Combustion characteristics of polymethyl methacrylate waste under different thicknesses for energy utilization

ABSTRACT Polymethyl methacrylate (PMMA), as a typical thermoplastic, has been widely used in numerous domains. However, large quantities of PMMA waste are generated due to the increasing demand. Combustion is one of the effective thermal-chemical methods to deal with solid waste and convert it into energy, so understanding the combustion characteristics of PMMA is essential. Furthermore, the thickness of a solid has significant effects on its combustion characteristics. Thus, combustion characteristics of PMMA with different thicknesses were studied by cone calorimeter experiments. The main combustion parameters were analyzed, such as combustion behavior, heat release, smoke production, etc. Results showed that the thermal thickness decreased as external heat flux increased. There was an excellent linear relationship between the peak values of three thicknesses and external heat flux. The ignition temperature increased, and the vaporization heat was 1.88 kJ/g. The thickness affected the effective combustion heat. Moreover, the positive relationship between smoke production rate peaks and heat release rate peaks indicated that PMMA was greatly flammable. The amount of CO2 released was almost 100 times that of CO.


Introduction
Polymethyl methacrylate (PMMA) is a common material in daily life.Due to its excellent properties such as optical properties, mechanical performances, easy processing, low cost, etc. (Zhang et al. 2022).PMMA has been broadly applied in transport, optical fibers, furniture, construction, and other fields (Luche et al. 2011).However, PMMA has inherent shortcomings, such as poor thermal stability and high flammability, which greatly limits its lifetime during use (Gao et al. 2004).Therefore, an amount of PMMA waste is produced.Because of recalcitrance to degradation, PMMA may raise environmental concerns as the waste accumulates in the environment (Parku, Collard, and Görgens 2020).There are several methods that can be adopted to dispose of PMMA waste, including landfill, reextrusion, chemical recycling, mechanical recycling, energy recovery, etc. (Szabo et al. 2011).
Considering the properties of PMMA, it is one of the few plastics that can offer valuable products (monomer, feedstock, and gasoline-range hydrocarbons) from its waste (Kaminsky and Eger 2001;Smolders and Baeyens 2004).In particular, pyrolysis and combustion are important and common thermo-chemical conversion methods, which can deal with PMMA waste in cleaner and more effective ways.Li, Ren, and Hu (2022) suggested that PMMA was extremely easy to be degraded into methyl methacrylate (MMA) monomer by pyrolysis, which could provide a lot of heat with burn characteristics.Chen and Xu (2020) noted that the MMA monomer obtained from the PMMA waste was a valuable chemical feedstock.Therefore, recycling the PMMA is a preferred way to dispose of the waste.
Since pyrolysis is a prior stage to combustion, compared with pyrolysis, combustion can meet more specific energy demands, such as heat energy.Ding et al. (2023) reported that combustion was a promising method to dispose of solid waste and convert it into energy.Szabo et al. (2011) noted that PMMA had high calorific values, so combustion was a proper energy production process.Furthermore, combustion greatly reduced the volume (90%-99%) of PMMA and mitigated the amount of waste.Ding et al. (2022) studied the combustion behavior and products of PMMA to deal with its waste and obtain valuable resources.To characterize the combustion properties, the combustion parameters and products are necessary.Rhodes and Quintiere (1996) investigated the combustion rate of PMMA with a cone calorimeter so as to understand the combustion characteristics.Luche et al. (2011) determined the main combustion products of PMMA with Fourier infrared transform spectroscopy technique.
Although the mentioned above studies provide much valuable insight into PMMA combustion, dimension such as thickness is not further considered, which has an effect on combustion characteristics.An et al. (2015) analyzed the effects of thickness on thermoplastic combustion behavior, which displayed that thickness affected the ignition time of the sample.Furthermore, Li et al. (2022) noted that the thickness could affect the combustion heat release and smoke characteristics of thermoplastics.However, when combustion is used to dispose of PMMA waste, there is a concern about which dimension or thickness is appropriate so that the combustion can release maximum heat and generate minimum environmental impact.Therefore, this paper studied the influence of PMMA thickness on its combustion behavior, heat release, and smoke production, which had no studies on PMMA combustion in the previous literature.The main objective of the work is to study whether thicknesses can affect PMMA combustion, and which thickness contributes to dealing with PMMA waste and converting the waste into heat energy in a more efficient and cleaner way.

