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The Torsion Pendulum in the Investigation of Polymers

J . HEIJBOER

Divis ion of Technology for Socie ty TN O

2600 A E Del f t , The Nether lands

Th e early history of the use of the torsion pendulum in the

investigation of polymers is described together with the de-

velopment of dynamic mechanical testing at TNO. Examples

are listed of studies of structure-property relationships by

means of the torsion pendulum. Techniques using supported

samples are compared with those using unsupported samples,

particular attention being paid to the advantages and restric-

tions of torsional braid analysis (TBA). Th e comprehensive

application of TBA by Professor Gillham is reviewed; a few

TBA results are compared with our torsion pendulum mea-

surements. A rheologist’s view on the so-called liquid-liquid

transition ( T l l ) n polymer melts, as observed by TBA, is

presented.

EARLY HISTORY O F THE TORSION PEND ULUM

AND DYNAMIC MECHANICAL TESTI NG

s an introduction to th e discussion of torsional braid

Aanalysis (TBA), which has been so successfully de-

veloped and applied by Professor Gillham, I will first

present a retrospective view of the use of the torsion

pendu lum, including some early uses of other dynamic

mechanical techniques for testing solid polymers.

The oldest reference I found to a torsion pendulum in

the investigation of polymers was a paper by Mooney

and Gerke (1)of the U. S . Rubber Co., who used it in the

testing of rubber. They attached a horizontal circular

disc to the lower end ofa vertical rubber str ip clamped at

its upper end, and made th e disc oscillate about a verti-

cal axis, measuring the oscillation period by noting the

passage of a mark on the edge of the disc.

The next example found, also concerning rubber, was

the inst rument of Kuhn and Kuenzle (2), at the Univer-

sity of Basel, who as early as 1947 counterbalanced th e

load on th e sample and used different moments of inertiaby applying different discs between th e suspension wire

and the sample. The motion was traced by means of a

beam of light reflected by a mirror.

Application of th e torsion pendul um to plastics began

in the early fifties. In the USA, Nielsen and Buchdahl

(3-6)of Monsanto were t he first to publish an investiga-

tion of plastics with a torsion pendulum. Their first

equipm ent was built according to Kuhn and Kuenzle’s

principles. As early as 1953 (6), they investigated four

important topics using a torsion pendu lum: th e effect of

plasticization on the glass transition of PVC; the be-

havior of‘two-phase systems (high-impact polystyrene),the effect of crystallization on th e modulus of polyethyl-

ene , and the minimum in th e damping of plastics above

their glass-transition temperature, T o . Later , Cox, Isak-

son, and Merz (7) correlated the position of this

niiniinum in polystyrene with its molecular weight.

The first major development in Europe was made bySchmieder and Wolf (8-lo), of B A SF , who used the

equipm ent shown in Fig. 1. They applied Mooney and

Gerke’s principle by using a sample loaded with an

oscillating disc, but dete rmi ned the oscillation period bymeans of Kuhn’s optical method. In 1953, they pub-

l ished curves of the temperature-dependence of

modulus and damping (as the logarithmic decrem ent A= T tan 6) for about 50 polymers. They also paid at ten-

tion to the frequency-dependence of these properties.

As their data were more accurate than those of Nielsen,

et al. , they were able to define a secondary maximum

more precisely, e.g., that of poly(methy1 methacryla te)

(9). Later, BASF investigators extended t he frequency

range of their mechanical measurements to the ul-

trasonic region (11).In 1957, Thurn, Schmieder, and

Wolf (12) published a spatial representation of the

logarithmic decrem ent of high and low density polyeth-

ylene from 1 to lo’ Hz an d from -150 to +150°C. This

representation was reproduced in a survey paper byWoodward and Sauer (13). A representation of Young’s

modulus and damping of a rubber over so broad a fre-

quency range had already been given in 1950 by A. W .Nolle (14)of the Massachusetts Institute ofTechnology.)

-Specimen

,Thermal

locket

Fig. 1 . Schematic druuing of Schmieder und Wolfs torsionpendulum.

664 POLYMER ENGINEERING AND SCIENCE, MID-AUGUST, 1979, Vol. 19, NO .10



The Tors ion Pendulum in the Inves t igat ion of Polymers

At TNO we have from the outset been interested in

measurements over a broad frequency range. For this

purpose, Dekking (15)developed two pieces of equip-

ment, shown schematically in F ig . 2. For the torsion

pendulum we took a counterbalanced system. The

movement of the arm was recorded by means of an

electric spark striking on a thin strip of paper attached to

a rotating drum. By using dfierent moments of inertia,

we covered the frequency range from about 0.3 to 3 Hz.

