Reconstruction of the Microstructure of Cyanate Ester Resin by Using

applied sciences

Article Reconstruction of the Microstructure of Cyanate Ester Resin by Using Prepared Cyanate Ester Resin Nanoparticles and Analysis of the Curing Kinetics Using the Avrami Equation of Phase Change

Hongtao Cao, Beijun Liu, Yiwen Ye, Yunfang Liu * and Peng Li *

Research Institute of Carbon Fiber and Composite Materials, Beijing University of Chemical Technology, Beijing 100029, China; [email protected] (H.C.); [email protected] (B.L.); [email protected] (Y.Y.) * Correspondence: [email protected] (Y.L.); [email protected] (P.L.); Tel.: +86-010-644-34914 (Y.L.) Received: 4 May 2019; Accepted: 5 June 2019; Published: 10 June 2019

Featured Application: The addition of the BADCy resin nanoparticles can accelerate the formation of the microgels in the BADCy resin prepolymer. The kinetic paraments of systems with diﬀerent BADCy resin nanoparticles contents were obtained using the Avrami equation and Arrhenius equation and explained the formation and growth of the microgels.

Abstract: Bisphenol A dicyanate (BADCy) resin nanoparticles were synthesized by precipitation polymerization and used to modulate the microstructure of the BADCy resin matrix. A microscopic mechanism model was used to characterize the curing process of BADCy resin systems with different contents of the prepared nanoparticles. Due to the curing process of the thermosetting resin being analogous to the crystallization process of the polymer, the Avrami equation was used to analyze the microscopic mechanism of the curing process. The reactive functional groups, structure, and size of the prepared BADCy resin nanoparticles were characterized by FT-IR, SEM, and TEM, respectively. The kinetic parameters of different systems were then obtained using the Avrami equation, and they adequately explained the microscopic mechanism of the curing process. The results showed that the Avrami equation effectively described the formation and growth of gel particles during the curing process of the BADCy resins. The addition of nanoparticles can affect the curing behavior and curing rate. Since the reaction between the BADCy resin nanoparticles and the matrix is dominant, the formation process of the gel particles was neglected. This phenomenon can be understood as the added BADCy resin nanoparticles replacing the formation of gel particles. The reasons for accelerated curing were analyzed from the perspective of thermodynamics and kinetics. Besides this, the Arrhenius equation for non-isothermal conditions correctly accounted for the change in the cross-linked mechanism in the late-stage curing process. A comparison of the theoretical prediction with the experimental data shows that the Avrami theory of phase change can simulate the curing kinetics of different BADCy resin systems well and explain the effects of BADCy resin nanoparticles on the formation of the microstructure.

Keywords: bisphenol a dicyanate resin; Avrami equation; Arrhenius equation; curing behavior

1. Introduction Cyanate ester (CE) resins are novel high-performance thermosetting resins similar to epoxy (EP) and bimaleimide (BMI) that have been developed in recent decades [1]. CE monomers contain two

Appl. Sci. 2019, 9, 2365; doi:10.3390/app9112365 www.mdpi.com/journal/applsci Appl.Appl. Sci. Sci.2019 2019,,9 9,, 2365 x 2 2of of 15 15

or more -OCN functional groups which can form a highly symmetrical triazine ring structure after or more -OCN functional groups which can form a highly symmetrical triazine ring structure after the curing reaction [2]. It is the chemical nature of the CE monomers and the unique structure of the the curing reaction [2]. It is the chemical nature of the CE monomers and the unique structure of the cured resin that give rise to a series of properties, such as excellent mechanical properties, a high glass curedtransition resin thattemperature, give rise tolow a series contractibility of properties, rate, such low as water excellent absorption, mechanical and properties, ultralow a dielectric high glass transitionconstant temperature,and dielectric low loss contractibility values [3–6]. rate, Compared low water with absorption, other thermosetting and ultralow resins, dielectric CEs constant have andexcellent dielectric overall loss performance. values [3–6]. Therefore, Compared CEs with are other a proven thermosetting replacement resins, for thermosets, CEs have excellent such as epoxy overall performance.or polyimide, Therefore, in applications CEs are in the a proven aerospace, replacement electronics, for thermosets,and communications such as epoxy industries or polyimide, [4,7–11]. in applicationsCE monomers in the aerospace, polymerize electronics, via a ring-forming and communications reaction under industries the [conditions4,7–11]. of heating or catalysts.CE monomers Simmon first polymerize proposed via the a ring-forming self-polymeri reactionzation mechanism under the conditions of CE resins of heatingin the absence or catalysts. of a Simmoncatalyst first[12]. proposed The curing the reaction self-polymerization of the CE resins mechanism was initiated of CEresins and catalyzed in the absence by impurities of a catalyst in the [12 ]. Themonomer curing or reaction moisture of in the the CE environment. resins was initiated However, and this catalyzed process proceeds by impurities with difficulty in the monomer when the or moisturepurity of inthe the monomer environment. is high [13]. However, Active hydrogen this process containing proceeds compounds, with difficulty such as when phenols, the purityamines, of theand monomer imidazole, is in high concert [13]. with Active metal hydrogen ions can containing catalyze the compounds, curing of CE such resins as phenols,[14]. This amines, reaction and is imidazole,depicted in in concertFigure 1. with A metalrange ionsof such can catalyzemetal ions the curinghas been of CE reported, resins [ 14including]. This reaction chromium is depicted [15], inmanganese Figure1. A [16], range iron of such[17], metalcobalt ions[18], hastin been[19], reported,zinc [20], includingand copper chromium [21]. However, [ 15], manganese the metal ion [16 ], ironcompounds [17], cobalt have [18 poor], tin solubility [19], zinc in [ 20the], CE and resins copper and [ 21promote]. However, the hydrolysis the metal reaction ion compounds of the triazine have poorring solubilityas well; as in a theresult, CE these resins metal andpromote salts are therare hydrolysisly used as reactiona catalyst. of Alternative the triazine catalytic ring as well;systems as a result,have always these metal been salts an important are rarely useddirection as a catalyst.of research. Alternative At present, catalytic room systems temperature have always ionic liquids been an important(RTILs) and direction organically of research. modified At layered present, silicate room have temperature been proved ionic to liquidsaccelerate (RTILs) CE resin and curing organically [22– modified24]. layered silicate have been proved to accelerate CE resin curing [22–24].

FigureFigure 1.1. Self-polymerizationSelf-polymerization mechanism of cyanate ester ester in in the the presence presence of of catalysts. catalysts.

