Hyperbranched copolymers versus linear copolymers: A comparative study of thermal properties

Article abstract of DOI:10.1021/ma0508146

Copolymerization of two AB₂-type monomers that incorporate spacer segments of similar lengths but different flexibility permitted, for the first time, the preparation of a range of hyperbranched copolymers, wherein the backbone rigidity was varied while maintaining similar branching densities. The copolymers were prepared via a recently developed melt transetherification methodology to yield moderately high molecular weight polymers, with molecular weights ranging from 20 000 to 50 000. ¹H NMR spectroscopic studies revealed that the composition of the copolymers varied linearly with monomer composition, confirming the formation of truly random copolymers. Analogous linear copolymers based on suitably designed AB-type monomers, containing the same two spacers, were also prepared for comparison. Thermal analysis of these copolymers using DSC indicated that the T_g's of both linear copolymers and hyperbranched copolymers varied with composition in a manner that was in complete accordance with the Fox equation, although all the linear copolymers exhibited significantly higher T_g values than their hyperbranched counterparts. It is interesting that, despite their very different topology and the presence of large number of chain ends, hyperbranched copolymers exhibit a similar T_g variation as their linear analogues. The generality of this observation in the broader context of hyperbranched copolymers, such as those possessing different branching densities and terminal functionalities, remains to be tested.

Full text of DOI:10.1021/ma0508146

Macromolecules 2005, 38, 7695-7701
7695
Hyperbranched Copolymers versus Linear Copolymers: A Comparative
Study of Thermal Properties
Girish Ch. Behera, Animesh Saha, and S. Ramakrishnan*
Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India
Received April 18, 2005; Revised Manuscript Received June 27, 2005
ABSTRACT: Copolymerization of two AB2-type monomers that incorporate spacer segments of similar
lengths but different flexibility permitted, for the first time, the preparation of a range of hyperbranched
copolymers, wherein the backbone rigidity was varied while maintaining similar branching densities.
The copolymers were prepared via a recently developed melt transetherification methodology to yield
1
moderately high molecular weight polymers, with molecular weights ranging from 20 000 to 50 000. H
NMR spectroscopic studies revealed that the composition of the copolymers varied linearly with monomer
composition, confirming the formation of truly random copolymers. Analogous linear copolymers based
on suitably designed AB-type monomers, containing the same two spacers, were also prepared for
comparison. Thermal analysis of these copolymers using DSC indicated that the Tg’s of both linear
copolymers and hyperbranched copolymers varied with composition in a manner that was in complete
accordance with the Fox equation, although all the linear copolymers exhibited significantly higher Tg
values than their hyperbranched counterparts. It is interesting that, despite their very different topology
and the presence of large number of chain ends, hyperbranched copolymers exhibit a similar Tg variation
as their linear analogues. The generality of this observation in the broader context of hyperbranched
copolymers, such as those possessing different branching densities and terminal functionalities, remains
to be tested.
Introduction
segments. For instance, it has been shown that the
nature of the end groups have a very strong influence
on the glass transition temperatures of hyperbranched
polymers.12 Copolymerizations using AB + AB2 type
monomers,13-16 and self-condensing vinyl copolymeri-
zation (SCVCP) methodologies,17 have helped reveal
several interesting property variations of hyperbranched
polymers as a function of branching density. In a very
recent study,18 we showed that the length of the spacer
segment that links the branch points greatly influences
the compactness of the conformation of hyperbranched
polymers. Furthermore, we also showed that, just as in
the case of dendrimers, in hyperbranched structures too
compact conformations are adopted only beyond a
certain molecular weight.
It is evident from the published literature that copo-
lymerization in the context of hyperbranched structures
primarily refers to systems wherein branching mono-
mers of the ABn type are copolymerized with simple
linear AB-type ones. Several others have examined the
use of A3 + B2,19 ABB′ + A2,20 etc., most of which have
focused on improving the preparation methodologies,
primarily to enhance the branching densities and
preclude the formation of cross-linked species. Copoly-
merizations using two different AB2-type monomers are
very rare, and more importantly, attempts to under-
stand copolymer properties as a function of composition
have never been made. It is in this context that we have
undertaken the present investigation wherein two types
of AB2 monomers, which have spacer segments of
similar lengths but different flexibility, have been
copolymerized. This approach ensures that while one
molecular feature, namely flexibility of the spacer, is
varied the other features, specifically the branching
density, remain invariant. The variation of the Tg’s of
the hyperbranched copolymers with composition has
been compared with an analogous linear counterpart.
