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DOI: 10.1039/C4RA11735B (Paper) RSC Adv., 2015, 5, 2677-2683

Using the Ozawa method to study the thermally initiated curing kinetics of vinyl ester resin

Hui-Wang Cui*a, Katsuaki Suganumaa and Hiroshi Uchidab
aInstitute of Scientific and Industrial Research, Osaka University, Mihogaoka 8-1, Ibaraki, Osaka 567, Japan. E-mail: cuihuiwang@eco.sanken.osaka-u.ac.jp; cuihuiwang@hotmail.com
bInstitute for Polymers and Chemicals Business Development Center, Showa Denko K. K., 5-1 Yawata Kaigan Dori, Ichihara, Chiba 290-0067, Japan

Received 3rd October 2014 , Accepted 2nd December 2014

First published on 3rd December 2014

Abstract

In this study, a thermal initiator of 1,1-bis(t-hexylperoxy)-3,3,5-trimethyl cyclohexane was introduced to thermally initiate the curing of vinyl ester resin, and then a dynamic differential scanning calorimetry method was applied to investigate the thermally initiated curing procedures. Thermally initiated by the thermal initiator under heating, the end double bonds of vinyl ester resin macromolecules were opened to accomplish the crosslinking, polymerizing, and curing. The increasing thermal initiator advanced the curing procedures and shifted the initial temperature, exothermic peak temperature, and final temperature to a low temperature zone. The curing kinetics of thermally initiated vinyl ester rein was studied using the Ozawa method and deduced by assuming a constant activation energy. The thermally initiated curing kinetic equations, e.g., dα/dt = e30.16(1 − α)2.88α0.01e−106.60/RT, dα/dt = e29.43(1 − α)2.72α0.16e−105.17/RT, dα/dt = e29.43(1 − α)2.85α0.03e−104.48/RT, dα/dt = e29.41(1 − α)2.87α0.01e−104.11/RT, dα/dt = e27.70(1 − α)2.64α0.05e−99.63/RT, and dα/dt = e26.26(1 − α)2.32α0.30e−96.16/RT, respectively corresponding to the weight ratios between the thermal initiator and the vinyl ester resin at 0.5[thin space (1/6-em)]:[thin space (1/6-em)]100, 1[thin space (1/6-em)]:[thin space (1/6-em)]100, 2[thin space (1/6-em)]:[thin space (1/6-em)]100, 3[thin space (1/6-em)]:[thin space (1/6-em)]100, 4[thin space (1/6-em)]:[thin space (1/6-em)]100, and 5[thin space (1/6-em)]:[thin space (1/6-em)]100, were obtained. The increasing thermal initiator significantly influenced the thermally initiated curing kinetic parameters, such as the exothermic peak temperature, the fractional extent conversion, the rate of conversion, the overall order of reaction, the activation energy, the preexponential factor, and the reaction rate constant, and the thermally initiated curing kinetic equations. The data calculated from the kinetic equation agreed well with the experimental data, showing that the Ozawa method could evaluate the curing kinetics effectively.

Introduction

Vinyl ester resin (VER) is always polyadditionally polymerized from epoxy resin and unsaturated monocarboxylic acid, which thus possesses the advantages of both unsaturated polyester resin and epoxy resin. The VER has low viscosity, is easy to manipulate, can be cured at room temperature using initiator or catalyst, and can be applied not subject to seasonal restrictions. The VER has displayed super excellent mechanical properties, corrosion resistance, alkali resistance, acid resistance, oxidation resistance, and thermal stability, and the corresponding VER, such as low shrink VER, impact resistant VER, thickening VER, high temperature resistant VER, photosensitive VER, air drying VER, low styrene volatilizing VER, corrosion resistant VER, etc., have been developed already.1,2

