polymers

Article Polymerization Kinetics of Cyanate Confined to Hydrophilic Nanopores of Silica Colloidal Crystals with Different Surface-Grafted Groups

Andrey Galukhin 1,* , Guzel Taimova 1, Roman Nosov 1, Tatsiana Liavitskaya 2 and Sergey Vyazovkin 1,2,*

1 Alexander Butlerov Institute of Chemistry, Kazan Federal University, Kremlevskaya Str. 18, 420008 Kazan, Russia; [email protected] (G.T.); [email protected] (R.N.) 2 Department of Chemistry, University of Alabama at Birmingham, 901 S. 14th Street, Birmingham, AL 35294, USA; [email protected] * Correspondence: [email protected] (A.G.); [email protected] (S.V.)

 Received: 29 September 2020; Accepted: 11 October 2020; Published: 12 October 2020 

Abstract: This study investigates the kinetics of confined polymerization of bisphenol E cyanate ester in the nanopores of the three types of silica colloidal crystals that differ in the concentration and acidity of the surface-grafted proton-donor groups. In all three types of pores, the polymerization has released less heat and demonstrated a very similar significant acceleration as compared to the bulk process. Isoconversional kinetic analysis of the differential scanning calorimetry measurements has revealed that the confinement causes not only a dramatic change in the Arrhenius parameters, but also in the reaction model of the polymerization process. The obtained results have been explained by the active role of the silica surface that can adsorb the residual and immobilize intermediate iminocarbonate products by reaction of the monomer molecules with the surface silanols. The observed acceleration has been quantified by introducing a new isoconversional-isothermal acceleration factor Zα,T that affords comparing the process rates at respectively identical conversions and temperatures. In accord with this factor, the confined polymerization is 15–30 times faster than that in bulk.

Keywords: cyanate ; polymerization kinetics; confinement; colloidal crystals; thermal analysis; isoconversional kinetic analysis

1. Introduction Exploring chemical reactions under confinement, e.g., inside nanopores [1–3], nanobrushes [4], or self-assembled monolayers [5–8], has been of major research interest in the areas of catalysis, polymer, supramolecular, and biochemistry. Studying the effects of confinement on the reactivity is a key to understanding of biological systems, where many processes in living cells occur in a confined space [9], as well as chemical systems, where various novel materials are created under spaciously confined conditions that give rise to unusual properties and chemical mechanisms [10]. Confined polymerization attracts research attention as a means of controlling the properties of polymers, such as molecular weight distribution [11–13], crystallinity [14–16], tacticity [13,17,18], and glass transition temperature [19–21]. Currently, the most studied type of confined polymerization is radical polymerization. For this type of polymerization the changes in the reactivity of monomers have been explained as the effects of confinement on the rates of the initiation [11] and termination [17,22]. Polycyclotrimerization of cyanate esters is another type of reaction for which the effect of confinement on both reactivity of the reactant monomer and product polymer has been well documented [23–28].

Polymers 2020, 12, 2329; doi:10.3390/polym12102329 www.mdpi.com/journal/polymers Polymers 2020, 12, 2329 2 of 17 Polymers 2020, 12, x FOR PEER REVIEW 2 of 17

Foracceleration these reactions, in terms there of the have reaction been no mechanisms. specific studies The ofincreased the significant reactivity acceleration of monomers in terms has of been the reactionattributed mechanisms. mostly to increased The increased collision reactivity efficiency of monomersinduced by hasthe beennanopore attributed surface mostly in the to layer increased of the collisionadsorbed e ffi monomerciency induced [25,26,28]. by the Although nanopore surface the effect in the of layer the of surface the adsorbed silanols monomer groups [ 25 on,26 ,28 the]. Althoughpolymerization the eff ofect cyanate of the surfaceesters has silanols been invoked, groups on it has the polymerizationnever been studied of cyanate in detail esters [29,30]. has been invoked,This itcurrent has never study been focuses studied on in the detail thermal [29,30 polymerization]. of bisphenol E cyanate ester under both Thisbulk currentand confined study focusesconditions. on theSilica thermal colloidal polymerization crystals (SCCs) of are bisphenol used as E a cyanateconfining ester medium. under bothTo the bulk best and of confined our knowledge, conditions. this Silica is the colloidal first study crystals that (SCCs) makes areuse usedof SCC as a to confining explore medium.confined Tochemical the best reactions. of our knowledge, Chemical this modification is the first studyof SCC that is makesused to use reveal of SCC the to influence explore confined of the nature chemical of reactions.surface-grafted Chemical proton modification-donor groups of SCC on is used the reactivity to reveal the of influence the confined of the monomer. nature of surface-grafted The resulting proton-donorreactions have groups been studied on the by reactivity differential of the scanning confined calorimetry monomer. (DSC) The resulting, and their reactions kinetics have has been studiedanalyzed by by di meansfferential of scanningthe isoconversional calorimetry methodology (DSC), and their [31]. kinetics The analysis has been reveals analyzed that confinement by means of thecauses isoconversional a change of the methodology reaction kinetics [31]. The and analysis mechanisms reveals of thatpolymerization confinement that causes has abeen change linked of the to reactionthe surface kinetics silanol and groups mechanisms participating of polymerization in the polymerization that has been process. linked to the surface silanol groups participating in the polymerization process. 2. Materials and Methods 2. Materials and Methods 2.1. Materials 2.1. Materials Ammonium hydroxide solution (25% of NH3, TatChemProduct, Kazan, Russia), tetraethylorthosilicateAmmonium hydroxide (TEOS, solution >99.9%, (25% of NH ALDRICH3, TatChemProduct, Chemistry Kazan,, Saint Russia), Louis, tetraethylorthosilicate MI, USA), (TEOS,tetrabutylammonium>99.9%, ALDRICH hydroxide Chemistry, solution Saint (40% Louis, in water, MI, USA), Fluka tetrabutylammonium Analytical, Saint Louis, hydroxide MI, USA solution), 1,3- (40%propanesultone in water, Fluka (98%, Analytical, ALDRICH Saint Chemistry Louis, MI,, USA), Saint 1,3-propanesultone Louis, MI, USA), (98%, bisphenol ALDRICH E (>98%, Chemistry, TCI, SaintZwijndrecht, Louis, MI, Belgium USA), bisphenol), phosphorus E (>98%, pentoxide TCI, Zwijndrecht, (99%, Vect Belgium),on, Saint phosphorus Petersburg, pentoxide Russia (99%,), n-hexane Vecton, Saint(>98%, Petersburg, EKOS-1, Moscow, Russia), n -hexaneRussia), (>toluene98%, EKOS-1, (99.5%, Moscow, EKOS-1, Russia), Moscow, toluene Russia (99.5%,), and EKOS-1,tetrahydrofuran Moscow, Russia),(THF, >98%, andtetrahydrofuran ChemMed, Kazan, (THF, Russia>98%,) ChemMed,were purchased Kazan, and Russia) used were without purchased additional and usedpurification. without additionalBisphenol purification.E cyanate ester Bisphenol of purity E cyanate99.5% was ester synthesized of purity 99.5% according was synthesizedto the previously according described to the previouslysynthetic procedure described synthetic(Figure 1) procedure [32,33]. The (Figure purity1) [ 32of, 33synthesized]. The purity monomer of synthesized was no monomer less than was 99.5% no lessaccording than 99.5% to high according-performance to high-performance liquid chromatography liquid chromatography (HPLC). Absolute (HPLC). ethanol Absolute was obtained ethanol was by obtainedconsecutive by consecutivedistillations distillations of 96% ethanol of 96% over ethanol CaO and over CaH CaO2. and Deionized CaH2. Deionized water (18.2 water MΩ) (18.2 was MobtainedΩ) was obtainedby Arium by mini Arium instrument mini instrument (Sartorius (Sartorius,, Goettingen, Goettingen, Germany Germany).).

Figure 1. Scheme of synthesis of target cyanate ester.

