Polyesters by a Radical Pathway: Rationalization of the Cyclic Ketene Acetal Efficiency

Article abstract of DOI:10.1002/ange.202005114

Radical ring-opening polymerization (rROP) of cyclic ketene acetals (CKAs) combines the advantages of both ring-opening polymerization and radical polymerization thereby allowing the robust production of polyesters coupled with the mild polymerization conditions of a radical process. rROP was recently rejuvenated by the possibility to copolymerize CKAs with classic vinyl monomers leading to the insertion of cleavable functionality into a vinyl-based copolymer backbone and thus imparting (bio)degradability. Such materials are suitable for a large scope of applications, particularly within the biomedical field. The competition between the ring-opening and ring-retaining propagation routes is a major complication in the development of efficient CKA monomers, ultimately leading to the use of only four monomers that are known to completely ring-open under all experimental conditions. In this article we investigate the radical ring-opening polymerization of model CKA monomers and demonstrate by the combination of DFT calculations and kinetic modeling using PREDICI software that we are now able to predict in silico the ring-opening ability of CKA monomers.

Full text of DOI:10.1002/ange.202005114

Angewandte
Eine Zeitschrift der Gesellschaft Deutscher Chemiker
Chemie
www.angewandte.de
Akzeptierter Artikel
Titel: Polyesters by a Radical Pathway: Rationalization of the Cyclic
Ketene Acetal Efficiency
Autoren: Antoine Tardy, Noemie Gil, Christopher M Plummer, Didier
Siri, Didier Gigmes, Catherine Lefay, and Yohann Guillaneuf
Dieser Beitrag wurde nach Begutachtung und Überarbeitung sofort als
"akzeptierter Artikel" (Accepted Article; AA) publiziert und kann unter
Angabe der unten stehenden Digitalobjekt-Identifizierungsnummer
(DOI) zitiert werden. Die deutsche Übersetzung wird gemeinsam mit der
endgültigen englischen Fassung erscheinen. Die endgültige englische
Fassung (Version of Record) wird ehestmöglich nach dem Redigieren
und einem Korrekturgang als Early-View-Beitrag erscheinen und kann
sich naturgemäß von der AA-Fassung unterscheiden. Leser sollten
daher die endgültige Fassung, sobald sie veröffentlicht ist, verwenden.
Für die AA-Fassung trägt der Autor die alleinige Verantwortung.
Zitierweise: Angew. Chem. Int. Ed. 10.1002/anie.202005114
Link zur VoR: https://doi.org/10.1002/anie.202005114

10.1002/ange.202005114
Angewandte Chemie
RESEARCH ARTICLE
Polyesters by a Radical Pathway: Rationalization of the Cyclic
Ketene Acetal Efficiency
Antoine Tardy, Noémie Gil, Christopher M. Plummer, Didier Siri, Didier Gigmes, Catherine Lefay,*
Yohann Guillaneuf*
[a]
Dr. A. Tardy, N. Gil, Dr. C. M. Plummer, Pr. D. Siri, Dr. D. Gigmes, Dr. C. Lefay, Dr. Y. Guillaneuf
Aix-Marseille Université, CNRS
Institut de Chimie Radicalaire, UMR 7273
Marseille, France
E-mail: yohann.guillaneuf@univ-amu.fr
Supporting information for this article is given via a link at the end of the document
Abstract: Radical Ring-Opening polymerization (rROP) of Cyclic
Ketene Acetals (CKAs) combines the advantages of both ring-
opening polymerization and radical polymerization thereby allowing
the robust production of polyesters coupled with the mild
polymerization conditions of a radical process. rROP was recently
rejuvenated by the possibility to copolymerize CKAs with classic vinyl
monomers leading to the insertion of cleavable functionality into a
the environment.[1-3] To overcome this problem the use of
biodegradable polymers such as polyesters, in particular
polylactides, has been widely investigated.[4-6] These polymers
are commonly prepared by polycondensation or Ring-Opening
Polymerization (ROP).[7] Nevertheless, a large part of commodity
and specialty polymers are produced by radical polymerization
techniques that impede the introduction of ester linkages into the
backbone of the polymer chains.[8] Relatively few studies,[9-10]
initiated by the pioneering work of Bailey et al.[11], have
demonstrated that various cyclic monomers bearing vinyl or
exomethylene groups could be polymerized radically through a
ring-opening process (Scheme 1a).
Radical Ring-Opening Polymerization (rROP) presents the
advantages of both ring-opening polymerization and radical
polymerization, specifically the production of (co)polymers with
the possibility to insert heteroatoms and/or functional groups into
the main chain by facile polymerization procedures (Scheme
1a).[10] The ring-opening polymerization of Cyclic Ketene Acetals
(CKAs) by free radical or controlled radical mechanisms has
attracted considerable interest since it presents an alternative
route for the synthesis of functionalized aliphatic polyesters[12-15]
and is a powerful tool for imparting degradability to vinyl
polymers[16-20] by introducing ester linkages into their backbone
(Scheme 1b).[9-10]
vinyl-based
copolymer
backbone
and
thus
imparting
(bio)degradability. Such materials are suitable for a large scope of
applications, particularly within the biomedical field. The competition
between the ring-opening and ring-retaining propagation routes is a
major complication in the development of efficient CKA monomers,
ultimately leading to the use of only four monomers that are known to
completely ring-open under all experimental conditions. In this article
we investigate in detail the radical ring-opening polymerization of
model CKA monomers and demonstrate by the combination of DFT
calculations and kinetic modeling using PREDICI software that we are
now able to predict in silico the ring-opening ability of CKA monomers.