Hyperbranched polymers represent an interesting
class of highly branched soluble macromolecules, which
has witnessed growing attention during the past de-
cade.1 Typically, they are prepared in a single step by
polycondensation of ABx-type monomers (where x g 2),
in contrast to the stepwise approach for the preparation
of dendrimers. Despite the presence of structural im-
perfections, hyperbranched polymers have attracted a
great deal of attention primarily due to their potential
applications, such as in coatings, modifiers, additives,
nanomaterials, biomaterials, etc.2 Many of these ap-
plications exploit the unique properties of these poly-
mers, such as their very low viscosities and/or the
presence of a very large number of peripheral functional
end groups. Several types of hyperbranched polymers,
such as polyphenylenes,3 polyesters,4 polyurethanes,5
polyamides,6 polyethers,7 polyacrylates,8 etc., have been
synthesized using different approaches, like polycon-
densation of ABn-type monomers, self-condensing vinyl
polymerization (SCVP),9 self-condensing ring-opening
polymerization (SCROP),10 proton-transfer polymeriza-
tion (PTP),11 etc. Although a large number of hyper-
branched polymers have been synthesized and well
documented in the literature, understanding of the
fundamental structure-property correlations has lagged
behind. The molecular structural variables associated
with hyperbranched structures are many more than in
their linear counterparts, which make them more
interesting at the same time complex. The typical
structural variables are molecular weight, molecular
weight distribution, degree of branching, nature and
length of the spacer segments, nature of the end groups,
etc. Several attempts have been made to systematically
vary these structural features, such as the degree of
branching, molecular weights, end groups and spacer
* Corresponding author. E-mail: raman@ipc.iisc.ernet.in.
10.1021/ma0508146 CCC: $30.25 © 2005 American Chemical Society
Published on Web 08/04/2005

7696 Behera et al.
Macromolecules, Vol. 38, No. 18, 2005
recrystallization from hot petroleum ether (yield ) 52%, mp
) 110-111 °C).
Experimental Section
2,4,6-Trimethylphenol (Mesitol), 1,6-hexanediol, 1,4-cyclo-
hexanedimethanol, and camphorsulfonic acid were purchased
from Aldrich Chemical Co. Structures of all intermediates,
monomers, and polymers were confirmed by 1H NMR spec-
troscopy. NMR spectra were recorded on a Bruker AV400 MHz
spectrometer, using CDCl3 and TMS as the solvent and
reference, respectively. GPC measurements were carried out
using Viscotek TDA model 300 system, coupled to a refractive
index (RI) and a differential viscometer (DV) in series. The
separation was achieved using a series of two PLgel mixed
bed columns (300 × 7.5 mm) operated at 30 °C using THF as
the eluent. Molecular weights were determined using a
universal calibration curve based on the data from the refrac-
tive index (RI) and differential viscometeric (DV) detectors
using narrow polystyrene standards. The glass transition
temperature of the samples was determined using a Rheo-
metric Scientific DSC PLUS instrument at a heating rate of
10 °C/min under a dry N2 atmosphere. The samples were first
heated to about 180 °C (to ensure that the sample flows and
makes adequate contact with the pan) and quenched prior to
recording their Tg. The glass transition temperature was taken
as the midpoint of the inflection tangent.
1H NMR (δ, ppm, CDCl3): 0.9-2.0 (m, 10H, cyclohexane);
2.30 (s, 6H, Ar(CH3)2); 2.37 (s, 3H, Ar(CH3)); 3.39 (s, 6H,
ArCH2OCH3); 3.44-3.49 (m, 4H, CH2-cyclohexyl); 4.46 (s, 4H,
ArCH2OCH3).
3-Bromomethyl-2,4,6-trimethylphenol (4). 30 mL of
glacial acetic acid was added to the mixture of 4.0 g (29.4
mmol) of mesitol (1), 1.7 g (18.8 mmol) of trioxane, and 16.0 g
(155.0 mmol) of NaBr followed by dropwise addition 5 mL of
concentrated H2SO4. The mixture was stirred for 1 h at RT,
and the contents were poured into 1.0 L of cold water. The
precipitate formed was filtered, washed thoroughly with water,
and dried under reduced pressure (yield ) 92%, mp ) 130 °C).
