Calorimetric Method To Determine Self-Accelerating Polymerization

Article pubs.acs.org/OPRD

Cite This: Org. Process Res. Dev. XXXX, XXX, XXX−XXX

Calorimetric Method To Determine Self-Accelerating Polymerization Temperature (SAPT) for Monomer Transportation Regulation: Kinetics and Screening Criteria Min Sheng,† Florin Dan,*,‡ Steve Horsch,§ Robert Bellair,§ Marabeth Holsinger,† Travis Scholtz,† Stephan Weinberg,∥ and Alan Sopchik⊥ †

Reactive Chemicals, The Dow Chemical Company, Midland, Michigan 48667, United States Analytical Sciences, The Dow Chemical Company, Midland, Michigan 48667, United States § Reactive Chemicals, The Dow Chemical Company, Freeport, Texas 77566, United States ∥ PM Tech Center Methacrylates, The Dow Chemical Company, Deer Park, Texas 77536, United States ⊥ Process Dev & Optimization, The Dow Chemical Company, Deer Park, Texas 77536, United States

Org. Process Res. Dev. Downloaded from pubs.acs.org by ALBRIGHT COLG on 04/29/19. For personal use only.

‡

ABSTRACT: The United Nations Recommendations on the Transport of Dangerous Goods, Model Regulations, Rev.19 (2015) has a new requirement for the determination of the SAPT (Self-Accelerating Polymerization Temperature) for polymerizing substances. Accordingly, polymerizing substances may be subject to temperature monitoring or temperature control depending upon their SAPT and type of transportation packaging. The requirement states the SAPT shall be determined in accordance with test procedures established for SADT (Self Accelerating Decomposition Temperature) for selfreactive substances. There are several SADT methods which differ in their measurement techniques. Recent work has shown that SADT results for materials with autocatalytic or autoaccelerated reactions can differ significantly depending upon which SADT method was applied. To ensure consistent SAPT values for safe transportation, several industry consortia committees (Basic Acrylic Monomer Manufacturers, European Basic Acrylate Manufacturers, and Methacrylate Producers Association), of which Dow is a member, met in a joint session and agreed to an intercompany effort to identify the best method on the basis of good science, readily available technology, and flexibility in packaging applications. This study highlights the technical approach developed and validated at Dow for inhibited methyl methacrylate (MMA) using isothermal micro calorimetry, modeling, simulations, and SADT H1 testing. In this paper, several calorimetric methods were evaluated and the corresponding kinetic equations describing the monomer polymerization were established. Isothermal experiments performed in micro calorimeters with a well-controlled temperature and high sensitivity were determined as the best method for estimating the polymerization kinetics. The studied monomer was methyl methacrylate, and the effect of inhibitor concentration, headspace volume, and mixing during sample preparation on PIT were carefully examined. KEYWORDS: methyl methacrylate, self-accelerating polymerization temperature (SAPT), calorimetric method, polymerization kinetics

1. INTRODUCTION The United Nations Recommendations on the Transport of Dangerous Goods, Model Regulations, Rev.19 (2015)1 has a new requirement for the determination of the Self-Accelerating Polymerization Temperature (SAPT) for polymerizing substances. Accordingly, polymerizing substances may be subject to temperature monitoring or temperature control depending upon their SAPT and type of transportation packaging. The requirement also states the SAPT shall be determined in accordance with test procedures established for the determination of Self-Accelerating Decomposition Temperature (SADT) for self-reactive substances. According to “Recommendations on the Transport of Dangerous Goods, Manual of Tests and Criteria”,2 SADT is the lowest environmental temperature at which the temperature increase of a chemical substance in a specified commercial package is at least 6 °C during a period of 7 days, starting from the time when the chemical substance temperature is 2 °C lower than the environmental temperature. There are four recommended test © XXXX American Chemical Society

methods for SADT determination which differ in their measurement techniques: H1, United States SADT test (isothermal oven test with an actual transport package); H2, Adiabatic storage test (adiabatic test with a 1.0 or 1.5 L glass Dewar and heat balance evaluation of the transport package); H3, Isothermal storage test (heat flow measurement of 20 g sample and heat balance evaluation of the transport package); and H4, Heat accumulation storage test (isothermal test with 400 mL sample in a Dewar vessel which has the heat loss per unit sample mass characteristics similar to the transport package). Obviously, performing an H1 test for large volume packages is not practical based on available oven size, high cost, and the challenge to mitigate potential hazards related to a runaway reaction while the H4 method carries the difficulty to build a vessel with the same heat loss characteristics as the packages.3 Therefore, H2 or H3 methods are preferred in Received: January 8, 2019 Published: April 18, 2019 A

DOI: 10.1021/acs.oprd.9b00011 Org. Process Res. Dev. XXXX, XXX, XXX−XXX

Organic Process Research & Development

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industry, especially with the wide application of commercial calorimeters.4,5 Both H2 and H3 methods involve reaction kinetic measurements with a relatively small quantity of sample and then determining SADT by performing the heat balance calculation for a desired package. However, recent work6 has shown that SADT results for materials with induction times can differ significantly depending upon which SADT method was applied. Considering the cost to implement the temperature control as well as the potential hazards that could be present in a large transportation vessel, such as railcar or a ship, an incorrect SAPT result is unacceptable. To ensure consistent SAPT values for safe transportation, several industry consortia committees (Basic Acrylic Monomer Manufacturers, BAMM, European Basic Acrylate Manufacturers, EBAM, and Methacrylate Producers Association, EPA), of which Dow is a member, met in a joint session and agreed to an intercompany effort to identify the best method on the basis of good science, readily available technology, and flexibility in packaging applications. It is well-known that spontaneous polymerization is a safety concern during transportation of polymerizing substances.7−9 Large quantities of monomers are transported worldwide by railcars, ships, and trucks, which are not designed to mitigate the hazards of a runaway polymerization. Inhibitors are widely used to prevent the polymerization from occurring during transportation and storage.8,10 Inhibitors can stabilize monomers for some period of time (polymerization induction time, PIT) until either oxygen or inhibitors have been depleted, after which the polymerization reaction proceeds at its normal rate. Typical inhibitors work by having the ability to stabilize free radicals thereby reducing the bulk polymerization rate. For instance, 4-methoxyphenol (MEHQ) can transfer a hydrogen atom to an active radical to form a less active, stabilized radical,11 while oxygen or quinone-based compounds can be added to an active radical to reduce the activity.8 However, the effectiveness of inhibitors depends on the temperature, the nature and the concentration of the added inhibitors, the availability of molecular oxygen (aerobic inhibitors), the byproducts spectrum, and the concentration of impurities. The mutual interaction of these parameters makes the measurement and prediction of monomer stability more challenging.12,13 Since many effective inhibitors are being used worldwide to significantly extend the shelf life of monomers for transportation purposes, a good method for monomer SAPT determination should include the PIT of monomers. In this paper, several calorimetric methods reported for SADT determination were evaluated to determine the PIT and full chemical kinetics for a monomer, methyl methacrylate (MMA) with 4-methoxyphenol (MEHQ) as the inhibitor. An additional paper will present the measurement of the overall heat transfer coefficient, H1 test with MMA in a 1 gallon drum, and SAPT determination.

