Hyperbranched polyethers with tunable glass transition temperature: Controlled synthesis and mixing rules

Article abstract of DOI:10.1039/c4ra04077e

By taking advantage of competing side reactions, controlled synthesis of a series of homo- and co-polymerized hyperbranched polyethers (HBPEs) is demonstrated using AB₂ monomers of different spacer lengths. This reacting system shows good controllability and scalability. More importantly, the degree of branching is found to be insensitive to the molecular weight and spacer length in monomers. Thus, the value and width of T_g can be tuned by varying monomer spacer length, terminal groups, molecular weight, as well as by copolymerization and physical blending. The dependence of T _g in binary homopolymer blends on composition and the dependence of T_g in copolymers on monomer ratio are established and compared for the first time. T_g of copolymers obeys the Fox equation, whereas T_g in binary blends only follows the Kwei equation. Copolymerization does not increase the width of T_g. In contrast, the width of T _g of binary blends is much broader than that of copolymers, even though the broadening in T_g can be reduced by increasing the polarity of terminal groups. the Partner Organisations 2014.

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PAPER
Hyperbranched polyethers with tunable glass
transition temperature: controlled synthesis and
Cite this: RSC Adv., 2014, 4, 30250
mixing rules†
a
a
b
Tuan Liu,ab Xinxin Geng,a Yongxing Nie,ab Ruoshi Chen, Yan Meng and Xiaoyu Li
*
*
By taking advantage of competing side reactions, controlled synthesis of a series of homo- and co-
polymerized hyperbranched polyethers (HBPEs) is demonstrated using AB2 monomers of different
spacer lengths. This reacting system shows good controllability and scalability. More importantly, the
degree of branching is found to be insensitive to the molecular weight and spacer length in monomers.
Thus, the value and width of Tg can be tuned by varying monomer spacer length, terminal groups,
molecular weight, as well as by copolymerization and physical blending. The dependence of Tg in binary
homopolymer blends on composition and the dependence of Tg in copolymers on monomer ratio are
established and compared for the first time. Tg of copolymers obeys the Fox equation, whereas Tg in
binary blends only follows the Kwei equation. Copolymerization does not increase the width of Tg. In
contrast, the width of Tg of binary blends is much broader than that of copolymers, even though the
broadening in Tg can be reduced by increasing the polarity of terminal groups.
Received 4th May 2014
Accepted 11th June 2014
DOI: 10.1039/c4ra04077e
www.rsc.org/advances
High DB values (>90%) have been achieved using the Suzuki–
Miyaura coupling reaction7 and click chemistry.8 Recently, HBP
Introduction
with tunable DB (from 0 to 100%) has been achieved by
adjusting catalyst dosage.9 Min and Cao10 also showed that the
microemulsion polymerization technique is benecial in
obtaining HPBs with high DB and low PDI.
Hyperbranched polymers (HBPs) have been a growing research
area1 for two decades due to their unique structures, such as
highly branched structure, compact shape, and ample and
modiable terminal groups. The special structure imparts
unique properties and leads to wide applications in various
elds.2 Properties of HBPs depend on many factors, including
backbone structure, terminal group, molecular weight (MW),
and degree of branching (DB).3 However, their random growth
nature in one-pot synthesis oen leads to poor controllability,
which is a big issue not only for industrial applications but also
for in-depth scientic studies.4 Progress has been made to
overcome that issue; however, most efforts have been focused
on controlling molecular weight distribution (or polydispersity,
PDI) and DB.8 On one hand, addition of a polyfunctional core
and slow monomer addition are found to be effective in
lowering PDI to as low as 1.3.5 For certain reacting systems, in
which the reactivity of formed oligomers is much higher than
that of monomers, PDI can be further lowered to 1.13.6 On the
other hand, progress has also been made in controlling DB.
