Impact of high pressure on the progress of polymerization of DGEBA cured with different amine hardeners: dielectric and DSC studies

Abstract

Kinetics and dynamics of the curing of bisphenol-A diglycidyl ether (DGEBA) with various agents i.e. cyclohexylamine, aniline and 2-ethylhexylamine, were investigated by means of Broadband Dielectric Spectroscopy (BDS) over a wide range of thermodynamic conditions. We proposed a novel method of dielectric data analysis to extract information on the progress of the curing reaction. This approach was validated by complementary calorimetry measurements. High pressure studies indicated that compression significantly reduces the time of the reaction. At the same time, a decrease in monomer conversion and the glass transition temperature of the recovered product was observed. This was due to vitrification of the system that occurs in a relatively short time. We found a linear correspondence between the time of the polymerization after which the investigated system undergoes glass transition and the degree of monomer conversion. Additionally, activation volumes for the investigated reactions were determined and found to lie in the range −18 and −38 cm³ mol⁻¹. The calculated values are lower than ΔV estimated for the ring opening reaction provided in the literature. However our data unquestionably showed that this quantity depends strongly on both the chemical structure of the substrates as well as thermodynamic conditions.

---

1. Introduction

In considering the effect of compression on polymerization, one needs to distinguish the impact of pressure on the reaction kinetics^1–5 from the reaction product.^3,6–10 Studies of kinetics studies at high pressure revealed that the polymerization rates can either increase or decrease due to compression of the system. It is directly related to the nature of the kinetics of polymerization, whether it is a mass- or diffusion-controlled regime. In the first case, pressure is expected to accelerate the process because it increases the number density of reacting molecules. On the other hand, as polymerization proceeds, viscosity increases as macromolecules of increasingly higher molecular weight are formed. Hence, further compression of the system may lead to a dramatic drop in the diffusion of the remaining monomers. Consequently, polymerization slows down or becomes suppressed. Such scenario was recently observed upon curing of epoxy resin with 2-ethylhexylamine⁴ and the polymerization of isoprene¹¹ at ambient temperature above 440 MPa and 2.5 GPa, respectively.

As proposed by Waite¹² the nature of the kinetics can be described by the s parameter:

where: E_R is the activation energy of the reaction and E_D is the activation energy for the diffusion of the reacting molecules. It was shown that this parameter reaches value lower and higher than 1 for the mass- and diffusion-controlled regime, respectively. Unfortunately, the s parameter does not describe conditions between these two regimes.

The application of elevated pressure might also increase the selectivity and tune the reaction toward the formation of macromolecules of well-defined chemical structure. It might be related to the activation volume of competing reaction pathways. It was suggested that at higher compression, the reaction pathway of the smallest activation volume is promoted.⁸ In fact, such scenario was observed for 1,3-butadiene⁹ and ethylene,¹⁰ where the elimination of side reactions (dimerization) and the formation of a highly stereoregular product with full conversion of the monomer were reported. A similar situation was observed also in the case of glycidol,³ where it was demonstrated that side reactions connected to the macrocyclization and deprotonation were suppressed, and one polymer of given structure was recovered from the polymerization carried out at high pressures. The other obvious benefit of applying pressure during the course of polymerization is the possibility of producing macromolecules of very high molecular weight not attainable at ambient pressures.^13,14 Moreover at high compression, the control over the reaction is enhanced leading to production of polymers of lower polydispersity index (PDI) relative to ambient pressure polymerization.

Other than the activation energy barrier, the activation volume (ΔV) seems to be another key parameter governing the kinetics of the chemical reaction under consideration. According to the transition state theory,¹⁵ the activation volume is a difference between the volumes of the transition state V^# and the reactants V^R:

ΔV = V^# − V^R (2)

It can be determined experimentally from the pressure dependence of the rate constant:

The activation volume is often used in the discussion of the reaction mechanisms. In the literature there are concrete cases, where the activation volume was assigned to a given chemical transformations or polymerization.^16–18 It is also worthwhile to mention that the value of ΔV can be affected by many factors including the property of substrates, initiators and solvents (mostly by their polarity).¹⁹ However, recent high pressure studies revealed that the value of the activation volume changes with the thermodynamic conditions. In the case of isoprene,¹¹ the increase in pressure increases the value of the activation volume from −24.3 cm³ mol⁻¹ to −7.9 cm³ mol⁻¹ in the pressure range from 0.1 MPa to 2.6 GPa. Interesting results were also reported for the curing of DGEBA with 2-ethylhexylamine,⁴ where the activation volume determined by high pressure measurements carried out at 293 and 313 K have different values of −38 cm³ mol⁻¹ and −46 cm³ mol⁻¹, respectively.