PhysicalPhysical and and structural structural changes changes a ffaffectect the the polymerization polymerization kinetics kinetics and and the the structure. structure. Therefore, Therefore, the identificationthe identification of relevant of relevant kinetic models kinetic can models provide can insight provide into theinsight curing into process the of curing thermosetting process resin of systems.thermosetting In the curingresin systems. process, In identifying the curing each process, step of identifying the chemical each reaction step of is the very chemical difficult. reaction Especially, is invery the difficult. late curing Especially, stage, the in the diff usionlate curing factor stage, plays the a controllingdiffusion factor role. plays Thus, a controlling the phenomenological role. Thus, model,the phenomenological rather than the mechanismmodel, rather model, than isthe used me [chanism25]. The model, Kamal kineticis used model[25]. The considers Kamal bothkinetic the autocatalyticmodel considers behavior both andthe theautocatalytic n-stage reaction, behavior and and it canthe ben-stage used toreaction, describe and the it curing can be process used to of thermosettingdescribe the curing resins process precisely of [ 26thermosetting]. However, theseresins models precisely are [26]. limited However, to describing these models the curing are limited reaction processto describing and do the not curing give specificreactionphysical process and meaning do not to give the specific parameters. physical Previous meaning studies to the demonstrated parameters. thatPrevious the Avrami studies equation demonstrated considerably that the illustrated Avrami equa thetion isothermal considerably and non-isothermal illustrated the isothermal curing behavior and ofnon-isothermal thermosetting curing resins [behavior25,27–29 ].of thermosetting resins [25,27–29]. TheThe essence essence ofof thermosettingthermosetting resinresin curing is the cross-linked chemical chemical reaction reaction of of linear linear polymer polymer chains.chains. Meanwhile, Meanwhile, this this is is accompanied accompanied by by microphase microphase separation, separation, the the shift shift of theof the glass glass transition, transition, and otherand processes,other processes, eventually eventually forming forming a three-dimensional a three-dimensional network structure.network Itstructure. is generally It is believed generally that thebelieved crystallization that the processcrystallization of the polymerprocess of includes the po twolymer processes includes of two nucleation processes and of growthnucleation [30]. and The firstgrowth step [30]. is the The formation first step of is crystal the formation nuclei. Due of crystal to local nuclei. fluctuations Due to in local the parentfluctuations phase, in the the local parent free energyphase, increases,the local free resulting energy in increases, a small range resulting of new in a phases small range (clusters). of new The phases clusters (clusters). can continue The clusters to grow andcan becomecontinue macroscopic to grow and crystals,become macroscopic which can also crys dissolvetals, which and can disappear. also dissolve When and the disappear. cluster reaches When a certainthe cluster size—that reaches is, a acertain critical size—that size—it becomes is, a critical a crystal size—it nucleus. becomes The a crystal second nucleus. step is theThe growth second ofstep the crystalis the nucleus,growth of which the crystal is characterized nucleus, which by the is di chffusionaracterized and stacking by the diffusion of the polymer and stacking segment of to the the nucleus.polymer In segment terms of to the the microscopic nucleus. In mechanism, terms of the the microscopic curing process mechanism, of the thermosetting the curing process resins isof quitethe similarthermosetting to the crystallization resins is quite of polymers.similar to the The crys curingtallization process of is apolymers. chemical The cross-linked curing process process, is and a chemical cross-linked process, and crystallization can be seen as a physical cross-linked process. In Appl. Sci. 2019, 9, 2365 3 of 15 Appl. Sci. 2019, 9, x 3 of 15 crystallizationthe process of can the becross-linking seen as a physical of linear cross-linked polymers, there process. are many In the molecular process of aggregates the cross-linking or high- of linearaverage-molecular-mass polymers, there are manyparticles molecular [31]. These aggregates microgel or high-average-molecular-massparticles are stably dispersed particles in the low [31]. Thesemolecular microgel oligomers. particles As are the stably curing dispersed reaction inprogre the lowsses, molecular the number oligomers. of microgel As particles the curing increases, reaction progresses,their volume the becomes number larger, of microgel and they particles collide increases, with each their other, volume resulting becomes in the larger,viscosity and of theythe system collide withincreasing. each other, Finally, resulting the initial in the phase viscosity is wrapped of the system by the increasing. new phase Finally,to undergo the initial two-phase phase conversion, is wrapped bywith the newthe result phase being to undergo that the two-phase gel phase conversion, becomes witha continuous the result phase. being thatThe theformation gel phase of becomesmicrogel a continuousparticles can phase. be analogized The formation to the of nucleation microgel particles process, can and be the analogized volume increase to the nucleation can be analogized process, and to thethe volume growth increase of crystal can nuclei. be analogized In summary, to the the growth Avrami of crystal equation nuclei. based In on summary, phase transition the Avrami theory equation can basedbe applied on phase to study transition the curing theory kinetics can be of applied thermosetting to study resins. the curing kinetics of thermosetting resins. InIn this this work, work, we we prepared prepared bisphenol bisphenol AA dicyanatedicyanate (BADCy)(BADCy) resin nanoparticles using using BADCy BADCy monomermonomer by by precipitationprecipitation polymerization.polymerization. The The nano nanoparticlesparticles were were dispersed dispersed in inthe the prepolymer prepolymer to tostudy study changes changes in in the the formation formation process process of of the the microgels, microgels, in in which which the the nanoparticles nanoparticles and and matrix matrix belongedbelonged to to the the same same polymer polymer family family but had but di ffhaderent different chemical chemical structure [structure32]. The BADCy[32]. The prepolymer BADCy wasprepolymer synthesized was in synthesized our laboratory. in our The laborato added BADCyry. The resinadded nanoparticles BADCy resin were nanoparticles equivalent towere the microgels,equivalent and to the their microgels, function and was their to serve function as a was reaction to serve site, as inducing a reaction curing site, inducing of the BADCy curingmatrix. of the ThisBADCy process matrix. is shown This process in Figure is shown2. The in dynamic Figure 2. curing The dynamic behavior curing of the behavior BADCy of resin the BADCy systems resin was studiedsystems and was the studied kinetic parametersand the kinetic were parameters obtained by were using obtained the modified by using Avrami the equation. modified Avrami equation.

