Introduction

Acrylic acid is widely used as a feedstock for highly transparent and water absorptive polymer. Due to its high reactivity, there are thermal hazards in the manufacturing process of acrylic acid monomer. Acrylic acid is prone to free radical polymerization, which releases heats and pressure when radical inhibitors or oxygen are absent. This unintended polymerization causes many explosive accidents [1–8]. Due to its high melting point (14 °C), acrylic acid typically requires heating to be melted down and processed in an industrial plant. There have been accidents [1–3] when overheating during this melting process initiates unintended polymerization. Generally, in storage tanks, a radical inhibitor is added to acrylic acid to prevent free radical polymerization, and the polymerization is prevented when the temperature increasing. However, the radical inhibitor cannot inhibit the ionic reaction called the Michael addition reaction (MAR) [9], which occurs exothermically in acrylic acid at relatively low temperature. Levy et al. [2] proposed that MAR is one of the causes of increasing temperature in acrylic acid. MAR which forms acrylic acid dimers at ordinary temperature as shown in Fig. 1 is a mildly exothermic reaction. The heat generation is small (heat of dimer formation: 130–150 J g−1 [2]) and the reaction rate is slow (rate of dimer formation: 0.02 mass% day−1 at 25 °C [16]). At high temperature under adiabatic conditions caused by cooling and stirring failures, however, accelerated MAR gradually increases acrylic acid temperature. At temperatures above the inactivation temperature of the inhibitor, polymerization is initiated. Previous studies [10–15] have focused on the radical inhibitor and induction period of acrylic acid polymerization. However, it is important to investigate MAR, which occurs exothermically in the presence or absence of a radical inhibitor. Levy et al. [2] reported that MAR becomes a factor in temperature rise. In the incident referenced [2], it is considered that MAR accounted for 55.5% of the distribution of heat input to initiate polymerization and that steam accounted for the rest. CCPS guidelines [1] caution against melting acrylic acid with direct steam impingement or electrical resistance heating elements since it is easy to overheat acrylic acid. The guidelines also caution that the temperature of tempered water for preventing the freezing of acrylic acid should not exceed 45 °C to prevent runaway polymerization due to MAR.

Fig. 1
figure 1

Formation scheme of acrylic acid dimer by Michael addition reaction

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Unfortunately, in 2012, an acrylic acid tank explosion occurred in Japan. According to the investigative report [3], one of the causes was temperature rise induced by MAR and it lead to runaway polymerization. Acrylic acid heated by steam and its temperature was thought to be above 90 °C. The fact that considerable amounts of radical inhibitor existed in the acrylic acid tank decreased operators’ awareness and became a contributing factor in the accident. Serious incidents such as these have occurred about once per year.

Basic Acrylic Monomer Manufacturers (BAMM) [16, 17] issued a dimer formation rate for the purpose of quality control. The formation rates of higher oligomers, e.g., trimers, tetramers and pentamers, are not well known. The investigative report [3] and Levy et al. [2] stated that production of trimers occurred in the explosion tanks. Once proton dissociation from acrylic acid occurs, MAR can produce unlimited numbers of oligomers [18]. The oligomerization generates heat and increases the acrylic acid temperature unchecked. The heat of oligomerization has never been measured experimentally, and rate of heat release above 100 °C is not understood well. It is important to investigate the thermal characteristics and production of MAR for understanding thermal hazards of runaway polymerization induced by MAR.

The purpose of this study is to obtain a better understanding on MAR of acrylic acid. We measured the heat of MAR and analyzed MAR kinetics. First, the heat of MAR containing not only dimers but also oligomers formation was measured. High-sensitivity calorimetry was used to detect and analyze the MAR exotherm, which is extremely small and slow. After the calorimetry, the molecular weight distribution of the heated samples was obtained by gel permeation chromatography (GPC) in order to clarify products of MAR. In addition, we estimated the appearance rate constant of MAR using isothermal tests and kinetic analysis.