2.2. Methods Scanning electron electron microscopy microscopy (SEM) (SEM) measurements measurements were were carried carried out using out a using Merlin a field-emissionMerlin field- high-resolutionemission high-resolution scanning electron scanning microscope electron microscope (Carl Zeiss, (Carl Oberkochen, Zeiss, Oberkochen, Germany). Germany) An UP200Ht. An ultrasonicUP200Ht ultrasonic homogenizer homogenizer (Hielscher ( Ultrasonics,Hielscher Ultrasonics, Teltow, Germany) Teltow, was Germany used) forwas all used sonications. for all Asonications. MF48 centrifuge A MF48 (AWEL, centrifuge Blain, (AWEL France), Blain, was France used) forwas all used centrifugations. for all centrifugations. A LF-7/11-G1 A LF- furnace7/11-G1 (furnaceLOIP, Saint (LOIP, Petersburg, Saint Petersburg, Russia) was Russia used) was for calcinationused for calcination and sintering. and sintering. Contact angles Contact were angles measured were measured using a drop shape analyzer DSA100 (KRUSS GmbH, Hamburg, Germany); the water drop

Polymers 2020, 12, 2329 3 of 17 using a drop shape analyzer DSA100 (KRUSS GmbH, Hamburg, Germany); the water drop volume was 2 µL. High-performance liquid chromatography (HPLC) analyses were carried out with a Dionex Ultimate 3000 chromatograph (Thermo Fisher Scientific, Waltham, MA, USA) equipped with an UV detector and a Dionex Acclaim 120 chromatographic column (C18-bonded silica, 5 µm, 120 Å, 4.6 250 mm2). adsorption and desorption measurements were carried out at 77 K with an × ASAP 2020 MP instrument (Micromeritics, Norcross, GA, USA). The specific surface areas of the SCCs were determined by applying the Brunauer–Emmett–Teller (BET) equation to adsorption data in a range of nitrogen relative pressure (P/P0) of 0.05–0.30, as recommended by IUPAC [34]. The total pore volume of the SCCs samples was measured at P/P0 = 0.999. All calorimetric measurements were carried out using a heat flux DSC 3+ (Mettler-Toledo, Greifensee, Switzerland). Indium and zinc standards were used to perform temperature, heat flow, 1 and tau-lag calibrations. The experiments were performed under an argon flow (80 mL min− ) at the 1 heating rates of 2.5, 5.0, 7.5, 10.0, and 12.5 ◦C min− in 40 µL sealed aluminum pans. Because moisture could potentially affect polymerization, before sealing the samples were placed in 40 µL aluminum pans and kept in a vacuum desiccator containing P2O5 for 1 day to remove traces of water. The mass of the bulk cyanate ester samples for each run was ~1 mg. The mass of the SCCs samples loaded with the cyanate ester was taken to be ~5 mg that was the amount necessary to introduce ~1 mg of the cyanate ester into the available pores. Preparation of silica spheres. Silica spheres with radii of 110 4 nm were prepared by two-step ± controllable growth technique based on regrowth of silica seeds [35]. A detailed description of the procedure has been previously reported [36]. Preparation of sintered SCC (Sample A). SCCs were prepared by modified vertical deposition method based on isothermal heating evaporation-induced self-assembly (IHEISA) method [37]. Silica particles were dispersed in ethanol by sonication, and then a glass beaker containing the dispersion was placed in a homemade set-up at 79.8 ◦C. Obtained pieces of SCCs were carefully removed from the beaker’s walls and sintered at 850 ◦C for 12 h, and the desired temperature was 1 achieved at a heating rate of 300 ◦C h− . The particle size in SCCs was estimated by measuring 100 individual particles using SEM. Surface modification of sintered SCCs. Rehydroxylation (Sample B): SCC synthesized with a mass of ~8 g was placed in a tetrabutylammonium hydroxide water solution with pH = 9.5 and T = 60 ◦C for 24 h [38]. Then, the sample was consistently washed by 1 M HNO3, methanol, deionized water, and acetonitrile and dried in vacuum at 200 ◦C for 2 h. Introduction of 3-propylsulfonic acid groups (Sample C): ~1.5 g of rehydroxylated SCC was placed in 50 mL of toluene solution containing 3 mL of 1,3-propansultone and was refluxed for 24 h. Then, the samples were sequentially washed with toluene, THF, methanol, and hexane and dried in a furnace at 150 ◦C for 2 h. Pore filling of SCCs. Loading of cyanate ester into colloidal crystals was carried as follows. A ~100 mg piece of a previously degassed colloidal crystal and a tenfold excess of the cyanate ester with respect to the pore volume of the SCC sample were placed into a vial and heated to 60 ◦C. Filling the pores of SCCs by the cyanate ester is driven by capillary forces and is readily monitored by the naked eye. An excess of the monomer on the piece of SCCs was carefully removed by fiber-free wipers. The extent of pore filling was estimated by as the difference in the mass of SCCs before and after impregnation and turned out to be close to 100% of pore volume for all samples.

3. Computations The recommendations of the ICTAC Kinetic Committee were followed to evaluate the activation energy, preexponential factor, and the reaction model [39]. The extent of conversion, α, was determined as the partial area of the DSC peaks measured for polymerization of the cyanate ester. The effective activation energy, Eα, was evaluated as a function of conversion with the aid of the flexible integral isoconversional method of Vyazovkin. The method affords eliminating a systematic error in Eα when Polymers 2020, 12, 2329 4 of 17 it varies with α [40]. This is accomplished by employing the so-called flexible integration that assumes the constancy of Eα within a very narrow integration range, ∆α. The value of ∆α was taken as 0.01. Within each ∆α, Eα is determined by finding a minimum of the function:

n n X X J[Eα, Ti(tα)] Ψ(Eα) = h i (1) i=1 j,i J Eα, Tj(tα)

where Z tα " # Eα J[E , T (t )] exp − dt (2) α i α ( ) ≡ tα ∆α RTi t − and n is the number of the temperature programs. The integral was calculated by the trapezoid rule. The COBYLA non-gradient method from the NLopt library was utilized to determine a minimum of Equation (1). The uncertainties in the Eα values were evaluated as described earlier [41]. The pre-exponential factor values were estimated by substituting the values of Eα into the equation of the compensation effect. ln Aα = a + bEα (3)

The parameters a and b were determined by fitting the pairs of lnAi and Ei into Equation (4). The respective pairs were found by substituting the reaction models fi(α) into the linear form of the basic rate equation: ! dα E ln ln[ f (α)] = ln A i (4) dt − i i − RT

For each reaction model, the values of lnAi and Ei were evaluated, respectively, from the slope and intercept of the linear plot of left-hand side of Equation (4) vs. the reciprocal temperature. In addition, the model f (α) = αm(1 α)n with five different pairs 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) was used for calculations of the pre-exponential factor values. This model was used because of its ability to imitate the autocatalytic kinetics which appears to be characteristic of the cyanate esters polymerization [42]. Furthermore, this model is similar to the Kamal reaction model [43], which has been used successfully to treat the kinetics of cyanate ester polymerization [32,44]. The isoconversional values of Eα and lnAα were used to determine the rate constant. The rate constant was determined in the form of the Arrhenius plot (Equation (5)) [45].

Eα ln k(Tα) = ln Aα (5) − RT Independently, the reaction model for the confined polymerization of bisphenol E cyanate ester was determined in the numerical form of Equation (6). X g(α) = Aα J[Eα, Ti(tα)] (6) α

4. Results and Discussion

4.1. Synthesis and Characterization of SCCs Having Different Surface Chemistry Studying the influence of confinement on chemical reactions usually makes use of porous media whose pores play the role of tiny reactors. The present study appears to be the first time when SCCs are used as a model porous medium. SCCs consist of silica spheres close-packed in a face-centered cubic arrangement, which implies existence of octahedral and tetrahedral pores. These two types of pores form an interconnected three-dimensional porous system (Figure2). Polymers 2020, 12, 2329 5 of 17 Polymers 2020, 12, x FOR PEER REVIEW 5 of 17 Polymers 2020, 12, x FOR PEER REVIEW 5 of 17

Figure 2. 2. InterconnectedInterconnected octahedral octahedral (orange) (orange) and andtetrahedral tetrahedral (purple) (purple) pores poresof silica of colloidal silica colloidal crystal Figure 2. Interconnected octahedral (orange) and tetrahedral (purple) pores of silica colloidal crystal (crystalSCC). (SCC). (SCC).