Materials and experiments
PMMA used in this study was a typical semi-transparent thermoplastic, provided by Sanshuo Electronics Co., Ltd, China.The sample was made into a cube, and the dimension was 100 mm long and 100 mm wide.The thicknesses were 3, 6, and 10 mm, respectively.To decrease heat loss, two types of insulation materials were adopted, namely, the aluminum foil and ceramic fiber blanket, and they were used to wrap the rear surface and edges.Based on ISO 5660 standard (ISO5660, 2002), a cone calorimeter experiment was performed by Cone Calorimeter.The cone heater could provide several external heat fluxes to heat samples, and the ignition spark was employed to ignite the sample, which was located above the sample (Ding et al. 2020).The distance between the cone heater and the sample was 25 mm, which was adjusted by a lifting platform below the sample holder.
According to the set of external heat fluxes, the cone heater provided the required heat, and the ignition spark continuedly ignited the sample.If the sample was not ignited after 32 min, the experiment was terminated (ISO 17554 1998).Once PMMA was ignited, and some parameters were recorded by the computer, such as ignition time, mass loss rate, and heat release rate.There was a gas collection system, so the gas and smoke generated during the combustion were collected and analyzed by the gas analysis device.Therein, CO/CO 2 gas analyzer was the main component.In the current study, five external heat flows (20,35,50,65, and 80 kW/m 2 ) were selected.Each experiment was performed three times, and the data were average.

Thermal thickness
The thermal thickness of samples is regarded as the thermal penetration depth when they are heated to a specific temperature (Shi and Chew 2013), which can be used to distinguish whether the samples are thermally thick or thermally thin materials.If the thermal thickness of samples at ignition time is less than its physical thickness, samples are regarded as thermally thick materials.That is, the external heat cannot completely heat the entire samples, so the inner temperature of samples distributes unevenly.On the contrary, if the thermal thickness is more than its physical thickness, samples are thermally thin materials.The thermal penetration depth δ p (m) of samples can be calculated by the following formula (Torero 2004): where A is a constant, which in this study is 1 (Mikkola and Wichman 1989).λ is thermal conductivity (W/ m•K), ρ represents the density (kg/m 3 ), and c denotes specific heat (J/kg•K).In this study, λ = 0.432, ρ = 1.15�10 3 , c = 4.12�10 3 (Hopkins and Quintiere 1996;Rhodes and Quintiere 1996).t ig is the ignition time.
There is a linear relationship between δ p and ρ=q 00 e , which can be expressed as: where B and C 1 are constants.q 00 e is the external heat flux (kW/m 2 ). Figure 1 illustrates the linear relationship, and it shows that the thermal thickness of samples increases as external heat flux decreases.For the 3 mm PMMA, the thermal thicknesses of the samples are all less than 3 mm (the physical thickness).For 6 mm and 10 mm of PMMA, the maximum thermal thicknesses of samples are all less than 5 mm.Hence, three different thicknesses of PMMA are thermally thick materials.The linear relation between the δ p and ρ=q 00 e is shown as: The relationship between the thermal thickness, density of PMMA and the external heat flux.
ENERGY SOURCES, PART A: RECOVERY, UTILIZATION, AND ENVIRONMENTAL EFFECTS

