Art Branched Polyesters

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Branched polyesters: recent advances in synthesis and performance

Matthew G. McKeeb, Serkan Unala, Garth L. Wilkesb, Timothy E. Longa,*

aDepartment of Chemistry, Virginia Polytechnic Institute and State University, 124A Davidson Hall, Blacksburg, VA 24061, USA

bDepartment of Chemical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA

Received 28 September 2004; revised 12 January 2005; accepted 12 January 2005

Abstract

The synthesis, characterization, physical properties, and applications of branched polyesters are discussed. This review

describes recent efforts in the synthesis of statistically and tailored branched systems, and performance advantages compared to

linear counterparts. In particular, an emphasis is placed on long-chain branching, where the branches are sufficiently long

enough to form entanglements. Step-growth polymerization methodologies that employ various combinations of multi and

mono-functional groups to achieve different levels of branching are reviewed in detail. The performance of branched

polyesters, including behavior in dilute and semi-dilute solutions, and melt and solid-state properties are discussed. The

implications of topological parameters including branch length, number of branches, and branching architecture on rheological

performance are also reviewed. Although the majority of this review focuses on the synthesis and rheological behavior of

branched polyesters, some discussion is devoted to the influence of branching on solid-state properties, sub-micron fiber

formation, and controlled biodegradation for drug-delivery applications. Finally, a perspective of future directions in highperformance applications for branched polyesters is provided.

q 2005 Elsevier Ltd. All rights reserved.

Keywords: Branching; Polyesters; Rheology; Entanglements; Crystallization; Step-growth polymerization

Contents

1. Scientific rationale and perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508

2. Synthesis of long-chain branched polyesters via step-growth polymerization . . . . . . . . . . . . . . . . . . . . . . . . . . . 509

2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509

2.2. Synthesis of branched polyesters via A2 and B2 monomers in the presence of An or Bn (nO2) monomers 511

2.3. Synthesis of branched polyesters via A2 and B2 monomers in the presence of An or Bn (nO2) Monomers

and a monofunctional endcapping reagent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513

2.4. Synthesis of branched polyesters via AB monomers in the presence of A2B monomers . . . . . . . . . . . . . . 514

Prog. Polym. Sci. 30 (2005) 507539

www.elsevier.com/locate/ppolysci

0079-6700/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.progpolymsci.2005.01.009

* Corresponding author. Tel.: C1 540 231 2480; fax: C1 540 231 8517.

E-mail address: [email protected] (T.E. Long).
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3. Characterization of branched polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516

3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516

3.2. Contraction factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516

3.3. Endgroup analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517

4. Influence of branching on melt rheological properties: model systems and long-chain branched polyesters . . . . . 518

4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518

4.2. Number of branches per chain and branch length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519

4.2.1. Randomly branched polyesters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519

4.2.2. Star-branched polyesters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522

4.2.3. H-shaped and comb-branched polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524

4.3. Flow activation energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525

5. The influence of branching on solution rheology properties in the semidilute regime . . . . . . . . . . . . . . . . . . . . . 526

5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526

5.2. Effect of branching on the entanglement concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526

5.3. Recent advances in electrospinning of long-chain branched polyesters . . . . . . . . . . . . . . . . . . . . . . . . . . 527

6. Influence of branching on thermal properties of polyesters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529

6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529

6.2. Glass transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530

6.3. Melting behavior and quiescent crystallization growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531

6.4. Controlling the biodegradation of aliphatic polyesters through branching . . . . . . . . . . . . . . . . . . . . . . . . . 532

7. Conclusions and future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539

1. Scientific rationale and perspective

Branched polymers are characterized by the

presence of branch points or the presence of more

than two end groups and comprise a class of polymers

between linear polymers and polymer networks [1].

Although undesirable branching can occur in many

polymerization reactions, controlled branching is

readily achieved. In fact, numerous studies on polymer

structure-property relationships have shown that

branched polymers display enhanced properties and

performance for certain applications [2]. Long-chainbranched polymers offer significantly different physi-

cal properties than linear polymers and polymer

networks. For example, a low concentration of long

chain branching in the polymer backbone influences

melt rheology, mechanical behavior, and solution

properties, while large degrees of branching readily

affects crystallinity [3,4]. The strong influence of only

one long chain branch per chain can be visualized by

looking at Fig. 1. The slip-links along the polymer

backbone represent entanglements with other chains.

The linear polymer is free to diffuse along a tubeimposed by other chains, while it is obvious from

Fig. 1b that the mobility of the long-chain branched

polymer is restricted, and must diffuse through

some other mechanism. Thus, it is not surprising that

long-chain branched polymers exhibit very different

properties where chain entanglements play a role.

(a) (b)

Fig. 1. Cartoon representing entangled linear chains (a), and long

chain branched chains (b). The slip links represent entanglements

due to other polymers.

M.G. McKee et al. / Prog. Polym. Sci. 30 (2005) 507539508


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It is widely documented that a high degree of

branching in a polymer backbone provides enhanced

solubility, lower viscosity and lower crystallinity, for

the case of symmetric chains that readily crystallize,than a linear polymer of equal molecular weight [5].

Therefore, a fundamental understanding of branching

and how it influences polymer properties is essential

for tailoring a polymeric material for high perform-

ance applications. Numerous types of branched

polymers can be prepared using different polymeriz-

ation techniques. In a living polymerization, multi-

functional initiators or multifunctional linking agents

yield well-defined star-branched polymers. Alkyl-

lithium initiators are particularly efficient types of

multifunctional initiators, and polyfunctional silyl

halides are highly efficient multifunctional linking

agents [2]. Comb polymers, which contain extensive

branching along the polymer backbone, are syn-

thesized in the presence of a polyfunctional coupling

agent. Polyfunctional or multifunctional monomers of

a functionality greater than two result in randomly

branched polymers. Randomly branched polymers are

often prepared by step-growth or chain polymeriz-

ation in the presence of a multifunctional comonomer

[1]. Highly branched (hyperbranched) polymers are

prepared without gelation via the self condensation of

an ABx monomer containing one A functionalgroup, and two or more B functional groups that

are capable of co-reacting. Unlike dendrimers, which

exhibit a regular, tree-like branch structure from a

central core, hyperbranched polymers contain linear

segments (defects) due to a more randomly branched

architecture. Hyperbranched polymers are generally

produced more easily than dendrimers and exhibit

several similar properties [6,7].

The effect of branching on polymers prepared by

chain-growth polymerization and single site catalyzed

polymerizations has received significant attention.However, structure/property relationships for

branched polyesters are limited and further studies

are needed [8]. Polyesters offer good mechanical and

thermal properties and high chemical resistance at

relatively low cost. Many polyesters, such as poly

(ethylene terephthalate)s (PET), polycarbonates, bio-

degradable aliphatic polyesters, and liquid crystalline

polyesters are commercially available [9]. PET is

utilized for a wide range of applications including

injection-molding and blow-molding [10]. Processing

of some polyesters, however, is limited due to

insufficient melt strength and melt viscosity. For

example, while aliphatic polyesters such as poly

(butylene adipate) (PBA) and poly(butylene succi-nate) (PBS) decompose rapidly under natural environ-

mental conditions and are replacing some commodity

polymers due to environmental concerns, processing

these resins is often difficult due to low melt strength

and melt viscosity [1113]. Thus, many researchers

have focused on modifying polyesters for enhanced

melt strength and melt viscosity by introducing long

chain branches into the polyester backbone. In this

review, the synthetic methods for preparing various

long-chain branched polyesters are reported. More-

over, the influence of branching on polyester proper-

ties for new high performance applications is

discussed.

2. Synthesis of long-chain branched polyesters

via step-growth polymerization

2.1. Introduction

Multifunctional comonomer branching agents are

introduced into polycondensation reactions to obtainlong-chain branched polyesters. Unlike short chain

branches (SCB), a long chain branch (LCB) is long

enough to entangle with other chains in the melt and

concentrated solutions thereby drastically altering the

flow properties. The critical molecular weight (Mc) is

the minimum molecular weight at which a polymer

chain entangles, as often measured by the molecular

weight dependence of viscosity [14]. The value Mcseparates two regimes in the dependence of zero shear

rate viscosity (h0) on weight average molecular

weight (Mw

) for linear chains. Below Mc

the value

ofh0 scales directly with Mw and above Mc h0 scales

with M3:4w . The value of Mc for a given polymer is

directly related to the entanglement molecular weight

(Me), which is typically determined from the plateau

modulus G0N as shown in Eq (1),

MeZrRT

G0N(1)

where r is the polymer melt density, R is the gas

constant, and T is the absolute temperature. Fetters

M.G. McKee et al. / Prog. Polym. Sci. 30 (2005) 507539 509


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et al. relatedMc andMe through the packing length (p),

which is proportional to the cross-sectional area of a

polymer chain [15]. Values ofMc were reported in the

literature for several linear polyesters, including PET(3300 g/mol), poly(decamethylene succinate) (4600 g/

mol), poly(decamethylene adipate) (4400 g/mol), and

poly(decamethylene sebacate) (4500 g/mol) [16]. The

parametersMc andMe are discussed further in Sections

4.1 and 4.2 of this review.

