Formation kinetics and scaling of "defect-free" hyperbranched polystyrene chains with uniform subchains prepared from seesaw-type macromonomers

Article abstract of DOI:10.1021/ma201687s

Using a facile approach, we successfully made large "defect-free" hyperbranched polystyrene (PSt) chains with uniform subchains between two branching points from the interchain "clicking" of a seesaw-type linear macromonomer [azide～～～alkyne～～～azide] prepared by ATRP with a following conversion of two bromine-ends into two azide-ends, where ～～～ denotes a PSt chain (1.65-31.0 kg/mol). The "click" reaction kinetics monitored by a combination of size exclusion chromatography (SEC) and laser light scattering (LLS) reveals that the degree of self-polycondensation (DP) is related to the reaction time (t) as ln(DP+ 1)/2 = ([A]₀k_AB,0)/β arctan(βt), where [A]₀ and k_AB,0 are the initial alkyne concentration and the initial reaction rate between the azide and alkyne groups, respectively; β is a constant and its reciprocal (1/β) represents the time at which k _AB = k_AB,0/2. The results reveal that 1/β is scaled to the macromonomer's molar concentration ([C]) and molar mass (M) as 1/β ～ [C]^-0.35M^0.55, indicating that 1/β is governed by the interchain distance and diffusion, respectively. Each hyperbranched sample can be further fractionated into a set of narrowly distributed "defect-free" hyperbranched chains with different molar masses by precipitation. The LLS results show, for the first time, that the root-mean-square radius of gyration (〈R_g〉) and hydrodynamic radius (〈R_h〉) of "defect-free" hyperbranched polystyrenes in toluene at 25 °C are scaled to the weight-average molar mass (M_w) as 〈R_g〉 = 5.53 × 10 ^-2M_w^0.464 and 〈R_h〉 = 2.95 × 10^-2M_w^0.489, respectively, where the exponents are smaller than the predicted ¹/₂.

Full text of DOI:10.1021/ma201687s

ARTICLE
pubs.acs.org/Macromolecules
Formation Kinetics and Scaling of “Defect-Free” Hyperbranched
Polystyrene Chains with Uniform Subchains Prepared from
Seesaw-Type Macromonomers
Lianwei Li,† Chen He,‡ Weidong He,*,‡ and Chi Wu*,†,§
†Hefei National Laboratory for Physical Sciences at Microscale, Department of Chemical Physics, University of Science and Technology
of China, Hefei, China 230026
‡CAS Key Laboratory of Soft Matter Chemistry, Department of Polymer Science and Engineering, University of Science and Technology
of China, Hefei, China 230026
§Department of Chemistry, The Chinese University of Hong Kong, Shatin N. T., Hong Kong
ABSTRACT: Using a facile approach, we successfully made
large “defect-free” hyperbranched polystyrene (PSt) chains
with uniform subchains between two branching points from
the interchain “clicking” of a seesaw-type linear macromonomer
[azide∼∼∼alkyne∼∼∼azide] prepared by ATRP with a fol-
lowing conversion of two bromine-ends into two azide-ends,
where ∼∼∼ denotes a PSt chain (1.65ꢀ31.0 kg/mol). The
“click” reaction kinetics monitored by a combination of size
exclusion chromatography (SEC) and laser light scattering
(LLS) reveals that the degree of self-polycondensation (DP) is related to the reaction time (t) as ln(DP + 1)/2 = ([A]0kAB,0)/β
arctan(βt), where [A]0 and kAB,0 are the initial alkyne concentration and the initial reaction rate between the azide and alkyne
groups, respectively; β is a constant and its reciprocal (1/β) represents the time at which kAB = kAB,0/2. The results reveal that 1/β is
scaled to the macromonomer’s molar concentration ([C]) and molar mass (M) as 1/β ∼ [C]ꢀ0.35M 0.55, indicating that 1/β is
governed by the interchain distance and diffusion, respectively. Each hyperbranched sample can be further fractionated into a set of
narrowly distributed “defect-free” hyperbranched chains with different molar masses by precipitation. The LLS results show, for the
first time, that the root-mean-square radius of gyration (ÆRgæ) and hydrodynamic radius (ÆRhæ) of “defect-free” hyperbranched
polystyrenes in toluene at 25 ꢀC are scaled to the weight-average molar mass (Mw) as ÆRgæ = 5.53 ꢁ 10ꢀ2Mw0.464 and ÆRhæ = 2.95 ꢁ
10ꢀ2 Mw0.489, respectively, where the exponents are smaller than the predicted 1/2.
’ INTRODUCTION
As expected, hyperbranched polymers with long subchains
between two neighboring branching points are easier to form
interchain entanglements in semi/concentrated solutions as well
as in bulk, resulting in much tougher polymer materials with an
excellent mechanical property. Up to now, hyperbranched poly-
mers can be prepared by self-condensing vinyl or ring-opening
polymerization (SCVP16ꢀ19 and SCROP20,21) or more used
polycondensation.22ꢀ28 The SCVP initially reported by Frꢀechet
et al.19 is fairly versatile, in which hyperbranched chains are
formed via polymerization of vinyl macromonomers with an
initiating group. While in SCROP, a polymerizable cyclic group is
used instead of a vinyl group. However, SCVP and SCROP have
their own disadvantages. For example, side reactions could lead
to the formation of a gel and a broad distribution of the subchain
length.29 Note that an ideal hyperbranched chain should have an
identical number of strands that are connected onto each
Hyperbranched polymers have unique properties in solution,
melt and bulk because of their branched and relatively compact
structure in comparison with linear counterparts. Therefore, they
have received much attention in the last few decades due to some
potential applications in biomedicines, energy storages and
polymer blends, to name but a few.1ꢀ5 It has been known that
their molecular parameters, such as monomer nature, overall
molar mass, polydispersity, branching degree, and distribution of
subchain lengths, strongly affect their final macroscopic proper-
ties. In order to establish a structureꢀproperty relationship, a set
of narrowly distributed hyperbranched samples (standards) with
a well-defined structure and uniform subchains but different
overall molar masses have to be prepared before any possible
study. Previously, great efforts have been spent in synthesizing
well-defined cyclic,6ꢀ8 star branched,9,10 mikto-star,11,12 and
H-shaped13 polymers. Some of their structureꢀproperty rela-
tionships have been revealed. However, the preparation and
study of “defect-free” hyperbranched polymers with uniform and
long subchains is rather difficult if not impossible, which hinders
the study of their structureꢀproperty relationships.14,15
Received: July 22, 2011
Revised:
September 6, 2011
Published: September 28, 2011
r
2011 American Chemical Society
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Scheme 1. Comparison of Topological Structures of a Ran-
domly Branched Chain and a Hyperbranched Chain Prepared
by Using Different Types of Macromonomers
chains with uniform subchains; namely, each subchain is exactly
made of half a macromonomer. For such formed large hyper-
branched chains, one possible “defect” (self-looping) has nearly
no effect on their properties. This is why we still name them as
“defect-free”. It should be emphasized that such formed chains
are different from dendrimers. Hedrick et al.39 and Kwak et al.40
previously used this approach to synthesize hyperbranched
chains, starting with short B∼A∼B oligomers containing 5ꢀ20
monomer units. Their resultant hyperbranched polymers are too
small to be accurately characterized by laser light scattering
(LLS), presumably because they used a relatively lower efficient
esterification.
To the best of our knowledge, no one has tried to use this kind
of linear seesaw-type long B∼∼∼∼A∼∼∼∼B chains to pre-
pare large hyperbranched polymers with long and uniform
subchains and seriously study their formation kinetics and scaling
laws between their size and overall mass. Recently, we first
studied how the macromonomer length and concentration affect
the cyclization of linear seesaw-type macromonomers and their
influence on resultant hyperbranched chains.41 In the current
study, using similar linear B∼∼PSt∼∼A∼∼PSt∼∼B macro-
monomers with different lengths, we were able to prepare and
characterize a series of large hyperbranched polystyrenes with
uniform subchains by a combination of the activators regener-
ated by electron transfer for atom transfer radical polymerization
(ARGET ATRP) and “click” chemistry. The self-polycondensa-
tion kinetics was monitored by a combination of size exclusion
chromatography (SEC) and LLS. We purposely varied the
subchain length from shorter to twice longer than the entangle-
ment length (Me ∼ 1.8 ꢁ 104 g/mol for polystyrene). The
fractionation of each resultant broadly distributed hyper-
branched polystyrene sample by precipitation led to a set of
“defect-free” narrowly distributed hyperbranched polystyrene
chains with uniform subchains but different overall molar masses.