For the frequencies from 200 to 3000 Hz we used the

same specimen that was tested with the torsion pen-

dulum, but now suspended horizontally by two loops of

rayon threads at its nodes. Small fragments of a razor

blade were glued to the end of the specimen; one end

was excited electromagnetically, and the movement of

the other end recorded. The frequency was varied by

means of an audiofrequency oscillator. We thus ob-

tained Young‘s modulus from the resonance frequency

of the sample, and the losses from the width of the

resonance peak. As a rule, we measured four or fivemodes of vibrational harmonics. Using this equipment,

we studied the effect of chemical modifications on the

secondary loss peak of poly(methy1 methacrylate) (15-

17), and were able to show that this loss peak is due to

the rotational motion of the methoxycarbonyl side group

being hindered by adjacent methyl groups on the main

chain.

In an early stage, the thermostat of our flexural vibra-

tion equipment could only be heated and not cooled. At

that time, J . Seffelaar of our Institu te observed that, at

room temperature, the losses of a copolymer of methyl

methacrylate and cyclohexyl methacrylate showed atendency to increase at the upper extreme of the

measuring range then available. This finding prompted

us to repeat the experiment in the cold (2OC) outside,

and in fact we found that the losses at high frequencies

had increased considerably. This experiment was the

beginning of a long line of research into the motion of

saturated rings incorporated as side groups into amor-

phous polymers (16-22). One result of this research was

our determination of the energy barrier opposing the

chair-chair transition of the cyclohexyl group (16), about

four years before it was determined by NMR (23). Our

result for the energy of activation, 11.5kcal/mole, is ingood agreement with what is probably the best experi-

mental value available for cyclohexane, and obtained by

NMR, viz., 11.2 kcal/mole (24).

A further development at T N O was the extension by

Waterman (25, 26) of the measuring range to higher

frequencies, viz., the kHz and the MHz range.

-. TI

i I

rors iond free vb r o im Flexura/ forced wbrohon

Fig. 2. Schematic drawin g of the originul apparatusfor vibra-

t ion measurements at T N O .

In the course of many years, our torsion pendulum

was improved considerably by Drent, Nederveen,

Schwippert and van der Wal(27). With some modifica-

tion, the same equipment can also be used for torsional

creep measurements, which extend the lower limit of

the effective frequency range to Hz (28). The

equipment is provided with a special thermostat whose

temperature can be rapidly and accurately adjusted (29).

Our fully automated version of the torsional creep in-

strument became available and proved to be very useful

in the investigation of physical aging (30).

The standard specimens we use are 7 mm wide and

3.5 mm thick. Fortuitously, at this ratio of width-to-

thickness the clamping correction is a minimum (31).

Some results of our torsional pendulum mea-

surements on commercial polymers are presented in a

review paper (32). A recent paper (33)on the charac-

teristics of secondary maxima contains a survey of our

dynamic mechanical measuring methods. A more de-

tailed description of our present measuring techniques

is given by Struik (30).

Apart from Monsanto, BASF and TNO, some other

laboratories have as early as the fifties published about

the dynamic mechanical properties of polymers below

the glass transition. The torsion pendulum was applied.

at the Technische Hochschule, Aachen, by Jenckel and

Illers (34-39), and at DuPont by McCrum and Sinnott

(40-43). A t Princeton University, Maxwell used a rotat-

ing bar to measure the mechanical losses of poly(methy1

methacrylate) (44). At an early stage, the vibrating reed

technique was extensively applied at the Plastics Re-

search Laboratory of ICI by Willbourn, Deutsch, Hoff,Reddish and Robinson (45-48).

At the Technisch-Physikalische Bundesanstalt in

Braunschweig (Germany), Oberst, Becker and Kop-

pelmann made very important contributions to the

study of the dynamic mechanical properties of hard

plastics over a broad frequency range (49-52). At

Pennsylvania State University, Kline, Sauer, and

Woodward (53-55) studied semicrystalline polymers by

flexural resonance vibration of a rod (56).At the Univer-

sity of Pisa, Baccaredda and Butta (57)also studied semi-

crystalline polymers, but by longitudinal vibration of a

bar.

To conclude our survey of papers on the dynamic

mechanical studies of hard polymers, already published

in the fifties, we should mention also the early contri-

butions of Fukada (58) and of Iwayanagi and Hideshima

(59, 60) on poly(methy1 methacrylate) and poly(methy1

acrylate).

It has been our intention to mention only those labo-

ratories which made early contributions to the determi-

nation of the dynamic mechanical properties of hard

polymers. We have therefore omitted the very impor-

tant work by Ferry and coworkers at Madison (61), sincethis is especially concerned with the glass transition.

