Effect of sequence distribution on copolymer interfacial activity

Article abstract of DOI:10.1021/ma0509762

Interfacial segregation of diblock, gradient, and random copolymers was measured using forward recoil spectrometry. The polymers were synthesized by a ring-opening metathesis polymerization, allowing a high degree of control over the sequence distribution

Full text of DOI:10.1021/ma0509762

10494
Macromolecules 2005, 38, 10494-10502
Effect of Sequence Distribution on Copolymer Interfacial Activity
†
‡
†
§
Michelle D. Lefebvre, Christine M. Dettmer, Rachel L. McSwain, Chen Xu,
‡
§
‡
Jonathan R. Davila, Russell J. Composto, SonBinh T. Nguyen, and
Kenneth R. Shull*,†
Department of Materials Science and Engineering and Department of Chemistry, Northwestern
University, Evanston, Illinois 60208, and Department of Materials Science and Engineering and
Laboratory for Research on the Structure of Matter, University of Pennsylvania,
Philadelphia, Pennsylvania 19104-6272
Received May 10, 2005; Revised Manuscript Received September 2, 2005
ABSTRACT: Interfacial segregation of diblock, gradient, and random copolymers was measured using
forward recoil spectrometry. The polymers were synthesized by a ring-opening metathesis polymerization,
allowing a high degree of control over the sequence distribution. The norbornene-based monomers have
reactivity ratios close to unity, which makes them ideal for facile tailoring of different gradient copolymer
profiles. The copolymers form a good weakly segregating model system for which we can obtain an estimate
of the interaction parameter ø. Mean-field theory was used to describe the interfacial segregation results
and to relate the measured quantities to the detailed molecular structure of the interface. The diblock
copolymer forms a monolayer at the interface and significantly reduces the interfacial tension, while the
random copolymer forms an interfacial wetting layer. The gradient copolymer exhibits intermediate
behavior, forming a monolayer with a larger interfacial width than that of the diblock copolymer.
Introduction
ties.3,4,6,8,9,12,13,28 Many of these studies have resulted in
data that indicate similarity between gradient copoly-
mers and either their random or block copolymer
counterparts. Farcet and Charleux detected only one
glass transition in their styrene/n-butyl acrylate copoly-
Recent advances in living polymerization chemistry
have made possible the synthesis of a variety of new
gradient copolymers where the average composition of
the copolymer varies continuously along the backbone
of the polymer molecule.1-22 These gradient copolymers
have properties that are intermediate between those of
random copolymers, which have a uniform average com-
position along the contour length of the polymer mole-
cule, and traditional block copolymers, which exhibit a
step function change in composition at the junction point
between the blocks. To date, gradient copolymers have
been successfully synthesized by nitroxide-mediated
6
mers with weak gradients. Matyjaszewski et al. dem-
onstrated microphase separation of copolymers with a
much stronger gradient through both thermal and
rheological analysis for styrene/methyl acrylate gradient
copolymers12 and by small-angle X-ray scattering (SAXS)
13
in styrene/acrylonitrile gradient copolymers. They
observed a single glass transition in a thermally
quenched gradient copolymer and two glass transitions
in an annealed gradient copolymer. Gray and co-workers
observed differences in the enthaply recovery behavior
3
,6-10
controlled radical polymerization (NM-CRP),
atom-
and
1
-4,11-19
transfer radical polymerization (ATRP),
9
of styrene/4-methylstyrene gradient and styrene/4-
reversible addition-fragmentation transfer polymeri-
8
acetoxystyrene “blocky” gradient copolymers in com-
4
,5
zation (RAFT). Recently, we reported the first syn-
thesis of gradient copolymers by ring-opening meta-
thesis polymerization (ROMP).2
parison to their random counterparts. Recently, Kim
and co-workers demonstrated the compatibilization
potential of gradient copolymers in melt-processed
0
Several theoretical studies have been conducted re-
garding the properties and applications of gradient
28
blends. They observed that a gradient copolymer
significantly stabilized immiscible blends and reduced
coarsening. Using only 5% gradient copolymer, coales-
cence was prevented in a styrene/methyl methacrylate
system and was significantly reduced in the more
incompatible styrene/n-butyl methacrylate system.
2
3-27
copolymers.
The order-disorder transition and
microphase separation morphology have been examined
2
3-25
in bulk gradient copolymers,
and numerical self-
consistent field theory was used to describe the equi-
librium interfacial behavior of gradient copolymers in
26
Studies of the segregation of gradient copolymers to
the interface between immiscible homopolymers are
particularly important, both in the development of new
routes for polymer blend compatibilization and in the
development of a robust theory for the thermodynamic
properties of gradient copolymer systems. Polymer
blends are important for the development of new
materials, but most polymer blends are incompatible
and result in poor morphology, weak adhesion between
phases, high interfacial tension, loss of mechanical
properties, and coalescence and breakup during pro-
cessing. Copolymers added as compatibilizers act as
surfactants by localizing at the interface, lowering the
interfacial tension, and dividing the immiscible poly-
immiscible polymer blends. Pickett also described how
the significance of the gradient affects the density of
free polymer ends at the surface of gradient copolymer
2
7
brushes.
While there is a growing number of reports on the
synthesis of gradient copolymers, there have been few
experimental studies that report on their proper-
†
Department of Materials Science and Engineering, North-
western University.
‡
Department of Chemistry, Northwestern University.
§
University of Pennsylvania.
*
To whom correspondence should be addressed: e-mail
k-shull@northwestern.edu.
1
0.1021/ma0509762 CCC: $30.25 © 2005 American Chemical Society
Published on Web 11/10/2005

Macromolecules, Vol. 38, No. 25, 2005
Copolymer Interfacial Activity 10495
Scheme 1. Synthesis of 1a and 1b
Figure 1. Repeat units of the two homopolymers.
mers into smaller domains. In an AB block compatibi-
lizer, the A block inserts into the A homopolymer
domain and the B block inserts into the B homopolymer
2
9
domain. Theoretical studies have shown that random
copolymers will weave in and out of the interface,
t
tion temperature Tg ) 6.4 °C) and “ butyl” (Tg ) 36.4
20
°
C). The corresponding monomers, 1a and 1b, are
3
0,31
forming loops in each homopolymer domain.
These
shown in Scheme 1. A deuterated version of the benzyl
monomer, 2, was synthesized and used in the copolymer
synthesis so that the copolymers could be detected using
forward recoil spectrometry (FRES). Interfacial segrega-
tion of the copolymers to an interface between the two
immiscible homopolymers was measured using FRES,
and mean-field theory was used to fit the data and
calculate the interfacial excess, interfacial tension, and
degree of incompatibility for each sample.
entanglements strengthen the interface by “tying” the
phases together, but a single copolymer monolayer is
not obtained; instead, a third phase or wetting layer is
3
2-34
observed, which limits compatibilization.