Introduction
Recently, the final outcome of synthetic polymers has become a
major issue due to the accumulation of wastes that are damaging
Scheme 1. a) Mechanism of Radical Ring-Opening Polymerization (rROP). b) rROP of Cyclic Ketene Acetals (CKAs) and their use in the preparation of
functionalized polyester or segmentable vinyl-based polymers.
1
This article is protected by copyright. All rights reserved.

10.1002/ange.202005114
Angewandte Chemie
RESEARCH ARTICLE
Indeed, the copolymerization of vinyl-based monomers and CKAs
has been used to prepare (bio)degradable polyethylene,[21]
fluoropolymers,[22] polymethyl methacrylate materials,[18] marine
anti-biofouling coatings,[23-24] etc., offering a promising route to
reduce plastic pollution. This approach has also been used to
confer (bio)degradability to many vinyl-based biomaterials such
as polymer prodrugs,[25] nanoparticles,[26-27] thermo-responsive
materials,[20, 28-29] ice-recrystallization inhibitors,[30] etc. To confer
efficient (bio)degradability, the incorporation of ester bonds into
the polymer backbone has to be performed randomly, as
demonstrated theoretically by Lefay et al.[31] using kinetic
modelling. Even though the rROP has been known since the
eighties, very few mechanistic studies have been performed and
no clear structure–reactivity relationships have been established
for those monomers.[10, 32-33] Indeed, the major drawback of this
family of monomer is related to the competition between the ring-
opening process and the undesired direct vinyl propagation that
leads to polyacetal (Scheme 2). Thus, for the majority of CKA
monomers, the resultant polymer is a random copolymer of ester
and acetal units.
polyacetals of high molar mass (> 30,000 g.mol-1).[34] On the
contrary, an analogous chemical modification of the 5-membered
monomer (2-methylene-4-phenyl-1,3-dioxolane or MPDL, C5P,
Scheme 3) increases the ring-opening ability.[35-36] There are
many similar examples showing that the aforementioned factors
were not key parameters for rationalizing the reactivity of such
monomers.[10]
These results demonstrate why only a few known monomers are
used within the literature and why the versatility of the rROP
technique to prepare a wide range of functionalized polyesters
has not been extensively investigated. In order to efficiently
design new monomers, it would be useful to be able to predict the
efficiency of a given monomer in rROP before its synthesis and
polymerization. Herein, we propose a theoretical approach that
combines quantum calculations and kinetic modeling based on
the competitive process described above (Scheme 2) to achieve
this goal.
More precisely, our strategy is to use Density Functional Theory
(DFT) to calculate the various rate coefficients that will be later
implemented into a kinetic model to obtain the theoretical
composition of ester and acetal units in a polymer backbone.
These theoretical results were then experimentally confirmed by
studying the radical polymerization of C5, C5H, C6 and C7 CKA
monomers (Scheme 3). Such an approach allows the in silico
prediction of the behavior of new CKA monomers.
C5
C5H
C5P
C6
C6P
O
O
O
O
O
O
O
O
O
O
C7
C7B
C8O
Scheme 2. Competition between ring-opening and direct vinylic propagation
O
O
O
O
O
O
leading to either ester units or acetal units.
O
This situation leads to the predominant use of two cyclic
monomers in all of the literature; 2-methylene-1,3-dioxepane
(MDO, C7, Scheme 3) and the 5,6-benzo-2-methylene-1,3-
dioxepane (BMDO, C7B, Scheme 3), both known to undergo
complete ring-opening polymerization independent of the
conditions.[10] Promising results have been obtained for
biomedical applications with these two monomers (gene
transfection, etc.).[10] The development of new CKA monomers
that can extend the properties of the corresponding polyester by
tuning the mechanical properties, degradation rate, etc. is para-
R5
R5H
R5P
R6
R6P
O
O
O
O
O
O
O
O
O
O
R7
R7B
R8O
O
O
O
O
O
O
mount. To design
a
monomer for radical ring-opening
O
polymerization, originally two factors were taken into account in
order to improve the selectivity of the ring-opening process: (i) the
ring strain and (ii) the stabilization of the ring-opened radical. For
example, 6-membered ring monomers are recognized to be
difficult to polymerize via a ring-opening process. This is usually
explained by the low ring-strain of monomers analogous to
Scheme 3. Structures of CKA monomers and their corresponding intermediate
acetalyl radicals.
cyclohexane (whose ring-strain is set to zero). The addition of an Results and Discussion
aromatic ring close to one oxygen (2 methylene-4-phenyl-1,3-
dioxane, C6P, Scheme 3) was also expected to increase the ring-
opening ability via the stabilization of the released alkyl radical,
but the radical polymerization of such monomers, under both UV
at 25−50 °C and thermal initiation at 80 and 120 °C, gave
Experimental Study
A significant problem when rationalizing the reactivity of CKA
monomers arises from the many experimental conditions that
1
This article is protected by copyright. All rights reserved.

10.1002/ange.202005114
Angewandte Chemie
RESEARCH ARTICLE
have been reported within the literature (initiator nature and
concentration, temperature, etc.). Additionally, since many of the
published studies were performed in the 80-90s, some non-
reliable characterization methods have been used to assess the
ratio between acetal and ester repeating units. To ensure the
validity of the experimental data before implementing the
modeling, we performed the polymerization of monomers C5,
C5H, C6 and C7 coupled with careful microstructure analysis to
obtain an accurate ratio between the acetal and ester units for
these model CKA polymers.
temperatures. The quantity of precipitated polymer was lower
than previous reactions and therefore the uncertainty was higher,
and thus a sample polymerized at 100 °C was added to
compensate.