Ignition time
Ignition time characterizes the combustion and decomposition characteristics of samples (Dao et al. 2013).Samples with shorter ignition time mean that they are more easily to be ignited.Moreover, the correlation between ignition time and external heat flux can be applied to obtain the combustion characteristic parameters, such as ignition temperature and critical heat flux, etc.The variation tendency of ignition time against external heat flux is shown in Figure 2(a), which depicts that the ignition time decreases dramatically as the external heat fluxes increase to 35 kW/m 2 , while under higher external heat radiation fluxes (50 kW/m 2 to 80 kW/m 2 ), the ignition time basically remains stable.
Based on ignition time, external heat flux and thermal physical characteristics, numerous relation equations have been proposed to analyze the combustion process of different samples (Shi and Chew 2013;Torero 2004).Therein, there is a linear relationship between the transformation form of ignition time t ig À n and q 00 e , which also is utilized to determine thermally thick (n = 1/2) or thermally thin (n = 1) characteristics (Janssens 1991;L 1993).The results show that PMMA is thermally thick, which is the same as the results of Section 3.1.As shown in Figure 2(b), the plots between the t ig À n and q 00 e have high linear relationships, which are shown as follows: The error analysis of the prediction formula is listed in Table 1S (Supplementary file).
Theoretically, the ignition time can be calculated by the following formula (Delichatsios, Panagiotou, and Kiley 1991): where T ig is ignition temperature (K), and T ∞ is circumstance temperature (298 K).Moreover, the thermal response parameter (TRP) can reflect the thermal behaviors of samples.The value of TRP is higher, the longer it takes for the sample to heat and ignite (Dao et al. 2013).The equation of TRP can be written as: Combined with Eq. ( 9), after a simple transformation, Eq. ( 10) can be expressed as: where C 2 is a constant.It can be seen from Eq. ( 11) that t À 1=2 ig and q 00 e can be plotted as a straight line when TRP is an invariant value.That is, there is a linear relationship between the two parameters (t À 1=2 ig and q 00 e ), which is in agreement with the above thermal thick ignition model.It can be known from the slope of Eqs.(6-8) that TRP values of different values are 250.00,263.16, and 312.50 kW/s −1/2 /m 2 , and the average value is 275.22 kW/s −1/2 /m 2 .Then, according to Eq. ( 10), the ignition temperatures of PMMA are 509.45K, 520.58 K, and 562.31K for three thicknesses (3, 6, and 10 mm), and the average ignition temperature is 530.78K.

Mass loss rate
The mass loss rate (MLR) is the mass flow rate of gasification or decomposition of solid or liquid fuels (Chen et al. 2020).Figure 3(a-c) show the MLR of PMMA with 3, 6, and 10 mm for different external heat fluxes.
Only one steep peak value can be found in the entire combustion process of PMMA with a thickness of 3 mm, and the entire sample burns completely after igniting.For 6 mm and 10 mm thicknesses, there are several decomposition stages.Furthermore, the external heat flux leads to a shift in the MLR curves and an increase in the peak values.After a period of delay time, the first stage begins at the ignition of PMMA samples and the rapid ascent of MLR after igniting.Subsequently, PMMA decomposition continues in the second and third stages, which corresponds to a plateau after the evolution of MLR and reaching a peak.The last decomposition stage is the reduction of MLR and consumption of the remaining PMMA sample.Finally, there is no residue in the sample holder.Furthermore, under the same thickness, the peak value increases as external heat flux rises.Figure 3(d) shows the variation of MLR of three thicknesses under 50 kW/m 2 .MLR rapidly increases in the initial stage, and then MLR of 3 mm remains rapidly increasing until reaching the maximum peak value of 34.5 g/s/m 2 , while the growth rate of MLR of 6 mm and 10 mm decreases significantly.Table 2S (Supplementary file) shows the MLR peak values, the corresponding time of MLR peak value, and the MLR average value of different thicknesses.MLR peak value and MLR average value increase, while the corresponding time shortens.Based on the model of Rhodes and Quintiere (Rhodes and Quintiere 1996), the transient value of MLR can be gained, which is written as: where m'' is the transient value of MLR (g/s/m 2 ).L denotes the latent heat of the vaporization of samples (kJ/g).q 00 f ;c and q 00 f ;r represent convective heat flux and radiation heat flux (kW/m 2 ).q 00 cond is heat conduction loss of samples (kW/m 2 ).σðT 4 v À T 4 1 Þ represents radiation heat loss on the surface of samples (kW/m 2 ).T v denotes the vaporization temperature of samples (K).
To simplify the difficulty of calculation, previous studies (Janssens 2003;Quintiere and Rangwala 2004) point out that q 00 f ;c and q 00 f ;r can be deemed as constants approximately under the case of steadystate (or quasi-steady-state) combustion or reaching the MLR peak values for specific materials and sample size.Additionally, q 00 cond can be considered in the latent heat of the vaporization of the sample (L).The value of the T v is approximately the same as the ignition temperature.Therefore, Eq. ( 12) can be written as.
where C 3 is a constant.
Figure 4 shows the relationship between MLR peak, average values, and external heat flux, and there are good linear relationships, which are shown in Eq. ( 14)-( 19), respectively: 3 mm: where subscripts p and a represent the peak value and the average value, respectively.According to Eq. ( 13) and Figure 4, the latent heat of vaporization L can be obtained by the slope, which are 2.08 kJ/g (L 1 ), 7.32 kJ/g (L 2 ), 1.82 kJ/g (L 3 ), 5.32 kJ/g (L 4 ), 1.75 kJ/g (L 5 ) and 3.72 kJ/g L 6 ), respectively.L 2 , L4, and L 6 are much larger than L 1 , L3, and L 5 , and the reason for this may be that the entire thermal decomposition process of PMMA cannot be regarded as a steady-state or quasi-steadystate combustion process so that the MLR average values and external heat flux cannot have a strictly linear relationship given by Eq. ( 13).Therefore, the average latent heat of vaporization L is 1.88 kJ/g.