Total porosity of an idealideal close-packedclose-packed face-centeredface-centered cubic lattice is independent of the sphere Total porosity of an ideal close-packed face-centered cubic lattice is independent of the sphere size and and equals equals to to 0.2596, 0.2596, where where share share of of octahedral octahedral pores pores is ~ is72% ~72% [36]. [36 The]. Theporosity porosity of real of SCC real SCCmay size and equals to 0.2596, where share of octahedral pores is ~72% [36]. The porosity of real SCC may deviatemay deviate to higher to higher values values because because of the of unavoidable the unavoidable polyd polydispersityispersity of the of particlesthe particles forming forming the deviate to higher values because of the unavoidable polydispersity of the particles forming the crystal,the crystal, which which leads leads to different to different kinds kinds of packing of packing defects defects and and results results in reducedin reduced effectiveness effectiveness of crystal, which leads to different kinds of packing defects and results in reduced effectiveness of packing.of packing. Recently, Recently, it has it hasbeen been shown shown that that despite despite the thecomplex complex shape shape of the of pores the pores in SCCs in SCCs they theycan packing. Recently, it has been shown that despite the complex shape of the pores in SCCs they can becan satisfactorily be satisfactorily treated treated in terms in terms of a ofspherical a spherical pore pore model model [36]. [ 36It ].has It hasbeen been demonstrated demonstrated that thatthe be satisfactorily treated in terms of a spherical pore model [36]. It has been demonstrated that the effectivethe effective diameters diameters of the of octahedral the octahedral and tetrahedral and tetrahedral pores pores equal equal,, respectively respectively,, to 0.631 to 0.631× d and d0.368and effective diameters of the octahedral and tetrahedral pores equal, respectively, to 0.631 × d and× 0.368 ×0.368 d, whered, where d is thed is diameter the diameter of silica of silica spheres spheres forming forming SCCs SCCs [36]. [ 36These]. These estimates estimates derive derive from from the × d, where× d is the diameter of silica spheres forming SCCs [36]. These estimates derive from the geometrythe geometry of a of face a face-centered-centered cubic cubic lattice lattice and and match match closely closely the the main main modes modes of of bimodal bimodal pore pore size geometry of a face-centered cubic lattice and match closely the main modes of bimodal pore size distribution obtained from nitrogen adsorption data forfor mesoporousmesoporous SCCsSCCs [[46].46]. distribution obtained from nitrogen adsorption data for mesoporous SCCs [46]. In the the present present study study we wehave have synthesized synthesized SCC consisting SCC consisting of 110 nm of 110silica nm spheres. silica Scanning spheres. In the present study we have synthesized SCC consisting of 110 nm silica spheres. Scanning electronScanning microscopy electron microscopy revealed the revealed absence the of macroscopic absence of macroscopic defects, e.g., defects,cracks (Figure e.g., cracks 3). On (Figure the other3). electron microscopy revealed the absence of macroscopic defects, e.g., cracks (Figure 3). On the other hand,On the some other microscopic hand, some defects microscopic can be defectsdetected can on be(111 detected) plane of on SCC (111). Based plane on of the SCC. aforementioned Based on the hand, some microscopic defects can be detected on (111) plane of SCC. Based on the aforementioned estimatesaforementioned, one can estimates, calculate onethe sizes can calculateof octahedral the sizesand tetrahedral of octahedral pores and of tetrahedral the synthesized pores SCC of the as estimates, one can calculate the sizes of octahedral and tetrahedral pores of the synthesized SCC as ~70synthesized and 40 nm SCC, respectively as ~70 and. 40 nm, respectively. ~70 and 40 nm, respectively.

Figure 3. SEM imageimage ofof (111)(111) plane plane of of the the synthesized synthesized SCC SCC made made of 110of 1104 ± nm 4 nm silica silica spheres. spheres. Scale Scale bar Figure 3. SEM image of (111) plane of the synthesized SCC made of 110± ± 4 nm silica spheres. Scale bar isµ 1 µm. isbar 1 ism. 1 µm.

Chemical modificationmodification of the synthesized SCC has been employed to alter the nature of the Chemical modification of the synthesized SCC has been employed to alter the nature of the surfacesurface-grafted-grafted groups groups in in order order to to assess assess their their influence influence on the on thereactivity reactivity of the of confined the confined cyanate cyanate ester surface-grafted groups in order to assess their influence on the reactivity of the confined cyanate ester monomer.ester monomer. We have We prepared have prepared three kinds three of kinds SCCs of(A, SCCs B, and (A, C) B,that and have C) different that have su dirfacefferent chemistry. surface monomer. We have prepared three kinds of SCCs (A, B, and C) that have different surface chemistry. Namely,chemistry. calcined Namely, crystals calcined containing crystals primarily containing siloxane primarily surface siloxane fragments surface and fragments surface silanols and surface with Namely, calcined crystals containing primarily siloxane surface fragments and surface silanols with thesilanols density with ~0.6 the silanols density per ~0.6 nm silanols2 (A), rehydroxylated per nm2 (A), rehydroxylated crystals containing crystals ~5 containing silanols per ~5 nm silanols2 (B) [47], per the density ~0.6 silanols per nm2 (A), rehydroxylated crystals containing ~5 silanols per nm2 (B) [47], andnm2 the(B) crystals, [47], and in the which crystals, the sila in whichnols have the silanolsbeen replaced have been by strong replaced acid by 3 strong-propylsulfonic acid 3-propylsulfonic groups (C). and the crystals, in which the silanols have been replaced by strong acid 3-propylsulfonic groups (C). Accordinggroups (C). to According the literature, to the sulfonation literature, sulfonation of rehydroxylated of rehydroxylated SCC by 1,3 SCC-propanesultone by 1,3-propanesultone results in According to the literature, sulfonation of rehydroxylated SCC by 1,3-propanesultone results in

Polymers 2020, 12, 2329 6 of 17 Polymers 2020, 12, x FOR PEER REVIEW 6 of 17 Polymers 2020, 12, x FOR PEER REVIEW 6 of 17 approximately half of the silanols to be replaced by the sulfonic groups [48]. Scheme of the resultsapproximately in approximately half of the half silanols of the silanols to be to replaced be replaced by the by the sulfonic sulfonic groups groups [48]. [48 ]. Scheme Scheme of of the modification is presented in Figure 4. modificationmodification isis presentedpresented inin FigureFigure4 4..

Figure 4. Surface modification of SCC. Figure 4. Surface modificationmodification of SCC. Water drop contact angle measurements show how the modification of the SCCs affects the Water drop drop contact contact angle angle measurementsmeasurements show how the modificationmodification of the SCCs aaffectsffects the properties of the surface (Figure 5). It is seen that the SCCs with siloxane, silanols, and 3- properties of of the the surface surface (Figure (Figure5). It is 5). seen It isthat seen the SCCs that withthe SCCs siloxane, with silanols, siloxane, and 3-propylsulfonic silanols, and 3- propylsulfonic acid groups possess hydrophilic properties (Figure 5A–C). acidpropylsulfonic groups possess acid groups hydrophilic possess properties hydrophilic (Figure properties5A–C). (Figure 5A–C).

