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Flexibilised styrene-N-substituted maleimide copolymers withenhanced entanglement densityCitation for published version (APA):Suwier, D. R. (2001). Flexibilised styrene-N-substituted maleimide copolymers with enhanced entanglementdensity. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR550152

DOI:10.6100/IR550152

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https://doi.org/10.6100/IR550152https://doi.org/10.6100/IR550152https://research.tue.nl/en/publications/flexibilised-styrenensubstituted-maleimide-copolymers-with-enhanced-entanglement-density(cfecdf43-4f32-447d-bd12-85b4525f619f).html

Flexibilised Styrene-N-substituted Maleimide

Copolymers with Enhanced Entanglement Density

Davy Roger Suwier

CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN Suwier, Davy R. Flexibilised styrene-N-substituted maleimide copolymers with enhanced entanglement density/ by Davy R. Suwier. - Eindhoven: Technische Universiteit Eindhoven, 2001. Proefschrift. - ISBN 90-386-2633-9 NUGI 813 Trefwoorden: polymerisatie / copolymeren; synthese / styreen-maleimide copolymeren; taaiheid / polymeerketens; omstrengelings dichtheid / polymerisatie katalysatoren; iniferters Subject headings: polymerisation / copolymers; synthesis / styrene-maleimide copolymers; toughness / polymer chains; entanglement density / polymer catalysts; iniferters © 2001, Davy Suwier Druk: Universiteitsdrukkerij Technische Universiteit Eindhoven Foto: Wouter Gerritsen Omslagontwerp: Paul Verspaget & Carin Bruinink

Flexibilised Styrene-N-substituted Maleimide

Copolymers with Enhanced Entanglement Density

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magnificus, prof.dr. R.A. van Santen, voor een commissie aangewezen door het College voor

Promoties in het openbaar te verdedigen op dinsdag 11 december 2001 om 16.00 uur

door

Davy Roger Suwier

geboren te Oostende (België)

Dit proefschrift is goedgekeurd door de promotoren:

prof.dr. C.E. Koning

en

prof.dr. E.J. Goethals

Copromotor:

dr. M.J. Monteiro

We are, I think, in the right road of improvement, for we are making experiments. We zijn, denk ik, aardig op weg naar vooruitgang, omdat we begonnen zijn met dingen uit te proberen. B.Franklin

Table of Contents TABLE OF CONTENTS 7 CHAPTER 1 GENERAL INTRODUCTION 11 1.1 History and aim of this research 12 1.2 General introduction to toughness of a polymer 15 1.3 Effects of polydispersity on the entanglement density of

linear polymers: The Wassserman-Greassley model 22 1.3.1 Introduction 22 1.3.2 Molecular dynamicss in polydisperse networks 24 1.3.3 Calculations of the stress relaxation modulus for

polydisperse systems 26 1.4 Outline of This Thesis 29 References 30 CHAPTER 2 FACTORS DETERMINING THE ENTANGLEMENT DENSITY OF N-SUBSTITUTED ALTERNATING STYRENE-MALEIMIDE

COPOLYMERS 33 2.1 Introduction 34

2.1.1 Entanglements and toughness 34 2.1.2 Alternating styrene-maleimide copolymers 36 2.1.3 Aims and scope of this chapter 41 2.2 Experimental Section 43 2.2.1 Materials 43

2.2.2 Synthesis of monomers 43 2.2.3 Synthesis of alternating copolymers of styrene and the

different N-substituted maleimides 44 2.2.4 Instruments 44 2.2.5 Molecular graphics 45

2.3 Results and Discussion 46 2.3.1 Molecular characterisation 46

2.3.2 Thermal characterisation 50 2.3.3 Rheological properties 51 2.4 Conclusions 57 References 58

CHAPTER 3 FIRST SYNTHETIC ROUTE TO INCREASE THE ENTANGLEMENT DENSITY OF SMI-COPOLYMERS:

POLYCONDENSATION REACTIONS BETWEEN SMI TELECHELICS AND POLY(TETRAHYDROFURAN) 59 3.1 Introduction 60 3.2 Experimental Section 64

3.2.1 Materials 64 3.2.2 Synthesis of N-(4-tert-butylphenyl)maleimide 64 3.2.3 Synthesis of SMI telechelics 64 3.2.4 Determination of functionality 65

3.2.5 Synthesis of multiblock copolymers 65 3.2.6 Instruments 66

3.3 Results and Discussion 67 3.3.1 SMI Telechelics with 50 mole % of styrene and their step

growth polymerisation with PTHF 67 3.3.2 SMI(N-phenylmaleimide) telechelics with 75 mole % of styrene and their step growth polymerisation with PTHF 71

3.3.3 Determination of the entanglement density 74 3.4 Conclusions 77 References 78 CHAPTER 4 THE POLYMERIC INIFERTER TECHNIQUE: A VERSATILE

ROUTE TO SYNTHESISE MULTIBLOCK COPOLYMERS ? 79

4.1 Introduction 80 4.1.1 Synthetic methods for introducing flexible segments into styrenic polymers 80 4.1.2 Is the iniferter technique really a ‘living’ radical polymerisation

technique? 81 4.2 Theoretical Background 83 4.3 Experimental Section 90

4.3.1 Materials 90 4.3.2 Instruments 90 4.3.3 Iniferter synthesis: N,N’-diethyl-N,N’-bis(2-hydroxyethyl)thiuram

disulfide (DHTD) 90 4.3.4 Polymerisation of styrene under thermal conditions 91 4.3.5 Polymerisation of styrene under UV-conditions 91

4.4 Results and Discussion 92 4.4.1 Synthesis of the OH-terminated iniferter 92

4.4.2 Evaluation of the first criterion for a living radical polymerisation reaction: chain extension 93

4.4.3 Evaluation of the second criterion for a living radical polymerisation reaction: linear increase of nM as a function of conversion 97

4.5 Conclusions 101 References 102 CHAPTER 5 SECOND SYNTHETIC ROUTE TO INCREASE THE ENTANGLEMENT DENSITY OF SMI COPOLYMERS: MULTIBLOCK COPOLYMERS PREPARED FROM PTHF-BASED INIFERTERS 105

5.1 Introduction 106 5.2 Experimental Section 109

5.2.1 Materials 109 5.2.2 Synthesis of the polymeric iniferter based on hydroxy-

terminated PTHF (Mn=1000 g/mole) 109 5.2.3 Synthesis of the segmented copolymers 110

5.2.4 Snipping of the SMI-PTHF multiblock copolymer 111 5.2.5 Instruments 111

5.3 Results and Discussion 113 5.3.1 Synthesis of PTHF-based polymeric iniferter 113 5.3.2 Synthesis and molecular characterisation of segmented

PTHF(SMI-block-PTHF)n copolymers 114 5.3.3 Thermal analysis and bulk characterisation of

PTHF(SMI-block-PTHF)n 127 5.4 Conclusions 138 References 139 EPILOGUE 141 SAMENVATTING 143 SUMMARY 147 DANKWOORD 151 CURRICULUM VITAE 153

General Introduction

11

1


Synopsis: A general introduction is presented, describing from a historical standpoint the importance of the work contained within this thesis. The main aim of this work is to increase the toughness of brittle materials. In this section, the concepts are described that allow one to determine the types of polymer materials that will fulfil this role. An important discussion of the Wasserman-Graessley model is given, which quantifies the effects of polydispersity on the entanglement density of linear polymers, and allowed us to further optimise the materials we made. Hereafter, the outline of the thesis is given in detail.

Chapter 1

12

1.1 HISTORY AND AIM OF THIS RESEARCH Since the history of this research finds its origin in an industrial problem, a brief overview of

the different steps leading to the need to toughen an SMI-copolymer will be given.

This research started when some problems had occurred in engineering plastics applications

of styrene maleic anhydride (SMA) copolymer. SMA is a very interesting copolymer [1]. Due

to the polarity and the stiffness of the co-monomer, the glass transition temperature (Tg) is

raised significantly in comparison to polystyrene (from ca. 100 oC to ca. 195 oC for SMA

containing 50 mole % MA) [2].

Unfortunately, the brittleness increased drastically with increasing MA content. Therefore,

SMA is mainly used in blends with tougher polymers. For instance, they are used in blends

with ABS (Acrylonitrile Butadiene Styrene), in which SMA containing ca. 28 wt % MA is

homogeneously miscible with the SAN phase of the ABS, thereby raising the Tg and the heat

distortion temperature.

A major disadvantage of SMA with relatively high MA contents is the decarboxylation that

can occur during processing at elevated temperatures. The degradation product CO2 causes

‘streaks’ at the surface of moulded parts.

It has been reported that decarboxylation only takes place in MSM (maleic anhydride-styrene-

maleic anhydride) sequences [3] (See Figure 1.1).


13

Figure 1.1: Decarboxylation reaction in styrene maleic anhydride copolymers

(SMA). A possible solution for this specific problem is replacing the oxygen atom in the five-

membered ring by a substituted nitrogen atom (See Figure 1.2).

Figure 1.2: SMA SMI

O OO O OO

- CO2

OOO O

spirodilacton

O O OO

HOOC

O OO O OO N OO

R

N OO

R

Chapter 1

14

However the resulting, thermally stable styrene-maleimide (SMI) copolymers are even more

brittle than the styrene-maleic anhydride (SMA) copolymers.