Heat release rate
The heat release rate (HRR) reflects the intensity of heat energy released during the combustion (Luche et al. 2012;Torero 2004), which can be estimated by using oxygen consumption thermal technology.That is, measuring the gas-phase composition (O 2 , CO 2 , CO, and so on) produced in the combustion process (Babrauskas and Peacock 1992;Janssens 1991).Figure 5(a-c) show HRR curves of different thicknesses, which indicates that the external heat flux affects the developmental process of HRR. Figure 5(d) shows the HRR of three thicknesses under 50 kW/m 2 .Significantly, the time for 6 and 10 mm to reach the peak is almost 2 times and 4 times that of 3 mm.
In addition to the oxygen consumption technology, transient HRR can also be gained Eq. ( 20): where q 00 is transient HRR (kW/m 2 ).∆H eff represents effective combustion heat (kJ/g).∆H C,S denotes the theoretical combustion heat (kJ/g).As described in Section 3.3, there is a linear relationship between MLR peak values, average values, and external heat flux.Because the effective combustion heat is constant for specific samples, which is shown in Eq. ( 20), HRR has a linear relationship with MLR.Therefore, HRR peak values and HRR average values may be similar to MLR peak values and average values.Therefore, there is a linear relationship between them and external heat flux, which is shown in Eq. ( 21): where C 4 is a constant.As shown in Eq. ( 21), after gaining the L of samples by MLR, ∆H eff can be obtained.

Fire performance index and fire growth index
In order to better characterize the combustion intension of samples, two representative evaluation parameters are adopted: fire performance index (FPI) and fire growth index (FGI) (Xie et al. 2015).FPI is a parameter to estimate the flash propensity during the ignition process.FPI is higher, which means that the combustion is more intense.Generally, FGI characterizes the flame development rate of combustion from the point of view of heat release, and the lower the FGI, the lower the combustion level.The values of the two parameters (FPI and FGI) can be estimated, which were written as: where pkHRR and t pkHRR represent HRR peak values (kW/m 2 ) and the corresponding time (s).C 5 is a constant.
Figure 7 shows the FPI pk and FGI pk values of different thicknesses of samples.As shown in Figure 7 (a), the FPI pk gradually increases.In the range of 20-50 kW/m 2 , the FPI increases slowly, while there is a significant increase from 50 kW/m 2 to 80 kW/m 2 .When the external heat fluxes are 20 and 35 kW/ m 2 , the FPI pk of three thickness samples remains consistent.When the external heat fluxes are larger (50-65 kW/m 2 ), the FPI pk of 3 mm and 6 mm is essentially the same, which is slightly higher than that of 10 mm samples.When the external heat flux is 80 kW/m 2 , the FPI pk of samples decreases with the increase of thicknesses.