50°C
4
As was previously stated by Bailey et al.[11] in their pioneering
studies, CKA monomers with 5- and 6-membered rings are prone
to cationic polymerization initiated by contact with glass making
purification steps particularly problematic. This is a crucial issue
when attempting to quantify the ester percentage obtained by
radical polymerization as cationic polymerization typically results
in a high quantity of acetal units, or even pure polyacetal (see ESI
Fig. S1). Thus, spontaneous cationic polymerization
contamination during monomer purification, storage, radical
polymerization and subsequent analysis was avoided through
strict experimental conditions. The bulk polymerizations were
performed using 3 mol% of the various radical initiators depending
on the polymerization temperature (see ESI for details). After the
polymerization of monomers C5, C5H, C6 and C7 and purification
70°C
3
120°C
2
150°C
189-190_13C P1S.1r.esp
1
184
176
68
1
112
104
9
(ppm)
BW.1r.esp
1
by precipitation, the four polymers were analyzed by H and 13C
1, 5, i
NMR. All 1H and 13C NMR signals can be assigned and are
consistent with the data reported within the literature. 2D NMR
techniques also confirmed these assignments (see ESI for details,
Figure S2 and S3 for PC5 for example). The analysis of the 13C
NMR spectra (Fig. 1 for the polymerization of monomer C5, other
NMR spectra are provided in ESI) confirmed the presence of two
repeating units within the copolymers. These spectra display
peaks in the characteristic zones of both acetal and ester units, at
100 and 170 ppm, respectively. We also noted a change in the
number (i.e. the presence of diads, see Figure 1) and intensity of
these peaks corresponding with the temperature of
polymerization. The acetal peaks were more intense at low
temperatures, while there was an inversion in the intensity of the
two main ester peaks with temperature. It is clear that an increase
in temperature promotes the presence of ester units, which are
w
w'
50°C
70°C
y
y'
120°C
6, i
150°C
BW.1r.esp
2.0
4.5
3.5
3.0
Chemical S
2.5
pm)
1.5
1.0
(ppm)
Figure 1. 1H and 13C NMR spectra and structure of PC5 obtained at different
1
highly prevalent at 150 °C. After full assignment of the H NMR
temperatures.
spectrum, quantification of the percentage of ester units in PC5
can be performed using multiple different calculation procedures.
The results are extremely close regardless of the applied method
(see ESI for details, Table S2). It should be noted that the
difference between the values is almost negligible at 120 and
150 ° C, while it is less than ± 5% at low temperatures. Accordingly,
there is a perfectly linear trend of ring-opening percentage and
temperature, allowing a change in ester unit percentage from ca.
50% to 80% by increasing the temperature from 50 to 100 °C.
Extrapolating these conditions, the polymerization of monomer
C5 should be performed beyond 200 °C to obtain pure polyester,
which is not relevant. These results are in good agreement with
those previously reported in the literature concerning the trend,
but also with ring-opening percentage values.
The obtained molar masses were also relatively small when
compared to PC5. We noted that the 13C NMR spectra had the
same basic characteristics as those presented in Figure 1 (the
presence of peaks corresponding to both ester and acetal units at
all temperatures; an increase in the temperature leading to better
ring-opening ability). However, whereas previously the ester peak
intensity significantly exceeded the intensity of acetal peaks at
temperatures above 120 °C, the intensities are much closer in this
case. Moreover, the peak b is almost absent at low temperatures
(Figure S6-S8), demonstrating a lower ring-opening ability of such
6-membered CKA monomer when compared to their 5-
membered analogues. Nevertheless, the results still
demonstrated a linear evolution in the ring-opening percentage in
relation to temperature. At 130 °C we calculate 50-60% ester units,
which is significantly below the value of 85% reported within the
literature[11] (Figure 2).
In the case of the C5H polymerization, only acetal units were
1
observed in the polymer chains by both H and 13C NMR (see
Figure S4 and S5), as was previously reported within the
literature.[37] Moreover, unlike the other CKA monomers, molar
masses were found to be very high (>30,000 g.mol-1). The six-
membered ring monomer (C6) was then polymerized at the same
1
This article is protected by copyright. All rights reserved.

10.1002/ange.202005114
Angewandte Chemie
RESEARCH ARTICLE
As expected from the literature data, the 7-membered ring
monomer (MDO, C7) provided only polyester regardless of the
temperature used (see ESI Figure S9-S10 for details).
UB3LYP, MO6-2X and G3(MP2)RAD) since it was shown that the
particular method applied could lead to drastic differences when
compared with experimental data. The results of the calculations
are displayed in Figure 3. Importantly, it was observed that
calculations performed using the UB3LYP method led to a lower
Ea than the experiment, while calculations made with
G3(MP2)RAD and MO6-2X are slightly and exceedingly higher
than the experimental data, respectively. This result is not
surprising as the UB3LYP method is known to generally
underestimate the energy of structures.[43] It is additionally
important to note that a difference of 5-8 kJ.mol-1 between the
energies of activation for the two species I1 and I2 is correctly
assessed by all techniques (difference between 3 and 6.5 kJ.mol-
1).
Figure 2. Ring-opening percentage as a function of temperature for the bulk
polymerization of monomers C5-C7.
