Synthesis and characterization of star polymers and cross-linked star polymer model networks containing a novel, silicon-based, hydrolyzable cross-linker

Article abstract of DOI:10.1021/ma049618+

An acid-labile dimethacrylate cross-linker, dimethyldi(methacryloyloxy-1-ethoxy)silane (DMDMAES), was synthesized by the reaction of 2-hydroxyethyl methacrylate (HEMA) and dichlorodimethylsilane in the presence of triethylamine. Group transfer polymerization (GTP) was employed to use this cross-linker in the preparation of six hydrolyzable polymer structures: one neat cross-linker network, one randomly cross-linked network of methyl methacrylate (MMA), two star-shaped polymers of MMA, and two cross-linked star polymer model networks (CSPMNs) of MMA. A nonhydrolyzable CSPMN of MMA, based on a stable cross-linker, was also synthesized. Gel permeation chromatography (GPC) in tetrahydrofuran (THF) confirmed the narrow molecular weight distributions (MWDs) of the linear polymer precursors and demonstrated the increase in molecular weight (MW) upon each successive addition of cross-linker or monomer. Characterization by static light scattering (SLS) and GPC showed that star polymers with DMDMAES cores bear a relatively small number of arms, around 7. All star polymers and polymer networks were hydrolyzed using hydrochloric acid in THF. While the MWs of the products from the hydrolysis of the star polymers, the neat cross-linker network, and the randomly cross-linked network were as expected, those from the CSPMNs were of a much higher than expected MW, indicating extensive star-star coupling.

Full text of DOI:10.1021/ma049618+

6734
Macromolecules 2004, 37, 6734-6743
Synthesis and Characterization of Star Polymers and Cross-Linked Star
Polymer Model Networks Containing a Novel, Silicon-Based,
Hydrolyzable Cross-Linker
Efr osyn i Th em istou a n d Costa s S. P a tr ick ios*
Department of Chemistry, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus
Received February 26, 2004; Revised Manuscript Received J une 17, 2004
ABSTRACT: An acid-labile dimethacrylate cross-linker, dimethyldi(methacryloyloxy-1-ethoxy)silane
(DMDMAES), was synthesized by the reaction of 2-hydroxyethyl methacrylate (HEMA) and dichlorodim-
ethylsilane in the presence of triethylamine. Group transfer polymerization (GTP) was employed to use
this cross-linker in the preparation of six hydrolyzable polymer structures: one neat cross-linker network,
one randomly cross-linked network of methyl methacrylate (MMA), two star-shaped polymers of MMA,
and two cross-linked star polymer model networks (CSPMNs) of MMA. A nonhydrolyzable CSPMN of
MMA, based on a stable cross-linker, was also synthesized. Gel permeation chromatography (GPC) in
tetrahydrofuran (THF) confirmed the narrow molecular weight distributions (MWDs) of the linear polymer
precursors and demonstrated the increase in molecular weight (MW) upon each successive addition of
cross-linker or monomer. Characterization by static light scattering (SLS) and GPC showed that star
polymers with DMDMAES cores bear a relatively small number of arms, around 7. All star polymers
and polymer networks were hydrolyzed using hydrochloric acid in THF. While the MWs of the products
from the hydrolysis of the star polymers, the neat cross-linker network, and the randomly cross-linked
network were as expected, those from the CSPMNs were of a much higher than expected MW, indicating
extensive star-star coupling.
In tr od u ction
zation diacrylate and dimethacrylate diesters of the di-
tertiary diols 2,5-dimethyl-2,5-hexanediol, 2,7-dimethyl-
2,7-octanediol, and 2,9-dimethyl-2,9-decanediol to obtain
highly cross-linked networks, which were subsequently
thermolyzed at temperatures above 180 °C. This re-
sulted in networks with anhydride cross-links, which
were hydrolyzed in alkaline aqueous solutions to give
soluble linear polymers of acrylic or methacrylic acid.
Examples of synthesis of polymers bearing hydrolyz-
able cross-linkers using “living” polymerization methods
are the anionic polymerizations reported by Ruckenstein
and Zhang12 and Long et al.13 Ruckenstein and Zhang12
synthesized star polymers, branched polymers, and
randomly cross-linked polymer networks of methyl
methacrylate (MMA) using the cross-linker ethylene
glycol di(1-methacryloyloxy)ethyl ether (EGDMOEE).
Because of the presence of acetal groups in this cross-
linker, the polymers of Ruckenstein and Zhang were
readily hydrolyzed in acetone or tetrahydrofuran (THF)
by the addition of aqueous hydrochloric acid solutions
to give lower molecular weight products. Long and co-
workers13 prepared, via anionic polymerization, star
polymers of MMA, isobutyl methacrylate, and tert-butyl
methacrylate cross-linked with 2,5-dimethyl-2,5-hex-
anediol dimethacrylate and dicumyl alcohol dimethacry-
late, whose core was subsequently hydrolyzed using
p-toluenesulfonic acid in dioxane at 100 °C.
Another interesting type of polymeric materials is
that of polymer model networks,14 which are also
prepared using “living” polymerization techniques to
ensure precise lengths of the chains between cross-links
(known as elastic chains), which is the main distin-
guishing feature of these materials. However, to the best
of our knowledge, no polymer model networks with
hydrolyzable cross-links have been reported to date. A
new type of polymer model networks, again based on
nonhydrolyzable cross-links, is that of cross-linked star
polymer model networks (CSPMNs)15-17 developed re-
Star,1 graft,2 and hyperbranched3 polymers, polymer
surfaces,4 and polymer networks with cleavable branches
are unique materials whose molecular weight (MW) and
properties dramatically change upon branch removal.
A particular category of these materials is that whose
labile component is a cleavable divinyl cross-linker.
Such materials can be exploited in various applications.