Smoke production rate
The smoke production rate (SPR) (Martinka et al. 2019) of three thicknesses is illustrated in Figure S1 (Supplementary file).Figure S1 (a-c) show the SPR against time.For the thinner sample (3 mm), only one peak is existing, while for thicker samples (6 and 10 mm), there are several peaks.shows the change in the total smoke production (TSP) of three thicknesses under 50 kW/m 2 .It can be found that TSP increases with the increase of thicknesses.To evaluate the SPR, Eq. ( 33) is used in this study.
SEA represents the ability of samples to decompose the smoke produced per unit mass of volatile combustibles.Figure S1 (e) shows the variation of SEA of 3, 6, and 10 mm under 50 kW/m 2 .The peak value of SEA decreases with the increase of sample thicknesses.Table 3S (Supplementary file) lists the SPR data.
In addition, the results of Xu, Yan, and Liu (2014) show that SPR peak values of flammable materials are linearly related to HRR peak values, and they suggest that the positive and negative relationship between the two parameters can be used to differentiate whether the materials are flammable or not. Figure S1 (f) shows the relationship between SPR peak values and HRR peak values.The correlation coefficients R 2 of three thicknesses are all higher than 0.91.The positive relationship between SPR peak values and HRR peak values means that PMMA is flammable.

CO and CO 2 production rate
CO and CO 2 , as the main toxic gases during combustion, gain more and more attention during combustion (Jing, Zhang, and Fang 2017).Figure S2 (a), (c), and (e) in the Supplementary file show the CO production rate of three thicknesses.For the same thickness, external heat flux results in the increase of production rate of CO.There are several peaks for 6 and 10 mm thicknesses, which are more than that of 3 mm thickness.
Figure 2 (b), (d) and (f) shows the CO 2 production rate.Similar to the CO production rate, the CO 2 production rate also increases.Furthermore, the variation of the CO curve is similar to that of CO 2 in total, and it is almost consistent with the trend of HRR.As for the amounts of CO 2 and CO, it can be found that CO 2 is about 100 times more abundant than CO.

Conclusions
This paper mainly studied the combustion characteristics of PMMA samples with 3, 6, and 10 mm thicknesses based on cone calorimeter experiments.The results showed that all three thicknesses of PMMA samples displayed the properties of thermally thick materials.The ignition temperature of different thicknesses increased from 509.45 K to 562.31 K.For 3 mm thickness, only one peak exists during combustion.As for 6 and 10 mm, there were several decomposition stages.There was a good linear relationship between the peak values of three thicknesses and external heat flux.The vaporization heat of PMMA was estimated as 1.88 kJ/g.Furthermore, the thickness affected the effective combustion heat.At the three thicknesses, the FPI value increased due to the effect of external heat flux.A linear correlation between FGI corresponding to the HRR peak and external heat flux was confirmed.Furthermore, the positive relationship between SPR peaks and HRR peaks also indicated the flammability of PMMA, with CO 2 released almost 100 times as much as CO.As a result, combustion can dispose of PMMA waste and simultaneously obtain heat energy.It is worth noting that thinner samples can combust and provide heat more quickly.The decrease in thicknesses can also reduce the total smoke production and the rate of toxic gas.Therefore, the next work may study the effects on combustion characteristics for different dimensions (particle, cube, and board) of PMMA.

Figure 2 .
Figure 2. The variation of ignition of PMMA against external heat flux.

Figure 6 .
Figure 6.Relationship between peak HRR and average HRR of PMMA and external heat flux.
Figure 7(b)  shows the fitting relationship between FGI pk , and external heat flux and its fitting relations are listed as follows:FGI 3pk ¼ 0:2117q 00 e À