SMI copolymers are intrinsically very rigid copolymers and have therefore limited

applications if toughness is a key property. Consequently, we postulated that to toughen these

SMI copolymers one should incorporate relatively short flexible main chain segments, which

are homogeneously miscible with the SMI blocks, into the rigid SMI main chain. These

flexibilised SMI copolymers, with an enhanced ability to form entanglements, and thereby

possibly with an increased toughness, would be more useful in engineering plastics

applications than their non-flexibilised counterparts. The aim of this research is to synthesise

polymers that have a relatively high Tg combined with an increased toughness. The approach

should result in a new concept concerning the enhancement of toughness of amorphous

polymers.


15

1.2 GENERAL INTRODUCTION TO TOUGHNESS OF A POLYMER [4,5] This section develops a basic discussion on the methods to enhance the toughness of brittle

SMI polymers. From this, suggestions on how these polymers can be toughened and the

methods used to measure this toughness are introduced.

Polymers are often thought of as being mechanically weak and their mechanical properties

have consequently been somewhat ignored in the past. These days many polymers are used in

structural engineering applications and are subjected to appreciable stresses. This increase in

use has been due to several factors. One of the most important reasons is that, although on an

absolute basis their mechanical strength and stiffness may be relatively low compared with

metals and ceramics, when the low density of polymers is taken into account their specific

strength and stiffness are comparable with those of conventional materials. Also the

fabrication costs for polymeric components are usually considerably lower than for other

materials. Polymers melt at relatively low temperatures and can readily be molded into quite

intricate components using a single molding operation. Although polymers are increasingly

being used in engineering applications because of their many advantages over more classical

materials such as wood and metals, for some applications their use is limited by the tendency

of many of these polymers to fail in a brittle fashion.

Toughness can be considered, in a first approximation, as the work to break during (tensile)

deformation, i.e. the area below the stress-strain curve during loading the specimen to failure

(See Figure 1.3).

Chapter 1

16

Figure 1.3: Stress-strain curves for a brittle polymer and a tough polymer.

In this respect, toughness should be related to the deformation of an entanglement network

(See Figure 1.4), similar to tensile drawing for obtaining high strength/high modulus, oriented

fibrous structures. It is obvious that this deformation is influenced by the density of the

entanglement network, in other words by the average molecular mass between two adjacent

entanglements.

Figure 1.4: Schematic representation of the molecular mass

between two adjacent entanglements.

x

x

Strain

Stre

ssBrittle Polymer

Tough Polymer

x

x

Strain

Stre

ssBrittle Polymer

Tough Polymer


17

The entanglement network in the case of amorphous polymers can change by a dissolution

procedure. But the disentanglement cannot be made permanent via crystallization and,

consequently, upon removal of the solvent, reentanglement occurs. Hence, in the case of

amorphous, glassy polymers, the entanglement network is dictated by the macromolecular

chemical structure.

The materials investigated here are amorphous polymers in their glassy state, which implies

that the mobility of the chains is strongly confined. Despite their similar character, the

intrinsic behaviour of the commonly used glassy polymers polystyrene (PS) and

polycarbonate (PC) differs a lot [6].

Figure 1.5: Typical stress strain curve of an amorphous polymer.

true strain

true

stres

s

I II III

A

B

true strain

true

stres

s

I II III

true strain

true

stres

s

I II III

A

B

Chapter 1

18

The intrinsic stress-strain curve of amorphous polymers, obtained in a compression test, can

roughly be subdivided into three regions (See figure 1.5).

The first region can be regarded as the visco-elastic region, which is dominated by weak

secondary interactions between the polymer chains (Van der Waals-bonds). In a mechanical

test, stress increases with the strain in this region. The first region (I) is bounded by the onset

of plastic deformation: the yield stress. From literature it is known that this yield stress is

strain rate and temperature dependent [7,8,9].

At this yield point the second region (II) is entered in which mobility of chains is increased

and movement on a segmental scale becomes possible. In a sense a glass-to-fluid transition is

established which is not temperature but stress induced. After yielding, true stress decreases

with ongoing strain, which is often referred to as intrinsic strain softening and has been

studied frequently in literature [8,10]. However the physical origin of this ‘facilitated’

deformation is not yet completely understood. What is known is that the strain softening is

strongly dependent on the thermal and loading history of the polymer. Thermal (quenching)

and mechanical treatments (rejuvenation) can reduce the yield stress and also the drop in

stress after yielding.

When this strain softening becomes saturated, the third region (III) is reached in which the

true stress rises again: the so-called strain-hardening region. After yielding, the mobility of the

polymer chains has increased and co-operative motion has become possible, resulting in

stretching of the chains. The polymer network is a physically entangled structure with steric

hindrances. The time-scale on which these entanglements relax in polymer glasses is much

longer than the time-scale of the experiment. Hence, stretching of the material loads the

entanglements and thus the polymer network, resisting further stretching and resulting in an

increased true stress.

In general, there are two ways to toughen a polymer. The first approach is by lowering the

yield point (A in Figure 1.5). This can e.g. be accomplished by adding plasticisers to the

polymer. A second approach is by increasing the slope of the strain hardening by increasing

the entanglement density of the polymer (B in Figure 1.5). We will combine both methods for

the toughening of the brittle SMI-polymers, by introducing flexible segments into the SMI

main chain as a kind of ‘internal plasticiser’ also enhancing the entanglement density.


19

Though the lowering of the yield point includes a diminishing area under the stress-strain

curve it is an excellent method for toughening polymeric materials. A beautiful example of

this approach is a decrement in the yield point by mechanical rejuvenation [11]. By flattening

a PS-bar, the craze-formation during folding can be suppressed and a tough behaviour is

observed.

Information concerning the entanglement network structure in the solid state can be obtained

via equilibrium rheological measurements, since the molecular weight between two adjacent

entanglement nodes, eM (See Figure 1.4), can be derived from the rubbery plateau modulus

in the melt [12]. In this respect, polystyrene can be considered as a rather loose network, the

value for eM being approximately 20 kg mol-1, compared with bisphenol-A based

polycarbonate and polyethylene, where eM is approximately 2 kg mol-1 and the network is

tight [13] (See Figure 1.6).

Figure 1.6: Influence of the molecular weight between two adjacent entanglements on the toughness.

It can be seen in Figure 1.6 that SMI copolymers have a very high eM and show consequently

a very brittle behaviour. To improve the possible applications of SMI we aim to shift from the

80

TOUGH

BRITTLE

431.510.5

2 9 12 19 24

PC,PEPPE

PMMASAN

PSSMA

SMITou

ghne

ss (k

J/m

2 )

Me (kg/mole)

80

TOUGH

BRITTLE

431.510.5

2 9 12 19 24

PC,PEPPE

PMMASAN

PSSMA

SMITou

ghne

ss (k

J/m

2 )

Me (kg/mole)

80

TOUGH

BRITTLE

431.510.5

2 9 12 19 24

PC,PEPPE

PMMASAN

PSSMA

SMITou

ghne

ss (k

J/m

2 )

Me (kg/mole)

Chapter 1

20

very brittle SMI-region to the PS-region in Figure 1.6 (indicated by the black arrow). Another

scientific way to describe the entanglement network is by the entanglement density, eν ,

which is related to eM and the density (ρ) according to: eM

eρν = .

From viscosity measurements performed on melts of polystyrene it is known that above a

certain critical molecular weight of polystyrene the viscosity suddenly increases strongly.

This effect is attributed to entanglement coupling; above a certain critical molecular weight

( crM ) entanglements are formed [14]. The formation of entanglements above this critical

molecular weight can also be found in an evaluation of the storage modulus, G’, of narrow

distribution polystyrenes with varying molecular weight as a function of the reduced

frequency [15].

The storage modulus reveals a plateau region above the glass transition. This so-called

rubbery plateau becomes more pronounced with increasing molecular weight, i.e., longer

relaxation times of the polymer chains. However, the height of this plateau oNG remains

unchanged upon increasing the molecular weight above the critical value. Similar to the

rheological behaviour of cross linked rubbers above their glass transition temperature, oNG can

be related to an average molecular weight between nodes of enhanced friction (i.e.,

entanglements in the case of amorphous thermoplastic polymers, and cross links for

chemically cured thermosets). In this thesis, we will use this relation to measure the

entanglement density of our polymers. Since the entanglement density is strongly related to

the toughness, we obtain an idea on this macroscopic quality. A qualitative idea of the value

of eM can be derived from T2 spin-spin relaxation time measurements (1H NMR) for a series

of polymers with different molecular weights [16,17].

Short chains, which are below the critical entanglement molecular weight, crM (= 2 eM )

undergo Rouse dynamics, whereas polymers with a molecular weight above the crM are

entangled and have therefore a restricted chain motion (‘reptation regime’). But this technique

is not suitable for determining the eM in our case because it requires the whole range of

molecular weights of polymers with the same chemical composition.


21

However, problems arise if one wants to determine the entanglement density from the rubbery

plateau derived from a DMA experiment on a polydisperse polymer with a broad molar mass

distribution. A possible solution to overcome these problems is given by the Wasserman-

Graessley model, which is subject of the next section.

Chapter 1

22

1.3 EFFECTS OF POLYDISPERSITY ON THE ENTANGLEMENT DENSITY OF LINEAR POLYMERS: THE WASSERMAN-GRAESSLEY MODEL

1.3.1 Introduction

Making a “Good Polymer” involves several steps in modern chemistry. First you have to use

reaction chemistry to synthesise polymers with a well-defined molecular shape. A molecular

shape, which will lead to a good melt rheology. Polymers with a good melt rheology will be

easy to process.