Table 1. Actual MEHQ Concentration in MMA Samples by GC Analysisa Sample

Actual MEHQ concentration by GC analysis (ppm)

Original MMA from SigmaAldrich Fresh MMA from distillation Fresh MMA with 5 ppm MEHQ Fresh MMA with 10 ppm MEHQ Fresh MMA with 20 ppm MEHQ Fresh MMA with 25 ppm MEHQ Fresh MMA with 50 ppm MEHQ a

25 3 4.8 12 21.3 26 59

Uncertainty of GC results is 10%.

MEHQ, which are not commercially available, to be obtained in order to study the effect of inhibitor concentration on the PIT. The distillation was controlled at 62.4 °C and 200 mmHg. The condenser and collector for uninhibited MMA were cooled with dry ice. The actual MEHQ concentration of the samples was determined by GC analysis, as listed in Table 1. 2.2. Calorimetric Testing To Determine Chemical Kinetic Parameters. 2.2.1. Stepwise Isothermal Tests on DSC (Differential Scanning Calorimetry). A SENSYS-evoDSC manufactured by Setaram, France, was employed for stepwise isothermal experiments. The sample and reference sensors in this instrument are composed of 120 thermocouples mounted in a cylinder that completely surrounds the measurement zone. The sensors are mounted in a calorimetric block that is water cooled to eliminate any environmental variations resulting in a highly precise and robust sensor with a unique level of specific sensitivity. High pressure crucibles (140 μL, Setaram) capable of withstanding pressures up to 7400 psi at 600 °C were used in this study. A 65 mg sample was transferred into the high pressure crucible, and the crucible was sealed by tightening the lid. The experiment involved “heat-isothermal” cycles. Heat steps were set from 50 to 140 °C with an interval of 5 °C. Each isothermal step was carried out for a period of 1 h. In order to create a baseline, a blank experiment, empty crucible, was run following the same temperature−time profile. 2.2.2. Adiabatic Test on ARC and Constant Heating Rate Test on DSC. An ARC manufactured by Thermal Hazard Technology was used in this study. 4.5 g of MMA sample was loaded into a standard Titanium ARC sphere with air as the headspace. The ARC experiment was performed with a HeatWait-Search (HWS) mode. A heat step of 5 °C, waiting time of 30 min, and a detection threshold of 0.02 °C/min were utilized. The Phi factor calculated from mass and heat capacity was 2.04.14 A Q2000 DSC from TA Instruments was used for the constant heating rate tests in this study. An ∼10 mg sample was loaded into a glass ampule and then flame-sealed with air as the headspace. During the flame sealing of the glass the sample-containing portion of the ampule was cooled with liquid nitrogen. The sealed ampule had a total internal volume of ∼25 μL and is able to withstand pressures up to 1000 psi at 400 °C. It effectively prevents the escape of any tested chemical or the products from reaction.15

2. EXPERIMENT 2.1. Sample Preparation. Chemicals used in this study include MMA (Aldrich 99%) with less than 30 ppm MEHQ (Aldrich 99%). Gas Chromatography (GC) analysis indicated an MEHQ concentration of 25 ppm (Table 1). A portion of the MMA sample was vacuum distilled to remove MEHQ, and the freshly distilled MMA was portioned into appropriate amounts and varying amounts of MEHQ were added. The approach allowed for specific concentrations of B



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2.2.3. Isothermal Tests with Micro Calorimeters. Micro calorimeters offer a well-controlled temperature and a high sensitivity to heat signal. The calorimeters used in this study were Setaram C80 (temperature resolution ±0.1 °C, resolution10 μW) and TAM III (temperature resolution < ±0.1 °C, resolution 0.2 μW). TAM III was used to study several parameters, such as liquid filling level and MEHQ concentration. Glass cells with a total internal volume of 4 mL were used for isothermal calorimetric tests. Typically, 3.2 mL of liquid sample (corresponding to 80% filling level) were loaded in the glass cell, while, in the reference side, there was another glass cell containing an equivalent mass of glass beads. Heat flow to/from a sample was recorded over the duration of the isothermal test. The moment the sample cell was placed into the calorimeter was taken to be the “zero” moment of the test. Since an isothermal test records heat flow over the duration of the test, a sensitive calorimeter can measure both the small heat signal during the induction period and the continuous heat flow generated by the bulk polymerization reaction. The moment when the heat signal becomes significant is the point when the bulk polymerization reaction starts to take place. Polymerization induction time (PIT) is defined by the time from the “zero” moment to the start point of bulk polymerization, an extrapolated onset time, determined on the thermogram as the intersection of the extrapolated baseline and a line tangent to the start of polymerization exotherm. The time elapsed to the measured onset was used to define the PIT for isothermal tests in this study (1390.92 min in Figure 1).16,17

3. RESULTS 3.1. Calorimetric Testing. 3.1.1. Method A: Stepwise Isothermal Method. Yu and Hasegawa18 reported a stepwise isothermal calorimetric method for SADT determination. On a SETARAM C80, they measured the stepwise isothermal heat flux of the same sample for a period of about 200 min at every 10 °C. With the assumption that the conversion, associated with the decomposition reaction, of the tested sample was insignificant in the temperature range of the experiment, the chemical kinetic parameters were derived from stepwise isothermal heat flux data. The Semenov model was used to determine the SADT. They showed a good agreement between their SADT results and others for a dozen self-reactive substances, most of them were organic peroxides. Since the investigated range of temperature is lower than the onset temperature measured by a conventional type of differential scanning calorimeter, the authors assumed that the mass of sample during the measurement, M, is equal to the initial mass, M0, because the reactant consumption was close to zero. The rate expression for the consumption of reactant is defined as M

dH = ΔHAM 0n exp( −E /RT ) dt

(1)

Taking the natural logarithms of both sides of eq 1, we obtain eq 2: E i dH zy zz = ln AΔH + n ln M 0 − lnjjjM RT k dt {

(2)

By plotting the heat flow values measured at each temperature at a constant mass (M0) by isothermal calorimetry on a graph of logarithms of heat flow (ln(M·dH/dt)) versus inverse temperature (1/T), we can easily calculate the activation energy (E) from the slope of the straight fitting line. With the stepwise isothermal calorimetric method applied and the temperature range extended up to 140 °C, MMA with 25 ppm MEHQ was tested on SENSYS-evo-DSC, Setaram, France, in high-pressure cells. The baseline signal (empty cell) was subtracted from the measured heat flux of the MMA sample and then plotted in Figure 2a. The measured heat is relatively small in the temperature steps from 60 to 100 °C, while the heat flow increased significantly in the isothermal step at 110 °C and reached the maximum during the ramping period from 110 to 120 °C; polymerization acceleration is not shown in Figure 2a. The activation energy, E, calculated from the slope in Figure 2b was about 139.78 kJ/mol. By assuming

Figure 1. Typical heat flow traces recorded during isothermal polymerization of MMA at 85 °C. The induction and polymerization regions are shown. The insert is a zoom-in at the PIT.