Hudson et al. showed that long-chain branching in

the polymer backbone permits control over the

rheology of the polymer [17]. More recent studies

on the modification of polyesters with long-chain

branching have involved the use of PET, an

engineering thermoplastic, with good thermal and

mechanical stability, high chemical resistance, and

ease of processing [10,18]. Early work by Manaresi et

al. describes the preparation of long-chain branched

PET using low levels of trimesic acid [19]. Intrinsic

viscosity measurements and the extent of reaction

were reported along with the degree of branching.

It is well known that polycondensation reactions

with multifunctional comonomers may form an

infinite molecular weight polymer network, or gel,

above a certain multifunctional comonomer concen-

tration or at high conversions. The onset of gelation

occurs at a critical point of conversion during thepolymerization, and is dependent on the degree of

functionality and the concentration of the multi-

functional (fO2) branching agent. For example,

polyester networks are prepared using dicarboxylic

acids and tri- or tetrafunctional monomers [20]. The

critical extent of reaction (ac) at which a polymer is

predicted to form a gel is shown in Eq. (2).

acZ1

rCrpfK21=2(2)

This equation is valid for polymerization mixtures

with bifunctional A and B monomers and a multi-

functional A monomer. In Eq. (2), r is the ratio of A

functional groups to B functional groups and p is the

ratio of A functional groups with fO2 to the total

number of A groups. Low concentrations of multi-

functional comonomers are used at low conversions to

obtain long chain branching, and this method has

yielded low molecular weight polymers. Neff et al.

suggested the use of a monofunctional comonomer

together with bifunctional and multifunctional mono-

mers to overcome the gelation problem in high

multifunctional comonomer concentrations or athigh conversions [21]. Manaresi et al. were first to

report the preparation and characterization of

PETs synthesized in the presence of a high content

(O1 mol%) of trifunctional comonomer (trimethyl

trimesate), as well as monofunctional comonomers

(methyl 2-benzoylbenzoate) [22]. Rosu et al. reported

branched PETs using multifunctional and monofunc-

tional comonomers and subsequent solid-state pol-

ymerization was employed to increase the molecular

weight of the final product [23].

Jayakannan and Ramakrishna synthesized high

molecular weight branched PETs through the copo-

lymerization of an A2 monomer with small amounts

of an AB2 monomer [24]. However, as discussed in

detail later in this review, insoluble crosslinked

polymers were obtained at higher conversions.

Hudson et al. synthesized and characterized branched

PETs to study the balance between the branching

reagents and endcapping reagents [17]. The objective

of their study was to examine various branching

agents used for PETs and other polyesters and their

influence on polymer properties, both with and

without an endcapping reagent. Molecular weightwas controlled via endcapping reagents on branched

polyesters using a variety of branching agents.

More recently, Yoon et al. studied the effects of

multifunctional comonomers such as trimethylo-

lethane (TME) and pentaerythritol on the properties

of PET copolymers [18]. Molecular weights increased

with increasing comonomer content while the mole-

cular weight distribution broadened. Although solid-

state mechanical properties did not differ significantly

from linear analogues, the branched copolymers

exhibited earlier shear-thinning onset in the meltcompared to linear PET. Moreover, the crystallization

rates of the copolymers decreased with increasing

comonomer content as would be expected. Similar to

branched PETs, branched poly(butylene isophthalate)

(PBI) and poly(butylene terephthalate) (PBT) were

synthesized and characterized to investigate their melt

and crystallization properties. Linear and branched

PBIs were synthesized from dimethylisophthalate

(DMI) and 1,4-butanediol (BD) in the presence of

trifunctional comonomers [25]. Branched PBTs were



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synthesized by incorporating the trifunctional como-

nomer, 1,3,5-tricarboxymethylbenzene [26].

High molecular weight branched aliphatic polye-

sters such as poly(ethylene succinate), poly(butylenesuccinate) (PBS), and poly(butylene adipate) (PBA),

known as Bionollee polymers, were also prepared

[27]. Bionollee polymers are used in a variety of

applications, including film blowing, blow molding,

extrusion coating and extrusion foaming [28]. Han

et al. described synthetic conditions and thermal and

mechanical properties for high molecular weight

branched PBAs [11]. Ramakrishnan et al. reported

the synthesis of a series of branched thermotropic

liquid crystalline polyesters and their structural

features [29]. Other novel branched polyesters

such as branched poly(3-hydroxy-benzoates) and

poly(4-ethyleneoxy benzoate) were synthesized by

Kricheldorf et al. and Ramakrishnan et al., respecti-

vely, [30,31].

2.2. Synthesis of branched polyesters via A2 and B2monomers in the presence of An or Bn (nO2)

monomers

The most common method for synthesizing

branched polyesters is via the addition of small

amounts of tri- or tetrafunctional comonomers to thepolymerization. Manaresi et al. first reported the

synthesis of branched PETs from dimethyl terephthal-

ate (DMT) and ethylene glycol (EG) using a trifunc-

tional branching agent, trimethyl trimesate (Fig. 2)

[19]. To prevent gelation, only small amounts (!2%)

of the trifunctional branching agent were used and the

influence of long chain branching on PET properties

was also reported. Although Manaresi et al. did not

report the absolute molecular weights of the polymers,

intrinsic viscosities in o-chlorophenol at 25 8C and the

extents of reaction by end-group analysis were

reported. After ester-interchange, only one type of

functional group remained, i.e. the hydroxyl group of

the hydroxy ethyl ester (Fig. 3). In the subsequent

polycondensation step, high molecular weight PET is

formed via the evolution of ethylene glycol. (Fig. 4)Weisskopf used different trifunctional agents to

synthesize high molecular weight branched PETs

[32]. Trimethylolpropane (TMP) was used as a

trifunctional branching agent and pentaerythritol

was a suitable tetrafunctional branching agent.

Trimethylolethane (TME) and trimesic acid were

also used as multifunctional comonomers (Fig. 5).

Hess et al. recently described the syntheses of both

linear and branched PETs [33]. Branched PETs were

obtained via the ester-interchange route starting from

DMT and a 2.5 M excess of EG. The reactions were

performed in a stainless-steel reactor with different

amounts (0.07 to 0.43 mol% with respect to DMT) of

trimethylolpropane (TMP) (branching agent, Fig. 5a)

present during the transesterification step. Transester-

ification was catalyzed with the addition of manga-

nese acetate at a maximum temperature of 230 8C.

Following transesterification, polycondensation was

catalyzed by antimony acetate at a maximum

temperature of 290 8C under vacuum.

Yoon et al. synthesized branched PETs in a similar

manner with TME as a branching agent at concen-

trations from 0.04 to 0.15 mol% [18]. Titanium

isopropoxide was used as the catalyst for the

polycondensation reaction. High molecular weight

PET copolymers were obtained with broad molecular

weight distributions. The thermal properties of the

copolymers were not significantly influenced by the

comonomers due to the low concentrations, however

the branched PET displayed enhanced zero shear rate

viscosity (h0) and shear thinning behavior. In a similar

fashion, branched PBI and PBT samples were prepared

O

O O

OHO

OH

OO

O

OO

O

(a) (b) (c)

Fig. 2. Bifunctional and trifunctional monomers used in the

synthesis of branched PET. (a) dimethyl terephthalate (DMT),

(b) ethylene glycol (EG), and (c) trimethyl trimesate (trimethyl

1,3,5-benzenetricarboxylate) (TMT).

COOCH2CH

2OH

COOCH2CH

2OH

COOCH2CH

2OHHOCH

2CH

2OOC

COOCH2CH

2OH

Fig. 3. Hydroxy ethyl esters formed after the ester-interchange step

during the polycondensation of PET.