A complete survey of the further investigations of

polymers by torsion penduIum would be far outside the

scope of this paper. Instead, we present a list of subjects

(Tuble 1 ) nvestigated by torsion pendulum and illustrat-

POLYMER ENGINEERING AND SCIENCE, MID-A UGUS T, 1979, Vol. 19,NO. 10 665



J. Heijboer

Table 1. Subjects of Torsion Pendulum Research

Reference

1. Plasticizers (5, 9, 38)2. Crystallinity, annealing (41, 62-68)

3. Crosslinking (10, 69-71)4. Polymer blends (72-82)5. High-impact homopolymers (83-87)

6. Block copolymers (88-92)

8. Side groups (19-22, 43,94-97)

9. Low-molecular weight additives (86, 98-103)

7. Interpenetrating networks (93)

10. Antiplasticization (104-107)

11. Physical aging (30)

ing its versatility. The references listed a re in tended as

examples and are not exhaustive.

The extension of the measurements down to liquid

helium temperatures (42, 96, 108) has essentially

broadened the scope of the torsion pendulum . A device

has been developed to perform torsion pendu lum mea-

surements at pressures up to 1500bar (109). The torsion

pendulum can also be used to measure fatigue proper-

ties (110).

In addition, the instrument is suitable for studying

other materials: a recent paper (111)describes a ver-

satile apparatus for measurements on metals.

Roller and Gillham (112) give a survey of equ ipmen t

for dynamic mechanical testing, including equipment

that is commercially available. An older, more detailed,

survey ofautomated equipment for the determination of

mechanical relaxation has been given by Becker (113).

In comparison with other dynamic mechanical

equipment, the conventional torsion pendulum is un-surpassed in accuracy and reliability: if the test bars are

large enough, the absolute modulus values can be ob-

tained with an accuracy of at least 2 percent. Other

dynamic mechanical equipment may yield absolute

modulus values which can be in error by 50 percent

(114).

The classical, accurate, version of the torsion pen-

dulum with free vibration has the disadvantage, how-

ever, that its operation is rather laborious and time-

consuming, particularly when several moments of iner-

tia are successively applied to obtain data at a num ber of

frequencies.

MEASURING TECHNIQU ES USING SUPP ORT ED

SAMPLES

When the amount of material available is small, or

when it cannot support a load, the conventional torsion

pendulum cannot be used. It is, therefore, not surpris-

ing that techniques for measuring supported samples

have been developed from the outset.

The easiest method, from a practical point of view,

uses flexural vibrations of thin metal strips, coated on

one side with the material to be investigated. The

method and theories have been described (1 15-118).They are more suitable for determining the damping

than the modulus and are of practical importance for

noise-abatement systems (119).

Thurn (120) has described an interest ing variation of

the method in which a quartz filament, bent into the

shape of a V, is fixed at the out er ends of its legs, and

coated by a thin layer of the material to be investigated.

The coated filament is placed in a vacuum and made to

vibrate. The method of attaching the V-shaped filament

has the advantage that its apex is constrained to vibrate

in a single plane, and so cannot describe Lissajous

figures. The amplitude of vibration of the apex decays to

half its initial value in a certain tim e. This “half time” is

measured, and is inversely proportional to the loss

modulus (in extension) of the coating. Thurn presents

data for, among others, PV C and PE.

A rather complicated method for dealing with tor-

sional vibrations of a coated st rip is described by Inoue

and Kobatake (121).

The most successful technique for measuring sup-

ported samples is no doubt that which is now called

torsional braid analysis (TBA). The first TBA inst rum ent

was developed at American Cyanamid, Stamford,

Conn ., by Lewis and Gillham (122-125). Later, when

Gillham was at Princeton University, he and his co-

workers developed the device into a highly sophisti-

cated instrumen t (126-132). An extensive review paper

(127) dating from 1972, gives as many as 49 references to

torsional braid analysis, and since then the rate of ap-

pearance of papers referring to the technique has still

increased. In many applications TBA has superseded

the conventional torsion pendulum.

The apparatus is shown schematically in Fi g . 3. It s

basic principle is the use of a loose glass braid made from

three or six yarns containing a total of about 3600 fila-

ments, each about 7 pm thick. The braid is eithe r soaked

1- D R ! V E G E A R T R A I N

L

S U P P O R T I N G R O D

T E M P E R A T U R E

C O N T R O L L E DI i E N C L O S U R F

S P E C I M E N

P O L A R I Z E R

V A C U U M

P H O T O T U B E

A N D D A T A

A T M O S P H E R E

P O R T

Fig. . Schemuti c drawing of Gillham’s automated torsion pen-dulum. Insert: part uf the braid and its attuchment t o the eyelet.

