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J. Anal. Appl. Pyrolysis 81 (2008) 237–242

Thermal degradation of polyethylene modeled on tetracontane

Andras Nemeth *, Marianne Blazso, Peter Baranyai, Tamas Vidoczy

Chemical Research Center, Hungarian Academy of Sciences, Pusztaszeri ut 59-67, H-1025 Budapest, Hungary

Received 4 May 2007; accepted 30 November 2007

Available online 17 December 2007

Abstract

The thermal degradation of tetracontane as an idealized monodisperse ‘‘polymer’’ of 40 carbon atoms was modeled based on a detailed reaction

mechanism consisting of simultaneous or subsequent H-abstraction, b-scission and backbiting reactions (intramolecular H-shifts). A stiff

differential equation solver with a postprocessor program to compute the concentrations of each species and the contribution of each reaction to

their production was used. The model correctly predicts degradation at low conversion and indicates objectives for further research to improve

accuracy at higher conversions. Rate of production analysis quantifies reaction pathways contributing to the formation and consumption of species

and reveals specific H-abstraction and b-scission reactions, the complex impact of backbiting reactions, interdependence between production rates

of alkyl and alkenyl radicals, dominant role of small alkyl radicals. The data obtained by the model are compared to the experimental product

distribution of the degradation of high density polyethylene measured at 500 8C and 20 s reaction time in a micropyrolizer reactor.

# 2008 Elsevier B.V. All rights reserved.

Keywords: HDPE; Polyethylene; Pyrolysis; Thermal decomposition model; Low conversion

1. Introduction

Several methods to dispose plastic waste are extensively

studied nowadays, amidst them the thermal decomposition is a

favored alternative because of its versatility to recover

monomers, other valuable chemicals, fuel and energy as well

[1–3]. The kinetics of the process has been also intensively

studied and it is now accepted that in the case of hydrocarbon

polymers the decomposition proceeds by free radical mechan-

ism involving multistep chain reactions. The description of

elaborated reaction mechanism has been published decades ago

[4,5]. It consists of consecutive H-abstraction and b-scission

reactions producing alkanes, alkenes and dienes. The first

model taking into consideration the detailed reaction mechan-

ism for the thermal degradation of high density polyethylene

(HDPE) was published by Ranzi et al. [6]. In modeling, key

simplification was that the same rate constant was assigned to

all propagation reactions, and steady state radical concentration

was assumed to obtain the solution of the differential equation

system in closed form. For better fit to measured gas product

distribution intramolecular hydrogen shift, called backbiting –

* Corresponding author. Tel.: +36 1 4381100x116; fax: +36 1 4381145.

E-mail address: anemeth@chemres.hu (A. Nemeth).

0165-2370/$ – see front matter # 2008 Elsevier B.V. All rights reserved.

doi:10.1016/j.jaap.2007.11.012

missing from the earlier model – was added to the scheme by

Faravelli et al. [7]. Poutsma compiled a more elaborate set of

elementary reactions including b-scission of primary radicals,

rate constants based on critical review of experimental data and

theoretical considerations, simulated the thermal degradation

of a monodisperse model polymer of 19 degree of polymeriza-

tion to investigate the initial product distribution and the

functionality of the reaction mechanism [8]. For numerical

integration Monte Carlo method was used.

The present research was aimed to explore in what extent

modeled product distribution of thermal degradation of a

polymer of 40 carbon atoms (tetracontane) based on a detailed

reaction mechanism consisting of elementary reactions produ-

cing alkanes, alkenes, dienes complies with measured HDPE

degradation using a stiff differential equation solver for the

numerical integration. Further object was to reveal the impact

of b-scission, H-abstraction and isomerization reactions on

product distribution and the role of radicals by contribution

analysis.