1H NMR (δ, ppm, CDCl3): 2.18-2.29 (m, 9H, Ar(CH3)3); 4.55
(s, 2H, ArCH2Br); 6.79 (s, 1H, Ar-H).
2,3,4,6-Tetramethylphenol (5). 1.0 g (4.3 mmol) of the
compound 4 in 25 mL of dry ether was added dropwise to the
mixture of 1.0 g (26.3 mmol) of LiAlH4 in 50 mL of dry ether
under a dry nitrogen atmosphere. The reaction mixture was
stirred for 0.5 h at RT, and then the excess LiAlH4 was
destroyed with 10% (v/v) aqueous HCl. The ethereal layer was
separated, washed with water, and dried over anhydrous Na2-
SO4. It was then concentrated and passed through silica gel
column to obtain the product (yield ) 77%, mp ) 72-73 °C).
1H NMR (δ, ppm, CDCl3): 2.15-2.19 (m, 12H, Ar(CH3)4);
6.78 (s, 1H, Ar-H).
3,5-Bisbromomethyl-2,4,6-trimethylphenol (2). 50 mL
of HBr in acetic acid (33 wt %) was added to the mixture of
4.0 g (29.4 mmol) of mesitol and 2.6 g (29.0 mmol) of trioxane.
The mixture was refluxed for 2 h, cooled to RT, and poured
into 1.0 L of cold water. The residue was filtered, washed
thoroughly with water (4-5 L) to ensure it is acid-free, and
then dried under vacuum (yield ) 90.0%, mp ) 145 °C; lit.21-
139 °C).
5-Methoxymethyl-2,3,4,6-tetramethylphenol (6). 60 mL
of glacial acetic acid was taken along with 4.0 g (26.6 mmol)
of 5, 6.0 g (66.6 mmol) of trioxane, and 17.0 g (165.0 mmol) of
NaBr in a round-bottom flask, and 10 mL of concentrated H2-
SO4 was added to it dropwise. The mixture was stirred for 12
h at RT, and the contents were poured into 1.0 L of cold water
and filtered. The precipitate formed was washed thoroughly
with water and dried under reduced pressure. 4.4 g (18.1
mmol) of the above bromomethylated product was dissolved
in 60 mL of dry methanol and added dropwise to sodium
methoxide solution (2.0 g, 86.9 mmol of sodium metal in 50
mL of dry methanol) under a N2 atmosphere. The reaction
mixture was refluxed for 13 h under a N2 atmosphere and
cooled to room temperature, and the methanol was removed
using a rotary evaporator. 70 mL of cold water was added to
the residue, and it was acidified with 50% HCl (v/v). The white
precipitate formed was extracted with ether (100 mL), dried
over anhydrous Na2SO4, and concentrated. The crude product
was distilled in a Kugelrohr at 150 °C/0.5 mm of Hg to yield
the desired product (yield ) 57%, mp ) 62 °C).
1H NMR (δ, ppm, CDCl3): 2.31 (s, 6H, Ar (CH3)2); 2.40 (s,
3H, Ar (CH3); 4.57 (s, 4H, ArCH2Br).
3,5-Bismethoxymethyl-2,4,6-trimethylphenol (3). So-
dium metal (3.2 g, 139.1 mmol) was added to 50 mL of dry
methanol in portions. The solution of 2 (7.5 g, 23.3 mmol) in
dry methanol (170 mL) was added dropwise to the degassed
sodium methoxide solution. The reaction mixture was refluxed
for 18 h under a N2 atmosphere and cooled to room temper-
ature, and the methanol was removed using a rotary evapora-
tor. 80 mL of cold water was added to the residue, and it was
acidified with 50% HCl (v/v). The white precipitate formed was
extracted with CHCl3 (120 mL), dried over anhydrous Na2-
SO4, and passed through a silica bed to remove some colored
impurities. The chloroform was then removed by a rotary
evaporator, and the residue was recrystallized from hot
petroleum ether to yield the desired product (yield ) 76%, mp
) 79 °C; lit.7a 77-79 °C).
1H NMR (δ, ppm, CDCl3): 2.23 (s, 6H, Ar(CH3)2); 2.29-2.30
(s, 6H, Ar(CH3)2); 3.45 (s, 3H, ArCH2OCH3); 4.51 (s, 2H,
ArCH2OCH3); 4.59 (s, 1H, ArOH).