We have, for the first time, experimentally elucidated their
formation kinetics and established scaling laws between their
size and overall mass. Armed with such prepared hyperbranched
chains, we will be able to further study correlations between their
microscopic structures and macroscopic properties.
branching point, resulting in uniform subchains between two
neighboring branching points.30,31
Scheme 1 shows two typical approaches in the preparation of
hyperbranched chains: (A) polycondensation32ꢀ34 and (B) self-
polycondensation.3,14,15,35ꢀ38 The polycondensation between
A2 and B3 is one of the earliest adopted synthetic strategies.
For example, Unal et al.32 used an A2-type isocyanate end-capped
propylene oxide or tetramethylene oxide oligomers and a B3-type
triamine branching agent to make randomly branched polyureas
and poly(urethane urea)s. Similarly, hyperbranched poly-
(esterurethane)s (HB-PEU) was prepared with a B3-type trifunc-
tional ε-caprolactone oligomers and an A2-type isocyanated 1,4-
butanediol monomer.33 On the other hand, the self-polycon-
densation of Y-type macromonomers (A∼∼∼∼B2) were ex-
tensively used to prepare hyperbranched polymers with long
subchains. Hedrick et al.34 prepared hyperbranched poly-
(ε-caprolactone)s (HPCL) using short PCL chains with one
carboxylic acid end and two hydroxyl groups at the other chain
end. Bo et al.27 started with a short chain with one boronic ester
at one end and two bromo functional groups at the other end to
synthesize hyperbranched chains via the Suzuki reaction. Hutch-
ings et al.14,15,35,36 prepared hyperbranched polystyrene (PSt)
made of a trifunctional macromonomer with one chloride at one
end and two phenol groups at the other end via the Williamson
reaction and studied their theology properties. Pan et al.37
synthesized hyperbranched PSt chains made of a macromono-
mer with two alkyne groups at one end and one azide group at the
other end using the “click” reaction. Konkolewicz et al.38 pre-
pared hyperbranched PSt chains using the thiolꢀyne “click”
trick, where one end contains a thiol group and the other end
contains a alkyne groups. As shown in Scheme 1, these two
mostly used approaches unavoidably result in subchains with
different lengths because of some unreacted B-groups; namely,
each unreacted B group extends the subchain by one macro-
monomer length.
’ EXPERIMENTAL SECTION
Materials. Styrene (St, Sinopharm, 97%) was first passed through a
basic alumina column to remove inhibitor and then distilled under
reduced pressure over CaH2. Dimethylformamide (DMF, Sinopharm,
AR) was first dried with anhydrous magnesium sulfate and then distilled
under reduced pressure prior to use. Dichloromethane (DCM) and
triethylamine (TEA) from Sinopharm were distilled over CaH2 just
prior to use. Tris(2-(dimethylamino)ethyl)amine (Me6TREN) was
synthesized by following a procedure described in literature.42 Copper-
(I) bromide (CuBr, Alfa, 98%) was washed with glacial acetic acid to
remove soluble oxidized species, filtrated, washed with ethanol and dried
under vacuum. N,N,N0,N0,N00-Pentamethyldiethylenetriamine (PMDETA,
Aldrich, 99%), anisole (Alfa, 99%), 2,20-bipyridine (bpy, Fluka, 99%),
sodium azide (NaN3, Aldrich, 99%), 2,2-bis(hydroxymethyl) propionic
acid (DMPA, Fluka, 97%), N,N-dimethyl-4-amidopyridine (DMAP,
Aladdin, 99%), dicyclohexyl carbodiimide (DCC, Aladdin, 99%), 2-bro-
moisobutyryl bromide (Aladdin, 98%), p-toluenesulfonic acid mono-
hydrate (PTSA, Aladdin, 99%), 2,2-dimethoxypropane (DMP, Aladdin,
99%), propargyl alcohol (Aldrich, 99%), and tin(II)-2-ethylhexanoate
(Sn(EH)2, Aladdin, 95%) and other analytic grade reagents from
Sinopharm were used as received.
Recently, we adopt a slightly different approach. Instead of
putting two reactive B groups on one end, we attach them,
respectively, at two ends of our macromonomer and move the
reactive A group to the middle, i.e., a seesaw-type B∼∼∼∼
A∼∼∼∼B chain, as schematically shown in Scheme 2. In this
way, each resultant hyperbranched chain, no matter how large it
is, contains no more than one unreacted A group if it does no
undergo an intrachain cyclization with one of B groups inside.
Otherwise, the cyclization will lead to a loop, the only possible
“defect” inside the entire hyperbranched chain. During the self-
polycondensation, macromonomers continuously react and add
to the branched chain, finally leading to large hyperbranched
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Scheme 2. Schematic Synthesis of Macromonomer and Hyperbranched Polystyrene
Size Exclusion Chromatography. The relative number- and
weight-average molar masses (Mn,SEC and Mw,SEC) and the absolute
light in a vacuum, respectively. The extrapolation of RVV(q) to q f 0
and C f 0 leads to Mw. The plot of [KC/RVV(q)]Cf0 vs q2 and [KC/
RVV(q)]qf0 vs C lead to ÆRg2æZ and A2, respectively. In a very dilute
solution, the term of 2A2C can be ignored. For relatively small scattering
objects, the Zimm plot on the basis of eq 2 incorporates the extrapola-
tions of q f 0 and C f 0 on a single grid. For long polymer chains, i.e.,
qÆRgæ > 1, the Berry plot is normally used. In static LLS, the scattering
intensity was recorded at each angle three times and each time was
averaged over 30 s. The scattering angle ranges from 12 to 120ꢀ. The
refractive index increment of hyperbranched polystyrenes in toluene
(dn/dC = 0.111 mL/g at 25 ꢀC and 633 nm) was determined by a precise
differential refractometer.45
number- and weight-average molar masses (Mw.MALLS and Mw,MALLS
)
were determined at 35 ꢀC by size exclusion chromatography (SEC,
Waters 1515) equipped with three Waters Styragel columns (HR2,
HR4, HR6), respectively, equipped with a refractive index (RI, Wyatt
WREX-02, using a conventional universal calibration with linear poly-
styrene standards) detector and a multiangle LLS (MALLS, Wyatt
DAWN EOS) detector. Note that SEC measures the weight distribution
of hyperbranched chains (W(M) or C(M). The values of Mn and Mw are
calculated, respectively, using
In dynamic LLS,46 the Laplace inversion of each measured intensityꢀ
intensity time correlation function G(2)(q,t) in the self-beating mode can
lead to a line-width distribution G(Γ), where q is the scattering vector.
For dilute solutions, Γ is related to the translational diffusion coefficient
D by (Γ/q2)qf0,Cf0 f D, so that G(Γ) can be converted into a
transitional diffusion coefficient distribution G(D) or further a hydro-
dynamic radius distribution f(Rh) via the StokesꢀEinstein equation,
Rh = (kBT/6πη0)/D, where kB, T and η0 are the Boltzmann constant,
the absolute temperature and the solvent viscosity, respectively. The
Ci
CiMi
Ci
∑
∑
Mn, MALLS
¼
,
Mw, MALLS
¼
ð1Þ
Ci=Mi
∑
∑
THF was used as an eluenting agent at a flow rate of 1.0 mL/min. The
MALLS detector uses a GaAs laser (685 nm and 30 mW) and has 18
diodes placed at different angles, ranging from 22.5 to 147.0ꢀ. The data
were analyzed using ASTRA for Windows software (Ver. 4.90.07,
Wyatt). The dn/dC of polystyrene in THF was 0.185 mL/g at 30 ꢀC.
For both SEC-RI and SEC-MALLS measurements, 1 mL of polymer
solution (2ꢀ8 mg/mL, depending on the molar mass) was prefiltered
through a 0.2-μm PVDF filter before injection.
polydispersity index Mw/Mn was estimated from Mw/Mn ≈ (1 + 4 μ2/
R
ÆDæ2), where μ2 = ∞G(D)(D ꢀ ÆDæ)2dD. In dynamic LLS experi-
0
Laser Light Scattering. A commercial LLS spectrometer (ALV/
DLS/SLS-5022F) equipped with a multi-τ digital time correlator
(ALV5000) and a cylindrical 22 mW UNIPHASE HeꢀNe laser (λ0 =
632.8 nm) as the light source was used. In static LLS,43,44 the angular
dependence of the absolute excess time-average scattering intensity,
known as the Rayleigh ratio RVV(q), can lead to the weight-average
ments, we used a fixed small angle (12ꢀ) to ensure that the effect of
extrapolating to the zero angle is minimum. The time correlation
functions were analyzed by both the cumulants and CONTIN analysis.
Chemical Synthesis. Scheme 2 shows a schematic chemical
synthesis of different chemicals required to prepare linear seesaw-type
macromonomer chains with two azide end groups and one middle
alkyne group as well as the self-polycondensation via “click” chemistry
between azide and alkyne.