The double bonds at both ends of VER macromolecules are extremely active that can let the VER be quickly cured to reach high strength, from which the VER can be potentially used in electrically conductive adhesives and thermally conductive adhesives for printed electronics, flexible electronics, and electronic packages.3,4 In a previous study, the electrically conductive adhesives were fabricated from VER and micro silver flakes, and then were photonically cured using a high intense pulse light under atmospheric ambient at room temperature; the cured electrically conductive adhesives presented low bulk resistivity (e.g., 7.54 × 10−6 Ω cm), high bonding strength (e.g., 6.75 MPa), and high pyrolysis temperatures above 350 °C.5 Then it is also found that the electrically conductive adhesives can be heat cured in the air surroundings, that the double bond conversion reached to 0.61%, 60.46%, 87.35%, and 98.27% after heat cured at 150, 200, 250, and 300 °C for 30 min, especially at 300 °C, the double bond conversion was 58.56%, 64.59%, 92.54%, 98.27%, 98.55%, 98.72%, and 98.88% after heat cured for 5, 10, 20, 30, 40, 50, and 60 min; and also found that the micro silver flakes influenced the heat-transferring rate, as well as the heat curing procedures.6 In the above photonic curing and heat curing, no initiator or no catalyst was used with VER. Especially the heat curing of VER, it often conducts at higher temperatures that consumes more energy and raises the cost in the application and production. Therefore, it is necessary to incorporate an initiator or a catalyst in the curing of VER.7,8

In this study, a thermal initiator of 1,1-bis(t-hexylperoxy)-3,3,5-trimethyl cyclohexane (called Perhexa TMH) was introduced to thermally initiate the curing of VER (Scheme 1). The influence of the loads of this thermal initiator on the curing procedures of VER were investigated by a dynamic differential scanning calorimetry (DSC) method, based on which the thermally initiated curing kinetics of VER was further studied using the Ozawa method to ensure the roles of the thermal initiator, determine the reaction mechanism, and obtain the activation energy (E) and preexponential factor (A) during the thermally initiated curing.


image file: c4ra11735b-s1.tif
Scheme 1 Free radical polymerization of VER initiated by Perhexa TMH under heating.

Experiments

Samples

The VER was a Ripoxy SP-1507 bisphenol A epoxy acrylate diluted by ethoxylated bisphenol A diacrylate (Scheme 1) from Showa Denko, Chibaken, Japan; the viscosity was 18[thin space (1/6-em)]700 mPa s (25 °C). The thermal initiator was 1,1-bis(t-hexylperoxy)-3,3,5-trimethyl cyclohexane (Scheme 1), called Perhexa TMH from NOF Corporation, Tokyo, Japan. The VER and thermal initiator were uniformly mixed together using a THINKY ARV-310 planetary vacuum mixer (THINKY Corporation, Laguna Hills, CA, USA.) under 2000 rpm for 5 min. The weight ratio between the thermal initiator and the VER was 0.5[thin space (1/6-em)]:[thin space (1/6-em)]100, 1[thin space (1/6-em)]:[thin space (1/6-em)]100, 2[thin space (1/6-em)]:[thin space (1/6-em)]100, 3[thin space (1/6-em)]:[thin space (1/6-em)]100, 4[thin space (1/6-em)]:[thin space (1/6-em)]100, and 5[thin space (1/6-em)]:[thin space (1/6-em)]100, corresponding to the samples named VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5, respectively.

Characterization

The structures of the samples were recorded using a PerkinElmer Frontier TN Fourier transform infrared spectrophotometer (FTIR) (PerkinElmer, Waltham, MA, USA); 32 scans were collected at a spectral resolution of 1 cm−1. The curing of the samples was studied using a NETZSCH 204 F1 DSC (NETZSCH, Selb, Germany) operated under an atmosphere of pure Ar atmosphere. The sample (ca. 5 mg) was placed in a sealed aluminum sample pan. The curing scans were conducted from 40 to 300 °C at the heating rates of 5, 10, 15, and 20 °C min−1 under an Ar flow rate of 25 mL min−1.

Results and discussion

The uncured VER (SP-1507), the thermal initiator, and the thermally initiated VER-1 were characterized using FTIR (Fig. 1). The SP-1507 presented a weak absorption peak at 1635 cm−1 featuring the stretching vibration of C[double bond, length as m-dash]C, a strong absorption peak at 1415 cm−1 featuring the in-plane bending vibration of C–H, and absorption peaks at 985 and 805 cm−1 featuring the out-plane bending vibration of C–H, all belonging to the alkenyl groups. While the thermally initiated VER-1 did not present these absorption peaks. Thermally initiated by the Perhexa TMH under heating, the end double bonds of VER macromolecules were opened to accomplish the crosslinking, polymerizing, and curing (Scheme 1),9,10 letting the thermally initiated VER-1 lose these absorption peaks.
image file: c4ra11735b-f1.tif
Fig. 1 FTIR spectra of Perhexa TMH, SP-1507, and VER-1.