Figure 2. (a) Recorded heat flow at each temperature step versus time. (b) Relationship between logarithmic heat flow and inverse temperature for 25 ppm MEHQ inhibited MMA. C



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Figure 3. Evolution of the self-heating rate (a) and pressure (b) with temperature for MMA polymerization by ARC in HWS mode; (c) best fitting of the ARC data to nth-order rate law.

301 °C, respectively. The third exotherm was accompanied by increasing pressure, indicating that a gas generation decomposition reaction was occurring. As a rule of thumb, the reaction rate of an nth-order reaction, and the corresponding heat-flow rate, doubles when the temperature increases by 10 °C (the rate does not always double for a temperature increase of 10 °C, and when it does it only does so for a narrow temperature range; however, it is used here for illustrative purposes only). When a sample is tested in an ARC with a temperature step of 10 °C, the heatflow rate at the onset temperature should be approximately 2 times that at the prior temperature step, which is less than the detection threshold (0.02 °C/min). In other words, the onset heat-flow rate for an nth-order reaction should fall into the range from the detection threshold to approximately two times that (0.02−0.04 °C/min). However, multiple mechanisms, autocatalysis, or autoaccelerated reaction significantly deviate from this rule of thumb. During the waiting period before the detection onset (30 min in this test), the reaction mechanism may change, or enough radical species may be generated and thus greatly accelerate the reaction rate. Both may result in a much higher heat-flow rate at onset. As shown in Figure 3a, the onset heat-flow rate of the first exotherm was 0.47 °C/min, which is more than 10-fold the typical value (0.02−0.04 °C/ min). Obviously, such ARC data do not provide information about the mechanism change. As concluded by Whitmore and Wilberforce,20 because of the limited thermal sensitivity of the ARC instrument, SADT from ARC data has resulted in the adoption of the wide safety margins to cover irregularities produced by changes in kinetic mechanism, autocatalysis, phase change, evaporation, and so on. As such, using ARC data

the reaction order, n, zero for the induction period in eq 2, a value of 40.878 was obtained tor the intercept (ln ΔH·A) and 2.79 × 1015 s−1 for the preexponential factor, A, respectively. Although the application of this method was successful for organic peroxides, which normally follow an nth-order decomposition reaction, we found it of limited use for the monomers with low thermal activity during the induction period, such as inhibited MMA and other acrylics, due to the uncertainties related to accurately measuring very weak signals with respect to the real baseline, which usually is reliant on temperature. Therefore, the stepwise isothermal calorimetric method is not an appropriate method to obtain the kinetic parameters for monomers behaving similarly to MMA. 3.1.2. Method B: Adiabatic Method and Dynamic Method. ARC alone or the combination of ARC with other calorimeters,19 such as the thermal activity monitor (TAM),20 the heat flux calorimeter (C80), and DSC,21,22 are one of the most popular methods to gain the kinetic parameters for SADT determination. The combination of ARC (adiabatic mode) and DSC (heat conduction mode) greatly improves the measurement efficiency and result accuracy. Figure 3 shows the heat-flow rate, and the pressure of the MMA samples with 25 ppm MEHQ measured by ARC operated in HWS mode. Since the sample heat-flow rates during the heating period and waiting period were mainly caused by the external heat source, only the heat-flow rate during the exotherm period was plotted. As shown in Figure 3a, there were three exotherms recorded by ARC: the first main exotherm had an onset of 113 °C and a heat-flow rate of 0.47 °C/min. The second and the third exotherms show a lower heat-flow rate of 0.03 °C/min, with onsets at 241 and D



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Figure 4. (a) Heat flow and (b) heat of polymerization evolution with temperature during the polymerization of MMA inhibited with 25 ppm MEHQ at different scan rates.

Figure 5. Nonisothermal polymerization of inhibited MMA. (a) Heat flow vs temperature at three scanning rates and (b) effect of inhibitor concentration on the polymerization onset temperature at the same scanning rate (0.2 °C/min).

but remarkable impact on the induction time. During the induction period, the heat release of the samples is negligible; therefore, the instrument initiates the next HWS step until polymerization is detected. Samples having shorter PIT values may have a lower detected onset temperature (106 °C vs 113 °C). However, owing to the long equilibration times required for accurate ARC data, it is challenging to accurately determine the kinetic parameters for the induction period. Figure 3c show a comparison of the measured ARC data of 25 ppm MEHQ inhibited MMA, open symbols, and fitted, according to nth-order rate law, black dashed line, respectively. The kinetic parameters were as follows: 1.006 × 1009 s−1, 95.532 kJ/mol, and 1.35 for the preexponential factor, A, activation energy, E, and reaction order, n. The kinetic equation accurately describes the self-heating rate on the ascending part of the curve but overestimates the peak rate. Dynamic DSC testing for the MMA samples with 25 ppm MEHQ was conducted at different temperature scanning rates, and the results are presented in Figure 4. Owing to the ceiling temperature, fast heating rates (2, 5, and 10 °C/min) result in a lower overall heat release (403.2, 213.3, and 138.9 kJ/g, respectively) and, consequently, low ultimate conversions (74.2%, 39.3%, and 25.6%, respectively). The faster the temperature scanning rate, the shorter the time to reach the ceiling temperature and the lower conversion of the polymerization reaction. At slow heating rates (0.2, 0.5, and 1 °C/min), the polymerization reaction was complete prior to reaching the ceiling temperature. The nonisothermal method is very attractive because the kinetic data can be obtained in a relatively short period. However, the analysis of nonisothermal kinetics is quite

as the sole source of calorimetric data to determine the SAPT of a monomer may result in an erroneous value, especially given such reactions typically involve multiple steps and an autoacceleration reaction. The reported heat of polymerization of MMA is −543.3 J/ g.16 The total heat from the first exotherm and second exotherm was only −326.2 J/g (ARC experiments often underestimate the heat of reaction owing to many factors but typically are within 20% of the expected value). As discussed by Dainton,23 the polymerization conversion of MMA is thermodynamically limited by the presence of a ceiling temperature (167−207 °C). Polymerization reaction of monomer to polymer dominates at a temperature below the ceiling temperature (first exotherm in ARC data), while the decomposition reaction from polymer to monomer or fragments takes over when the temperature is above the ceiling temperature (third exotherm in ARC data). An additional ARC test was also carried on a freshly distilled MMA sample (MMA with 3 ppm MEHQ) under the same testing conditions as those for the previous MMA sample (MMA with 25 ppm MEHQ). The result is presented in Figure 3 as well. The first exotherm of this less inhibited sample had a detected onset of 106 °C and a detection heatflow rate of 0.33 °C/min, which were both slightly lower than that of MMA with 25 ppm MEHQ. However, both samples showed a very similar thermal activity (heat-flow rate) and pressure behavior. This is consistent with isothermal calorimetric test results for these two MMA samples under the same testing conditions, which showed a similar peak, with different onset times. This confirms that the inhibitor level has little impact, once consumed, on the polymerization reactions E