All of the obtained experimental data is in good agreement with
the literature data. Indeed, the order for obtaining polyesters
follows the trend: C5H << C6 < C5 << C7. Nevertheless, we are
now able to examine these results in detail. The 5- and 6-
membered monomers both have the ability to form aliphatic
polyester, their ring-opening ability increasing also linearly with
temperature, with an almost identical slope, whatever the
monomer. It was also demonstrated that there is a clear difference
in the ring-opening ability of the 5- and 6-membered ring CKA
monomers, with the 6-membered CKA being less prone to ring-
opening. These obtained data were subsequently used as a
reference set for the following theoretical modeling.
Figure 3. Influence of the quantum method on the activation energies of the β-
scission reaction of acetalyl-based radicals and their comparison with
experimental data.[42]
The values obtained with the method UB3LYP/6-31G(d) are very
close but lower than the experimental values with a 3 kJ.mol-1
deviation. On the other hand, the use of a larger base (i. e. 6-
311++G(3df, 2p)) is not interesting as it further underestimates
the energies with a deviation of 5-6 kJ.mol-1. The G3(MP2)RAD
method,[43-44] known for the quality of its absolute values, is less
close to the experimental data than UB3LYP (10-11 kJ.mol-1
higher deviation). As the G3(MP2)RAD calculations require much
longer and are limited to a few atoms, the UB3LYP/6-31G(d)
method appeared to present the best compromise in
speed/performance. We already utilized the same DFT method
for other quantum calculations of CKA monomers.[14, 45-46]
The activation energy values of β-scission all range between 35
and 70 kJ mol-1 (Figure 4a). All of the 7-membered CKA
monomers known to polymerize exclusively by the ring-opening
mechanism have an activation enthalpy lower than 40 kJ mol-1, in
agreement with the previous calculations of Endo.[32] This study
also confirmed that the stabilization of the released radical is not
a key parameter since there is no direct link between the
percentage of ring-opening and the presence of an aromatic ring
in the β position to the cyclic acetal functionality. Moreover, these
calculations also do not allow a discrimination between a partial
and the absence of ring-opening. Thus far, only β-scission
reactions have been studied; here and within the literature. This
is only a part of the complete mechanism since radical ring-
opening polymerization is characterized by the competition
Computational study
The different structures of the monomer and adduct radicals have
been optimized by the DFT method B3LYP / 6-31G (d), commonly
used for its excellent quality of results and calculation times.[14, 38-
39]
Moreover, this method has already been efficiently used in
conformational studies of various heterocyclic rings.[40-41] The
acetalyl propagating macroradicals has been optimized by
simulating the polymer chain using a methyl group (Scheme 3,
R5-R7 radicals) to mimic steric hindrance without requiring
significant calculation costs, while simultaneously reducing
energy errors due to free rotation of the chains. In each case, the
two C–O bonds susceptible to β-scission were broken to find the
transition state of lowest energy. Here we only show the values
for the selected transition state. Concerning the various cyclic
radicals having an aromatic substituent (R5P, R6P and R7P) the
homolysis is always located on the same side as the substitution,
as expected. There is only scarce experimental data for the β-
scission of CKA monomers on which we can base a theoretical
approach. The only values originate in a 1982 study where
Ingold[42] studied I1 and I2 (Figure 3) intermediates by EPR and
measured their β-scission rate coefficient. To determine the
activation energies we used different quantum methods (i.e.,
1
This article is protected by copyright. All rights reserved.

10.1002/ange.202005114
Angewandte Chemie
RESEARCH ARTICLE
between the β-scission and the direct addition. The reactions
absolute rate constants that require more complex calculations
involved are not of the same order (unimolecular and bimolecular), are not necessary.
and thus they are not comparable in terms of thermodynamics or
activation energy, such comparisons usually being performed to
identify the most-favorable reaction mechanism.
The correct method to understand the role of the different
reactions is to achieve a kinetic model using not only the energy
of activation but also the rate coefficients kβ and kadd,closed (Scheme
4). Indeed, to describe the macroscopic result (the ratio between
the acetal and ester units in the polymer backbone) we need to
compute the number of the two propagation events that occurred
during the polymerization process, and thus the addition reaction
after opening kadd,open is also mandatory. Since our interest is
focused on the propagation steps, we used classic initiation and
termination steps and disregarded all side reactions such as chain
transfer reactions that are known to occur during the
polymerization of MDO, as an example.[47] To make an accurate
estimate of the addition rate coefficient of macroradicals onto
monomers it is recommended to model dimers or trimers instead
of unimers.[48]
However, as this work involves relatively large molecules (15-60
atoms) we thus chose to directly use the rate coefficient of simple
addition reactions to limit computing time. Moreover, in the case
of the addition of radicals after ring-opening, the penultimate
effect was not envisioned since the previous unit is at minimum 5
atoms away. In the case of the radical addition of acetalyl-based
radicals, it is assumed that the effects of steric hindrance and the
specificity of such radicals are well above any potential
penultimate effect. In the calculations we also did not take into
account any solvent effect. Indeed, this study aimed at comparing
ring-retaining and ring-opening reactions and in this case,
Scheme 4. Complex mechanism to theoretically determine the ester/acetal ratio
in a polymer backbone.
Figure 4. Enthalpies of activation ΔH‡ and reaction ΔHr for the ring-opening reaction (left) and the different radical addition (open-type radical, middle) and acetalyl-
based radical (right).
1
This article is protected by copyright. All rights reserved.