Figure 5. Water drop contact angle measurements of SCCs with different surface modifications (A– Figure 5.5. Water dropdrop contactcontact angle angle measurements measurements of of SCCs SCCs with with di ffdifferenterent surface surface modifications modifications (A–C (A).– C). C). Nitrogen adsorption measurements have provided textural parameters of synthesized porous materialsNitrogen (Table adsorption1). It should measurements be noted that thehave surface provided modification textural parameters does not a ff ofect synthesized the specific surfaceporous Nitrogen adsorption measurements have provided textural parameters of synthesized porous areamaterials (S )(Table and pore 1). It volume should ofbe thenoted synthesized that the surface SCCs. modification does not affect the specific surface materialsBET (Table 1). It should be noted that the surface modification does not affect the specific surface area (SBET) and pore volume of the synthesized SCCs. area (SBET) and pore volume of the synthesized SCCs. Table 1. Textural parameters of synthesized SCCs A–C. Table 1. Textural parameters of synthesized SCCs A–C. Table 1. Textural parameters of synthesized SCCs A–C. 2 1 Pore Volume, SBET, m g− 3 1 CBET Porecm Volumeg− , SBET, m2 g⁻1 Pore Volume, CBET A SBET 34, m21 g⁻1 0.26cm3 g0.01⁻1 103CBET 15 ± cm3± g⁻1 ± BA 34 33 ± 1 0.26 0.26 ± 0.010.01 103 182 ± 1553 A 34 ± 1 0.26 ±± 0.01 103 ±± 15 CB 33 34 ± 1 0.26 0.25 ± 0.010.01 182 135 ± 5333 B 33 ± 1 0.26 ±± 0.01 182 ±± 53 C 34 ± 1 0.25 ± 0.01 135 ± 33 C 34 ± 1 0.25 ± 0.01 135 ± 33 However,However, it it is is instructive instructive to toanalyze analyze the the changes changes in the in theCBETC parameterBET parameter of the of BET the equation BET equation (Table However, it is instructive to analyze the changes in the CBET parameter of the BET equation (Table 1(Table), which1), whichcharacterizes characterizes the strength the strength of adsorbate of adsorbate–adsorbent–adsorbent interaction interaction (Equation (Equation (7)) [49]: (7)) [49]: 1), which characterizes the strength of adsorbate–adsorbent interaction (Equation (7)) [49]: h  i 퐶퐵퐸푇 = 푒푥푝[(∆퐻푑푒푠 − ∆퐻푣푎푝)/푅푇] (7) C퐶BET = 푒푥푝exp [(∆∆H퐻des −∆∆H퐻vap )//RT푅푇] (7(7)) 퐵퐸푇 푑푒푠− 푣푎푝 According to Equation (7), the value of the CBET parameter increases with increasing the According to EquationEquation (7), (7), thethe value value of of the the CCBET parameter increases with increasing the difference between the enthalpy of adsorbate desorptionBET from a monolayer (ΔHdes) and the enthalpy didifferencefference betweenbetween the the enthalpy enthalpy of of adsorbate adsorbate desorption desorption from from a monolayera monolayer (∆ H(ΔH)des and) and the the enthalpy enthalpy of of vaporization of the liquid adsorbate (ΔHvap). Thus, for a series of adsorbentsdes with different surfaces vaporizationof vaporization of of the the liquid liquid adsorbate adsorbate (∆ (ΔHHvap).). Thus, Thus, for for a a series series ofof adsorbentsadsorbents withwith didifferentfferent surfacessurfaces larger values of CBET parameter correspondsvap to materials with higher polarity. The observed order of larger values of CBET parameter corresponds to materials with higher polarity. The observed order of largerthe surface values polarity of CBET fromparameter the nitrogen corresponds adsorption to materials measurements with higher is consistent polarity. Thewith observed the one from order the of the surface polarity from the nitrogen adsorption measurements is consistent with the one from the thewater surface drop polaritycontact angle from themeasurements nitrogen adsorption (Figure 5). measurements is consistent with the one from the waterwater dropdrop contactcontact angleangle measurementsmeasurements (Figure(Figure5 5).). 4.2. Kinetics of Polymerization Studied by DSC 4.2. Kinetics of Polymerization Studied by DSC As the polymerization of cyanate ester is highly exothermic its progress is conveniently followed As the polymerization of cyanate ester is highly exothermic its progress is conveniently followed by DSC. The polymerization of cyanate esters occurs via formation of 1,3,5-triazine fragments from by DSC. The polymerization of cyanate esters occurs via formation of 1,3,5-triazine fragments from three cyanate groups (Figure 6). three cyanate groups (Figure 6).

Polymers 2020, 12, 2329 7 of 17

4.2. Kinetics of Polymerization Studied by DSC As the polymerization of cyanate ester is highly exothermic its progress is conveniently followed by DSC. The polymerization of cyanate esters occurs via formation of 1,3,5-triazine fragments from Polymers 2020, 12, x FOR PEER REVIEW 7 of 17 threePolymers cyanate 2020, 12, groups x FOR PEER (Figure REVIEW6). 7 of 17

Figure 6. Scheme of cyclotrimerization of cyanate ester. Figure 6. SchemeScheme of cyclotrimerization of cyanate ester. In the present study non-isothermal DSC measurements were used instead of isothermal ones In the present studystudy non-isothermalnon-isothermal DSC measurements were used instead of isothermal ones to avoid possible incompleteness of the polymerization due to potential vitrification. The heat flow to avoid possible incompleteness of the polymerization due to potential vitrification.vitrification. The heat flow flow curves for polymerization of bulk and confined cyanate ester at a heating rate of 7.5 °C min⁻1 are curves for polymerization of bulk and confinedconfined cyanate ester atat aa heatingheating raterate ofof 7.57.5 °CC minmin⁻11 are presented in Figure 7. Clearly, confining the cyanate ester in the pores of any of the ◦three types− of presented inin FigureFigure7 .7. Clearly, Clearly, confining confining the the cyanate cyanate ester ester in the in poresthe pores of any of ofany the of three the typesthree oftypes SCCs of SCCs results in significant acceleration of the polymerization rate as manifested by a significant shift resultsSCCs results in significant in significant acceleration acceleration of the of polymerization the polymerization rate as rate manifested as manifested by a significant by a significant shift of shift the of the reaction peak temperature to lower value (Figure 7). reactionof the reaction peak temperature peak temperature to lower to valuelower (Figurevalue (Figure7). 7).

Figure 7. Heat flow curves for bisphenol E cyanate ester polymerization in bulk and nanoconfined 1 statesFigure at 7. 7.5 Heat◦C minflow− curves. ∆Tp showsfor bisphenol the magnitude E cyanate of ester the di polymerizationfference in the peakin bulk temperatures and nanoconfined of the Figure 7. Heat flow curves for bisphenol E cyanate ester polymerization in bulk and nanoconfined respectivestates at 7.5 DSC °C curves. min⁻1. ΔTp shows the magnitude of the difference in the peak temperatures of the states at 7.5 °C min⁻1. ΔTp shows the magnitude of the difference in the peak temperatures of the respective DSC curves. Averagerespective heatsDSC curves. of the cyanate ester polymerization in the nanopores of SCCs are as follows; 1 1 1 657 Average32 J g− (A)heats, 714 of the28 cyanate J g− (B), ester and polymerization 746 28 J g− in(C). the Thesenanopores values of SCCs are slightly are as follows lower than; 657 ±Average heats of the± cyanate ester polymerization1 ± in the nanopores of SCCs are as follows; 657 that± 32 ofJ g bulk⁻1 (A), polymerization 714 ± 28 J g⁻1 (B), (805 and 42746 J ± g −28). J Furtherg⁻1 (C). These insights values into are the slightly reactivity lower of the than cyanate that of ester bulk ± 32 J g⁻1 (A), 714 ± 28 J g⁻1 (B), and± 746 ± 28 J g⁻1 (C). These values are slightly lower than that of bulk confinedpolymerization inside SCCs (805 ± are 42 obtainedJ g⁻1). Further by isoconversional insights into the kinetic reactivity analysis. of the The cyanate isoconversional ester confined values inside of polymerization (805 ± 42 J g⁻1). Further insights into the reactivity of the cyanate ester confined inside theSCCs activation are obtained energy byE αisoconversionaland preexponential kinetic factor analysis.Aα for The bulk isoconversional and confined monomervalues of arethe displayedactivation SCCs are obtained by isoconversional kinetic analysis. The isoconversional values of the activation inenergy Figure E8α. and preexponential factor Aα for bulk and confined monomer are displayed in Figure 8. energy Eα and preexponential factor Aα for bulk and confined monomer are displayed in Figure 8.