Figure 2. Schematic diagram of the bisphenol A dicyanate (BADCy) resin nanoparticles initiating Figure 2. Schematic diagram of the bisphenol A dicyanate (BADCy) resin nanoparticles initiating matrix curing. matrix curing. 2. Materials and Methods 2. Materials and Methods 2.1. Reagents and Materials 2.1. Reagents and Materials BADCy monomer (white crystalline powder, 99% purity) was purchased from Yangzhou Techia MaterialBADCy Co., Ltd.monomer (Yangzhou, (white China).crystalline Zinc powder, acetylacetonate 99% purity) hydrate was purchased (97% purity) from Yangzhou and nonylphenol Techia wereMaterial purchased Co., Ltd. from (Yangzhou, Aladdin (Shanghai, China). Zinc China) acet andylacetonate Macklin hydrate (Shanghai, (97% China), purity) respectively. and nonylphenol Xylene waswere obtained purchased from from Beijing Aladdin Chemical (Shanghai, Co., Ltd. China) (Beijing, and China). Macklin All were(Shanghai, used as China), received. respectively. Xylene was obtained from Beijing Chemical Co., Ltd. (Beijing, China). All were used as received. 2.2. Preparation of BADCy Resin Nanoparticles 2.2. Preparation of BADCy Resin Nanoparticles A certain mass ratio (5:100) of xylene and BADCy monomer was added to a three-mouth ﬂask, A certain mass ratio (5:100) of xylene and BADCy monomer was added to a three-mouth flask, and stirred at 100 ◦C until the BADCy monomer totally dissolved. Then, zinc acetylacetonate hydrate andand nonylphenol stirred at 100 (two °C until thousandths the BADCy of themonomer mass of tota thelly monomer) dissolved. as Then, catalyst zinc were acetylacetonate dissolved in hydrate xylene and nonylphenol (two thousandths of the mass of the monomer) as catalyst were dissolved in xylene and quickly added to the three-mouth ﬂask. The mixture was heated at 100 ◦C, and stirred fast for and quickly added to the three-mouth flask. The mixture was heated at 100 °C, and stirred fast for 1 1 h. The temperature was raised to 130 ◦C and heating was continued for 3.5 h. The BADCy resin nanoparticlesh. The temperature were obtained was raised after to centrifugation, 130 °C and heating washing, was and continued decompression for 3.5 drying.h. The BADCy resin nanoparticles were obtained after centrifugation, washing, and decompression drying. Appl. Sci. 2019, 9, 2365 4 of 15

2.3. Preparation of BADCy Resin Prepolymer

First, the BADCy monomer was melted at 100 ◦C. Second, the moisture was removed under decompression at 80 ◦C. Finally, the liquid was heated at 200 ◦C for 2 h and the temperature was cooled to 180 ◦C and heating was continued for 8 h until a clear homogeneous melt was obtained. The viscous melt was deﬁned as the BADCy resin prepolymer.

2.4. Characterization and Measurements

1 Fourier transform infrared (FT-IR) spectra were measured between 400 and 4000 cm− using a Nicolet 8700 FT-IR spectrometer (Thermo Fisher Scientific, Shanghai, China). For each spectrum, 1 a resolution of 4 cm− , 32 scanning times, and a KBr table was used. Sample measurements were recorded at room temperature. Scanning electron microscopy (SEM) was carried out using an S-4700 cold-field scanning electron microscope (Hitachi, Japan). The accelerating voltage was 20 kV and the samples were coated with gold. Transmission electron microscopy (TEM) was performed using an HT7700 biological transmission electron microscope (Hitachi, Japan). Differential scanning calorimetry (DSC) was carried out using a TA Instruments DSC25 calorimeter (TA Instruments, New Castle, DE, USA). Each sample was tested at 5, 10, 15, and 20 ◦C/min, over a range of 50-380 ◦C and with a N2 flow of 50 mL/min.

3. Results and Discussion

3.1. Characterization of the BADCy Resin Microparticles The FT-IR spectra curves of the BADCy monomer and BADCy resin nanoparticles are shown in Figure3, from which the molecular structure characteristics of the BADCy monomer and BADCy resin nanoparticle were ascertained. Compared with the BADCy monomer, the most apparent diﬀerences are 1 the new peaks at 1568 and 1369 cm− . These two new peaks are due to the triazine ring structure formed by the monomer under the conditions of catalysts and heating [33]. Besides this, the -OCN functional 1 group of the BADCy resin nanoparticles at 2270 cm− is reduced compared with the monomer because the chemistry mechanism of the reaction is a trimerization of three -OCN groups into a triazine ring. 1 According to the result of the FT-IR spectra, the -OCN functional group peak at 2270 cm− does not completely disappear. It can be seen that the prepared BADCy resin nanoparticles still have an active -OCN functional group and can continue to react. Figure4 shows a dynamic DSC curve of the BADCy resin nanoparticles and the matrix, indicating that the nanoparticles are still exotherms during the dynamic heating process, but with less heat than the matrix. It can also be concluded that the prepared BADCy resin nanoparticles have reactivity. The structure and size of the prepared BADCy resin nanoparticles were characterized by SEM (a) and TEM (b) as shown in Figure5. After the reaction, the mixed solution was successively subjected to centrifugation, washing, and vacuum drying to obtain a pale yellow solid powder. The powders were subjected to SEM observation. From the SEM images of the BADCy resin nanoparticles, a large quantity of aggregates (micron-sized) was observed. A single aggregation particle ranged in size from 0.2 to 0.3 µm. The powder was then dispersed in an ethanol solvent via ultrasonic dispersion. A drop of stable dispersion was dropped on a copper grid, dried, and observed using the transmission electron microscope. It can be seen that the BADCy resin nanoparticles ranged in size from 40 to 60 nm and there was no aggregation. Appl. Sci. 2019, 9, x 5 of 15

Appl. Sci. 2019, 9, x 5 of 15

Appl. Sci. 2019, 9, 2365 5 of 15

Figure 3. FT-IR of the BADCy monomer and BADCy resin nanoparticle.

Figure 4. Diﬀerential scanning calorimetry (DSC) curves of the BADCy prepolymer matrix and BADCy resin nanoparticles. Figure 4. Differential scanning calorimetry (DSC) curves of the BADCy prepolymer matrix and BADCyFrom theresin above nanoparticles. results, when the reaction solution was subjected to post-treatment, especially the drying process, the nanoparticles were aggregated and nano-sized particles became micro-sized. DuringThe thestructure dying process,and size the of nano-sized the prepared particles BADCy tended resin to nanoparticles aggregate as the were solvent characterized evaporated by until SEM (a)a stableand TEM size was(b) reached.as shown in Figure 5. After the reaction, the mixed solution was successively Figure 4. Differential scanning calorimetry (DSC) curves of the BADCy prepolymer matrix and subjected to centrifugation, washing, and vacuum drying to obtain a pale yellow solid powder. The BADCy resin nanoparticles. powders were subjected to SEM observation. From the SEM images of the BADCy resin nanoparticles,The structure a large and sizequantity of the of prepared aggregates BADCy (micron-sized) resin nanoparticles was observed. were characterized A single aggregation by SEM (a)particle and TEMranged (b) in as size shown from in0.2 Figureto 0.3 μ 5.m. After The powderthe reaction, was then the dispersedmixed solution in an ethanol was successively solvent via subjected to centrifugation, washing, and vacuum drying to obtain a pale yellow solid powder. The powders were subjected to SEM observation. From the SEM images of the BADCy resin nanoparticles, a large quantity of aggregates (micron-sized) was observed. A single aggregation particle ranged in size from 0.2 to 0.3 μm. The powder was then dispersed in an ethanol solvent via Appl. Sci. 2019, 9, x 6 of 15

ultrasonic dispersion. A drop of stable dispersion was dropped on a copper grid, dried, and observed Appl.using Sci. the2019 transmission, 9, 2365 electron microscope. It can be seen that the BADCy resin nanoparticles ranged6 of 15 in size from 40 to 60 nm and there was no aggregation.

