whereas the
adamantane-based polymer during the second step of decomposition.
5. Conclusions
We have synthesized adamantane-based dicyanate ester and
confirmed its structure by X-ray analysis. The synthesized monomer
undergoes thermally-stimulated polymerization in the liquid state. The
polymerization process has been studied by conventional and
temperature-modulated DSC, which show that the reaction switches to
diffusion-controlled regime at the later stages of polymerization.
Detailed analysis of the polymerization kinetics in the reaction-control
regime has revealed that the process rate might be described as a
quasi-one-step process. The reaction is found to be auto-catalytic. A new
autocatalytic model has been proposed as an alternative to the broadly
used truncated Sestak-Berggren model. Unlike the latter, the proposed
model avoids arbitrarily guessing the value for the initial conversion.
The polymerization product has demonstrated the thermal stability and
glass transition temperature that are higher than those for dicyanate
esters with flexible hydrocarbon bridging units. Overall, the obtained
experimental results confirm our hypothesis about the effect of the rigid
adamantane fragment on the reactivity of the monomer and thermal
properties of the corresponding polymer product.
Fig. 11. Heat capacity curve for fully cured polymer sample measured at 1 ◦
C
minꢀ 1 with stochastic modulation.
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Fig. 12. TG and derivative TG curves of thermal decomposition of polymer at
10 ◦C minꢀ 1
.
Acknowledgments
adamantane bridging fragment swithes to diffusion-controlled regime at
This work was supported by the Russian Foundation of Basic
◦
α
= 0.75. Studies of the uncatalyzed polymerization kinetics of dicya-
Research (RFBR) (Project N 20-33-70174). AG acknowledges the
nate esters with flexible bridging units in non-isothermal conditions
show that reaction proceeds in a reaction-controlled regime in a whole
conversion range [36,38,50].
Assigned Spectral-Analytical Center of FRC Kazan Scientific Center of
RAS for the opportunity of conducting the NMR experiments.
To measure the glass transition temperature of the resulting polymer
we have employed TMDSC. Fig. 11 presents the results of the Tg mea-
surements at the heating rate of 1 ◦C minꢀ 1. As one can see, the syn-
thesized adamantane-based polymer possesses very high glass transition
temperature of 345 ◦C. It should be noted that dicyanate esters with
flexible hydrocarbon bridging fragments (namely, based on bisphenols
A, E, F, and M or dimer of p-tert-butylphenol) in general give rise to
polymers that feature much lower glass transition temperatures than
that of the presently studied polymer (192–289 ◦C vs 345 ◦C) [3,50,51].
Thus, the obtained results are consistent with our initial hypothesis that
the factors increasing Tg must favor earlier transition of the polymeri-
zation to diffusion control.
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8