In this study, the thermally initiated curing process of VER was studied using a dynamic DSC method, including VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5 (Fig. 2 and Table 1). For example, at the heating rates of 5, 10, 15, and 20 °C min−1, the VER-1 started the curing at the initial temperature (Ti) of 68.1, 74.1, 77.7, and 83.7 °C, reached the exothermic peak temperature (Tp) of 95.6, 103.3, 107.6, and 110.6 °C, and ended the curing at the final temperature (Tf) of 173.2, 183.2, 190.1, and 194.0 °C. For the heat curing of pure VER without any initiator or catalyst, the Ti was around 200 °C, the Tp was around 250 °C, and the Tf was around 300 °C.6 Apparently, the thermal initiator lowered the curing temperatures dramatically. Moreover, it can be seen that the increasing thermal initiator had advanced the curing procedures and shifted the Ti, Tp, and Tf to low temperature zone. Taking the results at the heating rate of 10 °C min−1 for an example, VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5 presented the Ti at 76.8, 74.1, 74.0, 71.1, 70.7, and 67.3 °C, presented the Tp at 108.8, 103.3, 99.6, 97.8, 97.0, and 96.0 °C, and presented the Tf at 184.6, 183.2, 183.1, 183.0, 182.9, and 182.7 °C. These phenomena closely related to the weight ratio of thermal initiator in the tested samples. The weight ratio between the thermal initiator and the VER was 0.5[thin space (1/6-em)]:[thin space (1/6-em)]100, 1[thin space (1/6-em)]:[thin space (1/6-em)]100, 2[thin space (1/6-em)]:[thin space (1/6-em)]100, 3[thin space (1/6-em)]:[thin space (1/6-em)]100, 4[thin space (1/6-em)]:[thin space (1/6-em)]100, and 5[thin space (1/6-em)]:[thin space (1/6-em)]100 in VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5, that the concentration of the thermal initiator increased accordingly in these VER. By the help of this increasing concentration, the effective collision probability between the thermal initiator molecules and the VER macromolecules accordingly increased and these two molecules consequently contacted fully that conducted the curing earlier. In addition, this increasing concentration had improved the reaction rate that also advanced the curing. Therefore, thermally initiated by the Perhexa TMH, the end double bonds in the VER macromolecules were opened to achieve crosslinking, polymerizing, and curing; the increasing concentration of thermal initiator increased the effective collisions, improved the curing rate, advanced the curing procedures, and shifted the Ti, Tp, and Tf to low temperature zone. As stated in Fig. 2 and Table 1, the Ti, Tp, and Tf of VER-0.5 to VER-5 decreased one by one as the weight ratio between the thermal initiator and the VER increased from 0.5[thin space (1/6-em)]:[thin space (1/6-em)]100 to 5[thin space (1/6-em)]:[thin space (1/6-em)]100.


image file: c4ra11735b-f2.tif
Fig. 2 DSC curves of (a) VER-0.5, (b) VER-1, (c) VER-2, (d) VER-3, (e) VER-4, and (f) VER-5 at the heating rate of 5, 10, 15, and 20 °C min−1.
Table 1 Ti, Tf, Tp, vp, and kp for VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5a
Items Ti/°C Tf/°C Tp/°C kp/min−1 Items Ti/°C Tf/°C Tp/°C kp/min−1
a Note: the items with −5, −10, −15, and −20 means the heating rate at 5, 10, 15, and 20 °C min−1, respectively.
VER-0.5–5 72.3 173.3 100.8 0.0161 VER-3–5 67.5 173.0 90.6 0.0066
VER-0.5–10 76.8 184.6 108.8 0.0331 VER-3–10 71.1 183.0 97.8 0.0129
VER-0.5–15 83.0 190.2 113.7 0.0506 VER-3–15 75.0 189.8 102.0 0.0189
VER-0.5–20 85.8 194.6 117.5 0.0698 VER-3–20 75.1 193.1 104.6 0.0238
VER-1–5 68.1 173.2 95.6 0.0076 VER-4–5 66.7 173.0 90.3 0.0051
VER-1–10 74.1 183.2 103.3 0.0154 VER-4–10 70.7 182.9 97.0 0.0093
VER-1–15 77.7 190.1 107.6 0.0255 VER-4–15 74.1 189.4 101.6 0.0139
VER-1–20 83.7 194.0 110.6 0.0292 VER-4–20 74.4 192.3 104.6 0.0179
VER-2–5 67.7 173.1 92.5 0.0072 VER-5–5 66.3 173.0 89.1 0.0035
VER-2–10 74.0 183.1 99.6 0.0138 VER-5–10 67.3 182.7 96.0 0.0063
VER-2–15 77.5 190.0 104.4 0.0212 VER-5–15 69.5 189.4 100.1 0.0088
VER-2–20 83.1 193.7 107.8 0.0285 VER-5–20 70.4 192.3 103.5 0.0117