The glass transition temperature (Tg) is the most important
parameter for polymers and is closely related to mechanical,
thermal, and other properties.11 However, due in large part to
the poor controllability, controlled synthesis of HBPs with
tunable Tg has not been reported, especially for HBPs with polar
terminal groups. Tg of linear polymers depends on the chemical
structure of the backbone and MW.12 Tg of HBPs, however,
depends on more factors,4 including backbone structure,
terminal groups, DB, and MW and thus is more difficult to
control. In HBPs, changes in MW are oen accompanied by
changes in DB, which is also an important factor in determining
Tg, making the control of Tg more challenging. In one-pot
synthesis of HBPs, the control of MW without changing DB is
notoriously difficult. In addition, reproducibility and scalability
are also difficult to achieve when the reactor size changes. This
paper is organized into three parts. First, one-pot controlled
synthesis of a series of hyperbranched polyethers (HBPEs) with
almost invariant DB, controllable MW, and good scalability is
presented using three AB2 monomers with different spacer
lengths. Second, the tuning of Tg was demonstrated using
several ways, including varying monomer spacer length,
terminal group, and MW, as well as physical blending and
copolymerization. Third, the relationship between Tg of copol-
ymers and monomer ratio and that between Tg of binary
aKey Laboratory of Carbon Fiber and Functional Polymers, Ministry of Education,
Beijing University of Chemical Technology, Beijing 100029, P.R. China. E-mail:
mengyan@mail.buct.edu.cn; Fax: +86-10-64452129; Tel: +86-10-64419631
bState Key Laboratory of Organic–Inorganic Composites, Beijing University of Chemical
Technology, Beijing 100029, P.R. China. E-mail: lixy@mail.buct.edu.cn; Fax: +86-10-
64452129; Tel: +86-10-64423162
† Electronic supplementary information (ESI) available: Experimental details of
synthetic procedures of model molecules, and NMR, GPC and DSC spectra that
are not shown in the text. See DOI: 10.1039/c4ta04077e
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homopolymer blends and composition are compared in detail
The rst step is the synthesis of 4-(2-bromine-oxethyl)-
for the rst time. The effects of terminal group on miscibility of benzaldehyde. Under mechanical stirring, PHBA (12.2 g, 0.1
binary blends were also discussed.
mol), 1,2-dibromoethane (75.2 g, 0.4 mol), K2CO3 (27.6 g, 0.2
mol), and 500 mL ethanol were added into a three-necked ask
and reuxed for 10 h. Aer cooling to room temperature, the
mixture was ltered, and ethanol was removed using a rotary
evaporator. The crude product was puried using silica gel
column chromatography with CH2Cl2/petroleum ether (1 : 1) as
the eluent. The obtained product is a light green crystal-like
solid. Yield: 19.01 g, 83%. Please note that the crude product
can be directly used in the next step without purifying, because
Experimental section
Materials
All chemicals were of analytical grade and used as received
unless otherwise stated. Phenol and p-toluenesulfonic acid
(PTSA) were purchased from Tianjin Fuguang Reagent Co.,
China. 1,2-dibromoethane (98%), 1,4-dibromobutane (98%),
and 1,6-dibromohexane (98%) were purchased from Beijing
Ouhe Technology Co., China. 2-Phenoxyethylbromide (98%), 4-
hydroxylbenzaldehyde (PHBA, 98%), and benzyl bromide (98%)
were obtained from Zhongsheng Huateng Reagent Co., China.
4-bromo-1-butene (98%) was obtained from Energy Chemical
Co., China. All other solvents and reagents were purchased from
Beijing Reagent Co., China. N,N-Dimethyl formamide (DMF)
was dried before use.
1
byproducts can be automatically removed in the next step. H-
NMR (600 MHz, CDCl3, d): 3.65 (t, 2H, OCH2CH2Br), 4.35 (t, 2H,
OCH2CH2Br), 6.99 (d, 2H, C6H4O), 7.81 (d, 2H, C6H4O), 9.87 (s,
1H, PhCHO). 13C-NMR (600 MHz, CDCl3, d): 28.56, 67.95,
114.89, 130.45, 132.01, 163.00, 190.70.