It has been suggested that long block copolymers
compatibilize better than random copolymers,35 but in
practice they can form micelles at low concentrations
so that individual molecules do not diffuse to the
3
6,37
interface.
Mean-field theory has been remarkably
successful in providing a quantitative description of the
surfactant-like monolayer that is formed at the interface
Experimental Section
by traditional block copolymers and of the limitations
Materials. HPLC-grade tetrahydrofuran (THF) was puri-
4
4
associated with micellization.35,38,39 Imposition of an
fied using the Dow-Grubbs purification system, collected
under argon, degassed under vacuum, and stored under
nitrogen in a Strauss flask prior to use. Ethyl vinyl ether was
increasingly broad composition gradient in the copoly-
mer broadens the width over which different segment
types mix with one another while preserving the mono-
2
dried over CaH , vacuum-transferred into an airtight solvent
bulb prior to transfer into an inert-atmosphere glovebox, and
stored at 0 °C. All monomers were synthesized and stored
under nitrogen at 0 °C. Deuterated solvents (Cambridge
Isotope Laboratories) and all other solvents and reagents were
purchased from commercial sources and used without further
purification.
26
layer-like character of the copolymer layer. Mean-field
theory predicts that the interfacial width depends on
the gradient copolymer’s radius of gyration and the
nature of the composition gradient. The critical micelle
concentration was also calculated to be larger for
gradient copolymers than block copolymers, meaning
gradient copolymers would be more likely to diffuse to
the interface and improve blend quality.
Methods. All reactions were carried out under a dry
nitrogen atmosphere using standard Schlenk techniques or in
an inert-atmosphere glovebox, unless otherwise noted. Conver-
sion of the copolymerizations was determined on a Hewlett-
Packard 5890A gas chromatograph equipped with a FID
detector and a 30 m HP-5 capillary column (0.32 mm inner
diameter, 0.25 mm film thickness; method: initial time ) 0
min, initial temp ) 50 °C, rate ) 10 °C/min, final temp ) 250
Previous studies on sequence distributions in copoly-
mers have focused on random copolymers. Fredrickson,
4
0
Milner, and Leibler as well as Shakhnovich and co-
41,42
workers
have developed theories to describe random
copolymers and the relationship between microphase
separation and the “blockiness” of the polymer. Balazs
and co-workers accounted for random copolymer se-
quence distributions explicitly in mean-field calculations
and found that the best random copolymer compatibi-
lizers have composition distributions very closely cen-
°
C, final time ) 5 min) using undecane as an internal
standard. Molecular weights relative to polystyrene standards
were measured on a Waters gel-permeation chromatograph
(GPC) equipped with Breeze software, a 717 autosampler,
Shodex KF-G guard column, KF-803L and KF-806L columns
in series, a Waters 2440 UV detector, and a 410 RI detector.
HPLC-grade THF was used as the eluent at a flow rate of 1.0
mL/min, and the instrument was calibrated using polystyrene
35,43
tered around 50%.
In this article we focus on an ideal
random copolymer with a uniform composition profile
and compare it to gradient and diblock copolymers.
Random and gradient copolymers are inherently differ-
ent from diblock copolymers because they are statistical
copolymers. While the sequence distribution for a
diblock copolymer is the same for every molecule, each
random and gradient copolymer molecule is different.
We describe a set of model experiments aimed at
studying the effect of sequence distribution on the
interfacial segregation of copolymer molecules.
1
standards (Aldrich, 15 standards, 760-1 800 000 Da). H NMR
spectra were recorded on a Varian Mercury 400 FT-NMR
1
13
spectrometer (400.178 MHz for H). C NMR spectra were
recorded on a Varian Inova 500 FT-NMR spectrometer (125.669
13
1
MHz for C). H NMR data are reported as follows: chemical
shift (multiplicity: br ) broad, s ) singlet, d ) doublet, t )
triplet, q ) quartet, and m ) multiplet), peak assignments,
1
13
and integration. H and C chemical shifts are reported in
ppm downfield from tetramethylsilane (TMS, δ scale) with the
residual solvent resonances as internal standards, while peak
assignments were made using ACD/Labs software packages
The model system we utilize consists of norbornene-
based polymers synthesized using ring-opening meta-
thesis polymerization (ROMP). ROMP is advantageous
in that it allows for polymerization at room temperature
with much faster rates of reaction than living free
(
Advanced Chemistry Development, Inc.). GC-MS experiments
were recorded on a Hewlett-Packard 6890 series instrument
equipped with a HP-5 column (initial time ) 2 min, initial
temp ) 50 °C, rate ) 10 °C/min, final temp ) 280 °C, final
time ) 5 min). All flash column chromatography was per-
formed under a positive pressure of nitrogen using 230-400
mesh silica gel (56 mm i.d. × 200 mm L), unless otherwise
noted. Monomer addition was carried out via either a Kd
2
0
radical approaches. Three copolymers and two ho-
mopolymers were synthesized using the repeat units
shown in Figure 1: “benzyl” (homopolymer glass transi-

10496 Lefebvre et al.
Macromolecules, Vol. 38, No. 25, 2005
Scientific KDS200 syringe pump or a Harvard Apparatus
syringe pump model 55-1111.
Table 1. Monomer Addition Rates (mmol/h) of 2 and 1b
throughout the Reaction for Dual-Ramping
Polymerization
exo-5-(Benzyloxy)norbornene (1a) was prepared as re-
2
0
ported previously.
time (min)
t
exo-5-[(4- Butyl)benzyloxy]norbornene (1b) was pre-
2
0
monomer
0
3
6
12
18
24
30
36
pared as reported previously.
Benzyl-d bromide was prepared from standard literature
7
5,46
2
1b
1.3
10.4
2.0
7.6
2.8
5.1
3.3
3.6
3.8
2.0
5.8
1.8
9.1
1.0
12.6
0.0
4
procedures.
The crude product was purified by flash column
chromatography with 20:80 methylene chloride:hexanes as the
elutant.
-1
-1
1
b (100 µL, 3.89 × 10 mmol), undecane (100 µL, 4.75 × 10
exo-5-(Benzyloxy)norbornene-d
7
(2) was prepared by the
mmol), and THF (140 mL) and capped with a rubber setpum.
The syringes and the flask were removed from the glovebox.