In this paper, we present high pressure studies on the curing of the epoxy resin (DGEBA) with different primary amines: cycloaliphatic (cyclohexylamine) and aromatic (aniline) in comparison to the aliphatic one (2-ethylhexylamine) studied before.⁴ The progress of polymerization was monitored by means of Differential Scanning Calorimetry (DSC) as well as Broadband Dielectric Spectroscopy (BDS) in a wide ranges of temperature and pressure. From the dielectric data, the activation barrier was determined to be 44.6 and 45.8 kJ mol⁻¹ respectively for the curing system with cyclohexylamine and aniline. The obtained values are in good agreement to those determined from DSC measurements (47.3 and 55.7 kJ mol⁻¹, respectively). Moreover, the isothermal pressure dependence of the rate constant and the respective activation volumes for the studied reactions was evaluated. High pressure studies revealed that the activation volume depends on the chemical structure of the substrates and increases from −38 cm³ mol⁻¹ to −18 cm³ mol⁻¹ for DGEBA polymerized with 2-ethylhexyl amine and aniline, respectively.

2. Experimental section

2.1 Materials

Bisphenol-A diglycidyl ether (known as EPON 828 or DGEBA, M_w = 340.41 g mol⁻¹), aniline (M_w = 93.13 g mol⁻¹) and cyclohexylamine (M_w = 99.17 g mol⁻¹) of purity higher than 99% were purchased from Sigma Aldrich. The epoxy resin and curing agent were mixed with molar ratio 1 : 1. In every measurement, we used 5 g of DGEBA with 1.37 g or 1.45 g of aniline or cyclohexylamine, respectively. All samples were prepared in a glove box in an identical manner. Immediately after preparation, the samples were measured by means of BDS and DSC techniques. The chemical structures of investigated systems were presented in Scheme 1. The sketch of polymerization reaction can be found in ref. 4 and 20.

Scheme 1 The chemical structures of DGEBA, aniline and cyclohexylamine.

2.2 Methods

BDS measurements. Dielectric permittivity ε*(ω) = ε′(ω) − iε′′(ω) values at ambient pressure were measured by using the impedance analyzer (Novocontrol Alpha) over a frequency range from 1 × 10⁻¹ to 3 × 10⁶ Hz. The samples were placed between two stainless-steel electrodes (diameter: 15 mm, gap: 0.14 mm) and mounted inside a cryostat. During the measurement, each sample was maintained under dry nitrogen gas flow. The temperature was controlled by Quatro Cryosystem using a nitrogen gas cryostat, with stability better than 0.1 K. The time dependent dielectric measurements of curing system were carried out at different temperatures in the range from 293 to 363 K.

High pressure dielectric measurements were performed by using the high pressure chamber with a special homemade flat parallel capacitor. Thin Teflon spacers (0.1 mm) were used to maintain a fixed distance between the plates. The sample capacitor was sealed and mounted inside a Teflon capsule to separate it from the silicone liquid used for elevating pressure. Pressure was measured by a Nova Swiss tensometric meter with a resolution of 0.1 MPa. Temperature was adjusted with a precision of 0.1 K by means of refrigerated and heating circulator. Complex dielectric permittivity was measured within the frequency range from 1 × 10⁻¹ to 3 × 10⁶ Hz.

DSC measurements. Calorimetric measurements of the isothermal curing of DGEBA were carried out by Mettler-Toledo DSC apparatus equipped with a liquid nitrogen cooling accessory and an HSS8 ceramic sensor (heat flux sensor with 120 thermocouples). Temperature and enthalpy calibrations were performed by using indium and zinc standards. The sample was prepared in an open aluminum crucible (40 μL) outside the DSC apparatus. Samples were scanned at various temperatures at constant heating rate of 10 K min⁻¹. After the polymerization, samples were measured on heating from 273 K to 523 K at constant heating rate of 10 K min⁻¹. Each measurement at a given temperature was repeated 3 times. For each experiment a new sample was prepared.

3. Results and discussion

3.1 Ambient pressure condition

The curing of epoxy resin with primary amines occurs accordingly to the step-growth polymerization mechanism. The process involves the opening of epoxide rings, addition of amine groups and formation of covalent bonds with the nitrogen and hydrogen.²⁰ The chemical structures of the substrates are presented in Scheme 1, while the mechanism of the process can be found in ref. 4.