In the second step, 4-(2-bromine-oxethyl)-benzaldehyde (11.5
g, 0.05 mol), phenol (0.25 mol, 23.5 g), ZnCl2 (0.7 g, 5 mmol),
and PTSA (0.95 g, 5 mmol) were added into a three-necked ask
under mechanical stirring. Aer stirring for 1 h, reactants were
heated to 45 ꢂC for 24 h and then washed at least twice with hot
water (>70 ꢂC) to remove residual salts. Aer evaporation at
Characterization
ꢂ
Nuclear magnetic resonance (NMR) spectra were collected on a
Bruker AV-600 spectrometer (600 MHz), and chemical shis are
reported in ppm. Fourier transform infrared spectroscopy
(FTIR) spectra were collected on a Bruker Tensor 37 spectro-
photometer using the potassium bromide (KBr) disc technique.
Molecular weights of the hyperbranched molecules were
determined using a Waters 515-2410 gel permeation chroma-
tography (GPC) system, which was calibrated using linear
polystyrene calibration standards and with tetrahydrofuran
(THF) as the eluent. Tg values of HBPEs were determined on
second heating runs (typically 10 K minꢀ1) under a dry nitrogen
atmosphere (40 ml minꢀ1) using a DSC-1 (Mettler-Toledo,
Switzerland) differential scanning calorimeter, which is equip-
ped witꢂh an intra-cooler. All measurements were performed at
25 ꢁ 3 C.
140 C, most phenol was removed, and the crude product was
then puried by silica gel column chromatography with 1 : 5
ethyl acetate/petroleum ether as the eluent, and the obtained
2C-AB2 is a yellow solid. Yield: 8.78 g, 44%. 1H-NMR (600 MHz,
acetone-d6, d): 3.76 (t, 2H, OCH2CH2Br), 4.33 (t, 2H,
OCH2CH2Br), 5.38 (s, 1H, CHPh3), 6.76 (d, 4H, C6H4O), 6.89 (d,
2H, C6H4O), 6.94 (d, 4H, C6H4O), 7.06 (d, 2H, C6H4O), 8.15 (s,
2H, PhOH). 13C-NMR (600 MHz, acetone-d6, d): 30.29, 54.30,
67.99, 114.29, 114.87, 130.05, 130.17, 135.64, 138.03, 155.64,
156.65.
Typical polymerization procedure
Procedures for homo- and co-polymerizing different monomers
are the same (Scheme 2). When describing the detailed proce-
dure, 2C-AB2 is used as an example. 2C-AB2 (0.8 g, 2 mmol),
K2CO3 (0.55 g, 4 mmol), and 20 mL DMF were added into a two-
necked ask. Under magnetic stirring, reactants were heated to
Synthesis of AB2 monomers
All three monomers were synthesized in a two-step procedure 80 ꢂC for 24 h under a dry nitrogen atmosphere. Aer cooling to
(Scheme 1). As an example, the procedure for synthesizing 2C- room temperature, the mixture was acidied with hydrochloric
AB2 (n ¼ 2) is given below. 4C-AB2 (n ¼ 4) and 6C-AB2 (n ¼ 6) acid and ltered. The ltrate was precipitated into water to
were synthesized using similar procedures but with different remove DMF and residual salts. The crude product was dis-
reactants, and the characterization results are supplied in the solved in THF and added dropwise into 2 : 1 ethanol/water
ESI.†
solution under strong agitation. Then, the precipitate was
Scheme 1 The synthesis route of AB2 monomer and its byproduct.
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Scheme 2 Typical synthesis route for synthesizing homopolymerized HBPEs.
collected, washed with ethanol, and dried under vacuum at
ꢂ
90 C to give a brick red solid product. Yield: 0.49 g, 77%.
Typical procedure for terminal group modication
The procedure for terminal group modication is shown in
Scheme 4. 1 g HBPE-2C or HBPE-6C, 5.2 g benzyl bromide, and
1.8 g K2CO3 were added into 20 mL DMF. Under magnetic
stirring, reactants were heated to 80 ꢂC for 24 h under a dry
nitrogen atmosphere. Aer cooling to room temperature, the
mixture was ltered and precipitated into petroleum ether
twice. Aer the precipitate was dried under vacuum at 90 ꢂC, the
Fig. 1 1H NMR spectra of HBPEs obtained from monomers with
different spacer lengths (i.e., n ¼ 2, 4, and 6).
obtained benzyl-terminated HBPE-2C (BHBPE-2C) is a light red
1
solid. Yield: 0.90 g, 70%. H-NMR (600 MHz, CDCl3, d): 4.22–
4.30 (br, O–CH2CH2–O), 5.00–5.05 (br, Ph3CH2–O), 5.36–5.42
(br, Ph3CH), 6.80–7.44 (br, C6H4O).