Outside the glovebox, the syringes were loaded onto two
different syringe pumps and immediately attached to the flask
by removing their septa and inserting the needles through the
flask’s septum while the flask was allowed to stir rapidly. The
catalyst solution was injected into the reaction flask, and the
solutions of 2 and 1b were simultaneously added via the
syringe pumps. The addition rate of the 2 solution was ramped
up while the 1b solution was ramped down every 3-6 min
same procedure used to prepare 1a and 1b. A colorless oil was
1
obtained (5.1813 g, 82.8%) H NMR (CDCl
3
): δ 1.58 (m,
7
4
5
2
2
-norbornenyl-H , 2H), 1.78 (d, 6-norbornenyl-H , 2H), 2.84 (s,
2
-norbornenyl-H, 1H), 2.97 (s, 1-norbornenyl-H, 1H), 3.62 (d,
-norbornenyl-H, 1H), 5.95 (m, 3-norbornenyl-H, 1H), 6.21 (m,
-norbornenyl-H, 1H). 13C NMR (CDCl
3
): δ 34.7 (6-norborne-
nyl-C), 40.6 (1-norbornenyl-C), 46.3 (7-norbornenyl-C), 46.7 (4-
norbornenyl-C), 70.4 (m, benzyl-C, J ) 87.2 Hz), 80.2 (5-
norbornenyl-C), 126.9 (m, p-aromatics-C, J ) 97.5 Hz), 127.2
(
m, m-aromatics-2C, J ) 96.5 Hz) 127.8 (m, o-aromatics-2C,
J ) 96.5 Hz), 133.4 (3-norbornenyl-C), 138.9 (ipso-C), 140.92
2-norbornenyl-C). EIMS: calcd for C14 O: 207.32; found:
07.2.
Synthesis of Homopolymers of 1a and 1b. In a typical
(
Table 1). Disposable syringes and needles used to remove
aliquots were purged with nitrogen before use. Aliquots (2 mL)
were taken 1 min after each change in addition rate and
(
2
9 7
H D
47
quenched with ethyl vinyl ether (1 mL). BHT (5 mg) and
triphenylphosphine oxide (20 mg) were then added to each
aliquot. A portion of each aliquot (0.3 mL) was loaded on a
polymerization, a scintillation vial equipped with a stir bar
was charged with either 1a or 1b (4.9 mmol) and diluted with
THF (10 mL). Another scintillation vial was charged with
plug of silica gel (3.55 cm L × 0.55 cm i.d.), eluted with CH
2
-
Cl (8 mL) and was analyzed by GC. The amount of monomer
2
-
3
Grubbs catalyst 3 (8.0 mg, 9.7 × 10 mmol) and diluted with
THF (1 mL). The catalyst solution was injected into the stirring
monomer solution, and the vial was capped. The vial was
removed from the glovebox, and after 40 min the polymeriza-
tion was quenched with ethyl vinyl ether (2 mL). 2,6-Di-tert-
butyl-4-methylphenol (BHT) (30 mg) was added, and the
polymer was precipitated in swirling methanol. The final
polymer was dried for 2 days under vacuum.
incorporated into the polymer was calculated from the amount
of remaining monomer. The remaining portion of each aliquot
was concentrated on a rotary evaporator to about 0.1 mL.
Methanol (2 mL) was then added to the residue to precipitate
the polymer, the mother liquor was decanted, and the polymer
was dried under vacuum overnight before being analyzed by
GPC.
The reaction was quenched after 42 min with ethyl vinyl
ether (5 mL). BHT (200 mg) and triphenylphosphine oxide (300
mg) were then added to the flask. The reaction solution was
concentrated on a rotary evaporator to about 5 mL and
precipitated in rapidly stirred methanol (250 mL). The pre-
cipitated polymer was collected and precipitated a second time
if necessary. The final polymer sample was collected and dried
under vacuum before analysis by GPC.
Synthesis of Asymmetrical Block Copolymer of 2 and
1
b. A scintillation vial equipped with a stir bar was charged
with 2 (500.9 mg, 2.420 mmol) and diluted with THF (7 mL).
Another scintillation vial was charged with Grubbs catalyst 3
-
3
(
2.5 mg, 3.0 × 10 mmol) and diluted with THF (1 mL). The
catalyst solution was injected into the stirring monomer
solution, and the vial was capped. Another scintillation vial
-1
was charged with 1b (145.4 mg, 5.67 × 10 mmol) and diluted
with THF (2 mL). After 40 min of polymerization, the 1b
solution was injected into the reaction mixture. The vial was
rinsed with THF (1 mL × 3) and added to the reaction mixture.
The reaction vial was removed from the glovebox, and after
Polymer Hydrogenation. This experiment was a modi-
48
fication of a literature procedure. For a typical hydrogenation,
in an inert nitrogen atmosphere glovebox, the ROMP polymer
(1046.5 mg) was dissolved in methylene chloride (25 mL) and
loaded into a 125 mL Parr reactor equipped with a magnetic
stir bar. To this solution, methanol (8 mL) was slowly added.
(If the polymer solution became cloudy, addition was ceased
early and additional methylene chloride was added until the
solution became clear again.) Grubbs catalyst 3 (22.2 mg, 27.0
mmol) was dissolved in methylene chloride (2 mL) in a
scintillation vial. The Grubbs catalyst 3 solution was then
added to the Parr reactor, and the vial was rinsed with
4
(
0 min the polymerization was quenched with ethyl vinyl ether
2 mL). BHT (30 mg) was added, and the polymer was
precipitated in swirling methanol. The final polymer was dried
for 2 days under vacuum.
Synthesis of Random Copolymers of 2 and 1b. A
scintillation vial equipped with a stir bar was charged with 2
(
459.6 mg, 2.220 mmol) and 1b (571.0 mg, 2.230 mmol) and
diluted with THF (15 mL). Another scintillation vial was
-3
charged with Grubbs catalyst 3 (7.5 mg, 9.1 × 10 mmol) and
diluted with THF (1 mL). The catalyst solution was injected
into the stirring monomer solution, and the vial was capped.
The vial was removed from the glovebox, and after 40 min the
polymerization was quenched with ethyl vinyl ether (2 mL).
BHT (30 mg) was added, and the polymer was precipitated in
swirling methanol. The final polymer was dried for 2 days
under vacuum.
methylene chloride (1.6 mL × 3). NEt
3
(15 µL) was added via
a gastight syringe, and the reactor was immediately sealed,
removed from the glovebox, pressurized with hydrogen (300
psig), and allowed to stir for 48 h in a 60 °C oil bath. The
1
reaction was monitored by H NMR spectroscopy though
opening the Parr reactor in the glovebox, removing an aliquot,
and precipitating the polymer. If the reaction was not com-
plete, the Parr reactor was repressurized with H and the
2
Synthesis of Gradient Copolymers, Dual Ramping. In
an inert-atmosphere glovebox, two 10 mL volumetric flaks
were charged with monomer 2 (0.8699 g, 4.202 mmol) and 1b
reaction was allowed to continue. Once hydrogenation was
complete, the reaction was transferred into a 500 mL round-
bottom flask and the reactor was rinsed with methylene
chloride (3 × 2 mL). The combined organics were concentrated
on a rotary evaporator to 5 mL and precipitated into rapidly
stirred methanol (200 mL). The precipitated polymer was
collected, dissolved, and precipitated a second time. The final
polymer sample was collected and dried under vacuum before
analysis by GPC. GPC analysis was performed on both the
hydrogenated and original polymer to verify that no degrada-
tion of the polymer had occurred.