Polymers 2020, 12, x FOR PEER REVIEW 8 of 17

Polymers 2020, 12, 2329 8 of 17 Polymers 2020, 12, x FOR PEER REVIEW 8 of 17

Figure 8. Dependencies of activation energy (A) and pre-exponential factor (B) as a function of Figureconversion 8. Dependencies for polymerization of activation of bulk and energy confined (A) and cyanate pre-exponential ester. factor (B) as a function of conversionFigure 8. forDependencies polymerization of activation of bulk and energy confined (A)cyanate and pre ester.-exponential factor (B) as a function of Comparingconversion for the polymerization isoconversional of bulk values and confined of the effectivecyanate ester. activation energy (Figure 8A) of the Comparing the isoconversional values of the effective activation energy (Figure8A) of the confined confined processes one can see that the reactions in SCCs of types A and B are characterized by almost processes one can see that the reactions in SCCs of types A and B are characterized by almost identical identicalComparing values of the Eα , isoconversional whereas the reaction values inside of the SCC effective of type activation B proceeds energy with (Figure larger activation 8A) of the values of E , whereas the reaction inside SCC of type B proceeds with larger activation energy that energyconfined that procα suggestsesses one that can this see process that the should reactions be slower in SCCs (Figure of types 8A). A andOn theB are other characterized hand, this byreaction almost suggests that this process should be slower (Figure8A). On the other hand, this reaction has larger values hasidentical larger values of of theEα, pre whereas-exponential the reaction factor insideAα (Figure SCC 8B) of , typeso it Bshould proceeds be faster with than larger two activation others. of the pre-exponential factor A (Figure8B), so it should be faster than two others. Combined e ffect Combinedenergy that effect suggests of both that Arrheniusthis αprocess parameters should be isslower reflected (Figure in the8A). corresponding On the other hand Arrhenius, this reaction plots of both Arrhenius parameters is reflected in the corresponding Arrhenius plots (Figure9) that show (Figurehas larger 9) that values show of ththeat preall -confinedexponential systems factor have Aα (Figure practically 8B), sothe it same should reactivity, be faster just than as two observed others. that all confined systems have practically the same reactivity, just as observed from heat flow curves fromCombined heat flow effect curves of both (Figure Arrhenius 7). Moreover, parameters one can is reflected see a nonlinear in the corresponding dependence of Arrhenius lnk on T⁻ 1plots for (Figure7). Moreover, one can see a nonlinear dependence of ln k on T 1 for polymerization of cyanate polymerization(Figure 9) that show of cyanate that all ester confined in the systems bulk and have an practically almost linear the− same dependence reactivity, of just lnk ason observed T⁻1 for 1 ester in the bulk and an almost linear dependence of lnk on T for polymerization in the hydrophilic1 polymerizationfrom heat flow in curves the hydrophilic (Figure 7). pores Moreover, of SCCs one A –canC. see a− nonlinear dependence of lnk on T⁻ for porespolymerization of SCCs A–C. of cyanate ester in the bulk and an almost linear dependence of lnk on T⁻1 for polymerization in the hydrophilic pores of SCCs A–C.

Figure 9. Arrhenius plots for polymerization of bulk and confined cyanate ester. Figure 9. Arrhenius plots for polymerization of bulk and confined cyanate ester.

Figure8A shows that polymerization of bulk cyanate ester demonstrates a significant variation of Figure 9. Arrhenius plots for polymerization of bulk and confined cyanate ester. the activationFigure 8A energy shows with that conversionpolymerization (variation of bulk of cyanateEα exceeds ester 60% demonstrates of average Eaα significant), which is variation a sign of complexof the activation (i.e., multistep) energy naturewith conversion of the polymerization (variation of process Eα exceeds [50]. 60% The of pre-exponential average Eα), which factor is values a sign Figure 8A shows that polymerization of bulk cyanate ester demonstrates a significant variation demonstrateof complex (i.e. a similar, multistep) variation nature (Figure of 8 theB). polymerization process [50]. The pre-exponential factor of the activation energy with conversion (variation of Eα exceeds 60% of average Eα), which is a sign valuesA variationdemonstrate of the a similar effective variation activation (Figure energy 8B). for bulk cyanate ester polymerization is expected, of complex (i.e., multistep) nature of the polymerization process [50]. The pre-exponential factor consideringA variation its complexof the effective mechanism activation that energy involves for thebulk formation cyanate ester of severalpolymerization intermediates is expected, [51]. values demonstrate a similar variation (Figure 8B). Usingconsidering different its complex assumptions, mechanism several that researchers involves the have formation arrived of s ateveral similar intermediates polymerization [51]. Using rate differentA variation assumptions, of the severaleffective researchers activation energy have arrived for bulk at cyanate similar ester polymerization polymerization rate is equations expected, considering its complex mechanism that involves the formation of several intermediates [51]. Using different assumptions, several researchers have arrived at similar polymerization rate equations

Polymers 2020, 12, x FOR PEER REVIEW 9 of 17 Polymers 2020, 12, 2329 9 of 17 [44,52,53] that boil down to a model of two parallel reactions, one of which is autocatalytic (Equation equations(8)). [44,52,53] that boil down to a model of two parallel reactions, one of which is autocatalytic

(Equation (8)). 푑훼 푛 푚 푛 = 푘1(1 − 훼) + 푘2훼 (1 − 훼) (8) d푑푡α n n = k (1 α) + k αm(1 α) (8) dt 1 − 2 − These two reactions are usually interpreted as a residual -catalyzed process (nth-order th reactionThese k1) two and reactions autocatalytic are usually process interpreted catalyzed as by a the residual formed phenol-catalyzed 1,3,5-triazine fragments process (n [52,53].-order It reactionshould bek1) mentioned and autocatalytic that the process same catalyzedequation, byknown the formed as the 1,3,5-triazineKamal model, fragments is used for [52 ,description53]. It should of bethe mentioned kinetics of that polymerization the same equation, of epoxy known- as thesystems Kamal [43]. model, is used for description of the kinetics of polymerizationIn the case of ofa process epoxy-amine comprising systems two [43 parallel]. reactions the effective activation energy should monotoIn thenically case vary of between a process the comprising activation energies two parallel of the reactionsindividual the reactions effective according activation to Equation energy should(9) [54]. monotonically This is exactly varythe trend between observed the activation for bulk polymerization. energies of the individual reactions according to Equation (9) [54]. This is exactly the trend observed for bulk polymerization. 푑훼 휕 ln ( ) 푚   푑푡 퐴1exp (−퐸1/푅푇)퐸1 + 훼 퐴2exp (−퐸2/푅푇)퐸2 퐸훼 = −푅 [ dα−1 ] = m푚 (9) ∂ ln휕dt푇  A1 exp퐴 (expE1 (/−RT퐸 /)푅푇E1 )++α훼A퐴2 expexp( (−E퐸2//RT푅푇))E2 E = R  = 1 − 1 2 − 2 (9) α  1  훼 m −  ∂T−  A1 exp( E1/RT) + α A2 exp( E2/RT) α − − To determine the kinetic parameters of the individual steps for bulk polymerization we have fittedTo E determinequation (10) the kinetic to the parameters dependence of the of theindividual effective steps activation for bulk polymerization energy on temperature we have fitted and Equationconversion. (10) to the dependence of the effective activation energy on temperature and conversion. 푚 ( (퐴1/퐴)2)exp( (−퐸1/푅푇))퐸1 ++ 훼m exp (−퐸2/푅푇))퐸2 퐸훼 =A1/A2 exp E1/RT E1 α exp E2/RT E2 (10) Eα = (퐴 /퐴 )exp− (−퐸 /푅푇) + 훼푚exp (−퐸 /푅푇) (10) (A /1A )2 exp( E 1/RT) + αm exp( E2/RT) 1 2 − 1 − 2 This equation is a modified form of Equation (9) that has to be used instead of Equation (9) This equation is a modified form of Equation (9) that has to be used instead of Equation (9) because because the Equation (9) contains A1 and A2 as linear multipliers, which hampers their reliable theevaluation Equation [55]. (9) containsFitting EquationA1 and A (10)2 as linearto the multipliers,experimentally which determined hampers theirdependence reliable evaluationof the effective [55]. Fitting Equation (10) to the experimentally determined dependence of the effective activation energy activation energy on temperature and conversion yields the A1/A2, E1, E2, and m parameters. An onexample temperature of the fit and is conversionpresented in yields Figure the 10.A 1/A2, E1, E2, and m parameters. An example of the fit is presented in Figure 10.