1
shown in the H NMR results (Fig. 1), Ph3CH protons at ꢃ5.3
ppm split into three peaks. For HBPE-2C, the three peaks are
well separated. As the spacer length increases, the three peaks
are closer to each other. Chemical shis of Ph3CH protons are
affected differently by the dendritic (D), linear (L), and terminal
(T) units and thus split into different peaks, which can be used
Physical blending
Binary blends were prepared by dissolving two homopolymers
in THF according to different designed weight ratios. Aer a
transparent solution was obtaꢂined, THF was completely
removed in a vacuum oven at 90 C.
to determine DB14
.
Results and discussion
Synthesis of AB2 monomers and HBPEs
Table
1 Characterization results of phenol-terminated HBPEs
The synthesis route for three AB2 monomers of different spacer
lengths (i.e., n ¼ 2, 4, and 6) is shown in Scheme 1. In the second
step, although both ortho- and para-substituted products are
obtained,13 the para-substituted products are the main products
and will be used as monomers in further polymerization
processes.
Using the three AB2 monomers, which have different spacer
lengths, a variety of homo- and copolymerized HBPEs were
prepared using one-pot polymerization. The synthesis route for
obtained at 80 ꢂ
C
Concentration
(mol Lꢀ1 Mn (kDa) Mw (kDa) PDI Tg (ꢂC) DBb
Codea
)
HBPE-2C-1 0.10
HBPE-2C-2 0.20
HBPE-2C-3 0.40
HBPE-4C-1 0.10
HBPE-4C-2 0.20
3.8
6.0
7.3
3.5
4.1
4.2
8.9
10.0
6.8
12.6
18.3
6.0
7.8
8.4
1.8 127
2.1 129
2.5 131
1.7 101
1.9 109
0.53
0.51
0.50
0.51
0.51
0.53
0.53
0.50
homopolymerized HBPEs is shown in Scheme 2. Homopoly- HBPE-6C-1 0.10
2.0
2.5
2.7
93
97
99
HBPE-6C-2 0.20
HBPE-6C-3 0.40
22.3
27.0
merized HBPEs synthesized from monomers of different spacer
lengths, (i.e., n ¼ 2, 4, and 6 in Scheme 1) are labelled as HBPE-
a
2C, HBPE-4C, and HBPE-6C, respectively. Moreover, polymeri-
zation reactions were carried out under nitrogen protection
using water-free solvents. Two types of terminal groups were
found in HBPEs: the double bond and the bromine group. As
The rst number in the code represents the number of carbon atoms
in the alkyl spacer, i.e., n in each structural unit. The second number in
the code distinguishes HBPEs of different MWs. b Degree of branching
is calculated according to Hawker's denition using 1H NMR.
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MW control in HBPEs
Effects of reaction conditions, including temperature, mono-
mer concentration, and reaction time, on MW were studied.
Characterization results of homopolymerized HBPEs, which
ꢂ
were all synthesized at 80 C, are summarized in Table 1. MW
was determined using GPC. We note that the MW of HBP
obtained from GPC may be smaller than the actual values.
However, studies also show that the MW of HBP is close to its
actual value when MW is not very high (i.e., < 10 000 g molꢀ1).13
HPBs show notable deviations only when the MW is high and
the backbone structure is stiff. In our HBPEs, MW is not very
high, and the backbone structure is not that stiff. Thus, no
notable deviations from the actual values are expected.
Fig. 3 The variation of number-average molecular weight (Mn) of
HBPE-2C with reaction temperature when polymerized for 24 h and at
a monomer concentration of 0.1 mol Lꢀ1
.
For easy comparison, normalized GPC curves corresponding
to different reaction times (from 4 h to 72 h) are shown in Fig. 2.