The formation of polymer chains is connected with continuous changes in its molecular weight, glass transition temperature, viscosity and dipole moments distribution, enabling one to monitor the reaction by means of dielectric spectroscopy. It should be added that the recent reports show that beside of standard techniques such as Fourier Transform Infrared (FTIR) spectroscopy, Raman spectroscopy, Nuclear Magnetic Resonance (NMR) and DSC,^2,21–26 BDS can also be successfully applied to follow the polymerization reaction and might provide simultaneous insight into the dynamics and kinetics of the chemical reaction.

In Fig. 1, dielectric dispersion and loss spectra collected upon curing of DGEBA with various curing agents are presented at a number of temperatures. One can observe that the static permittivity (Fig. 1(a) and (b)) decreases for each sample due to decreasing concentration of the polar epoxide rings. Moreover, segmental relaxation and dc-conductivity move toward lower frequency and eventually out of the experimental window, due to the formation of longer polymer chains (Fig. 1(c) and (d)). It should be stressed that the variation of segmental relaxation and static permittivity, as well as the dc-conductivity can be utilized to analyze the progress of the chemical reaction monitored by BDS spectroscopy.²⁷ However, in the case of the curing of epoxy resin, the proper way to analyze dielectric data is not certain and, is currently a matter of some debate. This is due to the lack of deep understanding of the fundamental relationship between measured quantities and their connections to the monomer conversion for the investigated reaction.

Fig. 1 Dielectric dispersion (panels (a) and (b)) and loss spectra (panels (c) and (d)) measured upon polymerization of DGEBA with different curing agents: aniline and cyclohexylamine at indicated thermodynamic conditions (at ambient pressure).

A promising way to follow the progress of reaction is to monitor the dielectric constant. The static permittivity (ε₀) is linearly proportional to the concentration of dipoles (N_i) and the mean square dipole moment (μ²) according to the Onsager–Kirkwood–Frohlich equation:

where ε₀ and ε_∞ are static and infinity permittivity, respectively. As mentioned above, the epoxy ring concentration and dipole moment distribution is modified during the course of the reaction. As a consequence, one can obtain information on the progress of polymerization by following this variable. However, due to vitrification of the curing system and parasitic polarization contributions, it is not possible to utilize this way to analyze the dielectric data. Hence, it was proposed to analyze permittivity measured at either low or high frequency range. The former approach was used to follow the progress of curing of epoxy resin with aniline^24,25 and cyclohexylamine²⁸ derivatives. However, one should remember that the low frequency range is usually highly affected by electrode polarization effects originating from the accumulation of the current on the surface of electrodes. Moreover, the additional step originating from the shift of the segmental relaxation dispersion can be observed in the kinetic curves constructed from the data in the low frequency range. This artifact can be easily eliminated by considering higher frequency range. Casalini et al. showed that analysis of the permittivity measured at GHz region yields almost the same information on the rate of reaction as FTIR investigations.²⁹ For the purpose of this paper, we modified this approach and analyzed the real part of the permittivity recorded at f = 0.3 MHz. This approach was successfully verified and validated by FTIR measurements of DGEBA–2-ethylhexylamine system.⁴

The data collected were renormalized (see Fig. 2) in plotting the kinetic curves, according to the following equation:

where ε′(0) and ε′(∞) are the initial and final values of the permittivity measured during the polymerization reaction. Here, it should be added that the dielectric conversion factor α does not reflect the monomer conversion and it is introduced to characterize the progress of the reaction by means of BDS. Furthermore, dielectric data were rescaled to the maximum value of the monomer conversion factor, which was determined from complementary DSC measurements. As it can be seen, increase in temperature accelerates the reaction for all studied samples. However, this effect is more significant in the case of the curing DGEBA with cyclohexylamine and aniline, when compared to 2-ethylhexylamine.⁴ Since kinetic analysis based solely on dielectric data might not be unequivocal, complementary DSC measurements were carried out to verify the results from the proposed model of data analysis.

Fig. 2 Time evolution of dielectric conversion obtained after renormalization of the permittivity ε′ measured at f = 0.3 MHz according to eqn (5) for the reaction carried out for different curing agents at various thermodynamic conditions. Solid lines represent the best fit to the Avrami equation [eqn (7)]. As insets in panels (a) and (b), time evaluations of DSC conversion of indicated systems are presented.

