Effect of core reactivity on the molecular weight, polydispersity, and degree of branching of hyperbranched poly(arylene ether phosphine oxide)s

Article abstract of DOI:10.1021/ma021510b

Synthesis of hyperbranched poly(arylene ether phosphine oxide)s, HB PAEPOs, from bis-(4-fluorophenyl)(4-hydroxyphenyl)phosphine oxide, la, in the presence of a series of core molecules with systematically altered reactivity of the aryl fluoride groups provides polymers with molecular weights, MWs, controlled by the concentration of the core molecule, and narrow polydispersity indices, PDIs. Polymers with number-average molecular weights ranging from 3270 to 8100 Da, and PDIs as low as 1.25 have been prepared. The core molecules utilized in this work consist of a series of fluorinated triarylphosphine oxides, tris(4-fluorophenyl)phosphine oxide, tris(3,4-difluorophenyl)phosphine oxide, and tris(3,4,5-trifluorophenyl)phosphine oxide, 2a, 2b, and 2c, respectively. The most highly activated core, 2c, provides the best control over the final MW and the lowest PDIs. The degree of branching, DB, for the HB PAEPOs decreases from 0.57 with no core to below 0.40 at higher concentrations of 2b and 2c.

Full text of DOI:10.1021/ma021510b

Macromolecules 2003, 36, 333-338
333
Effect of Core Reactivity on the Molecular Weight, Polydispersity, and
Degree of Branching of Hyperbranched Poly(arylene ether phosphine
oxide)s
Da vid P . Ber n a l, La u r a Bed r ossia n , Kelly Collin s, a n d Er ic F ossu m *
Department of Chemistry, Wright State University, 3640 Colonel Glenn Hwy., Dayton, Ohio 45435
Received September 19, 2002; Revised Manuscript Received November 22, 2002
ABSTRACT: Synthesis of hyperbranched poly(arylene ether phosphine oxide)s, HB PAEPOs, from bis-
(4-fluorophenyl)(4-hydroxyphenyl)phosphine oxide, 1a , in the presence of a series of core molecules with
systematically altered reactivity of the aryl fluoride groups provides polymers with molecular weights,
MWs, controlled by the concentration of the core molecule, and narrow polydispersity indices, PDIs.
Polymers with number-average molecular weights ranging from 3270 to 8100 Da, and PDIs as low as
1.25 have been prepared. The core molecules utilized in this work consist of a series of fluorinated
triarylphosphine oxides, tris(4-fluorophenyl)phosphine oxide, tris(3,4-difluorophenyl)phosphine oxide, and
tris(3,4,5-trifluorophenyl)phosphine oxide, 2a , 2b, and 2c, respectively. The most highly activated core,
2c, provides the best control over the final MW and the lowest PDIs. The degree of branching, DB, for
the HB PAEPOs decreases from 0.57 with no core to below 0.40 at higher concentrations of 2b and 2c.
Sch em e 1
In tr od u ction
Hyperbranched polymers have received considerable
attention over the past decade due to their interesting
properties such as large numbers of end groups, low
intrinsic viscosities, and three-dimensional structures.1-9
The physical properties and final applications of hyper-
branched polymers depend on the chemical composition,
the molecular weight (MW), the polydispersity index
(PDI), and the degree of branching (DB). Hyperbranched
polymers including alkyl10 and aryl11,12 esters and
amides13,14 to siloxanes15 have been prepared, and the
subject has been extensively reviewed.3-9
Several theoretical studies have described the struc-
tural development in terms of MW, PDI, and DB as the
polymerization reaction of an AB2 monomer proceeds.