At 60, 80, and 100 ꢂC, GPC results corresponding to 4 h and 6 h
almost overlap, indicating that MW and its distribution stabi-
lize in 6 h. When temperature increases from 40 to 100 ꢂC,
number-average molecular weight (Mn) of HBPE-2C goes
through a maximum at 80 ꢂC (Fig. 3). The fast stabilization and
temperature dependence in Mn are somewhat unexpected,
which will be explained in the following paragraph.
Fig. 4 The 1H NMR spectrum of HBPE-4C-1 (80 ꢂC, 24 h). Insets show
the enlarged views of boxed parts.
Two assumptions were made in Flory's classic treatment of
AB2 polymerization:15 the reactivity between A and B groups
remain unchanged during polymerization, and side reactions,
such as intermolecular cyclization, are absent. Based on those
assumptions, MW only stabilizes aer long times when steric
hindrance become dominant, making MW sensitive to local
reaction conditions, such as mixing and heat transfer. We
realize that a violation of either of the two assumptions can lead
to some degree of controllability. Similar fast stabilization has
been ascribed to intermolecular cyclization.16 However, cycli-
zation cannot occur in our system due to the short spacer length
in the monomers, which is conrmed by NMR. Rather, the
elimination reaction,17 which competes with the main substi-
tution (or propagation) reaction, is found to be responsible.
Comparing the corresponding peak areas in 1H NMR spectra of
HBPE-4C-2 (Fig. 4) to those of a model molecule, 4-bromo-1-
butene (see Fig. S9 in ESI†) reveals that more than 70% of Br
groups were converted to C]C aer reacting at 80 ꢂC for 24 h,
which essentially terminates the substitution reaction and leads
to a fast stabilization in MW. Thus, the relative speeds of the
elimination and substitution reactions change with tempera-
ture and lead to temperature-dependent MW. We note that fast
stabilization is not achieved at 60 ꢂC (Fig. 2A). This can be
explained by the low reaction speeds of both elimination and
substitution reactions at 60 ꢂC, which lead to incomplete
termination even aer 4 h of reaction. Thus, MW continues to
increase with time. In contrast, at the highest temperature of
100 ꢂC, the elimination reaction is favored and leads to a
decrease in MW (Fig. 3).
In the synthesis of HBPs, side reactions can lower MW and
are thus oen undesirable. In the absence of side reactions, MW
and DB are mainly determined by reaction kinetics, making
them sensitive to changes in local variations in temperature,
Fig. 2 Normalized GPC results of HBPE-2C as a function of reaction
time for polymerization carried out at (A) 60 ꢂC, (B) 80 ꢂC, and (C)
100 ꢂC.
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where D, T, and L represent the number of dendritic, terminal,
and linear units, respectively. In order to assign corresponding
chemical shis to the dendritic, terminal, and linear units,
three model compounds that have well dened NMR peaks for
D, L, and T units were synthesized (see Scheme 3 and Fig. 5A).
For HBPE-2C, three peaks corresponding to Ph3H protons are
well dened and isolated (Fig. 1). However, for HBPE-4C and
HBPE-6C, the three peaks are not well separated and but can be
deconvoluted by assuming a Gaussian distribution.18 A typical
convolution result of HBPE-4C-2 is given in Fig. 5B. DB values of
other HBPEs (prepared at 80 ꢂC) are summarized in Table 1. It is
clear that although HBPE samples are prepared from different
monomers and monomer concentrations, they all have a DB of
ꢃ0.51. The insensitivity of DB to monomer type could be
explained by the fact that the reactivity between A and B group is
insensitive to spacer length. This important nding implies that
DB of copolymerized HBPEs is similar to that of homopolymers.
Scheme 3 The synthesis route of three model molecules that have
well-defined 1H NMR peaks of dendritic (D), linear (L), and terminal (T)
units, respectively.
mixing, and concentrations of reactants and catalysts. As
aforementioned, the violation of two assumptions (i.e., constant
reactivity and/or absence of side reactions) can lead to better
controllability. Yokozawa7 showed that for reacting systems
with increasing reactivity, HBPs with narrow PDI can be
obtained. In our systems, which violate the second assumption,
good controllability and reproducibility can also be achieved. In
the right temperature range, the competing side reaction can
lead to fast stabilization and allows us to control MW simply by
controlling temperature and monomer concentration.