1H NMR (δ, ppm, CDCl3): 2.25 (s, 6H, Ar(CH3)2); 2.35 (s,
3H, Ar(CH3)); 3.40 (s, 6H, ArCH2OCH3); 4.47 (s, 4H, ArCH2-
OCH3); 4.72 (s, 1H, ArOH).
1-(6-Hydroxyhexyloxy)-5-methoxymethyl-2,3,4,6-tet-
ramethylbenzene (C). 6 was coupled with ω-bromohexanol
using same procedure as A, and the product was purified by
distillation using a Kugelrohr at 210 °C/0.5 mmHg (yield )
79%, mp ) 48-49 °C).
1-(6-Hydroxyhexyloxy)-3,5-bis(methoxymethyl)-2,4,6-
trimethylbenzene (A). A mixture of K2CO3 (5.5 g, 39.8
mmol), a catalytic amount of KI, and 1-bromohexanol (3.6 g,
20.0 mmol) were taken in 40 mL of dry CH3CN. The mixture
was degassed for 20 min, after which 1.5 g (6.7 mmol) of 3
was added to it. The reaction mixture was degassed for an
additional 20 min and then refluxed for 72 h under a N2
atmosphere. The solvent was then removed with a rotary
evaporator, and 50-60 mL of cold water was added to it. The
product was extracted with 100 mL (2 × 50 mL) of ether, and
the ether layer was washed with 10% (w/v) aqueous NaOH
solution (4 × 30 mL) followed by water. The ether layer was
dried over anhydrous Na2SO4 and concentrated, and the
residue was recrystallized from hot petroleum ether to give
the product (yield ) 73%, mp ) 73 °C).
1H NMR (δ, ppm, CDCl3): 1.42-1.83 (m, 8H, ArOCH2-
(CH2)4CH2OH); 2.16-2.30 (m, 12H, Ar(CH3)4); 3.41 (s, 3H,
ArCH2OCH3); 3.62-3.68 (m, 4H ArOCH2(CH2)4CH2OH); 4.46
(s, 2H, ArCH2OCH3).
1-(4-Hydroxymethylcyclohexylmethoxy)-5-methoxym-
ethyl-2,3,4,6-tetramethylbenzene (D). 6 was coupled with
4-bromomethylcyclohexylmethanol using the same procedure
as for the alkylene series A, and the product was purified by
recrystallization from hot petroleum ether (yield ) 91%, mp
) 62-64 °C).
1H NMR (δ, ppm, CDCl3): 0.9-2.03 (m, 10H, cyclohexane);
2.16-2.29 (m, 12H, Ar(CH3)4); 3.40 (s, 3H, ArCH2OCH3);
3.44-3.57 (m, 4H, CH2-cyclohexyl); 4.46 (s, 2H, ArCH2OCH3).
Typical Polymerization Procedure. Monomer A (600
mg, 1.8 mmol) along with 2 mol % of pyridinium camphorsul-
fonate (PCS) was placed in the test tube-shaped polymerization
tube. It was degassed for 10 min and dipped into an oil bath
at 110 °C under continuous N2 purge to ensure homogeneous
mixing of catalyst with monomer. The temperature of the oil
bath was raised to 150 °C, and polymerization was carried out
1H NMR (δ, ppm, CDCl3): 1.40-1.85 (m, 8H, ArOCH2-
(CH2)4CH2OH); 2.30 (s, 6H, Ar(CH3)2); 2.36 (s, 3H, Ar(CH3);
3.38 (s, 6H, ArCH2OCH3); 3.61-3.63 (m, 4H ArOCH2(CH2)4CH2-
OH); 4.45 (s, 4H, ArCH2OCH3).