As first predicted by Flory,1 rather high PDIs are
expected at high conversions of the A functional
groups.16-22 Because of the difficulty in determining
accurate structure-property relationships with ill-
defined systems, the high polydispersity indices are
considered to be one of the main drawbacks of hyper-
branched systems. Contributing to the high PDI values
in many of the more flexible systems, such as alkyl
esters and ethers, is the propensity for intramolecular
cyclization.23-25 Recently, attempts to prepare highly
branched polymers with low PDIs and controlled mo-
lecular weights have utilized multifunctional core mol-
ecules in conjunction with slow26,27 or batchwise10
monomer addition to the respective cores. The “core
dilution/slow monomer addition” method has been ex-
ploited to prepare hyperbranched polyglycerols26 and
poly(phenyl acetylene)s27 with controlled MWs and
narrow PDIs (<1.5).
the monomer. Of particular interest for our project is a
theoretical paper by Cheng and Wang28 where the effect
of core reactivity on the MW, PDI, and DB of hyper-
branched polymers is studied using AB2 monomers and
multifunctional cores (B′3) with varying reactivities of
B′. They have defined the reactivity ratio, â, as the ratio
of rate constants kAB′/kAB (Scheme 1). They indicate that,
at high conversions of functional groups, the final PDI
is decreased significantly with an increase in the ratio
of reactivity of B′ to B or when â . 1. In addition, it
should be possible to control the final MW of the
polymer by altering the concentration of the core. To
the best of our knowledge, no experimental work that
systematically alters the reactivity of the core functional
groups to study the effect on MW, PDI, and DB has been
reported.
We have been interested in synthesizing hyper-
branched polymers containing triarylphosphine or tri-
arylphosphine oxide groups at every repeat unit for use
as macromolecular ligands and rheological modifiers,
respectively. Our approach involves the preparation of
several AB2 monomers (Figure 1) and the subsequent
polymerization under nucleophilic aromatic substitution
conditions.33 Hyperbranched poly(arylene ether phos-
phine oxide)s (HB PAEPOs) with number-average mo-
lecular weights ranging from 9500 to 14600 Da and
molecular weight distributions from 2.44 to 3.43 have
been achieved. The degree of branching for these
polymers is approximately 0.57. Lee et al. have also
reported the polymerization of 1a .34
Other than the experimental examples of core sys-
tems that have been described above, most studies
involving the addition of core molecules have been
theoretical treatments.28-32 All of the theoretical studies
indicate that the addition of a core molecule provides
access to hyperbranched polymers with narrower PDIs
than polymers prepared in the absence of a core as long
as the reactivity of the functional groups in the core is
comparable to the reactivity of the functional groups in
The polymerization of 1a is an ideal system to study
the effect of core reactivity on MW, PDI, and DB because
10.1021/ma021510b CCC: $25.00 © 2003 American Chemical Society
Published on Web 01/01/2003

334 Bernal et al.
Macromolecules, Vol. 36, No. 2, 2003
After complete addition, the reaction mixture was allowed to
stir at room temperature for 6 h, at which time it was cooled
to 0 °C using an ice bath. A solution of 1.40 mL (16.0 mmol) of
PCl3 in 25 mL of anhydrous THF was slowly added to the
stirred mixture. The resulting mixture was allowed to stir
overnight and finally heated to reflux for 4 h. Excess Grignard
reagent was quenched with saturated aqueous ammonium
chloride. The resulting mixture was poured into a separatory
funnel, and 100 mL of ether was added. The layers were
separated; the organic layer was washed with water, dilute
sodium hydroxide, and distilled water, then dried over mag-
nesium sulfate, and filtered. The solvents were removed under
reduced pressure to afford 4.92 g (83%) of a yellow oil that
was used without further purification. GC/MS: m/z 369.
The yellow oil was dissolved in a mixture of 30 mL each of
ether and acetone. To the rapidly stirred mixture was slowly
added 3.0 mL of 30% hydrogen peroxide, and the reaction was
allowed to stir overnight. The reaction mixture was poured
into a separatory funnel, and 100 mL of toluene was added.
The layers were separated, and the organic layer was washed
with sodium thiosulfate and water and dried over magnesium
sulfate. The solvents were removed to afford a yellow solid that
was recrystallized from toluene to provide 4.32 g of 2b (84%)
as a white solid (mp ) 93-95 °C). 1H NMR (CDCl3, δ): 7.25-
7.55 (m, 3H, Ar-H). 13C NMR (CDCl3, δ): 118.9 (m), 121.6
(m), 128.0 (m), 129.3 (m), 149.3 (dd), 152.1 (dd), 152.7 (dd),
155.3 (dd). Elem. Anal. Calcd for C18H9F6OP: C, 55.98%; H,
2.35%. Found: C, 55.96%; H, 2.42%.