Tg-Tuning in HBPEs
Tg of HBPs depends on many factors, including MW, DB, and
structures of the backbone and terminal group.19 One compli-
cation in HBPs is that changes in MW are oen accompanied by
changes in DB, which also has notable effects on Tg. Thus, the
control and tuning of Tg in HBPs is oen challenging. For our
HBPE systems, the fast stabilization in MW and the insensitivity
of DB make them a good model system for making HPBEs with
tunable Tg, which can be very useful for other scientic inves-
tigations. Several ways of preparing Tg tunable HBPEs are
demonstrated below. The reported Tg values were obtained
from second heating runs in DSC at 10 K minꢀ1 unless other-
wise stated.
Insensitivity of DB to MW and monomer spacer length
(1) Tg-Tuning by varying MW, monomer spacer length, and
terminal group. At 0.1 mol Lꢀ1 and 80 ꢂC, the one-pot approach
yields a Mn of ꢃ4000 g molꢀ1 in the case of HBPE-2C-1. By
increasing monomer concentration, Mn can be further
increased to ꢃ7000 g molꢀ1. Alternatively, by adding additional
batches of monomers into the already stabilized systems, the
propagation reaction can be reinitiated and yield HBPEs with a
Mn of more than 10 000 g molꢀ1. However, increꢂasing Mn from
4000 to 10 000 g molꢀ1 only increases Tg by 10 C, suggesting
changing Tg by varying MW is not very effective for our systems.
Thus, in studies concerning the binary blends and copolymer-
ization, effects of Mn on Tg are not shown.
It is well known that DB in HBPs plays crucial roles in deter-
mining physical properties, such as Tg and viscosity.6 One of the
most used denitions of DB is that proposed by Hawker and
14
´
Frechet:
DB ¼ (D + T)/(D + T + L)
Tg of HBPEs can also be varied by changing the backbone
structure. As shown in Table 1, at comparable Mn, Tg of HBPE-
2C is approximately 30 ꢂC higher than that of HBPE-6C.
Fig. 5 (A) 1H NMR spectra of three model molecules with well-defined
D, L, and T units. Isolated peaks of HBPE-2C-1 at corresponding
locations are also shown. (B) The typical curve-fitting result for HBPE-
4C-2, showing the deconvolution of each type of structural unit.
Scheme 4 The reaction route for terminal group modification.
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copolymerized HBPEs is in the range of 3800–4300 g molꢀ1
.
Please note that DB of copolymerized HBPEs (80 ꢂC, 0.1 mol
Lꢀ1) cannot be accurately determined due to the stronger
overlaps in 1H NMR peaks. However, as explained before, DBs of
copolymers are expected to be close to those of homopolymers.
As shown in Fig. 6, both copolymers and binary blends of HBPE-
2C and HBPE-6C show only one Tg. In copolymers, Tg increases
systematically when the molar fraction of 6C-AB2 monomer (X)
decreases; in binary blends, Tg also increases systematically
with decreasing weight fraction of HBPE-6C (w).
For miscible blends and copolymers without interactions,
the variation of Tg with composition can be described by the
Couchman equation based on entropy continuity20 or a
simplied version of the Couchman equation, i.e., the Gordon-
Taylor equation, which can be derived from volume additivity.21
Due to its simplicity, the Gordon-Taylor equation is oen used
to predict the composition-dependent Tg of binary blends of
linear polymers:
Scheme 5 The route of copolymerized HBPEs using 2C-AB2 and 6C-
AB2. X denotes the mole fraction of 6C-AB2.
Terminal groups in HBPs also have notable effects on Tg. Aer
converting the phenolic terminal groups in HBPE-2C-1 into
benzyl groups (Scheme 4), Tg decreases approximately 50 ꢂC due
to the weaker interactions between terminal groups. Thus,
changing the backbone structure and terminal group are more
effective ways of tuning Tg.