1/2
molar mass (Mw), the root-mean-square gyration radius ÆRg2æZ
(or simply written as ÆRgæ) and the second virial coefficient A2 by using
ꢀ
ꢁ
Isopropylidene-2,2-bis(methoxy)propionic Acid (I). 2,2-Bis(hydroxy-
methyl)propionic acid 30.00 g (223.7 mmol), 2,2-dimethoxypropane
(41.4 mL, 335.4 mmol), and p-toluenesulfonic acid monohydrate (2.10 g,
11.1 mmol) were dissolved in 100 mL of acetone. The mixture was stirred
for 4 h at room temperature before 3.0 mL of a mixture of an ammonia
solution (25%) and EtOH (50/50, v/v)) was added into the reaction
KC
1
1
2
=
1 þ ÆRg æZq2 þ 2A2C
ð2Þ
RVV ðqÞ Mw
3
where K = 4π2(dn/dC)2/(NAλ0 ) and q = (4π/λ0) sin(θ/2) with C, dn/
dC, NA, and λ0 being concentration of the polymer solution, the specific
refractive index increment, Avogadro’s number, and the wavelength of
4
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mixture to neutralize the catalyst. The solvent was removed by evaporation
under reduced pressure at room temperature. The residue was then
dissolved in CH2Cl2 (600 mL) and extracted with two portions of water
(80 mL). The organic phase was dried with anhydrous Na2SO4 and
evaporated to give I as white powder (33.0 g, 84%). The 1H NMR spectra
were recorded on a commercial Bruker AV400 NMR spectrometer using
CDCl3 as solvent and tetramethylsilane (TMS) as an internal standard. 1H
NMR (CDCl3, ppm): δ 4.18 (d, 2H, ꢀCH2O(CH3)C(CH3)OCH2ꢀ),
3.65 (d, 2H, ꢀCH2O(CH3)Cꢀ(CH3)OCH2ꢀ), 1.41(s, 3H, ꢀCH2O-
(CH3)C(CH3)OCH2ꢀ), 1.38 (s, 3H, ꢀCH2O(CH3)C(CH3)ꢀ
OCH2ꢀ), 1.20 (s, 3H, CH3C(CH2Oꢀ)2COOH).
Table 1. Characterization of Linear PSt Chains Prepared by
Normal and ARGET ATRP
molar ratios
Mn,c g/ Mw/
entrya,b ligand PBMP St CuBr ligand Sn(EH)2
mol
Mn
c
1
2
3
4
5
6
7
8
9
bpy
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
500
1000
1000
1000
1000
500
2
2
2
2
2
2
2
2
2
4
4
4
4
4
2
2
2
2
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1.32 ꢁ 104 1.22
2.33 ꢁ 104 1.25
2.71 ꢁ 104 1.27
3.38 ꢁ 104 1.35
4.36 ꢁ 104 1.46
5.80 ꢁ 103 1.08
7.90 ꢁ 103 1.09
1.43 ꢁ 104 1.09
3.71 ꢁ 104 1.13
3.30 ꢁ 103 1.07
7.60 ꢁ 103 1.09
1.87 ꢁ 104 1.13
3.10 ꢁ 104 1.11
4.50 ꢁ 104 1.13
6.21 ꢁ 104 1.15
bpy
bpy
bpy
Propargyl 2,2,5-Trimethyl-1,3-dioxane-5-carboxylate (II). Propargyl
alcohol (14.7 mL, 256 mmol), isopropylidene-2,2-bis(methoxy)-
propionic acid (I) (29.8 g, 172 mmol), and DMAP (10.2 g, 84 mmol)
was dissolved in 300 mL CH2Cl2. After stirring at room temperature for
10 min, DCC (42 g, 204 mmol) dissolved in 100 mL of CH2Cl2 was
added dropwise into the mixture within 30 min under N2 flow. Reaction
mixture was stirred overnight at room temperature and urea byproduct
was filtrated. The solution was then diluted by CH2Cl2 (800 mL) and
extracted with two portions of water (150 mL), and the organic phase
was dried with anhydrous Na2SO4. The solvent was evaporated, and the
remaining product was purified by column chromatography over silica
gel eluting with hexane/ethyl acetate (25:1, v/v) to give a colorless
clear oil: 25.0 g (69%). 1H NMR (CDCl3, ppm): δ 4.74 (d, 2H,
CHtCCH2Oꢀ), 4.20 (d, 2H, ꢀCH2O(CH3)C(CH3)OCH2ꢀ), 3.67
(d, 2H, ꢀCH2O(CH3)C(CH3)OCH2-), 2.48 (t, 1H, CHtCCH2Oꢀ),
1.43 (s, 3H, ꢀCH2O(CH3)C(CH3)OCH2ꢀ), 1.39 (s, 3H, ꢀCH2O-
(CH3)C(CH3)Oꢀ CH2ꢀ), 1.22 (s, 3H, CH3 C(CH2Oꢀ)2COOH).
Propargyl 3-Hydroxy-2-(hydroxymethyl)-2-methylpropanoate (III).
Propargyl 2,2,5-trimethyl-1,3-dioxane-5-carboxylate (II) (10.0 g, 47.5
mmol) was dissolved in a mixture of 1 M HCl (25 mL) and THF
(25 mL). The reaction mixture was stirred for 4 h at room temperature.
The precipitated product was filtrated off, and reaction mixture was then
diluted by CH2Cl2 (400 mL) and extracted with two portions of water
(70 mL) and the organic phase was dried with anhydrous Na2SO4 and
concentrated. Hexane was added to the reaction mixture, and it was kept
bpy
PMDETA
PMDETA
PMDETA
PMDETA
500
500
1000
10 ME6TREN
11 ME6TREN
12 ME6TREN
13 ME6TREN
14 ME6TREN
15 ME6TREN
100 0.1
200 0.1
300 0.1
500 0.1
1000 0.1
1000 0.1
a The polymerization temperatures of entries 1ꢀ5, 6ꢀ9, and 10ꢀ15 are
110, 90, and 90 ꢀC, respectively. b The polymerization of entries 1ꢀ9
and 10ꢀ15 was performed in bulk and in anisole (0.75 volume equiv vs
c
monomer), respectively. The number-average molar mass and molar
mass distribution were determined by SEC on the basis of a conventional
linear PSt calibration.
quenched with CuBr2. The polymer mixture was diluted with THF, and
passed through a short column of neutral alumina for the removal of
metal salt. After removing all the solvents by a rotary evaporator, the
residue was dissolved in THF and precipitated into an excess of
methanol. The above purification cycle was repeated twice. After drying
in a vacuum oven overnight at room temperature, polystyrene
[alkyne-(PSt-bromine)2] (V) was obtained (Table 1, entry 14). Yield:
8.1 g (37%). Mn: 4.50 ꢁ 104 g/mol. Mw/Mn: 1.13 (by SEC).
1
in deep freeze for 48 h to give white solid: 7.0 g (90%). H NMR
(CDCl3, ppm): 4.77 (d, 2H, CHtCCH2Oꢀ), 3.93 (d, 2H, ꢀCH2OH),
3.74 (d, 2H, ꢀCH2OH), 2.73 (br, 2H, -OH), 2.50 (t, 1H, CHt
CCH2Oꢀ), 1.10 (s, 3H, ꢀCH3).
Polystyrene [alkyne-(PSt-azide)2] (VI). A 100 mL round-bottom flask
was charged with alkyne-(PSt-bromine)2 (5.0 g, 0.66 mmol), DMF
(30 mL), and NaN3 (0.325 g, 5 mmol). The mixture was allowed to stir
at room temperature for 36 h. After removing most of the solvent under
reduced pressure, the remaining portion was diluted with CH2Cl2, and
then precipitated into an excess of methanol. The sediments were
redissolved in CH2Cl2 and passed through a neutral alumina column
to remove residual sodium salts, and then precipitated into an excess of
methanol. After it was dried in a vacuum oven overnight at room
temperature, a linear seesaw-type polystyrene with one alkyne functional
group and two azide functional groups was obtained.
Propargyl 2,2-Bis((20-bromo-20-methylpropanoyloxy)methyl)pro-
pionate (IV). Propargyl 3-hydroxy-2-(hydroxymethyl)-2-methylpro-
panoate (III) (4.5 g, 26.0 mmol) was first dissolved in 90 mL of
CH2Cl2, and then triethyl amine (8.0 mL, 57.5 mmol) was added. After
the mixture was cooled to 0 ꢀC, 2-bromoisobutryl bromide (6.05 g, 26.0
mmol) in 40 mL of CH2Cl2 was added dropwise within 30 min. The
reaction mixture was stirred overnight. After filtration, the mixture was
extracted with CH2Cl2 (200 mL) and saturated aq. NaHCO3 (50 mL).