F igu r e 1. AB2 monomers utilized for the preparation of
hyperbranched PAEPOs via nucleophilic aromatic substitu-
tion.
the preparation of core molecules with varied reactivity
of the aryl fluoride moieties is relatively straightfor-
ward. We now wish to present our results from poly-
merizations of 1a in the presence of three triarylphos-
phine oxide core molecules, 2a , 2b, and 2c (Figure 2),
in which the reactivity of the aryl fluorides in the para
positions has been systematically altered by the pres-
ence of adjacent fluorine atoms, to study the effect of â
on MW, PDI, and DB.
Syn th esis of Tr is(3,4,5-tr iflu or op h en yl)p h osp h in e Ox-
id e, 2c. Core 2c was prepared according to the procedure used
for 2b to afford 2.37 g (97%) of 2c as a white solid (mp ) 219-
Exp er im en ta l Section
1
221 °C). H NMR (CDCl3, δ): 7.23-7.31 (m, 2H, Ar-H). 13C
NMR (CDCl3, δ): 116.9 (m), 126.0 (m), 127.5 (m), 141.7 (dt),
145.2 (dt), 150.5 (m), 153.9 (m). Elem. Anal. Calcd for C18H6F9-
OP: C, 49.11%; H, 1.37%. Found: C, 49.09%; H, 1.41%.
Gen er a l P r oced u r e for P olym er iza tion Rea ction of 1a
w ith 2b Cor e. A 100 mL round-bottom flask was charged with
1.32 g (4.10 mmol) of 1a , 0.15 g (0.4 mmol) of core 2b, 0.61 g
(4.4 mmol) of potassium carbonate, 14 mL of NMP, and 12
mL of toluene. The reaction was heated to reflux for 4 h, during
which time any water was azeotropically removed to ensure
dryness. The toluene was distilled, and the temperature of the
reaction mixture was raised to ca. 202 °C and held there for 4
h. The reaction mixture was cooled to room temperature,
filtered to remove any salts, and precipitated into 300 mL of
10% acetic acid to afford the polymer as an off-white solid.
The polymer was dissolved in THF and reprecipitated from
water to provide a low-density, white solid that was filtered,
washed with water, and dried under vacuum to yield 1.10 g
of polymer. 1H NMR (CDCl3, δ): 7.08-7.25 (b, 4 H), 7.60-
7.64 (b, 4 H). 13C NMR (CDCl3, δ): 116.6 (m), 119.4 (m), 127.1
(m), 127.9 (m), 128.6 (m), 129.3 (m), 134.9 (m), 159.8 (s), 163.9
(s), 167.2 (s). 31P NMR (CDCl3, δ): 28.5 (s), 28.7 (s), 28.9 (s).
All reactions were performed under a nitrogen atmosphere,
and all transfers were done using syringes or cannula as
necessary. All of the chemicals were purchased from Aldrich
Chemical Co., with the exceptions of 1-bromo-3,4-difluoroben-
zene and 1-bromo-3,4,5-trifluorobenzene which were purchased
from Fluorochem USA. All reagents were distilled or otherwise
purified prior to use. Tetrahydrofuran and toluene were dried
over and distilled from sodium/benzophenone prior to use.
N-Methylpyrrolidinone was dried over CaH2 and distilled prior
to use. Monomer 1a was prepared according to a previously
reported procedure.33 The phosphine precursor to core 2a is
available from Aldrich.
1H, 13C, and 31P NMR spectra were obtained using a Bruker
Avance DMX 300 MHz instrument operating at 300, 75.5, and
121.5 MHz, respectively. Samples were dissolved in CDCl3.
GPC analysis was performed using a Viscotek model 300 TDA
system equipped with refractive index, viscosity, and light
scattering detectors operating at 70 °C. Polymer Laboratories
5 µm PL gel columns (guard column, 103 and 104 Å) were used
with NMP (with 0.5% LiBr) as the eluent and a Thermosepa-
ration model P1000 pump operating at 0.8 mL/min.
