Synthesis and characterization of well-defined, regularly branched polystyrenes utilizing multifunctional initiators

Article abstract of DOI:10.1021/ma050207i

A series of well-defined, long-branched polystyrenes (PS) of various architectures, but the same overall molecular weight, suited to the systematic study of branching effects, have been synthesized by anionic polymerization and characterized. Three end-branched, star-branched polystyrenes with 6, 9, and 13 end branches were synthesized with a trifunctional organolithium initiator; the synthesis of the 13-end molecule required a recently developed methoxysilyl functionalization and precipitation procedure to remove excess linking agent. In these architectures the number of branch points was fixed at four, while the number of chain ends varied. A 6-end, pom-pom (dumbbell-shaped) PS with two branch points was synthesized with a difunctional organolithium initiator. A regular 6-arm star polystyrene having one branch point was included to provide a comparison among three polymers, each having 6 ends, but having the number of branch points equal to 1, 2, or 4, The intrinsic viscosities and infinite dilution diffusion coefficients (and therefore the branching factors and hydrodynamic radii) decrease with increasing number of chain ends but do not vary monotonically with number of branch points. The values of T_g for the molecules reflect both the effects of tethering by junction points and increases in free volume due to the multiplication of chain ends as well as the presence of butadiene units used to facilitate linking.

Full text of DOI:10.1021/ma050207i

Macromolecules 2005, 38, 5381-5392
5381
Synthesis and Characterization of Well-Defined, Regularly Branched
Polystyrenes Utilizing Multifunctional Initiators
Jae S. Lee, Roderic P. Quirk, and Mark D. Foster*
Maurice Morton Institute of Polymer Science. The University of Akron, Akron, Ohio 44325-3909
Received January 31, 2005; Revised Manuscript Received April 27, 2005
ABSTRACT: A series of well-defined, long-branched polystyrenes (PS) of various architectures, but the
same overall molecular weight, suited to the systematic study of branching effects, have been synthesized
by anionic polymerization and characterized. Three end-branched, star-branched polystyrenes with 6, 9,
and 13 end branches were synthesized with a trifunctional organolithium initiator; the synthesis of the
13-end molecule required a recently developed methoxysilyl functionalization and precipitation procedure
to remove excess linking agent. In these architectures the number of branch points was fixed at four,
while the number of chain ends varied. A 6-end, pom-pom (dumbbell-shaped) PS with two branch points
was synthesized with a difunctional organolithium initiator. A regular 6-arm star polystyrene having
one branch point was included to provide a comparison among three polymers, each having 6 ends, but
having the number of branch points equal to 1, 2, or 4. The intrinsic viscosities and infinite dilution
diffusion coefficients (and therefore the branching factors and hydrodynamic radii) decrease with increasing
number of chain ends but do not vary monotonically with number of branch points. The values of Tg for
the molecules reflect both the effects of tethering by junction points and increases in free volume due to
the multiplication of chain ends as well as the presence of butadiene units used to facilitate linking.
Introduction
nately, attempts to prepare multifunctional initiators
generally have resulted in the formation of insoluble,
three-dimensionally associated species in hydrocarbon
media21,26-29 because of the tendency of chain ends to
exist as associated species.
Over the past few decades, the physical properties of
branched polymers have attracted considerable
attention.1-11 Branching in a polymer can result in
solution,12 surface,13-16 and bulk properties17-20 mark-
edly different than those of its linear homologue. In
these studies, the availability of well-defined branched
polymers with controlled architectures and narrow
molecular weight distributions is crucial to understand
the branching effect.9 One of the most powerful methods
for the creation of such polymers has been anionic
polymerization.21
In recent years the synthesis of the highly branched
polymers with complex architectures having internal
branch points has gone beyond the synthesis of regular
star polymers using anionic polymerization. Specifically,
highly branched polymers can be prepared by the “core-
first” method using multifunctional initiators.22-24 The
general synthetic procedure for the core-first method is
shown schematically in Scheme 1. First, a precursor
polymer having multiple living end groups is created
using the multifunctional initiator. Then the precursor
can be reacted with an excess of a multifunctional
electrophilic linking agent depending on the number of
arms one desires to attach. The resulting precursor
polymer end-capped with linking agent can be reacted
with living arm polymer prepared using anionic polym-
erization. Furthermore, it is possible to prepare highly
branched polymers using an end-linking reaction be-
tween a polymeric organolithium compound and a star
precursor prepared with a multifunctional initiator and
functionalized with an electrophilic linking agent.22,25
The advantages of the multifunctional initiator ap-
proach are primarily a consequence of the fact that the
star precursor retains the carbanionic living chain ends
of the arms after the monomer is consumed. Unfortu-
The core-first method has been used with a difunc-
tional initiator to produce H-shaped,25 pom-pom,22 or
dumbbell-shaped30 polymers via anionic polymerization.
Using sodium naphthalenide25 as a difunctional initiator
required the use of a polar medium such as tetrahydro-
furan (THF) at low temperature (4 °C) to break the
association of the initiator molecules, but these condi-
tions led to a loss of microstructure control in the
synthesis of polybutadienes. Another difunctional initia-
tor has been prepared by the treatment of divinylben-
zene with butyllithium. However, it was not effective
for the synthesis of hyperbranched polymers using the
core-first method.26 Since the difunctional initiator could
be contaminated by higher functionality initiator result-
ing from oligomerization of the divinylbenzene, the core
precursor polymer created this way had a substantial
polydispersity (Mw/Mn ) 1.2-4.1). Recently, the reaction
of high-purity sec-butyllithium with pure m-divinylben-
zene at -79 °C in the presence of 10 mol % triethyl-
amine was reported to result in an initiator with overall
functionality of 1.98 and no traces of tri- and tetrafunc-
tional impurities.31 A similar reaction with pure p-
divinylbenzene at 0 °C was reported to form a similar
dilithium initiator with 96% difunctionality and 4%
monofunctitionality.32 Another simple, stable, reproduc-
ible difunctional initiator that is soluble in hydrocarbon
media has been created using the titration of 1,3-bis-
(1-phenyethyl)benzene with butyllithium.33-36 1,1-
Diphenylethylene and its analogues usually are classi-
fied as nonhomopolymerizable monomers.37 Specifically,
Quirk and Ma35 produced a hydrocarbon-soluble difunc-
tional initiator by the quantitative addition of 2 mol of
sec-butyllithium (s-BuLi) to 1,3-bis(1-phenylethenyl)-
benzene and prepared polystyrene and polybutadiene
* Corresponding author: Tel 330-972-5323; Fax 330-972-5290;
e-mail mfoster@uakron.edu.
10.1021/ma050207i CCC: $30.25 © 2005 American Chemical Society
Published on Web 05/27/2005

5382 Lee et al.
Macromolecules, Vol. 38, No. 13, 2005
Scheme 1. General Synthetic Scheme Using the Core-First Method
were used for initiation after double-titration analysis.41 1,3,5-
Tris(benzoyl)benzene, mp 113-115 °C [lit.38 mp 113-114 °C],
was synthesized in 56% yield by a Friedel-Crafts reaction of
1,3,5-benzenetricarbonyl trichloride (Aldrich, 98%) with alu-
minum chloride in benzene followed by recrystallization in
methanol. 1,3,5-Tris(1-phenylethenyl)benzene and 1,3-bis(1-
phenylethenyl)benzene were synthesized from purified 1,3,5-
tris(benzoyl)benzene and 1,3-bis(benzoyl)benzene, respectively,
via the Wittig reagent42 generated from methyltriphenylphos-
phonium iodide and methyllithium in THF using a procedure
analogous to that reported by Schulz and Ho¨cker.43 Silica gel
chromatography with toluene as the eluent was used to purify
both crude products. Recrystallization in methanol produced
having narrow, monomodal molecular weight distribu-
tions using the dilithium initiator in the presence of
THF ([THF]/[Li] ) 14-32) or lithium sec-butoxide
([LiOBu]/[difunctional initiator] ) 1.1), respectively.