(
0.6508 g, 2.542 mmol), respectively, and diluted with THF.
Both solutions were taken up into 10 mL gastight syringes
and then plugged with a septa. In a 20 mL vial, Grubbs
-
1
catalyst 3 (8.3 mg, 1.0 × 10 mmol) was dissolved in THF (2
mL), loaded into a 2.5 mL gastight syringe, and plugged with
a septa.
Next, a 500 mL round-bottom flask equipped with a
-2
magnetic stir bar was charged with 2 (4 µL, 2.4 × 10 mmol),

Macromolecules, Vol. 38, No. 25, 2005
Copolymer Interfacial Activity 10497
Scheme 2. Synthesis of 2
Scheme 3. General Reaction for Polymerization of
a
Monomers and Subsequent Hydrogenation
Figure 2. Linear change in the fraction of monomer 2 in the
feed during the polymerization time span for the synthesis of
the gradient copolymer via the dual ramping method.
in comparison to its random and block copolymer
counterparts, a gradient copolymer with a linear change
in chain composition and an overall monomer composi-
tion of 50% was desired. We previously described a dual
ramping method to synthesize 50/50 linear gradient
copolymers from monomers with reactivity ratios near
unity.20 The dual ramping method allows for more
precise control of the feed ratio than continuous addition
of one monomer at a set rate by changing the addition
rate of both monomers in a semicontinuous fashion. This
process forces the fraction of monomer in the feed to
change linearly in relation to the polymerization time
span, as shown in Figure 2.
a
(
a) THF; (b) 2:8 methanol:methylene chloride, 0.5 mol %
, 300 psig of H , 60 °C, 2 days.
Grubbs catalyst, 5 equiv of NEt
3
2
Sample Preparation. Samples were made for FRES by
layering the polymers on a silicon substrate. The benzyl
g
homopolymer has a T below room temperature; therefore, it
was chosen as the bottom layer for the samples. For each
sample, the benzyl homopolymer was blended in a toluene
solution with one of the copolymers at 5, 10, 20, or 30%
copolymer and was then spun-coat from the solution onto a
t
silicon wafer. The butyl homopolymer was spun-coat from a
For ease of experiment, we determined the extent of
polymerization and monomer incorporation via GC
quantification of unreacted monomer, an indirect but
facile method. However, the percentage of monomer
incorporated into the copolymer can also be followed by
toluene solution onto a salt crystal, floated onto water, and
picked up by the benzyl homopolymer on silicon. The benzyl/
t
copolymer layer was 600 nm thick and the butyl layer was
1
65 nm thick, as measured by profilometry of test samples
with a Tencor P-10 profilometer.
1
H NMR spectroscopy at long reaction times when
FRES. The parameters used for the FRES tests were a
beam energy of 2.6 MeV and an 8 µm filter of Mylar, which
correspond to a depth resolution of 50 nm and an accessible
depth of 600 nm. The FRES spectra were converted to volume
fraction depth profiles using deuterated standards and mea-
sured values of the relevant stopping cross sections according
to the calculations presented in the review article by Composto,
sufficient amounts of polymer can be recovered for
analysis. From the monomer conversion data, cumula-
1
tive (Fcum) and instantaneous compositions (Finst) were
calculated from eqs 1 and 2, where X and Y are the
quantities (mol) of monomers x and y in the polymer,
respectively, and F is conversion.
4
9
Walters, and Genzer.
X
X + Y
Fcum
)
(1)
(2)
Results and Discussion
Synthesis. Monomers exo-5-(benzyloxy)norbornene
t
∆Fcum
(
1a) and exo-5-[(4- butyl)benzyloxy]norbornene (1b) were
Finst ) Fcum + F
synthesized in three steps from norbornadiene (Scheme
∆F
2
0
1
1
), as described previously. The deuterated version of
a, monomer 2, was synthesized by the same procedure
Figure 3 shows Fcum and Finst of monomer 2 in the
gradient copolymer synthesized via the dual ramping
method as a function of normalized chain length (n/Nc).
Because the reactivity ratios of the two monomers are
very close to unity, the instantaneous composition (Finst)
is expected to track with the fraction of monomer 2 in
the feed monomer, shown in Figure 2. Figure 3 shows
that the polymer does have a linear gradient with an
overall composition of 50% 2, as desired.
To allow the copolymer chains to reach equilibrium
in the thin film samples, long anneal times at temper-
atures 100-120 °C above the Tg of 1b were required.
To prevent cross-linking during the annealing, the
polymers were hydrogenated (Scheme 3b) by a proce-
dure reported by Dourin et al.48 This procedure hydro-
genates ROMP polymers efficiently at moderate hydro-
gen pressures with the same catalyst 3 and avoids the
thermal degradation and loss of the benzyl ether that
results from other common polymer hydrogenation
from benzyl-d7 bromide and norbornenol (Scheme 2).
Benzyl-d7 bromide, while commercially available, was
easily synthesized through bromination of toluene-d8.
We previously demonstrated the living nature of cata-
lyst 3 toward the ROM polymerization of 1a and 1b for
the formation of “controlled” copolymers with linear
increases in Mn over time and consistently low PDI’s
(
Scheme 3a).
The reactivity ratios for 1a and 1b via ROMP using
catalyst 3 were previously measured to be 0.99 ( 0.06
2
0
and 1.13 ( 0.09, respectively. To form a gradient
copolymer from 1b and 2 with a significant change in
chain composition, a semibatch method is used. Previous
mean-field calculations predict that a symmetrical, fully
tapered gradient copolymer results in a large increase
in interfacial width between two immiscible homopoly-
2
6
mers. Therefore, to begin an experimental investiga-
tion into the interfacial behavior of gradient copolymers

10498 Lefebvre et al.
Macromolecules, Vol. 38, No. 25, 2005
Figure 3. Change in instantaneous (Finst) and cumulative
(Fcum) composition as a function of normalized chain length
for the gradient copolymer synthesized via the dual ramping
method.
