Characterization of polychlorinated alkane mixtures - A Monte Carlo modeling approach

Article abstract of DOI:10.1007/s10532-007-9099-5

A Monte Carlo model was developed to characterize the molecular composition of polychlorinated alkane mixtures. The model is based upon a simulation of the free-radical chlorination process by which polychlorinated alkane mixtures are produced industrially from n-alkanes. In the model, the free-radical chlorination reaction was simulated by randomly selecting a position on a partially converted alkane molecule for target by chlorine free-radical attack. The relative reactivities of the hydrogen atoms on the alkane chain towards chlorine free-radical substitution were either determined experimentally or extrapolated from experimental results and incorporated into the model. The result of the simulation is the prediction of the detailed molecular composition of any PCA mixture. Good agreement was found when comparing the distribution of molecules predicted by the model to analytically determined distributions of real PCA mixtures. Results from the model were then coupled with rules describing the action of biological enzymes to estimate the upper limit possible for the aerobic biodegradation of PCA mixtures.

Full text of DOI:10.1007/s10532-007-9099-5

Biodegradation (2007) 18:703–717
DOI 10.1007/s10532-007-9099-5
ORIGINAL PAPER
Characterization of polychlorinated alkane mixtures—a
Monte Carlo modeling approach
Soren R. Jensen Æ Wayne A. Brown Æ
Ester Heath Æ David G. Cooper
Received: 3 February 2006 / Accepted: 1 January 2007 / Published online: 20 January 2007
ꢀ Springer Science+Business Media B.V. 2007
Abstract A Monte Carlo model was developed to
characterize the molecular composition of poly-
chlorinated alkane mixtures. The model is based
upon a simulation of the free-radical chlorination
process by which polychlorinated alkane mixtures
are produced industrially from n-alkanes. In the
model, the free-radical chlorination reaction was
simulated by randomly selecting a position on a
partially converted alkane molecule for target by
chlorine free-radical attack. The relative reactivi-
ties of the hydrogen atoms on the alkane chain
towards chlorine free-radical substitution were
either determined experimentally or extrapolated
from experimental results and incorporated into
the model. The result of the simulation is the
prediction of the detailed molecular composition
of any PCA mixture. Good agreement was found
when comparing the distribution of molecules
predicted by the model to analytically determined
distributions of real PCA mixtures. Results from
the model were then coupled with rules describing
the action of biological enzymes to estimate the
upper limit possible for the aerobic biodegradation
of PCA mixtures.
Keywords Biodegradation ꢀ Composition ꢀ
Modeling ꢀ Monte Carlo ꢀ PCA, polychlorinated
alkanes
Abbreviations
1,10-DCD 1,10-dichlorodecane
1,2-DCD 1,2-dichlorodecane
1-CD 1-chlorodecane
3-CD 3-chlorodecane
5,6-DCD 5,6-dichlorodecane
A1-CD
A3-CD
EPA
The GC chromatogram peak areas
associated with 1-CD
The GC chromatogram peak areas
associated with 3-CD
United States Environmental
Protection Agency
Gas Chromatograph
GC
N
Number of carbon atoms in an
unbranched carbon chain
Nuclear Magnetic Resonance
spectroscopy
NMR
S. R. Jensen ꢀ W. A. Brown ꢀ D. G. Cooper (&)
Department of Chemical Engineering, McGill
University, 3610 University Street, Montreal, QC,
Canada H3A 2B2
PCA
RP/S
Polychlorinated Alkane
The relative reactivity of a hydrogen
atom located on a primary carbon to
a hydrogen atom located on a
secondary carbon atom
Ultraviolet
e-mail: david.cooper@mcgill.ca
E. Heath
Department of Environmental Sciences, ‘‘Jozef
UV
h m
ˇ
Stefan’’ Institute, Jamova 39, 1001 Ljubljana, Slovenia
Light source (photon)
123

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Biodegradation (2007) 18:703–717
2000a, b; Wyatt et al. 1993; Madeley and Robin
1980; Environment-Canada, 1993, 1997; Vogel
et al. 1987).
b
Number of chlorine atoms bound to
a PCA molecule
(pP/pS )
The probability of encountering a
hydrogen atom on a secondary
carbon relative to the probability of
encountering a hydrogen atom on a
primary carbon
Commercial PCA products are comprised of
thousands of isomers and congeners. The large
number of isomers results from the free radical
mechanism by which PCAs are produced. In the
synthesis process ultraviolet light is used to
generate two radicals from molecular chlorine.
The free radicals then interact with the tar-
get alkane, resulting in the displacement of
hydrogen atoms by chlorine. To date, no analyt-
ical technique has been developed that is capable
of resolving these mixtures into its various con-
stituent elements (Tomy et al. 1998; Shojania
1999; Muller and Schmid 1984).
Introduction
Polychlorinated alkanes (PCAs), also known as
chlorinated paraffins, are produced industrially by
the free-radical chlorination of n-alkanes. PCAs
are classified according to their chlorine content
(30–70% by mass) and carbon chain length, as
being short (C10–C13), medium (C14–C17) or long
(>C17). Most of the PCAs produced are used as
high-temperature lubricants in the metal working
industry, but the compounds also find utility as
flame-retardants, plasticizers and additives in
paints and rubbers. In 1992, the estimated world-
wide production of PCA products was
300,000 tons per year, making them the largest
class of chlorinated organic compounds produced
in Western Europe and North America in that
year (Tomy et al. 1998, 2000a, b; Allpress and
Gowland 1999).
Work aimed at the understanding the underly-
ing processes associated with biological dechlo-
rination has focused for the most part on pure
compounds. These efforts have identified chain
length, degree of chlorination, and stereochemis-
try as key determinants in assessing the degra-
dability of pure chloroalkanes. A suite of enzyme
systems and their substrate specificity have also
been identified (Wyatt et al. 1993; Environment-
Canada 1997).
Extrapolating towards more relevant cases, the
complexity and logistics increase dramatically
when mixtures of chlorinated alkanes are consid-
ered. It is recognized that some isomers or
congeners within a mixture of chlorinated alkanes
may be readily biodegradable, while others may
only be partially degradable or altogether recal-
citrant (Damborsky et al. 2001). Furthermore,
some isomers or congeners are likely to be toxic
or carcinogenic whereas others are not. As a
result the toxicity of PCA mixtures found in the
environment will change as the biodegradable
molecules are completely or partially mineralized
by microorganisms (Tomy et al. 1998).