Quirk and Tsai38 developed a novel hydrocarbon-
soluble, trifunctional initiator by an extension of the
quantitative addition chemistry of organolithium com-
pounds to 1,1-diphenylethylene compounds.37 The tri-
functional initiator was prepared by the reaction of 3
mol of sec-butyllithium with 1,3,5-tris(1-phenylethenyl)-
benzene. Using this initiator, living 3-armed, star-
branched polystyrene with a narrow, monomodal mo-
lecular weight distribution was prepared in the presence
of THF ([THF]/[sec-BuLi] ) 20), and its carbonation
product exhibited a functionality close to 3. The g′ value
of the resulting 3-armed star polystyrene compared well
to that of a 3-arm star-branched polymer made using
1,3,5-tris(1-phenylethenyl)benzene as a linking agent.
Well-defined 3-arm star-branched polybutadiene could
also be produced using the same initiator in the pres-
ence of lithium sec-butoxide ([s-BuLi]/[s-BuOLi] ) 2).37
In the present work, a series of well-defined, highly
branched polystyrenes of various architectures, but the
same overall molecular weight, useful for the study of
branching effects, have been synthesized by reactions
between living arm polymers and appropriate chlorosilyl
end-functionalized precursor polymers or methoxysilyl
end-functionalized precursor polymers. The precursor
polymers have been prepared using a difunctional or
trifunctional initiator. In the end-branched polymers,
the number of end branches was varied from 6 to 13
while the number of branching points was fixed at 4.
Inclusion of other architectures in the series allows
comparison among three polymers all having 6-end
groups, but with the number of branch points varying
from 1 to 4. Measurements of the intrinsic viscosities,
hydrodynamics radii, and glass transition temperatures
of these molecules of varying architecture revealed how
each of these important properties varies with the
details of the chain topology.
1
pure samples of 1: mp 46-48 °C [lit.43 mp 46], 300 MHz H
NMR (CDCl3): δ 7.36 (m, 14 H, arom CH), 5.47 ppm (m, 4 H,
dCH2). The same recrystallization method was also used to
purify 4: mp 90-91 °C [lit.38 mp 90-91 °C], 300 MHz 1H NMR
(CDCl3): δ 7.36 (m, 18 H, arom CH), 5.47 ppm (m, 6 H, dCH2).
Each white crystalline product (1 and 4) showed only one peak
by HPLC analysis, and the carbonyl absorption at 1656 cm-1
,
characteristic of the ketone precursor, was absent from the
FTIR spectrum of each product.
Initiatior Preparations. The addition reactions of sec-
butyllithium with 1 or 4 were performed in an argon atmo-
sphere glovebox. The argon atmosphere was purified by
continuous recirculation through towers of molecular sieves
and manganous oxide as described by Brown et al.44 To obtain
precise stoichiometric control, sec-butyllithium was added
stepwise to a benzene solution of 1 (ca. 5.0 × 10-3 mol, 3.29
mL) or 4 (ca. 1.6 × 10-2 mol, 11.49 mL) at room temperature.
Following each addition, a sample was removed from the
reaction mixture, quenched with degassed methanol, and
analyzed by SEC using a UV detector to monitor the extent of
the addition reaction.38 The concentrations of the difunctional
and trifunctional initiator solutions were 2.3 × 10-2 and 1.98
× 10-2 M, respectively; these solutions were distributed into
calibrated ampules and sealed under high vacuum, using
previously described procedures.35,38
Polymerizations. All polymerizations were carried out
using standard high-vacuum techniques.45 The precursor
polystyrene for the 6-end pom-pom polystyrene was prepared
by anionic polymerization of styrene (10.1 g, 9.7 × 10-2 mol)
in benzene (160 mL) using dilithium initiator 2 (1.1 × 10-3
mol, 2.3 × 10-2 M in 46.6 mL of benzene) in the presence of
THF (0.0438 mol, [THF]/[RLi] ) 20). After 90 min of reaction
in an ice-water bath (8 °C), the reaction solution with R,ω-
poly(styryl)lithium was slowly added into another solution
containing a large excess of tetrachlorosilane ([SiCl4]/[Li] >
200) in order to convert the anionic living ends to trichlorosilyl
end groups. The excess linking agent was removed from the
desired star polymer precursor by freeze-drying a benzene
solution of the products on a high-vacuum line.46 The living
3-armed star polystyrene precursors for the targeted 6-, 9-,
and 15-end branched polymers were prepared from the trilith-
ium initiator using a similar procedure as described for the
6-end pom-pom polymer. Each polymerization was monitored
by UV-vis spectroscopy via a UV cell attached to the reactor.
Each precursor polymer was end-capped with a large excess
of the appropriate linking agent: methyltrichlorosilane ([SiCH3-
Cl3]/[Li] > 200) for the 6-end branched, tetrachlorosilane
([SiCl4]/[Li] > 200) for the 9-end branched, and 1,2-bis-
(trichlorosilyl)ethane [Cl3(CH3)SiCH2CH2Si(CH3)Cl3]/[Li] > 50)
for the targeted 15-end branched polystyrene. The precursor
polymer for the targeted 15-end branched polystyrene was
treated with anhydrous methanol in the presence of TEA to
Experimental Section
Materials. Styrene (Aldrich, >99%), benzene (Fisher, >99%),
and tetrahydrofuran (EMD Chemicals Inc., 99.8%) were puri-
fied as described previously.39,40 The purification of the tri-
ethylamine (Aldrich, 99.5%) was carried out by stirring,
degassing, and distilling from freshly crushed CaH2 and then
n-butyllithium. Butadiene (Air Products, 99%) was treated
with sodium metal, vacuum transferred onto neat n-butyl-
lithium, and then distilled into a calibrated ampule which was
heat-sealed with a flame. Tetrachlorosilane (Aldrich, 99.998%)
and methyltrichlorosilane (Aldrich, 99%) were purified by
stirring and degassing over freshly crushed CaH2 and then
distilled. In each case the second one-third of the distillate was
collected while both the first and third portions of the distillate
were discarded. 1,2-Bis(trichlorosilyl)ethane (Aldrich, 98%)
was purified by vacuum distillation at 120 °C. Methanol
(Fisher, 99.8%) was dried by stirring with freshly crushed
CaH2 and, after degassing, was distilled into a storage
reservoir with 4 Å molecular sieves. Solutions of sec-butyl-
lithium (Chemetall Foote Corp., 12.16 wt % in cyclohexane)

Macromolecules, Vol. 38, No. 13, 2005
Polystyrenes Utilizing Multifunctional Initiators 5383
Scheme 2. Preparation of Difunctional Initiator (2) from 1,3-Bis(1-phenylethenyl)benzene (1) and Trifunctional
Initiator (5) from 1,3,5-Tris(1-phenylethenyl)benzene (4) by the Titration with sec-Butyllithium and the
Methanolysis of Its Initiators
convert the silyl chlorides into methoxy groups.47 The precursor
polystyrene was precipitated into anhydrous methanol in a
drybox to separate the methoxysilyl functionalized precursor
from the transformed excess linking agent according to a
recently developed method.47 The living arm polystyrenes for
each branched polymer were synthesized by the sec-butyl-
lithium-initiated polymerization of styrene in benzene, and the
ends were then converted to butadienyllithiums using 2 equiv
of purified butadiene for each equivalent of poly(styryl)lithium
to reduce the steric hindrance during the linking reaction.48,49
The crossover reaction was monitored using UV-vis spectros-
copy.