Syn th esis of Tr is(3,4-d iflu or op h en yl)p h osp h in e Ox-
id e, 2b. A 100 mL round-bottom flask, equipped with an
addition funnel and reflux condenser, was charged with 1.26
g of magnesium turnings. A solution of 9.75 g (50.5 mmol) of
1-bromo-3,4-difluorobenzene in 50 mL of anhydrous THF was
added dropwise over a period of 1 h to maintain a gentle reflux.
Resu lts a n d Discu ssion
In order for the core to effectively control the MW and
PDI in the polymerization of 1a , similar, if not better,
reactivity of the aryl fluoride moieties toward nucleo-
F igu r e 2. Phenoxide derivative, 1d , of 1a and the core molecules for the polymerization of 1a .

Macromolecules, Vol. 36, No. 2, 2003
Hyperbranched Poly(arylene ether phosphine oxide)s 335
Sch em e 2
F igu r e 3. GPC traces of the polymers prepared with no core
and 3% of core 2a , 2b, and 2c.
Sch em e 3
F igu r e 4. GPC traces of the polymers prepared with 5% of
core 2a , 2b, and 2c.
conditions (K2CO3, NMP at reflux) with reaction times
of 8 h (see Scheme 3). To ensure that no oligomeric
species are lost during precipitation, slightly acidic
water has been used as the nonsolvent. GPC traces of
the products from the polymerization reactions are
displayed graphically for the 3, 5, and 10% core reac-
tions in Figures 3, 4, and 5, respectively, and the results
are listed in Table 1. It should be kept in mind that the
number-average molecular weights given in Table 1 are
reported relative to linear polystyrene standards and,
as such, cannot be taken as absolute values, but only
used for comparison purposes in the following discus-
sion.
As expected from the theoretical predictions, the
presence of the core molecules decreases the number-
average molecular weights of the polymers with a
concurrent reduction in the molecular weight distribu-
tions. It is noted that, in stark contrast to previous
examples of narrow molecular weight distribution poly-
mers prepared by the core dilution/slow monomer ad-
dition method,26,27 the current work involves addition
of all of the monomer at the onset of the reaction.
philic aromatic substitution is required. Core 2a pro-
vides aryl fluorides with reactivities toward nucleophilic
aromatic substitution that are slightly greater than
those in the phenoxide derivative of 1a (Figure 2, 1d )
due to the decreased electron-withdrawing capability of
the phosphoryl group in the presence of phenoxide (i.e.,
â > 1). Derivatives 2b and 2c provide core molecules
with â . 1 since substitution of the para fluorine atom
should be highly activated by the presence of the
additional fluorine atoms. We have previously shown
that substitution reactions of the methoxy protected
analogues of 1b and 1c occur exclusively at the para
positions, and identical behavior is expected in this
study.33
The synthesis of core molecules 2a , 2b, and 2c is
shown in Scheme 2. Reaction of 3.15 equiv of the
appropriate Grignard reagent with phosphorus trichlo-
ride provides the precursor phosphines. Oxidation to the
desired phosphine oxides, 2a , 2b, and 2c, is achieved
by reaction with an excess of 30% hydrogen peroxide.
Washing with sodium thiosulfate removes any residual
hydrogen peroxide. After removal of the solvents, re-
crystallization from toluene provides the phosphine
oxides in analytically pure form in good to excellent
yields (69.9-95.5%).
In principle, if monomer reacts exclusively with core
molecules or growing polymeric species rather than with
another monomer, polymers will be prepared with
approximately 33 repeat units per macromolecule when
3% core is used, 20 repeat units when 5% core is used,
and 10 repeat units when 10% core is used. The
theoretical Mn is calculated according to eq 1. In our
case the repeat unit formula mass is 310 Da.
Polymerization reactions of 1a in the presence of 3,
5, and 10 mol % of 2a , 2b, and 2c have been carried
out under typical nucleophilic aromatic substitution
theor. # of repeat units
× repeat unit formula mass (1)
molecule

336 Bernal et al.
Macromolecules, Vol. 36, No. 2, 2003
Sch em e 4
F igu r e 5. GPC traces of the polymers prepared with 10% of
core 2a , 2b, and 2c.