2. Modeling

Initiation occurs by C–C homolysis in the tetracontane

polymer (P) backbone to form primary alkyl radicals (Rp�) at

Table 1

Kinetic parameters used for modeling product distribution

Process A E k773

(i) 7.94 � 1014 77,000 1.86 � 10�7 s�1

(i)a 3.16 � 1013 67,000 4.77 � 10�6 s�1

A. Nemeth et al. / J. Anal. Appl. Pyrolysis 81 (2008) 237–242238

random position

P ! Rp� þ Rp

� (i)

In the propagation steps primary alkyl radicals have three

competitive fates:

(ii) 1.90 � 108 12,800 4.83 � 104 M�1 s�1

(iii) 1.99 � 1013 27,800 1.66 � 105 s�1

(iii) 5.75 � 1012 30,100 2.01 � 104 s�1

(1) H Me

(iv)14 1.58 � 1011 20,800 2.27 � 105 s�1

(iv)15 1.81 � 1010 13,700 2.57 � 106 s�1

(iv) 1.04 � 1010 14,300 1.00 � 106 s�1

-abstraction from the polymer forms n-alkanes (ANE) and

secondary alkyl radicals (Rs�)

Rp� þ P ! ANE þ Rs

� (ii)

16

(v) 3.01 � 1014 31,700 3.76 � 105 s�1

(2) b (v)Me 1.10 � 1014 32,800 6.70 � 104 s�1

(vi) 1.28 � 108 14,200 1.32 � 104 M�1 s�1

(vii) 1.90 � 108 12,800 4.83 � 104 M�1 s�1

-Scission produces ethene and smaller primary alkyl

radicals

Rp� ! C2H4þRp

� (iii)

(viii) 3.01 � 1014 31,700 3.76 � 105 s�1

(viii) 1.10 � 1014 32,800 6.70 � 104 s�1

(3) a Me

(ix) 3.01 � 1014 31,700 3.76 � 105 s�1

(x) 1.99 � 1013 27,800 1.66 � 105 s�1

(xi) 1.90 � 108 12,800 4.83 � 104 M�1 s�1

(xii) 4.18 � 1010 6,000 8.41 � 108 M�1 s�1

A units are M, s, and E units cal mol�1 as appropriate, index a denotes formation

nd rearrangement to create 5-, 6- and 7-membered rings

producing secondary alkyl radicals by 1-4, 1-5 and 1-6 H-

shifts called backbiting

Rp� ! Rs

� (iv)

b-scission of secondary alkyl radicals produces 1-alkenes

of an allyl type radical in initiation, Me methyl radical expelled in b-scission

and 14, 15, 16 denote 1,4-; 1,5-; 1,6-hydrogen shifts. Rate constants of initiation

and termination are from Ref. [4], of propagation from Ref. [6].

The

(ENE) and chain propagating primary alkyl radicals

Rs� ! ENE þ Rp

� (v)

Secondary alkyl radicals formed in backbiting reactions can

abstract hydrogen from the polymer

Rs� þ P ! ANE þ Rs

� (vi)

Diene (DIENE) formation is assumed to proceed according to a

similar scheme where primary alkyl radicals formed in the

previous propagation steps are converted by H-abstraction from

1-alkenes into secondary 1-alkenyl radicals (0Rs�)

Rp� þ ENE ! ANE þ 0Rs

� (vii)

Subsequent b-scission of the secondary 1-alkenyl radicals

forms either a, v-dienes and primary alkyl radicals in b-

scission away from the existing double bond,

0Rs� ! DIENE þ Rp

� (viii)

or 1-alkenes and primary v-alkenyl radicals (0Rp�) in b-scission

in the other direction

0Rs� ! ENE þ 0Rp

� (ix)

b-scission of the primary v-alkenyl radicals produces ethene

and smaller primary v-alkenyl radicals

0Rp� ! C2H4þ 0Rp

� (x)

H-abstraction from 1-alkenes by primary v-alkenyl radicals

(0Rp�) produces 1-alkenes and secondary 1-alkenyl radicals

0Rp� þ ENE ! 0Rs

� þ ENE (xi)

Termination, step (xii) is represented by recombination of all

radicals participating in the process.