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complicated, since the sample during dynamic step may progress through multiple paths, each of them may have a different temperature dependence. Considering the shape of the polymerization peak, the number of peaks and/or shoulders in the isothermal and nonisothermal DSC thermograms may be different. Consequently, the kinetic parameters obtained from a nonisothermal study may not be good in predicting the isothermal behaviors. Comparing the shapes of the heat flow curves under isothermal, Figure 1, and dynamic mode, Figure 4a, the complete curves measured at scanning rates up to 1 °C/min, one can observe common characteristics such as the peak shape, with a log tail at the beginning of the accelerating part and an instantaneous onset as well as a sharp termination on the decelerating part, respectively. However, the induction period so noticeable in the isothermal measurements is difficult to deconvolute in the dynamic experiments. Its presence can only be assessed by the shift in the polymerization onset temperature, POT, when comparing MMA samples stabilized at different inhibitor concentrations. As Figure 5b shows increasing the MEHQ concentration from 3 to 25 ppm increases the polymerization onset temperature from about 99 to 116.4 °C, respectively. Only the thermograms showing the complete polymerization of MMA, i.e. taken at scanning rates up to 1 °C/min, were considered for nonisothermal kinetic evaluation, Figure 5a. Often the reaction rate dα/dt is described as a product of two functions, one of which is solely a function of temperature, k(T), and the other that is solely a function of conversion, f(α), as shown below: dα = k(T ) ·f (α) dt

Figure 6. Kissinger and Ozawa plots for Ea determination of inhibited MMA polymerization.

Table 2. Ea of Inhibited MMA Polymerization Obtained by Kissinger and Ozawa Methods Kissinger Ea

(3)

ij E yz i AE y ln β = jjj a zzz − ln F(α) − 5.331 − 1.052jjjj a zzzz j RTp z k R { k {

1000/Tp (K−1)

αp

0.2 0.5

125.12 135.03

2.5108 2.4499

0.819 0.853

1

146.96

2.3803

0.840

(kJ/mol) 95.2535 Kissinger A (min−1) 4.77 × 1010

E dα i dα y = lnjjjβ zzz = ln[A f (α)] − a RT dt k dt { For the autocatalytic reaction:

(4)

ln

where A is the preexponential factor, Ea is the apparent activation energy, R is the ideal gas constant, and T is the absolute temperature in Kelvin. Four kinetic methods are widely used to study the dynamic kinetics of thermosetting polymers, namely Kissinger, Ozawa, Friedman, and Flynn−Wall−Ozawa methods. The Kissinger, eq 5, and Qzawa, eq 6, are simple methods to calculate Ea: ij β yz E ji Q pAR zyz zz − a lnjjjj 2 zzzz = lnjjjj z j Tp z RTp k Ea { k {

Tp (°C)

96.8676

As shown in Table 2 the activation energies obtained by Kissinger and Ozawa methods are close each other, i.e. 95.25 kJ/mol and 96.87 kJ/mol, respectively. Since the Kissinger method allows determination of the preexponential factor, A, the corresponding activation energy is used for further determining the reaction order. The next step involves the estimation of the kinetic factor f(α). Based on the above Ea and A pair, the other parameters of the polymerization can be determined by the Friedman method which is based on eq 7:

An Arrhenius relationship is typically used for the temperature dependent function: ij −Ea yz jj zz dα = A ·e k RT {·f (α) dt

β (°C/min)

Ozawa Ea

f (α) = α m(1 − α)n

(7)

(8)

where m and n are kinetic exponents. Combining eqs 7 and 8 results in eq 9: ln

(5)

E dα i dα y = lnjjjβ zzz = ln A − a + m ln α + n ln(1 − α) t RT dt d k { (9)

Equation 9 can be solved by multiple linear regression, in which the dependent variable is ln(dα/dt), and the independent variables are ln α, ln(1 − α), and 1/T. Therefore, the values of A, m, and n can be obtained using the calculated Ea. The results of the multiple linear regression analysis are listed in Table 3. From here, the following final cure kinetics expression MMA inhibited with 25 ppm MEHQ was obtained:

(6)

where Tp is the peak temperature for the exothermic reaction and β is the temperature scanning rate, Q p = −[df (α)/dt ]α = αp α

and F(α) = ∫ dα /f (α). 0 Kissinger and Ozawa plots are shown in Figure 6. Good linear relationships were observed by using both kinetic methods. From the slopes of the straight lines of ln β/Tp2 vs 1/ Tp and ln β vs 1/Tp, Ea values of inhibited MMA polymerization were obtained and listed in Table 2.

i −95253.5 yz m dα zzα (1 − α)n = 7.54· 108 expjjj dt k 8.314·T {

(10)

In eq 10, m and n are the temperature scanning rate dependent reaction orders. In this study, in order to find a representative F



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AKTS − Thermokinetics and Thermal Safety Software was used for this part of kinetic modeling.24 Based on the Arrhenius equation, the logarithm of the conversion rate, dα/dt, as a function of the reciprocal temperature, 1/T(tα), at any conversion α can be expressed as

Table 3. Kinetic Parameters Evaluated for Inhibited MMA Polymerization in Dynamic Mode β (°C/min) 0.2 0.5 1.0

Ea (kJ/mol) 95.2535

A (min−1) 4.498 × 10 4.544 × 1010 4.531 × 1010 10

mean 4.524 × 10

10

m

n

3.24 3.41 3.77

1.13 1.14 1.47

E (α ) i dα y lnjjj zzz = ln(A′(α)) − RT (tα) k dt { α

expression between the nonisothermal conditions, they were represented in the form of a first-order polynomial expression, Figure 7, represented by eqs 11 and 12 for m and n, respectively. m = 0.6784·β + 3.0892

(11)

n = 0.4451·β + 0.9921

(12)