The release of PCAs into the environment
during production and use in industry is a cause
for concern. The short chain PCAs are toxic to
marine life, bioaccumulate and have been impli-
cated as carcinogens and endocrine disrupters
(Tomy et al. 2000b; Wyatt et al. 1993). Although
the highest levels of PCAs are found near
production facilities, the compounds are suscep-
tible to long range transport. Detectable levels of
PCAs are found in water, soil and biota world-
wide, including human tissue and arctic mammals
(Madeley and Robin 1980; Environment-Canada
1993). Because of these attributes, the US Envi-
ronmental Protection Agency (EPA) has placed
short chain PCAs on the Toxic Release Inven-
tory. In Canada, these mixtures are classified as
Track 1 Priority Toxic Substances in the Cana-
dian Environmental Protection act (Tomy et al.
For ill-defined mixtures in which the compo-
sition cannot even be resolved, pre-assessment
of the biodegradability of the oil becomes
impossible. Since the chemical disposition is
unknown, researchers are relegated to a ‘‘trial
and error’’ approach, and the ultimate degree
of biological removal achievable remains an
unknown. For instance it has been established
that short chain PCA mixtures have higher
123

Biodegradation (2007) 18:703–717
705
toxicity than medium and long chain PCAs
and that more extensively chlorinated mixtures
are more recalcitrant to biodegradation than
less chlorinated mixtures (Tomy et al. 1998;
Madeley and Robin 1980; Environment-Canada
1993, 1997; Vogel et al. 1987). However, for a
given PCA formulation the ultimate degrada-
tion remains an open question, with claims
between 0% through 100% being claimed by
different researchers for some mixtures (Tomy
et al. 1998; Wyatt et al. 1993).
The work presented here represents a first
attempt at addressing the shortcomings in the
collective ability of current analytical techniques
to adequately characterize PCA mixtures. These
deficiencies are addressed through a novel mod-
eling approach that captures the mechanism by
which PCAs are produced. The model incorpo-
rates experimentally determined reactivity data
and information found in the chemistry literature
to arrive at a complete, detailed estimate of the
distribution of the molecules contained in a PCA
mixture of any carbon chain length and any
degree of chlorination.
Knowledge of the chemical composition of
the oil under consideration is a key consider-
ation when assessing the applicability of biolog-
ical treatment. As a simple example, it has been
well established that pure hexadecane can be
completely mineralized under aerobic conditions
by a number of organisms. If this result is not
realized in practice then it follows that factors
other than the genetic capabilities of the
organism must be responsible. These may
include the absence of trace minerals, availabil-
ity and transport issues, or others. Without
adequate definition of the disposition of the
substrate it is impossible to ascertain whether
the ultimate level of degradation has been
achieved as determined by the genetic potential,
or whether higher levels can be reached through
manipulation of various environmental condi-
tions. The literature concerned with the biolog-
ical degradation of PCA mixtures has been
hindered by the lack of definition of the oils
under study. It has been impossible to critically
assess the levels of degradation realized exper-
imentally since an estimate of the maximum
degree of removal attainable remains an
unknown as the oils are chemically ill-defined.
From this discussion it is apparent that an
estimate of the compositions of PCA mixtures is
required as a compliment to biological studies
involving defined substrates. Results from the
studies involving pure compounds can then be
applied to the characterization, providing a first
approximation as to the action of the microbes
on PCA mixtures. The result would allow for an
assessment of the feasibility of biodegradation
as it applies to a particular PCA mixture, and
will also provide an estimate of the maximum
amount of degradation achievable.
The chemical distribution generated by the
model was then coupled with published biological
degradation involving pure compounds, to arrive
at an estimate of the maximum degree of degra-
dation attainable for the given mixture. To assess
the validity of this approach this result was then
compared with published studies concerned with
the biodegradation of the corresponding PCA
mixtures.
Materials and methods
Chemicals
Decane, 1-chlorodecane (1-CD), 1-decene, 5-
decene, 1,10-dichlorodecane (1,10-DCD) and
chlorine gas were purchased from Sigma-Aldrich
(Mississauga, Ontario, Canada). All chemicals
had purities ranging from 95% to 99.5%. Di-
chloromethane (CH2Cl2, spectrophotometric
grade) was purchased from J.T. Baker Chemical
Co. (Phillipsburg, N.J., USA).
Analysis of chlorinated alkanes
Analyses of the chlorinated alkanes were carried
out with a gas chromatograph (Varian CP-3800)
equipped with
a
Supelco SPB-5 column
(30 m · 0.32 mm ID, 0.25 lm film thickness)
and a flame ionization detector. The carrier gas
(UHP grade helium) was set at a column flow of
4 ml/min and split ratio of 40:1. The temperature
program for all hydrocarbon analyses was as
follows: initial temperature of 70ꢁC; ramp to
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Biodegradation (2007) 18:703–717
Model description
300ꢁC at 15ꢁC/min; and held for 5 min. The
injector temperature was constant at 300ꢁC and
the detector temperature was fixed at 320ꢁC.
Chlorinated decanes were dissolved in dichlo-
romethane before injection.
Background
The industrial production of PCAs is typically
carried out in a batch process where mixtures of
pure n-alkanes are contacted with chlorine gas in
the presence of ultraviolet light (Tomy et al. 1998;
McMurry 1994). In general, chlorine atoms are
exchanged for hydrogen atoms according to the
equation:
Measurements of 1H and 13C nuclear magnetic
resonance (NMR) spectra were performed using
a 300 MHz Varian Mercury spectrometer.
Syntheses of di-chlorinated alkanes
Pure chlorinated alkanes were synthesized from
alkenes as described elsewhere (Heath et al.