(2) Tg-tuning by varying copolymerization and binary
blending. Copolymerization and physical blending have been
used to change Tgs of linear polymer systems, and prediction of
Tg with composition in those systems (Tg mixing laws) has been
well documented. However, mixing laws for hyperbranched
systems have not been systematically studied. Based on our
HBPEs, the variation of Tg in binary homopolymerized blends
with composition and variation of Tg in copolymers with
monomer ratio was demonstrated. Furthermore, the difference
in two mixing laws was investigated in detail for the rst time.
Random copolymerized HBPEs were obtained using two
monomers (i.e., n ¼ 2 and 6) at different monomer molar ratios,
and the synthetic route is shown in Scheme 5. Mn of
w1Tg1 þ kw2Tg2
Tg ¼
(1)
w1 þ kw2
where Tg, Tg1 and Tg2 are Tg values of the binary blend (or
copolymer) of homopolymers 1 and 2, respectively; w1 and w2
are weight fractions of homopolymers 1 and 2; k is a tting
parameter. Further simplications (r1/r2 ¼ 1; Da1Tg1 ¼ Da2Tg2)
lead to the Fox equation:12,22
1
w1
w2
¼
þ
(2)
Tg Tg1 Tg2
Theoretically, for systems with strong interactions such as
our phenol-terminated HBPEs, neither the Gordon-Taylor
equation nor the Fox equation are adequate; instead, the Kwei23
equation, which considers the strong interactions between
different components, has to be used:
w1Tg1 þ kw2Tg2
Tg ¼
þ qw1w2
(3)
w1 þ kw2
where q quanties the degree of interactions, including the
effects of both steric hindrance and hydrogen bonding.
Generally, hydrogen bonding gives a positive q, and steric
effects give a negative q.
Variations of Tg in both copolymers and binary blends along
with ttings from the Kwei (dashed curve) and Fox Eq.
(solid curve) are shown in Fig. 7. Notable differences
between copolymers and blends are clearly shown: Tg values of
copolymers follow the Fox Eq., whereas Tg values in binary
blends show negative deviations from the Fox Eq. In both cases,
the Kwei Eq. can t data well, with k ¼ 1 and q ¼ 0.6 for
copolymers, and k ¼ 1 and q ¼ ꢀ10.6 for binary blends. Inter-
estingly, for Tg of copolymers, the Fox Eq., which does not
consider effects of interactions, can also t data well. Satisfac-
tory tting using the Fox Eq. has also been reported for hyper-
branched copolymers with nonpolar terminal groups.24,25 In our
systems, the unexpected good t from the Fox Eq. could be
explained by two competing effects: on one hand, phenolic
terminal groups can form hydrogen bonds and lead to an
Fig. 6 DSC traces of copolymers and binary blends. (A) Tgs of copo-
lymerized HBPEs (2C-AB2 and 6C-AB2) as a function of molar fraction
of 6C monomer (X); (B) Tgs of binary homopolymers of HBPE-2C and
HBPE-6C as a function of the weight fraction of HBPE6C (w).
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Fig. 7 (A) Variations of Tg in copolymers with weight fraction of 6C-
AB2 monomer HBPEs; (B) variation of Tg in binary blends with weight
fraction of HBPE-6C. Data are shown in symbols; predictions from the
Kwei and Fox equations are shown as dashed and solid curves,
respectively.
Fig. 8 (A) Tg of benzyl-terminated binary blends as a function of
weight fraction of HBPE-6C, and predictions from the Kwei equation
(solid curve) and Fox equation (dashed curve). (B) DSC traces of binary
blends (w/w
phenol-terminated HBPE-2C-1.
¼
50 : 50) of benzyl-terminated BHBPE-2C-1 and
increase in q; on the other hand, ample terminal groups and the
highly branched structure can also lead to steric hindrance and
thus decrease q. The two competing factors result in a small q
(0.6) and negligible qw1w2 term in the Kwei Eq., and thus lead to
a satisfactory tting with the Fox Eq. In contrast, in binary
blends, the steric hindrance effects dominate and lead to a large
negative q (ꢀ10.6); thus, the Fox Eq. does not apply. The effects
of heating rate on Tg are demonstrated by reducing the heating
rate from 10 K minꢀ1 to 2 K minꢀ1. Results show that the Tgs in
blends and copolymers obtained at 2 K minꢀ1 are all ca. 2.3 ꢂC
lower than those obtained at 10 K minꢀ1. Again, the new sets of
Tg values can still be tted by the Fox or Kwei Eqs.