Table 2. Molecular Weight and Composition of ROMP
Polymers
b
fraction 1b
a
polymer
M
w
(g/mol)
N
c
PDI
(1 - Fcum)
hydrogenated poly(1a)
hydrogenated poly(1b)
hydrogenated asymmetrical
block poly(2-b-1b)
161 000
128 000
251 000
700 1.12
555 1.16
1090 1.20
0
1
0.18
hydrogenated random
155 000
166 000
675 1.14
720 1.17
0.49
0.48
poly(2-r-1b)
hydrogenated gradient
poly(2-g-1b)
Figure 5. FRES volume fraction profiles (circles) and mean-
field theory fits (lines) for diblock copolymer samples annealed
for 89 h at 140 °C. The fits are calculated using ø ) 0.036, or
a
Based on repeat unit molecular weight of 230 g/mol. b Deter-
mined by NMR.
(
c
1 - f)øN ) 7.1, which was determined by the adsorption
isotherm shown in the inset.
convolving the profiles predicted by mean-field theory
with a Gaussian broadening function with a full width
at half-maximum of 100 nm. In this theoretical treat-
ment of the interfacial copolymer behavior, we use “A”
to denote the benzyl repeat units and “B” to denote the
t
butyl repeat units. We consider a model where an AB
copolymer segregates to a flat interface between A and
B homopolymer phases. The three copolymerssdiblock,
gradient, and randomsare defined by their composition
profiles along the chain backbone using the function
g(n), the average volume fraction of A at repeat unit n
in a chain of Nc repeat units. The overall composition
of the polymer, f, is defined as the average value of g:
Figure 4. Sample geometry for FRES experiments. Copoly-
mers are initially blended with benzyl homopolymer with x )
5, 10, 20, and 30% and segregate to the interface upon
annealing.
methods.20 The molecular weights and final composi-
tions of the polymers are listed in Table 2.
Interfacial Segregation. Samples for FRES were
prepared by blending each of the three deuterated
copolymers with the benzyl homopolymer at 5, 10, 20,
and 30% and creating a layered sample, as shown in
Figure 4. Each sample was then annealed at 140 °C for
1
Nc
Nc
1
f )
∫
g(n) dn )
∫
g(n′) dn′
(3)
0
0
with n′ ≡ n/Nc. If the two repeat units have the same
volume, the volume fractions f and g are equal to the
mol fractions Fcum and Finst, respectively, and eq 3 is an
integral representation of eq 2. We choose a reference
volume v0 that is the same for each repeat unit and
corresponds to the average repeat unit molecular weight
(230 g/mol) and make the approximations that f ) Fcum
and g ) Finst. We use (1 - f) to describe the interactions
in this system because the B block of the copolymer is
the incompatible block in the initial sample geometry.
An additional parameter, λ, is used to describe the
4
1 and 89 h and analyzed with FRES to examine the
effects of initial concentration and annealing time on
the interfacial segregation of the copolymer. The FRES
spectra were converted to copolymer volume fraction
profiles as functions of depth into the sample using
deuterated standards and measured values of the
4
9
relevant stopping cross sections.
Diblock Copolymer. Volume fraction profiles for the
asymmetric diblock copolymer at 5, 10, and 20% initial
copolymer concentration are shown in Figure 5. The
diblock copolymer behaves as expected, with an excess
of copolymer at the interface between the homopolymers
and equilibrium concentrations in each homopolymer
phase. The solid line in the figure is a fit to the data
using mean-field theory. The instrumental resolution
of the FRES technique has been accounted for by
fractional length of the gradient along the chain back-
bone.2
5,26
The gradient copolymer used here has (1 - f)
) 0.5 and a linear gradient profile that extends the
entire length of the chain, i.e., λ ) 1 (Figure 3). The
diblock copolymer has (1 - f) ) 0.2 and a step function
concentration profile, λ ) 0, and the random copolymer
has (1 - f) ) 0.5 and a uniform composition profile for
which λ is infinite.

Macromolecules, Vol. 38, No. 25, 2005
Copolymer Interfacial Activity 10499
The theoretical description of the copolymer interac-
tions begins with the Flory-Huggins expression for the
free energy of the system. The free energy per unit
volume, ∆f, is given by the following expression
kBT φha ln φha
φ
ln φhb φc ln φc
hb
∆
f )
+
+
+
{
v0
Nha
Nhb
Nc
2
ø
φ (g - φ )
(4)
∑
k
k
a
}
k
where Nha, Nhb, φha, and φhb are the degrees of poly-
merization and volume fractions of A and B homopoly-
mers, and Nc and φc are the degree of polymerization
and volume fraction of the AB copolymer. The subscript
k denotes each component in the system (ha, hb, or c),
and the volume fraction φa refers to the total volume
fraction of A repeat units. The degrees of polymerization
are the weight-average molecular weights as deter-
mined by GPC, normalized by the reference volume v0.
The interaction parameter ø is defined in terms of the
same reference volume.
The expression for the chemical potentials of the
components, µk, is derived from the free energy. For a
homogeneous mixture, it can be written as
µk
ln φ + 1
φ
k
k
Nk
2
)
-
+ ø
∫
(g (n) - φ ) dn (5)
Figure 6. FRES volume fraction profiles (circles) and mean-
field theory fits (lines) for random copolymer samples annealed
for 89 h at 140 °C. The fits are calculated using ø ) 0.036, or
∑
k
Nk
k
a
0
k T
Nk
B
(
1 - f)øN
c
) 11.9, at the coexistence chemical potential, µcoex
The first two terms represent the ideal entropy of
mixing, and the third term is the enthalpic contribution.
)
-0.002, with z*/Rgc ) 2.6.
It includes the function g(n) to account for the specific
composition distribution of each polymer.26 Equilibrium
nealed for 41 h, indicating that the samples have
reached equilibrium. The mean-field theory fits show ø
is obtained when the chemical potential of each com-
ponent is uniform throughout the entire system. To
determine the volume fraction profiles that satisfy this
condition for a multiphase system, a set of mean-field
equations is solved self-consistently using an expression
for the mean field that is based on the chemical
)
0.036, or (1 - f)øNc ) 7.1, for the diblock copolymer
samples with 5, 10, and 20% initial concentration of
copolymer. The adsorption isotherm, the interfacial
excess as a function of the depleted concentration of
copolymer, for this value of ø is shown in the inset in
Figure 5 with data points for the three samples. Based
on the mean-field theory, the value of ø would need to
be about 35% larger for micelles to form, demonstrating
that the diblock copolymers diffuse to the interface
without forming micelles in the benzyl phase. These
results are based on an assumed degree of polymeriza-
tion calculated from the chromatographically deter-
mined weight-average molecular weight. Using the
number-average molecular weight to calculate Nc re-
sults in only a small change, ø ) 0.043, and there is
not an appreciable difference in the remaining results
presented.
3
8,50
potential.
The measurable interfacial quantity that is calculated
from the results is the interfacial excess, z*. It is defined
as the excess volume fraction of copolymer at the
interface with respect to the volume fraction of copoly-
mer in the bulk and is often normalized by the copoly-
mer radius of gyration, Rgc ) a N /6, where a is the
x
c
statistical segment length. We assume a value for a that
results in an Rgc equivalent to the Rg of a polystyrene
molecule of the same molecular weight.