For example, hydrolyzable polymer networks can be
used as biodegradable orthopaedic implants5,6 and as
drug7 and protein8 delivery matrices. Thermally cleav-
able polymer networks can be applied for the “rework-
ing” of components in electronics and optics industries,
where defective parts may be easily replaced or com-
ponents may be held firmly in place during manufacture
but may be removed if so desired.9
The preparation of these polymeric systems can be
performed either by “living” polymerization methods10
that secure better structural control or by “nonliving”
methods which are synthetically easier. From the
“nonliving” methods, free radical polymerization is the
most common. For example, Mikos and co-workers5,6
prepared by free radical cross-linking poly(propylene
fumarate) diacrylate networks with main-chain hydro-
lyzable ester bonds. Ulbrich and colleagues7 prepared
degradable networks based on a cross-linker containing
-COONHCO- groups, hydrolyzable at neutral and
alkaline pH. Fre´chet and co-workers8 synthesized, using
free radical polymerization, polyacrylamide networks
cross-linked randomly via a diacrylamide methoxyben-
zaldehyde acetal, cleavable at acidic pH. Horkay and
colleagues11 prepared dextran hydroxyethyl methacr-
ylate hydrogels with labile carbonate ester bonds. Ober
and colleagues9 polymerized by free radical polymeri-
* To whom correspondence should be addressed: e-mail
costasp@ucy.ac.cy.
10.1021/ma049618+ CCC: $27.50 © 2004 American Chemical Society
Published on Web 08/06/2004

Macromolecules, Vol. 37, No. 18, 2004
Hydrolyzable Star Polymer Model Networks 6735
cently by our research team, using a “living” polymer-
ization technique, group transfer polymerization
(GTP).18-21 The characteristic feature of CSPMNs is the
presence of a large number of dangling chains in
addition to the elastic chains. These networks are
prepared by the sequential addition of monomer-cross-
linker-monomer-cross-linker under GTP conditions.
The dangling chains are formed upon the first addition
of monomer, whereas the elastic chains are formed upon
the second addition of monomer. The two additions of
cross-linker give rise to the formation of two different
types of cores, the primary cores and the secondary
cores, formed upon the first and second additions of
cross-linker, respectively. Primary cores are only con-
nected to secondary cores, and secondary cores are only
connected to primary cores. The secondary cores bear
only elastic chains, while the primary cores bear an
equal number of dangling and elastic chains.
F igu r e 1. 1H NMR spectrum of the dimethyldi(methacrylo-
yloxy-1-ethoxy)silane (DMDMAES) cross-linker in CDCl3.
The purpose of this investigation was the synthesis
of CSPMNs containing a hydrolyzable cross-linker and
the examination of their hydrolysis. To this end, the
preparation and purification of a novel, acid-labile,
silicon-containing dimethacrylate cross-linker were nec-
essary. A nonhydrolyzable cross-linker was also em-
ployed in the syntheses. Thus, one type of core of the
CSPMNs, primary or secondary, was based on the
hydrolyzable cross-linker, while the other type of core
was based on the nonhydrolyzable one. To the best of
our knowledge, this is the first report on the GTP of a
hydrolyzable cross-linker, and this is also the first report
on hydrolyzable CSPMNs.
Exp er im en ta l Section
F igu r e 2. Chemical structures and names of the main
reagents used for the polymer synthesis: the monofunctional
initiator MTS, the monomer MMA, and the cross-linkers
EGDMA and DMDMAES.
Ma ter ia ls a n d Meth od s. 2-Hydroxyethyl methacrylate
(HEMA, 97%) was purchased from Merck, Germany. Dichloro-
dimethylsilane (99%), triethylamine (Et3N, 99.5%), tetrabu-
tylammonium hydroxide (40% w/w solution in water), benzoic
acid (99.5%), MMA (99%), ethylene glycol dimethacrylate
(EGDMA, 98%), 1-methoxy-1-trimethylsiloxy-2-methyl pro-
pene (MTS, 95%), and 2,2-diphenyl-1-picrylhydrazyl hydrate
(DPPH, 95%) were purchased from Aldrich, Germany. Tet-
rahydrofuran (THF, 99.8%) was purchased from Labscan,
Ireland, and was used as the mobile phase in chromatography
(HPLC grade) and as a solvent (reagent grade) both in the
reaction for the synthesis of the cross-linker and for the
polymerizations.
The solvent, THF, was dried by refluxing it over a potas-
sium-sodium mixture for 3 days and was freshly distilled prior
to use. Et3N was dried by stirring it for 3 days over calcium
hydride and was vacuum-distilled just before its use. HEMA
and dichlorodimethylsilane were freshly distilled under vacuum
just before their use and kept under a dry nitrogen atmo-
sphere. The polymerization catalyst TBABB was synthesized
by the reaction of tetrabutylammonium hydroxide and benzoic
acid in water, following the procedure of Dicker et al.,20 and
was kept under vacuum until use. MMA and EGDMA were
passed through basic alumina columns to remove protonic
impurities and polymerization inhibitors. They were subse-
quently stirred over calcium hydride (to remove the last traces
of moisture and protic impurities) in the presence of an added
free-radical inhibitor, DPPH, and stored in the fridge at about
5 °C. Both MMA and EGDMA were freshly distilled under
vacuum just before their use and kept under a dry nitrogen
atmosphere. The initiator was distilled once prior to the
polymerization, but it was neither contacted with calcium
hydride nor passed through basic alumina columns because
of the risk of hydrolysis. All glassware was dried overnight at
120 °C and assembled hot under dynamic vacuum prior to use.
Cr oss-Lin k er Syn th esis. The acid-labile cross-linker, di-
methyldi(methacryloyloxy-1-ethoxy)silane (DMDMAES), was
prepared by the etherification reaction of HEMA with di-
chlorodimethylsilane in THF and in the presence of Et3N base.
A typical synthesis is detailed in the following. THF (100 mL),
Et3N (24.7 mL, 17.9 g, 0.177 mol), and HEMA (18.3 mL, 19.6
g, 0.151 mol) were syringed to a 250 mL round-bottom flask,
kept under a dry nitrogen atmosphere, and equipped with a
mechanical stirrer and a thermometer. The contents were
stirred and cooled to 0-5 °C. Then, dichlorodimethylsilane (7.3
mL, 7.8 g, 0.060 mol) was added slowly under stirring, giving
an exotherm (3.2-10.8 °C). The reaction mixture was stored
in the refrigerator overnight, after the addition of the free
radical inhibitor DPPH to avoid thermal polymerization. The
reaction mixture was filtered in order to remove the precipi-
tated salt of triethylamine hydrochloride. THF (50 mL) was
added to wash the filtrate. THF and unreacted Et3N were
subsequently removed under reduced pressure using a rotary
evaporator at room temperature. The resulting oily residue
was purified by column chromatography (silica gel/CΗ2Cl2:
hexane 75:25). An oily liquid was obtained (yield 7.2 g, 40.1%),
which was then distilled under vacuum. The high purity of
1
the cross-linker was confirmed by H NMR spectroscopy, and
the relevant spectrum is displayed in Figure 1. 1H NMR: 0.16
[s, (CH3)2Si, 6 H], 1.94 [s, 2 (CH3C), 6 H], 3.92 [t, (OCH2CH2O)2-
Si, 4 H], 4.24 [t, (OCH2CH2O)2Si, 4 H], 5.58 (s, olefinic H trans
to CO2, 2 H), 6.13 (s, olefinic H cis to CO2, 2 H). Anal.