Linking Reactions. The linking reactions between the
precursor polymers with chlorosilyl functionalized end groups
and excess polystyrene-b-oligo(butadienyl)lithium (PS-b-oli-
goBDLi) ([PLi]/[SiCl] ) 1.2-1.4) were carried out in benzene
for 1 week at 40 °C in the presence of triethylamine ([Et3N]/
[PLi] ) 20). For an end-branched star PS with a target of 15
ends, the linking reaction between the precursor polymer with
methoxysilyl-functionalized end groups and excess PS-b-
oligoBDLi ([PLi]/[SiOCH3] ) 1.3) was continued for 3 weeks.
After 1 or 3 weeks, all end-branched polystyrenes were
separated from excess arm polystyrene by fractionation using
toluene as the good solvent and methanol as the poor solvent.50
For comparison, linear and 6-arm star polystyrenes with
overall molecular weights matching those of the newly pro-
duced branched polystyrenes were also prepared using con-
ventional approaches.48
Characterization. Size-exclusion chromatographic (SEC)
analyses of the titration products of initiators were performed
at a flow rate 1.0 mL/min in THF at 30 °C using a Waters
HPLC component system (RI and Hewlett-Packard 1040 diode
array detector) equipped with ultra-microstyragel columns (50
and 100 Å). Absolute molecular weights of the precursor
polystyrenes, the arm polystyrenes, and branched polystyrenes
were determined by using a SEC-RI-viscometer-LS system.
The system consisted of a gel permeation chromatograph
(Waters 510), a differential refractometer (Waters 410), a
differential viscometer (Viscotek 100), and a laser light scat-
tering detector (Wyatt Technology, DAWN EOS, λ ) 670 nm).
The eluting solvent was THF at a flow rate of 1 mL/min at 30
°C. The UV-vis absorption spectra of the polymeric organo-
lithiums were obtained using a Hewlett-Packard 8452A diode
array spectrophotometer with a 1 mm UV cell attached to the
reactor. The 1H NMR (300 MHz) and 13C NMR (75.4 MHz)
spectra were recorded on a Varian 300 MHz spectrometer
using CDCl3 as the solvent at room temperature. To determine
the number of butadiene (BD) units on the arm polymers for
each branched polymer before and after the butadiene end-
capping, mass spectra were obtained on a Bruker Daltonics
Reflex III matrix-assisted laser desorption ionization time-of-
flight (MALDI-TOF) mass spectrometer. Individual solutions
of dithranol (20 mg/mL) as the matrix, silver trifluoroacetate
(10 mg/mL) as the metal salt, and the polymer (10 mg/mL)
were made in THF. These solutions were mixed in matrix/
metal salt/polymer ratios of 10:1:2, and a small aliquot (0.5
µL) of the final mixture was applied to the sample holder. All
ions observed were Ag+ adducts of PS and PS-b-oligoBD
oligomers. To determine the intrinsic viscosities of each
branched polystyrene, toluene solutions at four concentrations
were made, and then the flow time for each concentration was
determined as the average for five trials measured using a
Cannon-Ubbelohde viscometer at 35 °C. The intrinsic viscosity
was determined by simultaneously extrapolating to zero
concentration using the Huggins and Kraemer equations and
averaging the values of the intercepts.51 The dynamic light
scattering measurements were made using a Brookhaven
Instruments Corp. package which includes a computer-
controlled BI-200SM goniometer, BI-9000AT correlator, and
an EMI-9863 photomultiplier tube for photon counting. A
Melles Griot 35 mW He-Ne laser was used as light source
(632.8 nm). A cylindrical glass scattering cell with diameter
of 12 or 27 mm was placed in the center of a thermostated
bath ((0.01 °C) with decahydronaphthalene used for refractive
index matching. The measurements were carried out at a 90°
scattering angle at 25 °C. The scattered light was evaluated
by an autocorrelator with 80 channels and the correlation
function determined using the Non-Negatively Constrained
Least Squares (NNLS) algorithm. Solutions of nine different
concentrations were prepared in toluene (99.5%, spectropho-
tometric grade, Aldrich) for each polymer. Before light scat-
tering measurements, each solution was filtered with a
poly(tetrafluoroethylene) 0.2 µm filter three times into a
thoroughly clean, dust-free sample cell. Glass transition tem-
peratures were measured using a Perkin-Elmer PYRIS Dia-
mond differential scanning calorimeter. Samples weighing 4-6
mg were run under a stream of N2 with equal heating and
cooling rates of 10 °C/min. Data were recorded only for the
second heating cycle. The value of Tg was taken as the
temperature at which half of the specific heat change had been
accomplished during the glass transition.47
Results and Discussion
Initiator Preparation and Stoichiometric Con-
trol. The preparation of the dilithium initiator (2) and
trilithium initiator (5) by the gradual addition of 2 mol
of sec-BuLi to 1,3-bis(1-phenylethenyl)benzene (1) or of
3 mol sec-BuLi to 1,3,5-tris(1-phenylethenyl)benzene (4),
respectively, in benzene requires careful attention to
stoichiometric control (see Scheme 2). The addition
products from the reaction of sec-BuLi with 1 or 4 in
benzene were monitored by SEC. After the addition of
the stoichimetric amount (100 mol %), only one SEC
peak was observed for each initiator (2 and 5). The
structures of the dilithium adduct (2) and trilithium
1
adduct (5) were confirmed by H NMR analyses of the
products isolated after methanol quenching of the
solution of 2 or 5.35,38 If the precursors for the difunc-
tional initiator and trifunctional initiator were stoichi-
ometrically titrated by sec-Bu initiator, the values of the

5384 Lee et al.
Macromolecules, Vol. 38, No. 13, 2005
Scheme 3. Anionic Synthesis of
presence of THF and methanolysis, 8, exhibited a
monomodal peak. The SEC chromatogram [curve (1) in
Figure 2] of the product, 11 (see Scheme 4), after the
methanolysis of the tris[poly(styryl)lithium], 10, for the
6-end, 9-end, and targeted 15-end branched polymers
showed a small peak next to the big peak corresponding
to 3-armed star-branched polystyrene. The retention
volume corresponding to the maximum of the small
peak agrees with the retention volume expected for the
arm polystyrene. Thus, the small peak probably is due
to the existence of a small amount of sec-BuLi in the
initiator mixture, and the free “arm” resulting from the
presence of this sec-BuLi accounted for about 5 wt % of
the total product.
r,ω-Poly(styryl)lithium (7) Initiated by Difunctional
Initiator (2) and End-Functionalization of
r,ω-Poly(styryl)lithium (7) with Tetrachlorosilane
The molecular weights of the precursor polymers, 8
and 11, prepared in the presence of THF, after metha-
nolysis, are listed in Table 1. The observed number-
average molecular weight of the precursor for the 6-end
pom-pom polymer was in good agreement with the
molecular weight calculated on the basis of the initiator
stoichiometry. The molecular weight of the 3-arm star
precursor was 15% larger than the calculated molecular
weight due to the presence of excess sec-BuLi, estimated
from the area of the small peak in the SEC chromato-
gram [see curve (1) in Figures 2 and 3] to be of the order
of 5 wt %. The observed narrow molecular weight
distributions show that the rate of initiation is competi-
tive with or faster than the rate of propagation.21 Thus,
the initiators 2 and 5 are efficient and sufficiently
reactive in the presence of THF to polymerize styrene
to form the well-defined precursor polymers 7 and 10.