2006). In summary, chlorine gas was bubbled
through a volume of 2 ml decene dissolved in
10 ml dichloromethane, while stirring. The extent
of the reaction was tracked by gas chromatogra-
phy (see above). The chemicals 1-decene and
5-decene were used as reactants to obtain
1,2-dichlorodecane (1,2-DCD) and 5,6-dichlo-
rodecane (5,6-DCD) respectively. The final prod-
ucts were confirmed using 1H and 13C-NMR
spectroscopy.
hm
CnH2nþ2ꢁbClb þ Cl2 ! CnH2nþ1ꢁbClbþ1 þ HCl
ð1Þ
Any of the hydrogen atoms on the alkane
carbon chain can potentially be replaced by a
chlorine atom upon encountering a chlorine free-
radical. The reactivity of a hydrogen atom to
chlorine free-radical attack depends upon the
stability of the carbon free-radical intermediate
formed in the chlorination reaction. This stability
is primarily affected by the intra-molecular loca-
tion of the carbon atom on which the hydrogen
resides (primary or secondary) and the number
and intra-molecular distribution of chlorine atoms
already incorporated in the molecule (Huyser
1969; McMurry 1994).
Free-radical chlorination of decane
and chlorinated decanes
Glass vials (4 ml) were charged with approxi-
mately 2 ml of neat decane or chlorinated decane
(1-CD, 1,2-DCD or 5,6-DCD). Chlorine gas was
bubbled through the alkane using a Pasteur
pipette, which was connected to the chlorine gas
supply by teflon tubing and a vacuum trap. The
chlorine gas was supplied at a rate of 3–6 bubbles
per second. The free-radical chlorination reaction
was carried out in the presence of ultraviolet
Mathematically, the process can be viewed as
being comprised of a series of discrete events,
with each step having only two possible outcomes.
Any given chlorine radical either encounters a
hydrogen atom or it does not. If an interaction
occurs, then the chlorine free radical either
displaces the hydrogen atom or it does not. By
defining appropriate probabilities describing the
outcome of these events, the chlorination process
can be modeled, and the molecular makeup of the
resulting distribution can be estimated.
light supplied by
a
UV-lamp (UVGL-25,
MINERALIGHTꢂ Lamp, UVP Inc.) placed in
close proximity to the glass vial. The following
reactants were used for these experiments:
n-decane, 1-CD, 1,2-DCD, 5,6-DCD and 1,10-
DCD. The extent of the reaction was tracked by
gas chromatography. Retention times of individ-
ual chlorinated decane products were determined
either by using pure standards of chlorinated
decanes or by comparison with published values.
The overall chlorine content of each chlorinated
From a modeling perspective, this description
lends itself to a Monte Carlo approach. In
the Monte Carlo framework a pool of alkane
molecules is established of a magnitude large
enough so as to give reproducible results, typi-
cally 4,000–20,000. An alkane molecule is selected
randomly from the pool. A specific atom on the
molecule, selected at random, is then targeted for
possible chlorine free-radical attack through the
1
alkane mixtures was determined by H-NMR.
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Biodegradation (2007) 18:703–717
707
mechanism described in equation (1) (Tomy et al.
1998). Whether the encounter is successful in
substituting a chlorine atom for a hydrogen atom
depends upon the reactivity of the hydrogen atom
selected.
computing power. Typically, 20,000 molecules
were considered.
When a hydrogen atom is substituted by a
chlorine atom during an iteration of the model
the zero character that corresponds to the
position of the hydrogen atom under consider-
ation is replaced by a ‘‘1’’. The characters on the
text strings, shown on the worksheet, are changed
in real time, which allows the user to visually
follow the progress of the virtual chlorination
process. The result of the simulation is a complete
representation of the set of molecules in the PCA
mixture.
Each hydrogen atom is assigned a reactivity
that represents the probability that the selected
hydrogen atom will be replaced by a chlorine free
radical. From the literature, the reactivity of a
given hydrogen atom is related to the stability of
the resulting carbon free radical. Stability is
affected by such factors as the position of the
carbon atom in the chain, and the intra-molecular
distribution of chlorine atoms (Huyser 1969;
McMurry 1994). The complete set of reactivity
values represents the parameters in the Monte
Carlo model.
Model assumptions and limitations
A number of assumptions were required in
formulating the model. Most importantly, the
reactants were assumed to be well mixed. As a
consequence of this assumption, the chlorine free-
radicals are distributed uniformly in the mixture
and each molecule has an equal probability of
encountering a chlorine free-radical.
For convenience, reactivities of the various
hydrogen atoms were considered relative to that
associated with a hydrogen atom residing on a
secondary carbon atom on the pure alkane. From
the literature, hydrogen atoms located on sec-
ondary carbon atoms on unchlorinated alkane
chains had the highest reactivity (Colburne and
Stern 1965). The relative reactivities associated
with all other hydrogen atoms were a fraction of
this value. Relative reactivities defined in this way
are bounded between 0 and 1, coupling easily
with the Monte Carlo approach.
The relative reactivity of a hydrogen atom was
assumed to be unaffected by the alkane chain
length. Studies on the relative reactivities of
hydrogen atoms on octane and decane have
shown that the effect of chain lengths is negligible
(Huyser 1969; Colburne and Stern 1965). The
reactivities of all hydrogen atoms bonded to
secondary carbon atoms were assumed to be
equal for unchlorinated alkane molecules. In
reality, the relative reactivities for hydrogen
bound to secondary carbon adjacent to primary
carbon have slightly lower reactivity than those
associated with more centrally located secondary
carbons. However, this difference in reactivity is
small compared to the effect of the presence of
proximal chlorine atoms on the carbon chain and
was therefore assumed to be negligible (Huyser,
1969). In all cases, the relative reactivities used
were averages of available values.
The Monte Carlo model was written in Visual
Basic for Applications in the Microsoft Excel
environment. Incorporating the spreadsheet
interface enables the user to easily specify the
desired carbon chain length, number of molecules
used for the simulation and the final overall
degree of chlorination. Each chlorinated alkane
molecule is represented by a text string. The
characters in each string represent the carbon–
hydrogen and carbon–chlorine r-bonds. Hence an
alkane chain with n carbon atoms is represented
by a text string with 2n + 2 characters. In the
text string, a ‘‘0’’ character represents a car-
bon–hydrogen bond, while the character ‘‘1’’
represents a carbon–chlorine bonds. With these
definitions, a collection of non-chlorinated alkane
molecules is represented on the worksheet by a
set of strings consisting only of the ‘‘0’’ character.