The aqueous phase was again extracted with CH2Cl2 (100 mL) and the
combined organic phase was dried with anhydrous Na2SO4. The
solution was concentrated and the crude product was purified by column
chromatography over silica gel eluting with hexane/ethyl acetate (4:1,
v/v) to give white crystal: 7.1 g (87%). 1H NMR (CDCl3, ppm): δ 4.74
(d, 2H, CHtCCH2Oꢀ), 4.37 (m, 4H, ꢀCOOCH2ꢀ), 2.47 (t, 1H,
CHtCCH2Oꢀ), 1.92 (s, 12H, ꢀCBr(CH3)2), 1.37 (s, 3H, ꢀCH3).
Polystyrene [alkyne-(PSt-bromine)2] (V) via an ARGET ATRP. The
general procedure was as follows. A three-necked flask equipped with a
magnetic stirring bar and three rubber septum was charged with PBMP
(0.1 g, 0.210 mmol), St (24 mL, 210.0 mmol), Me6TREN (55.4 μL,
0.210 mmol), Sn(EH)2 (68.0 μL, 0.210 mmol) and anisole (24 mL).
The flask was degassed by four freezeꢀpumpꢀthaw cycles, and then
placed in an oil bath thermostated at 90 ꢀC. After ∼2 min, CuBr (3 mg,
0.021 mmol) was introduced to start the polymerization under N2 flow.
After a few hours, the flask was rapidly cooled to room temperature and
Defect-Free Hyperbranched PSt (VII). The general procedure em-
ployed was as follows.37 A three-necked flask equipped with a magnetic
stirring bar and three rubber septum was charged with alkyne-(PSt-
azide)2 macromonomer (2 g, 0.263 mmol), PMDETA (109.5 μL, 0.526
mmol), and DMF (13.3 mL). The flask was degassed by four free-
zeꢀpumpꢀthaw cycles, and then placed in a water bath thermostated at
35 ꢀC. After ∼2 min, CuBr (75 mg, 0.526 mmol) was introduced to start
the polycondensation under N2 flow. Samples were taken at timed
intervals and precipitated into a mixture of methanol/water (90/10, v/v)
and the products were washed with excess methanol. After drying in a
vacuum oven overnight at 40 ꢀC, the resultant hyperbranched poly-
styrene was analyzed by SEC and LLS.
Furthermore, the resultant hyperbranched polystyrene chains were
fractionated by precipitation as follows. (1) The sample was dissolved in
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Figure 1. SEC curves of linear polystyrene macromonomers prepared
via ATRP using bpy, PMDETA, ME6TREN as ligand, respectively, and
curves 1ꢀ5, 6ꢀ9, and 10ꢀ15 correspond to entries 1ꢀ5, 6ꢀ9, and
10ꢀ15 in Table 1.
Figure 2. Comparison of 1H NMR spectra of alkyne-(PSt-azide)2 (A)
toluene at room temperature with a concentration around 0.01 g/mL in
a round-bottom flask; (2) methanol was slowly dropped in until the
solution became milky; (3) the solution temperature controlled by a
water bath ((0.1 ꢀC) was slightly raised until the solution became clear
again; (4) the solution was slowly cooled until it became slightly milky;
and (5) the solution temperature was maintained to allow a very small
fraction of longest chains to precipitate. Steps 2ꢀ5 were repeated to
obtain a total of 10 fractions with different overall molar masses, ranging
from 4.80 ꢁ 105 to 3.05 ꢁ 107 g/mol.
and alkyne-(PSt-bromine)2 (B, entry 10 in Table 1).
to a narrow molar mass distribution, slightly broadening as the
chains are getting longer. There is a shoulder on the left of
the SEC curve, marked by an arrow in Figure 1, when the average
molar mass reaches 3ꢀ4 ꢁ 104 g/mol, presumably due to the
increase of solution viscosity and some side reactions induced by
CuBr.50,54 The ARGET ATRP was carried out in anisole using
Me6TREN as a ligand and Sn(EH)2 as a reductant, resulting in
the longest macromonomers with the narrowest molar mass
distribution. Our results reveal that lowering the CuBr concen-
tration can effectively reduce side reactions. Hereafter, the linear
macromonomer chains used are all prepared by the ARGET
ATRP method.
Azidation of Linear PSt Macromonomers [alkyne-(PSt-
bromine)2]. Alkyne-(PSt-azide)2 were prepared by an efficient
substitution reaction of bromine in alkyne-(PSt-bromine)2 with
NaN3 in DMF for 36 h.48 Figure 2 shows a comparison of two 1H
NMR spectra of alkyne-(PSt-bromine)2 and alkyne-(PSt-azide)2.
Besides the broad aromatic and aliphatic regions of styrene
monomer and some signals from the initiator, two signals
(Hh), originating from each end of the chain, are visible in their
1H NMR spectra. The signal of the proton located at the chain
end changes from 3.80 to 4.10 ppm (Hh in Figure 2B) to
4.30ꢀ4.50 ppm (Hh in Figure 2A), indicating a successful
substitution. We estimated the average azide chain-end function-
ality (f) of the chains prepared by ARGET ATRP to be ∼99%
from the area ratio of the Hh and Hb peaks in Figure 2A, i.e., f =
functionality (%) = 100(Hh/Hb), which indicates that the loss of
terminal bromine group is negligible and the azidation reaction
was nearly complete, resulting in a set of narrowly distributed and
highly functional linear seesaw-type macromonomer chains
(azide∼∼∼∼alkyne∼∼∼∼azide) with different lengths.
Self-Polycondensation of Alkyne-(PSt-azide)2 Macromo-
nomer via “Click” Chemistry. As discussed before, using linear
long B∼∼∼∼A∼∼∼∼B macromonomers, we are able to
prepare large “defect-free” hyperbranched chains with uniform
subchains, as shown in Scheme 2. Note that there still exists one
inevitable and possible “defect” inside each resultant hyper-
branched chain, i.e., the cyclization (self-looping) due to the
intrachain coupling. As expected, the cyclization of each macro-
monomer itself in dilute solution is more serious but it can be
reduced if the initial macromonomer concentration is high.
However, the cyclization should not strongly affect the reaction
’ RESULTS AND DISCUSSION
Scheme 2 shows our strategy of synthesizing seesaw-type
macromonomer B∼∼∼∼A∼∼∼∼B. In this study, both nor-
mal ATRP and ARGET ATRP were adopted. PBMP was used as
an initiator due to its high efficiency.47 The two terminal bromo
functional groups were converted to two azide end groups via
their reaction with NaN3.48
Synthesis of Alkyne-(PSt-bromine)2 Macromonomer via
ATRP. It has been known that chains with some highly reactive
end-groups are required to prepare well-defined polymer materi-
als made of telechelic or block chains. In ATRP, side reactions
induced by outer sphere electron-transfer (OSET) not only
reduce the functionality of polymer chains but also limit the
chain length attainable with some monomers.49 Although much
effort has been devoted to improving the end-group functionality
of polymer chains synthesized by ATRP, the results reported in
literature were inconsistent.50ꢀ52 Datta et al.51 found that poly-
(ethyl acrylate) made with bpy as a ligand contained more
remaining bromine end-groups than that prepared with PMDE-
TA. However, Matyjaszewski et al.50,52 showed that a more
reducing catalytic system, such as PMDETA and Me6TREN,
could increase the chain end-group functionality. Here we
compared the ATRP by using bpy, PMDETA and Me6TREN,
respectively, as a ligand.
The polymerization conditions and results are summarized in
Figure 1 and Table 1. All the results indicate that using CuBrꢀ
Me6TRENꢀSn(EH)2 as a catalyst, the polymerization is better
controlled. When bpy is used as a ligand, the reaction tempera-
ture should be relatively higher because the CuBrꢀbpy complex
has a higher redox potential than the CuBrꢀPMDETA and
CuꢀMe6TREN complexes.53 The width of molar mass distribu-
tion rapidly increases as the macromonomers become longer.
The SEC curves clearly show a long low-molar-mass tail;
presumably due to the serious chain termination at the relatively
higher reaction temperature. The CuBrꢀPMDETA system leads
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Figure 4. Macromonomer length dependent hyperbranched poly-
styrenes, where filled and hollow symbols represent results from
stand-alone static LLS and SECꢀMALLS, respectively.
Figure 3. Reaction time dependent SEC curves of hyperbranched
polystyrenes obtained from poly condensation of PS-18.7K, where C0
= 0.15 g/mL.
kinetics on the basis of our novel design. In order to obtain large
hyperbranched chains, we need a highly efficient reaction
between functional groups A and B without any side reactions.