After completion of the polymerization, the living
precursor for each branched polymer was end-capped
using an excess of the corresponding linking agent. To
make the 6-end pom-pom polystyrene, a solution with
R,ω-poly(styryl)lithium, 7, prepared using difunctional
initiator 2, was slowly added in a drybox into a solution
having a large excess of tetrachlorosilane ([SiCl4]/[Li]
> 200) in order to convert the anionic living ends to
trichlorosilyl end groups (9). Curve (2) in Figure 1
presents the SEC chromatogram after freeze-drying of
the end-capped precursor polystyrene for the 6-end pom-
pom, 9. The small bump at retention volume of 20.3 mL
in curve (2) corresponds to a small amount of coupled
product with more than twice the Mn of the precursor
polymer (Mn ) 36.0 kg/mol). The coupled polymer
comprised less than 6 wt % of the total polymer based
on comparison of the areas of the various peaks in the
SEC chromatogram. The main peak at 21.4 mL corre-
sponds to the functionalized precursor polymer, 9, in
Scheme 3.
To prepare the precursor polystyrenes (15-17) for
each end-branched star polymer, the solution with tris-
[poly(styryl)lithium], 10, was added slowly, after 90 min
of polymerization, into three solutions, each containing
a different linking agent (see Scheme 4): methyltri-
chlorosilane (12) for the 6-end branched polymer, tetra-
chlorosilane (13) for the 9-end branched polymer, and
1,2-bis(trichlorosilyl)ethane (14) for the targeted 15-end
branched polymer. After these additions, the reaction
mixtures no longer had the dark red color characteristic
of 10, but rather were colorless, which indicated that
the anionic living ends had been converted to chlorosilyl
end groups. It was known that the methyltrichlorosilane
linking agent used to synthesize the functionalized
6-end branched polystyrene precursor and the tetra-
chlorosilane linking agent used to synthesize the func-
ratios of the integrals for the two methyl protons from
the initiator at δ 0.7-0.95 ppm and the tertiary 1,1-
diphenyalkyl CH protons at δ 3.9-4.05 ppm should be
1
6.35,38 The calculated integral ratios from the H NMR
spectra of the methanolysis products (3 and 6) for the
difunctional initiator and the trifunctional initiator were
5.9 ( 0.1 (85.5/14.5) and 6.0 ( 0.1 (85.7/14.3), respec-
tively. Thus, the values of both ratios were equal to the
target value to within experimental uncertainty.
Preparation of Precursor Polystyrenes from 2
and 5 and End-Capping with Linking Agents.
Previous studies35,38 using the dilithium initiator (2) and
trilithium initiator (5) suggested that inefficient initia-
tion resulted when the initiator molecules were strongly
associated with one another. To promote efficient initia-
tion, this strong association or cross-association of
organolithium chain ends can be reduced by the addition
of a Lewis base such as THF, since it is known that THF
and other Lewis bases break up highly aggregated
organolithiums either to aggregates of lower degree of
aggregation or to unassociated species.45,53,54 However,
the amount of THF added should be minimized because
proton transfer by the reaction between an organo-
lithium compound and THF forms an ethylene molecule
and a lithium enolate of acetaldehyde and results in the
deactivation of a living end.21,55 Therefore, an amount
of THF corresponding to [THF]/[RLi] ) 20 was added
before the crossover reaction from either 2 or 5 to
styrene. Previous studies have established that 14-32
equiv of THF are effective for eliminating the effects of
chain end association on initiation rates for the multi-
functional initiators.35,38,54
The crossover reactions from 2 and 5 with styrene to
form poly(styryl)lithium active centers, presented in
Schemes 3 and 4, were monitored by UV-vis spectros-
copy as described previously.35,38 When styrene mono-
mer was added to a solution with initiator 2 or 5, the
decrease in the absorbance of the initiators, 2 and 5 at
480 nm,35,38 and the appearance of the poly(styryl)-
lithium absorbance at 332 nm were monitored. The
polymerization was completed after 90 min in an ice-
water bath. For the bis[poly(styryl)lithium] precursor,
7 (see Scheme 3), of the 6-end pom-pom (dumbbell-
shaped) polystyrene, the SEC chromatogram [curve (1)
in Figure 1] of the product of the polymerization in the

Macromolecules, Vol. 38, No. 13, 2005
Polystyrenes Utilizing Multifunctional Initiators 5385
Scheme 4. Anionic Synthesis of Tris[poly(styryl)lithium] (10) Initiated by Trifunctional Initiator (5), the
End-Functionalization of 10 with Three Different Linking Agents (12-14), and the Methoxyl-Functionalization of
the ω,ω,ω-Chlorosilyl-Functionalized, 3-Arm Polystyrene (17)
tionalized 9-end branched polystyrene precursor can be
easily removed by the freeze-drying method because of
their low boiling points.47 Curve (2) in Figure 2 is the
SEC chromatogram of the precursor polystyrene (15)
for the 6-end branched polystyrene after the chlorosilyl
functionalization with methyltrichlorosilane and freeze-
drying. The small peak at 20.6 mL retention volume
before the big peak is due to the presence of coupled
precursor polymer formed during functionalization. For
the targeted 15-end branched polystyrene, excess 1,2-
bis(trichlorosilyl)ethane (14) was used to end-function-
alize the tris[poly(styryl)lithium] in order to attach five
chlorosilyl groups at the end of each of the three arms
of the 3-arm precursor polystyrene (17). Chlorosilane
linking agents with more than one silicon such as 1,2-
bis(trichlorosilyl)ethane (14) have such high boiling
points that they cannot be removed effectively by
distillation or freeze-drying. Curve (2) in Figure 3 is the
SEC chromatogram of the ω,ω,ω-pentachlorosilyl-func-
tionalized, 3-arm star polystyrene (17) and excess 1,2-
bis(trichlorosilyl)ethane (14) after end-functionalization
and freeze-drying. The chromatogram shows a small
peak due to the coupled polymer at 20.6 mL retention
volume next to the main peak, another small peak due
to the linear polystyrene from excess sec-BuLi at 22.7
mL, and a new peak at 27.7 mL. The new peak at 27.7
mL corresponds to the excess linking agent (14) which
remained with the functionalized polymer. This excess
1,2-bis(trichlorosilyl)ethane was removed using a new
method recently developed by our group.47 The solution
with the ω,ω,ω-chlorosilyl-functionalized, 3-arm star
polystyrene, 17, and excess 1,2-bis(trichlorosilyl)ethane,
14, was treated with anhydrous methanol. Before the
treatment, triethylamine was added to scavenge the
hydrochloric acid byproduct of the reaction to eliminate
unwanted side reactions that can be caused by the
hydrochloric acid.47 The SEC chromatogram (3) in
Figure 3 is for the precursor (18) for the 13-end
branched PS after methoxysilyl functionalization and
precipitation. The peak that had appeared in SEC

5386 Lee et al.
Macromolecules, Vol. 38, No. 13, 2005
Figure 3. SEC chromatograms for various stages of the
synthesis of the 13-end branched polystyrene: curve (1), three-
armed star polystyrene before end-capping with excess 1,2-
bis(trichlorosilyl)ethane; curve (2), after freeze-drying of end
capped precursor polystyrene with excess 1,2-bis(trichlorosi-
lyl)ethane; curve (3), ω,ω,ω-methoxysilyl-functionalized poly-
styrene after functionalization and precipitation into anhy-
drous methanol with TEA; curve (4), arm PS-b-oligoBD after
end-capping with BD units; curve (5), after 3 weeks linking
reaction between ω,ω,ω-methoxysilyl-functionalized polysty-
rene and PS-b-oligoBDLi; curve (6), after fractionation.