Figure 5. Representative SEM (a) and TEM (b) images of the BADCy resin nanoparticles. Figure 5. Representative SEM (a) and TEM (b) images of the BADCy resin nanoparticles. 3.2. Cure Acceleration From the above results, when the reaction solution was subjected to post-treatment, especially the dryingFigure 6process, shows thethe results nanoparticles of the 10 were◦C/ minaggreg temperatureated and nano-sized ramp dynamic partic DSCles became experiments micro-sized. in which theDuring prepared the dying BADCy process, resin the nanoparticles nano-sized wereparticle addeds tended into theto aggregate neat BADCy as the prepolymer solvent evaporated at various contentsuntil a stable (neat, size 4, 8, was and reached. 10 wt%). It can be seen that the added BADCy resin nanoparticles had a strong eﬀect on the curing temperature and enthalpy changes. The curves reveal a decrease in the curing peak3.2. Cure temperature, AccelerationTp , as well as an increase in the curing enthalpy, ∆H, with the addition of BADCy resin nanoparticles (Table1). This indicates that a range of BADCy resin nanoparticles can be used for Figure 6 shows the results of the 10 °C/min temperature ramp dynamic DSC experiments in accelerating curing and improving the degree of curing. This conclusion is consistent with the FT-IR which the prepared BADCy resin nanoparticles were added into the neat BADCy prepolymer at spectra. The initially polymerized nanoparticles still have reactive functional groups, and can directly various contents (neat, 4, 8, and 10 wt%). It can be seen that the added BADCy resin nanoparticles initiate the self-polymerization reaction. Compared with the 4 and 8 wt% systems, the curing enthalpy, had a strong effect on the curing temperature and enthalpy changes. The curves reveal a decrease in ∆H, of the 10 wt% system is reduced. This is because the excessive quantity of nanoparticles results in the curing peak temperature, Tp, as well as an increase in the curing enthalpy, ΔH, with the addition theAppl. distance Sci. 2019, between 9, x the nanoparticles becoming small. The nanoparticles react with the matrix7 andof 15 of BADCy resin nanoparticles (Table 1). This indicates that a range of BADCy resin nanoparticles can also react with other nanoparticles. The heat of reaction between the nanoparticles themselves is less be used for accelerating curing and improving the degree of curing. This conclusion is consistent with than that between the particles and the matrix. Therefore, the total exotherm is reduced. the FT-IR spectra. The initially polymerized nanoparticles still have reactive functional groups, and can directly initiate the self-polymerization reaction. Compared with the 4 and 8 wt% systems, the curing enthalpy, ΔH, of the 10 wt% system is reduced. This is because the excessive quantity of nanoparticles results in the distance between the nanoparticles becoming small. The nanoparticles react with the matrix and also react with other nanoparticles. The heat of reaction between the nanoparticles themselves is less than that between the particles and the matrix. Therefore, the total exotherm is reduced.

Figure 6. DSC curves of the BADCy matrix with diﬀerent BADCy resin nanoparticles contents.

Figure 6. DSC curves of the BADCy matrix with different BADCy resin nanoparticles contents.

Table 1. Thermal characteristics of samples. BADCy: Bisphenol A dicyanate.

BADCy Resin Nanoparticles Tonset Tpeak ΔH wt% °C °C J/g 0 248 308 303.19 4 209 238 423.16 8 212 235 441.15 10 201 229 370.60

The formation of microgel particles can occur from a thermodynamic point of view. Analogous to the thermodynamic equations of the crystallization process, the thermodynamic equations of the microgel particles can be expressed as:

𝛥𝐺 =𝐺 −𝐺, (1) where ΔG is the change in Gibbs free energy during the curing process and the curing reaction occurs when the ΔG is negative. At the beginning of the curing reaction, the gel particles have a small volume and a large specific surface area. If the surface effect is considered, the total free energy of the system can be accurately expressed as:

𝐺 =𝐺 + ∑ 𝜎𝐴, (2)

where Gbulk is the change in the matrix free energy without considering the surface effect, σ is the surface free energy coefficient, and A is the surface area of the gel particles. Therefore, the thermodynamic equation (Equation (1)) of the curing process can be rewritten as:

𝛥𝐺 = Δ𝐺 + ∑ 𝜎𝐴. (3)

Here, ΔGc represents the free energy change of the matrix. ΔG is a negative value when the reaction temperature reaches curing conditions. Since the surface free energy coefficient, A, is a positive value, only at the condition of the curing temperature, ΔGc, is a negative value, making ΔG still less than zero. Therefore, curing of the resin system will proceed. Figure 7 is a schematic illustration of the free energy changes in the gel particle formation and growth stages. Appl. Sci. 2019, 9, 2365 7 of 15

Table 1. Thermal characteristics of samples. BADCy: Bisphenol A dicyanate.

BADCy Resin Nanoparticles Tonset Tpeak ∆H wt% ◦C ◦C J/g 0 248 308 303.19 4 209 238 423.16 8 212 235 441.15 10 201 229 370.60

∆G = Gcure G , (1) − melt where ∆G is the change in Gibbs free energy during the curing process and the curing reaction occurs when the ∆G is negative. At the beginning of the curing reaction, the gel particles have a small volume and a large specific surface area. If the surface effect is considered, the total free energy of the system can be accurately expressed as: X Gcure = Gbulk + σA, (2) where Gbulk is the change in the matrix free energy without considering the surface effect, σ is the surface free energy coefficient, and A is the surface area of the gel particles. Therefore, the thermodynamic equation (Equation (1)) of the curing process can be rewritten as: X ∆G = ∆Gc + σA. (3)

Here, ∆Gc represents the free energy change of the matrix. ∆G is a negative value when the reaction temperature reaches curing conditions. Since the surface free energy coefficient, A, is a positive value, only at the condition of the curing temperature, ∆Gc, is a negative value, making ∆G still less than zero. Therefore, curing of the resin system will proceed. Figure7 is a schematic illustration of the free energy changes in the gel particle formation and growth stages. During the heating process of the resin systems, ∆G is greater than zero before the formation of the thermodynamically stable gel particles, and ∆G has a maximum value. This stage is mainly a cross-linked reaction of polymer segments and is primarily controlled by kinetic factors. Once the gel particles are formed, the growth of the gel particles can reduce the free energy of the systems and the gel particles enable automatic growth. At this stage, the viscosity of the system increases due to the growth of the gel particles, and the movement of the molecular segments is limited, so it is mainly controlled by the diffusion factors. In our study, when nanoparticles were added into the matrix, there were two reaction processes. The first is that the matrix itself undergoes a curing reaction which includes the formation and growth of gel particles. The second is the reaction of the particles with the matrix, which only appears as the growth of the gel particles. These two reaction processes are carried out simultaneously. However, the first case requires overcoming a considerable surface energy barrier to nucleate. In the second case, since the matrix is heterogeneous, the surface energy barrier at the time of nucleation of the gel particles can be effectively reduced, resulting in preferential formation of the gel particle cores at these uneven places. These two cases are similar to homogeneous nucleation and heterogeneous nucleation. Appl. Sci. 2019, 9, x 8 of 15 Appl. Sci. 2019, 9, 2365 8 of 15