This scheme has been applied to construct elementary

reactions in a systematic way including all possible radical

centers along the chain. At present, due to computational

constraints, decomposition of alkanes was not taken into

account, i.e. modeling was limited to low polymer conversion

and H-abstraction from the polymer by primary alkenyl radicals

and H-shifts toward an inner position though possible, albeit

with a lower probability, were also neglected. According to

these restrictions the reaction mechanism comprises of about

1000 species and 7500 elementary reactions.

Modeling degradation of tetracontane was performed with

kinetic parameters summarized in Table 1.

Initiation kinetic parameters were corrected to the number of

carbon atoms in tetracontane as detailed in [6], those for H-

abstraction multiplied with the factor of reaction path

degeneracy gH = 4 [8]. Kinetic parameters of diene formation

are assumed to be the same as assigned to the formation of

alkenes, derived for alkanes and alkenes of low carbon numbers

[9–13].

For computation the DASAC program package [14] was

used modeling tube reactor operating at constant pressure, the

dimensions of corresponding arrays extended to numbers of

species and reactions as required. Kinetic analysis of the

simulated data was assisted by a postprocessor program [15].

3. Experimental

Py-GC/MS experiments were performed at 500 8C for 20 s

in a Pyroprobe 2000 pyrolyser (Chemical Data System)

equipped with a platinum coil and quartz sample tube

interfaced to a gas chromatograph (Agilent 6890) coupled

with a mass selective detector (Agilent 5973) operating in

electron impact mode (EI) at 70 eV. The temperature of the GC/

MS interface was held at 280 8C.

A helium carrier gas of 20 ml/min flow rate purged the

pyrolysis chamber held at 250 8C. A split of the carrier gas

(1:20) was applied. The GC separation was carried out on a

Fig. 2. Modeled product distribution of non-gaseous products backbiting

reactions excluded, residence time 20 s.

A. Nemeth et al. / J. Anal. Appl. Pyrolysis 81 (2008) 237–242 239

fused silica capillary column (Hewlett-Packard 5MS),

30 m � 0.25 mm. A temperature program from 50 to 300 8Cat 10 8C/min was applied with an isotherm period of 1 min at

50 8C and of 4 min at 300 8C.

4. Results and discussion

Because of different purpose of polyethylene pyrolysis,

experimental work available in literature is focused either on

gaseous products or on oil components (distillable, volatile non-

gaseous components) of the pyrolysate. We wanted to compare

the results of the present calculations on tetracontane to those of

experimental studies on polyethylene, thus the discussion of the

formation of gaseous and non-gaseous products is divided.

4.1. Non-gaseous products

Modeled distribution of non-gaseous products from tetra-

contane degradation is equimolar from carbon numbers of 8 to

35 (Fig. 1).

The exceptionally high molar ratio value of components of

36–37 carbon atoms is a modeling artifact, due to the choice of

tetracontane representing the polymer. Secondary alkyl radicals

formed from tetracontane undergo b-scission reactions, process

(v), however in case of CH3(CH2)37�CHCH3 there is only a

single possibility for b-scission (yielding the C37 primary alkyl

radical)

CH3�ðCH2Þ35�CH2�CH2��CH�CH3

! CH3�ðCH2Þ35��CH2þCH2¼CH�CH3

while for CH3(CH2)36�CHCH2CH3 the b-scission channel

yielding methyl radical is of much lower probability

CH3�ðCH2Þ34�CH2�CH2��CH�CH2�CH3

! CH3�ðCH2Þ34�CH2�CH2�CH¼CH2þ �CH3

than the other one yielding the C36 primary alkyl radical

CH3�ðCH2Þ34�CH2�CH2��CH�CH2�CH3

! CH3�ðCH2Þ34��CH2þCH2¼CH�CH2�CH3

Since the whole process is a long free radical chain process,

recombination (chain termination) has practically no effect on

Fig. 1. Modeled product distribution of non-gaseous products, residence time

20 s.

the stationary radical concentrations, the latter being deter-

mined by the consumption of the radicals in chain propagation

reactions. The secondary alkyl radicals formed from P have

only the b-scission as consuming reactions (besides the neg-

ligible termination reactions). Consequently reducing the cor-

responding rate constant (in case of the former one to one half,

in case of the latter one to about 65%) automatically means that

the stationary radical concentration is raised correspondingly.