The number of text strings generated for the
simulations is limited only by the available
Finally, the effect of temperature is implicitly
considered by virtue of the approach taken. The
literature has shown that while the absolute
reactivity of a hydrogen atom in a particular
intra-molecular environment increases signifi-
cantly with increasing temperature, hydrogen
atoms in all environments are affected to a
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Biodegradation (2007) 18:703–717
similar magnitude. Therefore, on a relative basis,
the effect is minor. Since the extent of the
reaction is considered in this approach instead
of reaction time the temperature has no impact
on the final results (McMurry 1994; Colburne and
Stern 1965).
(Huyser 1969; Colburne and Stern 1965;
McMurry 1994). It is not necessary to consider
tertiary carbon atoms because they are absent in
the starting materials (n-alkanes). The effect of
chlorine atoms located in close proximity to the
reacting hydrogen is determined by two opposing
phenomena—polar deactivation and resonance
activation. Polar deactivation is caused by the
electron-withdrawing nature of the chlorine
atoms making the carbon–hydrogen bonds in
close proximity electron-poor and, thus, less
reactive. Resonance stabilization is a result of
an increase in the degree of bonding between the
carbon and chlorine atoms and by charge transfer
between the two during the formation of reaction
intermediates. The net result of the two effects is
a reduction in reactivity of the hydrogen atoms
residing close to a chlorine atom (Huyser 1969).
Literature data have shown that the deactivating
effect of chlorine substitutes acts only on the
carbon–hydrogen bonds on both the a and b
carbon atoms (see Fig. 1 for naming conventions)
(Huyser 1969). Considering all possible arrange-
ments of chlorine atoms located near a hydrogen
atom of interest, there are a total of 77 model
parameters, or possible values, for relative
reactivities of the hydrogen atoms that must be
specified.
Results and discussion
Parameter estimation
The reactivity of a hydrogen atom depends upon
its intra-molecular environment. In the most
general case each hydrogen atom must be con-
sidered as unique, with all possible chlorinated
isomers considered. This approach leads to an
unmanageable number of model parameters (see
Appendix). Fortunately, there is no justification
for this level of complexity based on the prevail-
ing literature. The relative reactivities of hydro-
gen atoms on an n-alkane chain are higher for
those on secondary carbon atoms than for those
on a primary carbon atom (Tables 1 and 2). This
well-known effect is attributed to the resonance
stability of the intermediate carbon radical
Table 1 Relative reactivity for hydrogen atoms located on
terminal carbon atoms
Of the 77 parameters required by the Monte
Carlo model, only 12 could be derived from
experimental data. These values are shown in
parentheses in Tables 1 and 2. For moderately
chlorinated PCAs (<55% w/w chlorine), this
subset was sufficient for describing the majority
(77%) of chlorination events. This is due to the
fact that, for mixtures of this degree of chlorina-
tion, most hydrogen atoms are in close proximity
to only one or, more commonly, no chlorine
atoms. As the chlorine content of the alkane
chain increases, so does the probability that a
hydrogen atom of interests is located adjacent to
two or more chlorine atoms. For these cases
more accurate estimates of the unknown model
parameters are required.
# chlorine
atoms
# chlorine
atoms on
terminal carbon
atom bound to
the
# chlorine atoms on
a-carbona atom
on b-
carbona
atom
0
1
2
hydrogen atom
of interest
0
0
0.370
0.067 0.021
(0.37–0.40)
0.074
0.037
1
2
0.022 0.011
0.020 0.011
1
2
0
1
2
0.310 (0.30) 0.067 0.021
0.062
0.033
0.022 0.011
0.020 0.011
0
1
2
0.279
0.062
0.033
0.067 0.021
0.022 0.011
0.020 0.011
To supplement the available data free-radical
chlorination experiments were carried out
with selected pure and chlorinated alkanes. The
intent was to determine the effect of the intra-
molecular chlorine distribution on the reactivity
Values shown in bold font are experimentally determined
values; values shown in regular font are interpolated
values; values shown in parenthesis are from the literature
[14]
a
See naming convention on Fig. 8
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Biodegradation (2007) 18:703–717
709
Table 2 Relative
Total # chlorine # chlorine atoms on
Total # chlorine atoms on a- and a ¢-carbona
atoms
reactivity for hydrogen
atoms for hydrogen atoms
located on secondary
carbon atoms
atoms on b- and secondary carbon atom
bound to the hydrogen
atom of interest
b ¢-carbona
atom
0
1
2
3
4
0
0
1
0
1
0
1
0
1
0
1
1.000 (0.93–1.00) 0.500 0.111 0.025 0.025
Values shown in bold font
are experimentally
determined values; values
shown in regular font are
interpolated values;
values shown in
0.095
0.720
0.080
0.600
0.070
0.540
0.065
0.540
0.065
0.067 0.030 0.007 0.007
0.410 0.090 0.025 0.025
0.052 0.028 0.007 0.007
0.350 0.081 0.025 0.025
0.042 0.026 0.007 0.007
0.320 0.077 0.025 0.025
0.037 0.025 0.007 0.007
0.320 0.077 0.025 0.025
0.037 0.025 0.007 0.007
1
2
3
parenthesis are from the
literature [14]
‡ 4
a
See naming convention
on Fig. 8
1-CD
,
0.02
0.01
0
,
a
b
1,10-DCD
1,2-DCD
2
3
4
5
6
Retention time (minutes)
Fig. 1 Naming convention: Carbon atoms adjacent to the
carbon atom bound to the hydrogen atom of interest are
referred to as a or a ¢ carbon atoms. Carbon atoms
adjacent to a or a ¢ carbon atoms are referred to as b or b ¢
carbon atoms
Fig. 2 Gas chromatogram of products of 1-chlorodecane
free-radical chlorination
alkanes were shown to be equivalent on a molar
basis, within statistical error (data not shown).
Therefore, peak areas were assumed to be pro-
portional to the molar concentration of the
particular species, independent of its degree of
chlorination. On this basis, the relative reactivity
of the individual hydrogen atoms was obtained
directly from the relative quantity of the chlori-
nated products formed.
of a hydrogen atom on chlorine free-radical
substitution. These data were then used to derive
values for relative reactivities of hydrogen atoms
for incorporation in the Monte Carlo model. The
relative reactivities of the hydrogen atoms were
determined by quantifying the formation of some
selected chlorinated products of the free-radical
chlorination reaction.