(13)

where T, t, A, E, and R are the temperature, time, preexponential factor, activation energy, and gas constant, respectively. The logarithm of the conversion rate, dα/dt, versus the inverse temperature, 1/T(tα), shows a straight line dependence with the slope m = −E(α)/R and the intercept on the y-axis equal to ln(A′(α)) with A′(α) = A(α)f(α). The dependences of E(α) and A′(α) on the reaction progress, α, obtained from dynamic method are presented in Figure 9a. The apparent activation energy and the preexponential factor are not constant and change with increasing reaction progress, α. After the determination of the values of E(α) and A′(α), it is possible to predict the reaction rate, dα/ dt, or reaction progress, α, for any temperature profile, T(t). Figure 9b shows the measured (color lines) and predicted normalized reaction rates for MMA polymerization at three temperature scanning rates. Details on the numerical optimization routine of the software can be found in ref 24. Clearly, the isoconversional kinetic (model free) method provides a superior prediction of inhibited MMA polymerization under dynamic conditions as compared to the model fitting method (Figure 8). 3.1.3. Method C: Isothermal Method on Microcalorimeter. An isothermal calorimetric method utilizing a TAM has been used for SADT evaluation of autocatalytic or autoaccelerated materials.25 The method allows for characterization of complex reaction mechanisms where autocatalysis or some physical phenomena takes place. Most importantly, a well-controlled temperature and the high heat flux sensitivity of micro calorimeters is essential to reliable measurement of the monomer PIT. Isothermal calorimetric tests were carried out for MMA samples with 25 ppm MEHQ at four different temperatures in a C80 calorimeter. The results are presented in Figure 10b and also listed in Table 4. The average heat of polymerization was −531.6 J/g with a standard deviation of 8.9 J/g. This corresponds to a conversion of 97.9 ± 1.5%, which indicated that the polymerization progress at low temperatures, but yet in the proximity of the polymer’s Tg, is not influenced by neither the diffusion or ceiling temperature, respectively. Based on the shape of the heat flow curves, Figure 10a, one can identify the characteristic induction and the autocatalytic periods, respectively; autocatalysis is characterized by a long accelerating part, with instantaneous rate right at the end of the induction time and a sharp descending part, indicating rapid termination. It is known that the acrylic monomers, excepting acrylic acid, show a well-defined induction period, with very low thermal activity during this period, and the beginning of polymerization is marked by a sharp change in the heat flow. The PIT is the period in which the inhibitor depletion takes place. The reciprocal PIT is a measure of the overall reaction rate for all reactions occurring during inhibitor depletion. It was found that PIT increases exponentially with decreasing the temperature. Thus, an Arrhenius-like relationship is found by plotting the logarithm of PIT against the inverse of absolute

Figure 7. Reaction orders m and n as a function of temperature scanning rate.

The fittings, Figure 8, were in reasonable agreement with the measured polymerization rate (dα/dt) versus polymerization

Figure 8. Comparison of the experimental values (color symbols) and calculated values (black lines), eqs 8−10, at three scanning rates.

degree (α) data for each temperature scanning experiment. The model underestimates the reaction rate at low degrees of conversion, α < 0.3, since the simple autocatalytic model does not account for the instantaneous rate at the beginning of polymerization, i.e. the shoulder at α = 0. An alternative approach for the evaluation of the kinetic parameters, particularly the activation energy E and the preexponential factor A, makes use of the isoconversional methods. The advanced thermokinetic software package G



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Figure 9. (a) Activation energy E (kJ/mol) and pre-exponential factor term expressed as A′(α) = A(α)f(α) (s−1) in logarithmic form determined by differential isoconversional kinetic analysis. (b) Comparison between experimental (colored) and predicted (dashed black) normalized reaction rates of the MMA polymerization under nonisothermal conditions.

Figure 10. Isothermal polymerization of MMA with 25 ppm MEHQ: (a) heat flow and (b) released heat vs time at different temperatures.

Table 4, was obtained and the fitting parameters are given in eq 14.

Table 4. Isothermal Calorimetric Result of MMA Polymerization Inhibited with 25 ppm MEHQ and 80% Filling Level Sample Temp (°C)

Bath Temp (°C)

Sample Size (g)

PIT (min)

Total Heat (J/g)

89.4 84.3 81.0 76.8

90.0 85.0 81.6 77.5

3.033 3.058 3.051 3.063

800.3 1388.8 2403.9 4110.9

−544.4 −536.5 −526.8 −528.9

ln

1 1000 = −16.752· + 39.555 PIT T

(14)

with PIT in min. In order to validate eq 11, an additional experiment was carried out at a lower temperature (69.85 °C). The measured PIT of 10929.6 min compares well to the extrapolated value according to eq 11, i.e. 10919.5 min, which is within the 99% confidence interval. Since almost no polymerization takes place with most acrylic monomers during the induction period, one can exploit this future to estimate, in a conservative manner, the monomer’s stability under the transportation and storage conditions. In Figure 12, the shelf life of MMA with the same inhibitor level from the Dow monomer reference27 was plotted against the measured PIT in this study. It was noticed that the shelf life of the Dow product was always longer than the measured PIT. There are multiple reasons for this deviation. First, the different sample sources could cause this difference. The Dow sample was freshly produced, while the sample in the measurements was shipped from Aldrich. In addition, Dow’s monomer shelf life is determined by using an open sample cell with ambient oxygen access to the monomer. In other words, they were measured with an infinitely small liquid filling level. Finally, in the historic stability tests, significant reaction progress has to occur in order to determine that the induction time has been exceeded; conversely, almost no conversion has occurred when the micro calorimeter detects the exothermic polymerization reaction.

temperature (1/K).8−11,26 As shown in Figure 11, a linear relationship between the logarithms of PIT from the isothermal calorimetric data and the inverse of temperature,

Figure 11. PIT estimation and validation. PIT estimation based on four temperatures and validation of the PIT at a new temperature. H



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the diffusion of oxygen molecules from the top to the bottom in a big vessel may require considerable time. In order to study the effect of the inhibitor level on MMA PIT, a fresh MMA sample was prepared by distilling the MMA purchased from Aldrich. The distilled samples were spiked to different concentrations of MEHQ (Table 1). To reduce the variation caused by mixing, the samples were vigorously shaken, for about 2 min, prior to being loaded into the testing cell. The PITs of the MMA samples at 84.3 °C were plotted against the MEHQ concentration (Figure 14). A linear

Figure 12. Shelf life of the investigated MMA samples (filled triangles and circles) vs the historic shelf life of Dow stabilized MMA product (full line).