The alkyneꢀazide “click” cycloaddition used in the current study
is the most suitable because of its high efficiency and low
susceptibility to side reactions without oxygen.55ꢀ57 DMF was
used as solvent in the self-poly condensation of alkyne-(PSt-
azide)2 after the removal of oxygen at 35 ꢀC with a catalyst of
CuBrꢀPMDETA. We first investigated how the initial molar
mass and concentration of alkyne-(PSt-azide)2 affect the kinetics
of the self-polycondensation of linear seesaw-type macro-
monomers.
Note that it is better to describe the self-polycondensation in
terms of the average degree of polycondensation (DP), instead of
the number and weight-average molar mass (Mn and Mw),
because initial macromonomers have different lengths, where
DP is defined as the number of macromonomers chemically
coupled together inside each hyperbranched polystyrene chain;
namely, (DP)n = Mn,hyperbranched/Mn,macromonomer and (DP)w =
Mw,hyperbranched/Mw,macromonomer. We prefer to use (DP)w to
describe the polycondensation kinetics because it is the weight-
average molar mass that was measured in SECꢀRI or
SECꢀMALLS. As the reaction proceeds, Mw and (DP)w increase
more rapidly than Mn and (DP)n (we will discuss this point later
in Figure 4). Hereafter for the convenience of discussion, we
rename entries 11, 12, and 14 in Table 1 as PS-7.6K, PS-18.7K
and PS-45K to reflect their molar mass, respectively.
Effect of Macromonomer Length. Figure 3 shows SEC
curves of hyperbranched polymers obtained from the self-poly-
condensation of PS-18.7K in DMF at 35 ꢀC after different
reaction times. As the reaction proceeds, the macromonomer
peak becomes smaller and the large hyperbranched polymer
peaks are emerging after a few hours, as shown by the shoulder
with a retention volume less than 20 mL. However, there still
exist about 10% macromonomers estimated from its peak area
and the whole area of GPC trace. Figure 3 shows that the self-
polycondensation reaction essentially stops after ∼10 h, faster
than what we expected. However, it is known that refractive index
(RI) detector measures the polymer concentration, insensitive to
the molar mass and chain size. Moreover, SECꢀRIꢀPSt-calibra-
tion is not able to effectively distinguish polymer chains with a
similar hydrodynamic volume but different topologic structures.
Therefore, a large deviation from the true molar mass could occur
Figure 5. Reaction time dependent polydispersity index (Mw/Mn) of
hyperbranched polystyrenes prepared with different initial macro-
monomers.
in the high molar mass range, leading to a notable change in
(DP)w. To avoid such a problem, we further used a combination
of SEC and MALLS as well as our stand-alone static LLS to
characterize the absolute weight-average molar mass of each
hyperbranched sample to obtain the true (DP)w and Mw/Mn.
The results are summarized in Figures 4ꢀ7.
Figure 4 shows that large hyperbranched PSt chains are
formed and their final average degree of self-polycondensation
(DP)w increases from 40 to 81 as the initial molar mass of
macromonomers decreases from 4.50 ꢁ 104 to 7.60 ꢁ 103 g/
mol, presumably because of two following reasons. (1) The
functional end groups on longer initial chains are much less
reactive because they are wrapped inside individual coiled chains,
and (2) the total concentration of the functional end groups is
less for a given weight concentration (g/mL), also reflecting in its
relatively lower reaction rate. Hutchings et al.35,36 previously
reported the preparation of hyperbranched polystyrenes with a
moderate (DP)w (10ꢀ17) via the Williamson coupling reaction.
Pan et al.37 synthesized hyperbranched polystyrenes with a
higher (DP)w (39ꢀ65) but much shorter Y-type macromono-
mers (∼103 g/mol). It is worth noting that by increasing the
initial macromonomer concentration, we are able to further
increase (DP)w, resulting in huge hyperbranched polystyrene
chains but their characterization is rather difficult.
An attentive reader might notice that (DP)w,LLS is slightly
higher than (DP)w,MALLS in the high molar mass range. Such a
difference is attributed to few possible reasons. (1) In MALLS, 18
diodes, starting with the lowest angle of 22.5ꢀ, are less sensitive
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Figure 6. Reaction time dependence of (DP)w,SEC-MALLS/(DP)w,SEC-RI
of hyperbranched polystyrenes, where (DP)w,SEC-MALLS and (DP)w,SEC-RI
were respectively measured using a combination of SEC with a RI and a
MALLS detector.
Figure 7. Reaction time dependent ln[(DP + 1)/2]/[A]o for macro-
monomers with different lengths, where filled symbols, hollow symbols
and lines, respectively, represent experimental (DP)n, (DP)w and fitting
curves using eq 7 with kAB,0 = 1.2 ꢁ 105 and 2.8 ꢁ 105 mL/(mol h) for
3
(DP)n and (DP)w, respectively.
with a high dark counters in comparison with the specially
selected APD detector used in our stand-alone LLS, (2) for large
hyperbranched chains, the condition of qÆRgæ < 1 is not main-
tainable with a sufficient number of angles in MALLS, and (3) the
concentration of each fraction in SEC-MALLS is relatively lower
so that the measured intensity of the scattered light is much
weaker than that in our stand-alone LLS, especially in the lower
and higher molar mass tails. Nevertheless, (DP)w,MALLS generally
agrees well with (DP)w,LLS, and the difference is less than ∼7%.
Figure 5 shows that the polydispersity index (Mw/Mn)
(determined by MALLS detector) increases with the reaction
time, partially because of the slower increase of Mn (not shown).
It is known that in the self-polycondensation of B∼∼∼∼
A∼∼∼∼B, hyperbranched chains with more azide groups are
ready to react with macromonomers but more difficult to react
with each other because there is only one hiding A group inside
each hyperbranched chain. However, the coupling between two
hyperbranched chains in the later stage of reaction makes Mw
to increase much fast than Mn. This is why Mw/Mn quickly rises
to 5.8ꢀ7.7.
where [A] and [B] represent the molar concentrations of alkyne
and azide groups, respectively; [B]o = 2[A]o at t = 0; [B] = [B]o
ꢀ ([A]o ꢀ [A]) = [A]o + [A] at t = t so that eq 3 is rewritten as
ꢀ d½Aꢂ=dt ¼ kABð½Aꢂo þ ½AꢂÞ½Aꢂ
ð4Þ
where [A] can be replaced by DP because DP = [A]o/[A] by its
definition. Finally, we have
Z
t
DP þ 1
ln
¼ ½Aꢂ0 kAB dt
ð5Þ
2
0
It shows that at t = 0, DP = 1, and at t . 1, DP approaches an
infinite if kAB is a constant, i.e., resulting in one infinitely large
hyperbranched polymer chain, which is chemically reasonable.
However, our results reveal that the reaction slows down and DP
approaches a constant when t . 1, presumably due to a decrease
of the reactivity of the alkyne group inside each hyperbranched
chain. At the initial stage, most of the alkyne groups are on linear
macromonomers so that they can easily react with each other and
with the azide groups on the periphery of a hyperbranched chain.
As the reaction proceeds, the number of macromonomers
decreases. When most of initial macromonomers are consumed,
further polycondensation mostly involves the intrachain cycliza-
tion or the self-looping. It would be rather difficult for one alkyne
group entrapped inside one hyperbranched chain to react with
the azide groups on another chain. Note that the self-looping has
no contribution to our experimentally measured values of DP.
Considering such a physical nature, we assume that
Figure 6 shows the ratio of (DP)w,SEC-MALLS/(DP)w,SEC-RI of
hyperbranched polystyrenes rapidly increases to 3.1 (PS-7.6K),
2.3 (PS-18.7K), and 2.1 (PS-45K), respectively, with the reaction
time. The deviation of (DP)w,SEC-MALLS away from (DP)w,SEC-RI
clearly shows that SEC with the conventional universal poly-
styrene calibration leads to a much underestimated molar mass
for large hyperbranched chains. Therefore, it should be avoided
in the study of branched chains because they have a much smaller
hydrodynamic volume than their linear counterparts with a similar
molar mass. In other words, (DP)w,SEC-MALLS/(DP)w,SEC-RI re-
flects the hydrodynamic volume difference between hyperbranched
and linear chains; namely, (DP)w,SEC-MALLS/(DP)w,SEC-RI in-
creases with the compactness of hyperbranched chains. For a
meaningful comparison between hyperbranched and linear chains,
we have to fractionate each resultant hyperbranched polystyrene
sample to obtain narrowly distributed chains with uniform sub-
chains but different overall molar masses. We will come back to this
point later.