(C14H24O6Si) C, H, Si: calcd 53.16, 7.59, 8.86: found 53.34,
7.59, 8.47.
P olym er Syn th esis. Figure 2 shows the chemical struc-
tures and names of the main reagents used for the synthesis
of the star polymers and the polymer networks. All syntheses
were performed using GTP. The following polymeric materials
were prepared: one neat DMDMAES network, one MMA-
DMDMAES randomly cross-linked network, two “arm-first”
star polymers of MMA-DMDMAES, two CSPMNs of MMA-
DMDMAES-EGDMA, and one CSPMN of MMA-EGDMA.
The synthetic sequences employed for the preparation of these
materials are summarized in Figure 3.

6736 Themistou and Patrickios
Macromolecules, Vol. 37, No. 18, 2004
F igu r e 3. Synthetic sequences employed for the preparation of the polymers of this study. TBABB ) tetrabutylammonium
bibenzoate, polymerization catalyst; THF ) tetrahydrofuran, polymerization solvent; DMDMAES ) dimethyldi(methacryloyloxy-
1-ethoxy)silane, hydrolyzable cross-linker (prepared in this study); MTS ) 1-methoxy-1-(trimethylsiloxy)-2-methyl propene,
monofunctional initiator; MMA ) methyl methacrylate, monomer; EGDMA ) ethylene glycol dimethacrylate, nonhydrolyzable
cross-linker.
A typical polymerization yielding the first-core-hydrolyzable
MMA CSPMN MMA20-b-DMDMAES6-b-MMA20-b-EGDMA4 is
detailed in the following. TBABB catalyst (∼10 mg, ∼20 µmol),
freshly distilled THF (27 mL), and MTS initiator (0.2 mL, 0.17
g, 0.98 mmol) were added, in this order, to a 100 mL round-
bottom flask kept under a dry nitrogen atmosphere and sealed
with a rubber septum. Subsequently, MMA (2.1 mL, 2.0 g, 20
mmol) was syringed slowly under stirring, giving a polymer-
ization exotherm (25.7-33.2 °C), which abated within 5 min.
A sample of 0.1 mL was extracted from the reaction solution
for GPC analysis (full monomer conversion, polymer Mn ) 6260
g mol-1 and Mw/Mn ) 1.06), and DMDMAES (1.9 mL, 1.9 g,
5.9 mmol) was added. The reaction temperature rose from 30.1
to 32.9 °C. After sampling for GPC (full cross-linker conversion,
apparent star polymer Mn ) 13 100 g mol-1 and Mw/Mn ) 1.99),
MMA (2.1 mL, 2.0 g, 20 mmol) was added again slowly, which
produced an exotherm (30.3-34.9 °C), and a sample was
withdrawn again for GPC analysis (full monomer conversion,
apparent star polymer Mn ) 33 300 g mol-1 and Mw/Mn ) 1.58).
Finally, EGDMA (0.74 mL, 0.77 g, 3.9 mmol) was added, which
promoted the gelation of the solution within seconds and
caused a temperature increase from 32.4 to 33.1 °C.
Deter m in a tion of th e Sol F r a ction (Extr a cta bles) of
th e CSP MNs. The networks were taken out of the polymer-
ization flasks by breaking the flasks, and they were transferred
in glass bottles, where they were washed in 200 mL of THF
for 1 week to remove the sol fraction. Subsequently, the THF
solution was recovered by filtration, and the solvent was
removed using a rotary evaporator. The sol fraction was
calculated as the ratio of the mass of the dried extracted
polymer to the theoretical dry mass of the network, estimated
as the sum of monomer, cross-linkers, and initiator used for
its synthesis. The extractables were characterized in terms of
their MWDs using GPC (for the extractables of the H-N
network whose synthesis was described above, their weight
fraction was 12.7%, whereas their Mn ) 6680 g mol-1 and Mw/
Mn ) 1.62).
P olym er Hyd r olysis. All polymers formed using the
hydrolyzable cross-linker DMDMAES were hydrolyzed suc-
cessfully in THF in the presence of a small amount of
hydrochloric acid, at room temperature. For instance, 0.3 g of
the CSPMN MMA20-b-DMDMAES6-b-MMA20-b-EGDMA4 (0.27
mmol DMDMAES) in THF was hydrolyzed after 5 min in a
solution in 0.25 mL of THF, to which a drop of concentrated
HCl (12 M) (0.48 mmol) was added. The hydrolyzed polymers
were recovered by precipitation in n-hexane and were subse-
quently dried in a vacuum oven at room temperature.
P olym er Ch a r a cter iza tion . Gel Permeation Chromatog-
raphy. Molecular weights (MWs) and molecular weight dis-
tributions (MWDs) of the star polymers and their precursors,
of the network precursors, of the extractables from the
CSPMNs, and of the hydrolyzed polymer products were
determined by gel permeation chromatography (GPC) using
a single Polymer Laboratories PL-Mixed “D” column (bead size
) 5 µm; pore sizes ) 100, 500, 103, and 104 Å). The mobile
phase was THF (flow rate 1 mL min-1), delivered using a
Polymer Laboratories PL-LC1120 isocratic pump. The refrac-
tive index signal was measured using an ERC-7515A refractive
index detector supplied by Polymer Laboratories. The calibra-
tion curve was based on eight narrow MW (630, 4250, 13 000,
28 900, 50 000, 128 000, 260 000, and 520 000 g mol-1) linear
polyMMA standards supplied by Polymer Laboratories, which
provided accurate MW calculations for the linear precursors
but only qualitative estimates of the MWs of the star polymers.
In particular, the following quantities were calculated: the
number-average MWs, Mns, the polydispersity indices (PDIs)
Mw/Mn, where Mw is the weight-average MW, and the peak
MWs, Mps, which are the MWs at the peak maximum.