The raw calorimetric data obtained upon curing DGEBA with various amines are shown in Fig. 3(a) and (b). It can be seen that, the exothermic peak of polymerization shifts towards shorter times with increasing temperature of polymerization, which is a typical behavior of polymerization^30,31 carried out under isothermal conditions. One can add that a similar scenario is reported for the crystallization process.³² It should be stressed that calorimetric studies enable one to obtain insight into the kinetics of the reactions, as well as to determine the degree of monomer conversion. For this purpose, time and temperature dependent DSC measurements were carried out. The progress of the reaction monitored by the application of the DSC method is presented by the insets in panels (b) and (c) in Fig. 2. The kinetic curves shown in Fig. 2 were obtained according to the equation:

where α_DSC is the DSC conversion, ΔH(t) is the enthalpy variation as a function of the time spent at a given temperature condition, ΔH_total is the total heat of the reaction. It should be added that ΔH_total = ΔH(t) + ΔH(T) is the sum of the isothermal enthalpy ΔH(t) (Fig. 3(a) and (b)) and the enthalpy of nonisothermal experiments ΔH(T) (Fig. 3(c)).^30,31,33,34 From the presented kinetic curves (insets in Fig. 2), it is clear that the reaction gets faster with increasing temperature. Simultaneously, the degree of monomer conversion increases up to 91% and 98% for DGEBA polymerized with cyclohexylamine and aniline, respectively, at the highest temperatures. For comparison, α determined for the similar systems studied in literature varies between 80 and 90%.⁴ In addition, our calorimetric data revealed that in each case, the curing system undergoes vitrification with the glass transition temperature located within experimental uncertainty at a temperature at which reaction was carried out.

Fig. 3 Panels (a) and (b): raw calorimetric data obtained upon the curing of epoxy resin with aniline and cyclohexylamine, respectively. Panel (c): DSC thermograms obtained after the curing of DGEBA with aniline at indicated isothermal condition. As an inset in panel (a), the temperature dependency of the degree of conversion for all systems is presented.

The next step of the analysis was to model the cure kinetics and to determine the rate constants of the reaction. Due to complexity of the studied reaction, the curing kinetics of thermosetting materials can be analyzed by the application of three alternative models: (i) n-th order,³⁵ (ii) autocatalytic^36–38 and (iii) Avrami.³⁹ For the purpose of this paper, we decided to apply the last one, which is the commonly used approach in the literature to describe kinetics of step growth polymerization.^40–45 Although the Avrami equation is mostly used to model the kinetics of crystallization, it can be applied also successfully to describe the kinetics of polymerization. As the reaction continues, the formation of many molecular aggregates (microgels) or high-molecular weight particles can be observed as a result of curing.⁴⁶ A similar scenario can also be observed in the case of crystallization, where the nucleation also proceeds with time. Thus, it has been considered that, in a broad sense, crystallization can be considered as a physical form of polymerization.^41,47 The equation we applied reads as follows:³⁹

where α is the dielectric or DSC conversion, α_m is the maximum monomer conversion, k is the rate constant of the reaction, and n is the Avrami exponent that can be related to the mechanism of either crystallization or chemical reaction. As can be observed in Fig. 2, the Avrami model describes the kinetics data obtained for the various systems in the studied range of times and temperatures quite well, enabling accurate characterization of the rate constants.

In Fig. 4, the temperature dependent rate constants determined for both investigated systems are presented. It can be seen that the value of the rate constant increases with temperature. Moreover, it is worth noting that k determined from dielectric and calorimetric data is almost the same (within experimental uncertainty) in the studied range of temperatures. However, despite the good correspondence of the rate constants determined from BDS and DSC, clear differences in time evolution of the kinetic curves are observed. To explain these discrepancies, one should go to the fundamentals of the step growth polymerization. In this specific case, increasing molecular weight of the newly formed macromolecules is not linearly correlated with the monomer conversion. On the other hand, dielectric spectroscopy follows the shifting of the segmental relaxation process which is attributed to the increasing molecular weight of the formed macromolecules, while DSC traces the real monomer conversion upon polymerization. Hence, it is expected that kinetic curves constructed from the dielectric and calorimetric data should differ. Nevertheless, both techniques give almost the same information on the rate constant as is demonstrated in Fig. 4(a) and (b).