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using A2, B2, and A3/B3 type monomers. Branched

PBIs were synthesized with the trifunctional branching

agent tris(hydroxyethyl) isocyanurate (THEIC) during

the polymerization reaction of dimethyl isophthalate

(DMI) with 1,4-butanediol (BD) in the presence of aTi(OBu)4 catalyst (Fig. 6) [25]. The branched PBIs

were prepared via a two step polycondensation

reaction. In the first step, the reaction temperature

was raised from 140 to 200 8C and held at 200 8C until

about 90% of the theoretical amount of methanol was

collected. In the second step, the pressure was reduced

and the temperature was maintained in the range of

200230 8C. The temperature was maintained lower

than normally employed for polyesters, such as PBT, to

prevent side reactions. Compositional and structural

characterization included elemental analysis, mass

spectroscopy, 1H NMR spectroscopy, HPLC, and end

group analysis. Linear and branched PBTs were also

recently synthesized using DMT and BD as bifunc-

tional monomers and trimethyl trimesate (TMT) as a

trifunctional comonomer [26]. Using titanium tetra-

butoxide at 250 8C in the second step yielded randomly

branched PBTs [28].

Han et al. synthesized high molecular weight

branched PBAs from aliphatic dicarboxylic acids and

glycols in the presence of glycerol or pentaerythritol

[11]. The influence of reaction parameters such as

catalyst concentration, reaction time, temperature,

and concentration of branching agent on molecular

weight was examined. These branched PBAs were

prepared via the synthesis of linear PBA from adipicacid and BD in the presence of a titanium(IV)

isopropoxide (TIP) catalyst and a triethylamine

(TEA) cocatalyst. The resulting linear polymer was

reacted with adipic acid in the presence of TIP to

obtain prepolymers with carboxylic acid end groups.

In a second step, the carboxylic acid terminated PBA

prepolymers were condensed with the branching

agent (glycerol or pentaerythritol) in the presence of

TIP to obtain branched PBS. Han et al. studied

molecular weight with respect to multifunctional

comonomer concentration and showed that both the

molecular weight and the molecular weight distri-

bution of branched PBAs increased with increasing

concentration of glycerol up to 0.6 wt% relative to the

PBA prepolymer. The gel content of the branched

PBAs also increased with increasing glycerol con-

centration up to 0.6 wt%. Surprisingly, 0.9 wt% or

more glycerol resulted in lower gel content and lower

molecular weights. The authors did not offer an

explanation for this dependence of gel content and

molecular weight on branching content.

C C

C

O O

OCH2CH2OOCH2CH2O CC

O O

CC

O O

O

x y

z

OCH2CH2O C

O

C

O

Fig. 4. Structure of randomly branched PET.

(c) (d)(b)(a)

OOH

O OH

OHO

HO OH

OH

OH

HO

HO

OH

OH

HO OH

Fig. 5. Trifunctional and tetrafunctional branching agents used in the synthesis of branched PET. (a) trimethylolpropane (TMP),

(b) pentaerythritol, (c) trimethylolethane (TME), and (d) trimesic acid (TMA).



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When branched PBAs were prepared with either

glycerol or pentaerythritol, it was found that the

molecular weight of branched PBAs with pentaery-

thritol was higher due to the higher degree of

functionality. The introduction of a branching agent,

TMP, to the polycondensation system of succinic acidand BD resulted in high molecular weight randomly

branched poly(butylene succinate) (PBS) [34]. The

esterification was conducted using a 1.0 to 1.1 ratio of

succinic acid to BD under nitrogen in the presence of

a titanium isopropoxide catalyst. The temperature was

raised from 140 to 200 8C as water was removed. The

ensuing polycondensation step was performed by

introducing 0.10.5 wt% of TMP to the reaction

mixture at 140 8C. The reaction temperature was

raised to 240 8C and the reaction was completed at a

pressure less than 1 Torr. Absolute molecular weightsand molecular weight distributions were determined

using SEC (size exclusion chromatography) with a

multi-angle laser light-scattering (MALLS) detector.

The molecular weight distribution and the weight

average molecular weight increased with increasing

amounts of TMP, while the number-average molecu-

lar weight decreased.

It is possible to synthesize numerous types of

branched polyesters by introducing A3/B3 or A4/B4monomers into a polymerization of A2 and B2

monomers that involve transesterification and poly-condensation. Long chain branched polymers gener-

ally have higher weight average molecular weights

and broader molecular weight distributions compared

with linear polymers synthesized at equivalent reac-

tion conditions. In fact, a high level of multifunctional

comonomer results in insoluble crosslinked systems

or high gel content if the conversion proceeds too far.

Long chain branching strongly influences thermal,

mechanical, and rheological behaviors of polymers as

discussed in subsequent sections.

2.3. Synthesis of branched polyesters via A2 and B2monomers in the presence of An or Bn (nO2)

monomers and a monofunctional endcapping reagent

The introduction of long chain branches in

polyesters is accomplished using low levels of a

multifunctional comonomer and low conversions

since gelation occurs at high levels of multifunctional

comonomer and at higher conversions. However, the

use of monofunctional comonomers in the presence of

bifunctional and multifunctional monomers prevents

or decreases gel content, and high molecular weight

polymers with long chain branches are attainable at

higher conversions. Neff et al. incorporated a mono-

functional reagent as a chain terminator to prevent or

decrease gel formation [21]. Branched PETs were

synthesized from DMT, EG, and diethylene glycol

(DEG) as bifunctional monomers, with trimellitic

anhydride as the branching agent and stearic acid as a

monofunctional reagent (Fig. 7). Manaresi et al.

synthesized highly branched PETs using a two step

polycondensation reaction in the presence of a

monofunctional comonomer, methyl 2-benzoylbenzo-

ate, with bifunctional monomers, DMT and EG, and

the trifunctional monomer, trimethyl trimesate

(Fig. 2) [22]. Munari et al. used a monofunctional

comonomer to shift the gel point to higher percentconversions, and no gelation occurred when the ratio

of monofunctional monomer to trifunctional mono-

mer was greater than 3. When the ratio was less than

3, the gel point was reached at lower conversions.

Methyl 2-benzoylbenzoate was used as the mono-

functional comonomer, and polycondensation tem-

peratures caused an approximately 30 wt% loss of

monofunctional comonomer.

Rosu et al. recently reported the synthesis and

characterization of high molecular weight branched

PETs that were prepared using a two step polycon-densation reaction in the presence of monofunctional

NC N

CNC

O

O

O

OH

OH

HOO

O

O

O

HOOH

(a) (b) (c)

Fig. 6. Bifunctional and trifunctional monomers used in the

synthesis of branched PBI. (a) dimethyl isophthalate (DMI),

(b) 1,4-butanediol (BD), and (c) tris(hydroxyethyl) isocyanurate

(THEIC).

O

O

OO

HOO

HO

(a) (b)

Fig. 7. Trifunctional and monofunctional comonomers used by Neff

et al.29 in the synthesis of branched PETs. (a) trimellitic anhydride,

and (b) stearic acid.



8/33

dodecanol or benzyl alcohol, DMT and EG, and

multifunctional monomers, glycerol or pentaerythritol

[23]. The polymers with glycerol and pentaerythritol

displayed different degrees of branching as pentaer-ythritol has four primary alcohol groups, while

glycerol has two primary and one secondary alcohol

group. Therefore, the degree of branching was

expected to be higher with pentaerythritol. In addition

to two-step polycondensation reactions, solid-state

polymerization was used to obtain high molecular

weights. Solid-state polymerization increases polye-

ster molecular weight, while avoiding thermal degra-

dation [35,36]. This method enables the preparation of

linear and branched ultra-high-molecular-weight

PETs with intrinsic viscosities of more than 2 dl/g

(which corresponds to number-average molecular

weights of 110,000 g/mole approximately) [37].

Solid-state polymerization of PET is typically con-

ducted 1535 8C below the melting point of the

polymer for various times [35]. It is also possible to

perform these reactions at various temperatures

(220, 230, 235 8C) under vacuum [36]. Rosu et al.

reported molecular weight control for branched PETs

when the reaction time in the solid-state polymeriz-

ation step was controlled and specific compositions of

reagents were used [23]. The branched PETs were

characterized by solution viscometry, thermal anal-ysis, and melt rheology.

Recently, Hudson et al. studied branched PETs

based on various branching agents and different

endcapping reagent compositions [17]. Branched

PETs were prepared using conventional polyconden-

sation reactions with a monofunctional monomer and

various multifunctional monomers with DMT and EG

or bis(2-hydroxyethyl) terephthalate. In addition to

branching agents such as glycerol, pentaerythritol,

and benzene-1,3,5-tricarboxylic acid (trimesic acid),

Hudson et al. used benzene-1,2,4,5-tetracarboxylicacid, dipentaerythritol, and tripentaerythritol as

branching agents with the endcapping reagent benzyl

alcohol (Fig. 8). A wide range of branched PETs (with

various branching agents) as well as their compo-

sitions with and without the presence of an end-capping reagent were subsequently reported. The

polymers were characterized using FTIR and 1H

NMR spectroscopy, light scattering, dilute solution

viscometry, and melt rheology to investigate the

influence of branching on solution and melt

properties.