Figure 10. Fitting of the Kamal model to the experimental Eα dependence for bulk polymerization.

Figure 10. Fitting of the Kamal model to the experimental Eα dependence for bulk polymerization. Evaluation of A1, A2, n, as well as refining the value of the m parameter has been the next step in our kineticEvaluation analysis. of A To1, A do2, that,n, as thewellA as1, Arefining2, n, and them parametersvalue of the of m Equationparameter (8) has have been been the evaluated next step by in fittingour kinetic this equation analysis. to To the do rate that, data the for A1 all, A heating2, n, and rates. m parameters The E1 and ofE E2quationvalues have (8) have not beenbeen optimizedevaluated inby this fitting fit. Their this equation values have to the been rate kept data equal for to all those heating found rates. from The fitting E1 and Equation E2 values (10). have The results not been of theseoptimized fittings in recalculatedthis fit. Their for values heat have flow databeen arekept presented equal to those in Figure found 11 .from fitting Equation (10). The results of these fittings recalculated for heat flow data are presented in Figure 11.

PolymersPolymers2020 2020, ,12 12,, 2329 x FOR PEER REVIEW 1010 of of 17 17

Figure 11. Comparison of the experimental heat flow curves (circles) with the calculated ones (lines) forFigure bulk 11. cyanate Comparison ester polymerization of the experimental at different heat heatingflow curves rates. (circles) with the calculated ones (lines) for bulk cyanate ester polymerization at different heating rates. The resulting kinetics parameters for bulk polymerization of the cyanate ester are presented in Table2The. The resulting parameters kinetics for bulkparameters polymerization for bulk ofpolymerization the cyanate ester of the are cyanate similar ester to those are reportedpresented for in dicyanateTable 2. The esters parameters of similar for structure bulk polymerization [32,44,53]. of the cyanate ester are similar to those reported for dicyanate esters of similar structure [32,44,53]. Table 2. Calculated kinetic parameters for bulk and confined polymerization of cyanate ester.

Table 2. Calculated1 kinetic parameters1 for bulk and 1confined polymerization1 of cyanate ester. E1/kJ mol− logA1/A in s− E2/kJ mol− logA2/A in s− m n

BulkE1/kJ mol⁻ 65 11 logA 3.11/A in0.1 s⁻1 E2/kJ 154 mol3−1 log 12.0A2/A0.1 in s−1 0.9 0.3m 1.2 0.1n ± ± ± ± ± ± A - - 79 6 6.6 0.1 1.0 0.1 1.4 0.1 Bulk 65 ± 1 3.1 ± 0.1 154 ±± 3 12.0± ± 0.1 0.9± ± 0.3 ±1.2 ± 0.1 B - - 83 6 6.9 0.1 1.0 0.1 1.4 0.1 A - - 79 ± 6 6.6± ± 0.1 1.0± ± 0.1 ±1.4 ± 0.1 C - - 90 4 7.5 0.1 0.9 0.1 1.1 0.1 B - - 83 ± 6 6.9± ± 0.1 1.0± ± 0.1 ±1.4 ± 0.1 C - - 90 ± 4 7.5 ± 0.1 0.9 ± 0.1 1.1 ± 0.1 Analysis of the obtained E and logA dependencies for polymerization in the pores of SCCs Analysis of the obtained Eαα and logAαα dependencies for polymerization in the pores of SCCs (Figure(Figure8 )8) shows shows that that accelerationacceleration ofof thethe polymerization at at α α< <0.50.5 is due is due to the to thefact factthat thatthe pre the- pre-exponentialexponential factor factor values values increase increase relative relative to bulk to bulk polymerization polymerization values. values. This This agrees agrees well well with with the theliterature literature data data on the on reaction the reaction of cyanate of cyanate esters esters in silica in nanopores, silica nanopores, where acceleration where acceleration of the reaction of the reactionhas been has attributed been attributed to increased to increased collision collision efficiency efficiency (higher (higher pre-exponential pre-exponential factor factor values) values) in the in themonomer monomer layer layer near near the the silica silica surface surface [25,26,28]. [25,26,28 ]. AsAs seen seen in in Figure Figure8 A, 8A, polymerizations polymerizations of of the the confined confined cyanate cyanate ester ester are are characterized characterized by by significantlysignificantly smaller smaller variation variation of of activation activation energy energy that that does does not not exceed exceed 20% 20% of the of the respective respectiveaverage averageEα. Such variation can be considered insignificant so that the processes can be treated kinetically as a Eα. Such variation can be considered insignificant so that the processes can be treated kinetically as a th singlesingle step step reactionreaction [ 50[50].]. WeWe proposepropose that that one one of of thethe parallelparallel reactionsreactions (i.e., (i.e.,n nth-order-order oror autocatalytic),autocatalytic), includedincluded in in the the rate rateEquation Equation (8), might (8), be might depressed be depressed in confinement in confinement conditions, so conditions, the polymerization so the processpolymerization possesses pro singlecess rate-limitingpossesses single step. rate-limiting step. ToTo figure figure out out which which reaction reaction is depressed is depressed we have we calculated have calculated the g(α ) the values g(α according) values according to Equation to (6)Equation for polymerization (6) for polymerization of the cyanate of the ester cyanate in the ester pores in of the the pores SCCs of A–C the (Figure SCCs A 12–C). (Figure As one can12). seeAs theone gcan(α) plotssee the for g( allα) plots three for cases all three are nearly cases identical,are nearly so identical, we can so conclude we can thatconclude confined that reactionsconfined reactions proceed accordingproceed acc similarording reaction similar models. reaction models.

Polymers 20202020,, 1212,, 2329x FOR PEER REVIEW 11 of 17

Figure 12. Experimental g(α) data for polymerization of cyanate ester confined to SCCs (A–C). Figure 12. Experimental g(α) data for polymerization of cyanate ester confined to SCCs (A–C). Then we have fitted the expressions of g(α) for both aforementioned models (Equations (11) and (12))Then to experimental we have fitted data. the It expressions should be noted of g(α that) for unlike both aforementioned the nth-order reaction models model (Equations (11) and (12)) to experimental data. It should be noted that unlike the nth-order reaction model α Z훼 1 n dα 1 (1 α) 1−−푛 g(α) = 푑훼 n = 1 −− (1 − 훼) (11) 푔(훼) = ∫ (1 α) 푛 = 1 n (11) 0 (1 − 훼) 1 − 푛 0 the autocatalytic modelmodel doesdoes notnot havehave anan analyticalanalytical formform forfor g((αα).). Thus, the respective integral model has been evaluated numerically. Zα 훼 dα g(α) = 푑훼 (12) m n 푔(훼) = ∫ α푚(1 α) 푛 (12) 0 훼 (1 − 훼) 0 th It turns out that nth--orderorder reaction reaction model model has has produced produced fits fits of of poor poor quality, quality, whereas autocatalytic model has has provided provided good good results results (Figure (Figure 13). 13 Thus,). Thus, one can one conclude can conclude that under that confinement under confinement the nth- th theordern reaction-order reactionis likely suppressed is likely suppressed so that the so overall that the reaction overall kinetics reaction is controlled kinetics is by controlled an autocatalytic by an autocatalyticprocess (Equation process (13)). (Equation (13)).