Fig. 4 Panels (a) and (b): temperature dependence of the rate constants obtained from dielectric (circles) and DSC (squares) measurements performed at ambient pressure for polymerization performed with two curing agents: aniline and cyclohexylamine, respectively. Red lines represent the best fit to eqn (7). Panel (c): pressure dependence of the rate constants obtained from dielectric measurements for different epoxy resin curing systems. Data for DGEBA–2-ethylhexylamine system are from ref. 4. Dashed lines represent the best fit to either the linear or parabolic equation.

As a final point of this part of the paper, activation energies for the curing DGEBA with various amines were estimated using the Arrhenius function:

k = k₀ exp(E_a/RT) (8)

where k₀ is a pre-exponential factor, E_a is the activation barrier and R is the gas constant. The activation energy determined from the dielectric measurements was equaled to 44.6 and 45.8 kJ mol⁻¹ for aniline and cyclohexylamine, respectively (Fig. 4(a) and (b)). The determined values are in good agreement with those determined from DSC measurements (47.3 and 55.7 kJ mol⁻¹, respectively). It should be stressed that similar value of the activation energy E_a = 46 and 59 kJ mol⁻¹ was calculated for the curing of DGEBA with 2-ethylhexylamine⁴ and 4,4′-diaminodicyclohexylmethane (PACM),² respectively.

3.2 Elevated pressure condition

Since it is well known that pressure accelerates progress of the majority of the chemical reactions, we decided to probe the impact of compression on the dynamics, properties of the formed polymers, as well as the monomer conversion and the kinetics of step growth polymerization. Unfortunately, we were not able to carry out calorimetric measurements at high pressure. Hence, all further analysis will be done, based mainly on the dielectric data.

As a first, dielectric loss spectra obtained during polymerization of DGEBA with aniline and cyclohexylamine performed at different thermodynamic conditions were analyzed with the use of the Havriliak–Negami function with a conductivity term added.⁴⁸ The fitting function is given by:

where α and β are the shape parameters representing the symmetric and asymmetric broadening of given relaxation peaks, Δε is the dielectric relaxation strength, τ is the relaxation time, ε₀ is vacuum permittivity, and ω is an angular frequency (ω = 2πf). In Fig. 5, the time evolution of the segmental relaxation times at ambient and elevated pressure is presented. One can observe the significant shift of τ_α over more than seven decades which is comparable to the data presented in literature.⁴ Moreover, it is clear that the effect of pressure is more pronounced than the one induced by temperature variation. In this context, it is worth adding that the curing of DGEBA with aniline at 293 K at ambient pressure takes almost 7 days (data not shown).⁴⁹ The application of pressure of p = 100 MPa decreases the time of the reaction to almost 3 days, making the reaction more than two times faster with respect to the ambient conditions. Further compression up to 400 MPa reduces the time at which system undergoes vitrification down to less than 24 h. Hence when we compare this data to that obtained at ambient pressure, it will be clear that the time of the reaction was shortened by more than seven times. It should be stressed that the similar situation occurred in the case of pressure polymerization of DGEBA with cyclohexylamine and 2-ethylhexylamine.⁴ Although the impact of pressure was not as pronounced as in the case of the DGEBA–aniline system.

Fig. 5 Time evolution of structural relaxation times of polymerization performed at ambient ((a) and (b)) and elevated pressure conditions ((c) and (d)).

In the next step, DSC measurements were carried out to determine the monomer conversion as well as the glass transition temperatures of macromolecules produced at high pressures. It should be stressed that these investigations were done immediately after pressure was released to avoid further curing of each system and water uptake. For this purpose, temperature dependent DSC measurements were carried out on the cured samples. These investigations enabled determination of the residual heat of polymerization ΔH(T). Thus, assuming ΔH_total to be pressure independent and applying eqn (6), we were able to evaluate the degree of monomer conversion for all examined systems polymerized at elevated pressures. In Fig. 6(a), the evolution of the degree of monomer conversion as a function of pressure is presented for each studied system. As it can be seen, α drops around 10% for the highest compression with respect to the ambient pressure polymerization and reaches approximately 62% and 54% for DGEBA cured with cyclohexylamine, 2-ethylhexylamine and aniline respectively. Additionally, the evolution of the glass transition temperature (T_g) of the polymers recovered at different thermodynamic conditions was shown in panel (b) in Fig. 6. It can be seen that T_g decreases with compression and falls within the range 273–280 K for the reactions carried out at T = 293 K and p = 400 MPa for all examined systems. Hence, the glass transition temperatures of the macromolecules recovered from the polymerization performed at high compression are 10–20 K lower than that of the reactions carried out at ambient conditions. This finding is quite surprising in the light of the literature data showing that at elevated pressures macromolecules of higher molecular weight and lower PDI index are obtained, and the degree of monomer conversion is usually significantly higher. However, this situation is reported for systems with very low viscosity.^13,14

Fig. 6 Panel (a): the evolution of the degree of conversion of the curing of DGEBA with various curing agents as a function of pressure. Panel (b): the pressure dependency of the glass transition temperature of polymerized systems. As inset in panel (b), the time dependency of the degree of conversion of examined systems is presented.