Although end-group modification of linear PETs

for enhanced solubility and blend compatibility was

previously reported, Kim and Oh investigated the

effect of functional end groups on the physical

properties of PETs by synthesizing hydroxyl and

carboxylic acid end-capped linear and branched PETs

[38]. The end-capped polymers were characterized

using NMR spectroscopy, viscosity measurements,

SEC, and thermal analysis. The high molecular

weight branched PETs (MwO100,000) had broad

molecular weight distributions, and diethylene glycol

(DEG) units were present in the polymer backbone,

which was attributed to side reactions of ethylene

glycol during polycondensation.

2.4. Synthesis of branched polyesters via AB

monomers in the presence of A2B monomers

An alternate method for synthesizing branched

polyesters involves the copolymerization of A2/B2 or

AB monomers with AB2/A2B monomers Ramak-

rishnan et al. reported the synthesis and character-

ization of branched and kinked PETs through the

copolymerization of an A2 monomer with small

amounts of an AB2 monomer [24]. The term

kinked describes linear disruption in the PET

backbone due to meta substitution of the aromatic

group. Therefore, in order to understand theinfluence of kinks, linear and branched polymers

O

O

OH

OH

O

O

HO

HO

OH

OH

OHO OH

OH

OH

OH

OH

OH

OH

OH

OHO O

OH

OH

(a) (b) (c)

Fig. 8. Branching agents used by Hudson et al. (a) benzene-1,2,4,5-tetracarboxylic acid, (b) dipentaerythritol, and (c) tripentaerythritol.



9/33

were also prepared. Branched and kinked PETs were

synthesized using melt polymerization of bis-(2-

hydroxyethyl) terephthalate (BHET) as A2 monomer

and ethyl-3,5-(2-hydroxyethoxy)benzoate (EBHEB)as the AB2 monomer (Fig. 9). Linear and kinked

PETs were synthesized via the polycondensation of a

BHET monomer with a 3-(2-hydroxyethoxy) benzo-

ate (E3HEB) monomer that has a 1,3 connectivity

rather than a 1,4 connectivity, and the reaction was

terminated early to prevent gel formation. Early gel

formation was attributed to the fact that the EBHEB

monomer behaved similarly to an A3 type instead of

AB2, primarily due to the polycondensation reaction.

Therefore, BHET was able to react with all three

sites of EBHEB during polycondensation, whichresulted in gel formation during the early stages

of the polymerization. Unfortunately, stopping

the reaction early to avoid gelation yielded low

molecular weight polymers.

In addition to PETs, poly(4-ethyleneoxy benzoate)

was synthesized using ethyl 4-(2-hyroxyethoxy)benzoate (E4HEB) as AB monomer and EBHEB as

AB2 monomer [31]. Crosslinked polymers were

formed at branching agent levels higher than

50 mol%. When compared to branched PETs, the

branching content in these materials was higher and

therefore, a wider range of branched polymers were

prepared to study the effect of branching on the

thermal properties. Kricheldorf et al. prepared linear,

long chain branched, and hyperbranched poly

(3-hydroxy-benzoates) via condensation of acid

chlorides, 3-(trimethylsiloxyl) benzoyl chloride asan AB type monomer, and 3,5-(bistrimethylsiloxyl)

benzoyl chloride as AB2 type monomer [30].

Fig. 9. Reaction schemes for the synthesis of branched and kinked PETs.



10/33

3. Characterization of branched polymers

3.1. Introduction

Since branching has such a dramatic influence on

polymer properties, it is important to characterize

polymer architecture on a molecular level. Short chain

branches are recognized with spectroscopic methods,

while sparsely long chain branched polymers are

much more difficult to characterize. In practice, most

branched polyesters are random in nature, with

heterogeneous distributions of molecular weight,

number of branch points, and length of the branches.

Since random branching influences polymer molecu-

lar weight and molecular weight distribution, it is

important to deconvolute the effects of chain archi-tecture and molecular weight. The determination of

molecular weight of a branched polymer using size

exclusion chromatography (SEC) and a calibration

curve based on linear polystyrene results in large

errors since separation is based on hydrodynamic

volume and linear and branched chains can possess

the same hydrodynamic size, but different molecular

weights [39]. Consequently, light scattering, a method

that does not depend on any standards or shapes, is

critical for measuring the absolute Mw of branched

polymer chains [40].

3.2. Contraction factors

When compared in the same environment (tempe-

rature and solvent), a branched polymer has a higher

segment density and a lower hydrodynamic volume

than that of a linear polymer of equal molecular

weight. Solution or melt viscosity measurements,

coupled with SEC and light scattering experiments

yield information regarding polymer size [41]. The

mean square radius of gyration, hR2gi, is a measure of a

polymers hydrodynamic volume as measured using

static light scattering. Consequently, the ratio of the

hR2gi of a branched polymer to that of a linear polymer

of the same molecular weight in the environment

expresses the degree of branching, a quantity, g,

referred to as the index of branching or contraction

factor, shown in Eq. (3).

gZhR2gibranched

hR2gilinear(3)

Similarly, the ratio of the intrinsic viscosity ([h]) of

a branched chain to a linear chain, conventionally

denoted as g 0, is employed as shown in Eq. (4).

g0Z

hbranchedhlinear

(4)

The value of g 0 is easily determined using the

procedure of Hudson et al., where a multi-angle laser

light scattering (MALLS) detector and a viscosity

detector are coupled with SEC [17]. The value of

[h]branched is measured directly using the viscosity

detector and [h]linear is calculated using the Mark

Houwink relationship shown in Eq. (5).

hlinearZKMaw (5)

The parameters, K and a, are the MarkHouwink

constants for a linear polymer. For a linear chain, g

and g 0 are equal to 1.0 and decrease as the level of

branching increases. Fig. 10 shows the decrease ofg,

denoted gM in the figure, for branched poly(vinyl

acetate) as a function of molecular weight [42]. The

contraction factor decreases from about 0.95 at low

molecular weight to 0.45 at higher molecular weights,

indicating the high molecular chains have a larger

degree of branching.

Since the value of [h] of a branched polymer is

lower than that of its linear analog, the MarkHouwink exponent, a, for a branched polymer is

generally smaller than that of a linear chain.

Comparison of the intrinsic viscosity dependence on

Mw for a series of linear and branched polystyrenes

showed a systematic decrease in the MarkHouwink

Fig. 10. Contraction factor vs. molecular weight for randomly

branched poly(vinyl acetate). The contraction factor decreases from

about 0.95 for low molecular weight species to 0.45 for the higher

molecular weight chains, indicating the high molecular chains have

a larger degree of branching.



11/33

exponent from 0.73 to 0.68 to 0.39 for linear, star-

branched, and hyperbranched topologies, respectively

[43,44]. It should be noted that other researchers have

showed that, in the limit of high molecular weights,linear polymer and star polymers that possessed

a large range of arm numbers exhibited equal

MarkHouwink exponents for polybutadienes and

polyisoprenes [45,46]. This discrepancy between the

dependence of [h] on molecular weight for star-

shaped polymers may possibly be attributed to the

lower polystyrene molecular weights that were

investigated in Ref. [43]. Lusignan, Mourey, Wilson,

and Colby utilized the disparity in the MarkHouwink

exponent for linear and branched chains to estimate

the average distance between branch points for a

randomly branched polyester [47]. Fig. 11 shows the

intrinsic viscosity as a function of Mw for SEC

fractions of the branched polyester. The two slopes

correspond to a values of 0.80 and 0.43, typical for

linear and branched chains, respectively, and the two

lines intersect at 66,000 g/mol. The authors concluded

that this crossover from linear behavior to branched

behavior marks the average linear chain length in the

polymer system and the weight average molecular

weight between branch points.

The contraction factor has been theoretically

correlated to the branching parameters of a polymer

chain. Zimm and Stockmayer related g values to the

average functionality and the number of branchingunits for randomly branched chains [48]. For star

polymers with monodisperse arms under theta con-

ditions, g can be calculated using Eq. (6),

gZ3fK2

f2(6)

where fis the number of arms. Unfortunately, it is not

possible to measure the mean square radius of

gyration for low molecular weight chains due to the

limitation of MALLS. In fact, hR2gi1=2 measurements

are unreliable for values less than 10 nm, which isroughly a value ofMw on the order of 104 g/mol [49].