10.1002/ange.202005114
Angewandte Chemie
RESEARCH ARTICLE
Moreover, since the polymerizations are performed in bulk, the
solvent’s parameters are related to the monomers themselves
and are thus unknown. It is therefore beyond the scope of the
manuscript to take them into account.
knowing the free energy of activation ∆G‡ or from the Eyring
equation through the various components of enthalpy and entropy
of activation (∆H‡ and ∆S‡, respectively). However, DFT methods
are known to give erroneous evaluations of entropy.[50-51]
Concerning the addition of ring-opened radicals, the growing
number of possible rotations along the length of the aliphatic
chains gives access to a very large amount of possible
geometries. In this way, there is too great an uncertainty in the
values of calculated energies. To avoid this limitation, simple
representative radicals mimicking the macroradical were
modelled i.e. the ethyl radical for monomers C5-C7 and the styryl-
or methyl-benzyl-type radical for the C5P-C7B monomers (Figure
4b). The work of Fisher and Radom[38] which was dedicated to
modeling additions of radical reactions by DFT indicates that in
the case of relatively large systems the B3LYP method is
appropriate and has a good compromise between time and result,
also later confirmed by Moscatelli.[39] Thus, and also to be
consistent in the various calculations (addition and β-scission),
this method was chosen to be applied.
Indeed, the Gaussian software treats all vibrations like harmonic
oscillators. This is correct for certain vibrations, but the entropy
associated with certain hindered rotations is not properly taken
into account. In the cyclic ketal intermediate, such hindered
rotations are important and thus ∆S‡ leads to erroneous results.
The use of the Arrhenius equation simplifies the problem. Indeed,
the pre-exponential factor A contains the component of entropy
and its value is rather similar for the same type of reaction in a
narrow range of temperatures.[38] For the addition of open radicals,
the values of log A that are recommended are 7.5, 8, and 8.5
depending on whether the groups are tertiary, secondary or
primary, respectively.[38] However, no value for the addition of
tertiary acetalyl-based radicals exist in the literature, the presence
of more oxygen atoms appears to increase the value of log A in
different cases.[38] Therefore, we chose to use the average value
of 8 for such acetalyl radicals. In the case of the ring-opening
reaction, it is recommended to take a log A value of 13.[42, 52]
Kinetic modeling was then performed using PREDICI software.
This software is based on the deterministic Galerkin h-p-method
has been widely used for describing molecular weight
The results for the addition of ring-opened radicals onto the CKA
monomers are described in Figure 3b. Since in all cases the
polarity of both adding radicals and CKA are similar, thus the rate
of addition is dependent only on the stabilization of the alkyl
radical (primary, secondary or tertiary alkyl radicals or the
presence of a stabilizing aromatic ring). For example, the
activation enthalpies of primary alkyl radicals are centered around
28 ± 5 kJ.mol-1, while are higher in the case of secondary radicals
(35,5 kJ.mol-1 for C5H). For aromatic-based monomers, the
benzylic type radical has a lower activation enthalpy (43 kJ.mol-1
for C7B) than styryl-based radicals (48±1 kJ.mol-1 for C5P - C6P).
These obtained values can be compared to the values described
by Fischer and Radom[38] dealing with the addition of methyl and
benzyl radicals onto vinyl ethers. In this case, activation energies
of 25 and 40 kJ.mol-1 were given, respectively, that are both 3
kJ.mol-1 lower than the values that we obtained for CKA, which
are vinyl ethers in which an additional oxygen atom is located in
the α position to the vinyl functionality. Moreover, for the C5
monomer, Coote et al.[49] proposed a value of 30 ± 5 kJ.mol-1 via
high level ab initio calculations for the propagation rate coefficient
that is coherent with our value. From these results we could
conclude that the ring-size does not greatly affect the activation
enthalpies for similar structures (C5-C6-C7 and C5P-C6P).
To our knowledge, there is no data within the literature reporting
the radical addition of acetalyl-type radicals, especially onto cyclic
ketene acetals. The obtained results are summarized in Figure 4c.
The data shows that the calculated energy values do not differ
significantly, i.e. all the activation enthalpies being centered
around 27 ± 5 kJ.mol-1 and the reaction enthalpies around -66 ± 8
kJ.mol-1. It can be observed that only the ring size seems to
influence such values since C5, C5H and C5P are similar, and
such behavior holds true for 6- and 7-membered ring CKA
monomers. It should be noted that these values are of the same
order of magnitude as the addition of primary alkyl radicals on the
CKA while the acetalyl radicals here are tertiary, showing the
specific reactivity of such radicals. The activation energies
calculated for different reactions are not directly comparable to
know whether a monomer is more likely to propagate directly or
undergo β-scission. Indeed, there are different order reactions; i.e.
monomolecular and bi-molecular. Therefore, kinetic modeling is
required. Kinetic modeling is performed from the rate coefficients
of the various reactions. These coefficients can be obtained by
distributions and polymer reaction kinetics for a large range of
53]
polymer processes.[45-46,
The kinetic scheme is depicted in
Scheme 5 while the coefficients, hypotheses and applied
approximations are detailed within the ESI (Table S7 and S8).
The propagating species are simply either closed or open type.
We assumed that the rate coefficients are independent to the
chain length. This assumption is more relevant for the propagation
step than for the termination step, since diffusional limitations are
more important in the latter case.[54]
Scheme 5. Kinetic model used in the PREDICI software.
1
This article is protected by copyright. All rights reserved.