∞
bulk
c
z* )
∫
(φ (z) - φ ) dz
∞
(6)
c
Random Copolymer. Volume fraction profiles for
the symmetric random copolymer at 5, 10, and 30%
initial copolymer concentration are shown in Figure 6.
While the 5% sample has a low copolymer content and
has reached equilibrium, the 10 and 30% random
copolymer samples, unlike the diblock copolymer, have
not yet reached equilibrium. In the high copolymer
content samples, there is still an excess of copolymer
near the sample substrate. The random copolymers have
a slow equilibration time because the random copolymer
is not completely soluble in the benzyl homopolymer
matrix phase. While the diblock copolymer contains only
-
The set of mean-field equations is solved using boundary
conditions corresponding to the depleted concentration
of copolymer in the benzyl phase from the FRES results.
The value of ø is a variable parameter that can be
changed to obtain a good theoretical fit to the experi-
mental volume fraction profile. We report our results
in terms of (1 - f)øNc because it is a more appropriate
measure of incompatibility for copolymers than ø or øNc
alone due to the uncertainty in the value of N obtained
by GPC. For reference, the critical point for microphase
separation in diblock copolymer melts is (1 - f)øNc )
t
20% of the incompatible butyl component, the random
2
5
t
5
.25 and increases with λ. After annealing the diblock
and gradient copolymers are 50% butyl, and are thus
copolymer samples for 89 h at 140 °C, there is very little
change in the composition profiles from samples an-
more incompatible with the benzyl homopolymer. Mac-
rophase separation between a random copolymer with

10500 Lefebvre et al.
Macromolecules, Vol. 38, No. 25, 2005
Figure 7. FRES volume fraction profiles (circles) and mean-
field theory fits (lines) for 20% initial concentration random
copolymer samples annealed for 41, 89, and 361 h at 140 °C.
Figure 8. FRES volume fraction profiles (closed circles) and
mean-field theory fits (lines) for gradient copolymer samples
annealed for 89 h at 140 °C. The fits are calculated using ø )
c
The fits are calculated using ø ) 0.036, or (1 - f)øN
at the coexistence chemical potential, µcoex ) -0.002, with z*/
gc ) 2.6.
c
) 11.9,
0.036, or (1 - f)øN ) 12.5, at the coexistence chemical
potential, µ
coex
gc
) 2.16, with z*/R ) 1.9. The open circles show
R
the unannealed volume fraction profile for 30% initial con-
centration for comparison.
f ) 0.5 and a homopolymer of equal length occurs at (1
f)øNc ) 4. Using the value of ø determined by the
random copolymer. The 30% initial concentration sample
exhibits a different behavior, with a moderate volume
fraction of gradient copolymer throughout the sample
after annealing. As discussed below, this result is
suggestive of the formation of an emulsion phase at the
interface, but the FRES data do not give us enough
information to determine the structure of this sample.
Interface Character. Mean-field fits to the data are
shown as the solid lines in Figures 6-8 at the solubility
limits for the respective copolymers. For the random
copolymer, this occurs at a copolymer coexistence chemi-
cal potential, µcoex, of -0.002, with z*/Rgc ) 2.6. For the
gradient copolymer, coexistence is at µcoex ) 2.16 with
z*/Rgc ) 1.9. At low initial concentrations of copolymer,
-
diblock copolymer samples, ø ) 0.036, this random
copolymer has (1 - f)øNc ) 11.9, which is well above
the phase separation limit. In fact, the random copoly-
mer has a calculated maximum solubility of 0.24% in
the benzyl homopolymer, and it undergoes phase sepa-
ration to form domains of a second, copolymer-rich
phase within this layer.
Additional tests were performed on the random
copolymer samples at a very long annealing time of 361
h. Figure 7 shows the volume fraction profiles after 41,
8
9, and 361 h for the 20% initial concentration sample.
After 361 h, the sample has still not reached equilibri-
um. Because the copolymer and homopolymer are
phase-separated, there can only be 0.24% of solubilized
copolymer in the benzyl phase, and thus only a very
small fraction of copolymer can be diffusing toward the
interface at a given time. Thus, the remaining copoly-
mer is “tied up” in the copolymer-rich domains, and the
sample has a very slow equilibration time.
5
and 10%, the calculated volume fraction profiles fit
the experimental data well for both of the statistical
copolymers. However, at high concentrations of random
copolymer, 20 and 30%, the experimental interfacial
excess is 2-2.5 times larger than the predicted value
at coexistence. This is because the random copolymer
molecules have small variations in chemical composition
and molecular weight among themselves. While the
mean-field theory assumes that every chain is the same
and has an average composition of 50%, the actual
random copolymer molecules will differ from each other,
with some having a higher interfacial activity.3
Gradient Copolymer. Volume fraction profiles for
the symmetric gradient copolymer at 5, 20, and 30%
initial copolymer concentration are shown in Figure 8.
Like the random copolymer, the gradient copolymer has
low solubility in the benzyl homopolymer matrix. At ø
5,43,51-54
)
0.036, the gradient copolymer has (1 - f)øNc ) 12.5
For an ideal random copolymer, the chemical composi-
tion portion of a Stockmayer distribution5
5,56
suggests
and a maximum solubility of 0.15% in the benzyl
homopolymer. Thus, the gradient copolymer phase
separates to form copolymer-rich domains in the benzyl
layer, and the 10% sample has not yet reached equilib-
rium after 89 h of annealing. The 5% sample has a low
enough copolymer content so that all of the copolymer
has reached the interface, similar to the results for the
that about 5% of the molecules will differ in composition
from the mean by more than 4%. Assuming a Gaussian
distribution in molecular weight and a polydispersity
index of 1.14, 10% of the molecules will have a molecular
weight more than 1.5 times greater than the mean.
These differences within the population of random

Macromolecules, Vol. 38, No. 25, 2005
Copolymer Interfacial Activity 10501
in the 20% and 30% samples, because the coexistence
chemical potential is very close to the wetting transition.
For diblock copolymers with λ ) 0, however, the
interfacial tension between the phases reaches zero for
a relatively small value of z*/Rgc, corresponding to the
existence of a single copolymer monolayer at the inter-
face that remains relatively sharp and well-defined. The
gradient copolymer with λ ) 1 yields an interface that
is intermediate between these two extremes but is
similar to the monolayer formed by the diblock. At
coexistence, the interfacial energy of the gradient
copolymer interface is close to zero. A small variation
in chemical potential due to chemical composition and
molecular weight distributions similar to the ones seen
in the random copolymer would cause the interfacial
energy to reach zero, indicating that the copolymer
forms a single monolayer at the interface. This also
gives us some insight into the behavior seen in the 30%
gradient copolymer sample. With an interfacial energy
very close to zero, the copolymer may be facilitating the
formation of an emulsion phase.