666 POLYMER ENGINEERING AN D SCIENCE, MID-AUGUST, 1979, YO/. 19 , NO. 10



The Tors ion Pendulum i n the lnves t iga t ion of Polymers

in a polymer solution, or dipped in a polymer melt, or

dipped in a liquid that reacts to form a crosslinked

polymer. The braid soaks up the liquid by capillary

action. The impregnated braid is used as a specimen to

be tested in a sensitive torsion pendulum. To this end it

is provided with eyelets, by the upper one of which it is

clamped to a supporting rod and by the lower one to an

extender rod, the two rods protruding from the oven of

the torsion pendulum. As the braid has a small cross-

section (diameter about 0.5mm), only a small moment of

inertia can be applied. The braid is kept in a vertical

position by a magnetic stabilizer at the lower end of the

extender rod. The torsional motion is recorded electro-

optically by the rotation of a horizontal polarizer disc,

whose transmission is a linear function of the position

angle. By virtue of this ingenious system, the specimen

can make well-defined undisturbed motions in spite of

the low moment of inertia. Moreover, this motion can berecorded electronically and is amenable to processing by

a computer. The logarithmic decrement, A = m tan 6,and the period P of the vibration are calculated. P-’ is

proportional to the rigidity G, of the system polymer-

braid. Both A and G, can be plotted on logarithmic

scales as a function of temperature or time.

One might wonder why torsional braid analysis has

taken such a wide scope. First, the method has a num ber

of inherent advantages over unsupported techniques.

There is no doubt, however, that the inventiveness and

perseverance of Professor Gillham and coworkers have

greatly contributed to the success of the technique.

Particularly their early success in fully automating the

instrument has promoted its practical application.The advantages ofTBA are listed, together with a few

restrictions, in Table 2 and will be discussed below.

First of all, the measurement requires only a small

amount of material: a few mg. This is, of course, an

advantage in investigations of exotic materials. The clas-

sical torsion pendulum requires an amount of material in

the order of 1 g.A second advantage is the simple way in which the

polymer can be converted into a suitable specimen from

a solution, melt or suspension. N o compression molding

or machining is required.

By TBA, measurements through transition ranges canbe made in a simple fashion. In the glass transition range

Table 2. Torsional Braid Analysis

Advantages

-The amount of material needed is small-The material can be applied from a solution, melt, or suspen-

-Measurements can be made through majortransition ranges,

-In situ monitoring of chemical reactions is possible-The sample rapidly approaches equilibrium with the sur-

-The support ing system has a favorable geometry

Restrictions

-The physical quantities obtained are not absolute-“Modulus curves are squashed non-linearly”-It is difficult to apply different moments of inertia

sion

even into the melt

rounding atmosphere

the conventional torsion pendulum needs additional

stiffnesses, owing to the high damping. Crystalline

polymers cannot be measured through their ent ire melt-

ing range by the conventional torsion pendulum, be-

cause in tha t range they will not support sufficient loads.

In my opinion, the most important feature of TBA is

the possibility it affords of following chemical reactions

i n situ. Examples are the gelation of a crosslinking sys-

tem starting from the liquid, and the degradation of a

high-temperature polymer until it completely disinte-

grates.

In this connection it is worth mentioning that the

small size of the sample used in TBA allows for ready

removal of volatiles and for rapid thermostating. The

sample approaches thermal, physical and thermal

equilibrium in a shorter time than does the larger sam-

ple of the conventional torsion pendulum.

One point remains to be discussed: the favorable

geometry of the special supporting system used in TBA.

The frequency of flexural vibration of a coated quartzfilament is only slightly influenced by the modulus of the

thin coating and, hence, this vibration method is unsuit-

able for the determination of the storage modulus of the

coating. By contrast, t he shear deformation of a loosely

woven impregnated braid depends much more on the

polymer than on the glass, so that the total stiffness in

shear is determined mainly by the polymer. This situa-

tion changes only when the polymer has a very low

stiffness, as, e .g . , a liquid polymer.

As far as th e determination of the modulus is con-

cerned , the torsional braid also has .a more favorable

geometry than the impregnated strip of blotting paper,which has been applied by Koleske and Faucher (133-

135). This does.not detract from the suitability of the

latter method for the determination of the glass transi-

tion temperature of low molecular weight compounds,

because the glass transition is accompanied by a very

large decrease in modulus.

The supported technique used by Fava and Chaney

(136), in which the polymer is encapsulated in a rigid

matrix of a phenolic resin, is suitable only for the location

of loss peaks and does not permit the determination of

the storage modulus.