Experimental

Materials

Acrylic acid and p-methoxyphenol (hydroquinone monomethyl ether, MQ) obtained from Kanto chemical were used. Acrylic acid (99.6%) and MQ as a radical inhibitor were mixed in a mass% ratio of 99.98/0.02 [1]. In this study, polymerization at low temperature must be inhibited by MQ in order to analyze the thermal behavior of MAR alone. We prepared samples containing several MQ ratios up to 2 mass%, which is much higher than industrially suitable ratios.

Heat of Michael addition reaction

The heat of MAR was measured with high-sensitivity calorimetry. A Setaram C80 (Fig. 2) equipped with a heat flux calorimeter of the Calvet type is distinguished by its accurate and reproducible calorimetric measurements. The sensitivity is 5–10 μW. It is adapted to an isothermal calorimeter as well as a mixing calorimeter and temperature scanning calorimeter. In this study, the samples were placed in the high-pressure stainless steel vessel with an inner glass vessel. They were heated to 30 °C, held for 2 h to stabilize heat flow, and then heated to 140 °C at rates of 0.01, 0.1 and 1 K min−1. The reason, why the maximum temperature of this test is 140 °C, is to avoid the radical polymerization initiation. The C80 was calibrated for temperature and heat flow using melting of high-purity indium (99.99%).

Fig. 2
figure 2

Setaram C80

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After the calorimetry, we determined the molecular weight distribution (MWD) of the samples in order to identify products of MAR. The MWD was estimated based on qualitative analysis using GPC. GPC was performed on a Shimadzu HPLC prominence with a Shodex GPC KF-802 column (particle size: 6 μL and molecular weight range of polystyrene: 0–5 × 103 g mol−1). Tetrahydrofuran (THF, 99.9%, stabilizer free) at a flow rate of 1.0 mL min−1 was the eluent. Sample solutions of 1 mass% concentration were prepared in THF, and 50 µL injected in each case. A UV detector (254 nm) was employed. As a standard sample, we used 2-carboxyethyl acrylate oligomers, which is a mixture of monomers, dimers, trimers and tetramers obtained from Sigma-Aldrich. Quantitative analysis was conducted on samples with differing acrylic acid monomer concentrations. Based on a previous study [18], in order to obtain a quantitative calibration curve, acrylic acid monomers were weighed and dissolved into THF. We prepared 1.0, 0.7 and 0.4 mass% acrylic acid/THF mixture samples. A quantitative calibration curve could be charted by the peak area data at different concentrations. Samples were dissolved at 1 mass% to THF.

Reaction kinetics of Michael addition reaction

Generally, the thermal kinetic parameters (e.g., activation energy and reaction order) can be obtained from thermal analysis, which is conducted under non-isothermal conditions [19] or adiabatic conditions [20]. However, the thermal behavior of MAR is thought to be too slow and mild to detect. To identify the overall reaction order and reaction rate of MAR, MAR kinetics were analyzed with isothermal tests. The MQ concentration of samples was 2 mass%. In these tests, 50 mL samples were placed into a glass vessel that was inserted in an aluminum block bath. The isothermal tests were performed at 120, 125, 130 and 135 °C under a stirring condition of 250 rpm. The GPC analysis method was identical to the estimation of MWD to identify acrylic acid monomer concentrations of samples successively in the isothermal test.

Results and discussion

Heat of Michael addition reaction

Figure 3 shows C80 profiles obtained with heating rates of 0.01, 0.1 and 1 K min−1. From the result for 0.01 K min−1, a micro-exotherm was detected at the start of the calorimetry, and its heat flow peaked at approximately 120 °C. The result for 0.1 K min−1 shows that the exotherm was detected at 80 °C, and the test ended before heat flow peaked. For the 1 K min−1 test, the temperature reached 60 °C before the heat flow became stable, and an exotherm was detected at 120 °C. In all of the tests, the heat flow did not return to its baseline level during the calorimetry. Therefore, it was considered that the exothermic reaction did not end at the completion of the calorimetry run. To obtain the heat of reaction, we should calculate the heat of reaction through the integration of the C80 curve and conversion of the sample. Table 1 shows the result of heat of MAR with integrated heat flow between 70 and 140 °C in Fig. 3, the C80 profile at 0.01 K min−1. The experimental heat value of MAR (ΔH) was 109 J g−1. This value was part of the whole amount of MAR heat generation. We calculated the whole amount of heat generation as following equation.