For example, two distinguishable chlorinated
products from chlorination of decane are
1-chlorodecane (1-CD) and 3-chlorodecane
(3-CD). The selectivity of the chlorination
reactions for 1-CD relative to 3-CD follows from
a simple analysis of competing parallel reactions,
and is given by:
Figure 2 shows a typical GC-chromatogram
associated with the free-radical chlorination of 1-
chlorodecane. The peaks associated with 1-chlo-
rodecane and the dichlorinated reaction products
are well resolved, making it possible to quantify
the amount of individual chlorination products.
Each chlorination experiment was performed in
at least triplicate and average values for areas
under GC-chromatogram peaks were used to
determine the quantity of each chlorinated prod-
uct species. The calibration curves associated with
various pure mono-, di-, tri-, and tetra-chlorinated
ꢀ
ꢁ
6
4
A1ꢁCD
A3ꢁCD
SP=S
¼
ð2Þ
where A1-CD and A3-CD are the chromatograph
peak areas associated with 1-CD and 3-CD
respectively. Since the selectivity is unbounded,
123

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Biodegradation (2007) 18:703–717
it is more convenient to considering the rate of
formation of the species of interest relative to all
possible outcomes. This quantity was termed the
‘relative reactivity’. With regards to the current
example, all hydrogen atoms on secondary
carbons on the pure alkane have been shown to
have approximately the same reactivity (Huyser
1969; Colburne and Stern 1965). The same has
been demonstrated for hydrogen atoms residing
on primary carbons. Therefore the relative
reactivity of a primary carbon is given by:
appropriate starting compounds. However, such
starting materials are decidedly difficult to
synthesize and are not commercially available.
Fortunately, it is possible to obtain reasonable
estimates of the parameters that could not be
determined experimentally by extrapolating the
trends associated with the experimental values.
From the literature, it is known that the hydrogen
reactivity decrease as the number of chlorine
atoms near the hydrogen of interest increases. For
an unchlorinated alkane chain, the decrease in
hydrogen reactivity is most pronounced upon
addition of the first chlorine atom, with additional
chlorination having less of an impact, suggesting a
‘‘saturation’’ effect. Figure 4 shows a plot of data
from the literature showing the effect of the
relative reactivities of hydrogen atoms on ethane
molecules with different numbers of chlorine
atoms (Huyser 1969; Colburne and Stern 1965).
The asymptotic convergence of the relative reac-
tion values for hydrogen atoms with increasing
numbers of adjacent chlorinated carbon atoms
ꢀ
ꢁ
6
4
A1ꢁCD
6A1ꢁCD þ 4A3ꢁCD
3
2
RP=S
¼
¼
X1ꢁCD
ð3Þ
Here X1-CD is the mole fraction of 1-CD in the
organic phase, considering only chlorinated spe-
cies. Hydrogen atoms for which relative react-
ivities could be determined using Eq. (3) are
indicated by the bold entries in Tables 1 and 2. In
these tables, it can be seen that, where available,
reactivity data obtained from the literature
compares favorably with estimates determined
experimentally, validating the approach.
supports the notion of
a saturating effect.
Figure 5 shows some of the relative hydrogen
reactivities determined experimentally in this
study and the parameters that were estimated
by extrapolating those data. The ‘‘saturation’’
effect discussed above is again illustrated by the
asymptotic convergence of the relative reaction
Figure 3 shows the dependence of the model
output on experimentally determined parameters
as a function of the overall degree of chlorination.
It is apparent that the possible impact of
more highly chlorinated species becomes more
important as higher degrees of chlorination
targeted. Ideally, additional free-radical chlorina-
tion experiments should be carried out using
100
80
60
40
20
0
100
80
60
40
20
0
0
1
2
3
10
30
50
70
90
Number of Chlorine Atoms on α-Carbon atoms
% Chlorination
Fig. 4 Relative reactivity of hydrogen atoms on an ethane
molecule towards chlorine free-radical substitution.
(—r—) No chlorine atoms, (—h—) one chlorine atom,
and (—m—) two chlorine atoms bound to the carbon atom
with the hydrogen of interest [50]
Fig. 3 The percent reliance by the Monte Carlo Model on
experimentally measured model parameters (as opposed
to estimated parameters) versus overall degree of chlori-
nation
123

Biodegradation (2007) 18:703–717
711
representation of all molecules in any given PCA
mixture. Although it is easy to determine any
number of physical characteristics from the set of
virtual molecules, it is difficult to obtain experi-
mental data that allow for comparison with the
model results. Tomy et al. (1998, 2000a) per-
formed a gross chemical analysis on sPCA-60, a
short chain PCA product with 60% w/w chlorine
content. In this study, the researchers were able to
quantify the distribution of isomers, grouped by
the number of chlorine atoms present on the
alkane molecules. Figure 6 shows the distribution
of isomers grouped by the number of chlorine
atoms from this study and the distribution pre-
dicted by the Monte Carlo model presented here.
For comparison, the results from the analytical
model were also plotted, in which the impact of
chlorination on reactivity was not considered. The
Monte Carlo model did a reasonable job at
1
Increasing number of chlorine
atoms on -carbon atoms
0
β
1
2
3
0.5
0
0
1
2
3
4
Number of Chlorine Atoms on α-Carbon atoms
Fig. 5 Graphical representation of selected model param-
eters from Table 1. (—n—) experimentally measured
parameters and (—h—) estimated parameters
values for hydrogen atoms with increasing num-
bers of adjacent chlorinated carbon atoms. The
model parameters that could not be calculated
from experimental results were estimated using a
non-linear extrapolation procedure similar to that
shown in Fig. 5. These estimated model parame-
ters are shown by the entries in regular font in
Tables 1 and 2.
60
C10
Model validation
40
20
0
The basic model structure was validated against a
simplified version of the model. The purpose of
this validation was to ensure that the programmed
model algorithm was free or errors. In the
simplified version of the model it was assumed
that all hydrogen atoms on the alkane chain had
equal reactivity. This assumption made it possible
to derive an analytical solution describing the
change in molecular weight distribution of any
PCA mixture as a function of reaction extent (see
Appendix). The analytical solution was compared
to a molecular weight profile generated by the
Monte Carlo model where all relative reactivities
were assigned a value of unity. Both models
predicted identical molecular weight distribu-
tions, as expected (data not shown). This result
validates the program algorithm. Upon valida-
tion, the actual relative reactivities shown in
Tables 1 and 2 were incorporated into the model.