We conclude that, among the supported techniques,TBA is particularly suited to the observation of changes

in modulus with temperature. Nevertheless, it should

be borne in mind that the method gives only relative

values and that the ratio of the relative to the real shear

modulus is not a constant. As Gillham puts it (Ref. 127,

p. 165) “the relative rigidity curves are not quantita-

tively relative and are squashed non-linearly”. This is

particularly evident in the glass transition of amorphous

polymers: going from the glassy to the rubberlike state,

the modulus decreases by a factor of the order of 1000,

whereas TBA yields only a factor of about 10 (compare,

e.g. , t he curves for the poly(methacry1ates) in Ref. (137)and Ref. (138) with those in Ref. (17) or Ref. (32);see

also, Figs. 6a and 6b).Therefore, considerable caution

should be exercised in drawing quantitative conclusions

from TBA data on G’ or the loss modulus G” = G’ tan 6

(138, 139). As we will see in the section on the liquid-

POLYMER ENGINEERING AND SCIENCE, MID-AUGUS T, 797 9, Vol. 19,No . 70 667



J. Heijboer

liquid transition, the situation for polymer melts is not

yet settled. In the glassy region the relative modulus-

temperature curve is much less distorted. Hartmann

and Lee (140)maintain that in this region the multiplica-

tion factor between the relative and the absolute

modulus is a constant. However, a closer examination of

their Fig. 6 reveals that this conclusion is a rather op-

timistic one: in the temperature range from -160 to

+20° C , where the absolute modulus decreases by 45

percent, the multiplication factor already increases by

about 8 percent.

Another restriction of the torsional braid method is

due to the fact that the frequency changes with tempera-

ture, owing to the changing stiffness. This, however,

applies to most conventional torsion pendulums. To

obtain data at a constant frequency, one has to apply

different moments of inertia and to interpolate the re-

sults to a constant frequency. TBA usually gives data

near 1 Hz.

For a further comparison of TBA with the torsionpendulum and with the Rheovibron, we refer to Boyer

(141). In this connection it should be ment ioned that , in

spite of considerable effort (142-144), absolute modulus

values obtained by Rheovibron are less reliable than

those obtained by the conventional torsion pendulum

(114). The Rheovibron and the torsional braid instru-

ment are very suitable for finding the exact values of

transition temperatures.

EXAMPLES O F TH E APPLICATION OF

TORSIONAL BRAID ANALYSIS

In the foregoing, I have stressed the great versatility of

TBA. The number of papers describing the technique

and its results has already exceeded 100.

I shall now proceed to present a general survey of the

topics tackled by Professor Gillham and coworkers by

means of TBA, and to compare a few of their results with

our own torsion pendulum measurements.

To start with epoxy-crosslinking systems: Gillham and

coworkers (127, 145-151) have increased the under-

standing of these systems by showing that in isothermal

curing two characteristic temperatu res can be observed:

an upper temperature, above which the material only

gelates and does not vitrify, and a lower temperature,below which the material only vitrifies. Between these

temperatures the two processes, gelation and vitrifica-

tion, are seen as separate loss peaks in the time-loss

curve during curing.

The influence of catalyst content on phase separation

in rubber-epoxy systems can also be understood from

results of TBA. At this symposium, the subject of

crosslinking systems will be introduced by Professor

Gillham himself (151).

TBA has proved to be particularly useful in the study

of the high-temperature polymers. The classical exam-

ple is polybenzimidazole (127, 152). Extensive investi-gations have been made into the effect ofchemical struc-

ture on the properties of polyimides (127, 153-155).

The formation of the tough poly(chromium I11

triphosphinate) from th e brittle poly(chromium I1

biphosphinate) could also be followed by TBA (156).The

effect of various fluorinated side groups R on the melt-

ing, the glass transitions and the subglass transitions of

polyphosphazenes, [NPR2],, have been studied on

homopolymers, copolymers, and polymer mixtures

(157, 158).

Roller and Gillham (127, 159-162) have made a very

extensive study of silicon-based high-temperature elas-

tomers, containing carborane cages (CB5H5C and/or

CBIoHIoC)n their polymer chain. They studied glass

temperatures, crystallization and thermal stability in

nitrogen and air. This investigation neatly illustrates the

wealth of information that- can be obtained on small

amounts of exotic polymers by TBA. These high-

temperatu re elastomers, and also the polyimides, often

crosslink at high temperatures. This crosslinking is

unambiguously revealed by TBA. So the technique is

particularly suitable for selecting systems having op-

timum high-temperature properties.

TBA has demonstra ted an unexpected relationship

between glass temperature and structure in two series ofpolyolefins, viz.