Normally, a low liquid filling level implies a large amount of headspace air in a closed sample cell, as well as a large amount of available oxygen per a unit volume of liquid monomer, which extends the monomer’s PIT. In order to confirm this effect of liquid filling level on monomer PIT, additional isothermal calorimetric tests were carried out by using the same MMA sample and temperature. As shown in Figure 13a the monomer PIT decreased with increasing the liquid level. In addition, getting more dissolved oxygen gas into monomer liquid increases the PIT. In this study, the dissolved oxygen content of the monomer was increased by shaking the MMA sample in a large vial with a 1:3 volume ratio of liquid to air prior to being loaded into the testing cell. As presented in Figure 13b the PITs of such shaken samples at different temperatures were from 44% to 64% longer than that of the unshaken samples. Based on the inhibition mechanism proposed in literature,8−11,26 during the induction time the dissolved oxygen combines with the free radicals to form less active peroxide radicals, while MEHQ functions by reacting with these peroxide radicals to form stable products. Without oxygen molecules, MEHQ is a poor inhibitor because it cannot directly terminate the activity of the initial free radicals. In addition, even with the depletion of MEHQ, excess oxygen hinders the activity of the radicals resulting in some degree of inhibition. Therefore, both a large headspace and enhanced mixing can increase the PIT of inhibited monomers. On the other hand, the PIT of an inhibited monomer stored in a static vessel without any mixing may be significantly shorter than what’s expected by measuring with a small sample size, because

Figure 14. Impact of MEHQ concentration on the monomer PIT: (●) fresh MMA; (◆) as-received MMA.

relationship was found between the PIT and the inhibitor concentration in the low range of MEHQ concentration, while the PIT of the sample with a high concentration of MEHQ (59 ppm) significantly deviated from the linear relationship but was fitted to a second-order polynomial. As discussed previously, the effectiveness of MEHQ requires the presence of oxygen. If there is not enough oxygen, MEHQ will not stabilize the monomer. As such, samples with a low level of MEHQ (3−25 ppm) were not oxygen limited and a linear relationship existed between the inhibitor level and the induction time. Conversely, the sample prepared with a high concentration of MEHQ (59 ppm) was oxygen deficient in the sealed system and the relationship between inhibitor concentration and induction time did not correlate with the samples having lower concentrations of MEHQ. As shown in Figure 14, the as-received MMA sample (shaken) had a PIT of 34.1 h, which was only 67.8% of the value calculated using the linear equation obtained from MMA samples prepared via distillation and subsequent addition of

Figure 13. Impact of oxygen availability on monomer PIT: (a) liquid filling level; (b) shaken vs unshaken vials. I



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acrylic acid is in the range of 2400 to 3500 at 55 °C and that of oxygen in MMA is 33 000 at 50 °C.11 Such high values ensure the free radicals generated from the precursors become deactivated by inhibitors, provided there is enough inhibitor, so that the concentration of active free radicals in the monomer is maintained at a significantly low level. Thus, the kinetics of inhibited MMA polymerization is offered as a combination of two models, a lag time and polymerization model, respectively. They can accurately predict the total polymerization of the inhibited monomer, starting with the depletion of the inhibitor and continuing with the kinetic reaction. 3.2.1. Lag Time (Zero-Order) Method. If the concentration of the monomer or other precursor is constant during the induction period, the inhibitor consumption follows a pseudozero-order reaction. The rate of inhibitor consumption can be expressed as below:

MEHQ. The reason for the shorter PIT was not studied but could be the result of peroxide formation or other impurities that were removed during the distillation when preparing the new samples. The PITs of the newly prepared samples were in better agreement with historical shelf life data of Dow MMA (Figure 12). Therefore, calorimetric studies to determine SAPT should be performed on samples that are representative (same source) as the product being shipped. Isothermal DSC tests are widely used to compare the effectiveness of inhibitors. Since the available oxygen is a critical variable for accurate PIT measurement, the calorimetric test to simulate a transportation condition should control the ratio of headspace to liquid monomer. Because of the small sample size utilized in most DSC testing, obtaining a reasonable headspace to liquid ratio can be challenging, but for liquid volumes greater than 1 mL in a sealed system, we have been able to achieve consistent and reasonable results. Further, under quiescent conditions, in a large container, the diffusion rate of oxygen in monomer may result in inadequate oxygen concentration to maintain inhibitor effectiveness in the lower portions of the vessel. Therefore, care should be taken when applying PIT results obtained at the small scale to such systems. Conversely, vessels during shipping (road, track or sea) are expected to have enough convection to ensure good distribution of oxygen on a short time scale making results obtained on the small scale quite reasonable. In addition, it was observed that the escape of monomer sample from the testing vial during an isothermal calorimetric test resulted in a significantly longer PIT. This is not surprising given the monomer is more volatile than the MEHQ effectively increasing the concentration of MEHQ in the remaining monomer. Therefore, the sample mass should be checked before and after the calorimetric test to verify no leaking occurred during the test. 3.2. Kinetic Model of Inhibited MMA Polymerization. As shown in Figure 1, the thermally initiated polymerization reaction of MMA involves an induction region and an autocatalytic region. The kinetic model for the entire polymerization profile should be able to predict the reaction rate in each step (Figure 15). Due to thermal initiation, free radicals are generated from the monomer molecule or other precursors. During the induction period, inhibitors are able to stabilize the monomer by combining with the free radicals to form stable products. Normally, an effective inhibitor has a high inhibitor constant (kz/ki). For instance, the inhibitor constant of MEHQ in

i E y i E y d[Inhibitor] = k inC = CA in ·expjjj− a zzz = A z ·expjjj− a zzz dt k RT { k RT {

(15)

Since the inhibitor consumption rate is constant during the induction period in isothermal tests, this rate can be obtained as the total inhibitor concentration (Xin) divided by time (PIT). Therefore, there is a relationship between the PIT and temperature for the samples with the same inhibitor level, as below: ij A yz E 1 i 1 yz zz = lnjjj z zzz − a · lnjjj j z R T k PIT { k X in {

(16)

As plotted in Figure 11, the measured PIT of MMA with 25 ppm MEHQ at 80% filling level and at different temperatures by isothermal calorimetric tests gives the kinetic information on the pseudo-zero-order inhibitor consumption reaction. The corresponding rate constants, k0, as well as the activation energy, Ea0, and the apparent preexponential factor, A0 = Az/ xin, are collected in Table 5. Table 5. Kinetic Parameters of the Zero-Order Inhibition Period of MMA Polymerization Temp (°C)

1000/T (K−1)

89.4 84.3 81 76.8

2.7582 2.7976 2.8237 2.8576

k0 (s−1) 2.0826 1.2001 6.9332 4.0543

× × × ×

10−05 10−05 10−06 10−06

Ea = A0 = A0 =

139.276 2.512 × 1015 4.187 × 1013

kJ/mol min−1 s−1

The rate of reaction during the lag time (induction period) is described by eq 17: i −139276 yz dα zz = 4.187· 1013 expjjj dt k 8.314·T {

(17)

Determining whether the MEHQ or oxygen was depleted first at the end of induction period is not possible solely based on calorimetric results. Therefore, modification of the inhibitor concentration term (Xin) in the equation is not suggested without a full understanding of the relationship among MEHQ, oxygen, and free radicals. Assuming the oxygen is depleted first, a constant consumption rate at a single temperature results in a shorter PIT for a test with a higher filling level, since a high filling level reduces the volume of the

Figure 15. Simplified mechanism for thermally initiated polymerization reactions. J



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Figure 16. (a) Heat flow vs time; and (b) dα/dt vs α for inhibited MMA polymerization kinetic model.