10.1002/ange.202005114
Angewandte Chemie
RESEARCH ARTICLE
It has been already stated that the chain length was not taken into
account because the larger molecular size requires too much
computation time. Moreover, by modeling propagating radicals in
the form of dimers or trimers, the penultimate unit would be
different according to the previous addition (e.g. closed-closed,
open-closed, closed-open or open-open dimers), which would
complexify the system and thus would require many additional
calculations that are not necessarily useful in this particular case.
Counters have been inserted into the model to quantify the
amount of ester and acetal functions introduced in the copolymer.
The acetal counter was increased when there is an addition of a
closed-type radical. The ester counter increased when ring-
opening occurred. In that way, it does not include counting when
there is an addition of an open-type radical since the resulting
chain end is then of a closed type and can therefore react in both
ways. At the end of the modelling, the number of acetal and ester
counters were recorded and compared to determine the
percentage of ester units in the final polymer backbone.
C5, C6 and C7. Indeed, Figure 5 shows relatively identical
behavior between the simulation and the experimental
observations for these monomers; C7 monomer gives only ester
units at 50 °C while C5 and C6 form copolymers. Moreover, the
difference in ability between C5 and C6 to form polyesters is also
in good agreement with the experimental results, with 75% and
45% polyester at 100 ° C, respectively, (on average 20% more for
C5 than C6) and an increase in percentage of polyester with an
increase in temperature. In contrast, the slope defining the
increase in ester percentage depending on the temperature is
slightly steeper for the simulation results in comparison to the
experimental data. This discrepancy could originate from the
assumptions made regarding chain length independency of the
various kinetic rate coefficients. Nevertheless, this modeling
approach provides an interesting and relatively accurate tool to
describe the reactivity of CKA monomers. We additionally
performed such modeling on more complex monomers. With C5P,
C7B and C8O the model gives complete ring-opening, in
accordance to the literature data.[10] In contrast to experimental
data, the model predicts that C5H should contain some ester units
even if such a monomer has a lower tendency to ring-open.[37] The
results obtained for C6P (Figure 6) is not in agreement with the
literature data[34] since the modeling showed an enhancement in
the ring-opening ability in comparison to the C6 CKA monomer
(75% instead of 25% at 70 °C).
The discrepancy between the theoretical results and the literature
data can be explained by cationic polymerization that was not
inhibited.[34] This explanation is further supported by a study on
C6 CKA derivatives bearing methyl groups on the carbon in the α
position relative to the cyclic acetal functionality. In that case,
using base to prevent cationic polymerization, they obtained 89%
ester units at 120°C.[55] Another parameter that could be used to
increase the ring-opening ability of CKA monomers is to decrease
the monomer concentration in order to favor the unimolecular
reaction compared to the undesired bimolecular acetal
propagation. To simulate the monomer dilution, the ring-opening
percentage of the C6 monomer at different initial monomer
concentrations and temperatures was modeled (Figure 6). As
expected, an evolution towards the production of more polyester
at high dilution was observed.
Figure 5. a) Theoretical (plain symbol and straight line) and experimental
(empty symbol and dashed-dotted line) ring opening percentage as a function
of the temperature for the bulk polymerization of C5 (), C6 (▲) and C7 (✭)
monomers; b) Theoretical ring opening percentage as a function of the
temperature for the bulk polymerization of C5H (●) and C6P () monomers.
Figure 6. Theoretical ring-opening percentage as a function of temperature and
initial monomer concentration [M]0 for the C6 monomer.
The result of the modeling is depicted in Figure 5. A good
agreement between the experimental values and those obtained
from the model can be observed in the case of simple monomers
1
This article is protected by copyright. All rights reserved.

10.1002/ange.202005114
Angewandte Chemie
RESEARCH ARTICLE
On the other hand, the curves level out at the limit values of
around 10 and 50% polyester at 50 and 120 °C, respectively for
an initial monomer concentration of 8 mol.L-1, confirming that the
value we used in previous simulations is representative of the bulk
polymerization. Although relatively simple, the kinetic model we
have developed appears robust enough to allow an
approximation of the behavior of a CKA monomer. The model
requires the determination of three activation energies to
investigate the reactivity of new CKA monomers. According to the
calculations performed for the addition reactions, it appeared
possible to approximate the rate of acetal-based addition
according to the monomer ring size and the rate of addition of
open-type alkyl radicals by using previously determined values for
the addition of model alkyl radicals onto simple CKA monomers.
the ring-retaining acetalyl lower than 13-15 kJ.mol-1 to efficiently
obtain polyester. If we assume that the radical addition of the
acetalyl intermediate is only determined by the ring size, this
approach gives an upper limit for the β-scission reaction
depending of the ring size (Table 1).
Conclusion
The competitive process of ring-retaining propagation is a major
obstacle in the development of efficient CKA monomers. In this
study we investigated this key parameter by a combination of
experimental and theoretical approaches. First, it was
demonstrated that the ratio between ester and acetal units in the
polymer backbone is linearly correlated to the polymerization
temperature, with the ease of ring-opening following the order C7
> C5 > C6. DFT calculations of the ring-opening reaction showed
that complete ring-opening behavior could be obtained with a ΔH‡
< 40 kJ.mol-1 but it was not possible to discriminate or quantify the
behavior for other monomers. By further utilizing the kinetic
modeling software PREDICI the behavior of CKA monomers was
able to be rationalized by considering the impact of the addition
of acetalyl and open-type radicals onto the CKA monomer.