CH3

+(cH~)nJ-~rnIR

with n = 1,2, and 3, and R = CH3 or C2H5 (127, 163).

Figure 4 assigns the T , values obtained by Martin and

Gillham to the polymers in question.

It is very surprising that in both series an increase in n

from 1 to 2 is accompanied by an increase in T,; one

would, by contrast, expect a greater flexibility of the

main chain for n = 2. However, when the number of

interceding methylene groups is increased from two to

three, T , decreases as expected. To explain the

maximum in T , for n = 2, Martin and Gillham intro-

duced the concept of intermolecular interlocking. In the

first member of each series, the side groups shield the

main chain from the approach of neighboring chains; for

n = 2, the re is just space enough for two main chains to

T IKI OF P O L Y O L E F I N S

2 5 3 I 2 6 8 1 2 78 258

I296

Fig. . Glasr temperatures T,,(i n K ) of polyolejins, de terminedby T B A a nd by the torsion pendu lum ( i n paren theses ) .

668 POLYMER EN GINEERING AND SCKNCE, MID-AUGUST, 1979, Vol. 19 , No . 70




fit nicely together at contact points between th e side

groups, whereas for n = 3, there is more space left,

resulting in a higher mobility. Martin and Gillham argue

that intermolecular interlocking can also manifest itself

in a lower density.

The rise of T , (forn = 1and n = 2) found when R =

methyl is exchanged for R = ethyl is also unexpected.

However, it does fit the concept of interlocking: the

lower symmetry of the chain favors interlocking.

At TNO we measured by torsion pendulum the first

number of the second series: poly(2-methylbutene-1),

and also the corresponding polymer with an n-propyl side

group: poly(2-methylpentene-1) (164).Our T , values are

included (in parentheses) in Fig. 4 . The storage and loss

moduli are given, as functions of temperature, in Fig. 5 .

Considering the greater flexibility and length of

n-propyl, we were quite surprised to find an increase in

T , when it was substituted for ethyl. This curious finding

may perhaps be explained by the interlocking concept:

n-propyl groups protrude farther from the main chain,which therefore interact more strongly with neighbor-

ing chains. The puzzling fact that the polymer with the

lower modulus in the glassy state has a higher T , points

in the same direction: interlocking reduces the density

and, hence, the modulus in the glassy state.

Closely related to the concept of interlocking is that of

the sweeping volume (32), i.e. , the volume required for

the motion of the main chain parts at the glass transition.

l o s

10

10

lo 6

X G '

0 G "

7. 7 Hz

-,"c

I -700 0 100

Fig.5. Storuge niodulus in sheur, G', an d Loss modulus, G", u t

a b o u t I H z a s a f u n c t i o n of t e m p e r a t u r e , 8, of poly(2-

methy lbutene -1 ) und po l !y (2 -me thy lpentene - l ) .

This concept explains why bulky stiff side groups will

cause an increase of T,, whereas long flexible side

groups, which can easily accommodate themselves in

the available space, will cause a decrease of T,. The loss

curves in Fig. 5 show no appreciable increase in the

damping in the region of -180°C when R = ethyl is

substituted by R = n-propyl. This indicates that the

n-propyl group has a rather low mobility. When the side

group is further lengthened, the effect of flexibility willdominate, and T , will decrease.

Returning to Gillham and Martin we note that these

investigators, in cooperation with Hiltner and Baer of

Case Western Reserve University (165), have measured

the two series of polyolefins mentioned above down to

liquid-helium temperatures to study their secondary

loss peaks. They attributed the loss peaks observed at

about - 10°C forn = 2 and 3 to local main chain motion,

and the one observed near - 60°C to the motion of the

ethyl side group.

Other polyhydrocarbons studied by TBA are 1,5-polypentamers (166), -(C HZCHzCH2CH=C H-)n.

These have low T,'s, viz., - 09 and -95"C, depending

on ratios of cis- to trans-isomer, which are 98 to 2 and 18

to 82 respectively. The polymer with the higher trans

content tended to crystallization. Poly(2,5-

norbornadiene) (167)has a very high T,, viz., 320°C and

a broad low-temperature loss region, with peaks at about

-150°C and about -60°C.

Poly(ethy1ene carbonate),

--(CHZ--CHz--0<--0-),,

II0

has a T , of 22"C, poly(propy1ene carbonate),

-(CHz--CH-0-C-0-),, of 41°C (168). The glass

I IICH3 0

temperature is raised by the introduction of the methyl

side group. This is in contrast with poly(ethy1ene oxide)

(T, = -57"C), compared with poly(propy1ene oxide)(T ,

= -62°C) (169), but agrees with the T,'s of polyethylene

and polypropylene. Poly(ethy1ene carbonate) and

poly(propy1ene carbonate) both have a pronounced sec-

ondary maximum near -85"C, which for the former

polymer is about twice as high as for the latter.