1H NMR Spectroscopy. The compositions of the hydrolyzed
polymer products were determined by proton nuclear magnetic

Macromolecules, Vol. 37, No. 18, 2004
Hydrolyzable Star Polymer Model Networks 6737
Ta ble 1. Resu lts of GP C a n d 1H NMR Ch a r a cter iza tion of th e Hyd r olysis P r od u cts of th e Nea t DMDMAES Netw or k a n d
th e Ra n d om ly Cr oss-Lin k ed MMA-DMDMAES Netw or k
GPC results
composition (mol % HEMA)
1
initial network
DMDMAES4
MMA30-co-DMDMAES8
hydrolysis product
theoretical MWa
Mn
Mw/Mn
theoretical
by H NMR
HEMA8
MMA30-co-HEMA16
1140
5180
1270
11100
1.38
1.22
100.0
34.8
100.0
39.1
a
The molecular weight of the initiator fragment of 100 g mol-1 has also been included in the calculation.
resonance (1H NMR) spectroscopy in deuterated chloroform
(CDCl3) or in deuterated dimethyl sulfoxide (d6-DMSO). The
spectra were recorded using a 300 MHz Avance Bruker
spectrometer equipped with an Ultrashield magnet.
dissolved in THF, giving transparent solutions. The ease
of hydrolysis of the networks based on this cross-linker
was better than that of the tertiary esters of Long and
co-workers13 and Ober et al.9 and comparable to the
acetal-based cross-linkers of Ruckenstein and Zhang12
and Fre´chet and co-workers.8
Static Light Scattering. Absolute Mws were measured by
static light scattering (SLS) using a Brookhaven molecular
weight analyzer, BI-MwA, equipped with a 30 mW red diode
laser emitting at 673 nm and a multiangle detector which
determines the intensity of scattered light at seven different
angles (35°, 50°, 75°, 90°, 105°, 130°, 145°). Polymer samples
were dissolved in HPLC-grade THF at different polymer
concentrations and were filtered through 0.45 µm pore size
syringe filters. From this information, a Zimm plot was
constructed using standard BI-MwAZP software from which
the absolute Mw was calculated as the inverse of the intercept.
The refractive index increments (dn/dc) in white light of the
polymer solutions in THF were determined using an ABBE
refractometer.
The resulting soluble polymer samples were recovered
by precipitation in n-hexane and were vacuum-dried at
room temperature. They were subsequently character-
ized in terms of their MWs and compositions by GPC
and 1H NMR, respectively. Each DMDMAES cross-
linker unit is expected to be converted upon hydrolysis
to two HEMA units. Thus, the neat DMDMAES net-
work should be converted to a linear HEMA homopoly-
mer, while the randomly cross-linked MMA-
DMDMAES network should yield a linear MMA-
HEMA random copolymer. Given that the DMDMAES/
initiator molar ratio upon synthesis was 4/1, the former
polymer should be the linear 8-mer of HEMA, while the
latter should have the formula MMA30-co-HEMA16.
Table 1 displays the experimental molecular weights
and compositions of the hydrolysis products, which
appear to be along the lines expected from the basis of
the “livingness” of GTP and the full hydrolysis of
DMDMAES. The Mn of the hydrolyzed neat DMDMAES
network is very close to the theoretically expected, while
its PDI is somewhat high (∼1.4), but still within the
limits for a “living” polymerization, especially for these
low MWs. On the other hand, the Mn of the hydrolyzed
randomly cross-linked MMA-DMDMAES network is
higher (by a factor of 2) than the theoretically expected,
indicating some initiator deactivation, while its PDI is
sufficiently low (∼1.2); the HEMA content (calculated
from the area of the peak of the methoxy protons of
MMA and the methylene esteric protons of HEMA) of
the hydrolysis products is very close to the theoretically
expected.
P r ep a r a tion a n d Hyd r olysis of Sta r P olym er s of
MMA. After demonstrating the cross-linking ability of
DMDMAES from the network formation mentioned
above, we pursued the synthesis of “arm-first” star
polymers by the sequential GTP of MMA and
DMDMAES, which are shown in reactions 3 and 4 in
Figure 3. Subsequently, we pursued the hydrolysis of
the star polymers. The synthesis and hydrolysis are
depicted schematically in Figure 4, and both proved to
be successful. The synthesis of the star polymer is based
on the ability of this polymerization method to produce
linear “living” polymers upon the addition of a meth-
acrylate monomer to a THF solution of monofunctional
initiator and catalyst and the conversion of these linear
polymers to star polymers upon the addition of a
dimethacrylate cross-linker. The labile nature of the
present cross-linker leads to its hydrolysis and its
separation into two HEMA units, thus eliminating the
interconnection between different linear chains and
converting the star polymers into linear polymers.
Table 2 shows the results for the synthesis and
hydrolysis of such a MMA-DMDMAES star polymer
Resu lts a n d Discu ssion
P r ep a r a t ion of Cr oss-Lin k er . The acid-sensitive
cross-linker DMDMAES was prepared by an etherifi-
cation reaction between HEMA and a dichlorosilane in
the presence of triethylamine base in absolute THF. A
25% mol excess of HEMA was used relative to the
reactive chlorines of dichlorodimethylsilane to ensure
a high conversion of the latter. Use of excess of the
dichlorosilane was avoided as it would lead to the
formation of the monosubstituted product as well. The
excess HEMA was removed by column chromatography,
which was used for product purification. The prepara-
tion of DMDMAES is similar to the synthesis of tri-
methylsilyl-protected HEMA, 2-(trimethylsiloxy)ethyl
methacrylate (TMSEMA).22,23 In the latter, however, an
excess of trimethylsilyl chloride is used to ensure
complete conversion of HEMA to TMSEMA, while
the volatile unreacted trimethylsilyl chloride is
easily removed by evaporation. Thus, the purification
of TMSEMA is simply accomplished by vacuum distil-
lation, requiring no column chromatography. Typical
yields of the reaction for the DMDMAES preparation
were 75%, while overall yields after column chromatog-
raphy and distillation were 41%.
P r ep a r a tion a n d Hyd r olysis of th e Nea t Cr oss-
Lin k er Netw or k a n d th e Ra n d om ly Cr oss-Lin k ed
Netw or k of MMA. To prove the efficiency of the
hydrolyzable cross-linker in forming networks via GTP,
we performed preliminary experiments in which we
prepared two simple network structures. First, a DM-
DMAES “homopolymer” (neat cross-linker) network
and, second,
a
randomly cross-linked MMA-
DMDMAES network. As shown in reactions 1 and 2 of
Figure 3, for these syntheses, the MTS initiator was
added last. In both cases, successful gelation took place
a few seconds after the MTS addition, demonstrating
the action of DMDMAES as a cross-linker.