Certainly, the increasing thermal initiator also influenced the thermally initiated curing kinetics of VER. In study, the thermally initiated curing kinetics of VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5 were investigated, which often started with the fractional extent conversion (α) at a given temperature T. The α can be expressed as:

image file: c4ra11735b-t1.tif
where ΔHT is the heat at a given temperature T and ΔH is the total heat of the curing reaction.

In this study, The weight ratio between the thermal initiator and the VER was 0.5[thin space (1/6-em)]:[thin space (1/6-em)]100, 1[thin space (1/6-em)]:[thin space (1/6-em)]100, 2[thin space (1/6-em)]:[thin space (1/6-em)]100, 3[thin space (1/6-em)]:[thin space (1/6-em)]100, 4[thin space (1/6-em)]:[thin space (1/6-em)]100, and 5[thin space (1/6-em)]:[thin space (1/6-em)]100 in VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5; all the thermal initiator weight was fixed in each of them. Moreover, only a main exothermic peak representing the curing reaction appeared on DSC curves (Fig. 2), thus the heat of the exothermic peak was approximately equal to the total heat of the curing reaction. In other words, ΔH can be considered as a constant over the whole curing reaction. The rate of conversion dα/dt at a given temperature T can be expressed as:

 
image file: c4ra11735b-t2.tif(1)
where dH/dt is the heat flow, can be obtained from the DSC curves in Fig. 2.

The thermally initiated curing kinetic study always starts with a basic equation of the rate of conversion (dα/dt) equation:11,12

 
image file: c4ra11735b-t3.tif(2)
where A and E are kinetic parameters, the preexponential factor and the activation energy, respectively, R is the universal gas constant, and T is the absolute temperature at a time t.

Thermally initiated by the Perhexa TMH, the VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5 all were well cured; the heat from a high temperature and long time process gave enough activation energy to the VER and opened the end double bonds in VER macromolecules to achieve crosslinking, polymerizing, and curing. The curing was a single polyaddition reaction only occurred between the end double bonds of VER macromolecules; this was a one-step reaction. However, for a process with participation of a solid phase, the E could depend on the α, even this process consists in a single reaction, because of the continuous change of the structure of solid phases during the process. So it is not sure that E does not depend on the curing conversion.

In addition, when non-isothermal DSC is used to study the kinetics of curing reactions, the α at the exothermic peak is a constant, although the temperature at which the exothermic peak occurs depends on the heating rate: the α at the Tp was 0.30 for VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5, constant in this study (Fig. 3). Consequently, a kinetic analysis must begin with the evaluation of the dependence of E on α by applying a model-free method, like Ozawa method representing the relationship between the heating rate (β, °C min−1) and Tp:13,14

image file: c4ra11735b-t4.tif


image file: c4ra11735b-f3.tif
Fig. 3 Comparisons of experimental data (Exp.) with the kinetic method results (Cal.) of (a) VER-0.5, (b) VER-1, (c) VER-2, (d) VER-3, (e) VER-4, and (f) VER-5 at the heating rate of 5, 10, 15, and 20 °C min−1.