Ta ble 1. Molecu la r Weigh t a n d P olyd isp er sity In d ex
Resu lts fr om P olym er iza tion Rea ction s of 1a in th e
P r esen ce of Cor e Molecu les
amount time Mn(theor)
polymer
core
(mol %)
(h)
(Da)
Mna (Da) PDI
3a
3b
3c
3d
3e
3f
3g
3h
3i
none
2a
2a
N/A
3
5
10
3
5
10
3
5
8
8
8
8
8
8
8
8
8
8
12500
6720
6370
4470
7910
6740
4360
8100
5840
3270
2.64
2.28
2.10
1.62
1.83
1.93
1.38
1.55
1.39
1.25
10400
6220
3110
10400
6220
3110
10400
6220
3110
the PDI is only 1.55 and decreases to 1.25 when 10% of
2c is added. The MWs that are observed approach the
theoretical values for the 3, 5, and 10% levels, indicating
that 2c is the ideal core for the polymerization of 1a by
providing a reactivity ratio, â, much greater than 1.
Degr ee of Br a n ch in g. It has been predicted that
higher percentages of core molecules (i.e., lower MW)
should lead to a slight decrease in the observed degree
of branching.28,31,32 This is observed experimentally as
a decrease in the number of dendritic units relative to
linear units present in each macromolecule and can be
quantified using NMR spectroscopy. The degree of
branching, DB, for hyperbranched systems can be
calculated using two different methods. Hawker and
Frechet12 have defined the degree of branching as
2a
2b
2b
2b
2c
2c
2c
3j
10
a
Molecular weights are reported relative to polystyrene stan-
dards.
Core 2a decreases the molecular weight compared to
the control polymer with no core and provides a signifi-
cant decrease in PDI from 2.64 down to 1.62 with 10%
of 2a . This indicates that the reactivity of the fluorine
atoms in 2a is slightly higher than that of the fluorine
atoms in 1d but that the PDI cannot be sufficiently
lowered when 2a is used at lower concentrations. The
polymer that is formed using 3% of 2a shows a slightly
lower MW than the theoretical value. This may be
explained by a change in the reactivity of the aryl
fluorides upon the initial reaction of 1d as shown in
Scheme 4.
DB(Hawker) ) (NT + ND)/(total number of units) (2)
where NT is the number of terminal units, ND is the
number of dendritic units, and the total number of units
includes the linear units. The second method has been
proposed by Holter and Frey17 and is defined as
The reaction of 1d with another 1d would lead to a
dimeric species, 1f, in which the reactivity of the aryl
fluorides (Fa) of the “end group” is similar to that of the
aryl fluorides in 2a (i.e., â is close to one; see Scheme
4). If the rate of formation of 1f is comparable to the
reaction of 1d with 2a to form 2f, the result is es-
sentially an increased number of growing polymer
species giving rise to an “apparent” concentration of core
higher than 3% with the end result being lower molec-
ular weight polymers. The effect is less noticeable at
higher concentrations of 2a , and the MWs are much
closer to the predicted values.
Polymerizations in the presence of 2b provide hyper-
branched polymers with MWs much closer to what has
been predicted and with considerably narrower PDI
values compared to those with 2a . The additional
activation that is provided by the adjacent fluorine
atoms in 2b is sufficient to provide a polymerization
process closer to the ideal case where the reaction of
1d with 2b is preferred (i.e., â . 1).
DB(Holter) ) (2ND)/(2ND + NL)
(3)
where NL is the number of linear units.
We have previously reported the degree of branching,
as defined by Hawker, for the polymer from 1a to be
0.57 (0.55 by the Holter method) by utilizing model
compounds and 13C NMR spectroscopy.33 The use of 31
P
NMR spectroscopy (Figure 6) provides a more time-
efficient estimate of the number of dendritic, linear, and
terminal units present in the HB PAEPOs. In agree-
ment with the results from 13C NMR spectra, the
upfield, middle, and downfield resonances from the
polymerization of 1a without a core have been assigned
to terminal, linear, and dendritic units, respectively.