Figure 1. SEC chromatograms for various stages of the
synthesis of the 6-end pom-pom polystyrene: curve (1), precur-
sor polystyrene (7) before end-capping with excess tetrachlo-
rosilane; curve (2), after freeze-drying of the end capped
precursor polystyrene with excess tetrachlorosilane; curve (3),
arm PS-b-oligoBD after end-capping with BD units; curve (4),
after 1 week linking reaction between R,ω-chlorosilyl-func-
tionalized polystyrene and PS-b-oligoBDLi; curve (5), after
fractionation.
1200 g/mol for the targeted 15-end branched polystyrene
to achieve the same overall molecular weight for each
molecule in the series (see Table 2). Each arm was then
end-capped using 2 equiv of butadiene to convert the
chain ends to less-hindered butadienyllithium chain
ends (22).49 The crossover reaction was investigated
using UV-vis spectroscopy. In the UV-vis absorbance
spectra, the poly(styryl)lithium (PSLi) peak at 334 nm
disappeared, and a new peak at 290 nm, corresponding
to poly(butadienyl)lithium (PBDLi), was observed after
adding the butadiene. Correspondingly, the solution
changed from dark red (PSLi) to light yellow (PBDLi).
This indicates that the poly(styryl)lithium was com-
pletely end-capped by the butadiene. An aliquot of each
end-capped polymer was terminated with methanol (23)
and analyzed by SEC, NMR, and MALDI-TOF mass
spectrometry. The molecular weights of the arm poly-
styrenes for each branched polymer increased slightly
after the crossover reaction (see Table 2). Curve (3) in
Figures 1 and 2 and curve (4) in Figure 3 are the
chromatograms of PS-b-oligo(butadiene)s (PS-b-BDs)
with different molecular weights, 23, in Scheme 5.
The mass spectra of the arm polymer for the 6-end
pom-pom polymer before and after the crossover reac-
tion are shown in Figure 4. In the mass spectra of the
unfunctionalized arm polystyrene (21), shown in Figure
4a,b, each major peak was assigned to a homopolysty-
rene with a different number of repeating units [e.g.,
sec-Bu-(C8H8)27-H‚Ag+, calcd monoisotopic mass 2974.7
Da, m/z observed ) 2974.7]. In Figure 4b, the first major
peak was assigned to the unfunctionalized arm poly-
styrene containing 27 units of styrene, and the second
major peak was assigned to the arm polystyrene having
28 units of styrene. After the crossover reaction (23),
peaks appeared in the spectrum separated by 54.0 m/z
units, as shown in Figure 4c, confirming the incorpora-
tion of butadiene units. The first big peak in the inset
in Figure 4d was assigned to arm precursors containing
27 units of styrene and one unit of BD [i.e., C4H9-
(C8H8)27-C4H7‚Ag+, calcd monoisotopic mass 3028.7 Da,
m/z observed ) 3029.1], and the smaller peak at higher
m/z was assigned to arm precursors also having 27
polystyrene units, but having two units of BD [i.e., C4H9-
(C8H8)27-C8H13‚Ag+, calcd monoisotopic mass 3082.8 Da,
Figure 2. SEC chromatograms for various stages of the
synthesis of the 6 end branched polystyrene: curve (1), three-
armed star polystyrene before the end-capping with excess
methyltrichlorosilane; curve (2), after the freeze-drying of the
mixture of end capped precursor polystyrene and excess
methyltrichlorosilane; curve (3), arm PS-b-oligoBD after end-
capping with BD units; curve (4), after 1 week linking reaction
between ω,ω,ω-dichlorosilyl-functionalized polystyrene and PS-
b-oligoBDLi; curve (5), after fractionation.
Table 1. Molecular Weight Characterization of Precursor
Polystyrenes for Each Branched Polystyrene
precursor PS
a
a
Mn
(calcd)
Mn
Mw
a
polymer
(g/mol)
(g/mol)
Mw/Mn
6-pom
18 000
15 000
15 000
15 000
18 200
18 100
17 700
17 700
18 400
18 500
18 200
18 200
1.01
1.02
1.03
1.03
6-branch
9-branch
13-branch
a Determined by SEC coupled with light scattering ((5%).
chromatogram (2) of Figure 3 at a retention volume of
27.7 mL is no longer seen in chromatogram (3). It has
been shown previously that the functionalization from
chlorosilyl into methoxysilyl goes to completion.47
Preparation of Living Arm Polystyrenes and
Linking Reactions. Poly(styryl)lithiums (20 in Scheme
5) for the arms to be attached to the linear and star-
branched polystyrene precursors were synthesized by
the sec-butyllithium-initiated polymerization of styrene
in benzene. An aliquot was removed from the reactor
and terminated with methanol (21) for SEC analysis.
The molecular weights of the arm polystyrenes were
varied from 6100 g/mol for 6-arm star polystyrene to

Macromolecules, Vol. 38, No. 13, 2005
Polystyrenes Utilizing Multifunctional Initiators 5387
Scheme 5. Anionic Synthesis of Poly(styryl)lithium (20) Arms for Each Branched Polymer, the Crossover
Reaction of 20 with Two Units of Butadiene, and the Linking Reactions between the Precursor Polymers (9, 15,
16, and 18) and Excess PS-b-oligo(butadienyl)lithium (22)
Table 2. Molecular Weight Characterization and Butadiene Unit Determination for Arm Polystyrenes before and after
the Butadiene End-Capping
after end-capping (PS-b-BD)
before end-capping (PS)
Mna (g/mol)
Mw/Mn
no. BD units
a
a
arm polymer
Mna (g/mol)
Mw/Mn
NMRb
massc
6-star
6100
3500
2900
2300
1200
1.02
1.03
1.03
1.04
1.04
6200
3800
3000
2400
1300
1.02
1.02
1.03
1.03
1.05
1.1
2.1
1.6
1.4
1.3
1.3
1.7
1.5
1.5
1.2
6-pom
6-branch
9-branch
13-branch
a Determined by SEC coupled with light scattering (see ref 49) ((5%). b Determined by 1H NMR (300 MHz) ((5%). c Determined by
MALDI-TOF mass spectrometry (see ref 49) ((2%).