Intrinsic viscosity and g 0 are more reliable measure-

ments, however a theoretical basis is not developed

that relates g 0 to molecular parameters since the

dependence ofg 0 and g is not understood. Much work

has focused on understanding this relationship, and

empirical correlations suggest the form

g0Zg

3 (7)

where 3 is between 0.5 and 1.5, and is dependent on

the type of branching [50]. Generally, 3 is equal to 0.5

for low levels of branching or for star polymers, while

3 is closer to 1.5 for comb-shaped polymers [51].

Jackson, Chen and Mays determined values of 3

between 0.8 and 1.0 for randomly branched poly

(methyl methacrylate), and concluded that the visco-

metric radius (Rv) is more sensitive to the radius of

gyration due to the higher segment density of the

branched chains [52]. Instead of trying to convert

intrinsic viscosity contraction factors to radius of

gyration contraction factors, Balke et al. developed an

empirical relationship between g 0 and number of

arms, ranging for star-branched poly(methyl metha-crylate) with 3270 arms [53]. The authors showed

the number of arms, f, was more accurately predicted

through the empirical fits than by estimating values of

3 and using Eqs. (6) and (7).

3.3. Endgroup analysis

The average number of branches per chain for a

step-growth polymer is determined from the basic

Fig. 11. Intrinsic viscosity as a function of Mw for a randomly

branched polyester. The intersection of the two slopes correspond-

ing to respective a values of 0.80 and 0.43 mark the average

molecular weight between branch points.



12/33

theoretical concepts of Flory and Stockmayer. The

models are dependent upon the number of polymer

chain ends, molecular weights, and initial concen-

tration of the mono-, bi-, and tri-functional repeatunits. End-group analysis on the branched polymer

reveals the number of total end-groups. Researchers

calculated the number of end groups for PET

branched with a trifunctional compound from the

concentration of hydroxyl and carboxylic acid end-

groups [54]. Utilizing the number of end-groups,

Manaresi et al. and others employed the number

average branching density or the average number of

branches per chain, Bn,

BnZ

2r

3KrK3p(8)

where r is a parameter that represents the initial

polymer composition,

rZ3ntrif

3ntrifC2nbif(9)

and ntrifis the number of initial trifunctional molecules,

nbif is the initial number of bifunctional molecules,

and p is the extent of reaction given by Eq. (10),

pZ

1K

E

Mb

2K

r

Mb

2K

Mt

3

(10)

where Eis the sum of all end-groups (equiv/g) and Mband Mt are the molecular weights of the bi- and tri-

substituted repeat units, respectively.

A mono-functional agent is often added to a step-

growth reaction mixture in tandem with the multi-

functional branching agent for facile control of

molecular weight. Theory developed by Flory and

Stockmayer predict that addition of a mono-functional

agent shifts the conversion at which gelation occurs to

higher values. Moreover, when the molar ratio of

mono- to tri- substituted agents is greater than or equal

to three, the gel point cannot be reached [22]. The

addition of a mono-functional compound is easily

accounted for in the above analysis by introducing the

parameters,

r0Z

nmono

nmonoC2nbifC3ntrif(11)

where nmono is the number of moles of mono-

functional agent. The extent of reaction, p, is

redefined as,

pZ1KEMb

2C

Mt

3K

Mb

2

rC MmK

Mb

2

r

0

(12)

where Mm is the molecular weight of the mono-

functional unit. Finally, the average number of

branches, Bn, is given by Eq. (13).

BnZ2r

3KrC3r0K3p(13)

It should be noted that long chain branches are often

below the detection limit of end-group analysis and

dilute solution measurements for mixtures of linear

and branched chains. Consequently, the aforemen-

tioned methods are often insensitive to sparsely

branched chains [55,56]. Typically spectroscopic

techniques and SEC methods are limited to detection

of branching levels of 1 branch point per 10,000

carbons [57]. Moreover, in polymer systems that

contain both short chain and long chain branches,

like polyolefins, the above methods cannot discrimi-

nate between the two thereby making LCB detection

difficult. More recently 13C NMR measurements

detected branching levels of 0.35 branches per

10,000 carbons in polyethylenes [58]. Since the flow

behavior of polymers is sensitive to long chainbranches at concentrations far below the detection

limit of the above methods, rheology becomes the only

feasible way to identify low levels of this type of

branching.

4. Influence of branching on melt rheological

properties: model systems and long-chain

branched polyesters

4.1. Introduction

The dependence of viscosity on shear rate for

branched chains is very different from that of linear

chains, aand varies with the chain architecture

(random, star-branched, comb-branched, H-shaped,

etc). Typically, long-chain branched polymers exhibit

shear and extensional viscosities that are unobtainable

with linear chains. For example at low shear rates,

branched chains can exhibit a viscosity greater than

100 times that of linear polymer of equal molecular



13/33

weight, while at high shear rates, the branched

polymer may exhibit a lower viscosity than the linear

polymer due to enhanced shear thinning [59].

The presence of less than one long-chain branchalong a polymer backbone on average is known to

significantly alter the flow properties [60]. Only long-

chain branches, branches with MwOMc, can greatly

alter rheological properties, while short-chain

branches (SCB) only do not affect the rheological

behavior [61]. Several branching parameters influence

rheological properties including branch length, degree

of branching, and chain architecture (random, star-

branched, comb, H-branched, etc.). Typically,

branches are introduced in a random fashion during

polymerization, thereby leading to a broad distri-

bution of branch lengths and branch density. Conse-

quently it becomes difficult to separate the effects of

branching distribution, molecular weight distribution,

and chain architecture.

As stated earlier, PET and other linear polyesters of

relatively low molecular weight and narrow molecular

weight distribution display poor melt strength and

shear sensitivity at typical processing conditions

[62,63]. Additives, molecular weight and molecular

weight distribution changes by chain extension during

reaction or post reactor processing, branching, chain

end functionalization, and controlled cross-linking areoften used to modify the melt rheology of polyesters

[64,65]. In addition, long chain branched polymers

display superior melt strength and extensional

viscosity compared to their linear analogs, which

aids in blow molding and other processing appli-

cations [62]. This section describes the influence of

branching on the melt and concentrated solution

rheological properties of polyesters, with particular

focus on the influence of the branching parameters

including number of branches, branch length, and

branch type on melt viscoelasticity.

4.2. Number of branches per chain and branch length

4.2.1. Randomly branched polyesters

For a randomly branched polymer chain, the

average number of branches per chain (degree of

branching) and the branch length are coupled for a

given molecular weigh t. For example, a

100,000 g/mol polymer with an average of one branch

per chain has an a ver age bra nc h l ength of

33,300 g/mol from the relationship,

MbZMw

2BnC1

(14)

where Mb is the molecular weight between branch

points, Mw is the total polymer molecular weight, and

Bn is the average number of branches per chain. Thus,

if a higher concentration of multi-functional agent

was added to a step-growth polymerization to yield a

polymer chain with the same overall molecular

weight, but with three branches per chain, the average

branch length becomes 14,300 g/mol. Since effects of

branch number and branch length cannot be separated

for equivalent molecular weights, this section

describes the influences of both parameters on

rheological properties.

The dependence ofh0 on Mw is well established for

linear, flexible chains. Two regimes are separated by a

critical molecular weight (Mc), below which h0 scales

directly with Mw and above which h0 generally scales

with M3:4w . Chains with molecular weights below Mcare too small to entangle, while the high molecular

weight chains are topologically constrained due to

entanglement couplings. Researchers have shown a

significant departure from the h0KMw relationship

exists for branched chains due to the reducedhydrodynamic volume of the branched chains at low

molecular weights, and increased entanglement coup-

lings at higher molecular weights [66].

Hess, Hirt, and Opperman varied the level of

random branching in PET by adding different levels of

trimethylolpropane (TMP) to the melt polymerization,

and the branched PET possessed a lower h0 compared

to linear chains of equal Mw (approximately

50,000 g/mol) [33]. Fig. 12 shows the systematic

decrease in the zero shear rate viscosity as the average

number of branches per chain was increased from 0.1to 0.5. The parameter g*, which is the ratio of the zero

shear rate viscosity of a branched and linear chain at

equal molecular weight, also decreased with the

average number of branches per chain. For a series

of linear and randomly branched poly(butylene

isophthalate) polymers, Munari et al. also showed a

decrease in h0 with w0.5 branches per chain

compared to a linear chain of equivalent Mw(55,000 g/mol) [67]. Moreover, when these same

authors employed the correlation that relates the ratio



14/33

ofh0 of a branched and linear chain of equal Mw as

developed by Ajroldi et al., the branching index

increased from 0 to 1.0 and the zero shear rate

viscosity systematically decreased by four orders of

magnitude. Similar behavior was exhibited for

branched PET and branched poly(butylene tereph-

thalate) [54,68].