푑훼dα m푚 n푛 = 푘k2α훼 ((1 −α훼)) (13(13)) 푑푡dt 2 − The calculated m and n parameters for all three studied reactions are very close to to each other, other, and the average average values values of of mm andand n aren are 0.67 0.67 ± 0.020.02 and and 1.391.39 ± 0.02, 0.02,respectively. respectively. The suppression The suppression of nth- ± ± ofordernth-order reaction, reaction, which which corresponds corresponds to the to the residual residual phenol phenol-catalyzed-catalyzed polymerization, polymerization, might might be explained by the preferential adsorption of these species onto the polar silica surface that diminishesdiminishes their catalyticcatalyticPolymers activity.activity. 2020, 12 , x FOR PEER REVIEW 12 of 17

th Figure 13. FittingFigure of13. theFittingn of-order the nth-order and and autocatalytic autocatalytic models models to the to experimental the experimental g(α) dependenceg(α) dependence for for polymerizationpolymerization of confined of confined cyanate cyanate ester ester (SCC (SCC of of typetype A). A).

The obtained m and n values have been further refined by fitting the rate data to Equation (13) for all heating rates with the fixed activation energy value while varying the A, m, and n parameters. Previously determined averaged values of A, m, and n were used as initial values for optimization. The resulting values of the obtained kinetic parameters are presented in Table 2. Table 2 shows that the reactions of the monomer in the pores of SCCs of the all three types are characterized by values of parameters of kinetic triplets, which are very close to each other and similar to those reported for catalytic polymerization of the same monomer [56]. It is instructional to compare the influence of phenols and proton-donor groups grafted onto the surface of SCCs. First, it is well known that an increase of the concentration of phenols results in an increase of the reaction rate, which is proportional to the phenol concentration raised to the power of 0.5–1.2 [57–59]. In contrast to the phenols an increase of the surface concentration of silanols by an order of magnitude from ~0.6 (sample A) to ~5 (sample B) silanols per nm2 as well as grafting of groups of high acidity (sample C) does not appear to cause any appreciable increase in the acceleration of the polymerization process. Comparison of parameters of the autocatalytic reactions for the bulk and confined processes shows that the parameters of the reaction model (m and n) are the practically the same within the experimental error. Yet, the Arrhenius parameters (E2 and A2) differ significantly. The activation energy of the autocatalytic step in the bulk twice as large as the one for this step under confinement, but the pre-exponential factor value for the bulk step is larger by five orders of magnitude. The observed difference in the reactivity of the confined monomer can be explained by the different nature of the species promoting the autocatalytic process. Such species might be immobilized iminocarbonates formed by reaction of the cyanate ester monomer with silanol groups (Figure 14). Formation of such species was detected by FTIR during thermal polymerization of cyanate ester/silsesquioxane nanocomposites [29]. A characteristic absorption band at 1595 cm⁻1 has been assigned to hydrogen-bonded iminocarbonate groups [29]. Hydrogen-bonding is likely to increase the mobility of hydrogen linked to an iminocarbonate group, and thus to increase its catalytic activity in polymerization process [55]. As a result, the activation energy of the processes should be expected to decrease.

Polymers 2020, 12, x FOR PEER REVIEW 12 of 17

Figure 13. Fitting of the nth-order and autocatalytic models to the experimental g(α) dependence for Polymerspolymerization2020, 12, 2329 of confined cyanate ester (SCC of type A). 12 of 17

The obtained m and n values have been further refined by fitting the rate data to Equation (13) for allThe heating obtained ratesm withand then values fixed activation have been energy further value refined while by fittingvarying the the rate A, datam, and to n Equation parameters. (13) Previouslyfor all heating determined rates with averaged the fixed values activation of A energy, m, and value n were while used varying as initial the valA,uesm, andfor optimization.n parameters. ThePreviously resulting determined values of the averaged obtained values kinetic of Aparam, m, andetersn arewere presented used as initialin Table values 2. for optimization. The resultingTable 2 shows values that of the the obtained reactions kinetic of the parametersmonomer in are the presented pores of inSCCs Table of2 the. all three types are characterizedTable2 shows by values that the of reactions parameters of the of kinetic monomer triplet in thes, which pores are of SCCs very of close the all to threeeach other types and are similarcharacterized to those by reported values of for parameters catalytic polymeriz of kinetic triplets,ation of whichthe same are monomer very close [56]. to each other and similar to thoseIt is reportedinstructional for catalytic to compare polymerization the influence of of the phenols same monomerand proton [56-donor]. groups grafted onto the surfaceIt is of instructional SCCs. First, toit is compare well known the influence that an increase of phenols of andthe concentration proton-donor of groups phenols grafted results onto in thean increasesurface of of SCCs. the reaction First, itrate, is well which known is proportional that an increase to the ofphenol the concentration concentration of raised phenols to the results power in anof 0.5increase–1.2 [57 of– the59]. reactionIn contrast rate, to which the phenols is proportional an increase to theof the phenol surface concentration concentration raised of silanols to the powerby an orderof 0.5–1.2 of magnitude [57–59]. In from contrast ~0.6 to(sample the phenols A) to an~5 increase(sample ofB) thesilanols surface per concentration nm2 as well as of grafting silanols byof sulfonican order acid of magnitude groups of fromhigh acidity ~0.6 (sample (sample A) C) to does ~5 (sample not appear B) silanols to cause per any nm appreciable2 as well as increase grafting in of thesulfonic acceleration acid groups of the of polymerization high acidity (sample process. C) does not appear to cause any appreciable increase in the accelerationComparison of of the parameters polymerization of the process. autocatalytic reactions for the bulk and confined processes showsComparison that the parameters of parameters of the of reaction the autocatalytic model (m and reactions n) are for the the practically bulk and the confined same within processes the experimentalshows that the error. parameters Yet, the of Arrhenius the reaction parameters model (m (Eand2 andn) areA2) the differ practically significantly. the same The within activation the energyexperimental of the autocatalytic error. Yet, the step Arrhenius in the bulk parameters twice as large (E2 and as theA2 one) di ffforer this significantly. step underThe confinement, activation butenergy the of pre the-exponential autocatalytic factor step in value the bulk for twice the bulk as large step as is the larger one for by this five step orders under of confinement, magnitude. The but observedthe pre-exponential difference factor in the value reactivity for the of bulk the step confined is larger monomer by five orders can be of explained magnitude. by The the observed different naturedifference of in the the species reactivity promoting of the confined the autocatalytic monomer can process.be explained Such by species the different might nature be immobilizedof the species promotingiminocarbonates the autocatalytic formed by process.reaction Suchof the species cyanate might ester be monomer immobilized with iminocarbonatessilanol groups (Figure formed 14). by Formationreaction of the of cyanate such species ester monomer was detected with silanol by FTIR groups during (Figure thermal 14). Formation polymerization of such species of cyanate was ester/silsesquioxanedetected by FTIR during nanocomposites thermal polymerization [29]. A characteristic of cyanate ester absorption/silsesquioxane band at nanocomposites 1595 cm⁻1 has been [29]. 1 Aassigned characteristic to hydrogen absorption-bonded band iminocarbonate at 1595 cm− has groups been assigned[29]. Hydrogen to hydrogen-bonded-bonding is likely iminocarbonate to increase thegroups mobility [29]. of hydrogen Hydrogen-bonding linked to an is iminocarbonate likely to increase group, the and mobility thus to increase of hydrogen its catalytic linked activity to an iniminocarbonate polymerization group, process and [55]. thus As a to result, increase the activation its catalytic energy activity of the in processes polymerization should processbe expected [55]. Asto decr a result,ease. the activation energy of the processes should be expected to decrease.