1
kAB ¼ kAB, 0
ð6Þ
2
1 þ ðβtÞ
where kAB,0 is the initial rate constant at t = 0 and β is a constant,
so that eq 5 is rewritten as
DP þ 1
½Aꢂ0kAB, 0
ð7Þ
ln
¼
arctanðβtÞ
2
β
On the basis of Figure 4 and considering the nature of the self-
polycondensation, we can assume that it follows the second-
order kinetics, i.e.
It describes our experimental results well; namely, DP = 1 at t =
0, and DP = kAB,0π/(2β), at t . 1. In principle, we can obtain
[A]okAB,0 from the initial slope, kAB,0π/(2β) from the plateau
value at t . 1, and β from a combination of [A]okAB,0 and
ꢀ d½Aꢂ=dt ¼ kAB½Aꢂ½Bꢂ
ð3Þ
k
AB,0π/(2β) since we know [A]0.
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Table 2. Calculated Values of β for Macromonomers with Different Initial Lengths
macromonomer
[A]o, μmol/mL
β/hꢀ1 from (DP)n, kAB,0 = 1.2 ꢁ 105 mL/(mol h)
β/hꢀ1 from (DP)w, kAB,0 = 2.8 ꢁ 105 mL/(mol h)
3
3
PS-7.6K
PS-18.7K
PS-45K
19.7
8.00
3.33
1.71
0.85
0.47
2.25
0.95
0.45
Figure 9. Reaction time dependence of ln[(DP + 1)/2] with different
initial PS-45K concentrations, where filled and hollow symbols, and lines
respectively represent experimental (DP)n, (DP)w and fitting curves
using eq 7, where the values of kAB,0 are previously determined.
Figure 8. Initial macromonomer concentration dependence of SEC
curves of resultant hyperbranched polystyrene samples after 48-h self-
polycondensation of PS-45K at 35 ꢀC.
However, we are not able to practically determine the accurate
initial slope ([A]okAB,0) because of a limited number of data
points. Physically, it is reasonable to assume that kAB,0 should be
much less dependent on the initial concentration and length of
macromonomers because it only reflects the initial reaction rate
between A and B. Therefore, we are able to first use the iteration
to estimate the average value of kAB,0 for three different macro-
monomers used and then fix it in the fitting of our experimental
data with eq 7, as shown in Figure 7. In this way, β is the only
adjustable parameter in the fitting. It is clear that eq 7 represents
our experimental data well for both (DP)w and (DP)n.
Table 2 summarizes the fitting results of β for different
macromonomers when (DP)n and (DP)w are respectively used.
β decreases as the macromonomer becomes longer. Note that
physically, 1/β is the time at which kAB decreases to 50% of its
initial value. The decrease of β means that it takes a longer time
for the reaction between A and B on longer macromonomer
chains to slow down, which is physically reasonable because most
of the reaction occurs between macromonomers and hyper-
branched chains except at the very initial stage wherein linear
azide∼∼∼∼alkyne∼∼∼∼azide macromonomers react with
each other.
Effect of Initial Macromonomer Concentration. Figure 8
shows that the macromonomer peak nearly remains at the same
position but its relative height decreases during the reaction,
clearly indicating that there is no obvious self-cyclization of
individual macromonomer chains even at a concentration as
low as 0.02 mg/mL. Otherwise, the macromonomer peak would
shift to the right, toward a slightly larger retention volume.
Figure 9 shows how the average degree of self-polycondensa-
tion (DP) obtained using a combination of SEC and LLS varies
with the reaction time (t) when different initial macromonomer
(PS-45K) concentrations are used. The lines in Figure 9 are
calculated using eq 7. It shows that for a given ratio of
[macromonomer]:[CuBr]:[PMDETA] = 1:2:2, both the initial
reaction rate and final degree of the self-polycondensation
increase with the initial macromonomer concentration, agreeing
well with the prediction of eq 7. It is worth-noting that eq 7 also
shows that both the initial rate and final degree of the self-
polycondensation are related to β. On the other hand, Figure 7
and Table 2 show that β is related to the molar mass (length) of
macromonomer used.
As mentioned before, 1/β reflects the time at which kAB
decreases to 50% of its initial value; namely, kAB = kAB,0/2 at
t = 1/β, where kAB,0 is a constant. Let us assume that the reaction
rate is mainly controlled by diffusion, related to the interchain
distance (L) and the translational diffusion coefficient (D). As
expected, L increases as the initial macromonomer concentration
(C0) decreases, i.e., L ∼ C0ꢀ1/3. Therefore, it should take a longer
time for one macromonomer to react with another when C0
decreases. On the other hand, it has been well-known that D is
scaled to the molar mass of a polymer chain as D ∼ Mꢀα with α =
0.5ꢀ0.6, depending on the solvent quality. As discussed before,
each hyperbranched chain contains no more than one alkyne
group wrapped inside. Therefore, it is rather difficult for an azide
group on one hyperbranched chain to react with the alkyne group
hidden inside another hyperbranched chain. The reaction should
mainly occur between macromonomers (in the very initial stage)
and between one macromonomers and one hyperbranched chain.
0.90
Figure 10 shows two scalings: 1/β ∼ [C]ꢀ0.35 and ∼ Mw
,
where we have converted the weight concentration (C) in
Figure 7 to the molar concentration ([C]) by [C] = C/Mw. It
is also worth-noting that in Figure 4 we varied the molar mass of
macromonomer but fixed its initial weight concentration (C).
Therefore, we have to convert C to [C] and introduce an
additional Mwꢀ0.35 into the scaling; namely, the exponent (0.90)
on Mw should be reduced to 0.55. A combination of both the [C]
and Mw dependence of 1/β finally leads to 1/β ∼ [C]ꢀ0.35Mw
,
0.55
indicating that 1/β is related to both the interchain distance and
diffusion.
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Figure 11. Typical Zimm plot of one hyperbranched polystyrene
fraction in toluene at 25 ꢀC, where C ranges from 5.0 ꢁ 10ꢀ5 to 1.5
ꢁ 10ꢀ4 g/mL.
Figure 10. Macromonomer’s molar concentration ([C]) and weight-
average molar mass (Mw) dependence of 1/β obtained from reaction
time dependence of (DP)w in Figures 7 and 9.
Table 3. LLS Characterization of Hyperbranched Polystyr-
ene Fractions in Toluene at 25 ꢀC
fraction Mw/(g/mol) ÆRgæ/nm ÆRhæ/nma ÆRgæ/ÆRhæ Mw/Mn
LLS Characterization of Fractionated Hyperbranched
Chains. Figure 11 shows a typical Zimm plot of one narrowly
distributed hyperbranched polystyrene fraction (Fraction 3 in
Table 3). On the basis of eq 2, we are able to obtain the values of
the weight-average molar mass (Mw), the average radius of
gyration (ÆRgæ) and the second virial coefficient (A2) from the
intercept and two slopes, respectively. The results together with
the average hydrodynamic radius (ÆRhæ) from dynamic LLS are
summarized in Table 3, where PS-18.7K was used.
Table 3 shows that the fractional precipitation method has
successfully led to 10 relatively narrowly distributed hyper-
branched polystyrene samples with Mw/Mn < 1.3 and over a
wide range of molar mass. It is known that for hard spheres,
hyperbranched chains and coiled linear chains, ÆRgæ/ÆRhæ are
0.774, 1.0ꢀ1.4, and 1.5ꢀ1.8, respectively, depending on their
distributions and solvent quality.58ꢀ60 For these fractionated
hyperbranched polystyrenes, ÆRgæ/ÆRhæ varies between 1.2 and
1.4, as shown in Table 3, indicating that they are swollen in
toluene (a very good solvent) with a relatively loose structure.
Also note that smaller chains have a higher value of ÆRgæ/ÆRhæ,
revealing that they have an even more open and lose chain
conformation.
The difference between linear and branched chains become
more obvious when the scattering factor P(qRg) versus qRg is
plotted,62,63 as shown in Figure 12. Note that both P(qRg) and
qRg are dimensionless so that such a plot should be universal for a
given type of chain topology. Indeed, the scattering factors of
different fractions collapse into a master curve in the qRg range
studied, indicating that all the fractions are self-similar and
following a similar scaling law at qRg > 1.5. The negative slope
represents the ensemble fractal dimension (df) that is close to the
prediction for the reaction-limited clusterꢀcluster aggregation.62,63
The effect of branching is even better displayed in the Kratky
plot; namely, (qRg)2P(qRg) versus qRg, as shown in Figure 13.