The influence of the level of random branching on

the rheological properties of aliphatic polyesters hasalso been investigated. Kim et al. observed a

systematic decrease in shear thinning onset for

branched poly(butylene succinate) (PBS) as the level

of trifunctional branching agent was increased from 0

to 0.5 wt% [34]. The onset of shear thinning behavior

was attributed to a higher entanglement density of the

branched chains [69]. Moreover, the authors observed

an increase in h0 for branched PBS over linear PBS.

However the authors of this review believe the

enhancement in both shear thinning and h0 was more

likely due to the significant increase in Mw and

polydispersity (Mw/Mn) for the branched chains

relative to the linear chains. Short-chain, ethyl and

n-octyl branches were also introduced into poly

(ethylene adipate) (PEA) and PBS. In contrast to

long-chain branched systems, a decrease in melt

viscosity and increase in shear thinning onset were

observed when compared to linear PEA and PBS of

approximately equal weight average molecular weight

[70]. The ethyl and n-octyl branches were not long

enough to form entanglements, and consequently shear

thinning and h0 enhancement were not as pronounced.

The melt viscosity of the branched polyester was lower

than that of the linear polyester due to the reduced

hydrodynamic volume of the branched chains. Leher-meier and Dorgan studied the influence of blending

linear polylactide and polylactides that were randomly

branched through a peroxide cross-linking reaction on

the melt rheological properties [71]. The authors

ensured that the polylactides did not undergo degra-

dation at the rheological conditions by adding the

stabilizer, tris(nonylphenyl) phosphite. They observed

excellent control over the rheological performance

with the blend composition. In particular, the authors

reported an increase in h0 and decrease in the

frequency at which shear thinning occurred with

increasing blend compositions of the branched chain.

Unfortunately, molecular weight information was not

reported, and the branching structures of the polylac-

tides were not characterized. Thus, it was difficult to

assess the relationships between branch structure and

rheological behavior.

Lusignan, Mourey, Wilson, and Colby studied the

linear viscoelastic properties of randomly branched

polyesters with varying branch lengths [47]. The

authors showed for low branch length of NZ2

monomeric units, the chains were unentangled and

accurately described by the Rouse model withouthydrodynamic or topological interactions [72]. More-

over, further studies showed that entanglements

between the randomly branched chains did not form

for N!20, since the Rouse model was adequate for

branched polyesters with up to 20 repeat units

between branch points [73]. Branched polyesters

with NZ900 were synthesized to demonstrate that

topological constraints dominate the viscoelastic

response of chains with branch lengths long enough

to entangle [47]. The average molecular weight

between branch points, Mb, was determined byanalyzing the intrinsic viscosity dependence of Mwas shown in Fig. 11. The Mb (66,000 g/mol) was

defined as the crossover from linear to branched

behavior, and was measured by the reduction of the

[h] vs. Mw slope. Below Mb, h0 scaled with M3:6w

which was consistent with experimental results for

entangled linear chains, and above Mb, h0wM6:0w due

to the increased entanglement constraints imposed by

the branched chains. Fig. 13 shows that the Rouse

model breaks down for N/NeO2, where N/Ne is

Fig. 12. Systematic decrease in (h0,b/h0,l) as a function of average

number of branches per chain for randomly branched PET withMwZ50,000 g/mol.



15/33

the number of entanglements per branch, due to

entangled dynamics as the viscosity exponent, s,

varies significantly from the Rouse prediction of 1.33.

Consequently, the authors concluded that Mbw2Mefor entanglements to dominate the flow behavior.

Earlier experiments by Long, Berry, and Hobbs

observed that the rheological behavior of randomly

branched polymers is dependent on the branch length

[74]. They observed a larger h0 for branched

poly(vinyl acetate) compared to a linear chain of

equal molecular weight when the average molecular

weight between branches (Mb) was greater than

28,000 g/mol. Using MeZ9,100 g/mol, which was

reported by Fetters et al. for poly(vinyl acetate) [75],

Mbw3Me for entanglements between branches to

control the melt rheological performance. Several

other researchers have also investigated the rheologi-

cal response of randomly branched chains. Valles and

Macosko showed that Mc is higher for randomly

branched poly(dimethylsiloxane) (PDMS) chains

compared to linear chains as measured by the Mwdependence of h0 [76]. Moreover, the number of

branches per chain also influenced Mc, as Mc

increased from 33,000 for the linear chain to 98,000

and 110,000 g/mol for the trifunctional and tetrafunc-

tional polymers, respectively. Unlike the randomly

branched polyesters, the researchers observed aweaker h0KMw relationship for branched PDMS

above Mc. However, when h0 was plotted against the

product gMw (where g is the contraction factor) in Fig.

14, a viscosity enhancement was observed for the

randomly branched PDMS as seen previously with

star-branched polyisoprene. Finally, Masuda et al.

reported a dependence of viscoelastic properties on

Mb for randomly branched polystyrene in 50 wt%

solutions [77]. A clear plateau region was not

Fig. 13. For N/NeO2 deviation from the Rouse models is evident

due to entangled dynamics as the viscosity exponent, s, significantly

varies from the Rouse prediction of 1.33. The solid line is the Rouse

prediction for N/Ne!2, and a phenomenological equation that

describes entanglements for N/NeO2.

Fig. 14. Dependence of h0 on the product gMw for randomly

branched PDMS. The triangles and squares correspond to tri and

tetra functionally branched PDMS, respectively.



16/33

observed for Mb/Me!2, due to relaxation of the short

backbone segments via Rouse-like motions, while

branched chains with Mb/MeZ6 showed h0

enhancement.

4.2.2. Star-branched polyesters

This review has focused on randomly branched

polyesters that contain a distribution of branch

lengths. Unlike randomly branched polymers, the

synthesis of star polymers allows for a high degree of

control over the molecular structure. Due to the well-

defined chain architectures that result from more

controlled synthetic strategies, star polymers have

received much attention in the area of structure/

property relationships. Fundamental investigations of

the dynamics of star polymers will provide useful

information for understanding the behavior of com-

mercially produced, randomly branched materials

[78]. At relatively low molecular weight, the viscosity

of a star polymer is lower than its linear analog,

however, the viscosity of the a star polymer increases

faster with molecular weight and exceeds that of the

linear analog at some specific molecular weight [79].

This molecular weight dependence occurs because the

star polymer exhibits a reduced hydrodynamic

volume compared to a linear polymer due to the

higher segment density, however, a competing effectarises since the star polymer possesses restricted chain

motion due to the constraint that one end of the arm is

anchored to the star core. Consequently, the branch

point hinders reptation, and relaxation only occurs

when the arm retracts back along the confining tube

and seeks a new direction [80]. McLeish and Milner

suggested two modes of relaxation of a star polymer.

Short relaxations occur at the chain end, where the

branch point does not restrict the arm, and long-scale

relaxations occur near the star core [80]. Experimental

results by Ye and Sridhar corroborated this theory andrelaxation times for a concentrated solution of

polystyrene stars were 20 to 150 times greater than

the relaxation times predicted for linear chains by

reptation theory [81]. In addition, star polymer

polymer blend miscibility was highly influenced due

to the impenetrable core of the star from which the

arms diffuse outward [82].

As mentioned previously, the zero shear rate

viscosity for linear polymers follows a power law

dependence above the critical molecular weight for

entanglements, Mc. However, for star-shaped poly-

mers with Mw greater than Mc, the zero shear rate

viscosity increases exponentially with the weight

average arm molecular weight [83]. Fetters et al.observed that the value h0 of a star-branched chain

does not depend on the total Mw, but only on the arm

molecular weight, Ma. Thus, h0 is independent of the

number of arms. Later, Fetters et al. showed that the

h0 of a 3-arm polyisoprene star was approximately

20% lower than that of a 4-arm star of equivalent Ma,

while for fO4, the degree of functionality is saturated

and the viscosity is only dependent on Ma [84]. These

experimental results were consistent with previously

developed theories that suggested 3-arm stars have an

additional mechanism of stress relaxation that stars of

higher functionality do not exhibit [85]. They

proposed for 3-arm stars, an arm could relax if the

branch point diffuses down one of the tubes. The

rheology of stars with higher degrees of functionality

was also studied. Pakula et al. performed linear

viscoelastic studies on polybutadiene stars with a

significantly larger number of arms than previously

studied [86]. The authors observed a high frequency

and low frequency relaxation corresponding to chain

segmental motion and terminal response, respecti-

vely. Fig. 15 shows stars with fZ64 and fZ128 arms

display an additional transition in the terminal flowrange that is not present for stars with fZ4 arms. This

additional transition for stars with high degrees of

functionality is attributed to cooperative rearrange-

ment of the colloidal or liquid like structures in the

melt [87]. It should be noted this additional relaxation

would not be applicable for randomly branched

polymer chains.