Figure 7. Schematic illustration of free energy changes with size in the gel particle formation and Figure 7. Schematic illustration of free energy changes with size in the gel particle formation and growth stages. Under thermodynamic control, the final structures are in the state of minimum free growth stages. Under thermodynamic control, the final structures are in the state of minimum free energy. If kinetic control intervenes, the structure can be trapped in a metastable state (gel). energy. If kinetic control intervenes, the structure can be trapped in a metastable state (gel). 3.3. Kinetic Analysis Using the Avrami Equation During the heating process of the resin systems, ΔG is greater than zero before the formation of the thermodynamicallyThe prepared BADCy stable resin gel nanoparticles particles, and were ΔG addedhas a intomaximum the BADCy value. prepolymer This stage is at mainly contents a ofcross-linked neat, 4, 8, reaction and 10 wt%. of polymer The nanoparticles segments and were is primarily dispersed controlled evenly in by the kinetic matrix factors. under Once high-sheer the gel conditions.particles are The formed, DSC the characterization growth of the was gel particle performeds can based reduce on the the free following energy assumptions. of the systems First, and thethe nanoparticlesgel particles enable do not automatic react with growth. the matrix At this during stage, the the mixing. viscosity Second, of the thesystem absolute increases area due under to thethe curvegrowth is of proportional the gel particles, to the degreeand the of movement cure, and αofis the defined molecular as the segments degree of is cure limited, at any so time, it is tmainly: controlled by the diffusion factors. In our study, ∆whenH nanoparticles were added into the matrix, there were two reaction processes. The first is αthat= the matrix, itself undergoes a curing reaction which (4) ∆H0 includes the formation and growth of gel particles. The second is the reaction of the particles with the wherematrix,∆ whichH is the only enthalpy appears changes as the growth at any of points, the gel andparticles.∆H0 is These the totaltwo reaction enthalpy processes change duringare carried the heatingout simultaneously. process. However, the first case requires overcoming a considerable surface energy barrierRepresentative to nucleate. In DSC the curves second are case, shown since in the Figure ma8trix, in is which heterogeneous, (a), (b), (c), andthe surface (d) represent energy the barrier neat, 4,at 8,the and time 10 wt%of nucleation system, respectively. of the gel Itparticles can be seencan thatbe effectively the curing reduced, temperature resulting is proportional in preferential to the rateformation of temperature of the gel increaseparticle cores for the atsame these system.uneven Also,places. the These onset two curing cases temperature are similar to decreases homogeneous as the BADCynucleation resin and nanoparticle heterogeneous content nucleation. increases. Figure9 is obtained from the integration of Figure8 and the curves of the degree of cure as a function3.3. Kinetic of Analysis temperature Using can the be Avrami obtained Equation correspondingly in Figure9. It shows that the degree of cure is inversely proportional to the rate of temperature increase for the same system. This is because a fast The prepared BADCy resin nanoparticles were added into the BADCy prepolymer at contents rate of temperature rise results in an incomplete curing reaction. At the same temperature, the degree of neat, 4, 8, and 10 wt%. The nanoparticles were dispersed evenly in the matrix under high-sheer of cure is proportional to the content of nanoparticles. This conclusion again demonstrates that the conditions. The DSC characterization was performed based on the following assumptions. First, the BADCy resin nanoparticles have a promoting effect on the matrix. nanoparticles do not react with the matrix during the mixing. Second, the absolute area under the curve is proportional to the degree of cure, and α is defined as the degree of cure at any time, t: 𝛼= , (4) where ΔH is the enthalpy changes at any points, and ΔH0 is the total enthalpy change during the heating process. Appl. Sci. 2019, 9, x 9 of 15

Representative DSC curves are shown in Figure 8, in which (a), (b), (c), and (d) represent the neat, 4, 8, and 10 wt% system, respectively. It can be seen that the curing temperature is proportional to the rate of temperature increase for the same system. Also, the onset curing temperature decreases as the BADCy resin nanoparticle content increases. Appl. Sci. 2019, 9, 2365 9 of 15

Figure 8. Dynamic DSC curves at diﬀerent heating rates of neat (a), 4 (b), 8 (c), and 10 wt% (d).

FigureThe 8. Dynamic Avrami equation DSC curves is: at different heating rates of neat (a), 4 (b), 8 (c), and 10 wt% (d). α = 1 exp( ktn), (5) Figure 9 is obtained from the integration of Figure− − 8 and the curves of the degree of cure as a functionwhere of temperatureα is the relative can be crystallinity, obtained correspondingn is the Avramily in index Figure reﬂecting 9. It shows the nucleationthat the degree and growthof cure is inverselymechanism, proportional and k is the to the rate rate constant. of temperatur Ozawa improvede increase the for Avrami the same equation system. to enable This is it because to be used a fast ratefor non-isothermalof temperature crystallization rise results in kinetics an incomp [34].lete Assuming curing that reaction. non-isothermal At the same crystallization temperature, consists the degreeof innumerableof cure is proportional tiny isothermal to the crystallization content of nanoparticles. steps, the Avrami Th equationis conclusion can be again modiﬁed demonstrates to: that the BADCy resin nanoparticles have a promoting effect on the matrix. α = 1 exp( k(T)/φm), (6) − − or ln[ ln(1 α)] = ln k(T) m ln φ, (7) − − − where the rate constant, k, is a function of T, φ is the heating rate, and m is the Ozawa index. Appl. Sci. 2019, 9, x 10 of 15 Appl. Sci. 2019, 9, 2365 10 of 15

Figure 9. Degree of cure at diﬀerent heating rates in the neat (a), 4 (b), 8 (c), and 10 wt% (d) systems. Figure 9. Degree of cure at different heating rates in the neat (a), 4 (b), 8 (c), and 10 wt% (d) systems. When Equation (7) is used to describe the curing process of thermosetting resins, α is the relative degreeThe Avrami of cure, equationk is the curing is: rate constant, and n is the relative index describing the curing mechanism. At a given temperature, n is a constant. Equation (6) can be written as: α=1−exp−𝑘𝑡, (5) n 1 α = exp( k0R ), (8) where α is the relative crystallinity, n is the− Avrami index− reflecting the nucleation and growth mechanism, and k is the rate constant. Ozawa improved the Avrami equation to enable it to be used where α is a function of temperature, R is the heating rate, and k is a function of temperature. for non-isothermal crystallization kinetics [34]. Assuming that non-isothermal0 crystallization consists Equation (8) also can be written as: of innumerable tiny isothermal crystallization steps, the Avrami equation can be modified to:

logα=1−exp[ ln(1 α)]−𝑘=𝑇log/фk0 ,n log R.(6) (9) − − − or Equation (9) shows that the curing kinetic parameters, k0 and n, can be determined according to the degrees of curing at diﬀerentln heating−ln1−𝛼 rates. At=ln𝑘 a given𝑇 −𝑚lnф temperature,, a plot of log[ ln(1 α)] on(7) log R − − should be a straight line with a slope of n and an intercept of logk . where the rate constant, k, is a function of T−, ф is the heating rate, and 0m is the Ozawa index. Figure 10 is a graph made according to Equation (9) and Figure9. The curves show an excellent When Equation (7) is used to describe the curing process of thermosetting resins, α is the relative linear relationship over the curing temperature range, which is consistent with the conclusions obtained degree of cure, k is the curing rate constant, and n is the relative index describing the curing from Equation (9). The result indicates that the modiﬁed Avrami equation can be used to describe the mechanism. At a given temperature, n is a constant. Equation (6) can be written as: non-isothermal curing process of the BADCy resin systems. A series of rate constants and indices are listed in Tables2 and3. 1−α=exp−𝑘𝑅, (8) where α is a function of temperature, R is the heating rate, and k’ is a function of temperature. Equation (8) also can be written as:

log−ln1−𝛼 =log𝑘 −𝑛log𝑅. (9) Appl. Sci. 2019, 9, x 11 of 15

Equation (9) shows that the curing kinetic parameters, k’ and n, can be determined according to the degrees of curing at different heating rates. At a given temperature, a plot of log[−ln(1−α)] on logR should be a straight line with a slope of –n and an intercept of logk’. Figure 10 is a graph made according to Equation (9) and Figure 9. The curves show an excellent linear relationship over the curing temperature range, which is consistent with the conclusions obtained from Equation (9). The result indicates that the modified Avrami equation can be used to describe the non-isothermal curing process of the BADCy resin systems. A series of rate constants andAppl. indices Sci. 2019 are, 9listed, 2365 in Table 2 and Table 3. 11 of 15

Figure 10. Avrami fitting plots of the non-isothermal curing at various temperatures in the neat (a), Figure4 (b ),10. 8 (Avramic), and 10 fitting wt% (dplots) systems. of the dynamic curing of cyanate ester (CE) systems at various temperatures. Table 2. Kinetic parameters obtained from Equation (9) at different temperatures under dynamic conditions for the neat system. Table 2. Kinetic parameters obtained from Equation (9) at different temperatures under dynamic n n conditions for the neatTemperature system. /◦C k /min K n 0 · − 270 4.26 1.51n −n 1.42 0.17 Temperature/°C k’±/min ·K ± n 280 7.41 1.47 1.46 0.17 270 4.26± ± 1.51 ± 1.42 ± 0.17 290 13.18 1.45 1.50 0.11 ± ± 280 300 20.42 7.411.35 ± 1.47 1.48 0.12 1.46 ± 0.17 ± ± 290 310 26.30 13.181.32 ± 1.45 1.40 0.11 1.50 ± 0.11 ± ± 300 320 26.92 20.421.38 ± 1.35 1.22 0.14 1.48 ± 0.12 ± ± 310 26.30 ± 1.32 1.40 ± 0.11 Table 3. Kinetic320 parameters obtained from Equation 26.92 ± (9) 1.38 at different temperatures 1.22 under ± 0.14 dynamic conditions for the 4, 8, and 10 wt% systems. Table 3. Kinetic parameters obtained from Equation (9) at different temperatures under dynamic T/ C 4 wt% 8 wt% 10 wt% conditions◦ for the 4, 8, and 10 wt% systems. k /minn K n n k /minn K n n k /minn K n n 0 · − 0 · − 0 · − 200 0.74 1.31 1.46 0.03 0.72 1.23 1.34 0.09 0.78 2.14 1.15 0.04 ± ± ± ± ± ± 210 1.35 1.17 1.50 0.07 1.90 1.26 1.46 0.10 2.14 1.10 1.25 0.03 ± ± ± ± ± ± 220 2.51 1.10 1.55 0.11 6.31 1.10 1.61 0.04 4.57 1.20 1.21 0.08 ± ± ± ± ± ± 230 4.47 1.15 1.59 0.06 10.47 1.26 1.52 0.10 7.07 1.17 1.08 0.07 ± ± ± ± ± ± 240 6.31 1.07 1.41 0.03 11.71 1.20 1.31 0.07 7.41 1.17 0.84 0.07 ± ± ± ± ± ± 250 7.24 1.02 1.17 0.01 13.08 1.51 1.03 0.16 8.32 1.09 0.74 0.04 ± ± ± ± ± ± Appl. Sci. 2019, 9, 2365 12 of 15

The following conclusions can be drawn from the above-described fitting straight line and data. First, k0 is a function of the temperature and is proportional to the temperature. Second, as can be seen from Tables2 and3, the n of all the systems shows a trend of increasing first and then decreasing. When the Avrami equation is used to study the curing of thermosetting resins, n is the scale for the formation and growth of microgel particles and will vary with the curing mechanism. An increase in the value of n represents the formation and initial growth of the microgel particles. However, in the late stage of curing, since the microgel particles are difficult to form and the growth of the gel particles is limited, the value of n is lowered. When the prepared BADCy resin nanoparticles were added into the matrix for curing, there were two processes. First, the matrix still underwent the formation and growth of microgel particles. Second, the added nanoparticles reacted with the matrix and appeared to undergo continuous growth in size. According to the results of the curing acceleration, it can be concluded that the reaction between the BADCy resin nanoparticles and the matrix is dominant. It is worth noting that the temperature corresponding to the change in n is markedly different. The turning points of the neat, 4, 8, and 10 wt% systems are 300, 240, 230, and 220 ◦C, respectively. This trend indicates that the mass content of the added BADCy resin nanoparticles is inversely proportional to the gelation time. Therefore, the added BADCy resin nanoparticles are capable of reconstructing the microscopic cross-linked network of the BADCy resin matrix. A difference in the trend of n means that the curing mechanism may change at the turning point. After all, curing and crystallization are not exactly the same. Although the formation and growth of the microgels during the curing process cannot give relatively clear qualitative information, like polymers’ crystallization, the slope of the line is the scale of the Avrami index, n, so it can be considered that this turning point explains the curing process with significant changes in the cross-linked mechanism. In the later stage of the curing process, the viscosity of the resin system shows an extreme increase, and the movement of the polymer segments is limited by the viscosity of the system. Therefore, the growth of microgels in the late curing process is probably affected by diffusion factors. To better illustrate this problem, a model of diffusion control was used for analysis. We assumed that the relationship between the rate constant, k(T), and temperature, (1/T), is consistent with the Arrhenius equation:

Ea k(T) = A exp − . (10) R0T

Equation (10) can be written as: E ln k = ln A a , (11) − RT where Ea is the apparent activation energy, R is the molar gas constant, and A is a pre-exponential factor. Figure 11 is a plot of lnk versus 1/T. It can be seen that the Arrhenius fitting plots of all the systems have an obvious turning point. The slope is a measure of the activation energy. It can be concluded that the activation energy in the low temperature stage is higher than that in the high-temperature stage. This indicates that the energy required for the formation and growth of the microgel particles has changed markedly. This phenomenon is common in heterogeneous reactions under diffusion-limited conditions [35,36]. It further indicates that the diffusion factor is dominant in the late stage of the curing reaction. During the curing process, the quantity of microgels increases, and when a higher temperature is reached, a mass transfer restriction mechanism is established, and the microgels aggregate with each other, so that phase inversion occurs. This point of change is the gel point. After gelation, the resin changes from the original viscous liquid to a semi-solid elastomeric gel and loses fluidity. Appl. Sci. 2019, 9, x 13 of 15

temperature stage. This indicates that the energy required for the formation and growth of the microgel particles has changed markedly. This phenomenon is common in heterogeneous reactions under diffusion-limited conditions [35,36]. It further indicates that the diffusion factor is dominant in the late stage of the curing reaction. During the curing process, the quantity of microgels increases, and when a higher temperature is reached, a mass transfer restriction mechanism is established, and the microgels aggregate with each other, so that phase inversion occurs. This point of change is the gel point. After gelation, the resin changes from the original viscous liquid to a semi-solid elastomeric gel and loses fluidity. Appl. Sci. 2019, 9, 2365 13 of 15

Figure 11. Temperature dependence of the rate constants for the diﬀerent BADCy systems.

4. ConclusionsFigure 11. Temperature dependence of the rate constants for the different BADCy systems. The BADCy resin nanoparticles prepared by precipitation polymerization can accelerate curing 4. Conclusions and reconstruct the microscopic network structure. From the results of dynamic DSC, the resin systems containingThe BADCy the BADCy resin nanoparticles resin nanoparticles prepared had by a markedly precipitation lower polymerization curing temperature can accelerate than the curing neat system,and reconstruct indicating the that microscopic the BADCy ne resintwork nanoparticles structure. From can accelerate the results the of curing dynamic of the DSC, BADCy the resinresin matrix.systems Fromcontaining a thermodynamic the BADCy resin point nanoparticles of view, since had the a Gibbsmarkedly free lower energy curing between temperature the particles than andthe theneat substrate system, isindicating low, the reactionthat the proceeds BADCy moreresin easily,nanoparticles thereby can accelerating accelerate the the progress curing ofof thethe curingBADCy reaction. resin matrix. The kinetic From parametersa thermodynamic determined point byof theview, Avrami since equationthe Gibbs were free usedenergy to between analyze thethe evolutionparticles and of the the microgels substrate andis low, indicate the reaction that the proc micromechanismeeds more easily, model thereby can accelerating accurately describethe progress the formationof the curing and growthreaction. of The microgel kinetic particles parameters during de thetermined curing by process the Avrami of BADCy equation resin. were used to analyzeThe the change evolution in the of curing the microgels mechanism and was indicate further that confirmed the micromechanism by the Arrhenius model equation. can accurately There wasdescribe also athe turning formation point and in thegrowth fitting of curve,microgel and particles the activation during energy the curing in the process low temperature of BADCy resin. stage was higherThe change than thatin the in curing the high mechanism temperature was stage. furthe Thisr confirmed phenomenon by the indicates Arrhenius that equation. the diff usionThere factorwas also dominates a turning in point the late in stagethe fitting of the curve, curing and reaction. the activation energy in the low temperature stage was higher than that in the high temperature stage. This phenomenon indicates that the diffusion Authorfactor dominates Contributions: in theConceptualization, late stage of the H.C., curing Y.L., reaction. and P.L.; Methodology, H.C., Y.L., and P.L.; Validation, B.L. and Y.Y.; Writing—original draft, H.C.; Writing—review and editing, Y.L. and P.L. Funding:Author Contributions:This research receivedConceptualization, no external H.C., funding. Y.L., and P.L.; Methodology, H.C., Y.L., and P.L.; Validation, B.L. and Y.Y.; Writing—original draft, H.C.; Writing—review and editing, Y.L. and P.L. Acknowledgments: The authors thank the other members of the lab for their contributions to this experiment. TheFunding: authors This also research thank the received teachers no in external the testing funding center for their contribution in the experiment. ConflictsAcknowledgments: of Interest: The authors thank declare the no other conflict members of interest. of the lab for their contributions to this experiment. The authors also thank the teachers in the testing center for their contribution in the experiment. References

1. Hamerton, I. Chemistry and Technology of Cyanate Ester Resins; Springer: Dordrecht, The Netherlands, 1994. [CrossRef] 2. Wooster, T.J.; Abrol, S.; Hey, J.M.; MacFarlane, D.R. Thermal, mechanical, and conductivity properties of cyanate ester composites. Compos. Part A Appl. Sci. Manuf. 2004, 35, 75–82. [CrossRef] 3. Gu, A. High performance bismaleimide/cyanate ester hybrid polymer networks with excellent dielectric properties. Compos. Sci. Technol. 2006, 66, 1749–1755. [CrossRef] Appl. Sci. 2019, 9, 2365 14 of 15