In order to predict the melt rheology for linear molecules, several models have been used,

based on the tube model. A polymer molecule is regarded as a string of spaghetti, which

moves in the pot by its one free mode. The molecules cannot move through each other, so

they only reptate. The only constraints in this model are the entanglements. The polymer can

only flow if all the “old entanglements” are gone, and the corresponding relaxation time τ is

proportional to the third power of the molecular weight. However, these ‘simple’ models

cannot be used to predict the melt-behaviour of industrial polymers because the molecular

weight distribution is too broad and in some cases too complex (too difficult architecture)

[18].

The study of the effect of molecular weight distribution on the rheology of polymer melts is

one of the most prominent concerns of macromolecular science [19-41]. Good knowledge of

this behaviour may contribute to improved material formulations by matching them to

particular processing and product needs. The Wasserman-Graessley model is based on a

molecular explanation of the dynamic modulus behaviour in a polymer system, i.e. in a

polymer system composed of entangled polymeric species of similar chemistry and molecular

architecture, but dissimilar molecular weight. This is accomplished by calculating the number

of densities and lifetimes of the various kinds of entanglements formed between chains of

(un)equal size. The knowledge of the dynamics of dissolution and renewal of the temporary

polymeric network is then used to predict the dynamic moduli of the polydisperse polymer

system.

According to the network theories of dense polymer systems, the stress relaxation modulus

depends on the extend of physical coupling between macromolecules and the rate of


23

conformational renewal of the individual chains. In a fluid composed of entangled polymers

of uniform molecular weight, Mi, a measure of the interchain associations is the number of

primitive steps per chain, Ni0 (i.e., the number of chain sub segments confined by two

consecutive entanglements). This is equal to:

Ni0= Mi/Me (eq.1.1)

where Me is the molecular weight between entanglements, a physical parameter which is

independent of the molecular weight but which decreases with increasing chain flexibility and

increases with dilution by a low molecular weight solvent.

Under quiescent conditions (or under small deformations) Ni0 remains constant in value,

although the entanglements of an individual chain with its neighbours are continuously

dissolved and reformed, subject to the Brownian motion of the polymer molecules.

A measure of the molecular agility and, consequently, of the rate of network renewal is the

time decaying fraction, Fi(t), of the original steps still surviving at time t after an initial

observation:

Ni(t) = Ni(0)Fi(t) = (Mi/Me)Fi(t) (eq. 1.2)

Here, Ni(t) is the number of the original segments still remaining intact, Ni(0) = Ni0 and,

evidently, Fi(0) = 1 ≥ Fi(t) ≥ 0 = Fi(∞). The functional form of Fi(t) depends on the large-

scale architecture of the macromolecular unit (linear, star, branched, etc.). The molecular size

and frictional resistance of the polymer chain control its rate of decrease with time during the

molecular motion. For the case of flexible linear chains, the most credible way of estimating

Fi(t) is provided by the reptation theory [42-44]. According to this theory, entangled chains

rearrange their conformations by curvilinear diffusion along their own contours. This motion

is assumed to take place within a medium of permanent topological obstacles representing the

surrounding entanglements. For a monodisperse system, the reptation theory predicts:

Fi(t) = F (t/τI) > exp(-t/τi) (eq. 1.3)

Chapter 1

24

where τi is the characteristic relaxation time

3iMkTm12

iM2

iR)0(iN

iD36

2iR

i αξ

τ =><

≈><

≈ (eq. 1.4)

is the end-to-end distance of the chain ( ~ Mi/m), Di the self-diffusion coefficient,

ξ the monomeric friction coefficient, m the molecular weight of the monomeric unit, k the

Boltzmann constant, and T the temperature.

In order to calculate the time-dependent stress relaxation modulus, the classical theory of

rubber elasticity is adopted for the case of temporary networks. In other words, it is assumed

that the stress value at any time t after a sudden strain imposition is proportional to the

number density of the original (t=0) primitive steps still surviving at that time:

)t(iFoNG)t(iF)eM/RT()t(iNikT)t(iG === ρν (eq. 1.5)

Where νi is the number of i chains per unit of volume:

νi = ρυINA/Mi (eq. 1.6)

ρ is the polymer density, NA is the Avogadro number, R is the gas constant, and GNo (RTρ/Me)

is the plateau modulus, an index of material rigidity.

1.3.2 Molecular Dynamics in Polydisperse Networks In a network of chains of unequal size, as opposed to a monodisperse system, there is no

qualitative equivalence between the different interchain associations and the primitive steps

they define. The average lifetime of a particular entanglement is proportional to the combined

length of the two chains from which it is formed. Consequently, primitive steps lying on and

defined by the longest chains are the last to relax. The number of different steps in the

network and their corresponding lifetimes can actually be calculated. Let us consider a


25

polymer system composed of entangling molecules of n different sizes; the molecular weight

of the ith component (i=1,2…n) is equal to Mi and its volume fraction is υi. Provided that all

Mi >> Me, the number of entanglements (or primitive steps) per chain (Ni0) is again given by

equation 1.1.

Let the index ij characterise a primitive step lying on an i polymer chain (of molecular weight

Mi) and defined by two j chains (of molecular weight Mj). This deliberately abstracted way of

looking at the network (in terms of overlapping segments) establishes a convenient

regrouping of the primitive step constituents according to their origin and lifetime expectancy

[45]. The number of ij steps surviving at time t after an initial counting is Nij(t) and the total

number of steps per i chain in the mixture is Ni(t). Neglecting end effects (Ni>>1), the total

number of steps along a single chain is equal to the sum of the number of entanglements

formed along its path, no matter whether these physical junctions are caused by neighbours of

similar or dissimilar length:

∑=

=n

1j)t(ijN)t(iN (eq. 1.7)

It is also reasonable to assume that the number of couplings of a chain i with its own size

decreases linearly with the volume fraction of the i species in the polymer system, and that the

ii steps are renewed at a rate identical to the one prevailing in the monodisperse state:

)t(iFi)eM/iM()t(iiN υ= (eq. 1.8)

On the other hand, the fraction of entanglements along chain i caused by random interactions

with j chains should be equal to the fractional participation of the j steps in the total step

population in the polymer system:

∑=

=n

1i)t(iNi

)t(jNi)t(iN

)t(ijN

ν

ν (eq. 1.9)

Chapter 1

26

An alternative way of explaining the physical meaning of equation 1.9 is to say that the

topological segmentation along a single chain is representative of that in the bulk of the

polymer system.

From the last two equations (1.8 and 1.9) and equation 1.6 it can be shown that the

entanglement probability between dissimilar chains is proportional to the geometric average

of the entanglement probabilities between similar chains:

[ ] 2/1)t(jF)t(iFeMiM

j

2/1

ji

)t(jjN)t(iiNj)t(ijN

=

= υ

ννν (eq. 1.10)

Consequently, the relaxation function and the characteristic relaxation time of an i molecule

in the polydisperse system (FiPD and τiPD), representing the rate of conformational renewal of

this molecule in an environment of dissimilar neighbours, may be related to the corresponding

properties of the monodisperse state in the following manner:

(eq. 1.11)

(eq. 1.12)

1.3.3 Calculations of the stress relaxation modulus for polydisperse systems

An expression for the stress relaxation modulus of an entangled polydisperse system, GiPD(t),

can be derived by following the same reasoning used for equation 1.5, i.e., by assuming that it

is proportional to the step density and surviving memory of the original network topology:

)t(n

1i

n

1i

n

1jijNikT)t(iNikT)t(PDG ∑ ∑ ∑

= = === νν (eq. 1.13)

[ ]

∫

∑∞

=

===

0dt)t(iPDFiPD

n

1j

2/1)t(jF)t(iFj)0(iN)t(iN)t(iPDF

τ

υ


27

Combination of equation 1.13 with equations 1.6, 1.7 and 1.10 results in the following

blending law, relating the viscoelastic behaviour of the polydisperse system to that of its

individual monodisperse components:

=>

= =

= ∑ ∑

n

1i

n

1j)t(jF)t(iFji

eMRT)t(PDG υυ

ρ

∑=

=n

1i)t(2/1iGi)t(2/1PDG υ (eq. 1.14)

This relationship always predicts a weaker modulus than the one estimated by a mere linear

averaging, since it accounts for the accelerated relaxation due to the earlier disengagement of

its shorter neighbours.

Several theories have been developed to describe the relaxation behaviour of polymers. Using

the generally accepted double-reptation model, eq. 1.14 can be rewritten into:

2N

1i)t,iM(

2/1FiwoNG

)t(G

== ∑ (eq. 1.15)

G(t) in the transition regime of the rubbery to the glassy state is observed to be linear (on a

log-log scale) for most of its range. The following equation describes this behaviour:

β−

=

*t

toNG

)t(trG (eq. 1.16)

As is necessary, the contribution due to the transition regime is independent of the molecular

weight. In addition, the parameters t* and β are determined by experimental data as the time at

which G(t) is 2 times the oNG and the slope of G(t) in the transition regime, respectively. With

equation 1.16, the low frequency tail of the glass transition, giving rise to higher modulus

values is taken into account in our calculations. The fraction in the molecular weight

distribution with a molecular weight lower than the entanglement molecular weight will not

Chapter 1

28

entangle and will dilute the network density. This fraction is used to calculate the corrected

G*-values as can be seen in the next expression:

[ ] *totalG2)solvent(fraction1*G)solvent(fraction)eMM(fraction

−==>

=< (eq. 1.17)

The fraction in the molecular weight distribution with a molecular weight higher than the

entanglement molecular weight (Me), but lower than the critical molecular weight (Mc, being

2 times Me) is characterised by a Rouse-type relaxation behaviour.