Since arm length controls the viscoelastic response

for stars with a relatively few number of arms, it is

important to understand the role of branch length in

order to provide viscosity enhancement. Kraus andGruver observed for equal overall molecular weight, a

3 arm star polymer with MaZ10Me showed viscosity

enhancement over the linear analog [83]. However,

rheological studies performed on a series of asym-

metric poly(ethylene-alt-propylene) stars showed that

the critical Ma for viscosity enhancement was less

than 10Me. Gell et al. studied a series of 3-arm

asymmetric stars where two branch lengths were kept

constant and one was varied, thereby providing a

constant molecular weight backbone [88]. The branch



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length ranged from Mb/MeZ0 to Mb/MeZ18, and was

shorter than the backbone length (Mbb/MeZ38).

Deviation from linear chain behavior and h0 enhance-

ment were observed for Mb/Mew23, with consider-

ably fewer entanglements per branch needed than for

symmetric stars due to the nature of the very long

backbone compared to the branch length. Dorgan et

al. showed that viscosity enhancement for 4 and 6-arm

star poly(lactic acid) occurred at approximately Mb/

MeZ4 [89]. The authors observed that the viscosity

enhancement factor, G,

GZh0;bM

h0:lM(15)

increased more rapidly for the 6-arm versus the 4-arm

star as shown in Fig. 16. In Eq. (15) h0,b and h0,l are

the respective zero shear viscosities of branched

and linear chains of equal molecular weight. This

result is in disagreement with theoretical treatments

and experimental results, which show viscosity to be

only dependent on arm length, but independent of the

number of arms [90]. The discrepancy was attributed

to a combination of polydispersity, hydrogen bonding

effects between ester groups, and the relatively short

arm lengths of the star polymers.

Claesson et al. prepared star-shaped polyesters

composed of poly(3-caprolactone) (PCL) initiated

from hydroxy-functional hyperbranched cores end-

capped with methacrylate units [91]. The end groups

served as a cross-linking agent for utilization in

powder coating applications. Due to the narrow range

of molecular weights studied, it was difficult to

determine if the star polymer exhibited exponential

or power law behavior, however, the h0 was an order

of magnitude lower compared to a linear polyester of

equal Mw. Since the Mw of the hyperbranched cores

cannot be neglected in the total Mw, there was a

dependence of arm number on the zero shear rate

melt viscosity for the PCL stars. The PCL star

polymers with methacrylate end groups were cured

with ultraviolet (UV) light [92]. Gelation occurred

within seconds of UV exposure based on the

crossover point of the storage modulus (G 0) and the

loss modulus (G 0). The time to reach gelation

increased linearly with the molecular weight of the

star polymer since the concentration of methacrylate

end groups decreased.

Fig. 15. Frequency dependence of polybutadiene stars with (a) fZ4,

(b) fZ64 and (c) fZ128 arms. The vertical dashed lines correspond

the frequencies associated with relaxation of the chain segment (us)

and arm (uR), respectively.

Fig. 16. Viscosity enhancement vs. branching length for 4 and 6 arm

star polylactide.



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4.2.3. H-shaped and comb-branched polymers

H-shaped architectures are considered the simplest

form of a comb polymer, where branching occurs only

at the two ends of the backbone. Although, little workhas focused on the synthesis and rheological analysis

of H-shaped polyesters, many structure/property

studies have been performed on model H-shaped

polymers. This section of the present review serves to

summarize work performed on model polymer

systems, as the results are applicable to polyester

architectures. Roovers studied the melt rheology of

H-shaped polystyrene and observed a decrease in h0for the branched polymers compared to linear analogs

at low molecular weight, and an increase in h0 at

high molecular weights similar to star polymers [93].

Fig. 17 shows that the viscosity enhancement factor,

G, increased faster for the H-shaped polymer than that

of either 3 or 4 arm stars as a function of chain

entanglement per branch (Mb/Me). This was attributed

to an additional mode of relaxation for the H cross-bar

which is not present for star polymers. Archer and

Varshney corroborated this extra relaxation mode for

H-shaped or multi-arm polybutadienes with three

branches per chain end [94]. The authors observed a

broader and lower frequency transition to the terminal

region for the multi-arm polybutadiene compared to

its linear counterpart, which was attributed to anincreased relaxation time of the cross-bar. Moreover,

they showed the terminal relaxation time and h0enhancement were primarily controlled by the branch

length when MbOMe and were relatively independent

of the cross-bar molecular weight. Houli et al. also

studied the rheological behavior of pom-pom type

polymers with a much greater number of arms (fZ

32)[95]. They also observed the dominant mechanism of

terminal relaxation was arm relaxation. However,

multi-arm polymers with Mb!Mc did not form

entanglements, which was marked by power law

behavior from the glass to the terminal region, typical

of Rouse-like motions. This is similar to the

unentangled behavior of high molecular weight

hyperbranched polymers that relax via segments that

are smaller than Me [96].

Although model star and pom-pom polymers were

extensively studied to determine the influence of

branching on rheological properties, most commer-

cially produced polymers are randomly branched.

Interest in the rheological characterization of comb-

branched chains may bridge the gap between the

behavior of model star polymers and randomly

branched commercial polymer. Noda et al. performed

viscoelastic measurements with polystyrene combs

and showed a lower h0 compared to linear polystyrene

of equal Mw, however when compared at equivalent

Rg, the combs displayed viscosity enhancement [97].

Roovers and Graessley also performed rheological

analyses on comb polystyrenes with backbonemolecular weights of 275,000 and 860,000 g/mol

with approximately 30 branches per chain varying in

Mw from 6,500 to 98,000 g/mol [98]. The comb

polystyrenes showed a reduction in h0 when com-

pared to linear chains of the same Mw and showed h0enhancement when compared at equivalent intrinsic

viscosity. Surprisingly, this enhancement was not

restricted to branch lengths above Me, and the h0enhancement was different for the combs with

different molecular weight backbones. However, the

authors found good agreement with the log GK

Mb/Merelationship for stars when the comb molecular weight

was normalized by the average end-to-end comb

molecular weight (MEE/Me). Daniels et al. studied the

linear rheological response of comb-branched poly-

butadiene and varied the molecular weight of the

polymer backbone, the molecular weight of the arms,

and the number of arms [99]. The researchers reported

the viscoelastic response was dependent on the

number of arms for low frequencies. At short time

scales, the comb polymers displayed Rouse-like

Fig. 17. Viscosity enhancement factor, G, as a function of the

number of entanglements per branch. Triangles and diamonds

denote H-polymers, the solid line denotes a 4-arm star, and the

dashed line denotes a 3-arm star.



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behavior similar to star polymers due to relaxation of

the dangling chain ends. For a relatively small number

of arms, the comb polymers behaved similar to H-

shaped polymers, marked by relaxation of the arms atintermediate frequencies and reptative motion of the

backbone at low frequencies [100]. For a larger

number of arms, the terminal region showed a

distinctly different response for the comb compared

to the H-shaped polymer, as a larger number of

relaxation modes were available to the comb-

branched polybutadiene. Roovers and Toporowski

attributed the broader low frequency relaxation to

additional couplings between a branch and a back-

bone that are unavailable to star polymers [101].

Namba et al. showed that branch spacing in comb

polymers is important in their viscoelastic response

[102]. They observed that highly branched comb

poly(methyl methacrylate), with approximately one

polystyrene branch (MbZ3450) per repeat unit did not

entangle, as a plateau region was not observed for the

storage modulus. Although Mb!Mc for the poly-

styrene branches, the backbone molecular weight was

well above Mc, so the lack of entanglements was

attributed to the high branch density of the comb

polymer. When the polystyrene macromonomer was

copolymerized with methyl methacrylate to yield a

branch structure of approximately 3 branches per 100repeat units, a clear plateau region was observed in the

dynamic shear modulus. However, the authors did not

address the incompatibility issues between poly-

styrene and poly(methyl methacrylate) chains.