On the other hand, in the case of the hardening of natural and synthetic resins, one should take into account also the chemical vitrification, which seems to have important influence on the kinetics of polymerization. This process assumes the ongoing polymerization of the constituent molecules is via the formation of irreversible chemical bonds, resulting in changes of the dynamics and the thermodynamic properties of the vitrified system.⁵⁰ Thus, once the curing system undergoes the glass transition, the reaction is essentially ended due to the immobilization of monomers. Therefore, further elongation of the chain is not possible. Hence, it seems that the time required for the system to reach the vitrification point is quite an important variable. In the inset to Fig. 6, we plot degree of monomer conversion versus time after which the polymerized samples undergo glass transition. It is well seen that there is linear dependency between both parameters indicating their interrelations.

As a final point of our discussion, we decided to utilize dielectric and calorimetric data obtained for the polymerization carried out at high pressures to evaluate rate constants and the activation volumes at different thermodynamic conditions for the investigated reactions. For this purpose, the same kind of analysis as the one described above was carried out and the kinetic curves constructed by normalizing the data with respect to the maximum degree of monomer conversion are presented in Fig. 7. Time dependences of α_BDS were fitted to the Avrami equation [eqn (7)]. This model describes experimental data very well enabling calculations of the rate constants, which were further plotted vs. pressure and presented in Fig. 4(c). It can be seen that the value of the rate constant increases with compression. However above 300 MPa, the slowing down of the reaction can be observed for the DGEBA–2-ethylhexylamine system.⁴ This indicates that above this pressure, the viscosity of the system at the beginning of the reaction becomes too large and reduces the monomer diffusion. As a consequence, pressure acts as an inhibitor of polymerization. We believe that this effect is related to the sensitivity of viscosity or structural dynamics of the given system to the applied pressure. The increase in viscosity due to compression is the highest for the binary mixture consisting of 2-etyhexylamine and DGEBA. Hence, even at moderate pressures, this system becomes very viscous in a relatively short time. As a consequence, molecular diffusion and the pace of the reaction is slowed down, as shown in Fig. 4(c). On the other hand, the impact of pressure on the viscosity in case of other examined herein samples is not so significant at the beginning of the reaction. Hence, polymerization is in the mass controlled regime in a wider range of pressures. It is worth adding that a similar scenario was also observed for the polymerization of isoprene, where similar slowing of the reaction was reported above 2 GPa.¹¹

Fig. 7 Time evolution of dielectric conversion obtained after renormalization of the permittivity ε′ measured at f = 0.3 MHz accordingly to eqn (5) for the reaction carried out for different curing agents at elevated pressure conditions. Solid lines represent the best fit to the Avrami equation [eqn (7)].

Additionally from the pressure dependency of the rate constants, activation volume of polymerization was calculated using eqn (3). It was found that in the limit of ambient pressure, ΔV varies significantly from −18, −24 up to −38 cm³ mol⁻¹ for DGEBA polymerized with aniline, cyclohexylamine and 2-ethylhexylamine respectively.⁴ Hence, it seems to be quite obvious that activation volume is directly related to the structure of the amine used for the reactions with DGEBA. What is more, the ΔV was the greatest in the case of system consisting of DGEBA and aromatic amine. Herein, it should be noted that typical values of ΔV for the epoxide ring opening reactions is in the range −15 to −20 cm³ mol⁻¹.^16–18 On the other hand, our data show that, dependent on the curing agent, the activation volume may change in much wider range. The other very interesting aspect is that activation volume tends to change and increase for DGEBA cured with 2-ethylhexylamine, while it stays constant in the range of studied pressures for DGEBA polymerized with aniline and cyclohexylamine. However, we are quite convinced that it is due to the range of compression applied in our studies. It is expected that for the reaction carried out at much higher pressures, activation volume will tend to increases even in the case of the latter systems.