Figure 7 displays 31P NMR spectra for the polymers
from 1a that have been prepared in the presence of 3,
5, and 10% of 2a , 2b, and 2c, respectively. The degree
of branching for polymers 3a -j according to eqs 2 and
3 are listed in Table 2. It is readily apparent that the
reactivity and percentage of core have a dramatic effect
With 2c, polymers with low PDI values are produced,
with as little as 3% of the core present. Using 3% of 2c,

Macromolecules, Vol. 36, No. 2, 2003
Hyperbranched Poly(arylene ether phosphine oxide)s 337
Ta ble 2. DB Deter m in a tion s for P olym er s fr om th e
Rea ction s of 1a in th e P r esen ce of Cor e Molecu les
polymer
core
percent
DBa
DBb
3a
3b
3c
3d
3e
3f
3g
3h
3i
none
2a
2a
N/A
3
5
10
3
5
10
3
5
0.57
0.55
0.55
0.54
0.55
0.57
0.60
0.56
0.61
N/A
0.55
0.53
0.55
0.50
0.51
0.48
0.38
0.43
0.40
N/A
2a
2b
2b
2b
2c
2c
2c
3j
10
a
Degree of branching calculated according to Hawker’s method
b
(see ref 12). Degree of branching calculated according to Holter’s
method (see ref 17).
is a slight increase in DB of 0.55 to 0.60 with 3 and 10%
core concentration, respectively. Core 2c lowers the DB
(Holter) to 0.43 at 3% and 0.40 at 5% while, again, the
Hawker method gives a slight increase in DB from 0.56
to 0.61. The DB at 10% of 2c is not discernible since
distinct peaks assigned to dendritic, linear, and terminal
units are not present in the 31P spectrum. While it has
been shown that the Hawker method favors an overes-
timation of DB for low molecular weight structures,18
it appears that with our system the core reactivity may
also play a significant role. For example, 3e and 3h have
essentially the same molecular weight (7910 and 8100
Da, respectively), yet the difference in DB between the
two methods increases significantly with an increase in
core reactivity.
F igu r e 6. 31P NMR spectrum in CDCl3 of the polymer from
polymerization of 1a without a core molecule present.
on the final microstructure of the polymer. Core 2a has
little effect on the resultant DB with only a slight
change in DB from 0.55 to 0.50 (Holter method) with
an increase in core concentration from 3 to 10% 2a .
The use of core 2b results in a more significant
decrease in DB from 0.51 to 0.38 with an increase in
core concentration from 3 to 10%, according to the
Holter method. According to the Hawker method, there
Con clu sion s
Hyperbranched poly(arylene ether phosphine oxide)s
with controlled molecular weights and narrow PDI’s
have been prepared by the polymerization of 1a in the
F igu r e 7. 31P NMR spectra in CDCl3 of the polymers from polymerization of 1a in the presence of 3%, 5%, and 10% of cores 2a ,
2b, and 2c, respectively.

338 Bernal et al.
Macromolecules, Vol. 36, No. 2, 2003
(9) Malmstrom, E.; Hult, A. J . Macromol. Sci., Rev. Macromol.
Chem. Phys. 1997, C37, 555.
(10) Malmstrom, E.; J ohansson, M.; Hult, A. Macromolecules
1995, 28, 1698.
(11) Krichjeldorf, H. R.; Zang, Q.-Z.; Schwarz, G. Polymer 1982,
23, 1821.
(12) Hawker, C. J .; Lee, R.; Frechet, J . M. J . J . Am. Chem. Soc.
1991, 113, 4583.
(13) Kim, Y. H. J . Am. Chem. Soc. 1992, 114, 4947.
(14) Ishida, Y.; Sun, A. C. E.; J ikei, M.; Kakimoto, M. Macromol-
ecules 2000, 33, 2832.
(15) Mathias, L. J .; Carothers, T. W. J . Am. Chem. Soc. 1991, 113,
4043.
(16) Parker, D.; Feast, W. J . Macromolecules 2001, 34, 5792.
(17) Holter, D.; Burgath, A.; Frey, H. Acta Polym. 1997, 48, 30.