$$\Delta H = 109\;{\text{J}}\;{\text{g}}^{ - 1} \times \frac{100}{82} = 133\;{\text{J}}\;{\text{g}}^{ - 1}$$
(1)

Thermal behaviors were different for every heating rate, indicating that the products in these tests were also different. Figure 4 shows GPC chromatograms of samples after the C80 tests. Conversion of monomer to Michael adducts in the C80 test at 0.01 K min−1 was 82.0 mass%, which was estimated based on the peak area at 19 min shown in Fig. 4. This result means 82 mass% of acrylic acid was converted to dimers and oligomers and generated the heat value of 109 J g−1. ΔH from 100 mass% can be calculated to be 133 J g−1 based on the C80 and GPC results. This value was in good agreement with the literature heat value of dimer formation (130–150 J g−1 [2]) and oligomer formation (<140 J g−1 [2]). GPC chromatograms of samples after the calorimetry as shown in Fig. 4 indicate production of dimers, trimers and tetramers. Therefore, this heat value involved step oligomerization that forms these oligomers.

Fig. 3
figure 3

C80 profile of acrylic acid containing 2 mass% MQ

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Fig. 4
figure 4

GPC chromatograms of samples after C80 tests

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Table 1 Heat of Michael addition reaction of acrylic acid in C80
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We succeeded in observing the exotherm of MAR, which is extremely small and slow, using C80. In the C80 tests, MAR did not end at the completion of the calorimetry run because its reaction rate was slow. MAR that may induce runaway polymerization is thought to be step oligomerization. It is necessary to analyze MAR kinetics inclusively as the formation reaction of several oligomers.

Reaction kinetics of Michael addition reaction

The rate of MAR r MAR can be represented by Eq. (2):

$$r_{\text{ MAR}} = - \frac{{{\text{d}}\left[ {\text{AA}} \right]}}{{{\text{d}}t}} = k\left[ {\text{AA}} \right]^{\text{n}}$$
(2)

where k is the rate constant [Ln−1 mol1−n s−1], [AA] is the monomer concentration [mol L−1], n is the order of MAR [–] and t is time [s].

Equation (2) is integrated as

$$\ln \frac{{[{\text{AA}}]}}{{[{\text{AA}}]_{ 0} }} = - kt\quad (n = 1)$$
(3)
$$\frac{1}{n - 1}\left\{ {\frac{1}{{\left[ {\text{AA}} \right]^{\text{n} - 1} }} - \frac{1}{{\left[ {\text{AA}} \right]_{0}^{\text{n} - 1} }}} \right\} = kt\quad (n \ne 1)$$
(4)

where [AA]0 is the initial concentration of acrylic acid [mol L−1].

We fitted the reaction order to the experimental results through a plot of ln[AA]/[AA]0 versus t or 1/(n − 1){1/[AA]n−1 − 1/[AA] n−10 } versus t on the assumption that n takes on various values. The slope of the plot equals the rate constant of MAR at the test temperature. We can also represent the rate constant based on the Arrhenius equation, as in Eq. (5):

$$k = A \times \exp \left( { - \frac{{E_{\text{a}} }}{RT}} \right)$$
(5)

where A is the frequency factor [Ln−1 mol1−n s−1], E a is the overall activation energy [kJ mol−1], R is the gas constant [kJ mol−1 K−1] and T is the temperature [K].

The natural log of Eq. (5) can then be taken:

$$\ln k = - \frac{{E_{\text{a}} }}{RT} + \ln A$$
(6)

The activation energy of MAR was determined based on the Arrhenius plot, which is ln k versus 1/T. The Arrhenius plot whose correlation coefficient was closest to 1 showed a MAR kinetics parameter that was the closest to the true value. The parameters obtained by this method are reaction order n, reaction rate constant k, activation energy E a and frequency factor A.