Tsukarhara et al. also observed fewer entanglement

couplings for highly branched combs with a backbone

molecular weight greater than Mc. The researchers

calculated Me of a highly branched poly(methyl

methacrylate) comb from the plateau region, where

Mb!Mc, and discovered Me was approximately 3

orders of magnitude larger for the highly branchedPMMA compared to linear PMMA [103]. The authors

attributed this to the increased cross-sectional area of

the highly branched PMMA comb, which excluded

other chains from a unit volume and thereby hindered

entanglement couplings.

4.3. Flow activation energy

The activation energy explains the temperature

dependence of viscosity for as shown in Eq (16),

h0TZA0expEa

RT

(16)

where h0 is the zero shear rate viscosity, A0 is a pre-exponential factor, Ea is the activation energy, R is the

gas constant, and Tis the temperature in K. Generally,

Eq. (14) is only valid for temperatures ca. 80 8C above

the polymer glass transition (Tg) due to the exponential

rise in viscosity at temperatures near the Tg. The value

of Ea is independent of molecular weight and is only

dependent on the local segmental nature of the chain

[104]. Typical values for the Ea are in the range of 5 to

30 kcal/mol. In general, Ea increases with either chain

stiffness or bumpiness [105]. Consequently, the

temperature dependence of viscosity for branched

polymers differs significantly from the corresponding

linear analogs. In particular, the rheological behavior

of the former shows a greater temperature dependence

and thus Ea is enhanced. One of the most outstanding

examples is that Ea depends on the degree of

branching and branch length in polyethylene, as

several researchers reported a larger Ea for low-

density polyethylene compared to high-density poly-

ethylene. However, limited work has focused on the

influence of branching on Ea in polyesters.

Munari et al. investigated the influence of long-

chain branching on the flow activation energy for aseries of partially aromatic polyesters, and found

inconsistent results for the different polyesters. They

reported a 35 to 100% increase in Ea for a series of

branched poly(butylene terephthalate)s (PBT) com-

pared to their linear analogs, however, only a slight

increase in the Ea for branched PET compared to

linear PET was observed [54,68]. Moreover, no

enhancement in Ea was observed for branched

poly(butylene isophthalate) (PBI) compared to linear

PBI [106]. The authors attributed these discrepancies

to differences in Mb between the branched polyestersand different temperature coefficients of the repeat

units. Graessley related this inconsistent behavior to

differences in the temperature coefficients of linear

and branched polymer melts [107]. This discrepancy

arises when considering the mode by which entangled

chains relax. In particular, linear chains undergo

reptation, while long chain branches relax by retrac-

tion or short time-scale fluctuations along the tube

contour length of an arm. As an arm relaxes, it must

pass through a higher energy barrier due to the more



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compact conformational states that are dependent on

the temperature coefficient of the chain. In the cases

where differences in activation energy for linear and

branched polymers are observed, the quantity, DEZ

(Ea)BK(Ea)L, is often used to quantify the degree of

Ea enhancement. The quantity DE was shown to

exponentially increase with the number of entangle-

ments per branch (Mb/Me), and decrease to zero with

decreasing branch length [108].

5. The influence of branching on solution rheology

properties in the semidilute regime

5.1. Introduction

The dilute solution properties of branched chains

are consistent with their reduced hydrodynamic

dimensions compared to linear polymers of equivalent

molecular weight. The properties of branched poly-

mers in dilute solution were discussed in some detail

in Section 3.2. In dilute solution, the polymer chains

are widely separated from each other, and only the

interactions between two chains need to be con-

sidered. At a critical concentration, C*, the polymer

chains begin to crowd each other and overlap in

solution, and COC* is termed the semidilute regime.

As the polymer chains overlap, intrachain interactionsare screened at length scales longer than the

correlation length, where the correlation length is

defined as the average distance between neighboring

contacts points [109]. Polymer concentrations above

C* do not indicate that entanglement couplings

between chains have formed [110]. Consequently,

in the semidilute unentangled regime, C*!C!Ce(where Ce is the entanglement concentration), chain

overlap is not sufficient to topologically constrain the

polymer chain motion. Above Ce, the semidilute

entangled regime, chain crowding and interpenetra-tion is sufficient to constrain the chain motion, and

topological interactions dominate at distances longer

than the tube diameter [111]. Limited rheological

studies have shown that typically Ce/C* is in the range

of 510 for neutral, linear polymers [111]. Finally, as

polymer concentration is increased further into the

concentrated regime, which is defined as the point

where chain dimensions become independent of

concentration, the polymer coils are highly entangled

and behave similar to a melt [112].

5.2. Effect of branching on the entanglement

concentration

The entanglement concentration is experimentallymeasured by analyzing the concentration dependence

of specific viscosity (hsp),

hspZh0Khs

hs(17)

where h0 is the zero shear rate viscosity of the

polymer solution and hs is the solvent viscosity. For

neutral, linear polymers in a good solvent, hspwC1.0

in the dilute regime, hspwC1.25 in the semidilute

unentangled regime, hspwC3.8 in the semidilute

entangled regime as predicted by the reptation theory.

Finally, the value of hsp generally shows a weakerdependence in the concentrated regime compared to

the semi-dilute entangled regime [111]. For example,

Colby et al. measured the onset of the semidilute

unentangled and semidilute entangled regime for an

aqueous solution of sodium hyaluranote [113]. Fig. 18

shows the concentration dependence of viscosity and

the determination of C* and Ce from the change in

slope. Takahashi et al. measured h0 for linear poly

(a-methylstyrene) in good, poor, and q solvents and

observed the transition to the semidilute regime

decreased with molecular weight as expected sincelarger chains begin to overlap at lower concentrations

compared to smaller chains [114]. Moreover, the

authors reported that the transition was dependent on

Fig. 18. Concentration dependence of specific viscosity for a

biopolymer, sodium hyaluranote. C* and Ce were determined as

0.59 and 2.4 mg/mL, respectively.



21/33

solvent quality. Other researchers investigated the

hspKC relationship for linear poly(a-methylstyrene)

in solvents of variable quality [115]. The investigators

discovered that in dilute solutions hsp was lower inpoor solvents compared to good solvents, while the

opposite was true in entangled solutions. It was

proposed that the viscosity increase in the poor

solvent was attributed to enhanced entanglement

couplings due to relatively weak interactions between

the chain segments and the solvent. Moreover, other

researchers have observed a weaker concentration

dependence for viscosity in the semidilute entangled

regime for a polymer in a good solvent compared to a

polymer in a theta solvent [116].

Our discussion of concentration dependence ofhspand the determination of C* and Ce has focused on

linear chains to this point. Not surprisingly, at equal

molecular weights, branched chains show different

behavior in solution compared to linear chains.

Generally, as shown in Fig. 19, a branched polymer

exhibits a higher overlap concentration compared to a

linear polymer of equal Mw since the branch points

act as obstacles to chain interpenetration [117].

Sendijarevic et al. studied the effect of branching of

AB/AB2 etherimide copolymer solutions on solution

rheology properties [118]. The authors observed a

weaker concentration dependence of h0 in thesemidilute entangled regime for more highly branched

structures. As the copolymer composition was varied

from 0 to 100 mol% AB2, corresponding to linear and

hyperbranched architectures, respectively, the expo-

nent decreased from 12.5 to 4.7, attributed to a largernumber of entanglements per chain in the linear

copolymers. Moreover, the overlap concentration

increased with higher levels of branching. Similarly,

solution rheology studies with linear and randomly

branched poly(ethylene terephthalate-co-ethylene iso-

phthalate) (PET-co-PEI) showed a weaker hsp vs. C

dependence for branched copolyesters compared to

linear copolyesters of similar molecular weight [119].

Furthermore, branching dramatically influenced the

onset of the entanglement regime, as Ce increased

from 4.5 to 10 wt% as g 0 for PET-co-PEI decreased

from 1.0 to 0.43. In a related study, Juliani and Archer

studied the rheology of unentangled and entangled

A3KAKA3 multi-arm polybutadiene solutions with

equivalent branch molecular weights and variable

backbone molecular weights [120]. The investigators

reported Ce decreased from 22 to 8 vol% as the

molecular weight of the cross-bar was increased by

w30% allowing a larger number of entanglements per

chain for the higher molecular weight crossbar.

5.3. Recent advances in electrospinning of long-chain

branched polyesters

Traditional melt processing of polyester fibers has

received significant commercial attention, however,

electrospinning has recently emerged as a specialized

processing technique for the formation of sub-micron,

high surface area fibers [121]. The utility of branched

polyesters in the electrospinning process has received

only limited attention. Typically, conventional poly-

mer fibers are melt spun using pressure-driven flow

through an extruder, yielding fibers on the order of

10100 m

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Art Branched Polyesters