The lack of analytical techniques for PCA
characterization made it difficult to validate the
Monte Carlo model with the actual reactivities
against experimental data. As stated above, the
result of the simulation is a complete virtual
4
5
6
7
8
9
60
40
20
0
C11
4
5
6
7
8
9
60
40
20
0
C12
4
5
6
7
8
9
Chlorine Atoms per Alkane Molecule
Fig. 6 Comparison of molecular distribution results from
experimental results (h) [3], the Monte Carlo model (n),
and the model assuming equal relative reactivity of all
hydrogen atoms (Eq. 6) (j) for a mixture of short chain
PCAs with 60% (w/w) chlorine content. The graphs show
the distribution for decane (C10), undecane (C11), and
dodecane (C12
)
123

712
Biodegradation (2007) 18:703–717
capturing the median and general character of the
expected distribution. Clearly, results from the
model with the actual reactivities incorporated
presented here resembled the experimental re-
sults much more closely than the results from the
model distribution given by the analytical model
in which all hydrogen atoms were assigned the
same reactivity. The distribution of molecules
derived from chlorinated undecane and dodecane
are in better agreement with the experimental
results than the distribution of molecules from
chlorinated decane. Unfortunately, uncertainties
in the experimental results were not reported by
Tomy et al. (1998, 2000a, b), making any statis-
tical comparisons impossible.
30
20
10
0
0
10
20
30
NMR Values
Fig. 7 The percentage of hydrogen atoms bound to
terminal carbon atoms with no chlorine atoms on the
associated a-carbon: Model prediction versus values
determined experimentally by NMR
1
Data obtained from H-NMR spectra of PCA
mixtures provide another means of validating the
1
model. The H-NMR spectra show distinct dou-
ble peaks at shifts below 1.1 ppm which corre-
spond to hydrogen atoms located on primary
carbon atoms that have no chlorine atoms substi-
tuted on associated a-carbon atoms. 1H-NMR
spectra of pure chlorinated decanes showed that
the peak areas are quantitative to within 2%
(data not shown). Figure 7 shows the percentage
of hydrogen atoms with no chlorine atoms
substituted on associated a-carbon atoms as
1
of chlorine atoms quantified by H-NMR repre-
sented the combined interaction of all model
parameters. The fact that this very specific pattern
was accurately reproduced by the model over a
wide range of chlorination degrees indicates that
the model has successfully captured the true
reaction mechanisms. Furthermore, the result
validates the assumption that the reactivity of
the carbon atoms adjacent to the terminal carbon
atoms on the alkane chains has the same reactiv-
ity as other secondary carbon atoms. Future
studies using 13C-NMR could provide further
validation of the Monte Carlo model.
1
determined by H-NMR versus the Monte Carlo
model prediction for eight PCA preparations
generated in the laboratory by free-radical chlo-
rination. Five mixtures were synthesized using
n-decane as the starting material, while 1-CD, 1,2-
CD, and 5,6-DCD were used for the remaining
three.
Application of the model
Model predictions were generated by running
the Monte Carlo model with a set of 20,000
virtual molecules. This number of molecules was
adequate for properly representing the PCA
mixture since the model results of consecutive
runs were identical (data not shown). In fact, the
number of molecules could be reduced to less
than 4,000 with no apparent impact on the model
predictions.
The Monte Carlo model is particularly well suited
to studies of how physical and environmental
properties of the PCA molecules relate to specific
chlorine atom arrangements on the alkane chain.
Possible applications include the quantification of
toxic components of PCA mixtures based on
knowledge of the toxic effects of specific chlorine
atom arrangements within the PCA molecules, or
estimation of the aqueous solubility of PCA
mixtures based on knowledge of how specific
chlorine atom arrangements within the PCA
molecules contribute to solubility. The example
application considered here is the investigation of
Figure 7 shows excellent agreement between
the modeled and experimentally measured re-
sults. These results indicate that the model has
captured the overall intra-molecular distribution
of chlorine atoms of the molecules in the chlori-
nated decane mixtures. The specific arrangement
123

Biodegradation (2007) 18:703–717
713
the theoretical upper limit of biodegradation of
PCAs in an aerobic environment.
et al. 1987). From these results it appears that
only chlorine atoms that are located in a position
on the alkane chain where there are no chlorine
atoms on the surrounding carbon atoms can be
removed by oxygenolytic dehalogenation.
A simple set of rules capturing the major
features of catabolism of pure chlorinated alkanes
was then formulated.
Many factors influence the rate at which the
degradation of recalcitrant compounds occurs in
nature. These include the toxicity of the com-
pounds, mass transfer limitations, nutrient lim-
itations, temperatures, pH or the absence of
microorganisms capable of metabolizing the
compounds of interests. However, given appro-
priate growth conditions, the biological degra-
dation process is ultimately limited by the
presence and specificity of the catabolic
enzymes (Baker and Herson 1994).
•
Dechlorination does not occur when vicinal
chlorine atoms are encountered or when a
carbon atom with two chlorine atoms is
encountered.
•
Dehalogenation and subsequent degradation
by beta oxidation of PCA molecules can be
initiated from either end of a molecule
(Mathews and Van Holde 1996). This rule
allows degradation to continue on a partially
consumed molecule that has become recalci-
trant to degradation on one end. This situation
can arise if biological activity yields a chlori-
nation pattern that cannot be handled by the
enzyme systems present.
In general the first step in the degradation of
chlorinated alkanes with chain lengths greater
than C9 is the hydroxylation of one of the two
primary carbon atoms on the alkane chain
(Allpress and Gowland 1999). This process is
carried out through the action of either an
oxygenolytic dehalogenase or the enzymes asso-
ciated with beta oxidation. For unchlorinated
alkane molecules the hydroxylation is carried
out by alkane hydroxylase or similar enzymes
´
(Marın et al. 2001). If a chlorine atom is present
The theoretical limit to aerobic degradation
on the primary carbon atom, or on the a-carbon
atom, the primary carbon atom is no longer
accessible for the hydroxylases due to steric
hindrance (Allpress and Gowland 1999). In these
circumstances, the oxygenolytic dehalogenases
are sometimes able to remove the chlorine, and
replace it with a hydroxyl group (Tomy et al.
