**Supplementary Information for “Thermolysis of fluoropolymers as a potential source of halogenated organic acids in the environment “****Nature, V412, 321**

**Two-Box model for the atmospheric fate for TFA produced through thermolysis of fluoropolymers**

A two-box model was developed to predict the concentration of TFA observed in Toronto rainwater. This type of modeling system was developed by the Dutch and has been validated by the European EPA. It is used to eliminate compartmental boundary problems. In order to create a model of this nature to estimate rainfall concentrations of TFA in metro Toronto, several assumptions and approximations had to be made. These assumptions and the justification in making them are as follows:

- The total amount of fluoropolymer available in year 2000 within N. America, which could undergo thermolytic degradation, is not known. However, we have used a figure that grossly under estimates the true value. As a result of this the predicted TFA concentration in rainwater will also be under estimated. A figure of 200, 000 tons (assuming a yearly total production of 40, 000 tons), the total amount produced in N. America in the last five years1 was arrived at on the following bases; most fluoropolymers have a life expectancy of up to 20 years2. It is reasonable to assume that the total amount of these polymers, which were produced in the last five years, would be a low base figure to use as the total amount present on the continent.
- The annual amount of fluoropolymers which were thermally degraded was 0.1% of the total amount present. This percent value used is conservative as it is known that a large fraction of fluoropolymers are designed for, and used in, areas of high thermal stress and as a result degrade thermally3.
- North America is considered to be a box in which there is no input to the system of TFA due to fluoropolymer degradation outside this area. This is a good approximation, as TFA is known to have a short residence time in the gas phase before rain out4.
- Atmospheric gaseous TFA is only deposited through rain and dry gaseous deposition to all types of surfaces. Given a Kaw value of 4.75 x 10-6 for TFA5, it is reasonable to assume that the dry deposition velocity of TFA was estimated using the equation - 1/192 s/m + 67 s/m+ 105 s/mx KH6. TFA is not known or expected to adhere to aerosols to an important extent.
- The system is at steady state. I.e. there is no net change in the rates of the processes taking place.
- There is no atmospheric degradation of TFA on the time scale of the model. No degradation processes of TFA in the environment are known7.
- The mass of fluoropolymer thermally degraded is proportional to population density. Fluoropolymers are used largely for industrial processes and therefore would be extensively used in urban areas. The input of TFA through non-industrial uses, such as in cookware would also be proportional to population density.
- TFA was seen to be produced at varying degrees from all subclasses of fluoropolymer, i.e., homo and co-polymers and fluoroelastomers. It is assumed that the approximate division of these polymers is as follows, PTFE 40%, fluoroelastomers 10% and all other homo- and co-polymers 50%. The average production of TFA from fluoropolymers is - 7.8 % based upon our results for PTFE, ~ 6.3 % for ECTFE (copolymer) and 2.5 % for PFPE (fluoroelastomer) and these values are representative of the average production from these classes. These relative percentages were used when estimating the potential total amount of TFA produced from all fluoropolymers in N. America.

The two box model employed is shown diagrammatically in Figure 1.

Figure 1. The box model employed.

Ncg and Ngc – amount of material moving between the continent and the globe and vise versa.

Ncm and Nmc – amount of material moving between the continent and the metro Toronto area and vise versa.

Ec and Em – emissions of TFA in the gas phase to the atmosphere through the thermal degradation of fluorinated polymers.

Ndm and Ndc – rain deposition of TFA to metro Toronto and the to the continent.

Nam and Nac – dry deposition of TFA on to water bodies within metro Toronto and the continent.

Each process (N) is defined as a flux of material (Eqn 1). This is the rate of movement as a function of the concentration of the material in the defined medium.

N = G (m3/h) x C (kg/ m3) Eqn 1.

where G = h.A/. h is the mixing height (6 km for the continent and 1 km for metro Toronto), A is the area and is the residence time ( 6 hours for metro and 5 days for the continent).

The rate of change of material, which is a function of net processes causing input minus net processes causing an output, in the continent and in Metro Toronto can now be expressed at steady state as:

Metro Toronto

dM/dt = Em + Ncm – Nmc – Ndm – Nam = 0

= Em + Gcm.Cac – Cam(Gmc + Grm.1/Kaw + am.Am) = 0 Eqn 2.

Gcm.Cac= continent metro flux x concentration in continental air.

Cam= concentration in metro air.

Gmc= metro continent flux.