Although relatively simple, the developed kinetic model is based
on relevant values and seems robust enough to allow for an
approximation of the behavior of
a CKA monomer after
completing the necessary energy calculations. Furthermore, this
model allows an attempt at the rationalization of behavioral
differences between the monomers through structure-reactivity
relationships. The analysis of molecular orbitals is also predicted
to be an excellent method for this because it can separate the
contributions due to hyper-conjugation and those due to other
energy contributions such as steric and electrostatic interactions.
This will be the subject of a subsequent study.
Figure 7. Theoretical ring-opening percentage as a function of the parameter
K=kβ/kadd,closed see Scheme 4 for the definition of the rate coefficients; () C6
monomer at 70 °C; (●) C6 monomer at 120 °C; (▲) C8O monomer at 70 °C.
Using such an approach, only the β-scission of the intermediate
acetalyl-radical has to be calculated. Secondly, we performed the
modeling using the parameters used for C6 and C8O monomers
(i.e. the monomers that have the highest and lowest activation
energies for ring-opening) and determined the percentage of
ester units in the polymer backbone versus a constant K that is
determined by the ratio kβ/kadd, closed (Figure 7). Interestingly all
the data followed a master curve. A threshold value of 1 × 103
seems mandatory to obtain pure polyester.
Acknowledgements
We thank the French Ministry of Research for the financial support
of the PhD thesis of A.T and the CNRS and the French National
Research Agency (ANR-15-CE08-0019 and ANR-11-JS08-0005).
This work was also supported by the ‘Centre Régional de
Compétences en Modélisation Moléculaire de Marseille’. Arkema
is acknowledged for providing DEAB.
Keywords: DFT Calculations • Polyester • Radical
Table 1. Upper values for the enthalpy of activation for the ring-opening reaction
to obtain pure polyester according to CKA ring size
polymerization • Cyclic Ketene Acetals • Kinetic modelling
[1]
[2]
M. Cole, P. Lindeque, C. Halsband, T. S. Galloway,
Marine Pollution Bulletin 2011, 62, 2588-2597.
M. Eriksen, L. C. M. Lebreton, H. S. Carson, M. Thiel, C.
J. Moore, J. C. Borerro, F. Galgani, P. G. Ryan, J.
Reisser, Plos One 2014, 9.
R. Geyer, J. R. Jambeck, K. L. Law, Science Advances
2017, 3.
E. Castro-Aguirre, F. Iniguez-Franco, H. Samsudin, X.
Fang, R. Auras, Advanced Drug Delivery Reviews 2016,
107, 333-366.
CKA Monomer
Size
Average
ΔH‡β max
ΔH‡
(kJ.mol-1)
add, closed
(kJ.mol-1)
5
6
7
27
24
31
40
37
44
[3]
[4]
[5]
[6]
K. M. Nampoothiri, N. R. Nair, R. P. John, Bioresource
Technology 2010, 101, 8493-8501.
C. Vilela, A. F. Sousa, A. C. Fonseca, A. C. Serra, J. F. J.
Coelho, C. S. R. Freire, A. J. D. Silvestre, Polymer
Chemistry 2014, 5, 3119-3141.
Using this threshold and the values of the pre-exponential factors,
we can estimate that a CKA monomer should have a difference
between the activation energies of ring-opening and addition of
1
This article is protected by copyright. All rights reserved.

10.1002/ange.202005114
Angewandte Chemie
RESEARCH ARTICLE
[7]
A. C. Albertsson, I. K. Varma, Degradable Aliphatic
Polyesters 2002, 157, 1-40.
V. Delplace, J. Nicolas, Nature Chemistry 2015, 7, 771-
784.
S. Agarwal, Polymer Chemistry 2010, 1, 953-964.
A. Tardy, J. Nicolas, D. Gigmes, C. Lefay, Y. Guillaneuf,
Chem. Rev. 2017, 117, 1319-1406.
W. J. Bailey, Z. Ni, S. R. Wu, Journal of Polymer Science
Part a-Polymer Chemistry 1982, 20, 3021-3030.
C. A. Bell, G. G. Hedir, R. K. O'Reilly, A. P. Dove, Polymer
Chemistry 2015, 6, 7447-7454.
[43]
E. I. Izgorodina, D. R. B. Brittain, J. L. Hodgson, E. H.
Krenske, C. Y. Lin, M. Namazian, M. L. Coote, Journal of
Physical Chemistry A 2007, 111, 10754-10768.
E. I. Izgorodina, M. L. Coote, L. Radom, Journal of
Physical Chemistry A 2005, 109, 7558-7566.
A. Tardy, J.-C. Honoré, D. Siri, J. Nicolas, D. Gigmes, C.
Lefay, Y. Guillaneuf, Polymer Chemistry 2017, 8, 5139-
5147.
A. Tardy, V. Delplace, D. Siri, C. Lefay, S. Harrisson, B. D.
A. Pereira, L. Charles, D. Gigmes, J. Nicolas, Y.
Guillaneuf, Polymer Chemistry 2013, 4, 4776-4787.
S. Jin, K. E. Gonsalves, Macromolecules 1997, 30, 3104-
3106.
[8]
[44]
[45]
[9]
[10]
[11]
[12]
[13]
[14]
[46]
S. Maji, M. Zheng, S. Agarwal, Macromolecular Chemistry
and Physics 2011, 212, 2573-2582.
[47]
[48]
[49]
A. Tardy, J. C. Honore, J. Tran, D. Siri, V. Delplace, I.
Bataille, D. Letourneur, J. Perrier, C. Nicoletti, M.
Maresca, C. Lefay, D. Gigmes, J. Nicolas, Y. Guillaneuf,
Angewandte Chemie-International Edition 2017, 56,
16515-16520.