Theoretically, Burchard62,63 deduced the scattering factor for
AB2-type hyperbranched chains as
gc
b
1
2
3.05 ꢁ 107
1.09 ꢁ 107
4.50 ꢁ 106
2.68 ꢁ 106
1.85 ꢁ 106
1.61 ꢁ 106
1.21 ꢁ 106
8.70 ꢁ 105
6.20 ꢁ 105
4.80 ꢁ 105
173
99
67
52
44
41
36
32
28
24
140
78
51
40
35
31
28
24
20
18
1.2
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.4
1.4
1.35
1.24
1.20
1.25
1.10
1.13
1.16
1.12
1.08
1.11
0.25
0.28
0.37
0.40
0.47
0.47
0.52
0.61
0.66
0.70
3
4
5
6
7
8
9
10
a Dynamic LLS was carried out at a fixed low angle of 12ꢀ. b Mw/Mn was
estimated from relative line-width (μ2) of diffusion coefficient distribu-
tion and average diffusion coefficient (ÆDæ) by using (1 + 4 μ2 /ÆDæ2). c g
= ÆRg æbranch/ÆRg ælinear and ÆRgælinear (nm) = 1.23 ꢁ 10ꢀ2 Mw
.
2
2
0.594 61
where nB is the number of branching points per hyperbranched
chain and expressed as
ðϕ þ jÞ ꢀ ðϕ2 þ j2Þ
nB ¼
ð9Þ
ðϕ2 þ j2Þ½1 ꢀ ðϕ þ jÞꢂ
where ϕ in our case is the probability of group A in one
macromonomer (B∼∼∼∼A∼∼∼∼B) reacted with the first
group B in another macromonomer; and j is the probability of
group A reacted with the second group B. Experimentally, we
found that nB ∼ 13.2, as shown in Figure 13, where we also plot
two limiting cases: nB = ∞ (hard sphere) and 1 (linear chains). It
is clear that our hyperbranched chains are less draining and close
to a hard sphere. In principle, ϕ = 0.5 because the two unreacted
A groups on a macromonomer should have an equal probability
to react the A group on another macromonomer. Using our
fitting result of value of nB = 13.2, we could numerically calculate
j = 0.42 on the basis of eq 9, smaller than 0.5, as expected,
because the steric effect makes the second B group less reactive. It
is worth-noting that in our simple discussion, the effect of
excluded volume is neglected.63,64
2
ðqRgÞ
1 þ
3nB
pðqR Þ ¼
ð8Þ
ꢂ
ꢀ
ꢁ
ꢃ
g
2
1 þ nB
6nB
1H NMR is often used to estimate the degree of branching
(DB) of hyperbranched chains made of small multifunctional
2
1 þ
ðqRgÞ
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Figure 12. qRg-dependence of scattering factor P(qRg) of different
fractions of hyperbranched polystyrenes synthesized using PS-18.7K.
Figure 14. Weight average molar mass (Mw) dependence of average
gyration and hydrodynamic radii (ÆRgæ and ÆRhæ) in toluene at 25 ꢀC,
where 10 fractions were obtained from hyperbranched chains synthe-
sized using PS-18.7K.
Figure 13. Kratky plots for hyperbranched polystyrenes synthesized
using PS-18.7K, where C = 1/nB, two solid lines represent fitting curves
for linear coiled chains and Debye-bueche hard spheres, respectively.
Figure 15. Weight-average molar mass (Mw) dependence of contrac-
tion factor (g = ÆRg æbranch/ÆRg ælinear) in toluene at 25 ꢀC, where 10
fractions were from hyperbranched chains synthesized using PS-18.7K.
2
2
monomers.34,40 However, it becomes much less effective for
hyperbranched chains prepared from large macromonomers
because of a limited branching points in comparison with a large
number of other chemical groups. As discussed before, large
hyperbranched chains have a smaller root-mean-square gyration
radius ÆRgæ and a lower intrinsic viscosity ([η]) than their
corresponding linear counterparts with a similar molar
mass.31,43,65,66 The ratio of the mean-square radii of gyration of
a hyperbranched chain and a linear chain with an identical molar
mass (ÆRg æbranch and ÆRg ælinear), known as the contraction factor
(g), is another way to describe the degree of branching (DB).
Lubensky et al.67 used the Flory’s approximation to find that in
an athermal solvent, the root-mean-square radius of gyration
(Rg) is scaled to the overall degree of polymerization of ideal
branched chains (N) with a scaling exponent (ν) of 0.5. Further,
Render68 found that for ideal branched chains, ν is in the range
0.43ꢀ0.53 in the Monte Carlo simulation, covering the Lubens-
ky’s prediction. Note that these previous studies were mostly
based on an assumption of ideal branched chains; namely, with
uniform subchains between two neighboring branching points.
To the best of our knowledge, there have been few reported
experimental studies on conformational properties of hyper-
branched polymers with long subchains but no study on truly
ideal or “defect-free” hyperbranched chains.
wide molar mass range, we are in a much better position to
determine the scaling law between the chain size and molar mass
of ideal branched chains. Figure 14 shows how the average root-
mean square radius of gyration ÆRgæ and the average hydrody-
namic radius ÆRhæ depend on the weight-average molar mass
(Mw) of “defect-free” hyperbranched chains. The lines represent
ÆRgæ (nm) = 5.53 ꢁ 10ꢀ2 Mw0.464 and ÆRhæ (nm) = 2.95 ꢁ 10ꢀ2
Mw0.489, which agrees well with previous predictions.67,68
Further, Figure 15 shows that in toluene at 25 ꢀC,ꢀt0h.2e6c0ontraction
2
2
factor (g) is scaled to Mw as g = 2.02 ꢁ 101 Mw
’ CONCLUSION
.
In conclusion, we have successfully prepared “defect-free”
hyperbranched polystyrene chains with uniform subchains by
using seesaw-type macromonomers [azide∼∼∼∼alkyne∼∼∼∼
azide], where ∼∼∼∼ is polystyrene chain with a controllable
length and two reactive functional groups (alkyne and azide) can be
“clicked” together. The chain length between two functional groups
can be precisely adjusted by atom transfer radical polymerization
(ATRP). Our results confirmed that each of the two ends of the
macromonomer chain can be effectively functionalized with a
reactive bromo group by using the activators regenerated by
electron transfer for atom transfer radical polymerization
(ARGET ATRP) method with propargyl 2,2-bis((20-bromo-
20-methylpropanoyloxy)methyl)propionate as an initiator. The
Armed with such 10 relatively narrowly distributed hyper-
branched polystyrene fractions with uniform subchains over a
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reaction rate of the self-polycondensation of alkyne-(PSt-azide)2
increases with the initial concentration of macromonomers but is
less influenced by the mocromonomer’s length. The kinetics is the
(16) Wang, W. J.; Wang, D.; Li, B. G.; Zhu, S. Macromolecules 2010,
43, 4062.
(17) Peleshanko, S.; Gunawidjaja, R.; Petrash, S.; Tsukruk, V. V.
Macromolecules 2006, 39, 4756.
(18) Hawker, C. J.; Frechet, J. M. J.; Grubbs, R. B.; Dao, J. J. Am.
Chem. Soc. 1995, 117, 10763.
(19) Frꢀechet, J. M. J.; Henmi, M.; Gitsov, I.; Aoshima, S.; Leduc,
M. R.; Grubbs, R. B. Science 1995, 269, 1080.
(20) Liu, M.; Vladimirov, N.; Frꢀechet, J. M. J. Macromolecules 1999,
32, 6881.
(21) Magnusson, H.; Malmstr€om, E.; Hult, A. Macromol. Rapid
Commun. 1999, 20, 453.
(22) Emrick, T.; Chang, H. T.; Frꢀechet, J. M. J. Macromolecules 1999,
32, 6380.
(23) Kong, J.; Schmalz, T.; Motz, G. N.; Mu_ller, A. H. E. Macro-
molecules 2011, 44, 1280.
(24) Oguz, C.; Unal, S.; Long, T. E.; Gallivan, M. A. Macromolecules
2007, 40, 6529.
(25) Vanjinathan, M.; Shanavas, A.; Raghavan, A.; Nasar, A. S.
J. Polym. Sci., Part A: Polym.Chem. 2007, 45, 3877.
(26) Zhu, Z.; Pan, C. Macromol. Chem. Phys. 2007, 208, 1274.
(27) Li, J.; Sun, M.; Bo, Z. J. Polym. Sci., Part A: Polym.Chem. 2007,
45, 1084.
second order but with a time-dependent rate constant: kAB
=
kAB,0/[1 + (βt)2], where kAB,0 is the rate constant at t = 0 and 1/β is
a time at which kAB becomes half of kAB,0. Our results reveal that
1/β is scaled to the macromonomer’s molar concentration ([C])
and molar mass (M) as 1/β ∼ [C]ꢀ0.35M 0.55, indicating that 1/β is
governed by the interchain distance and diffusion, simultaneously.