Next, to prove the hydrolyzability of the DMDMAES
cross-linker, samples from both of these networks were
subjected to hydrolysis in excess THF after the addition
of HCl. Within 5 min, both network samples were

6738 Themistou and Patrickios
Macromolecules, Vol. 37, No. 18, 2004
Ta ble 2. Resu lts of GP C a n d 1H NMR Ch a r a cter iza tion of th e “Ar m -F ir st” Sta r P olym er MMA20-b-DMDMAES4 a n d Its
Hyd r olysis P r od u cts
GPC results
composition (mol % HEMA)
static light scattering
1
polymer sample
MMA20
MMA20-b-DMDMAES4
MMA20-b-HEMA8
theor MWa
Mn
Mw/Mn
Mp
theor
by H NMR
Mw
no. of arms
2100
N/Ab
3140
4680
9710
6900
1.06
1.55
1.12
4870
8650, 19500
7850
N/Ab
N/Ab
28.6
N/Ab
N/Ab
31.7
N/Dc
34600
N/Dc
N/Ab
7
N/Ab
The molecular weight of the initiator fragment of 100 g mol-1 has also been included in the calculation. Not applicable. c Not
a
b
determined.
F igu r e 4. Schematic representation of the synthesis and hydrolysis of an “arm-first” star polymer with a core composed of a
hydrolyzable cross-linker. TBABB ) tetrabutylammonium bibenzoate, polymerization catalyst; THF ) tetrahydrofuran,
polymerization solvent; DMDMAES ) dimethyldi(methacryloyloxy-1-ethoxy)silane, hydrolyzable cross-linker (prepared in this
study); MTS ) 1-methoxy-1-(trimethylsiloxy)-2-methyl propene, monofunctional initiator; MMA ) methyl methacrylate, monomer;
HCl ) hydrochloric acid, hydrolysis reagent.
of DMDMAES than EGDMA. Some silicon-containing
monomethacrylate monomers have also been reported
to be less reactive toward oxyanion-catalyzed GTP,
which was confirmed to be due to their bulky structure26
rather than the competition between the alkosiloxy
groups of the initiator and the alkosiloxy groups of these
monomers for the oxyanion catalyst.27
SLS of THF solutions of MMA20-b-DMDMAES4 al-
lowed the determination of its absolute Mw and weight-
average number of arms, both presented in Table 2. The
Mw is greater than the corresponding GPC Mw based
on linear PMMA standards due to the compact nature
of the star structure. The weight-average number of
arms was calculated by dividing the Mw of the star
polymer determined by SLS by the Mw of the arms
determined by GPC and was found to be 7. This value
is lower than the values of 20,28 30,16 50,15 15-40,29 and
20-10030 reported in the literature for the number of
arms of “arm-first” star polymers with EGDMA cores
also prepared by GTP.
F igu r e 5. GPC chromatograms of the “arm-first” star poly-
mers of methyl methacrylate (MMA or M) with hydrolyzable
dimethyldi(methacryloyloxy-1-ethoxy)silane (DMDMAES or D)
and nonhydrolyzable ethylene glycol dimethacrylate (EGDMA
or E) cores.
in which the molar ratio of cross-linker/initiator was 4/1,
taken from our previous work on EGDMA stars.24,25
Table 2 shows that a linear MMA homopolymer of
narrow MWD was obtained in the first step of the
polymerization. Upon the addition of the DMDMAES
cross-linker to the “living” MMA20 homopolymer, the Mn
doubles and the MWD broadens, which is consistent
with the interlinking of the linear polymer to a starlike
structure. Table 2 also displays the Mps and reveals that
the MWD of the star polymer is bimodal with maxima
at MWs corresponding to 2 and 4 times the MW of the
arm. Figure 5 shows the GPC chromatogram of this star
polymer, where the bimodal nature of the MWD is clear.
A similar bimodal distribution was observed by Ruck-
enstein and Zhang12 with their MMA star polymers
cross-linked with another hydrolyzable cross-linker,
ethylene glycol di(1-methacryloyloxy)ethyl ether.
For comparison, Figure 5 also shows the GPC chro-
matogram of a star polymer with arms bearing 20 MMA
units, too, but cross-linked with the nonhydrolyzable
cross-linker EGDMA. This EGDMA-containing star
polymer exhibits a single peak in the higher MW region
(in addition to some linear MMA arm) and has a higher
MW than the DMDMAES-containing star polymer. This
indicates that EGDMA is a more efficient cross-linker
than DMDMAES. This is probably due to the bulkier
structure of DMDMAES than EGDMA (MWs 316 and
198 g mol-1, respectively), which leads to a greater
percentage of unreacted methacrylate groups in the case
Following the above characterization, we proceeded
to the hydrolysis of this star polymer. The hydrolysis
1
products were characterized by GPC and H NMR, and
the results are also displayed in Table 2. GPC showed
that, upon hydrolysis, the MW decreased, approaching
the value of the arm but remained higher due to the
incorporation of eight HEMA units. 1H NMR confirmed
the presence of the expected percentage of HEMA in the
hydrolyzed product.
To optimize the amount of hydrolyzable cross-linker
necessary for the synthesis of the star polymers, further
syntheses of star polymers were performed, where the
molar ratio of DMDMAES to initiator was varied
systematically. Thus, in a single reactor, after the
formation of linear MMA homopolymer with 20 units,
amounts of DMDMAES were successively added so that
the final DMDMAES/MTS molar ratio was 2, 4, 6, and
8. After the polymerization of each successive amount
of cross-linker, samples were withdrawn for GPC analy-
sis. The GPC chromatograms of the analyzed samples
are overlaid in Figure 6, and the results of the MW
calculation are summarized in Table 3.
Figure 6 shows that the linear homopolymer MMA20
has a unimodal and narrow molecular weight distribu-
tion, with a PDI of 1.07 and an Mn of 4050, listed in

Macromolecules, Vol. 37, No. 18, 2004
Hydrolyzable Star Polymer Model Networks 6739
large percentages (>30%) of unattached linear chains
and secure a number of arms larger than four. The low
efficiency of the EGDMA cross-linker in the work of
Held and Mu¨ller31 might be due to its polymerization
after that of the more reactive tert-butyl acrylate
monomer.