Fig. 4 shows the plots of −ln[thin space (1/6-em)]β vs. 1000/Tp. Linear regression analysis with correlation coefficient (r), e.g., y = 13.489x − 38.681 (r2 = 0.9998) for VER-0.5, y = 13.308x − 38.158 (r2 = 0.9993) for VER-1, y = 13.22x − 38.111 (r2 = 0.9992) for VER-2, y = 13.174x − 37.868 (r2 = 0.9989) for VER-3, y = 12.607x − 36.1 (r2 = 0.9992) for VER-4, and y = 12.167x − 34.151 (r2 = 0.9995) for VER-5, suggested that, to a good agreement, the calculated value of E was 106.60, 105.17, 104.48, 104.11, 99.63, and 96.16 kJ mol−1 for VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5, respectively (Table 2). The E, an important parameter for the thermally initiated curing kinetics, is the required minimum energy for the molecules from a reactant state to an activated state in chemical reactions; in the thermally initiated curing, it is the different energy between the onset point (Ti) and the offset point (Tf) from an uncured state to a cured state. As aforementioned, the increasing thermal initiator would certainly influence the thermally initiated curing kinetics, e.g., the thermally initiated curing kinetic parameters of α and E, as did that advancing the curing procedures and shifting the Ti, Tp, and Tf to low temperature zone. All the α was 0.30 at the decreasing Tp of VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5 (Fig. 3), caused by the advanced curing procedures. For example, when α = 0.30, Tp = 108.8, 103.3, 99.6, 97.8, 97.0, and 96.0 °C for VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5, respectively, all under the heating rate of 10 °C min−1 (Table 1). Similarly, the increasing thermal initiator also decreased the values of E, as listed in Table 2, the E was 106.60, 105.17, 104.48, 104.11, 99.63, and 96.16 kJ mol−1 for VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5, respectively. The weight ratio between the thermal initiator and the VER was 0.5[thin space (1/6-em)]:[thin space (1/6-em)]100, 1[thin space (1/6-em)]:[thin space (1/6-em)]100, 2[thin space (1/6-em)]:[thin space (1/6-em)]100, 3[thin space (1/6-em)]:[thin space (1/6-em)]100, 4[thin space (1/6-em)]:[thin space (1/6-em)]100, and 5[thin space (1/6-em)]:[thin space (1/6-em)]100 in VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5, that the concentration of the thermal initiator increased accordingly in these VER. By the help of this increasing concentration, the effective collision probability between the thermal initiator molecules and the VER macromolecules correspondingly increased and these two molecules consequently contacted fully that conducted the curing earlier. And the reaction rate was also improved by the increasing concentration of thermal initiator. Based on the increased effective collisions, improved curing rate, advanced curing procedures, and shifted Ti, Tp, and Tf to low temperature zone, less energy and lower temperatures were needed to let the end double bonds in the VER macromolecules open and achieve crosslinking, polymerizing, and curing. This was also reflected by the increasing values of dα/dt at the decreasing Tp for all VER (Fig. 2 and 3), caused by the increasing thermal initiator. For example, dα/dt = 0.0065 at Tp = 108.8 °C for VER-0.5, dα/dt = 0.0070 at Tp = 103.3 °C for VER-1, dα/dt = 0.0072 at Tp = 99.6 °C for VER-2, dα/dt = 0.0074 at Tp = 97.8 °C for VER-3, dα/dt = 0.0075 at Tp = 97.0 °C for VER-4, and dα/dt = 0.0077 at Tp = 96.0 °C for VER-5, all under the heating rate of 10 °C min−1.


image file: c4ra11735b-f4.tif
Fig. 4 Plots of −ln[thin space (1/6-em)]β vs. 1000/Tp for VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5.
Table 2 Calculated m, n, m + n, E, and ln[thin space (1/6-em)]A for VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5
Items m n m + n E/kJ mol−1 ln[thin space (1/6-em)]A
VER-0.5 0.01 2.88 2.89 106.60 30.16
VER-1 0.16 2.72 2.88 105.17 29.43
VER-2 0.03 2.85 2.88 104.48 29.43
VER-3 0.01 2.87 2.88 104.11 29.41
VER-4 0.05 2.64 2.69 99.63 27.70
VER-5 0.30 2.32 2.62 96.16 26.26

For the thermosetting resins that follow autocatalytic kinetics, the expression of f(α) is:15

 
f(α) = (1 − α)nαm (3)
where m + n is the overall order of reaction.16,17

Substitute eqn (3) into eqn (2), and logarithmic them as:

 
image file: c4ra11735b-t5.tif(4)
then
image file: c4ra11735b-t6.tif
where α′ is the fractional extent conversion at a given temperature T′; let α′ = 1 − α, and then:
 
image file: c4ra11735b-t7.tif(5)

Eqn (4) − eqn (5):

 
image file: c4ra11735b-t8.tif(6)

Eqn (4) + eqn (5):

 
image file: c4ra11735b-t9.tif(7)

The DSC curves of VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5 with the heating rates of 5, 10, 15, and 20 °C min−1 were studied.