The fraction in the molecular weight distribution with a molecular weight above Mc will

entangle, and the relaxation behaviour can be described by a single exponential equation:

)texp(oNG)t(G τ−≈ (eq. 1.18)

The experimentally determined oNG is used as a starting value in the iteration following the

WG-approach to model as good as possible the experimental G(t).

So by taking into account the effect of the molecular weight and the Tg on the relaxation

behaviour of polydispersed polymers, the Wasserman-Graessley approach is a powerful tool

to get a more quantitative indication of the plateau modulus. In chapter 2 and 5 it is used to

obtain a better appraisal of the entanglement density.


29

1.4 OUTLINE OF THIS THESIS Chapter 2 describes the influence of the chain diameter on the entanglement density. A series

of six differently N-substituted poly(styrene-alt-maleimide)s (SMIs) has been synthesised by a

conventional free radical polymerisation reaction.

In addition to the presence of flexible units in the main chain, the chain diameter may play an

important role in the formation of entanglements, since a thin thread will ply more readily

than a thick cable. So, in Chapter 2 the bulkiness of the substituent on the nitrogen atom of the

maleimide unit is varied, thereby changing the chain diameter, to determine the influence of

this diameter on the entanglement density.

A first attempt to synthesise flexibilised SMI copolymers with enhanced entanglement density

was carried out through polycondensation reactions of α,ω−diacid-terminated SMI telechelic

blocks with α,ω-dihydroxy-terminated poly (tetrahydrofuran) (PTHF) blocks, resulting in the

formation of multiblock copolymers of SMI and PTHF. This approach is described in Chapter

3. However, this technique was not an efficient method to get bifunctionality, resulting in

multiblock copolymers with a limited degree of polymerisation. Therefore a living radical

polymerisation technique was considered.

In Chapter 4 the living character of the iniferter technique is discussed. To check the living

characteristics of the technique, chain extension polymerisations were performed under

thermal as well as under UV conditions.

Another method to synthesise flexibilised SMI copolymers was reported in Chapter 5. The

formation of SMI-PTHF multiblock copolymers is achieved by using the polymeric iniferter

technique (described in Chapter 4). The weight % of flexible PTHF segments incorporated in

the stiff SMI main chain has been altered to examine the influence of the flexible spacer

content in the main chain on the entanglement density.

Finally, the results presented throughout the thesis will be brought in perspective in the

epilogue, with respect to the goals that have been achieved. Our toughening concept offers

new perspectives, this and future developments are also discussed. Parts of this thesis have

already been published [46, 47], or have been submitted for publication [48,49].

Chapter 1

30

REFERENCES [1] B.C. Trivedi, B.M. Culbertson, “Maleic Anhydride”, Ch. 9, appendix 2, Plenum Press, New York (1982). [2] Kim, J.H.; Barlow, J.W.; Paul, D.R. J. Polym. Sci. B, Polym. Phys. 1989, 27, 233. [3] Klumperman, B.; Smids, P.; Van Duin, M. Preprints IUPAC International Symposium Polymer Materials, Polymer ’91, 1991, 106. [4] Young, R.J. and P.A. Lovell, Introduction to Polymers, second edition, Chapman & Hall,1995. [5] Materials Science and Technology: a comprehensive treatment. Edited by R.W. Cahn,

P. Haasen and E.J. Kramer. Chapter 12: Deformation and Toughness of Polymers by M.C.M. van der Sanden from Volume 18: Processing of Polymers. Edited by H.E.H Meijer. Published by VCH Verlagsgesellschaft mbH, Germany, 1997.

[6] personal communication H.G.H. van Melick, L.E. Govaert and H.E.H. Meijer [7] Bouwens-Crowet, C.; Crowet, J.A.; Hòmes,G., J. Polym. Sci. 1969, A2, v7, 1745. [8] Hasan, O.A.; Boyce, M.C., Li, X.S.; Berko, S., J. Polym. Sci.: Part B: Polym. Phys.,

1993, 31, 185. [9] Arruda, E.A.; Boyce, M.C.; Jayachandran, R.; Mechanics of Materials, 1995, 19, 193. [10] Aboulfaray, M.; G’Sell, C.; Mangelinck D.; McKenna G.B., Journal of Non-Cryst.

Solids, 1994, 172-174, 615 . [11] personal communication H.E.H. Meijer and L. Govaert [12] Ferry, J.D., Viscoelastic Properties of Polymers. New York: Wiley. (1980) [13] Wu, S., J.Polym.Sci.,Polym.Phys. 1989, 27, 723. [14] Porter, R.S.; Johsnon, J.F., Chem.Rev. 1966, 66, 1. [15] Onogi, S.; Masuda,T.; Kitagawa, K., Macromolecules 1970, 3, 109. [16] Ries, M.E.; Brereton, M.G.; Cruickshank, J.M.; Klein, P.G.;. Ward, I.M Macromolecules, 1995, 28, 3282. [17] Ries, M.E.; Klein, P.G.; Brereton, M.G.; Ward, I.M. Macromolecules, 1998, 31, 4950. [18] T. Mc Leish DPI-lecture July 2001 [19] Tsenoglou, C. , Macromolecules, 1991, 24, 1762. [20] Graessley, W.W. J. Chem. Phys. 1967, 47, 1972. [21] Graessley, W.W. Adv. Polym. Sci. 1982, 47, 67. [22] Struglinski, M.J. ; Graessley, W.W. Macromolecules, 1985, 18, 2630. [23] Graessley, W.W., Struglinski,M.J. Macromolecules 1986, 19, 1754. [24] Kurata, M. ; Osaki, K.; Einaga, Y.; Sugie, T. J.Polym.Sci., Phys. Ed. 1974, 12, 849 [25] Kurata, M. Macromolecules 1984, 17, 895 [26] Watanabe, H. ; Kotaka, T. Macromolecules 1984, 17, 2316 [27] Watanabe, H.; Kotaka, T. Macromolecules 1987, 20, 530. [28] Wu, S. Macromolecules 1985, 18, 2023. [29] Monfort, J.P. ; Marin, G. ; Arman, J. ; Monge, P. Polymer 1978, 19, 277.


31

[30] Monfort, J.P. ; Marin, G. ; Arman, J. ; Monge, P. Rheol. Acta. 1979, 18, 623. [31] Monfort, J.P. ; Marin, G. ; Monge, P. Macromolecules 1984, 17, 1551. [32] Monfort, J.P. ; Marin, G. ; Monge, P. Macromolecules 1986, 19, 1979. [33] Rubinstein, M. ; Helfand, E. ; Pearson, D.S. Macromolecules 1987, 20, 822. [34] Doi, M.; Graessley, W.W.; Helfand, E.; Pearson, D.S. Macromolecules 1987, 20,

1900. [35] Rubinstein, M.; Colby, R.H. J. Chem. Phys. 1988, 89, 5291. [36] Kim, H.Y.; Chung, I.J. J. Polym. Sci., Phys. Ed. 1987, 25, 2039. [37] Choi, K.S.; Chung, I.J.; Kim, H.Y. Macromolecules 1988, 21, 3171. [38] Tuminello, W.H. Polym. Eng. Sci. 1986, 26, 1339. [39] Han, C.D. J. Appl. Polym. Sci. 1988, 35, 167. [40] Meister, B.J. Macromolecules 1989, 22, 3611. [41] Eder, G.; Janeschitz-Kriegel, H.; Liedauer, S.; Schausberger, A.; Stadlaur, S.;

Schindlaur, G. J. Rheol. 1989, 33, 805. [42] de Gennes, P.-G. Scaling Concepts in Polymer Physics ; Cornell University Press :

Ithaca, NY, 1979 ; Chapter 8. [43] Doi, M.; Edwards, S.F. The Theory of Polymer Dynamics; Clarendon Press: Oxford,

1986; Chapter 6 and 7. [44] Graessley, W.W. J. Polym. Sci., Polym. Phys. Ed. 1980, 18, 27. [45] Tsenoglou, C. Polym. Prepr. (Am. Chem. Soc., Div Polym. Chem.) 1987, 28(2), 185. [46] Teerenstra, M.N.; Suwier, D.R.; Van Mele, B.; Teuwen, L.; Maassen, M.; van den

Berg, H.J. and Koning C.E, J. Polym. Sci.: Part A: Polym. Chem., 2000, 38, 3550. [47] Suwier, D.R.; Teerenstra, M.N.; Vanhaecht, B. and Koning C.E., J. Polym. Sci.: Part

A: Polym. Chem., 2000, 38, 3558. [48] Teerenstra, M.N.; Steeman, P.A.M., Iwens, W.; Vandervelden, A.; Suwier, D.R.; Van

Mele, B. and Koning C.E., submitted to Macromolecules. [49] Suwier, D.R.; Steeman, P.A.M.; Teerenstra, M.N.; Schellekens, M.A.J.; Vanhaecht,

B.; Monteiro, M.J. and Koning C.E., submitted to Macromolecules.