1998), with the outcome dependant upon
the intra-molecular chlorine distribution. For
instance, the initial oxidation of a, x-dichlori-
nated n-alkanes requires an oxygenolytic
dehalogenase (Allpress and Gowland 1999;
Armfield et al. 1995; Wischnak et al. 1998,
2000). Further studies have been carried out by
Heath et al. (2002, 2006), which suggest that if
two chlorine atoms are present on the primary
carbon atom, or if both the primary carbon atom
and the adjacent a-carbon atom have chlorine
atoms associated with them then the oxygeno-
lytic dehalogenation process does not proceed.
Other studies have shown that the presence of
more than one chlorine atom on a carbon atom
in a polychlorinated carbon chain prevents the
action of aerobic dehalogenase enzymes (Vogel
was then estimated by applying these rules to the
distribution of molecules as estimated by the
Monte Carlo model. This was accomplished by
searching the set of virtual molecules for arrange-
ments of chlorine atoms that, in theory, are
accessible for removal by the enzymes. The
molecule was then modified to account for the
activity of the enzyme systems present.
In the literature, a number of studies have been
carried out that have attempted to determine the
ultimate degree of biological conversion possible
for a PCA mixture. Varied methodologies were
employed, utilizing either pure bacterial strains
containing oxygenolytic dehalogenases or unde-
fined consortia of microorganisms (Tomy et al.
1998; Allpress and Gowland 1999; Madeley and
Robin 1980; Heath et al. 2002). For a PCA
mixture of given chlorination extent, the degree
of biodegradation varied dramatically. In some
cases no biodegradation was observed while in
others over 80% of chlorine in the mixture was
released. However, a maximum degree of con-
version should exist, based on the potential
contained in the enzyme systems.
123

714
Biodegradation (2007) 18:703–717
The upper limit to aerobic biodegradation of
with little effort, be modified to include other
halides or functional groups such as bromium,
hydroxy or carboxy group. Existing knowledge
about the metabolic pathways responsible for
biodegradation as well as rate data could be
introduced implemented in the model for detailed
environmental fate studies. For example, esti-
mates of the identity and quantity of chlorinated
carboxylic acids that are generated as metabolic
byproducts during the incomplete degradation of
PCAs could be generated. Heath et al. (2006)
showed that no chloride release was detected
during the degradation of 5,6-DCD although all
of the chlorinated decane that was initially added
had been degraded. It was concluded that the
biodegradation of 5,6-DCD was a result of the
action of the regular alkane catabolic pathway
where hydroxyl groups are added to the terminal
carbon atoms on the alkane chains, which is
followed by beta oxidation (van Beilen et al.
1994). Recalcitrant di-chlorinated carboxylic
acids would accumulated in the culture broth as
by-products this degradation process (Heath et al.
2006). A prediction of the identity, toxicity and
stability of such chlorinated acids should be
considered when the toxicity and environmental
impact of PCAs are evaluated. To date this has
not occurred since neither data nor studies have
been published concerning the properties or
potential toxicity of the metabolic by-products
of PCA degradation.
PCAs with a carbon chain length of C11 was
estimated using the modeling approach described
above (Fig. 8). Also included on this figure are
the published dechlorination results from all
studies that could be extracted from the public
domain. Given the simplicity of the biodegrada-
tion rules applied the curve for theoretical max-
imum enzymatic chloride removal encompasses a
good deal of the experimental data reported. The
fact that results have been reported that exceed
the maximum predicted by the model suggests
that either the oxygenolytic enzymes are able to
dehalogenate internally located chlorine atoms on
the carbon chain or that some abiotic, or other
mechanism facilitates the degradation process.
Curragh et al. (1994) has suggested that lacton-
ization is a likely mechanism by which abiotic
dehalogenation can occur during aerobic biodeg-
radation. In this process, the carboxyl groups that
have been formed by beta-oxidation at the
terminal end of a chlorinated n-alkane can
spontaneously form a lactone if a chlorine atom
is bound to an appropriate carbon atom displac-
ing the chlorine atom in the process (Heath et al.
2006; Curragh et al. 1994). Mechanisms such as
this may explain why some of the data reported
appear to exceed the predictions.
The modeling approach outlined in this study
could be applied to any study involving PCA
mixtures. The model offers a complete charac-
terization of any PCA mixture, which can be
analyzed for any specific intra-molecular arrange-
ment of chlorine atoms. The model code could,
Conclusion
The current study has demonstrated that the
molecular composition of PCA mixtures can be
characterized by modeling of the free-radical
chlorination reaction of n-alkanes. The Monte
Carlo model relied on experimentally determined
parameters to estimate the outcome of chlorina-
tion events for low to moderate degrees of
chlorination. The model was particularly useful
for studies that sought to correlate the presence
and quantity of specific arrangements of chlorine
atoms on the alkane chains to the overall prop-
erties of the PCA mixtures. The model results are
in good agreement with available analytical
results. Although further model validation is
100
80
60
40
20
0
20
30
40
50
60
70
80
90
%(w/w) Chlorination
Fig. 8 Model prediction of the upper limit for the
percentage of chlorine atoms that can be removed by
oxygenolytic enzymatic action. PCA biodegradation
results from the literature (r) [1, 2, 5, 23]
123

Biodegradation (2007) 18:703–717
715
desirable, the model provides a good first esti-
mate of the compositions of PCA mixtures where
no alternative exists today.