In summary, the diblock, gradient, and random
copolymers all have a unique interfacial character,
varying from the monolayer of diblock copolymer to the
wetting layer of random copolymer. In a gradient
copolymer, the parameter λ can be tuned to achieve a
desired interfacial excess that is intermediate between
the two extremes. The ability to continuously tailor the
interfacial width by controlling the sequence distribu-
tion has important consequences on a variety of inter-
face properties, including, for example, the interface
mechanical toughness.57
Figure 9. Interfacial excess and interfacial energy as func-
tions of copolymer chemical potential for the diblock, gradient,
and random copolymers. The circles are results of the mean-
field fits to the FRES data for the diblock copolymer, and the
solid lines are calculated by mean-field theory using the value
of ø determined by the block copolymer samples, ø ) 0.036.
The squares correspond to the coexistence points for the
random and gradient copolymers, and the dotted lines are
extensions of the theory to the point where the interfacial
energy is zero.
Conclusions
We have synthesized diblock, random, and gradient
copolymers using ROMP. Because the two norbornene-
based monomers have reactivity ratios near unity, the
gradient copolymer has a linear gradient shape obtained
in conjunction with a 50/50 monomer cumulative com-
position using a dual ramping strategy. The ability to
precisely control the composition along the backbone of
the chain makes this an ideal model system for studying
the interfacial properties of the copolymers. The inter-
facial segregation of all three copolymers was measured
using FRES, and we find that the self-consistent mean-
field theory used in this work is a useful tool for
describing the copolymer interfacial activity and esti-
mating the degree of incompatibility between the two
weakly segregating repeat units. Using the diblock
copolymer data, we estimate ø to be 0.036. The gradient
parameter, λ, which describes the width of the composi-
tion gradient as a fraction of the length of the copolymer
chain, can be used to categorize the interfacial behavior
of a wide variety of copolymers. For λ ) 0, an adsorbed
monolayer is formed at the interface. The maximum
copolymer chemical potential in this case is generally
limited by the formation of micelles in one of the bulk
phases, although for the experimental system investi-
gated here, the thermodynamic interactions were weak
enough so that micellization is not expected. Instead,
the copolymer continues to adsorb at the interface until
the interfacial tension reaches zero in the high-
concentration samples. As λ increases toward the limit
of ∞ that corresponds to a random copolymer of uniform
composition, the thickness of the wetting layer at the
interface gradually increases. For sufficiently large
values of λ, the maximum copolymer chemical potential
copolymers cause some of the molecules to have a
slightly higher interfacial activity. At higher initial
concentrations of copolymer, the number of molecules
with a higher interfacial activity is proportionally larger,
so the effect is most prominent in the 20% and 30%
samples. These variations are particularly important for
the random copolymer because the coexistence chemical
potential is very close to the wetting transition where
the copolymer forms a third layer at the interface. This
effect is illustrated in Figure 9.
In Figure 9, the theoretical interfacial excess is plotted
for the diblock, gradient, and random copolymers using
ø ) 0.036, with the three diblock copolymer samples
plotted as dark circles. The normalized interfacial
energy γVc/RgckBT, where γ is the interfacial energy and
Vc is the volume of the copolymer (Vc ) v0Nc), is also
plotted as a function of copolymer chemical potential,
also for ø ) 0.036. The results for the three diblock
copolymer samples are plotted as dark circles, and the
end point of the line is where the interfacial energy is
zero. The end points (marked by squares) of the random
and gradient copolymer lines are at the coexistence
points, with dotted lines extending the theory to the
point where the interfacial energy is zero. This figure
illustrates the important differences in interfacial be-
havior as λ increases. A divergence in z*/Rgc at the
coexistence chemical potential corresponds to the for-
mation of a macroscopic wetting layer at the interface,
which is very nearly the situation for the random
copolymer (λ ) ∞). Thus, a small variation in chemical
potential could result in a large increase in z*, as seen

10502 Lefebvre et al.
Macromolecules, Vol. 38, No. 25, 2005
is no longer limited by the formation of micelles but is
instead limited by the phase separation of the ho-
mopolymer/copolymer blend into disordered copolymer-
rich domains within one of the homopolymer phases.
The gradient copolymer with λ ) 1 exhibits intermediate
behavior, forming a monolayer with low interfacial
energy at the interface but with a larger interfacial
excess and interfacial width than the monolayer formed
by the diblock copolymer. The exact value of λ can be
changed to create a tailored interfacial copolymer mono-
layer that has a desired interfacial width.
(21) Chojnowski, J.; Cypryk, M.; Fortuniak, W.; Kazmierski, K.;
Rozga-Wijas, K.; Scibiorek, M. In Synthesis and Properties
of Silicones and Silicone-Modified Materials; Clarson, S. J.,
Ed.; American Chemical Society: Washington, DC, 2003; Vol.
838, pp 12-25.
(
22) Jasso, C. F.; Lopez, L. C.; Gonzalez, I. R.; Monsebaiz, D.;
Gonzalez-Ortiz, L. J.; Garcia, R. L. H. Annu. Technol. Conf.
Soc. Plast. Eng. 2002, 60, 1640.
(
(
(
23) Pakula, T. Macromol. Theory Simul. 1996, 5, 987.
24) Aksimentiev, A.; Holyst, R. J. Chem. Phys. 1999, 111, 2329.
25) Lefebvre, M. D.; Olvera de la Cruz, M.; Shull, K. R. Macro-
molecules 2004, 37, 1118.
(
(
(
26) Shull, K. R. Macromolecules 2002, 35, 8631.
27) Pickett, G. T. J. Chem. Phys. 2003, 118, 3898.
28) Kim, J.; Gray, M. K.; Zhou, H. Y.; Nguyen, S. T.; Torkelson,
J. M. Macromolecules 2005, 38, 1037.
(
(
(
(
(
29) Brown, H. R.; Char, K.; Deline, V. R.; Green, P. F. Macro-
molecules 1993, 26, 4155.
30) Dai, C.-A.; Dair, B. J.; Dai, K. H.; Ober, C. K.; Kramer, E. J.;
Hui, C.-Y.; Jelinski, L. W. Phys. Rev. Lett. 1994, 73, 2472.
31) Yeung, C.; Balazs, A. C.; Jasnow, D. Macromolecules 1992,
25, 1357.
32) Faldi, A.; Genzer, J.; Composto, R. J.; Dozier, W. D. Phys.
Rev. Lett. 1995, 74, 3388.