Factors determining the entanglement density

33

2222

Factors determining the Entanglement Density of

N-substituted Alternating Styrene Maleimide Copolymers

Synopsis: Differently N-substituted maleimides were copolymerised with styrene to yield alternating SMI copolymers with a different chain diameter. The polymers were obtained by

free radical polymerisation and characterised by NMR and SEC/DV. Glass transition

temperatures (Tgs) were measured by DSC. An increase in chain diameter and chain stiffness

is accompanied by a decrease in the entanglement density, reflected in lower values of the

plateau modulus oNG , which were corrected for the low molecular weight portion using the

Wasserman/Graessley model. Increasing the chain diameter by a factor of 2 results in a

decrease of the entanglement density of a factor 3. SMI-Me showed a much lower

entanglement density than PS although they do have the same chain diameter. However, SMI-

Me is more rigid than PS because of the maleimide five-membered ring structure in the main

chain. Although SMI-Me and SMI-PhOPh show roughly the same Tg, SMI-PhOPh has a

much lower entanglement density because of its larger chain diameter. Thus, both the chain

flexibility and the chain diameter affect the entanglement density.

Chapter 2

34

2.1 INTRODUCTION 2.1.1 Entanglements and Toughness

Entanglements in amorphous polymers refer to the degree of topological constraint on the

relative chain motion. In glassy and rubbery states, the amorphous polymer can often be

idealised as a network of entangled strands linked at entanglement points. The entanglement

network is characterised either by the density of the entanglement points, eν , or by the

average molecular weight of the strands separating neighbouring entanglement points, eM .

From the elasticity theory for an ideal rubber it is known that the molecular weight between

two cross-links is inversely proportional to the rubbery plateau modulus. This relation has

been successfully adapted to calculate the entanglement density, eν , for thermoplastic

polymers [1-3]. The entanglement density eν , can be calculated from the experimentally

determined plateau modulus at the frequency of minimum damping oNG according to:

RT

oNG

eMe ==

ρν (eq. 2.1)

where ρ represents the mass density at temperature T at which the plateau modulus oNG is

measured, and R is the gas constant.

The toughness of amorphous polymers seems to depend on the entanglement density rather

than on their glass transition temperature, and the entanglement density of polymers is

thought to play a determining role in toughness of polymers by affecting the balance between

shear yielding (tough) and craze formation (brittle) (see e.g. refs. [4-7]). It is known that the

extremely high toughness of bisphenol-A polycarbonate is also related to main chain motions,

enabling the polymer to absorb a large amount of energy before fatal damage occurs [8].

However, in this work we concentrated on the role of entanglement density. According to

earlier work by Wu [1,9], the entanglement density is higher for polymers that contain

flexible units. Examples are bisphenol-A polycarbonate, which contains the flexible O-CO-O


35

unit, and poly(phenylene ether), which contains the -C-O-C- unit. The average molecular

weight between two adjacent entanglements, eM , for these intrinsically tough polymers was

determined to be relatively low, viz. ca. 2,000 and 3,600 g/mole respectively. These highly

entangled materials are extremely tough. Polystyrene (PS) and especially copolymers of

styrene and maleic anhydride (SMA) show rather high eM values in the order of 18,000 –

25,000 g/mole (these values increased with increasing maleic anhydride content), so that eν

is low and in agreement with materials that show a brittle behaviour. These polymers consist

of chains that do not fold easily which is a necessity to form entanglements. eM may not

only directly depend on the presence of flexible units (See chapter 3 & 5), but the chain

diameter of these chains may also play a role. In fact, such a relation was found by Wu [10]

for a series of poly(alkyl methacrylate)s, but to our knowledge this has never been studied for

styrene maleimide copolymers. Therefore, the main topic of this chapter is the influence of

the chain diameter on the entanglement density for a series of different N-substituted styrene-

maleimide copolymers (SMI).

It seems obvious that polymer toughness is related to the chain diameter. Thin chains can

form entanglements more easily than chains with a large chain diameter, and as a

consequence their entanglement density is expected to be higher (See Figure 2.1).

Figure 2.1: Visualisation of an entanglement in a “thin” and a “thick” polymer chain.

Chapter 2

36

2.1.2 Alternating Styrene-Maleimide Copolymers Styrene-N-substituted Maleimides have a predominantly alternating character; this is

expressed in the reactivity ratios (rMI =0.01 and rSt =0.05)[11].

The copolymerisation equation indicates that the ratio in which both monomers at a certain

moment will add to the growing copolymer chain is only dependent on the monomer feed

ratio at that moment and the reactivity ratios of the monomers.

]MI[]St[Str]St[]MI[MIr

]St[]MI[

]St[d]MI[d

++

= (eq. 2.2)

The development of this copolymerisation is described by the mole fraction fMI in the

monomer feed and the basic mol fraction FMI in the instantaneously formed copolymer.

]St[]MI[]MI[

MIf += (eq. 2.3)

]St[d]MI[d]MI[d

MIF += (eq. 2.4)


37

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

fMI (Maleimide)

F MI (

Mal

eim

ide)

Figure 2.2: Graphical relation between fMI and FMI.

As one can see in Figure 2.2, the copolymer composition (FMI) remains constant for a wide

range of fMI values (between 0.3 and 0.9).

This implies that if one starts with a monomer feed composition of 50% maleimide and 50%

styrene (fMI =0.5), then automatically an alternating copolymer is generated, because the

chance that a maleimide monomer will add to a growing polymer containing a terminal

maleimide radical is negligible

In this chapter we study a series of alternating styrene maleimide copolymers (SMI). The

alternating character of similar polymers has been discussed earlier by Brown et al. [12].

They assumed the presence of a styrene-maleimide charge transfer (CT) complex that is

radically attacked by the growing chain to give highly alternating polymers (See Figure 2.3).

It is also shown in this figure how the appearance of E/Z configurations can be explained.

Chapter 2

38

(Z)

(E)

NR

O

H

H

O

Ph

1

2

NR

O

O

H

Ph

H

NR

O

Ph

HH

Figure 2.3: CT complex during the polymerisation of styrene maleimide

copolymers and the corresponding polymerisation mechanism leading to zusammen (Z) and entgegen (E) configurations and an alternating character (analogues to Brown [12]).

Electron donor acceptor (EDA) complexes are observed spectroscopically in many of the

reaction mixtures that afford alternating copolymers, and convincing evidence has been

provided for complex participation in the initiation of polymerisation [13]. Although we do

not go into detail with respect to E and Z configurations, Brown’s scheme might very well

explain the alternating character of the SMI copolymer.

There is also evidence against the participation of EDA-complexes. Tirrell et al. [14] have

used a trapping method to analyse the simple olefin adducts formed during the reaction of N-

phenyl maleimide with styrene (See Scheme 2.1).


39

R

A

D

AD

DA

RA

RD

RAD

RDA

T

T

T

T

RAT

RDT

RADT

RDAT

(1)

(2)

(3)

(4)

Scheme 2.1: Different possible reaction pathways for the monomer addition

during a polymerisation reaction of styrene and N-

phenylmaleimide (A= acceptor olefin; D= donor olefin; AD=

complex; T= trap).

Determination of the yields of trapping products (1) and (2) then allows an estimate of the

maximum extent to which the complex participates in the consumption of monomers A and

D. This approach is based on the straightforward notion that concerted complex addition is

unlikely to play an important role in copolymerisation if it cannot be demonstrated that simple

alkyl radicals undergo this reaction.

They concluded that the yield of simple addition products is nearly quantitative and argues

against concerted addition of a 1:1 complex of the monomers as an important pathway for

monomer consumption.

Also from kinetic studies performed on the polymerisation rates of styrene and maleic

anhydride it is known that the maximum in the kp versus mole % MA curve is not at a 50/50

feed (as can be seen in figure 2.4)[15]. A CT-complex can be regarded as an activated state.

So the more CT-complexes can be formed the faster the reaction will take place. If

copolymerisation took place solely through a CT-complex mechanism, then the maximum kp

should be at a 50/50 co-monomer composition, and indeed this is clearly not the case.

Chapter 2

40

Figure 2.4: Mean propagation rate constant as a function of monomer feed

composition (mole% MA) for the polymerisation of styrene and maleic anhydride (Source: Free Radical Copolymerisation of Styrene and Maleic Anhydride, Ph.D.-thesis TU/e, Bert Klumperman, 1994).

Authors suggest that it is in between these extremes, depending on the nature of the

monomers, the solvent and the temperature, the equilibrium between CT complex and free

monomers shifts [12,16,17]. Other researchers ascribed the alternation to the formation of

stabilised transition states at the propagating chain end [18].


41

2.1.3 Aims and Scope of this Chapter The aim of this chapter (illustrated in Figure 2.5 and 2.6) is to synthesise SMI-copolymers

having identical styrene/N-substituted maleimide compositions but with different chain

diameter. Subsequently we want to investigate the influence of chain diameter on the

entanglement density.

Figure 2.5: Schematic representation of styrene-N-substituted maleimide copolymers having different chain diameters.

We obtained predominantly alternating SMI polymers with different chain diameters by using

maleimide monomers with different substituents on the nitrogen atom (See Figure 2.6).

SMI-H

SMI-CH3

SMI-tBu

SMI-Ph SMI-tBuPh

SMI-PhOPh

Chapter 2

42

Figure 2.6: Structure of the alternating styrene-N-substituted maleimide copolymers (SMI).

In Chapter 3 and 5 we study the relation between the flexibility of the polymer main chain and

the entanglement density of flexibilised SMI copolymers. Flexibility is achieved by

incorporating polytetramethylene oxide spacers into the main chain [3,19]. However, in this chapter we focus on the relation between chain diameter and chain stiffness

of the non-flexibilised SMI copolymers on the one hand, and the toughness related average

entanglement density, eν , on the other hand.

n

R

SMI-H

SMI-Me

SMI-Ph

SMI-tBuPh

HCH3

CCH3

CH3CH3

Polymer

OSMI-PhOPh

SMI-tBu CCH3

CH3CH3

CCHCH

CN

CH2CH

O OR


43

2.2 EXPERIMENTAL SECTION 2.2.1 Materials Styrene (Acros) was distilled under reduced N2 atmosphere and kept refrigerated until use.