4. Summary and conclusion

Kinetics and dynamics of the curing of DGEBA with various curing agents were measured by means of dielectric spectroscopy in wide ranges of temperatures and pressures. In addition, complementary DSC measurements were carried out to determine the degree of monomer conversion as well as glass transition temperatures for the samples polymerized at different thermodynamic conditions. It was found that compression enhances the rate of the reaction. Consequently, the reaction time was significantly reduced with respect to the ambient pressure polymerization procedure. However, due to quite fast vitrification of DGEBA cured with different amine hardeners, the degree of monomer conversion drops approximately 10% and the glass transition temperature of the recovered product is 10–20 K lower when compared to the reaction carried out at ambient pressure. Hence, it appears that in order to improve the degree of monomer conversion, increase the glass transition temperature of the macromolecules, and shorten the time of polymerization, one should change pressure continuously during polymerization. This will enable better control over viscosity, avoiding vitrification and allowing for the completion of the reaction. As a consequence, polymers of desired properties can be obtained during relatively short reaction times. In addition, activation volumes falling in the range −18 and −38 cm³ mol⁻¹ were determined for the studied systems. It can be stated that they are lower than the ΔV predicted in literature for the reaction involving opening of the epoxide ring. However, our studies clearly indicated that ΔV is a function of hardener as well as thermodynamic conditions. Thus, it can vary in much wider range than it is reported in literature.

Conflict of interest

The authors declare no competing financial interests.

Acknowledgements

K. K., S. P. and M. T. gratefully acknowledge financial support from the Polish National Science Centre within the program Sonata 2 entitled “High pressure polymerization. The kinetic studies” based on decision DEC-2012/05/D/ST4/00326. The authors thank K. L. Ngai and Philip J. Griffin for the language assistance during manuscript preparation.