33) Lee, M. S.; Lodge, T. P.; Macosko, C. W. J. Polym. Sci., Part
B: Polym. Phys. 1997, 35, 2835.
Acknowledgment. This work was supported by the
MRSEC program of the National Science Foundation
(
DMR-0520513) at the Materials Research Center of
Northwestern University and the MRSEC program
DMR05-20020) at the University of Pennsylvania.
(
References and Notes
(
(
34) Genzer, J.; Composto, R. J. Macromolecules 1998, 31, 870.
35) Lyatskaya, Y.; Gersappe, D.; Gross, N. A.; Balazs, A. C. J.
Phys. Chem. 1996, 100, 1449.
(
1) Matyjaszewski, K.; Ziegler, M. J.; Arehart, S. V.; Greszta, D.;
Pakula, T. J. Phys. Org. Chem. 2000, 13, 775.
(2) Matyjaszewski, K.; Xia, J. Chem. Rev. 2001, 101, 2921.
3) Davis, K. A.; Matyjaszewski, K. Adv. Polym. Sci. 2002, 159,
(
(
36) Adedeji, A.; Lyu, S.; Macosko, C. W. Macromolecules 2001,
(
34, 8663.
2.
37) Sundararaj, U.; Macosko, C. W. Macromolecules 1995, 28,
647.
(
(
4) Lutz, J.-F.; Pakula, T.; Matyjaszewski, K. In Advances in
Controlled/Living Radical Polymerization; Matyjazewski, K.,
Ed.; American Chemical Society: Washington, DC, 2003; Vol.
2
(
38) Shull, K. R.; Kramer, E. J. Macromolecules 1990, 23, 4769.
39) Shull, K. R.; Kramer, E. J.; Hadziioannou, G.; Tang, W.
Macromolecules 1990, 23, 4780.
(
854, pp 268-282.
5) Rizzardo, E.; Chiefari, J.; Chong, B. Y. K.; Ercole, F.; Krstina,
J.; Jeffery, J.; Le, T. P. T.; Mayadunne, R. T. A.; Meijs, G. F.;
Moad, C. L.; Moad, G.; Thang, S. H. Macromol. Symp. 1999,
(
(
(
40) Fredrickson, G. H.; Milner, S. T.; Leibler, L. Macromolecules
1992, 25, 6341.
41) Shakhnovich, E. I.; Gutin, A. M. J. Phys. (Paris) 1989, 50,
843.
42) Sfatos, C. D.; Gutin, A. M.; Shakhnovich, E. I. Phys. Rev. E
143, 291.
1
(
(
(
(
6) Farcet, C.; Charleux, B.; Pirri, R. Macromol. Symp. 2002, 182,
249.
1993, 48, 465.
7) Gray, M. K.; Nguyen, S. T.; Zhou, H.; Torkelson, J. M. Polym.
Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 2002, 43, 112.
8) Gray, M.; Zhou, H.; Nguyen, S. T.; Torkelson, J. M. Macro-
molecules 2004, 37, 5586.
(
(
43) Gersappe, D.; Balazs, A. C. Phys. Rev. E 1995, 52, 5061.
44) Pangborn, A. B.; Giardello, M. A.; Grubbs, R. H.; Rosen, R.
K.; Timmers, F. J. Organometallics 1996, 15, 1518.
(
(
(
(
(
45) Meddour, A.; Courtieu, J. Tetrahedron: Asymmetry 2000, 11,
9) Gray, M. Z.; H.; Nguyen, S. T.; Torkelson, J. Polymer 2004,
3635.
45, 4777.
46) Pedersen, A. K.; FitzGerald, G. A. J. Pharm. Sci. 1985, 74,
(
(
(
(
(
(
(
10) Mignard, E.; Leblanc, T.; Bertin, D.; Guerret, O.; Reed, W.
F. Macromolecules 2004, 37, 966.
188.
47) Wu, Z.; Nguyen, S. T.; Grubbs, R. H.; Ziller, J. W. J. Am.
Chem. Soc. 1995, 117, 5503.
48) Drouin, S. D.; Zamanian, F.; Fogg, D. E. Organometallics
11) Greszta, D.; Matyjaszewski, K. Polym. Prepr. (Am. Chem.
Soc., Div. Polym. Chem.) 1996, 37, 569.
12) Matyjaszewski, K.; Greszta, D.; Pakula, T. Polym. Prepr. (Am.
Chem. Soc., Div. Polym. Chem.) 1997, 38, 707.
2001, 20, 5495.
49) Composto, R. J.; Walters, R. M.; Genzer, J. Mater. Sci. Eng.
R 2002, 38, 107.
13) Greszta, D.; Matyjaszewski, K.; Pakula, T. Polym. Prepr. (Am.
Chem. Soc., Div. Polym. Chem.) 1997, 38, 709.
(50) Matsen, M. W. J. Phys.: Condens. Matter 2002, 14, R21.
51) van Lent, B.; Scheutjens, J. M. H. M. J. Phys. Chem. 1990,
14) Arehart, S. V.; Matyjaszewski, K. Macromolecules 1999, 32,
(
2221.
94, 5033.
15) Ziegler, M. J.; Matyjaszewski, K. Macromolecules 2001, 34,
(
52) Chen, Z. Y. J. Chem. Phys. 2000, 112, 8665.
53) Shi, T. F.; Ziegler, V. E.; Welge, I. C.; An, L. J.; Wolf, B. A.
Macromolecules 2004, 37, 1591.
415.
(
16) Boerner, H. G.; Duran, D.; Matyjaszewski, K.; da Silva, M.;
Sheiko, S. S. Macromolecules 2002, 35, 3387.
(
54) Sides, S. W.; Fredrickson, G. H. J. Chem. Phys. 2004, 121,
(
17) Gu, B.; Sen, A. Macromolecules 2002, 35, 8913.
18) Qin, S.; Pyun, J.; Saget, J.; Jia, S.; Kowalewski, T.; Maty-
jaszewski, K. Polym. Prepr. (Am. Chem. Soc., Div. Polym.
Chem.) 2002, 43, 235.
4974.
(
(
55) Stockmayer, W. H. J. Chem. Phys. 1945, 13, 199.
56) Soares, J. B. P.; Monrabal, B.; Nieto, J.; Blanco, J. Macromol.
Chem. Phys. 1998, 199, 1917.
(
(19) Neugebauer, D.; Matyjaszewski, K. Polym. Prepr. (Am. Chem.
Soc., Div. Polym. Chem.) 2003, 44, 508.
(
57) Creton, C.; Kramer, E. J.; Brown, H. R.; Hui, C.-Y. Adv.
Polym. Sci. 2002, 156, 53.
(20) Dettmer, C. M.; Gray, M. K.; Torkelson, J. M.; Nguyen, S. T.
Macromolecules 2004, 37, 5504.
MA0509762