J. Undin, A. Finne-Wistrand, A.-C. Albertsson,
Biomacromolecules 2013, 14, 2095-2102.
G. X. Dai, Q. Y. Xie, S. S. Chen, C. F. Ma, G. Z. Zhang,
Progress in Organic Coatings 2018, 124, 55-60.
V. Delplace, A. Tardy, S. Harrisson, S. Mura, D. Gigmes,
Y. Guillaneuf, J. Nicolas, Biomacromolecules 2013, 14,
3769-3779.
E. I. Izgorodina, M. L. Coote, Chemical Physics 2006, 324,
96-110.
G. E. Roberts, M. L. Coote, J. P. A. Heuts, L. M. Morris, T.
P. Davis, Macromolecules 1999, 32, 1332-1340.
C. J. Cramer, J. Wiley & Sons, 2004, pp. 375-377.
C. Y. Lin, E. I. Izgorodina, M. L. Coote, Journal of Physical
Chemistry A 2008, 112, 1956-1964.
S. W. Benson, Thermochemical Kinetics, Wiley, New
York, 1976.
M. Wulkow, Macromolecular Reaction Engineering 2008,
2, 461-494.
D. R. D’hooge, P. H. M. Van Steenberge, M.-F. Reyniers,
G. B. Marin, Progress in Polymer Science 2016, 58, 59-
89.
N. Zhende, Bailey, J. W, Acta Polymerica Sinica 1987, 1,
379-383.
[50]
[51]
[15]
[16]
[17]
[52]
[53]
[54]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
E. Guegain, J. P. Michel, T. Boissenot, J. Nicolase,
Macromolecules 2018, 51, 724-736.
Y. F. Shi, H. Schmalz, S. Agarwal, Polymer Chemistry
2015, 6, 6409-6415.
[55]
U. Wais, L. R. Chennamaneni, P. Thoniyot, H. F. Zhang,
A. W. Jackson, Polymer Chemistry 2018, 9.
T. Zeng, W. You, G. Chen, X. Nie, Z. Zhang, L. Xia, C.
Hong, C. Chen, Y. You, iScience 2020, 23, 100904.
J. H. Ko, T. Terashima, M. Sawamoto, H. D. Maynard,
Macromolecules 2017, 50, 9222-9232.
G. X. Dai, Q. Y. Xie, C. F. Ma, G. Z. Zhang, Acs Applied
Materials & Interfaces 2019, 11, 11947-11953.
Q. Y. Xie, Q. N. Xie, J. S. Pan, C. F. Ma, G. Z. Zhang, Acs
Applied Materials & Interfaces 2018, 10, 11213-11220.
E. Guegain, J. Tran, Q. Deguettes, J. Nicolas, Chemical
Science 2018, 9, 8291-8306.
E. Guegain, C. Zhu, E. Giovanardi, J. Nicolas,
Macromolecules 2019, 52, 3612-3624.
A. W. Jackson, L. R. Chennamaneni, P. Thoniyot,
European Polymer Journal 2020, 122.
S. Komatsu, T. A. Asoh, R. Ishihara, A. Kikuchi, Polymer
2017, 130, 68-73.
G. G. Hedir, M. C. Arno, M. Langlais, J. T. Husband, R. K.
O'Reilly, A. P. Dove, Angewandte Chemie-International
Edition 2017, 56, 9178-9182.
[30]
[31]
G. Hedir, C. Stubbs, P. Aston, A. P. Dove, M. I. Gibson,
Acs Macro Letters 2017, 6, 1404-1408.
D. Gigmes, P. H. M. Van Steenberge, D. Siri, D. R.
D'Hooge, Y. Guillaneuf, C. Lefay, Macromolecular Rapid
Communications 2018, 39.
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
B. Ochiai, T. Endo, J. Pol. Sci.: Part A: Polym. Chem.
2007, 45, 2827-2834.
J. B. Lena, A. M. Van Herk, Industrial & Engineering
Chemistry Research 2019, 58, 20923-20931.
T. Schulze, E. Klemm, Angew. Makromol. Chem. 1995,
229, 123.
W. J. Bailey, S.-R. Wu, Z. Ni, Makromol. Chem. 1982,
183, 1913-1920.
I. Cho, M. S. Gong, Journal of Polymer Science Part C-
Polymer Letters 1982, 20, 361-364.
T. Schultze, J. Letsch, E. Klemm, Journal of Polymer
Science: Part A Polymer Chemistry 1996, 34, 81-87.
H. Fischer, L. Radom, Angewandte Chemie International
Edition 2001, 40, 1340-1371.
D. Moscatelli, M. Dossi, C. Cavallotti, G. Storti, The
Journal of Physical Chemistry A 2011, 115, 52-62.
E. Taskinen, Structural Chemistry 2000, 11, 283-291.
E. Taskinen, Structural Chemistry 2001, 12, 419-429.
L. R. C. Barclay, D. Griller, K. U. Ingold, Journal of the
American Chemical Society 1982, 104, 4399-4403.
[40]
[41]
[42]
1
This article is protected by copyright. All rights reserved.

10.1002/ange.202005114
Angewandte Chemie
RESEARCH ARTICLE
Entry for the Table of Contents
Draw me a CKA: the radical ring-opening polymerization of model CKA monomers was investigated using quantum calculations and
kinetic modeling. The results were supported by a detailed experimental study. The new methodology we propose allows to predict in
silico the efficiency of CKA monomers to prepare polyester via a radical pathway.
1
This article is protected by copyright. All rights reserved.