Maleic anhydride (Aldrich) was recrystallised from chloroform. Tetrahydrofuran (THF), N,N-

dimethylformamide (DMF) and N-methylpyrrolidinone (NMP) were distilled before use.

Maleimide, N-methylmaleimide, N-tert-butylmaleimide and 4-phenoxyaniline (Aldrich) were

used without further purification. N-Phenylmaleimide (Aldrich) was recrystallised from

methanol. 2,2’-Azobisisobutyronitrile (AIBN) (Merck) was recrystallised twice from

methanol and kept refrigerated.

2.2.2 Synthesis of monomers N-(4-tert-Butylphenyl)maleimide was synthesised by reacting maleic anhydride with 4-tert-

butylaniline and a subsequent dehydration to yield the desired monomer [3,20].

N-(4-Phenoxyphenyl)maleimide was synthesised performing a condensation reaction of

maleic anhydride (MA) and 4-phenoxyaniline (4PA) using acetic anhydride as dehydrating

agent in combination with sodium acetate. MA (19.61 g, 0.20 mole) was dissolved in 250 mL

THF and heated to 40°C under nitrogen atmosphere. A solution of 4PA (37.05 g, 0.20 mole)

in 150 mL THF was added slowly. After stirring for 20 hours sodium acetate was added (4.10

g, 0.05 mole) and finally acetic anhydride was added (51.05 g, 0.50 mole) as the dehydrating

agent. Stirring continued for another 48 hours. THF was removed and the reaction product

was dissolved in chloroform and subsequently washed with: water, a saturated aqueous

solution of NaHCO3 and water. The organic fraction was dried using MgSO4. The solvent

was removed under reduced pressure and the crude reaction product was washed with

methanol. It appeared that the desired product was insoluble in methanol whereas the side

products were soluble. Yield 71%. 1H NMR (250 MHz, CDCl3) δ 6.8 (s,2H), 7.15-7.02

(m,5H), 7.38-7.25 (m,4H). 13C NMR (62.9 MHz, CDCl3) δ 118.8 (2C), 119.3 (2C), 123.8

(1C), 125.9 (1C), 127.5 (2C), 129.8 (2C), 134.1 (2C), 156.4 (1C), 156.9 (1C), 169.5 (2C).

Chapter 2

44

Elemental analysis: calculated for C16H11NO3: 72.4% C; 4.2% H; 5.3% N. Found: 71.7% C;

4.3% H; 5.4% N.

2.2.3 Synthesis of alternating copolymers of styrene and the different N-substituted

maleimides Copolymers of styrene and the different N-substituted maleimides were prepared by a free-

radical copolymerisation using AIBN as the radical initiator and DMF as the solvent. The

synthesis of poly(styrene-co-N-4-(phenoxyphenyl)maleimide) (SMI-PhOPh) (Figure 2.6),

which may serve as an example, was performed as follows: N-4-(Phenoxyphenyl)maleimide

(8.70 g, 32.8 mmole) was dissolved in 40 mL DMF at 70°C under N2 atmosphere. Styrene

(3.42 g, 32.8 mmole) was added and 27.0 mg AIBN (0.25 mole% with respect to the total

monomer concentration) dissolved in 5 mL DMF was added shortly thereafter. The

polymerisation was carried out for 1hr and 40 min. The polymer solution was precipitated into

methanol and the resulting polymer was washed with methanol and dried in vacuo at 80°C.

Finally the polymer was dissolved in chloroform (150 mL) and precipitated again using 2.8 L

methanol. After filtration, washing and drying the yield of the resulting polymer was 10.05 g

(83%). The procedure for the syntheses of the other SMI copolymers was very similar.

2.2.4 Instruments The number- and weight average molecular weights ( nM and wM ), as well as the molecular

weight distribution were determined using a Waters 2690 Alliance size exclusion

chromatograph (SEC) equipped with two Styragel HR 5E columns, a Waters 410 differential

refractometer and a Viscotek T50A differential viscometer (DV). The eluent used was

THF:acetic acid (95:5 v/v). Absolute molecular weights were calculated by performing

universal calibration using polystyrene standards.

Solution viscosimetry was performed with an Ubbelohde viscometer on 0.8 g/dL solutions in

THF at 25°C.


45

The composition of the copolymers was determined by 1H NMR spectroscopy. The NMR

spectra were obtained on approximately 10% wt/vol solutions in chloroform-d1 (CDCl3) or

dimethyl sulfoxide-d6 (DMSO-d6). 1H NMR spectra were recorded either on a Bruker AC-

250 or AMX-500 spectrometer.

The triad sequence distributions of the SMI copolymers were determined using 13C DEPT

NMR [18]. These experiments were carried out on the AMX-500 spectrometer.

The glass transition temperatures were measured on a Perkin Elmer DSC-7 using a heating

rate of 10°C·min-1.

Dynamic mechanical analyses were performed on a Rheometrics RMS 800 mechanical

spectrometer equipped with 25 mm parallel plates.

2.2.5 Molecular Graphics The dimensions of the chain diameter of the differently N-substituted maleimides were calculated using Rotational Isomeric State Metropolis Monte Carlo simulations (RISMMC). The RISMMC model is available in the MSI/BIOSYM software [21]. The input parameters were: Force field: PCFF Temperature: 298 K Number of steps equilibration stage: 500000 Production stage: 2500000 Dielectric constant (ε) Min bonds and max bonds: these two parameters determine the interacting pairs of atoms for the purpose of calculating non-bond energies. These non-bond energies are only computed for an atom pair in which the second atom is in the range of 3-6 atoms away from the first atom. With the optional parameter ‘Include side groups’ one computes also the interactions between side groups connected to backbone atoms, which are in the range of 3-6 atoms away from each other. In order to make the simulations more realistic we treat side groups as flexible in the calculations by setting their ‘so-called’ backbone flags. The parameters with which one can try to simulate θ-conditions are respectively, max bonds and the dielectric constant. With this dielectric constant one can mimic the conformational statistical properties in solution. Some of the results are used in Figure 2.8 and in Figure 2.14.

Chapter 2

46

2.3 RESULTS AND DISCUSSION 2.3.1 Molecular characterisation The different styrene N-substituted maleimide (SMI) copolymers (Figure 2.6) were prepared

from an equimolar monomer feed ratio up to high conversion, using AIBN as the free-radical

initiator. In using different amines in the monomer synthesis, we obtained copolymers with an

identical main chain structure but with a different chain diameter (Figure 2.7). The chain

diameter of SMI-PhOPh is about two times as large as the chain diameter of SMI-H.

n

C CH3CH3

CH3

CCHCH

CN

CH2CH

O OR H

O

CH3 C CH3CH3

CH3

CHAIN DIAMETER

Figure 2.7: Schematic representation of the increasing diameter of the

chain with larger substituents on the maleimide nitrogen.

In Figure 2.8, it is shown clearly that when the substituent on the nitrogen atom of the

maleimide unit is a proton or a methyl, then the chain diameter is determined by the styrene

units. The light-coloured phenyl rings constitute the outer limits of the diameter. In the case

where the substituent is bigger (R = Φ or R = tbutylΦ) then the substituent on the maleimide

unit determines the chain diameter of the SMI-copolymers, although the effect of R=Φ is still

limited. The chain diameter will only increase starting from SMI(tbutylΦ) and concomitantly

it would be expected that the etanglement density should only decrease starting from

SMI(tbutylΦ) as well.


47

Figure 2.8: Molecular graphics of styrene-N-maleimide(R=H) (D=12.5Å), styrene-N-methyl maleimide (R=CH3) (D

Chapter 2

48

The results of the molecular characterisation are summarised in Table 2.1. The molecular

weights, determined by SEC/DV, are sufficiently high for future rheological characterisation.

The intrinsic viscosities, measured by using an Ubbelohde type viscosimeter, correspond quite

well to intrinsic viscosities determined by SEC/DV. The compositions of the synthesised

polymers were derived from their 1H NMR spectra and, as expected, the mole percentages of

maleimide were close to 50 mole % (Table 2.2). It is well known that an alternating structure

is generated when an electron poor (maleimide) monomer and an electron rich (styrene)

monomer are being copolymerised [11]. A polydispersity of 1.5 is expected at low

conversions if bimolecular radical-radical termination is only by recombination (e.g. styrene

polymerisation). In a copolymerisation of styrene with maleimides, which undergoes

predominantly disproportionation [22], the polydispersity will increase, and this will further

broaden with conversion.

This consideration will play an important role if one wants to synthesise fully bifunctional

SMI-telechelics (See Chapter 3).

Table 2.1: Molecular characterisation of the SMI copolymers.

Polymer nM wM D [η]GPC [η]Ubb.

(kg·mole-1) (kg·mole-1) (dL·g-1) (dL·g-1)

SMI-H 133 266 2.0 0.526 0.55

SMI-Me 128 344 2.7 0.457 0.43

SMI-tBu 99 203 2.1 0.550 …

SMI-Ph 146 365 2.5 0.549 0.49

SMI-tBuPh 132 242 1.8 0.568 0.55

SMI-PhOPh 159 458 2.9 0.635 0.65

The alternating tendency of the copolymers of styrene (S) and the different substituted

maleimides (MI) was determined by recording DEPT 13C methylene sub-spectra, (Table 2.2).