Ruckenstein and Zhang12 also investigated the syn-
thesis of star-shaped poly(MMA) by anionic polymeri-
zation using ethylene glycol di(methacryloyloxy)ethyl
ether as a hydrolyzable cross-linker. These workers
varied the cross-linker to initiator molar ratio from 3
to 8. GPC analysis showed that the MWs increased as
the cross-linker ratio increased. Similar to our results,
the MWs were always relatively low and the PDIs high.
In particular, as the cross-linker to initiator molar ratio
increased from 3 to 8, the Mns increased from 8500 to
15 500 g mol-1, and the PDIs increased from 1.4 to 2.2,
again in agreement with our results.
F igu r e 6. GPC chromatograms of hydrolyzable “arm-first”
star polymers of methyl methacrylate (MMA or M) with
different loadings of the dimethyldi(methacryloyloxy-1-ethoxy)-
silane (DMDMAES or D) hydrolyzable cross-linker. The GPC
chromatograms of the linear polyMMA precursors and of the
linear hydrolysis product poly(MMA-b-HEMA) are also shown.
The final star polymer with DMDMAES/MTS molar
ratio of 8 was hydrolyzed using HCl. According to the
stoichiometry, the hydrolysis products should be MMA-
HEMA diblock copolymers with 20 units of MMA and
16 units of HEMA. The results from the GPC analysis
are listed in Table 3, indicating that the hydrolysis
Ta ble 3. Resu lts of GP C Ch a r a cter iza tion of th e
“Ar m -F ir st” Sta r P olym er s MMA20-b-DMDMAESx a n d
Th eir Hyd r olysis P r od u ct
GPC results
theor
polymer sample
MWa
2100
Mn
Mw/Mn
Mp
products have an Mn of approximately 8500 g mol-1
,
MMA20
4050
5680
7890
1.07
1.22
1.41
4310
which is twice the value of the Mn of the linear MMA
homopolymer precursor, just as expected. Note that
these two values of Mn are twice the corresponding
theoretical values listed in Table 3, due to partial
initiator deactivation.
MMA20-b-DMDMAES2 N/Ab
MMA20-b-DMDMAES4 N/Ab
5460, 12200
4740, 8350,
16200
5460, 11600,
22500
4970, 16200,
30700, 58000
9560
MMA20-b-DMDMAES6 N/Ab 10500
MMA20-b-DMDMAES8 N/Ab 13000
1.73
2.32
1.12
P r epar ation an d Hydr olysis of CSP MNs of MMA.
After establishing our ability to prepare and hydrolyze
star polymers of MMA, we proceeded to prepare and
hydrolyze model networks based on cross-linked star
polymers15-17 of MMA. The synthesis of these materials
involved two extra steps compared to that of the star
polymers, namely, a second addition of MMA to grow
arms from the center of the star polymers outward and
obtain the so-called “in-out” star polymers and a second
addition of cross-linker to interlink the “in-out” star
polymers to a network. The synthesis and hydrolysis of
two such networks are represented schematically in
Figures 7 and 8, where both the hydrolyzable and
nonhydrolyzable cross-linkers were used. In particular,
in Figure 7, the hydrolyzable DMDMAES cross-linker
was used for the formation of the cores of the “arm-first”
star polymers (primary cores) and the nonhydrolyzable
EGDMA cross-linker was used for the formation of the
cores that interconnect the “in-out” star polymers to
networks (secondary cores), while the reverse was
applied in Figure 8. In these figures, the hydrolyzable
DMDMAES cores are drawn in white, whereas the
nonhydrolyzable EGDMA cores are painted black. The
molar ratios of cross-linker to initiator were 6/1 for
DMDMAES, as determined in the star polymer synthe-
sis optimization study described above, and 4/1 for
EGDMA, as determined in previous studies.24,25 The
asterisks in the figures indicate the active (“living”)
polymerization sites. The CSPMNs in Figures 7 and 8
will be henceforth abbreviated as H-N and N-H,
respectively, indicating the order of addition of the
hydrolyzable (H) and nonhydrolyzable (N) cross-linkers.
A third CSPMN with both cores based on the nonhy-
drolyzable EGDMA cross-linker was also synthesized
as a control, and this will be abbreviated as N-N.
MMA20-b-HEMA16
4180
8610
a
The molecular weight of the initiator fragment of 100 g mol-1
b
has also been included in the calculation. Not applicable.
Table 3. With each successive addition of DMDMAES
cross-linker, the MWs of the polymer products grew and
their MWDs broadened significantly, presenting up to
four individual peaks. In particular, as the DMDMAES/
MTS ratio increased from 2 to 8, the Mns of the polymers
increased from approximately 5500 to 13 000 g mol-1
while the PDIs increased from 1.2 to 2.3. The increase
in MW is associated with the interconnection of the
linear chains to form star polymers, which are further
interconnected and get larger by each successive addi-
tion of cross-linker. The individual peaks, observed in
the MWDs, are due to star polymers with certain num-
ber of arms. For the MWDs of the star polymers with
the higher DMDMAES/MTS ratios, 6 and 8, the peak
of the linear MMA polymer can be seen on the lower
MW side of the chromatograms on the right. From the
relative peak areas, the linear polymers contributed 17.5
and 16.0% to the total mass of the samples with 6 and
8 DMDMAES/MTS molar ratio, respectively. Thus, by
increasing the DMDMAES/MTS ratio from 6 to 8, no
significant incorporation of linear polymer into the star
was achieved. It was, therefore, decided that a DMD-
MAES/MTS ratio of 6 was optimal for the synthesis.
Note that the optimal cross-linker/initiator molar ratio
may differ from cross-linker to cross-linker. For in-
stance, for the more effective EGDMA cross-linker, a
molar ratio of EGDMA/MTS of 4/1 has been deter-
mined.24,25
Held and Mu¨ller31 also had to use a relatively high
(10-15) molar ratio of cross-linker to initiator for the
preparation by anionic polymerization of “arm-first” tert-
butyl acrylate star polymers with EGDMA cores to avert
The network hydrolysis products are also shown in
Figures 7 and 8. The black and white colors in the linear

6740 Themistou and Patrickios
Macromolecules, Vol. 37, No. 18, 2004
F igu r e 7. Schematic representation of the synthesis and hydrolysis of the H-N cross-linked star polymer model network (CSPMN)
MMA20-b-DMDMAES6-b-MMA20-b-EGDMA4, containing the hydrolyzable dimethyldi(methacryloyloxy-1-ethoxy)silane (DMDMAES)
and the nonhydrolyzable ethylene glycol dimethacrylate (EGDMA) cross-linker in the primary and secondary cores, respectively.