References

1. N. S. Isaacs, Liquid Phase High Pressure Chemistry; Wiley, New 572 York, 1981.
2. J. Fournier, G. Williams, C. Duch and G. A. Aldridge, Macromolecules, 1996, 29, 7097–7107.
3. M. Tarnacka, T. Flak, M. Dulski, S. Pawlus, K. Adrjanowicz, A. Swinarew, K. Kaminski and M. Paluch, Polymer, 2014, 55, 1984–1990.
4. M. Tarnacka, O. Madejczyk, M. Dulski, M. Wikarek, S. Pawlus, K. Adrjanowicz, K. Kaminski and M. Paluch, Macromolecules, 2014, 47, 4288–4297.
5. K. Kaminski, M. Paluch, R. Wrzalik, J. Ziolo, R. Bogoslovov and C. M. Roland, J. Polym. Sci., Part A: Polym. Chem., 2008, 46, 3795–3801.
6. P. W. Bridgman and J. B. Conant, Proc. Natl. Acad. Sci. U. S. A., 1929, 15, 680–683.
7. D. Gourdain, J. C. Chervin and P. Pruzan, J. Chem. Phys., 1996, 105, 9040–9045.
8. F. Wurche and F. G. Klarne, High Pressure Chemistry, ed. R. van Eldik and F. G. Klarner, Wiley, New York, 2002.
9. M. Citroni, M. Ceppatelli, R. Bini and V. Schettino, Science, 2002, 295, 2058–2060.
10. D. Chelazzi, M. Ceppatelli, M. Santoro, R. Bini and V. Schettino, J. Phys. Chem. B, 2005, 109, 21658–21663.
11. M. Citrini, M. Ceppatelli, R. Bini and V. Scettino, J. Phys. Chem. B, 2007, 111, 3910–3917.
12. T. R. Waite, Phys. Rev., 1957, 107, 463–478.
13. L. Mueller, W. Jakubowski, K. Matyjaszewski, J. Pietrasik, P. Kwiatkowski, W. Chaladaj and J. Jurczak, Eur. Polym. J., 2011, 47, 730–734.
14. P. Kwiatkowski, J. Jurczak, J. Pietrasik, L. Mueller and K. Matyjaszewski, Macromolecules, 2008, 41, 1067–1069.
15. M. J. Evans and M. Polanyi, Trans. Faraday Soc., 1935, 31, 875–894.
16. T. Asano and W. J. le Noble, Chem. Rev., 1978, 78, 407–489.
17. R. van Eldik, T. Asano and W. J. le Noble, Chem. Rev., 1989, 89, 549–688.
18. A. Drljaca, C. D. Hubbard, R. van Eldik, T. Asano, M. V. Basilevsky and W. J. le Noble, Chem. Rev., 1998, 98, 2167–2289.
19. V. D. Kiselev, M. S. Shikhaab, G. G. Iskhakova and A. I. Konovalov, Russ. J. Gen. Chem., 2002, 72, 98–104.
20. L. V. McAdams and J. A. Gannon, in Encyclopedia of Polymer Science and Engineering, ed. H. F. Mark, N. M.Bikales, C. G.Overberger and J. I.Kroschwitz, John Wiley and Sons, New York, 1986, vol. 6, p. 322.
21. F. Ricciardi, W. A. Romanchick and M. M. Joullie, J. Polym. Sci., Part A: Polym. Chem., 1983, 21, 1475–1490.
22. G. Levita, A. Livi, P. A. Rolla and C. Culicchi, J. Polym. Sci., Part B: Polym. Phys., 1996, 34, 2731–2737.
23. E. Tombari, C. Ferrari, G. Salvetti and G. P. Johari, J. Phys.: Condens. Matter, 1997, 9, 7017–7037.
24. D. A. Wasylyshyn and G. P. Johari, J. Polym. Sci., Part B: Polym. Phys., 1997, 35, 437–456.
25. D. A. Wasylyshyn and G. P. Johari, J. Polym. Sci., Part B: Polym. Phys., 1999, 37, 3071–3083.
26. G. Galonne, S. Capaccioli, G. Levita, P. A. Rolla and S. Corezzi, Polym. Int., 2001, 50, 545–551.
27. J. Mijovic and B. D. Fitz, Dielectric Spectroscopy of Reactive Polymers: Application Note Dielectrics 2, Novocontrol, Hundsangen, Germany, vol. 591, 1998.
28. G. P. Johari, J. Chem. Soc. Faraday Trans., 1994, 90, 883–888.
29. R. Casalini, S. Corezzi, A. Livi, G. Levita and P. A. Rolla, J. Appl. Polym. Sci., 1997, 65, 17–25.
30. D. S. Achilias, J. Therm. Anal. Calorim., 2014, 116, 1379–1386.
31. M. T. Viciosa, J. Quiles Hoyo, M. Dionisio and J. L. Gomez Ribelles, J. Therm. Anal. Calorim., 2007, 90, 407–414.
32. H. F. Lu and J. N. Hay, Polymer, 2001, 42, 9423–9431.
33. A. T. Lorenzo, M. L. Arnal, J. Albuerne and A. J. Muller, Polym. Test., 2007, 26, 222–231.
34. M. G. Parthun and G. P. Johari, J. Chem. Phys., 1995, 103, 440–450.
35. I. T. Smith, Polymer, 1961, 2, 95–108.
36. K. Horie, H. Hiura, M. Souvada, I. Mita and H. Kambe, J. Appl. Polym. Sci. A: Polym. Chem., 1970, 8, 1357.
37. M. R. Kamal, Polym. Eng. Sci., 1974, 14, 23.
38. S. Sourour and M. R. Kamal, Thermochim. Acta, 1976, 14, 41.
39. M. Avrami, J. Chem. Phys., 1939, 7, 1103–1112 ; 1940, 8, 212–224; 1941, 9, 177–184.
40. V. Schetitino and R. Bini, Chem. Soc. Rev., 2007, 36, 869–880.
41. M. G. Lu, M. J. Shim and S. W. Kim, Mater. Sci. Commun., 1998, 56, 193.
42. S. W. Kim, M. G. Lu and M. J. Shim, Polym. J., 1998, 30, 90.
43. M. G. Lu, M. J. Shim and S. W. Kim, J. Therm. Anal. Calorim., 1999, 58, 701–709.
44. C. Yiyun, C. Dazhu, F. Rongqiang and H. Pingsheng, Polym. Int., 2005, 54, 495–499.
45. S. V. Muzumdar and L. J. Lee, Polym. Eng. Sci., 1996, 36, 943–952.
46. M. Pollard and J. L. Kardos, Polym. Eng. Sci., 1987, 27, 829.
47. X. Weibing, H. Pingsheng and C. Dazhu, Eur. Polym. J., 2003, 39, 617–625.
48. S. Havriliak and S. Negami, J. Polym. Sci., Part C: Polym. Symp., 1966, 14, 99–117.
49. M. Tarnacka, M. Dulski, S. Starzonek, K. Adrjanowicz, E. U. Mapesa, K. Kaminski and M. Paluch, Polymer, 2015, 68, 253–261.
50. S. Corezzi, D. Fioretto and P. Rolla, Nature, 2002, 420, 653.

---