Polymethacrylates of various tacticities have been ex-tensively investigated by TBA (127, 137, 138).Isotactic

poly(methy1 methacrylate) (PMMA) has a much lower T ,

than the syndiotactic polymer, the difference being

about 70 K . For poly(t-butyl methacrylate (PtBuMA)

this difference is very small, viz., only a few degrees.

The secondary loss peak of PtBuMA lies at the same

temperature as that of atactic PMMA, but is much

lower. The secondary loss peak of isotactic PMMA is

much lower than that of atactic PMMA.

To explain this difference in T , of the PMMA's, Gill-

ham again invokes the interlocking concept: in fact of

the two polymers isotactic PMMA has the higher den-sity and the higher modulus in the glassy state (17), and

the lower T o .Figure 6 compares results of torsion pendulum (17)

and torsional braid measurements (138)on atactic and

isotactic PMMA. The curves ofFig. 6b are derived from

POLYMER ENGINEERING AND SCIENCE, MID-AUGUST, 197 9, Vol. 19, No. 10 669



3 . Hegboer

TP 1Hz

_ _ _ o t o c t P M MA- s o t a c t P M M A

T / K I

TO O 200 3 0 0 LOO 500

( 0 )

T E A- _ _ a t a c t . P M MA

__ i s o t a c t P M M AI

l o 7 - - 01

__j l K lI100 20 0 300 LOO 500

(6)

Fig. 6. M o d u l u s , G', a n d d a m p i n g , t a n 8, a s a f u n c t i o n of t e m -

perature, T , of atac t ic and i so tac ti c po ly ime thy l me tha cy l a te ) .

a . A t 1 H z , a s d e t er m i n e d b y t h e t o r s io n p e n d u l u m . b. A s deter-mined b y tors ional bra id analysi s ( r e la t i ve ualues ).

Figs. 1 and 3 of Ref. (138).The modulus values are only

relative ones. The values of tan 6 have been obtained by

dividing the absolute logarithmic decrement by T.

Figure 6 shows that the p-maximum measured by

TBA is about 25 percent lower than that measured by

the torsion pendulum; the difference is due to the glass

content of the torsional braid. This relative lowering of

the damping is fairly constant below the &maximum,

but strongly increases in the region of the glass transi-

tion, where it amounts to a factor of 3 or more. In

addition, the relative modulus curve obtained by TBA is

distorted considerably in the glass transition region; the

modulus decreases by only about one decade rather than

3 decades.

Another interesting structure-property relationship

that has been studied by TBA (170-171) is the effect of

fluorocarbon groups R , and R z in bibenzoxazole poly-

mers of the formula

r 1

In the glassy region, these polymers show two sec-

ondary loss peaks, which were assigned to a specific

group: in the R , position -(CF&- gives rise to a

maximum at about -35°C and -(CF2)20(CFz)sO-

(CF&- to one at about -8O"C, in the R z position

-(CF&- gives a maximum at about -130"C, and

-(CFJIor 40(CF2)20CFz- one at about - 150°C.

Ether oxygen enhances the flexibility of a -(CFZ)n-

group, and the motion of groups in the R1 position is

more restricted than that in the Rz position. I t is remark-

able that a group as long as 11 chain atoms should still

experience such a strong influence of the linkages at itsends on its mobility: the two positions R , and R z cause a

difference of about 60 K in the temperature of the loss

peak. In their mobility, the fluorinated side groups in

the polyphosphazenes (158)are more like the groups in

position R z than like those in position R1, their loss peaks

lying in the region of -150°C to -180°C.

We now conclude this survey of structure-property

relationships studied by Professor Gillham and cowork-

ers by means of TBA, by mentioning that the equip-

ment is also suitable for measuring the effect of other

atmospheric environments, e.g., humid air, on the

dynamic mechanical properties of polymers. Examplesare the study of the effect of water on polyimides (127,

154, 172), PMMA (131) and polypeptides (173). The

effect of water on polypeptides is particularly strong, as

is shown by the interesting paper by Hiltner and Baer

(174),presented a t this symposium.

For literature on TBA before 1972, we refer to the

extensive survey paper by Gillham (127).The examples

given above clearly show how successfully Professor

Gillham and coworkers have applied their technique to a

variety of subjects.