The α at various values (α = 0.05, 0.10, 0.15, 0.20, …, 0.90, 0.95) covering the experimental range was submitted into eqn (6) and (7). Taking the calculation of VER-1 for an example, when α = 0.05 at 10 °C min−1, ln[(1 −α)/α] = 2.9444 and Value I = 6.0009, ln[α(1 − α)] = −3.0470 and Value II = 50.7298. Repeating this process, the different value of Value I corresponding to different ln[(1 − α)/α] and the different value of Value II corresponding to different ln[α(1 − α)] were obtained; the groups of Value I vs. ln[(1 − α)/α] and Value II vs. ln[α(1 − α)] were plotted in Fig. 5 and 6 for VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5. Then making fitted linear regression lines, the values of n − m were obtained from the slopes of the plots of Value I vs. ln[(1 − α)/α] (Fig. 5), and the values of m + n and 2[thin space (1/6-em)]ln[thin space (1/6-em)]A were obtained from the slopes and intercepts of the plots of Value II vs. ln[α(1 − α)] (Fig. 6). For example, at 10 °C min−1 for VER-1, a linear regression analysis of y = 2.5113x − 7 × 10−15 (r2 = 0.9634) for Value I vs. ln[(1 − α)/α] [Fig. 5(b)], n − m = 2.5113, and a linear regression analysis of y = 2.8195x + 58.812 (r2 = 0.9433) for Value II vs. ln[α(1 − α)] [Fig. 6(b)], n + m = 2.8195, ln[thin space (1/6-em)]A = 29.406. Repeating this process, the linear regression analysis, n − m, n + m, and ln[thin space (1/6-em)]A of VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5 at the heating rates of 5, 10, 15, and 20 °C min−1 were obtained (Fig. 5 and 6). In this study, we used the average values: m ≈ 0.01, n ≈ 2.88, and ln[thin space (1/6-em)]A ≈ 30.16 for VER-0.5, m ≈ 0.16, n ≈ 2.72, and ln[thin space (1/6-em)]A ≈ 29.43 for VER-1, m ≈ 0.03, n ≈ 2.85, and ln[thin space (1/6-em)]A ≈ 29.43 for VER-2, m ≈ 0.01, n ≈ 2.87, and ln[thin space (1/6-em)]A ≈ 29.41 for VER-3, m ≈ 0.05, n ≈ 2.64, and ln[thin space (1/6-em)]A ≈ 27.70 for VER-4, and m ≈ 0.30, n ≈ 2.32, and ln[thin space (1/6-em)]A ≈ 26.26 for VER-5 (Table 2).


image file: c4ra11735b-f5.tif
Fig. 5 Plots of Value I vs. ln[(1 − α)/α] for (a) VER-0.5, (b) VER-1, (c) VER-2, (d) VER-3, (e) VER-4, and (f) VER-5 at the heating rate of 5, 10, 15, and 20 °C min−1.

image file: c4ra11735b-f6.tif
Fig. 6 Plots of Value II vs. ln[α(1 − α)] for (a) VER-0.5, (b) VER-1, (c) VER-2, (d) VER-3, (e) VER-4, and (f) VER-5 at the heating rate of 5, 10, 15, and 20 °C min−1.

Apparently, the thermally initiated curing kinetic parameters of A, m, and n changed accordingly with the increasing thermal initiator (Table 2). The A is a constant determined by the reaction nature and there is nothing to do with the reaction temperature and concentration in the system. The A always follows the E in the kinetics; if the E increases, the A will increase, and vice versa. As stated above, the A was e30.16, e29.43, e29.43, e29.41, e27.70, and e26.26 min−1 for VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5, corresponding to their respective E of 106.60, 105.17, 104.48, 104.11, 99.63, and 96.16 kJ mol−1. The overall order of reaction of m + n decreased from 2.89 (VER-0.5) to 2.88 (VER-1), 2.88 (VER-2), 2.88 (VER-3), 2.69 (VER-4), and 2.62 (VER-5) due to the increasing thermal initiator in the obtained VER.