4. Wang, Y.; Wu, G.; Kou, K.; Pan, C.; Feng, A. Mechanical, thermal conductive and dielectrical properties of organic montmorillonite reinforced benzoxazine/cyanate ester copolymer for electronic packaging. J. Mater. Sci. Mater. Electron. 2016, 27, 8279–8287. [CrossRef] 5. Goertzen, W.K.; Kessler, M.R. Thermal and mechanical evaluation of cyanate ester composites with low-temperature processability. Compos. Part A Appl. Sci. Manuf. 2007, 38, 779–784. [CrossRef] 6. Gu, J.; Dong, W.; Tang, Y.; Guo, Y.; Tang, L.; Kong, J.; Tadakamalla, S.; Wang, B.; Guo, Z. Ultralow dielectric, fluoride-containing cyanate ester resins with improved mechanical properties and high thermal and dimensional stabilities. J. Mater. Chem. C 2017, 5, 6929–6936. [CrossRef] 7. Gu, X.; Zhang, Z.; Yuan, L.; Liang, G.; Gu, A. Developing high performance cyanate ester resin with significantly reduced postcuring temperature while improved toughness, rigidity, thermal and dielectric properties based on manganese-Schiff base hybridized graphene oxide. Chem. Eng. J. 2016, 298, 214–224. [CrossRef] 8. Ye, Y.; Yuan, L.; Liang, G.; Gu, A. Simultaneously toughening and strengthening cyanate ester resin with better dielectric properties by building nanostructures in its crosslinked network using polyimide-block-polysiloxane rod-coil block copolymers. RSC Adv. 2016, 6, 49436–49447. [CrossRef] 9. Ohashi, S.; Pandey, V.; Arza, C.R.; Froimowicz, P.; Ishida, H. Simple and low energy consuming synthesis of cyanate ester functional naphthoxazines and their properties. Polym. Chem. 2016, 7, 2245–2252. [CrossRef] 10. Sun, Z.; Zhang, L.; Dang, F.; Liu, Y.; Fei, Z.; Shao, Q.; Lin, H.; Guo, J.; Xiang, L.; Yerra, N.; et al. Experimental and simulation-based understanding of morphology controlled barium titanate nanoparticles under co-adsorption of surfactants. CrystEngComm 2017, 19, 3288–3298. [CrossRef] 11. Tang, Y.-S.; Kong, J.; Gu, J.-W.; Liang, G.-Z. Reinforced Cyanate Ester Resins with Carbon Nanotubes: Surface Modification, Reaction Activity and Mechanical Properties Analyses. Polym.-Plast. Tech. Eng. 2009, 48, 359–366. [CrossRef] 12. Simon, S.L.; Gillham, J.K. Cure kinetics of a thermosetting liquid dicyanate ester monomer/high-Tg polycyanurate material. Appl. Polym. Sci. 1993, 47, 461–485. [CrossRef] 13. Fang, T.; Shimp, D.A. Polycyanate esters: Science and applications. Prog. Polym. Sci. 1995, 20, 61–118. [CrossRef] 14. Wang, H.; Yuan, L.; Liang, G.; Gu, A. Tough and thermally resistant cyanate ester resin with significantly reduced curing temperature and low dielectric loss based on developing an efficient graphene oxide/Mn ion metal–organic framework hybrid. RSC Adv. 2016, 6, 3290–3300. [CrossRef] 15. Laskoski, M.; Dominguez, D.D.; Keller, T.M. Development of an oligomeric cyanate ester resin with enhanced processability. J. Chem. 2005, 15, 1611. [CrossRef] 16. Pradhan, S.; Brahmbhatt, P.; Sudha, J.D.; Unnikrishnan, J. Influence of manganese acetyl acetonate on the cure-kinetic parameters of cyanate ester–epoxy blend systems in fusion relevant magnets winding packs. J. Therm. Anal. Calorim. 2011, 105, 301–311. [CrossRef] 17. Mathew, D.; Nair, C.P.R.; Krishnan, K.; Ninan, K.N. Catalysis of the cure reaction of Bisphenol A dicyanate. A DSC study. J. Polym. Sci. Part A Polym. Chem. 2015, 37, 1103–1114. [CrossRef] 18. Gusakova, K.; Saiter, J.-M.; Grigoryeva, O.; Gouanve, F.; Fainleib, A.; Starostenko, O.; Grande, D. Annealing behavior and thermal stability of nanoporous polymer films based on high-performance Cyanate Ester Resins. Polym. Degrad. Stab. 2015, 120, 402–409. [CrossRef] 19. Li, W.; Liang, G.; Xin, W. Triazine reaction of cyanate ester resin systems catalyzed by organic tin compound: Kinetics and mechanism. Polym. Int. 2004, 53, 869–876. [CrossRef] 20. Augustine, D.; Mathew, D.; Nair, C.P.R. Phthalonitrile resin bearing cyanate ester groups: Synthesis and characterization. RSC Adv. 2015, 5, 91254–91261. [CrossRef] 21. Shah, S.S.A.; Nasir, H.; Ul-Haq, N. Synthesis of Cyanate Ester Based Thermoset Resin by Using Copper (II) Oxalate as Catalyst and its Application in Carbon Fiber Composites. Nano Hybrids Compos. 2018, 22, 1–9. [CrossRef] 22. Throckmorton, J.; Palmese, G. Acceleration of cyanate ester trimerization by dicyanamide RTILs. Polymer 2016, 91, 7–13. [CrossRef] 23. Wooster, T.J.; Abrol, S.; MacFarlane, D.R. Cyanate ester polymerization catalysis by layered-silicates. Polymer 2004, 45, 7845–7852. [CrossRef] 24. Fainleib, A.; Bardash, L.; Boiteux, G. Catalytic effect of carbon nanotubes on polymerization of cyanate ester resins. Express Polym. Lett. 2009, 3, 477–482. [CrossRef] Appl. Sci. 2019, 9, 2365 15 of 15

25. Kim, S.-W.; Lu, M.-G.; Shim, M.-J. The Isothermal Cure Kinetic of Epoxy/Amine System Analyzed by Phase Change Theory. Polym. J. 1998, 30, 90–94. [CrossRef] 26. Domínguez, J.C.; Alonso, M.V.; Oliet, M.; Rojo, E.; Rodríguez, F. Kinetic study of a phenolic-novolac resin curing process by rheological and DSC analysis. Thermochim. Acta 2010, 498, 39–44. [CrossRef] 27. Pollard, M.; Kardos, J.L. Analysis of epoxy resin curing kinetics using the Avrami theory of phase change. Polym. Eng. Sci. 1987, 27, 829–836. [CrossRef] 28. Lu, M.G.; Shim, M.J.; Kim, S.W. Dynamic DSC Characterization of Epoxy Resin by Means of the Avrami Equation. J. Therm. Anal. Calorim. 1999, 58, 701–709. [CrossRef] 29. Chen, D.Z.; He, P.S.; Pan, L.J. Cure kinetics of epoxy-based nanocomposites analyzed by Avrami theory of phase change. Polym. Test. 2003, 22, 689–697. [CrossRef] 30. Lu, M.G.; Shim, M.J.; Kim, S.W. The macrokinetic model of thermosetting polymers by phase-change theory. Mater. Chem. Phys. 1998, 56, 193–197. [CrossRef] 31. Peng, L.; Yang, X.; Yu, Y.; Yu, D. Cure kinetics, microheterogeneity, and mechanical properties of the high-temperature cure of vinyl ester resins. J. Appl. Polym. Sci. 2010, 92, 1124–1133. 32. Kmetty, Á.; Bárány, T.; Karger-Kocsis, J. Self-reinforced polymeric materials: A review. Prog. Polym. Sci. 2010, 35, 1288–1310. [CrossRef] 33. Ren, P.; Liang, G.; Zhang, Z.; Lu, T. ZnO whisker reinforced M40/BADCy composite. Compos. Part A Appl. Sci. Manuf. 2006, 37, 46–53. [CrossRef] 34. Ozawa, T. Kinetics of non-isothermal crystallization. Polymer 1971, 12, 150–158. [CrossRef] 35. Ortiz Vélez, A.; Siles Alvarado, S.; Avendaño-Gómez, J.R. Cure behavior and kinetic study of diglycidyl ether of bisphenol A with a tertiary amine salt by differential scanning calorimetry. Polym. Eng. Sci. 2018, 58, 784–792. [CrossRef] 36. Desio, G.P.; Rebenfeld, L. Crystallization of fiber-reinforced poly (phenylene sulfide) composites. II. Modeling the crystallization kinetics. Appl. Polym. Sci. 1992, 45, 2005–2020. [CrossRef]

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).