1-(4-Hydroxymethylcyclohexylmethoxy)-3,5-bis-
(methoxymethyl)-2,4,6-trimethyl-benzene (B). 3 was
coupled with 4-bromomethylcyclohexylmethanol using the
same procedure as A, and the product was purified by

Macromolecules, Vol. 38, No. 18, 2005
Hyperbranched Copolymers vs Linear Copolymers 7697
Scheme 1. Synthesis of Hyperbranched Copolymers
under N2 for 2 h with constant stirring. The polymerization
tube was cooled to room temperature and connected to a
Kugelrohr apparatus, in which the polymerization was con-
tinued for an additional 1 h at 150 °C under reduced pressure
(0.1 Torr), with continuous mixing of the melt by rotation. The
polymer was dissolved in THF, and the solution was neutral-
ized with solid NaHCO3 and filtered. The filtrate was concen-
trated and poured into methanol to obtain the polymer. Typical
yields of the purified polymer ranged from 50 to 60%. All the
copolymers, both linear and hyperbranched, were prepared
using a similar procedure by taking the required mole fraction
of the appropriate monomers. In the case of the linear
copolymers, a slightly longer polymerization time (2 h under
N2 flow and 4-5 h under vacuum) was used to ensure
formation of high molecular weight polymers. The copolymers
were all purified by two dissolution-reprecipitation steps
using THF-methanol.
clohexyldimethylene, were chosen because their lengths
are roughly the same. Also, the reactivities of the con-
densing functionalities during the polymerizations are
expected to be nearly the same, and therefore the copoly-
mers formed should be of a truly random nature. Addi-
tionally, the hyperbranched hompolymers prepared from
these two monomers were reported to have Tg’s of 1 and
77 °C, respectively,18 thereby providing a large enough
window to examine the variation in copolymer systems.
Polymerization of the AB2 monomers proceeded under
acid-catalyzed melt transetherification conditions,22
with the exclusion of methanol. The underlying mech-
anism for the transetherification process relies on the
facile generation of the benzylic carbocationic interme-
diate under the acid-catalyzed conditions. Therefore, the
three methyl groups on the benzene ring of the monomer
are essential to prevent cross-linking that can occur via
Results and Discussion
Synthesis and Structural Characterization. The
two AB2 monomers, A and B (Scheme 1), were synthe-
sized in good yields and purity by previously reported
procedures starting from mesitol.18 The spacer segments
in these monomers, namely hexamethylene and 1,4-cy-
1
an electrophilc aromatic substitution.22a The H NMR
spectra of the two monomers are shown in Figure 1,
along with that of one representative copolymer. Upon
polymerization the relative intensity of methoxy protons
Figure 1. 1H NMR spectra of the two monomers, A and B, along with that of a representative copolymer.

7698 Behera et al.
Macromolecules, Vol. 38, No. 18, 2005
Figure 3. Feed vs incorporation of A or C (from 1H NMR)
plot of hyperbranched (9) and linear (b) copolymers. Solid line
represents the variation for ideal copolymerization.
Scheme 2. Synthesis of Analogous Linear AB-Type
Monomer and Copolymers
Figure 2. 1H NMR spectra of all the hyperbranched copoly-
mers (HP1 to HP5). The weight fraction of the comonomer
with hexylene spacer (A) systematically varied from 0.0 to 1.0.
The regions indicated arrows were used for the determination
of copolymer composition.
(CH3OCH2- ∼3.4 ppm) decreases to nearly half its
original value, confirming that the condensation has
proceeded to high conversion. In further confirmation
of this, the benzylic proton peaks (∼4.5 ppm) split into
two peaks of equal intensity upon polymer formation:
one belonging to CH3OCH2- and the other to the -R-
OCH2- unit along the polymer backbone. The degree
of branching in this homopolymer was calculated to be
about 0.54,23 in near accordance with the theoretically
expected value of 0.5. Furthermore, the alkoxymethyl-
ene units of the spacer segment (-OCH2- and -CH2-
OH), which are not well-resolved in both the monomers,
separate into two sets of peaks each (in the region 3.3-
3.7 ppm) upon polymerization, giving rise to four
clusters of peaks of roughly equal intensity in the 1:1
copolymer.
units; in both cases they are six carbon atoms long with
the exception that in monomer B four of the carbons
are an integral part of a cyclohexane ring.
To compare the variation of properties of hyper-
branched copolymers, it is essential to ensure that while
one structural parameter is varied the others must
remain constant. Thus, in this case, while the flexibility
of the spacer in the two repeat units are different, the
branching density (defined as the number of branch
points per unit volume) remains roughly constant. In
our earlier paper, we had shown that the conformational
compactness, as reflected by the Mark-Howink expo-
nent, is roughly the same for the homopolymers pre-
pared from both these monomers.18
To compare the variation of properties in hyper-
branched copolymers with those in analogous linear
systems, a series of linear copolymers were also pre-
pared (Scheme 2). The AB-type monomers25 C and D
were prepared from the same starting materialsmesitols
but by carrying out a selective mono-bromomethylation
followed by reduction to yield the tetramethylphenol.