TBABB ) tetrabutylammonium bibenzoate, polymerization catalyst; THF ) tetrahydrofuran, polymerization solvent; MTS )
1-methoxy-1-(trimethylsiloxy)-2-methyl propene, monofunctional initiator; MMA ) methyl methacrylate, monomer; HCl )
hydrochloric acid, hydrolysis reagent.
F igu r e 8. Schematic representation of the synthesis and hydrolysis of the N-H cross-linked star polymer model network (CSPMN)
MMA20-b-EGDMA4-b-MMA20-b-DMDMAES6, containing the nonhydrolyzable ethylene glycol dimethacrylate (EGDMA) cross-
linker and the hydrolyzable dimethyldi(methacryloyloxy-1-ethoxy)silane (DMDMAES) cross-linker in the primary and secondary
cores, respectively. TBABB ) tetrabutylammonium bibenzoate, polymerization catalyst; THF ) tetrahydrofuran, polymerization
solvent; MTS ) 1-methoxy-1-(trimethylsiloxy)-2-methyl propene, monofunctional initiator; MMA ) methyl methacrylate, monomer;
HCl ) hydrochloric acid, hydrolysis reagent.
segments of the hydrolysis products denote the MMA
and HEMA units (the latter produced after the DMD-
MAES hydrolysis), respectively. The hydrolysis products
of both H-N and N-H networks are star copolymers
with EGDMA cores. The star copolymers resulting from
the H-N networks comprise arms approximately twice
as long as those of the N-H stars. Moreover, the former
copolymers are homo-arm star copolymers based on
ABA triblock copolymer arms of MMA-HEMA-MMA,
while the latter copolymers are hetero-arm copolymers
based on MMA homopolymer arms and diblock HEMA-
MMA copolymer arms with HEMA outer blocks.
polymer) to the three (H-N, N-H, and N-N) cross-
linked star polymer model networks were withdrawn
during synthesis and were characterized by GPC. The
GPC chromatograms are plotted in Figure 9, and the
calculated MWs and PDIs are listed in Table 4. The
chromatograms show that, with each addition of mono-
mer or cross-linker, the MWDs move to higher MWs,
as expected. The calculations of the average MWs in
Table 4 confirm this trend.
The top panel of Figure 9 shows the chromatograms
of the three precursors to the H-N network. Whereas
the chromatogram of the linear precursor MMA20 is
narrow and unimodal, the MWDs of the “arm-first” and
“in-out” star polymers, both based on the hydrolyzable
Samples of the three precursors (linear MMA homo-
polymer, “arm-first” star polymer, and “in-out” star

Macromolecules, Vol. 37, No. 18, 2004
Hydrolyzable Star Polymer Model Networks 6741
Ta ble 4. Resu lts of GP C Ch a r a cter iza tion of th e P r ecu r sor s to th e Cr oss-Lin k ed Sta r P olym er Mod el Netw or k s, th e
Extr a cta bles fr om th e Netw or k s, a n d th e Hyd r olysis P r od u cts of th e Netw or k s
GPC results
theor
sample name
polymer formula
H-N Network
MWa
Mn
Mw/Mn
Mp
homopolymer
“arm-first” star
“in-out” star
hydrolysis product
extractables
MMA20
2100
N/Ab
N/Ab
N/Ab
N/Ab
6260
1.06
1.99
1.58
1.46
1.62
6910
MMA20-b-DMDMAES6
13 100
33 300
1540000
6680
6290, 11600, 23000
4740, 19600, 41600, 63700
6600, 31100, 1560000
6070, 26600
MMA20-b-DMDMAES6-b-MMA20
MMA20-b-HEMA12-b-MMA20-b-EGDMA4
MMA20-b-DMDMAES6-b-MMA20-b-EGDMA4
N-H Network
homopolymer
“arm-first” star
“in-out” star
hydrolysis product
extractables
MMA20
MMA20-b-EGDMA4
2100
N/Ab
N/Ab
N/Ab
N/Ab
5120
73 100
135 000
7520000
77000
1.06
1.21
1.36
3.89
1.08
5460
5210, 80700
MMA20-b-EGDMA4-b-MMA20
MMA20-b-EGDMA4-b-MMA20-b-HEMA12
MMA20-b-EGDMA4-b-MMA20-b-DMDMAES6
N-N Network
MMA20
MMA20-b-EGDMA4
4970, 17000, 123000
5020, 106000, 7360000
5530, 18500, 79900
homopolymer
“arm-first” star
“in-out” star
extractables
2100
N/Ab
N/Ab
N/Ab
4490
66200
155000
6880
1.07
1.28
1.43
1.12
4780
4100, 72600
5020, 15000, 135000
8080, 24200
MMA20-b-EGDMA4-b-MMA20
MMA20-b-EGDMA4-b-MMA20-b-EGDMA4
a
b
The molecular weight of the initiator fragment of 100 g mol-1 has also been included in the calculation. Not applicable.
Ta ble 5. Sol F r a ction (Extr a cta bles) of th e Th r ee Cr oss-Lin k ed Sta r P olym er Netw or k s
linear content in
network name
network formula
sol fraction (% w/w)
sol fraction (% w/w)
H-N network
N-H network
N-N network
MMA20-b-DMDMAES6-b-MMA20-b-EGDMA4
MMA20-b-EGDMA4-b-MMA20-b-DMDMAES6
MMA20-b-EGDMA4-b-MMA20-b-EGDMA4
12.7
20.5
6.9
72.5
76.3
93.0
cross-linker, exhibit three and four peaks, respectively.
In both cases, the lowest MW peak corresponds to the
unattached linear polymer. The Mps of all these species
are listed in Table 4, where all lower Mps are around
6000 g mol-1. For the “arm-first” star polymer, the two
are again integer multiples of the lowest of the three
peaks: 20 000, 42 000, and 64 000 g mol-1, implying
again a star-star coupling mechanism. Unlike the
“arm-first” star polymer, the peak of the linear homo-
polymer was fully resolved from the three peaks of the
“in-out” star polymer. Thus, the PDI of the “in-out”
star polymer reported in Table 4 was calculated only
for the star polymers without the peak of the linear
polymer and came out to be near 1.6, lower than that
of the “arm-first” star polymer.
extra peaks are at around 12 000 and 23 000 g mol-1
,
which are 2 and 4 times the MW of the linear polymer.