The resonances have been designated as follows: MSM (alternating triad) 32.0-37.5 ppm;

MSS+SSM (semi-alternating triad) 37.5-42.5 ppm; SSS (non-alternating triad) 42.5-48.0 ppm


49

[12,23]. We can conclude that predominantly alternating polymers were prepared since the

MSM triad accounts for up to 96% of the total amount of triads and in the worst case only 5%

SSS triads were found. Because of the strong alternating tendency of the styrene and

maleimide units in the SMI-copolymer, the chain diameter is very well defined. The chain

diameter will roughly have the same dimensions uniformly throughout the chain. This in

contrast to the case where a styrene-random-maleimide copolymer would have been formed.

In this case, the copolymer would have a different chain diameter than the alternating

copolymer (compare Figure 2.9 and Figure 2.10).

Figure 2.9: Schematic representation of a completely alternating

copolymer, the chain diameter is the same over the whole chain.

Figure 2.10: Schematic representation of a random copolymer,

the chain diameter is not everywhere the same.

Chapter 2

50

Table 2.2: Composition and microstructure of the SMI-copolymers.

2.3.2 Thermal Characterisation As a result of the incorporation of monomers with a rigid five-membered ring structure into

the main chain, the Tg of all six SMI polymers is significantly higher than the Tg of

polystyrene (See Table 2.3). However, there seems to be no correlation between the Tg value

and the size of the substituents. This can possibly be related to the contribution of the side

chains to the overall Tg. The copolymer with the hydrogen substituent, SMI-H, shows the

highest Tg of all, most likely due to the fact that this polymer can form hydrogen bonds, and

restricts the rotation and translation of these units, reflected in a higher Tg (252 oC(See Table

2.3)).

CHCH

N

H

OO

CHCH

N

H

OO

Figure 2.11: The formation of hydrogen bonds in styrene-maleimide

copolymers.

Polymer 1H NMR 13C NMR methylene Carbon atom

mole%MI MSM MSS/SSM SSS

SMI-H 50 0.83 0.17 0.00

SMI-Me 52 0.94 0.05 0.01

SMI-tBu 53 0.80 0.16 0.04

SMI-Ph 48 0.82 0.13 0.05

SMI-tBuPh 48 0.94 0.05 0.01

SMI-PhOPh 49 0.96 0.04 0.00


51

2.3.3 Rheological Properties Figure 2.12 shows the results of the dynamic mechanical analysis of SMI-Ph, which serves as

a typical example of the dynamic mechanical properties of the SMI-materials. In this figure,

the dynamic modulus G* and the phase angle δ are plotted as functions of the angular

frequency ω. The dynamic measurements were performed at 280, 290 and 300°C. These

temperatures were selected so that the rubbery plateau, the transition region between glassy

state and flow, is in the experimental frequency window. For all of the materials a well-

developed rubbery plateau is not found. This is attributed to the insufficiently high molar

mass of the materials in view of their very high entanglement molecular weights. The

relatively broad molecular weight distribution implies that a significant part of the polymer,

viz. the part with M

Chapter 2

52

1000

10000

100000

1000000

0,01 0,1 1 10 100 1000

Angular frequency [rad/s]

G* [

Pa]

20

30

40

50

60

70

Phas

e an

gle

[deg

]

Figure 2.12: DMA curves of SMI-Ph at 280°C ( ), 290°C ( ), and 300°C

( ). Filled symbols correspond to the dynamic modulus G*

while open symbols correspond to the phase angle, δ.

The ill-developed rubbery plateau of the SMI-materials listed in Table 2.3 and the relatively

small differences between the plateau moduli of these copolymers urged us to a more in-depth

study of possible error sources and, consequently, the limited reliability of the calculated

entanglement densities.

From statistical process control measurements we have found that the error in the absolute

modulus values we obtain with dynamic mechanical analysis amounts to about ±5%. The

plateau modulus is extracted from the dynamic modulus at the frequency where the phase

angle shows a minimum. However, because of the limited number of measurement

frequencies per decade, an additional error arises from an inaccurate value of the frequency of

the phase angle minimum. For a phase angle of 30 degrees and three measurement

frequencies per decade, these frequency related errors add up to an error band of ±15% for the

equilibrium modulus. More importantly, the high values of the phase angle point out that

relaxation mechanisms are active at the frequency where the equilibrium modulus is


53

extracted. These mechanisms must be expected to contribute to the dynamic modulus as

follows:

1) the low frequency tail of the glass transition, giving rise to higher modulus values

2) unentangled/ relaxing polymeric chains, diluting the entanglement network and

therefore giving rise to lower modulus values.

For each of the SMI-materials, given its Tg and molecular weight distribution, both

mechanisms may have a significant contribution. In order to get a more quantitative

indication of the plateau modulus, the model of Wasserman and Graessley (WG) [24] (See

chapter 1, section 1.3) was used to predict the linear viscoelastic properties of the SMI-

melts from their molar mass distributions, as determined with SEC/DV. The dynamic

properties were calculated assuming a BSW type relaxation time spectrum for the terminal

regime (below 1 rad/s) and a power law for the glass transition regime (above 1 rad/s).

Since no relaxation parameters were available for the various SMI types, these were fitted

for the best description of the experimental results. Most attention was paid to a good

description of the rubbery region. Figure 2.13 illustrates a typical example of a model

calculation for SMI-Ph. A master curve at 280°C was constructed from the experimental

results obtained at 280, 290 and 300°C. The storage modulus G’, the loss modulus G” and

the phase angle δ, are depicted with symbols. The solid lines are the results of the

calculations with the Wasserman/Graessley model, with optimised relaxation parameters.

A good description of the experimental results was obtained. The relaxation parameters

were varied around the optimal values, to study their effect on the accuracy of describing

the experimental results. It was observed that especially for the equilibrium modulus GN°

only a limited range of values could be used. For SMI-H, SMI-Me, SMI-tBu and SMI-Ph

we found a WG-corrected value of 100±25 kPa, which is considerably lower than the

value of 200 kPa found for polystyrene [10,25]. For SMI-tBuPh and SMI-PhOPh we

found significantly lower WG-corrected values (75±20 kPa for SMI-tBuPh and 30±15

kPa for SMI-PhOPh).

Chapter 2

54

Figure 2.13: Experimental and calculated DMA master curves of SMI-Ph at a reference temperature of 280°C. WG-parameters: Gn= 100 kPa; Me=46,800 g/mole; Mc=93,600 g/mole; τk= 7.10-14; a=3.38; t*=0.025 s; β=0.67; Tref= 280 oC.

0.01 0.1 1 10 100103

104

105

106

0

10

20

30

40

50

60

70

80

90

G',

G" [

Pa]

Angular Frequency [rad/s]

G' G" δ model

del

ta [d

eg]


55

Table 2.3: Glass transition temperature, Tg, temperature at which the DMA measurements were carried out, WG-corrected plateau modulus and entanglement density of the investigated SMI copolymers.

Polymer Tg T(DMA) GN° eν

(°C) (°C) (kPa) (mole m-3)

SMI-H 252 280 – 300 100 ± 25 22 ± 5

SMI-Me 205 250 – 280 100 ± 25 22 ± 5

SMI-tBu 178 220 – 230 100 ± 25 22 ± 5

SMI-Ph 221 280 – 300 100 ± 25 22 ± 5

SMI-tBuPh 237 280 – 298 75 ± 20 16 ± 4

SMI-PhOPh 194 240 – 270 30 ± 15 7 ± 3

PS [10,20] 100 190 200 52.0

From the WG-corrected GN° values, the corresponding entanglement densities were calculated.

All SMI-materials exhibit a significantly lower entanglement density, as compared with pure

polystyrene ( eν =52 mole/m3 [1]). Table 2.3 shows that the entanglement density drastically

decreased upon using maleimide co monomers with bulky groups on the MI nitrogen,

whereas eν did not decrease in case of maleimide monomers with small N-substituents. In

contrast to the rather fluctuating Tg there is a rather good correlation between the

entanglement density and the size of the substituent (Table 2.3). The small substituents on the

maleimide nitrogen’s, in the case of SMI-H and SMI-Me, stay within the ‘tube’ formed by the

styrene phenyl groups, and hence they do not enlarge the chain diameter. Therefore, the

entanglement density is not affected. However, the large substituents, in the case of SMI-

tBuPh and SMI-PhOPh, show a decreased entanglement density, obviously because here the

chain diameter has been enhanced with respect to polystyrene. The substituent of the

maleimide unit extends further from the backbone than does the phenyl group of the styrene

unit (Figure 2.7 and 2.8). Thus, we conclude that the results of the model calculations further

substantiate our finding that large substituents on the maleimide group, extending beyond the

phenyl side group of the styrene co monomer, viz. tBuPh and PhOPh, cause a reduction of the

entanglement density because of their effect on the chain diameter. It is observed that an

Chapter 2

56

enhanced chain diameter, while keeping the Tg in the same order of magnitude, results in a

lower value of eν (compare SMI-Me and SMI-PhOPh in Table 3). On the other hand, SMI-

CH3 and PS, having similar chain diameters but significantly different Tgs (and thus rigidity),

have very different entanglement densities. Thus, not only is the chain flexibility important

for the entanglement density, but also the chain diameter plays an important role.

Comparing the data of Figure 2.7 and Table 2.3 points to a remarkable relation between the

chain diameter and the entanglement density (See Figure 2.14). Obviously such a relation

only makes sense if the different polymers of the series have the same backbone structure.