A second bromomethylation step followed by conversion
to the corresponding methoxymethyl derivative was
carried out as described previously to yield the pre-
monomer intermediate. Coupling this intermediate with
the appropriate bromoalcohol resulted in the two desired
monomers (Scheme 2).
1
The stack plot of the H NMR spectra of the hyper-
branched copolymers with varying composition along
with those of the two homopolymers is shown in Figure
2. It is evident from this figure that the compositional
variation is clearly reflected by the increase in the
relative intensities of the peaks corresponding to the two
kinds of repeat units. The most uncluttered and comono-
mer-specific regions in the spectra are the region
between 0.9 and 1.2 ppm due to the four axial protons
of the cyclohexyl ring of monomer B24 and the two sets
of oxymethylene proton peaks of the spacer of monomer
A in the region 3.5-3.7 ppm, each representing two
protons (see Figure 1). The composition of the copoly-
mers was thus readily calculated using the relative
intensities of the peaks in these two regions, and a plot
of the copolymer vs feed composition is shown in Figure
3. The excellent straight-line fit with a slope of nearly
one confirms the equal reactivity of the two monomers
toward the condensation process. This in turn also
ensures that the copolymers formed are statistically
random in nature. As mentioned earlier, one important
feature of these hyperbranched copolymers is the near
identical lengths of the spacer segment in the two repeat
The homopolymers and the various copolymers, using
monomers C and D, were prepared using the same acid-
catalyzed melt-transetherification methodology to yield
polymers of moderate molecular weights (see Table 1).

Macromolecules, Vol. 38, No. 18, 2005
Hyperbranched Copolymers vs Linear Copolymers 7699
Table 1. Molecular Weights of the Hyperbranched and
Linear Copolymers along with Their Corresponding
Glass Transition Temperatures (Tg)
content of
A or C (mol %)
a
copolymers
Mw
PDI
Tg (°C)
HP-1
HP-2
HP-3
HP-4
HP-5
P-1
0
20
50
80
100
0
20
50
80
100
28 300
22 600
40 200
32 300
51 100
16 000
10 100
13 200
18 600
39 600
2.1
2.5
2.2
2.1
2.5
3.0
2.4
2.4
2.4
5.1b
77
57
35
15
1
95
70
45
23
9
P-2
P-3
P-4
P-5
a Determined using universal calibration plot constructed from
refractive index (RI) and viscometry (DV) detector signals. b The
unusually high value in this case could be due to the inadvertent
formation of cyclics and/or due to physical inhomogeneities during
the polymerization.
The 1H NMR spectra of the homopolymers and the
copolymers are given in Figure 4. As in the case of the
hyperbranched copolymers, here again the peaks in the
same two regions (indicated by an arrow) could be used
to calculate the copolymer composition. However, in this
case a small peak to the left of the two sets of peaks
around ca. 3.6 ppm is seen even in the homopolymer
prepared from D. This is ascribed to the cis isomer in
the starting cyclohexane dimethanol, which is present
to the tune of about 20 mol %. This peak adds to the
intensity of one of the peaks due to the comonomer C
and hence complicates the calculation of the composi-
tion. As an alternate approach, the relative intensities
of the peak in the region 0.9-1.2 ppm was compared
with the single peak at 4.5 ppm, which is due to the
Figure 5. DSC thermograms of hyperbranched copolymer
(bottom) and linear (top) copolymers.
benzylic protons belonging to both the repeat units. A
plot of the variation of the copolymer composition, thus
obtained, with the feed composition in this case also is
seen to follow the expected linear variation with a slope
of nearly one (see Figure 3), once again confirming the
randomness of the copolymers formed.