Figure 14. Scheme of formation of immobilized iminocarbonate.

On the other hand, the immobilization of iminocarbonate decreases its mobility, and thus should cause a decrease of the preexponential factor for the reaction it is involved in. Furthermore, because a fraction of the cyanate ester molecules is immobilized on the surface, they cannot participate in the cyclization process, which should result in a reduction in the reaction heats, as has been observed in the present study for the confined systems. Moreover, since the monomer molecules are quite bulky, the formation of iminocarbonate should hinder the reaction of neighboring silanols, which can be a reason for the absence of additional reaction acceleration inside the CSS having increased surface concentration of silanol groups (Figure 15). Polymers 2020, 12, x FOR PEER REVIEW 13 of 17

Figure 14. Scheme of formation of immobilized iminocarbonate.

On the other hand, the immobilization of iminocarbonate decreases its mobility, and thus should cause a decrease of the preexponential factor for the reaction it is involved in. Furthermore, because a fraction of the cyanate ester molecules is immobilized on the surface, they cannot participate in the cyclization process, which should result in a reduction in the reaction heats, as has been observed in the present study for the confined systems. Moreover, since the monomer molecules are quite bulky, the formation of iminocarbonate should hinder the reaction of neighboring silanols, which can be a Polymersreason 2020for ,the12, 2329 absence of additional reaction acceleration inside the CSS having increased surface13 of 17 concentration of silanol groups (Figure 15).

FigureFigure 15.15. IllustrationIllustration ofof immobilizationimmobilization ofof iminocarbonatesiminocarbonates onon silicasilica surfacessurfaces withwith highhigh ((AA)) andand lowlow ((BB)) concentrationconcentration ofof silanols.silanols.

In order to quantify the acceleration of confined reaction, we have introduced the isoconversional In order to quantify the acceleration of confined reaction, we have introduced the and isothermal acceleration factor Zα,T. This factor has a straightforward meaning of how many times isoconversional and isothermal acceleration factor Zα,T. This factor has a straightforward meaning of the rate of the reaction under confinement is increased relative to that in the bulk at specific T and α how many times the rate of the reaction under confinement is increased relative to that in the bulk at (Equation (14)). specific T and α (Equation (14)). !con f !bulk dα dα Z = 푐표푛푓/ 푏푢푙푘 (14) α, T 푑훼dt 푑훼dt 푍훼,푇 = ( ) α, T / ( )α, T (14) 푑푡 훼,푇 푑푡 훼,푇 Isoconversional values (dα/dt)α obtained from non-isothermal DSC runs cannot be directly used in Equation (14) since they correspond to different temperatures. Therefore, we recalculate the (dα/dt)α values from non-isothermal experiments to isothermal conditions. This is readily accomplished by using the technique of isoconversional predictions [31]. In the case when the isoconversional calculation is performed by integration over small segment of α, the respective equation takes the following form,

X J[Eα, Ti(tα)] tα =   (15) exp Eα α − RT Polymers 2020, 12, x FOR PEER REVIEW 14 of 17

Isoconversional values (dα/dt)α obtained from non-isothermal DSC runs cannot be directly used in Equation (14) since they correspond to different temperatures. Therefore, we recalculate the (dα/dt)α values from non-isothermal experiments to isothermal conditions. This is readily accomplished by using the technique of isoconversional predictions [31]. In the case when the isoconversional calculation is performed by integration over small segment of α, the respective equation takes the following form, 퐽[퐸 , 푇 (푡 )] 푡 = ∑ 훼 푖 훼 훼 퐸 (15) 푒푥푝 (− 훼 ) 훼 푅푇 Polymers 2020, 12, 2329 14 of 17 where tα is the time to reach the conversion α at isothermal temperature, T. The resulting set of the α−tα pairs is then differentiated numerically to determine (dα/dt)α,T values. The latter are then where tα is the time to reach the conversion α at isothermal temperature, T. The resulting set of the α tα substituted into Equation (14) to calculate the variation of Zα,T factor with conversion. The resulting− pairsvalues is thenof Zα di,T atfferentiated T = 250 °C numericallyare shown in to Figure determine 16. This (dα temperature/dt)α,T values. was The chosen latter as are a reference then substituted because intoall studied Equation systems (14) to calculatereact with the measurable variation of ratesZα,T atfactor that withtemperature conversion. (see TheFigure resulting 6). Based values on oftheZ αZ,Tα,T atvaluesT = 250 we◦C can are shown conclude in Figure that the16. This confined temperature reactions was proceed chosen as about a reference 15–30 because times allfaster studied than systemspolymerization react with in measurable the bulk. rates at that temperature (see Figure6). Based on the Zα,T values we can conclude that the confined reactions proceed about 15–30 times faster than polymerization in the bulk.

Figure 16. Variation of the isoconversional-isothermal acceleration factor Zα,T with conversion at 250 ◦C. 5. ConclusionsFigure 16. Variation of the isoconversional-isothermal acceleration factor Zα,T with conversion at 250 °C. We have studied the kinetics of polymerization of the cyanate ester monomer confined to the5. C hydrophiliconclusions pores of SCCs. The crystal surface has been modified to probe the effect of the concentration of silanol groups and acidity of grafted 3-propylsulfonic groups. Significant acceleration We have studied the kinetics of polymerization of the cyanate ester monomer confined to the of polymerization has been observed in all three types of SCCs. Kinetic analysis has revealed that the hydrophilic pores of SCCs. The crystal surface has been modified to probe the effect of the bulk polymerization follows the model of two parallel reactions, namely, nth-order and autocatalytic. concentration of silanol groups and acidity of grafted 3-propylsulfonic groups. Significant Confining the monomer to the hydrophilic pores has simplified the polymerization kinetics making it acceleration of polymerization has been observed in all three types of SCCs. Kinetic analysis has essentially a single-step one. Kinetic analysis of the confined polymerization suggests that nth-order revealed that the bulk polymerization follows the model of two parallel reactions, namely, nth-order reaction, corresponding to phenol-catalyzed polymerization, is suppressed likely due to adsorption and autocatalytic. Confining the monomer to the hydrophilic pores has simplified the polymerization of residual phenols by the polar silica surface. Kinetic parameters of the confined autocatalytic kinetics making it essentially a single-step one. Kinetic analysis of the confined polymerization polymerization have been similar for all three types of SCCs so that no significant effect of the suggests that nth-order reaction, corresponding to phenol-catalyzed polymerization, is suppressed concentration and proton acidity of the surface-grafted groups has been found. On the other hand, likely due to adsorption of residual phenols by the polar silica surface. Kinetic parameters of the the activation energy of the confined autocatalytic polymerization has been determined to be about confined autocatalytic polymerization have been similar for all three types of SCCs so that no two times smaller than for the bulk process. Moreover, the confined process has demonstrated a significant effect of the concentration and proton acidity of the surface-grafted groups has been decrease in the pre-exponential factor and the reaction heat. These effects have been explained by the found. On the other hand, the activation energy of the confined autocatalytic polymerization has been formation of iminocarbonates that are immobilized on the silica surface but possess increased catalytic determined to be about two times smaller than for the bulk process. Moreover, the confined process activity due to hydrogen-bonding with residual silanol groups. In addition, we have introduced the has demonstrated a decrease in the pre-exponential factor and the reaction heat. These effects have acceleration factor Zα,T that permits to compare conveniently the reactivity of compounds reacting in different temperature ranges.

Author Contributions: Conceptualization, A.G. and S.V.; methodology, S.V.; investigation, A.G., G.T., R.N., and T.L.; writing—original draft preparation, A.G.; writing—review and editing, S.V. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the Russian Science Foundation (project no. 18-13-00149). Conflicts of Interest: The authors declare no conflict of interest. Polymers 2020, 12, 2329 15 of 17

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