Considering the compact nature of the star polymers,
confirmed previously by the SLS study, the above
numbers do not necessarily imply star polymers with
only two and four arms, respectively, but star polymers
with a larger number of arms, with the one being the
dimer of the other. The last observation is suggestive
of a star-star coupling mechanism.31 Because all three
peaks of the “arm-first” star polymer (including that of
the linear precursors) were unresolved in the GPC
chromatogram, the PDI reported in Table 4 was calcu-
lated for the whole distribution and came out to be near
2. The Mps of the peaks of the “in-out” star polymer
The other two panels in Figure 9 show the chromato-
grams of the three precursors to the N-H and N-N
networks. Again, the chromatograms of the linear pre-
cursors MMA20 are narrow and unimodal. The MWDs
of the “arm-first” and “in-out” star polymers, both based
on the nonhydrolyzable cross-linker, are at higher MWs
and exhibit higher PDIs compared to their linear pre-
cursors and also contain an amount of unattached linear
polymer. However, the MWDs of these star polymers
are not as broad as the MWDs of the stars based on the
hydrolyzable cross-linker, and they exhibit just one
main peak, with MW higher than that of the corre-
sponding hydrolyzable stars, and the amount of unat-
tached linear polymer is smaller. All of the above
indicate the higher linking efficiency of the nonhydro-
lyzable cross-linker compared to the hydrolyzable, as
explained in a previous section. By going from the “arm-
first” star polymer to the “in-out” star polymer, the MW
approximately doubles. The minor peak in the chro-
matograms of the “in-out” star polymers at approxi-
mately 16 000 g mol-1 has been observed before and has
been attributed to a dimer formed by the coupling
reaction between two “living” linear chains with one
EGDMA molecule16 or star polymers with a small
number of arms.
F igu r e 9. GPC chromatograms of the precursors and the
extractables of cross-linked star polymer model networks
(CSPMNs) H-N, N-H, and N-N. The GPC chromatograms
of the hydrolysis products of the H-N and N-H CSPMNs are
also shown. M, D, and E are (further) abbreviations for methyl
methacrylate (MMA), dimethyldi(methacryloyloxy-1-ethoxy)-
silane (DMDMAES), and ethylene glycol dimethacrylate
(EGDMA), respectively.
Sol F r a ction of th e CSP MNs. Table 5 shows the
sol fraction extracted from the CSPMNs H-N, N-H,
and N-N, as well as the content of the sol fraction in
linear polymer. The MWDs of the extractables are given
in Figure 9, and their calculated MWs are listed in Table

6742 Themistou and Patrickios
Macromolecules, Vol. 37, No. 18, 2004
4. Table 5 suggests that the lowest sol fraction was
extracted from the N-N network, 6.9%, whose both
types of cores are based exclusively on the more efficient
nonhydrolyzable cross-linker EGDMA. From the other
two networks, the N-H network contained a higher sol
fraction, 20.5%, because its secondary cores, more
essential for gel formation, are based on the hydrolyz-
able DMDMAES cross-linker. The sol fraction from the
H-N network was significantly lower, at 12.7%. From
the MWDs in Figure 9, it seems that the extractables
from all three networks contain a large percentage of
linear chains. Table 5 shows the percentage of the
extractables from each network in linear chains, as
calculated from the areas under the MWDs in Figure
9. The extractables from the N-N network are almost
exclusively linear chains, with 93.0% w/w linear poly-
mer, whereas the linear content of the extractables from
the other two networks are approximately 75% w/w, also
containing a respectable amount of star polymers. These
data are again consistent with the higher cross-linking
efficiency of EGDMA compared to that of DMDMAES,
which would imply that, once formed, star polymers
based on and cross-linked by EGDMA are less likely to
remain unattached to the network.
precursor to the network. Characterization by static
light scattering was possible only on the hydrolysis
product of the H-N network which could dissolve in
THF after precipitation and drying. The absolute MW
was determined to be 1 220 000 g mol-1, in fair agree-
ment with the GPC MW.
Con clu sion s
A novel hydrolyzable silicon-containing dimethacry-
late cross-linker was synthesized and polymerized by
GTP with MMA to prepare star polymers and CSPMNs.
The bulkiness of this cross-linker did not allow a large
number of arms at the cores as with more traditional
dimethacrylate cross-linkers such as EGDMA. The star
polymers and the CSPMNs were hydrolyzed in THF
using hydrochloric acid to give lower MW polymer
products. The star polymers yielded hydrolysis products
with the expected MWs, corresponding to the linear
arms. Although, upon hydrolysis, the CSPMNs readily
dissolved to give homogeneous polymer solutions, the
MWs of the resulting polymers were much higher than
expected, indicating extensive coupling of the star
polymers produced.
Ack n ow led gm en t. The Cyprus Research Promotion
Foundation is gratefully acknowledged for providing
financial support to E.T. via a PENEK 2001 Program.
The A. G. Leventis Foundation is also thanked for a
generous donation, which enabled the purchase of the
NMR spectrometer of the University of Cyprus. The
University of Cyprus Research Committee (Grant 2000-
2003) is thanked for providing funds for the purchase
of the static light scattering spectrophotometer.
Hyd r olysis P r od u cts of th e CSP MNs. The acid
hydrolysis of the H-N and N-H networks was first
confirmed qualitatively by observing the dissolution of
∼1 cm3 pieces of the THF-swollen gel in excess THF
containing HCl, in approximately 5 min. When the
network hydrolysis products were recovered by precipi-
tation in water and vacuum-dried at room temperature,
the redissolution in THF of the products from the N-H
network was impossible, either due to their very high
molecular weight or due to re-formation of some of the
network bonds upon drying. Thus, the hydrolysis prod-
ucts were characterized by GPC from the hydrolysis
solution, without recovery by precipitation. Their MWDs
are displayed in Figure 9, and the calculated MWs are
listed in Table 4. Very high MWs, with Mps at 1 600 000
and 7 400 000 g mol-1, much higher than that of the
“in-out” star precursors, were observed, indicating
interstar linkage.
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Macromolecules, Vol. 37, No. 18, 2004
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