m/z observed ) 3083.2]. Furthermore, there was no peak
corresponding to arm precursor containing 28 units of
styrene with no BD units [i.e., C4H9-(C8H8)28-H‚Ag+,
calcd monoisotopic mass 3078.8 Da, not observed]
between the two peaks. This meant that the number of
butadiene units attached to each poly(styryl)lithium was
exactly one or two. The average number of BD units per
arm was estimated from the relative intensities of the
two peaks, and the values are summarized in Table 2
where they are compared with the values determined
1,4-, trans-1,4-, and 1,2-microstructure are assigned to
peaks in the δ 5.03-5.6 ppm region. In the spectra, the
peak assignable to the CH2) protons in 1,2-microstruc-
tural units was not separated from the peak for the
-CH) protons in the cis-1,4-, trans-1,4-, and 1,2-
microstructural units. Allowing for the overlap of the
peaks, the best estimate of the amount of 1,2-micro-
structure was 2-7 mol %. Thus, the number of BD units
added to the arms was estimated from the ratio of the
area for peaks corresponding to the -CHdCH- and
CH2dCH- moieties in BD (2H; δ 4.8-5.6 ppm) to the
area for the methyl part of sec-Bu (6H; δ 0.45-0.8 ppm).
The results of this NMR determination of the butadiene
units per molecule for each arm polymer were in good
agreement with those of MALDI-TOF mass spectrom-
etry ((0.2 BD units; see Table 2).
1
by H NMR. After the crossover reaction, new peaks
assignable to the protons on the double bonds of the BD
units appeared in the 1H NMR spectra of all arm
polymers in the region δ 4.8-5.6 ppm. This region
included peaks for the protons from -CHdCH- units
in the oligomeric butadiene chain having cis-1,4- and
trans-1,4-microstructures as well as peaks for protons
from vinyl groups (CH2dCH-) in the units with 1,2-
microstructure. The vinylidene protons from the CH2)
groups in the 1,2-microstructure are assigned to the
resonances in the δ 4.8-5.01 ppm region, and the
protons from the -CH) groups in the units with cis-
The linking reaction between each chlorosilyl-end-
functionalized precursor polystyrene (9, 15, and 16 in
Scheme 5) for the 6-end pom-pom, 6-end branched, or
9-end branched polymer and an excess of the corre-
sponding polystyrene-b-oligo(butadienyl)lithum (PS-b-
oligoBDLi) (22) was carried out in benzene for 1 week

5388 Lee et al.
Macromolecules, Vol. 38, No. 13, 2005
Figure 4. Comparison of MALDI-TOF mass spectra: (a) entire spectrum of the unfunctionalized arm polystyrene for the 6-end
pom-pom polymer (11); (b) enlargement of m/z ) 2960-3120 region corresponding to polystyrenes with 27 styrene units (left
major peak) and with 28 styrene units (right major peak); (c) entire spectrum of the butadiene end-capped arm polystyrene for
the 6-end pom-pom polymer (13); and (d) enlargement of m/z ) 3020-3120 region corresponding to polystyrenes with 27 styrene
units and one (left major peak) or two (right major peak) BD units.
at 40 °C in the presence of triethylamine. After 1 week
of linking reaction, there was no further change with
time in the chromatograms shown as curves (4) in
Figures 1 and 2. Both chromatograms, after methanoly-
sis, contain two major peaks. The first peak at 20.4 mL
retention volume corresponds to the 6-end pom-pom
polystyrene in Figure 1 and to the 6-end branched
polymer in Figure 2. The second peaks at 23.6 mL
(Figure 1) and 24.0 mL (Figure 2) correspond to the
excess PS-b-oligoBD (23). The small peaks next to the
primary peaks are due to coupled polymer and linear
polymer contained in the precursor polymer.
The linking reaction between the methoxysilyl-func-
tionalized precursor polystyrene (18) for the targeted
15-end branched polymer and excess PS-b-oligoBDLi
(22) was allowed 3 weeks to reach a point beyond which
no further linking occurred. The methoxy groups on the
methoxysily end-functionalized precursor polymer are
not as reactive as the chlorides on the chlorosily end-
functionalized precursor polymers, and thus the reaction
with the methoxy groups takes longer.47 Curve (5) in
Figure 3 is the SEC chromatogram for the targeted 15-
end branched polymer formed after 3 weeks of reaction.
All branched polymers were separated from excess
arm polymer by fractionation50 using toluene as a good
solvent and methanol as a poor solvent. Curves (5) in
Figures 1 and 2 and curve (6) in Figure 3 are the SEC
chromatograms obtained after the fractionations. Each
SEC chromatogram taken after fractionation showed a
single narrow peak indicating that the desired branched
polymer was successfully separated from both excess
arm polymer and the more highly branched polymer
resulting from coupling.
Characterization of Branched Polystyrenes. Af-
ter fractionation, the molecular weight of each branched
polystyrene was characterized using SEC coupled with
light scattering. The overall molecular weights of all
branched polymers and an analogous linear polymer,
listed in Table 3, were controlled to be about 36 000
g/mol. The observed polydispersity (Mw/Mn) of each
branched polymer was e1.04. The number of end groups
(f) was calculated from the molecular weights of the arm
polymers, precursor polymer, and branched polymer,
except for the 6-arm star polymer and the linear
polymer, using the following equation:
Mn,branched - Mn,precursor
f )
(1)
Mn,arm
The calculated number of end groups based on molec-

Macromolecules, Vol. 38, No. 13, 2005
Polystyrenes Utilizing Multifunctional Initiators 5389
the theoretical model by Stockmayer and Fixman56
predicts a g′ value of 0.51. This is in good agreement
with the experimentally determined value (0.51) in
Table 4. We are unaware of a theoretical prediction for
a 6-end pom-pom polymer to which the experimental
value (0.87) may be compared. An empirical equation
for g′ for randomly branched polymers with a certain
average number of trifunctional branch units was
developed by Zimm and Stockmayer:57
Table 3. Molecular Characterization of Branched
Polystyrenes
final polystyrene
a
polymer
Mna (g/mol)
Mwa (g/mol)
Mw/Mn
f b
linear
40 000
36 300
40 500
35 800
38 900
34 200
40 800
37 800
41 700
36 500
39 700
35 600
1.02
1.04
1.03
1.02
1.02
1.04
2.0
6.0
6-star
6-pom
5.8
6-branch
9-branch
13-branch
5.9
9.0
13.0
g′ ) [(1 + M/7)1/2 + 4M/9π]-1/2
(3)
a Determined by SEC coupled with light scattering ((5%). b Arm
functionality calculated using eq 1 ((5%).
where M is the average number of branch units. Even
though eq 3 may not be expected to exactly apply for
regularly end-branched polymers, the values in Table
4 calculated using eq 3 were relatively close to the
experimentally determined values. The g′ value for the
13-end branched polymer was the smallest among those
for end-branched polymers having four junction points.