X ¼ ð0ÞCn;0 þ ð1ÞCn;1 þ ð2ÞCn;2 þ ꢀ ꢀ ꢀ
þ ð2n þ 2ÞCn;2nþ2
ð7Þ
In a closed batch process, the change in the
chlorine content in the hydrocarbon phase as
the extent of the reaction proceeds is given
by:
Acknowledgements This work was supported by the
National Science and Engineering Research Council of
Canada (NSERC), and the North Atlantic Treaty
Organization (NATO).
dX
dt
dCn;1
dt
dCn;2
dt
dCn;2nþ2
þꢀꢀꢀþð2nþ2Þ
dt
¼ ð1Þ
þð2Þ
Appendix: derivation of analytical solution
ð8Þ
For the chlorination process governed by equa-
tion (Tomy et al. 1998), each isomer i containing
b chlorine atoms can be identified by the set of b
elements Sbi , as:
The rate of formation of an isomer Sbi by the
replacement of a hydrogen atom at any position
ꢂ
ꢃ
pj in a reactant
where Sbi ꢁ1 ꢂ Sib and pj 2 p1; p2; p3; . . . ; pbꢁ1
Sibꢁ1 ¼ p1; p2; p3; . . . pbꢁ1
,
ꢂ
ꢃ
ꢂ
ꢃ
Sb ¼ p1; p2; p3; . . . pb
ð4Þ
i
is defined in the usual way in terms of the
Sbi ꢁ1
reacting species
Sbi ꢁ1!Sb
,
represented as
If the hydrogen atoms are numbered in
sequence from the end of the molecule, 1 £ pj £
2n + 2 represents the position of the hydrogen
atom in the alkane chain that has been replaced by
a chlorine atom. It follows that each element of
the set is unique, repeats are not permitted, and
the total number of elements in the set cannot
exceed 2n + 2. The molar concentration of an
isomer containing n carbon and b chlorine atoms
r
i .The total number of independent reac-
tants that can form the isomer Sbi is given by the
n;b
ꢀ
ꢁ
b
binomial coefficient formula
, which
b ꢁ 1
yields b as a result. The set of b reactants
includes all independent subsets of the set Sib
having b –1 elements. In the general case where
b < 2n + 2, the isomer Sbi can be lost from the
system if one of the hydrogen atoms is displaced
by a chlorine atom to yield an isomer with b + 1
chlorine atoms. For each isomer Sbi , there are
2n + 2–b possible products. The net rate of
formation of the isomer Sbi can be determined
by considering the sum of all b reactions
involving the complete set of isomers containing
b –1 chlorine atoms, less the 2n + 2–b possible
rates of destruction. Finally, the net rate of
removal considering all isomers containing b
chlorine atoms can be derived by summing the
expressions associated with all isomers containing
distributed according to the set Sbi is given by
b
i
CnS;b. The total concentration of all unique isomers
containing b chlorine atoms, Cn,b, is given by:
2nþ3ꢁb 2nþ4ꢁb 2nþ5ꢁb
2nþ1
X
X
X
X
Cn;b
¼
ꢀ ꢀ ꢀ
p1¼1
p2¼p1þ1 p3¼p2þ1
pbꢁ1¼pbꢁ2þ1
2nþ2
X
Sib
n;b
C
pb¼pbꢁ1þ1
The molar ratio of chloride atoms to alkane
molecules in the hydrocarbon phase is given by:
this degree of chlorination, and is equal to dCn,b
/
CCl
X ¼
ð6Þ
dt in Eq. (8). The complete expression is cum-
bersome, but is omitted here for clarity.
If chlorine is in excess, the reaction is first
order, described by a rate equation of the
form:
2nþ2
P
Cn;b
b¼0
Choosing a basis of one mole of alkane
2nþ2
P
chains,
C
¼ 1 and the total amount of
n;b
b¼0
Sbi ꢁ1!Sbi
n;b
Sbi ꢁ1!Sbi Sbi ꢁ1
chlorine contained in the hydrocarbon phase is
equal to:
r
¼ kn;b
Cn;b
ð9Þ
123

716
Biodegradation (2007) 18:703–717
dX
dt
For reactants consisting of pure n-alkane, the
initial conditions are given by:
¼ ð1ÞCn;2nþ1
þ ð2ÞCn;2n þ ꢀ ꢀ ꢀ þ ð2n þ 1ÞCn;1
þ ð2n þ 2ÞCn;0
2nþ2
X
ð16Þ
Cn ¼
Cn;i ¼ Cn;0
i¼1
By inspection, the above expression is equal to
the total moles of hydrogen, which can also be
written as:
It is more convenient to work in the chlorination
domain. Applying the chain rule to (8) provides
the necessary conversion from the time domain.
dX
¼ ð2n þ 2Þ ꢁ X
ð17Þ
dCn;b dCn;b dX
dt
¼
=
ð11Þ
dX
dt
dt
These equations can be integrated subject to the
condition Cn,b = 0 when X = 0 to yield the solution:
In the simplest case it can be assumed that all
hydrogen atoms are replaced at equal rates once
encountered by a chlorine free-radical. This is
equivalent to assuming that the rate constant of
any isomer is proportional to the number of
hydrogen atoms on the reacting alkane. From this
result, all molecules with the same number of
chlorine atoms will have the same reactivity.
Thus, from Eq. (9):
ꢀ
ꢁð2nþ2ꢁbÞ
Xb
ð2n þ 2Þ ꢁ X
ð2n þ 2Þ
Cn;b
¼
b
ð2n þ 2Þ
ð2n þ 2Þ!
ꢃ
ð18Þ
ð2n þ 2 ꢁ bÞ!ðbÞ!
An alternative solution to this problem, previ-
ously published was used by Colburne and Stern
(1965) for comparing experimental chlorination
data. This model is of the form:
rn;b ¼ kn;bCn;b
ð12Þ
At any instant during the chlorination process:
Cn;0
¼ eꢁX for b ¼ 0
ð19Þ
ð20Þ
Cn
dX dCn;1 2dCn;2 3dCn;3
¼
þ
þ
dt
dt
dt
dt
Cn;b Xb
¼
ꢀ eꢁX for b ¼ 1; . . . ; n ꢁ 1
b!
ð2n þ 1ÞdC
ð2n þ 2ÞdCn;ð2nþ2Þ
dt
n;ð2nþ1Þ þ
Cn
þ
dt
ð13Þ
The assumption that allows for this solution is
that all alkane molecules react with chlorine
radicals at equal rates regardless of the degree of
chlorination. However, the model violates the
Under the simplifying assumption, it follows
from a mass balance that:
mass
balance,
or
the
condition
that
dCn;b
lim Cn;2nþ2=Cn ¼ 1 and hence does not repre-
sent a correct solution.
¼ rn;bꢁ1 ꢁ rn;b
ð14Þ
b!2nþ2
dt
Combining:
dX
¼ kn;ð2nþ1Þ
C
ð2nþ1Þ þ ꢀ ꢀ ꢀ þ kn;1Cn;1 þ kn;0Cn;0
ð15Þ
The values of rate constants are proportional
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