The still operative b-scission channel thus yields increased

amounts of the corresponding primary alkyl radicals (as com-

pared to the shorter ones), and since their main consumption is

hydrogen abstraction from the polymer, this leads automati-

cally to increased C37 and C36 alkane levels. Simultaneously,

propene and butene are formed in the b-scission in increased

amounts, as compared to longer alkenes.

Backbiting does not affect equimolarity of non-gaseous

products (Fig. 2).

The consumption of tetracontane, however, increases from

89% to 93% at 20 s residence time as the consequence that H-

abstraction by primary alkyl radicals is more effective than by

secondary ones.

The experimentally observed non-gaseous product distribu-

tion of HDPE pyrolysed at around 500 8C is somewhat different

from that predicted by the model. The main reason of the

difference is certainly due to the high experimental conversion.

Nevertheless, a quasi-equimolar formation of 1-alkenes is

Fig. 3. Py-GC/MS total ion chromatogram of HDPE pyrolysis at 500 8C and

20 s residence time.

Fig. 4. Modeled product distribution of gaseous products, residence time 20 s.

Table 2

Yields of volatile products (wt%)

Measured [17] Modeled

Methane 0.09 0.021

Ethane 0.13 0.177

Ethene 0.64 0.461

Propane 0.19 0.215

Propene 0.37 0.385

Butane 0.04 0.243

Butene 0.35 0.438

A. Nemeth et al. / J. Anal. Appl. Pyrolysis 81 (2008) 237–242240

found in several carbon atom ranges, such as between C10–C13,

C14–C17, C18–C21, C22–C28 [16]. As an example the section of

the pyrolysis-gas chromatogram displaying the product

distribution of C18–C22 hydrocarbons obtained at 500 8C in a

micropyrolyser (see Section 3) is shown in Fig. 3.

The figure also demonstrates that experimental alkane–

alkene–diene ratios vary between 0.40:1:0.30 and 0.56:1:0.46.

Based on stoichiometric considerations [6,8], sequence of steps

((ii)–(v)) implies 1:1 alkane–alkene ratios if effects of end groups

in the polymer are ignored while 1:2:1 statistical ratio of alkanes–

alkenes–dienes if the product alkane and alkene molecules are

also decomposed by further H-abstraction and b-scission.

4.2. Gaseous products

Apart of ethene, alkenes are almost exclusively products of

b-scission of secondary tetracontyl radicals. The increase of

pentene, hexene and heptene (Fig. 4) is due to the already

discussed b-scission of secondary alkyl radicals formed in

backbiting reactions towards the farther end of the molecule.

This is illustrated for radical in position 5 involving the

favored six-membered ring transition state yielding 1-hexene

CH3�ðCH2Þn�CH2�CH2��CH�CH2�CH2�CH2�CH3

! CH3�ðCH2Þn��CH2þCH2¼CH�CH2�CH2�CH2�CH3

The b-scission in the direction to the nearer end of the molecule

results in propyl radical that forms propane after H-abstraction.

The quasi-equal contribution of the scissions in the two possible

directions is indicated by the nearly equal molar fraction values

obtained for hexene and propane. Moreover, a similarly

increased formation of the pairs of gaseous products (pen-

tene–ethane and heptene–butane) emerged from the model.

The increased rate of butene and propene originates from the

specific feature of b-scissions of tetracontyl radicals in position 3

or 2. Scissions of radical in position 3 is methyl cleavage to the

right

CH3�ðCH2Þ34�CH2�CH2��CH�CH2�CH3

! CH3�ðCH2Þ34�CH2�CH2�CH2¼CH þ �CH3

less effective than scission to the left producing 1-butene

CH3�ðCH2Þ34�CH2�CH2��CH�CH2�CH3

! CH3�ðCH2Þ34��CH2þCH2¼CH�CH2�CH3

For tetracontyl radical in position 2 b-scission is possible only

to the left with enhanced propene formation. Contrary to C2–C4

alkanes, production of methane is less, due to the less effective

b-scission yielding methyl radical compared to other primary

radicals. The contribution of b-scissions of all other tetracontyl

radicals between left and right is equal.