Table 6. Parameters for the Isothermal Kinetic Model Temp (°C) 89.4 84.29 76.82 69.85

k1 (s−1) 1.012 6.351 3.351 1.560

× × × ×

k2 (s−1) −05

10 10−06 10−06 10−06

1.727 9.548 4.848 2.254

× × × ×

10−03 10−04 10−04 10−04

m

n

3.431 3.221 3.056 2.815

1.173 1.052 1.103 1.02

Ea1 = A1 = Ea2 = A2 =

97.86 1.28 × 1009 105.83 2.95 × 1012

kJ/mol s−1 kJ/mol s−1

Figure 17. (a) Arrhenius plots of the rate constants for Kamal equation. (b) Reaction order m as a function of absolute temperature.

3.2.2. Kinetic Polymerization Method. When the exact reaction mechanism is not known, models based on empirical rate laws are frequently used to describe the reaction rate. The nth-order and autocatalytic kinetics are the two most commonly used reaction mechanisms that describe isothermal reactions. Since the polymerization of inhibited MMA presents the main features of an autocatalytic process with an instantaneous rate higher than of zero at the beginning of the reaction, the Kamal equation, eq 18, was the obvious choice for modeling the MMA polymerization:

headspace and the total amount of oxygen available to the monomer. Therefore, in order to maintain the linear relationship in eq 17, it is important to keep the same filling level in calorimetric tests. For the same reason, it is also important to apply the same filling level in calorimetric tests as that in a transportation vessel, in order to predict the PIT of the monomer in the transportation vessel. Otherwise, a correction term is needed when the kinetic parameters from calorimetric tests are applied to predict the PIT of monomer in a particular transportation vessel at a particular fill level. Such correction can be obtained by performing micro calorimetry at different filling degrees and measuring the corresponding PIT, Figure 13a. By the end of the induction period, either the depletion of oxygen or MEHQ results in a reduction of free radical scavenging. As a consequence, active free radicals in the monomer accumulate to a level where the polymerization propagation rate dominates and initiates the bulk polymerization reaction. On the isothermal calorimetric thermogram (Figure 1), this moment corresponds to the onset of the kinetic control reaction, before which the inhibition reaction dominates the kinetics and after which the bulk polymerization reaction starts. Because of this, the onset of the kinetic control reaction is used to define the PIT.

dα = (k1 + k 2α m)(1 − α)n dt

(18)

k1 and k2 are the temperature dependent reaction rate coefficients for the noncatalytic and autocatalytic reactions, and m and n are reaction orders; k1 and k2 follow the Arrhenius relationship as presented in eq 2 and are given in Figure 17. The heat flow curves, Figure 16a, show the same features, found and described for the nonisothermal curves. The highly asymmetric peaks with maximum ranging in the conversion range from 0.8 to 0.85 depending on temperature, Figure 16b. In eq 18, k1 is the initial reaction rate at a given temperature and was determined directly from the reaction rate curve. Once parameter k1 was obtained, remaining parameters k2, m, and n were identified by a least-squares fitting technique directly K



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inhibitor, after which the kinetic model takes over with a description of the polymerization reaction. The lag-time region is described by eq 17 while eq 22 describes the polymerization region, respectively.

applied on dα/dt experimental plots versus the whole range of experimental conversion for each isothermal curing, Figure 16b. The rate constants and reaction orders for each run are collected in Table 6. The reaction orders, m and n, are close to ones found in the dynamic kinetic modeling (see Table 3). Arrhenius plots for the two rate constants are shown in Figure 17a. Linear equations for the rate constants are given in eqs 19 and 20. The pre-exponential factors and activation energies were determined from the y-intercepts and slopes of the linear equations and are given in Table 6. ij 1000 yz zz ln k1 = 20.974 − 11.77·jjjj z j Tpolym zz { k

(19)

m = 0.0303·T − 7.5566

(21)

i i −97860 yz dα zz = jjjj1.28 × 109 expjjj dt k 8.314·T { k i −105830 yz myzz zzα zz(1 − α)1.087 + 2.95 × 1012 expjjj k 8.314·T { {

(22)

with m calculated with eq 21. One can see in Figure 18 that eq 22, black dashed lines, reasonably describes the profile of polymerization progress, except at the beginning and by the end of it, where α is overestimated and underestimated, respectively. Alternatively, similar to the dynamic method, the model-free isoconversional approach can be used to model the isothermal polymerization of MMA. Figure 19a shows the variation of the activation energy and the apparent preexponential factor with the reaction progress, and Figure 19b compares the experimental and the predicted normalized polymerization rates. Once again, the isoconversional kinetic model better fits the measured data as compared to the Kamal kinetic model (see Figure 16b).

ij 1000 yz zz ln k 2 = 28.715 − 12.729·jjjj z j Tpolym zz (20) { k The reaction order m increases with increasing the temperature, Figure 17b, and was fitted to a straight line represented by eq 21. The reaction order n does not vary significantly with temperature, and a mean value of 1.087 was taken.

Finally, Figure 18 shows how the two models combine. First, the lag-time model demonstrates the rate of depletion of the

4. CONCLUSION The United Nations Recommendations on the Transport of Dangerous Goods, Model Regulations, Rev.19 (2015) has a new requirement for the determination of the Self-Accelerating Polymerization Temperature (SAPT) for polymerizing substances. Recent work has shown that SADT results for materials with autocatalytic or autoaccelerated reactions can differ significantly depending upon which SADT method was applied. This research aims to identify the best method on the basis of good science, readily available technology, and flexibility in monomer packaging applications. The selected monomer showed a well-defined induction period, with very low heat release during this period, followed by autoacceleration and rapid termination, respectively. Several calorimetric instruments, working under adiabatic or heat conduction modes, and under isothermal, temperature scanning, or stepwise isothermal temperature conditions have been used to acquire experimental data further used for kinetic modeling and accurately predicting the SAPT. The temperature stepwise calorimetric method by DSC and adiabatic

Figure 18. Lag-time model combined with the kinetic model. After the inhibitor concentration reaches zero, the polymerization kinetic model begins.