Grm.1/Kaw= rain flux for metro x reciprocal of the air water partition coefficient.

am.Am= dry deposition velocity from metro air x area of metro.

Em= Fraction of population in Metro compared with North America = 0.811%. Thus, 200, 000 x 0.811 % = 1622 tons of fluoroplymer consumed per year. Of that 1622 tons 40% is PTFE (648.8 tons), 10% fluoroelastomers (162.2 tons) and 50% other homo and co-polymers (811 tons). Each class undergoes an average thermolysis rate of 0.1% y-1.

Contribution by each class to TFA burden

PTFE – 648.8 x 7.8% x 0.1% = 5.061 x 10-2 tons

Fluoroelastomers – 162.2 x 2.5% x 0.1% = 4.055 x 10-3 tons

Other fluoropolymers – 811 x 6.3% x 0.1% = 5.11 x 10-2 tons

Total Em= 1.207 x 10-2 kg/h

Gcm= 1.053 x 1011 m3/h

Gmc= 1.053 x 1011 m3/h

Cam= Unknown variable

Cac= Unknown variable

Grm= rain flux. Average yearly precipitation of 689.3 mm (0.6893 m). Volume of rain 0.6893 m x 6.32 x 108 m2 = 4.3564 x 108 m3.

= 4.973 x 104 m3/h.

Kaw= 4.75 x 10-6.

am.Am= 1/(192 s/m + 67 s/m+ 105 s/mx KH) x 6.32 x 108 m2.

= 8.7686 x 109 m3/h.

Substituting these variables into eqn 2.

0= 1.207 x 10-2 kg/h + (1.053 x 1011 m3/h x Cac) - Cam x 1.2454 x 1011 m3/h.

North America

dM/dt= Ec + Ngc + Nmc – Ncg– Ncm – Ndc – Nac = 0

= Ec + Ggc.Cag + Gmc.Cam – Cac(Gcg + Gcm + Grc.1/Kaw - ac.Ac) = 0 Eqn 3.

Gcg.Cag= global continent flux x concentration in air for globe.

Gmc.Cam= metro flux x concentration in air for metro.

Gcg.Cac= continent global flux x concentration in continent air.

Grc.Cac.1/Kaw= continental rain flux x concentration in content air x reciprocal of the air water partition coefficient.

ac.Ac = dry deposition velocity from continental air x area of the continent

Ec = 200, 000 tons of fluoropolymer present on continent. Of that 200, 000 tons 40% is PTFE (80, 0000 tons), 10% fluoroelastomers (20, 000 tons) and 50% other homo and co-polymers (100, 000 tons). Each class undergoes an average thermolysis rate of 0.1% y-1.

Contribution by each class to TFA burden

PTFE – 80, 000 x 7.8% x 0.1% = 6.24 tons

Fluoroelastomers – 20, 000 x 2.5% x 0.1% = 0.5 tons

Other fluoropolymers – 100, 000 x 6.3% x 0.1% = 6.3 tons

Total Ec= 1.489 kg/h

Ggc= 6 km x 19,348,750 km2/5 days

= 9.6744 x 1014 m3/h

Cag= 0 (considering only fluoropolymer emissions)

Gmc= 1 km x 632 km2/6 hours

= 1.053 x 1011 m3/h

Cam= Unknown variable

Cac= Unknown variable

Gcg= 9.6744 x 1014 m3/h

Gcm= 1.053 x 1011 m3/h

Grc= Average yearly precipitation of 876 mm (0.876 m). Volume of rain 0.876 m x 1.9348 x 1013 m2 = 1.695 x 1013 m3.

= 1.935 x 109 m3/h.

Kaw= 4.75 x 10-6.

ac.Ac= 1/(192 s/m + 67 s/m+ 105 s/mx KH) x 1.9349 x 1013 m2.

= 3.854 x 10-3 m/s x 1.9349 x 1013 m2

= 2.6455 x 1014 m3/h.

Substituting these variables into eqn 3.

0= 1.489 kg/h + (1.053 x 1011 m3/h x Cam) - Cac x 1.6394 x 1015 m3/h

Eqn 2 and Eqn 3 were then used in conjunction to obtain:

Cam= 9.769 x 10-14 g/L

Thus, if the air TFA concentration is primarily lost due to rain out

Cwater= Cam/Kaw

= 9.769 x 10-14 g/L / 4.75 x 10-6

Therefore the calculated concentration is 20.56 ng/L in rainwater for Metro Toronto.

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