Molecular Weights and Thermal Properties. The
molecular weights of the polymers were determined by
GPC using a dual detector system, consisting of a
refractive index (RI) and a differential viscometric (DV)
detector connected in series. The absolute molecular
weights of all the polymers were determined by the
universal calibration curve26 and were found to be
reasonably high, with Mw values ranging from 22 600
to 51 000, as shown in Table 1. These molecular weights
are adequately high to ensure that the properties, such
as Tg, will have become almost invariant with molecular
weight. In a recent study, we showed that the Tg values
of hyperbranched polymers begin to level off beyond Mw
values of about 9000.18 Similar observations have also
been made in the case of dendrimers.27
The DSC thermograms of the copolymers are shown
in Figure 5. All the copolymers are completely amor-
phous and exhibit only a single Tg and no melting
transition. It is evident that the Tg varied continuously
with composition in both hyperbranched copolymers as
well as the linear copolymers. The variation of the Tg
of copolymers, in general, has been fitted to a variety
of equations, such as the Gordon-Taylor equation,28
Gibbs-Di Marzio equation,29 etc., most of which are
formulated based on the assumption that the copolymer
can be treated as if it were a mixture of small molecules
that follows ideal mixing (without contraction or expan-
sion) behavior.30 The Gordon-Taylor equation can be
expressed as follows
w1Tg1 + Kw2Tg2
Tg(copolymer) )
w1 + Kw2
where Tg is the glass transition temperature of the
copolymer, Tg1 and Tg2 are the glass transition temper-
atures of the two homopolymers, and w1 and w2 are the
weight fractions of the two repeat units in the copoly-
Figure 4. 1H NMR spectra of the two monomers, C and D,
along with that of copolymers (P1 to P5). The region indicated
by the arrow was used for determination of copolymer com-
position.

7700 Behera et al.
Macromolecules, Vol. 38, No. 18, 2005
1
firmed by H NMR spectroscopy, and their molecular
weights were found to be moderately high by GPC
measurements. The glass transition temperatures of
both the hyperbranched and the linear counterparts
were found to vary in complete accordance with the Fox
equation, which has generally been applied only to
linear copolymers. It was, however, noticed that the
hyperbranched copolymers had consistently lower val-
ues of Tg compared to their linear analogues. This
difference is probably due to the absence of chain
entanglements and/or due to the presence of a very large
number of end groups in hyperbranched polymers.
Importantly, this study also confirms the applicability
of Fox equation to very highly branched copolymers,
provided that their branching density, as defined by the
number of branches per unit volume, is maintained
constant. However, under conditions wherein other
molecular structural parameters, such as the nature of
the end groups or the degree of branching, also vary
with copolymer composition, such a correlation may be
less straightforward. Further studies are needed to
probe the limits of the applicability of the Fox equation
to hyperbranched copolymers.
Figure 6. Variation of Tg of hyperbranched (b) and (1) linear
copolymers as a function of composition. The solid line
indicates the Tg calculated from the Fox equation.
mer. The constant K ) (F1/F2)(∆R2/∆R1), where Fi are the
densities and ∆Ri the increment of the expansion
coefficient at Tg. Assuming that the densities of both
the homopolymers are very similar, i.e., F1/F2 ) 1, the
Gordon-Taylor constant K becomes equal to Tg1/Tg2
under the Simha-Boyer approximation,31 i.e., ∆RTg )
0.113. Thus, the above G-T equation transforms to the
more popular Fox equation32
References and Notes
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1/Tg ) w1/Tg1 + w2/Tg2
A plot of 1/Tg vs w1 for the hyperbranched copolymers
is shown in Figure 6. It is clear that the variation closely
follows the expected behavior according to the Fox
equation, which is represented by the straight line
linking the two homopolymer Tg’s. A similar behavior
is also exhibited by the analogous linear copolymers,
although the line is shifted slightly reflecting their
consistently higher Tg values when compared to the
hyperbranched systems. The consistently lower Tg
values of the hyperbranched copolymers is probably a
reflection of the absence of chain entanglement and/or
due to the large number of end groups in them. The
remarkable agreement with the Fox equation demon-
strates its robustness and confirms its validity and
usefulness even for of highly branched copolymer sys-
tems. It may be added here that we have carefully
chosen the two monomers, such that they have similar
branching densities. However, when two monomers,
which generate hyperbranched polymers with different
branching densities and/or different types of terminal
functionality, are copolymerized, the resulting copoly-
mers may exhibit Tg’s that differ from this expected
behavior.
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The present study primarily attempts to address the
question: Do hyperbranched copolymers obey the Fox
equation? To do so, representative hyperbranched co-
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that incorporate spacer segments of different flexibility
but of similar lengths were prepared by a melt trans-
etherification strategy. One of the monomers contain a
flexible hexamethylene spacer while the other one has
a cyclohexyldimethylene spacer: the former yielded a
homopolymer with a Tg of 1 °C, while the latter yielded
one with a Tg of 77 °C. For comparison, analogous linear
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