Fig. 9 The width of Tg (DTg) in copolymers (circles) as a function of the
weight fraction of the 6C-AB2 monomer, DTg in blends of HBPE-2C
and HBPE-6C (squares) as a function of the weight fraction of HBPE-
6C, and DTg in blends of BHBPE-2C-1 and BHBPE-6C-1 (triangles) as a
function of the weight fraction of BHBPE-6C-1.
In order to investigate effects of terminal groups on the glass
transition phenomena in binary blends, HBPE-2C and HBPE-
6C, which have phenolic terminal groups, were converted to
BHBPE-2C and BHBPE-6C, which have less-polar benzyl
terminal groups. For binary blends of BHBPE-2C and BHBPE-
6C, dependence of Tg on the weight fraction of BHBPE-6C along
with tting results from the Kwei Eq. are shown in Fig. 8A.
Moreover, in benzyl-terminated binary blends, only one Tg is
observed for mixtures at all compositions. The Kwei Eq. can t
data well with k ¼ 1 and q ¼ ꢀ12.5. Compared with the phenol-
terminated blends, the more negative q value in benzyl-termi-
nated blends suggests that steric hindrance is more
pronounced in benzyl-terminated blends, which is reasonable,
considering the lack of hydrogen bonding and the bigger size of
benzyl groups. We note that only one Tg is observed in both the
phenol-terminated blends and benzyl-terminated blends. In
binary blends of linear polymers, stronger interactions, such as
hydrogen bonding, are oen necessary to ensure misciblility.26
However, our results suggest that strong interactions are not
necessary to ensure miscibility in blends of HBPEs. Owing to
the large numbers of contact sites in HBP blends, the same
terminal groups (though not polar) in both components are
enough to achieve adequate miscibility. This is further
conrmed by dual Tg values found in binary blends of phenol-
terminated HBPE-2C-1 and benzyl-terminated BHBPE-2C-1
(Fig. 8B). Please note that although two Tgs are observed, they
do move closer to each other compared with Tgs of pure
components.
Apart from the value of Tg, the width of Tg (DTg), which is
reported as the difference between the extrapolated onset and
endset temperatures, can provide additional information on
miscibility. Although only one Tg is observed in binary blends of
both phenol-terminated and benzyl-terminated HBEPs, DTg
does vary with composition (Fig. 9). DTg values of both phenol-
terminated blends of HBPE-2C-1 and HBPE-6C-1 (squares) and
benzyl-terminated blends of BHBPE-2C-1 and BHBPE-6C-1
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(triangles) are bigger than those of copolymers (circles). DTg
values of both blends go through maxima at intermediate
compositions. However, DTg in benzyl-terminated blends is
bigger than that in phenol-terminated blends, suggesting that
hydrogen bonding between polar terminal groups can enhance
miscibility and lead to a narrower Tg. In contrast, for copoly-
mers prepared from 2C-AB2 and 6C-AB2 monomers, DTg is
always close to that of homopolymers and is much smaller than
that in binary blends.
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A series of homo- and co-polymers were synthesized via one-
step polymerization using AB2 monomers of different spacer
lengths. Thanks to the elimination side reaction, fast stabili-
zation in Mn can be achieved in 6 h with good controllability and
scalability. More importantly, the degree of branching is found
to be insensitive to molecular weight and monomer type,
making it a good model system for producing HBPE with
tunable Tg at a large scale.
Tg-Tuning in HBPEs was demonstrated using several
methods, including terminal group modication, copolymeri-
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in binary blends on composition and the dependence of Tg in
copolymers on monomer ratio are compared in detail for the
rst time. For copolymers, variation of Tg with monomer ratio
can be tted with both the Kwei and Fox Eqs.; and the width of
Tg (DTg) in copolymers is similar to that of homopolymers. For
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ships between Tg and composition can be tted with the Kwei
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