Figure 19. (Left) Apparent activation energy and preexponential factor variation as function of reaction progress. (Right) Experimental (colored) and predicted (dashed black) normalized reaction rates of MMA polymerization under isothermal conditions. L



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(6) Kossoy, A. A.; Sheinman, I. Y. Comparative analysis of the methods for SADT determination. J. Hazard. Mater. 2007, 142, 626− 638. (7) Krause, G.; Wehrstedt, K.-D.; Malow, M.; Budde, K.; Mosler, J. Safe Transport of Acrylic Acid in Railroad Tank Cars. Part 1: Determination of the Self-Accelerating Decomposition Temperature. Chem. Eng. Technol. 2014, 37, 1460−1467. (8) Hartwig, A.; Brand, R. H.; Pfeifer, C.; Dürr, N.; Drochner, A.; Vogel, H. Safety and Quality Aspects of Acrylic Monomers. Macromol. Symp. 2011, 302, 280−288. (9) Kirch, L. S.; Kargol, J. A.; Magee, J. W.; Stuper, W. S. Stability of acrylic monomers. Plant/Oper. Prog. 1988, 7, 270−274. (10) Levy, L. B. Inhibition of acrylic acid polymerization by phenothiazine and p-methoxyphenol. II. Catalytic inhibition by phenothiazine. J. Polym. Sci., Part A: Polym. Chem. 1992, 30, 569−576. (11) Cutié, S. S.; Henton, D. E.; Powell, C.; Reim, R. E.; Smith, P. B.; Staples, T. L. The effects of MEHQ on the polymerization of acrylic acid in the preparation of superabsorbent gels. J. Appl. Polym. Sci. 1997, 64, 577−589. (12) Li, R.; Schork, F. J. Modeling of the Inhibition Mechanism of Acrylic Acid Polymerization. Ind. Eng. Chem. Res. 2006, 45, 3001− 3008. (13) Tüdos, F.; Földes-Berezsnich, T. Free-radical polymerization: Inhibition and retardation. Prog. Polym. Sci. 1989, 14, 717−761. (14) Townsend, D. I.; Tou, J. C. Thermal hazard evaluation by an accelerating rate calorimeter. Thermochim. Acta 1980, 37, 1−30. (15) Tou, J. C.; Whiting, L. F. A cradle-glass ampoule sample container for differential scanning calorimetric analysis. Thermochim. Acta 1980, 42, 21−34. (16) Casson, V.; Snee, T.; Maschio, G. Investigation of an accident in a resins manufacturing site: The role of accelerator on polymerisation of methyl methacrylate. J. Hazard. Mater. 2014, 270, 45−52. (17) Faldi, A.; Tirrell, M.; Lodge, T. P.; von Meerwall, E. Monomer Diffusion and the Kinetics of Methyl Methacrylate Radical Polymerization at Intermediate to High Conversion. Macromolecules 1994, 27, 4184−4192. (18) Yu, Y.; Hasegawa, K. Derivation of the self-accelerating decomposition temperature for self-reactive substances using isothermal calorimetry. J. Hazard. Mater. 1996, 45, 193−205. (19) Lin, W. H.; Wu, S. H.; Shiu, G. Y.; Shieh, S. S.; Shu, C. M. Selfaccelerating decomposition temperature (SADT) calculation of methyl ethyl ketone peroxide using an adiabatic calorimeter and model. J. Therm. Anal. Calorim. 2009, 95, 645−651. (20) Whitmore, M. W.; Wilberforce, J. K. Use of the accelerating rate calorimeter and the thermal activity monitor to estimate stability temperatures. J. Loss Prev. Process Ind. 1993, 6, 95−101. (21) Sun, J.; Li, Y.; Hasegawa, K. A study of self-accelerating decomposition temperature (SADT) using reaction calorimetry. J. Loss Prev. Process Ind. 2001, 14, 331−336. (22) Lv, J.; Chen, L.; Chen, W.; Gao, H.; Peng, M. Kinetic analysis and self-accelerating decomposition temperature (SADT) of dicumyl peroxide. Thermochim. Acta 2013, 571, 60−63. (23) Dainton, F. S.; Ivin, K. J. Some thermodynamic and kinetic aspects of addition polymerisation, Quarterly Reviews. Q. Rev., Chem. Soc. 1958, 12, 61−92. (24) AKTS, Advanced Kinetics and Technology Solutions. https:// www.akts.com (AKTS-Thermokinetics and Thermal Safety Software). (25) Li, X.-R.; Koseki, H. Thermal decomposition kinetic of liquid organic peroxides. J. Loss Prev. Process Ind. 2005, 18, 460−464. (26) Levy, L. B. The inhibition of butyl acrylate by pmethoxyphenol. J. Appl. Polym. Sci. 1996, 60, 2481−2487. (27) Kirch, L. S.; Kargol, J. A.; Magee, J. W.; Stuper, W. S. 19 Stability of acrylic monomers. Plant/Oper. Prog. 1988, 7, 270−274.

method by ARC were found to be not sensitive enough alone for obtaining the kinetic parameters of many monomers. Also, the dynamic method by DSC was not a sufficient to investigate the monomer PIT, although some improvement in predicting the PIT was achieved making use of isoconversional kinetic analysis. Isothermal heat conduction calorimetry provided reliable data, showing a well-defined and reproducible induction period. These data were modeled by combining two models (lag-time and Kamal autocatalytic model), and the resulted model can accurately predict the behavior of the monomer, starting with the depletion of the inhibitor and continuing with the polymerization reaction. The effect of the inhibitor level, headspace volume, and mixing during sample preparation impact the PIT, and careful sample preparation is required for good results.

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AUTHOR INFORMATION

Corresponding Author

*Tel. +01 989-636-6299. E-mail: [email protected]. ORCID

Min Sheng: 0000-0002-5321-2627 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank BAMM, EBAMM, and MPA committees for their suggestions. NOMENCLATURE A preexponential factor (1/s) C constant Ea activation energy (kJ/mol) k reaction rate constant PIT polymerization induction time (min) R universal gas constant (8.314 J/mol·K) T temperature (K) X concentration (ppm) ΔHr heat of reaction (J/g) α degree of conversion

Subscript

i in p t z 1 2

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initiation inhibitor propagation termination pseudo-zero-order reaction nth-order reaction autoacceleration reaction

REFERENCES

(1) UN Recommendations on the Transport of Dangerous Goods, Model Regulations, United Nations; New York and Geneva, 2015. (2) UN Recommendations on the Transport of Dangerous Goods, Manual of Tests and Criteria, United Nations; New York and Geneva, 2009. (3) Fierz, H. Influence of heat transport mechanisms on transport classification by SADT-measurement as measured by the Dewarmethod. J. Hazard. Mater. 2003, 96, 121−126. (4) Fisher, H. G.; Goetz, D. D. Determination of self-accelerating decomposition temperatures using the Accelerating Rate Calorimeter. J. Loss Prev. Process Ind. 1991, 4, 305−316. (5) Kotoyori, T. The self-accelerating decomposition temperature (SADT) of solids of the quasi-autocatalytic decomposition type1. J. Hazard. Mater. 1999, 64, 1−19. M


Calorimetric Method To Determine Self-Accelerating Polymerization

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