A combination of static and dynamic LLS characterization of 10
relatively narrowly distributed hyperbranched polystyrene frac-
tions, prepared by the gradual precipitation method, reveals that
the hyperbranched chains have (1) an open and loose structure due
to long subchains, (2) a fractal dimension of df ∼ 2, indicating that
they are formed by the reaction-limited clusterꢀcluster aggregation
mechanism, and (3) a hyperbranching parameter of nB = 13.2,
revealing that the chains are more in resemblance to a spherical
structure, and (4) the chain sizes are scaled to the weight-average
molar mass (Mw) as ÆRgæ ∼ Mw0.464 and ÆRhæ ∼ Mw0.489 in toluene
at 25 ꢀC, agreeingwellwithprevious predictionsin literature;Using
seesaw-type B∼∼∼∼A∼∼∼∼B macromonomers, we have de-
veloped a very powerful and convenient approach to prepare large
“defect-free” hyperbranched polymer chains for their subsequent
structureꢀproperty studies.
(28) Ghosh, A.; Banerjee, S.; Komber, H.; Lederer, A.; H€aussler, L.;
Voit, B. Macromolecules 2010, 43, 2846.
(29) Adam, M.; Delsanti, M.; Munch, J. P.; Durand, D. J. Phys. Paris
1987, 48, 1809.
(30) de Gennes, P. G. Biopolymers. 1968, 6, 715.
(31) Zimm, B. H.; Stockmayer, W. H. J. Chem. Phys. 1949, 17, 1301.
(32) Unal, S.; Yilgor, I.; Yilgor, E.; Sheth, J. P.; Wilkes, G. L.; Long,
T. E. Macromolecules 2004, 37, 7081.
(33) Unal, S.; Ozturk, G.; Sisson, K.; Long, T. E. J. Polym. Sci., Part A:
Polym.Chem. 2008, 46, 6285.
’ AUTHOR INFORMATION
Corresponding Author
*E-mail: (C.W.) chiwu@cuhk.edu.hk; (W.H.) wdhe@ustc.edu.cn.
(34) Trollsas, M.; Kelly, M. A.; Claesson, H.; Siemens, R.; Hedrick,
J. L. Macromolecules 1999, 32, 4917.
’ ACKNOWLEDGMENT
(35) Hutchings, L. R.; Dodds, J. M.; Roberts-Bleming, S. J. Macro-
molecules 2005, 38, 5970.
(36) Hutchings, L. R.; Dodds, J. M.; Roberts-Bleming, S. J. Macro-
mol. Symp. 2006, 240, 56.
(37) Kong, L. Z.; Sun, M.; Qiao, H. M.; Pan, C. Y. J. Polym. Sci., Part
A: Polym.Chem. 2010, 48, 454.
The financial support of the National Natural Scientific
Foundation of China Projects (51173177 and 20934005) and
the HongKong Special Administration Region Earmarked Projects
(CUHK4046/08P, 2160365; CUHK4039/08P, 2160361; and
CUHK4042/09P, 2160396) is gratefully acknowledged.
(38) Konkolewicz, D.; Gray-Weale, A.; Perrier, S. b. J. Am. Chem. Soc.
2009, 131, 18075.
(39) Trollsas, M.; Hedrick, J. L. Macromolecules 1998, 31, 4390.
ꢃ
’ REFERENCES
(40) Choi, J.; Kwak, S. Y. Macromolecules 2003, 36, 8630.
(41) He, C.; Li, L. W.; He, W. D.; Jiang, W. X.; Wu, C. Macro-
molecules 2011, 44, 6233.
(42) Queffelec, J.; Gaynor, S. G.; Matyjaszewski, K. Macromolecules
2000, 33, 8629.
(1) Cao, Q.; Liu, P. J. Mater. Sci. 2007, 42, 5661.
(2) Chen, Y.; Shen, Z.; Pastor-Pꢀerez, L.; Frey, H.; Stiriba, S. E.
Macromolecules 2004, 38, 227.
(3) Hawker, C. J.; Chu, F.; Pomery, P. J.; Hill, D. J. T. Macromolecules
1996, 29, 3831.
(43) Zimm, B. H. J. Chem. Phys. 1948, 16, 1099.
(44) Chu, B. Laser Scattering, 2nd ed.; Academic Press: New York,
1991.
(4) Liu, C.; Gao, C.; Yan, D. Macromolecules 2006, 39, 8102.
(5) Yang, Y.; Xie, X.; Yang, Z.; Wang, X.; Cui, W.; Yang, J.; Mai, Y. W.
Macromolecules 2007, 40, 5858.
(45) Wu, C.; Xia, K. Q. Rev. Sci. Instrum. 1994, 65, 587.
(46) Berne, B.; Pecroa, R. Dynamic Light Scattering; Plenum Press:
New York, 1976.
(47) Liu, Q.; Zhao, P.; Chen, Y. J. Polym. Sci., Part A: Polym.Chem.
2007, 45, 3330.
(6) Schulz, M.; Tanner, S.; Barqawi, H.; Binder, W. H. J. Polym. Sci.,
Part A: Polym.Chem. 2010, 48, 671.
(7) Xu, J.; Ye, J.; Liu, S. Macromolecules 2007, 40, 9103.
(8) Lonsdale, D. E.; Monteiro, M. J. Chem. Commun. 2010, 46, 7945.
(9) Furukawa, T.; Ishizu, K. Macromolecules 2005, 38, 2911.
(10) Okumoto, M.; Nakamura, Y.; Norisuye, T.; Teramoto, A.
Macromolecules 1998, 31, 1615.
(48) Laurent, B. A.; Grayson, S. M. J. Am. Chem. Soc. 2006, 128,
4238.
(49) Tsarevsky, N. V.; Braunecker, W. A.; Matyjaszewski, K. J. Orga-
nomet. Chem. 2007, 692, 3212.
(50) Lutz, J. F.; Matyjaszewski, K. J. Polym. Sci., Part A: Polym.Chem.
(11) Babin, J.; Taton, D.; Brinkmann, M.; Lecommandoux, S.
Macromolecules 2008, 41, 1384.
(12) Ishizu, K.; Furuta, Y.; Okamoto, N.; Uchida, S.; Ozawa, M.
Macromol. Chem. Phys. 2010, 211, 1984.
2005, 43, 897.
(51) Datta, H.; Bhowmick, A. K.; Singha, N. K. J. Polym. Sci., Part A:
Polym.Chem. 2007, 45, 1661.
(13) Gungor, E.; Durmaz, H.; Hizal, G.; Tunca, U. J. Polym. Sci., Part
A: Polym.Chem. 2008, 46, 4459.
(14) Clarke, N.; Luca, E. D.; Dodds, J. M.; Kimani, S. M.; Hutchings,
L. R. Eur. Polym. J. 2008, 44, 665.
(52) Jakubowski, W.; Kirci-Denizli, B.; Gil, R. R.; Matyjaszewski, K.
Macromol. Chem. Phys. 2008, 209, 32.
(15) Hutchings, L. R. Soft Matter 2008, 4, 2150.
(53) Xia, J.; Matyjaszewski, K. Macromolecules 1997, 30, 7697.
8205
dx.doi.org/10.1021/ma201687s |Macromolecules 2011, 44, 8195–8206

Macromolecules
ARTICLE
(54) Matyjaszewski, K.; Davis, K.; Patten, T. E.; Wei, M. Tetrahedron
1997, 53, 15321.
(55) Binder, W. H.; Sachsenhofer, R. Macromol. Rapid Commun.
2007, 28, 15.
(56) Binder, W. H.; Sachsenhofer, R. Macromol. Rapid Commun.
2008, 29, 952.
(57) Bock, V. D.; Hiemstra, H.; van Maarseveen, J. H. Eur. J. Org.
Chem. 2006, 51.
(58) Burchard, W.; Schmidt, M.; Stockmayer, W. H. Macromolecules
1980, 13, 1265.
(59) Vagberg, L. J. M.; Cogan, K. A.; Gast, A. P. Macromolecules
1991, 24, 1670.
(60) Peng, S. F.; Wu, C. Macromolecules 1999, 32, 585.
(61) Teraoka, I. Polymer Solution; John Wiley & Sons, Inc:
New York, 2002.
(62) Burchard, W. Macromolecules 1977, 10, 919.
(63) Burchard, W. Adv. Polym. Sci. 1983, 48, 1.
(64) Burchard, W. Macromolecules 2004, 37, 3841.
(65) Voit, B. I.; Lederer, A. Chem. Rev. 2009, 109, 5924.
(66) Gao, C.; Yan, D. Prog. Polym. Sci. 2004, 29, 183.
(67) Isaacson, J.; Lubensky, T. C. J. Phys., Lett. 1980, 41, 469.
(68) Render, S. J. Phys. A: Math. Gen 1979, 12, L239.
8206
dx.doi.org/10.1021/ma201687s |Macromolecules 2011, 44, 8195–8206