The hydrodynamic radius, Rh, of each branched
polystyrene in toluene was determined from dynamic
light scattering measurements of the translational
diffusion coefficient at infinite dilution, D0, by applying
the Stokes-Einstein equation:58
Table 4. Dilute Solution Properties of Branched
Polystyrenes
[η]a
D0 × 107 e
polymer (cm3/g) g′b (expt) g′ (calcd)
(cm2/s)
Rhf (Å)
linear
20.2
10.2
17.5
12.8
11.7
9.6
8.37
10.72
9.03
46.7
36.5
43.3
40.5
36.8
36.2
6-star
0.51
0.87
0.64
0.58
0.47
0.51c
6-pom
6-branch
9-branch
branch
0.60d
0.55d
0.47d
9.66
10.62
10.81
a Determined in toluene at 35 °C ((0.5). b Branching factor;
g’)[η]star/[η]linear ((0.04). c Reference 56. d Calculated using eq 3.
e Diffusion coefficient at infinite dilution determined by dynamic
light scattering in toluene at 25 °C. f Calculated using eq 4.
kBT
Rh )
(4)
ular weights in Table 3 compared well with the target
number of end groups except for the end-branched
polymer, which had a target of 15 arms and end groups
based on the 15 silyl chloride functional groups in the
star precursor, 18. The steric hindrance generated
during the formation of this highly branched star
limited the arm functionality to 13 during the synthesis.
Thus, such well-defined branched polymers can be
successfully synthesized by anionic polymerization using
multifunctional initiators as described herein.
The structural differences in the polymers arising
from the differences in their topologies were probed
using measurements of intrinsic viscosity. The intrinsic
viscosities of all branched polymers and the linear
analogue are listed in Table 4. Among the polymers with
6 chain ends, the intrinsic viscosity was lowest for the
6-arm star-branched polystyrene, next lowest for the
6-end branched polystyrene, and largest for the 6-end
pom-pom polystyrene. The 6-arm star is most compact
because it contains a single junction point. Though the
pom-pom polymer has two junctions, it is not the next
smallest in size due to the long linear portion in the
center of the molecule. The linear precursor polymer
was 6 times longer than the arm polymer. Thus, the
linear character of the 6-end pom-pom strongly mani-
fests itself, and its size is closer to that of the linear
polymer. Among the 6-end, 9-end, and 13-end branched
polymers which have four junction points, the intrinsic
viscosity decreased with increasing number of end
groups. Generally, the nature of the branching in a
branched polymer is characterized in terms of the
parameter g′, which is defined as
6πη0D0
where kB is Boltzmann’s constant and η0 is the solvent
viscosity. The diffusion coefficient depends on the
concentration, c, as D(c) ) D0(1 + kDc + ...). Thus, D0
could be determined as the value of the intercept from
an extrapolation on the plot of D(c) against concentra-
tion for the concentration going to zero. In these
measurements, nine concentrations from 4.5 to 100 mg/
mL were used. The diffusion coefficients and hydrody-
namic radii determined using eq 4 are presented in
Table 4. The hydrodynamic radii vary in a manner
consistent with the intrinsic viscosity results. The 6-arm
star-branched polymer was the smallest among the
three with 6-end groups, and the 13-end branched
polymer was smallest among the three with four junc-
tion points.
Finally, the effect of branching on the glass transition
temperatures of the polymers was investigated. All of
the values of Tg and width of the transition, ∆Tg, in
Table 5 were measured with the same instrumentation
and protocol and may be readily compared with one
another. To determine the width, a line was drawn
tangent to the curve at Tg. Then the width was taken
as the difference between the temperatures of intersec-
tion of this line with the solidus and liquidus lines. The
value of Tg for the linear chain is in good agreement
with literature values.59,60 Measurement of an ad-
ditional linear polystyrene standard (8.9 × 105 g/mol,
Polymer Source, Inc., Mw/Mn ) 1.04) provided the value
of Tg for infinite molecular weight, Tg,∞ (100 °C). The
variations in the values of Tg seem reasonable. First,
we note that the Tg’s of all branched polymers are
significantly lower than the Tg of the linear chain
analogue. We have to qualify this observation with the
distinction that the linear polymer does not present an
exact analogue for comparison with either the star or
the other branched polymers due to subtle differences
in the way the molecules were synthesized. The 6-arm
star contains a core that is reasonably flexible, and the
[η]b
g′ )
(2)
[η]l
where [η]b is the intrinsic viscosity of the branched
polymer and [η]l is the intrinsic viscosity of the corre-
sponding linear polymer with the same molecular
weight. For a regular 6-armed star-branched polymer,

5390 Lee et al.
Macromolecules, Vol. 38, No. 13, 2005
Table 5. Glass Transition Temperaturesa and Widths of Transitionsb of Arm Polystyrenes before and after BD
End-Capping, Precursor Polystyrenes, and Branched Polystyrenes
arm PS
before
end-capping
after
end-capping
precursor PS
branched PS
c
a
c
e
Mn
Tg
(°C)
∆Tg
(°C)
Tg
(°C)
∆Tg
(°C)
Mn
Tg
(°C)
∆Tg
(°C)
Mn
total BD
Tg
(°C)
∆Tg
(°C)
Tg,calc
(°C)
polymer
(g/mol)
(g/mol)
(g/mol)
(wt %)d
linear
40 000
36 300
40 500
35 800
38 900
34 200
98
86
87
83
79
76
5
9
7
9
8
8
6-star
6100
3500
2900
2300
1200
85
72
67
61
32
4
4
5
5
4
78
61
64
57
30
8
6
6
6
6
1.1
1.5
1.4
1.8
2.6
94
91
92
91
87
6-pom
18 200
18 100
17 700
17 700
94
92
92
92
4
5
6
6
6-branch
9-branch
13-branch
a Measured at a heating rate of 10 °C/min using DSC ((1 °C). b ∆Tg as defined in the text. c Determined by SEC coupled with light
scattering ((5%). d Calculated using BD wt % ) 100 × [54 × BD unit/Mn of branched PS] ((5%). e Tg expected on the basis of BD content
alone. Calculated using eq 5.
Tg of a linear PS containing such a connecting unit
would be reduced relative to that of a conventional
linear PS. The pom-pom and all end-branched stars each
contain a central unit (due to the initiator structure)
that is comparatively rigid, and the presence of this stiff
unit would tend to increase the value of Tg for all of
these polymers in the absence of BD end-capping of the
arms. The linear chain has no “core” unit that is
analogous.
measured here can only be attained when all three
effects are accounted for, but we can consider how far
we may get with simpler approaches. First we consider
the copolymer effect arising from the BD units used to
cap the arms. For linear polymers, the effect on Tg of
including BD units randomly in a poly(styrene-co-
butadiene) copolymer may be predicted well using an
empirical copolymer equation61
A second general observation is that the three mol-
ecules having 6 ends have Tg’s that vary over a 4 °C
range. It is not possible to explain the three values of
Tg by considering only the number of chain ends. Our
third general observation is that when the number of
branch points is held constant among the three end-
branched star polymers, the value of Tg does decrease
with increasing number of chain ends. Also, these
changes are much more subtle than are the changes in
the Tg’s of the respective arms of these end-branched
stars. That is, the Tg’s of the end-branched stars
decrease from 83 to 76 °C as the number of ends
increases from 6 to 13, while the Tg’s of the correspond-
ing arms decrease from 64 to 30 °C. Our final observa-
tion is that incorporation of BD units in a chain
increases the width of the transition. The widths for the
linear arms before end-capping are about 4-5 °C. The
widths after end-capping are larger. While the widths
are even larger (7-9 °C) for the complete branched
chains, it is difficult to separate an effect due to
branching alone from the effect due to inclusion of BD
units.
wPS
wPB
1
)
+
(5)
Tg Tg,PS Tg,PB
where wi is the weight fraction of BD or styrene units.