Ethene can be formed in b-scissions by primary alkyl and

alkenyl radicals.

Comparison to yields of C1–C4 products reported by Conesa

et al. [17] measured at 500 8C and 20 s reaction time in a CDS

Pyroprobe 1000 micropyrolizer is given in Table 2. The

pyrolysis conditions were the same as applied in this work

detailed in Section 3. The GC analysis was performed in

alumina column and with FID detector.

Agreement between measured and modeled yields of ethane,

ethene, propane, propene and butene is rather good, less so for

methane and butane.

4.3. Contribution analysis

The analysis is confined to small (1.5%) tetracontane

consumption (reaction time 0.1 s) where alkadiene formation

assumedly can be neglected, data of higher tetracontane

consumption are used at some instances to illustrate tendencies

as degradation proceeds. Computed reaction rates and their

contribution to the production of each species are expressed as

fraction of the total production (formation +, consumption �sign), neglecting reactions of less than 1% contribution.

Computed rates of alkenes of equimolar distribution are

3.05 � 10�3 M s�1 but 3.11 � 10�3 M s�1of heptene,

3.18 � 10�3 M s�1 of hexene, 3.80 � 10�3 M s�1 of pentene,

5.22 � 10�3 M s�1 of butene and 6.14 � 10�3 M s�1 propene

reflecting the already discussed effects of backbiting reactions

and specific features of b-scission. Contribution analysis also

quantified the ratio of contribution between scissions to right

and left of tetracontyl radicals in position 3 as 15:85.

Contributions to the degradation of the polymer at different

time points reveal the increasing role of small alkyl radicals as

the degradation proceeds. At 0.1 s, the highest contributors are

H-abstraction by primary alkyl radical of 37 carbon number

followed by ethyl radical, alkyl radical of 36 carbon number,

propyl and butyl radical. At 3.5 s the order still starts with H-

abstraction by the primary alkyl radical of 37 carbon atoms, but

followed by butyl radical. The rate of production of equimolar

alkanes is 3.00 � 10�3 M s�1, but that of heptatriacontane and

hexatriacontane (alkanes of 37 and 36 carbon number) are

Fig. 5. Modeled diene–alkene ratios at 0.01, 0.1 and 3.5 s residence times.

A. Nemeth et al. / J. Anal. Appl. Pyrolysis 81 (2008) 237–242 241

5.95 � 10�3 M s�1 and 5.04 � 10�3 M s�1 higher than the

equimolar rate for reasons already discussed.

Nevertheless, the modeled 1:1 alkane–alkene ratio is rather

time independent in the non-gaseous fraction but the diene–

alkene ratio increases with time (Fig. 5).

Fig. 6. Reaction graph of the main reactio

The latter trend indicates that stepping forward from the

early state of degradation dominated by steps (ii) and (v) a

forthcoming research should address reactions of enhanced

fragmentation of alkane and alkene products and improvement

of the mechanism with special emphasis on diene formation.

n pathways, low polymer conversion.

Table 4

Rate of production of the main reaction pathways (M s�1)