Figure 5 shows the monomer concentration change at 120, 125, 130 and 135 °C. The monomer concentration was detected with GPC absolute calibration method. Table 2 shows correlation coefficients R 2 of the Arrhenius plot, which are plotted as n = 0, 1, 1.5, 2, 2.5, 3 and 4. From Table 2, the plot of n equal to 2.5 had the highest linearity, thus the reaction order of MAR is 2.5th. Table 3 shows the comparison of our experimental values and previous studies on the reaction order of MAR [2, 16, 17]. Figure 6 shows GPC chromatograms of samples heated to 135 °C for several minutes in an isothermal test. The reaction order in this study is the highest value shown in Table 3. The reaction order is related to the number of reactant species. Previous studies [2, 16, 17] discussed reaction order only of dimer formation for monomer quality control. In this study, based on the GPC result of a sample that was analyzed at 135 °C after 1172 min, shown in Fig. 6, we took into account oligomer formation. The GPC chromatogram of this sample was almost the same as in Fig. 4, which indicated substantial amounts of dimers, trimers and tetramers. The reactive species were thought to be these oligomers. We concluded that the apparent reaction order for the MAR of the oligomers was 2.5.

Fig. 5
figure 5

Conversion of acrylic acid in isothermal test

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Table 2 Supposed reaction order and correlation coefficients of Arrhenius plots
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Table 3 Comparison of reaction order and activation energy of MAR in this study and previous studies
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Fig. 6
figure 6

GPC chromatograms of samples heated up to 135 °C

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Apparent activation energy E a and frequency factor A were identified based on Arrhenius plot shown in Fig. 7. The rate constant of MAR was estimated according to Eq. (7).

$$k/{\text{L}}^{1.5} \;{\text{mol}}^{ - 1.5} \;{\text{s}}^{ - 1} = 3.52 \times 10^{3} \times \exp \left( { - \frac{{1.18 \times 10^{5} }}{{T\left[ {\text{K}} \right]}}} \right)$$
(7)

Figure 8 shows a comparison of the monomer concentration change in the experimental and calculated results. The calculation results based on the rate constant in Eq. (7) show better agreement with the experimental results. Figure 9 shows a comparison of previous experimental results at 100 and 120 °C [3], and calculation results based on kinetic factors that were proposed in this study and previous studies [2, 16, 17]. The calculation results of this study give the best agreement with the experimental results at 120 °C [3]. Thus, we concluded that Eq. (7) is the correct rate constant of MAR around 120 °C.

Fig. 7
figure 7

Arrhenius plot of Michael addition reaction

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Fig. 8
figure 8

Monomer concentration change in the experimental and calculated results

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Fig. 9
figure 9

Comparison of monomer concentration change induced by MAR in previous studies and experimental results and calculation results at a 100 °C and b 120 °C

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Table 4 shows that the activation energy of oligomerization in this study is similar in value to that in previous studies [2, 16, 17]. This indicates that dimerization has the highest activation energy in oligomerization. In terms of the activation energy of MAR, dimer formation is the dominant reaction. Therefore, once a dimer is produced, other oligomers are thought to be produced spontaneously.

Table 4 Activation energies in this study and previous studies [2, 16, 17]
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Conclusions

Thermal and kinetic analyses on acrylic acid were performed in order to gain a better understanding of the Michael addition reaction (MAR), which may induce runaway polymerization of acrylic acid. High-sensitivity calorimetry using C80 revealed that the heat of MAR was 109 J g−1. GPC analysis showed that products of MAR were dimers, trimers and tetramers, and revealed that conversion of the monomer to these Michael adducts was 82 mass%. Thus, the heat value was composed of the heat of formation of these oligomers, and the value for 100 mass% conversion can be calculated as 133 J g−1. In C80 calorimetry heated to 140 °C, the heat release rate of MAR was extremely small.

Kinetic analysis on MAR showed that order of MAR was 2.5. The overall reaction rate constant was k = 3.52 × 103 × exp (−1.18 × 105/T [K]) L1.5 mol−1.5 s−1. Calculations based on this rate constant coincided well with a previous experimental result [3]. The activation energy of MAR was 98.0 kJ mol−1, which was similar to that of dimerization in previous studies [2, 16, 17]. This indicated that dimer formation is the dominant reaction in MAR.