0

5

10

15

20

25

30

12 14 16 18 20 22 24 26

Chain Diameter (Å)

ν ννν e (m

ole

m-3

)

Figure 2.14: Correlation between the chain diameter

and the entanglement density (νe).


57

2.4 CONCLUSIONS An increase in chain diameter and chain stiffness is accompanied by a decrease of the

entanglement density, reflected in lower values of the plateau modulus GN° , which were

corrected for the low molecular weight portion using the Wasserman/Graessley model.

Increasing the chain diameter by a factor of 2, results in a decrease of the entanglement

density of a factor 3. SMI-Me which is more rigid than PS because of the maleimide five-

membered ring structure in the main chain, showed a much lower entanglement density than

PS whereas they do have the same chain diameter. On the basis of that observation we can

conclude that chain rigidity affects the entanglement density. On the other hand, the Tgs of

SMI-Me and SMI-PhOPh were similar despite the fact that SMI-PhOPh has a much lower

entanglement density. This suggests that chain diameter also plays an important role.

Therefore, both chain flexibility and chain diameter will affect the entanglement density.

The Tg does not increase systematically upon the presence of a larger substituent on the

maleimide nitrogen, whereas the entanglement density does significantly decrease in the cases

where this substituent effectively enlarges the diameter of the chain. On the basis of this work

no conclusion can be made about the relative impact of chain diameter and chain flexibility on

the entanglement density. However it is clear that if we want to obtain SMI polymers with a

high entanglement density, it is necessary to use maleimides without bulky substituents.

Therefore in chapter 3 & 5, when we incorporate poly(tetrahydrofuran) into the stiff SMI

main chain to increase the flexibility, we will utilise phenyl and methyl N-substituted

maleimides.

Chapter 2

58

REFERENCES [1] Wu, S. Polym. Eng. Sci. 1992, 32, 823. [2] Ferry, J.D. Viscoelastic Properties of Polymers, 3rd ed., Wiley, New York (1980). [3] Teerenstra, M.N.; Suwier, D.R.; Van Mele, B.; Teuwen, L.; Maassen, M.; van den

Berg, H.J.; Koning, C.E. J. Polym. Sci., Part A: Polym. Chem. 2000, 38, 3550. [4] Kramer, E.J. Adv. Polym. Sci. 1983, 52/53, 1. [5] Donald, A.M.; Kramer, E.J. Philos. Mag. 1981, 43, 857. [6] Kramer, E.J.; Berger, L.L. Adv. Polym. Sci. 1990, 91/92, 1. [7] Kramer, E.J. Polym. Eng. Sci. 1984, 24, 761. [8] Xiao, C.; Jho, J.Y.; Yee, A.F. Macromolecules 1994, 27, 2761. [9] Wu, S.; Beckerbauer, R. Polymer 1992, 33, 509. [10] Wu, S. J. Polym. Sci., Part B: Polym. Phys. 1989, 27, 723. [11] P.J. Flory, Priciples of Polymer Chemistry, Cornell University Press, 15th

edition, New York (1992) [12] Brown, P.G.; Fujimori, K. Polymer 1995, 36, 1053. [13] Hall, H.K., Jr. Angew. Chem., Int. Ed. Engl. 1983,22, 440 [14] Permentine, G.S.; Jones, S.A.; Tirrell, D.A. Macromolecules 1989, 22, 770. [15] Klumperman, B. Ph.D. Thesis TU/e “Free Radical Copolymerization of Styrene and

Maleic Anhydride” 1994. [16] Butler, G.B.; Choon, H.D. Makromol. Chem. Suppl. 1989, 15, 93. [17] Brown, P.G.; Fujimori, K.; Tucker, D.J. Polym. Bull. 1992, 27, 543. [18] Lin, Q.; Talukder, M.; Pittman, C.U. J. Polym. Sci., Polym. Chem. Edn.

1995, 33, 2375. [19] Suwier, D.R.; Teerenstra, M.N.; Vanhaecht, B.; Koning, C.E. J. Polym. Sci., Part A:

Polym. Chem. 2000, 38, 3558. [20] Sung, P.H.; Chen, C-Y.; Wu, S-Y.; Huang, J.Y. J. Polym. Sci., Part A: Polym. Chem.

1996, 34, 2189. [21] Biosym software manual, Polymer modeling software, user guide, part 2, RIS module. [22] Bamford, C.H.; Bingham, J.F.; Block, H., Trans Faraday Soc., 1970,66,2612. [23] Barron, P.F.; Hill, D.J.T.; O’Donnell, J.H.; O’Sullivan, P.W. Macromolecules 1984,

17, 1967. [24] Wasserman, S.H.; Graessley, W.W. J. Rheol. 1992, 36(4), 543. [25] Aharoni, S.M. Macromolecules 1986, 19, 426.

Flexibilised SMI copolymers by using the Telechelic approach

59

3

First Synthetic Route to Increase the Entanglement Density of SMI

copolymers: Polycondensation reactions between

SMI-telechelics and Poly(tetrahydrofuran)

Synopsis: Telechelic copolymers of styrene and different N-substituted-maleimides (SMI), with a molecular weight range between 2000 – 8000 g/mole, were synthesised under starved-

feed-reactor conditions and were found to be nearly bifunctional when the monomer feed had

a high styrene concentration. The COOH terminated rigid SMI blocks were reacted (i.e.

through a polycondensation reaction) with the OH terminated poly(tetrahydrofuran) (PTHF)

blocks. The PTHF, with a molecular weight range between 250 – 1000 g/mole, which

constitute the flexible parts in the generated homogeneous multiblock copolymer. The

entanglement density, which is closely related to the toughness of materials, is increased in

these flexible SMI copolymers ( eν = 86 mole m-3), as compared to the unflexibilised ones

( eν = 40 mole m-3). The glass transition temperatures of these flexibilised, single-phase

multiblock copolymers are still high enough to qualify them as engineering plastics.

Chapter 3

60

3.1 INTRODUCTION Although polymers are increasingly being used in engineering applications because of their

many advantages over the more classical materials like wood and metals, for some

applications their use is limited by the tendency of many of these polymers to fail in a brittle

fashion.

Although more factors play a role, the toughness of polymeric materials seems to be linked

directly to the degree of entanglement of the polymer chains. Wu et al. [1,2] found that

polymer molecules with a smaller radius of gyration per unit of molecular weight (under θ-

conditions) contain more entanglements per unit of volume. It is obvious that there is a certain

degree of flexibility needed to form an entanglement. The rule of thumb is, that the smaller

the average molecular weight between two adjacent entanglements, eM , the tougher the

material is (see Figure 1.7 in Chapter 1).

The entanglement density is normally higher if the polymer chains are more flexible. To

illustrate this point, flexibility is increased with bonds that have a low rotational energy, e.g.

bisphenol-A based polycarbonate are the C-O bond in the carbonate group (± 10 kcal/mol) as

well as the C-C bonds in the isopropylidene unit, also the ether bonds in polyphenylene ether.

Accordingly, polycarbonate and poly(phenylene ether) are both tough polymers with

eM ≈2000 and 3600 g/mole, respectively [3,4].

Copolymers of styrene and N-substituted maleimides (SMI) are brittle. Their entanglement

density is low (at least a factor 2 lower than pure polystyrene, see Table 2.3 in Chapter 2) and

eM is high, i.e. in the order of at least 40.000 – 80.000 g/mole. These polymer chains are

very rigid and do not fold easily which is a necessity to form entanglements in the first place.

In a number of publications [5,6,7] it has been proven that the glass transition temperature

(Tg) gives no indication about the toughness or brittleness of polymers.

In the previous chapter we influenced the entanglement density by changing the chain

diameter. In this chapter we will incorporate flexible segments and compare the entanglement

density with non-flexibilised polymers.

We are trying to prepare flexible copolymers containing rigid SMI segments with the

possibility to form entanglements. These polymers are prepared by using low molecular

Flexibilised SMI copolymers by using the Telechelic approach

61

weight bifunctional SMI copolymers as building blocks in a polycondensation together with

bifunctional flexible units, miscible with the SMI blocks.

The incorporation of flexible units is not the only parameter that affects the entanglement

density. In Chapter 2 it was shown that the diameter of the chain also plays a role (a thin

thread will ply more readily than a big cable) [8,9]. Therefore, in this chapter we will only

compare multiblock copolymers with non-flexibilised polymers having the same chain

diameter, and will limit the size of the substituents on the maleimide N-atom.

An alternative approach in obtaining stiffer polymers is to start from flexible ones as been

described by Wimberger-Friedl et al. [10]. They introduced rigid spiro linkages into the main

chain of a polycarbonate in which eM was increased by a factor of 10.

O’Driscoll et al. [11] have proven that it is relatively easy to synthesise well defined low

molecular weight polymers with a narrow molecular weight distribution by free radical

polymerisation. They used the so-called starved-feed technique to synthesise polystyrene and

poly(methylmethacrylate) with a predetermined degree of polymerisation in the range of 20 –

140K. In this technique, a mixture of the two monomers and the initiator is added drop by

drop to the reaction mixture, which is at a high temperature. They used AIBN as the initiator.

However, the resulting polymers did not carry functional end groups like real telechelics.

Bamford et al. [12] described the preparation and use of telechelic oligo styrene with

carboxylic acid end-groups using 4,4’-azobis(4-cyanovaleric acid) as the initiator.

flexibilised styrene-n-substituted maleimide copolymers ... · wasserman-graessley model is given,...

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