Tg,PS and Tg,PB are taken as the Tg of a linear chain of
the same overall molecular weight as that of the
branched chain (Tg,PS ) 98 °C for linear PS and Tg,PB
)
-102 °C59 for linear PB at the same overall molecular
weight (38 000 g/mol); both measured here). If one
ignores the architecture of each chain and simply
predicts the Tg that would be expected for each molecule
due to the total composition of BD units in the chain,
one obtains the values listed in the tenth column of
Table 5. All calculated Tgs were up to 11 °C higher than
the experimentally determined values. One reason for
this could be that the BD units are not distributed
randomly in the molecules. They are always located in
a very particular spotsthe point at which an arm links
to a core or branch point. Nonetheless, it is also likely
that the branching and chain end effects (architecture
effects) are important as well.
In surveying the data, there is no simple, consistent
correspondence to be seen between the Tg of a given
branched chain and the Tg of either its precursor or the
end-capped arms used to make the branched molecule.
In recent work by Lee et al.,49 it was observed that the
Tg of the arm of a 4-arm PS star was the same as the
Tg of the star in the case that the arm was end-capped
with BD. This suggested that the BD units might be
serving to dynamically decouple the arm from the rest
of the star. If that were generally true, then we should
have seen here an equivalence of the Tg’s of the end-
capped arm for the 6-arm star and of the star itself.
However, this is not observed, suggesting that increas-
ing the functionality may limit the degree to which the
arm may be decoupled from the rest of the star.
There are at least three characteristics of each
branched molecule that may impact its value of Tg: the
weight fraction of BD units, the number of chain ends,
and the number of branch points. Thus, it is reasonable
to suppose that a proper accounting of the Tg values
Next we consider how successfully we can quantita-
tively rationalize the experimentally measured Tg val-
ues using a free-volume approach that accounts for the
effect of chain end free volume on Tg.62 Already the
observation that the Tg’s of the three different molecules
with six ends are distinct is sufficient to suggest that
this approach cannot be fully satisfying, but we consider
how far it may be taken. Fox and Flory62 proposed on
the basis of a chain-end free volume theory that the
value of Tg should vary with molecular weight as
K
Mn
Tg ) Tg,∞
-
(6)
where Tg,∞ is the value of Tg at infinitely high Mn, Mn
is the total molecular weight of the polymer, and K is a
constant characteristic of a particular polymer. Specif-
ically, K is related to the chain-end free volume varia-
tion with molecular weight. For a branched polymer,

Macromolecules, Vol. 38, No. 13, 2005
Polystyrenes Utilizing Multifunctional Initiators 5391
different molecular weights or different numbers of BD
units. A study of this sort is underway. Investigations
into the influences of the number of chain ends and
number of branch points on the bulk thermodynamics
and interfacial segregation of binary blends of linear PS
and the branched polystyrenes described herein should
soon be completed.
Conclusions
The use of trifunctional and difunctional initiators
prepared by the stoichiometric addition reaction of sec-
BuLi with 1,3,5-tris(1-phenylethyenyl)benzene and 1,3-
bis(1-phenylethenyl)benzene, respectively, provided the
precursor polymers needed to make a series of well-
defined branched polymers suited to studying system-
atically the effects of branching and chain ends on
polymer behavior. The precursor polymers for end-
branched, star-branched polystyrenes with 6-, 9-, and
13-end branches were synthesized using a trifunctional
initiator. The 3-arm precursor star polymer then was
end-functionalized with an excess of the appropriate
linking agent, purified, and then reacted with excess
living arm polymer. The most highly branched polymer
with 13-end groups was synthesized using a recently
developed methoxysilyl functionalization and precipita-
tion method, which addresses the challenge represented
by removal of the excess, low volatility linking agent of
high functionality. The precursor polymer for 6-end
pom-pom polystyrene was synthesized using a dilithium
initiator and was end-functionalized with the linking
agent to create 6-end arms.
The properties of the end-branched, star-branched
polystyrenes, all having four junction points, but with
6, 9, or 13 end groups, were compared to study the effect
of chain ends. Comparison among the polystyrenes all
having 6-end groups, but having a number of branch
points equal to 1, 2, or 4, was used to elucidate the
impact of changing the number of branch points. The
branching factor g′ and hydrodynamic radius decrease
with increasing number of branch points among the
polymers having six ends and also decreases with
increasing number of end groups among the polymers
having four branch points. The values of Tg vary among
the polymers in a manner reflecting the influence of not
only the number of chain ends but also the chain
topology and the inclusion of butadiene units to facilitate
linking.
Figure 5. Comparison of glass transition temperatures of
linear and branched polystyrenes as a function of ne/Mn. Data
points for linear chains (9) reflect the actual values measured.
For the data from branched chains (b) an attempt has been
made to correct for the presence of BD units by adjusting the
value of the Tg for each by the magnitude of the effect
anticipated by eq 5. The solid line has been obtained by fitting
the Tg data for the linear polymers using eq 7 with K′ ) 4600.
eq 6 can be expressed as63
ne
Tg ) Tg,∞ - K′
(7)
Mn
where ne is the number of chain ends per molecule and
K′ is a constant that depends on the density, the chain-
end free volume, and the free volume expansion coef-
ficient. Tg,∞ was determined from a measurement of a
monodisperse linear polymer with a molecular weight
of 8.9 × 105 g/mol and found to be 100 °C. Since ne and
Mn are known from the molecular characterization data
in Table 3, a value of K′ can be extracted by using eq 7
to fit the Tg value for all polymers. However, we could
not fit all of the Tgs using one value of K′. If the manner
in which each chain was branched were insignificant,
one could expect to be able to reconcile all the data for
the branched chains, including linear chains, with a
single value of K′, but this is not the case.
Finally, we attempt to account simultaneously for the
presence of BD units and the free volume of chain ends.
We do this by first estimating the value of Tg by just
accounting for the number of chain ends, as done in the
previous paragraph. This must be done using the same
value of K′ for all the branched chains. Then this value
of Tg is further corrected for the presence of BD units
in the polymer, as described above. Figure 5 displays
Tgs for all of the linear polymers and the branched
polymers after correcting the experimentally measured
values for the presence of BD units. The K′ value for
the fit of the Tg data from the linear polymers was 4600,
which compared well with the literature value of 5000.62
The corrected Tg of the 6-star having one branch point
and the corrected Tg of the 6-pom molecule having two
branch points, but also a long linear portion, fall also
reasonably close to the solid line. However, the Tgs of
the 6-end, 9-end, and 13-end branched polymers with
four branch points do not fall onto the solid line.
Probably, the branch points affect the glass transitions
of branched polymers. Thus, these results highlight the
need for detailed theoretical consideration of the role
of both branching (i.e., tethering at junctions) and chain
ends in determining Tg. It would also be interesting to
make measurements of Tg’s for a series of polymers in
which the molecules have the same architecture, but
Acknowledgment is made to the donors of The
American Chemical Society Petroleum Research Fund
for partial support of this research (#38915-AC7).
Partial support from an Ohio Board of Regents chal-
lenge grant is also gratefully acknowledged. The authors
are grateful to Chemetall Foote Corp. for samples of sec-
butyllithium and to Professor Chrys Wesdemiotis for
MALDI-TOF analysis of the arm polymers. We thank
Professor Stephen Z. D. Cheng, Dr. Ping Huang, Dr.
Alexander J. Jing, and Kwang-un Jeong for assistance
with the DSC and heat capacity measurements.
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