(18) Beginn, U.; Drohmann, C.; Moeller, M. Macromolecules 1997,
30, 4112.
presence of three core molecules, 2a , 2b, and 2c. The
more highly reactive the core is toward nucleophilic
aromatic substitution, the more control is provided over
the final molecular weight and the resultant PDI. In
our case, the most highly fluorinated core, 2c, generates
polymers with molecular weights approaching the theo-
retical values and the narrowest PDIs (as low as 1.25).
This work represents the first example of an experi-
mental synthetic study in which the reactivity of the
functional groups in the core molecules has been altered
systematically to provide hyperbranched polymers with
low PDI values without requiring slow monomer addi-
tion. These results correlate well with theoretical predi-
cations by Cheng28 based on reactivity ratios of kAB′/kAB
.
The degree of branching, as defined by Holter and
Frey,17 decreased significantly when high concentra-
tions, 5 and 10%, of core molecules 2b and 2c were
added.
(19) Yan, D.; Muller, A. H. E.; Matyjaszewski, K. Macromolecules
1997, 30, 7024.
(20) Lee, Y. U.; J ang, S. S.; J o, W. H. Macromol. Theory Simul.
2000, 9, 188.
(21) J o, W. H.; Lee, Y. U. Macromol. Theory Simul. 2001, 10, 225.
(22) Vazquez, B.; Fomina, L.; Salazar, R.; Fomine, S. Macromol.
Theory Simul. 2001, 10, 762.
(23) Komber, H.; Ziemer, A.; Voit, B. Macromolecules 2002, 35,
3514.
(24) Burgath, A.; Sunder, A.; Frey, H. Macromol. Chem. Phys.
2000, 201, 782.
(25) Chu, F.; Hawker, C. J .; Pomery, P. J .; Hill, D. J . T. J . Polym.
Sci., Part A: Polym. Chem. 1997, 35, 1627.
(26) Sunder, A.; Hanselmann, R.; Frey, H.; Mulhaupt, R. Macro-
molecules 1999, 32, 4240.
Ack n ow led gm en t. The authors thank the Research
Corporation, the donors of the Petroleum Research
Fund, administered by the American Chemical Society,
and Wright State University for financial support. The
Ohio NMR Consortium is acknowledged for providing
access to high field NMR facilities. The reviewers of this
manuscript are thanked for their helpful comments and
suggestions.
(27) Bharathi, P.; Moore, J . S. Macromolecules 2000, 33, 3212.
(28) Cheng, K.-C.; Wang, L. Y. Macromolecules 2002, 35, 5657.
(29) Zhou, Z.; Yan, D. Polymer 2000, 41, 4549.
(30) Yan, D.; Zhou, Z. Macromolecules 1999, 32, 819.
(31) Hanselmann, R.; Holter, D.; Frey, H. Macromolecules 1998,
31, 3790.
(32) Radke, W.; Litvinenko, G.; Muller, A. H. E. Macromolecules
1998, 31, 239.
(33) Bernal, D. P.; Bankey, N. B.; Cockayne, R. C.; Fossum, E. J .
Polym. Sci., Part A: Polym. Chem. 2002, 40, 1456.
(34) Lee, H. S.; Takeuchi, M.; Kakimoto, M.-a.; Kim, S. Y. Polym.
Bull. (Berlin) 2000, 45, 319.
Refer en ces a n d Notes
(1) Flory, P. J . J . Am. Chem. Soc. 1952, 74, 2718.
(2) Kim, Y. H.; Webster, O. W. Macromolecules 1992, 25, 5561.
(3) Tomalia, D. A.; Frechet, J . M. J . J . Polym. Sci., Part A:
Polym. Chem. 2002, 40, 2719.
(4) J ikei, M.; Kakimoto, M.-a. Prog. Polym. Sci. 2001, 26, 1233.
(5) Sunder, A.; Heinemann, J .; Frey, H. Chem. Eur. J . 2000, 6,
2499.
(6) Inoue, K. Prog. Polym. Sci. 2000, 25, 453.
(7) Voit, B. J . Polym. Sci., Part A: Polym. Chem. 2000, 38, 2505.
(8) Kim, Y. H. J . Polym. Sci., Part A: Polym. Chem. 1998, 36,
1685.
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