Process Residence time

0.01 s 0.1 s 3.5 s

Initiation (i) 1.89 � 10�5 1.83 � 10�5 1.09 � 10�5

H-transfer (ii) 8.89 � 10�2 8.80 � 10�2 5.63 � 10�2

b-Scission (iii) 5.35 � 10�4 5.37 � 10�4 5.65 � 10�4

H-shift (iv) 2.38 � 10�2 2.39 � 10�2 2.47 � 10�2

b-Scission (v) 1.09 � 10�1 1.08 � 10�1 7.85 � 10�1

H-transfer (vi) 2.19 � 10�2 2.19 � 10�2 2.24 � 10�2

H-transfer (vii) 1.82 � 10�6 2.03 � 10�5 6.41 � 10�4

b-Scission (viii) 1.76 � 10�6 1.97 � 10�5 6.18 � 10�4

b-Scission (ix) 1.61 � 10�6 1.80 � 10�5 5.65 � 10�4

b-Scission (x) 9.15 � 10�6 1.02 � 10�4 3.21 � 10�3

H-transfer (xi) 1.65 � 10�6 1.85 � 10�5 5.80 � 10�4

Termination (xii) 2.13 � 10�5 2.10 � 10�5 1.25 � 10�5

Table 3

Alkyl radical concentrations, molar fraction

Residence time

0.01 s 0.1 s 3.5 s

Methyl 2.8 � 10�11 2.8 � 10�11 3.1 � 10�11

Ethyl 1.1 � 10�10 1.1 � 10�10 1.3 � 10�10

Propyl 9.3 � 10�11 9.4 � 10�11 1.1 � 10�10

Butyl 9.0 � 10�11 9.0 � 10�11 1.1 � 10�10

Pentyl 8.7 � 10�11 8.8 � 10�11 1.0 � 10�10

Hexyl 8.5 � 10�11 8.6 � 10�11 1.0 � 10�10

C7–C35 alkyl 6.7 � 10�11 6.7 � 10�11 7.0 � 10�11

C36 alkyl 1.1 � 10�10 1.1 � 10�10 1.1 � 10�10

C37 alkyl 1.3 � 10�10 1.3 � 10�10 1.3 � 10�10

A. Nemeth et al. / J. Anal. Appl. Pyrolysis 81 (2008) 237–242242

At 1.5% tetracontane consumption the contribution of

primary alkyl radicals, and secondary alkyl radicals in position

5 and 6 to the formation of majority of alkanes is 0.80, 0.15 and

0.05, respectively. At 44% tetracontane consumption the

contribution of the above mentioned radicals changes to 0.70,

0.20 and 0.10, respectively. Contribution by secondary radicals

to the formation of hexane and pentane is less than the above

values, since 1,6-H-shift on hexyl carbon chain, 1,6 and 1,5-H-

shifts on pentyl cannot occur. C1–C4 alkanes are produced only

from the corresponding primary radicals by H-abstraction.

Concentration of alkyl radicals at 0.01, 0.1 and 3.5 s

residence times are summarized in Table 3 revealing quasi-

steady state radical concentration established within milli-

seconds.

Termination rates contribute less than 0.01% to radical

consumption for all types of radicals.

Reaction graph in Fig. 6 illustrates main reaction pathways

and corresponding rates of production at residence times 0.01,

0.1 and 3.5 s are summarized in Table 4.

Alkane production is dominated by arrow (ii), rate by arrow

(vi) is half of it even at higher tetracontane consumption.

b-Scission of secondary alkyl radicals, arrow (v) has the highest

rate at all conversion values studied, while the rate of

backbiting, arrow (iv) is almost a quarter of this value,

emphasizing the importance of such radical transformations.

Indeed, a secondary alkyl radical can yield several short

alkenes while cycling several times through arrows (v) and

(iv), contributing significantly to the increase of gaseous

products.

Though the sequences of the reaction mechanism are well

established in the literature and the compiled reactions are

thermochemically feasible, due to the complexity of the system

and scarcity of rate constants available as well as the scarcity of

current evidence the solution of the differential equation system

is not unique, the set represents only a possible reaction

mechanism. Sensitivity analysis can be informative in this

respect. Analysis of computed sensitivity coefficients reveals

that while both alkane and alkene concentrations are with order

of magnitude more sensitive to rate constants of b-scissions,

diene concentrations are sensitive to rate constants of

corresponding H-abstraction reactions. The system is most

sensitive to rate constants of b-scission of primary alkyl

radicals producing ethane. In our model these rate constant

values, together with those of the already discussed backbiting

reactions, are independent of the carbon chain lengths of the

reactants, more reliable experimental values would be needed

to improve the modeling, indicating priorities for further

research.

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