The thermally initiated curing kinetic equations were expressed as eqn (8) for VER-0.5, eqn (9) for VER-1, eqn (10) for VER-2, eqn (11) for VER-3, eqn (12) for VER-4, and eqn (13) for VER-5:

 
image file: c4ra11735b-t10.tif(8)
 
image file: c4ra11735b-t11.tif(9)
 
image file: c4ra11735b-t12.tif(10)
 
image file: c4ra11735b-t13.tif(11)
 
image file: c4ra11735b-t14.tif(12)
 
image file: c4ra11735b-t15.tif(13)

Finally, the applicability of the Ozawa method was verified between the calculated results from this kinetic method and those from experiments (Fig. 3). Here, the experimental data were from eqn (1) and DSC curves in Fig. 2; the calculated data were from the thermally initiated curing kinetic equations, e.g., eqn (8) for VER-0.5, eqn (9) for VER-1, eqn (10) for VER-2, eqn (11) for VER-3, eqn (12) for VER-4, and eqn (13) for VER-5. It can be seen that they were in good agreements with each other (Fig. 3), suggesting that the Ozawa method was a good method to evaluate the thermally initiated curing kinetics of VER. And the curing of VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5 underwent gelation (liquid-to-rubber) and vitrification (rubber-to-glass) transitions during the thermally initiated curing.6

The increasing thermal initiator also influenced the reaction rate constant (k) calculated by Arrhenius equation:18–20

image file: c4ra11735b-t16.tif

The k closely relates to the reaction temperature, reaction medium (or solvent), catalyst, etc., even to the shape and characteristics of reactors. Thus, the k at Tp (kp) for VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5 changed accordingly with the variations of Tp, E, A, and the increasing thermal initiator (Tables 1 and 2). For example, the kp was 0.0076, 0.0154, 0.0255, and 0.0292 min−1 at the heating rates of 5, 10, 15, and 20 °C min−1 for VER-1; and the kp was 0.0331, 0.0154, 0.0138, 0.0129, 0.0093, and 0.0063 min−1 for VER-0.5, VER-1, VER-2, VER-3, VER-4, and VER-5 at the heating rate of 10 °C min−1. In a word, the increasing thermal initiator significantly influenced the thermally initiated curing kinetic parameters, such as Tp, α, dα/dt, m + n, E, A, and kp, and the thermally initiated curing kinetic equations.

Conclusions

In this study, the thermal initiator of 1,1-bis(t-hexylperoxy)-3,3,5-trimethyl cyclohexane (called Perhexa TMH) was introduced to thermally initiate the curing of VER. The increasing thermal initiator advanced the curing procedures and shifted the Ti, Tp, and Tf to low temperature zone. The curing kinetics of thermally initiated VER was studied using the Ozawa method and deduced by assuming a constant E. The thermally initiated curing kinetic equations, e.g., dα/dt = e30.16(1 − α)2.88α0.01e−106.60/RT with E = 106.60 kJ mol−1 for VER-0.5, dα/dt = e29.43(1 − α)2.72α0.16e−105.17/RT with E = 105.17 kJ mol−1 for VER-1, dα/dt = e29.43(1 − α)2.85α0.03e−104.48/RT with E = 104.48 kJ mol−1 for VER-2, dα/dt = e29.41(1 − α)2.87α0.01e−104.11/RT with E = 104.11 kJ mol−1 for VER-3, dα/dt = e27.70(1 − α)2.64α0.05e−99.63/RT with E = 99.63 kJ mol−1 for VER-4, and dα/dt = e26.26(1 − α)2.32α0.30e−96.16/RT with E = 96.16 kJ mol−1 for VER-5, were obtained. The increasing thermal initiator significantly influenced the thermally initiated curing kinetic parameters, such as Tp, α, dα/dt, m + n, E, A, and kp, and the thermally initiated curing kinetic equations. The data calculated from the kinetic equation agreed well with the experimental data, showing that the Ozawa method could evaluate the curing kinetics effectively.

Notes and references

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