THE LIQUID-LIQUID TRANSITION

As early as 1963, Boyer (175)drew attention to evi-

dence of a transition in melts of polymers at a tempera-

ture above their glass transition. This he called the

liquid-liquid transition, T I [ .An example observed in

67 0 POLYMER ENGINEERING AND SCIENCE, MID-AUGUST, 1979, Vol. 19, NO. 10



The Torsion Pendulum in the Invest igation of Polymers

torsion pendulum measurements was the separate loss

peak in styrene-butadiene rubber near 280 K .

TBA clearly showed a loss peak in melts of mono-

disperse polystyrenes, and this observation prompted a

series of papers by Gillham, Boyer and coworkers on

studies of T t t by means of TBA (176-183).They investi-

gated monodisperse polystyrenes (176), mixtures ofmonodisperse polystyrenes (177), polystyrenes with

plasticizer (178, 179) and block-copolymers of styrene

(180, 182)with other monomers. A linear correlation has

been found between T t l and M;’, the inverse of the

number average molecular weight. Evidence for a

liquid-liquid transition has also been found in other

ways, e.g. , by DSC, by rheological measurements and

measurements of solubility and diffusion (181, 183-186).

In addition to polystyrene, many other polymers show

evidence of a Ttt-transition (181). Gillham and Boyer

(181) give a general review.

In this paper, I will restrict myself to the rheologicalaspects of T u. I will show how data obtained by TBA

compare with those obtained with a concentric-cylinder

viscometer, which measures physically well-defined

magnitudes. Den Otter (187) of TNO has developed a

very sensitive concentric-cylinder viscometer, which

enabled us to measure even the loss modulus ofcetane a t

25°C with an accuracy of 5 percent. By means of this

instrument we hoped to obtain interesting information

on the liquid-liquid transition. Den Otter (188) and

Wales (189)have published data on polystyrene (PS) and

polyethylene melts, obtained with the instrument.

To enable a good comparison to be made with dataobtained by TBA we investigated an atactic

“monodisperse” PS of Pressure Chemical Co., M , =

20,200, which had also been measured by Stadnicki,

Gillham and Boyer (176).Mr. J . L. B. de Groot at TNO

kindly performed the measurements. He immediately

ran into serious dimculties. As a rule, we fill our vis-

cometer by machining a cylindrical sample into a tube,

which exactly fits the gap of the viscometer. However,

this polystyrene sample proved to be too brittle to

machine. On the other hand its melt was too viscous to

fill the viscometer perfectly and tenaciously retained

some bubbles of air. We were therefore able to obtainaccurate data only for the loss modulus in shear, G ”, bu t

not for the storage modulus, G’. G” was measured at 9

temperatures and 3 frequencies. The reproducibility of

the results was checked by repeating a measurement at

an intermediate temperature after completion of the

series of measurements at increasing temperatures. The

results are given in F i g . 7 , together with data on the

relative loss modulus, calculated from curves of the

relative rigidity and the logarithmic decrement in Fig.

12 of Ref. (176). The loss modulus of the polymer mel t

can be seen to decrease sharply with temperature with-

out showing any clear-cut indication of a plateau or amaximum. By contrast, the loss modulus of the combi-

nation of support and polymer shows a T ll maximum at

420 K , 0.3Hz; at higher temperatures it levels off. From

this it follows that the G&l obtained by TBA dfiers

completely from the true G ” of the polymer melt.

P 5 , M n - 20,200

m e l t

t

T. K

3 5 0 LO O L 50 5

F i g . 7 .Loss modulus in shear , G“ , s a func t ion of t emperature ,T , at three f r equenc ies fo r m onodisperse P S M , = 20,200, d e-termined by a concen tr ic -cy l inder u iscometer, compared w i ththe re la t i ve modulus , G‘lrvl,btained b y tors ional braid analys isof t h e s am e p o l y m e r .

We would have preferred to compare tan 6 values ofthe torsional braid with tan 6 values of the polymer melt,

but the latter values were not available. However, a

comparison could be made for two polymers with an M ,

of about 200,000, viz., polystyrene S 111 of Dow Chemi-

cal Co., M , = 214 x lo3,M J M , = 1.04,which has been

measured by den Otter (188),and the very similar PS of

Pressure Chemical Co,, with M , = 193 x 103, which has

been measured by Stadnicki, et al . (176). From our

original data on G“ and G ‘,we calculated the tan 8values

of PS S111; these are shown in Fig. 8. Figure 9 shows

that the data could be reduced surprisingly well to a

master curve by horizontal shifts.

Figure 10 shows the shift factor, log uT, with respect

to 413 K) plotted as a function of the inverse of the

O S S l l l , M n . 1 L x l o 3

A

Fig. 8. T a n 6 a s a f u n c t io n of circular frequen cy w at threetemperatures , fo r P S S111.

POLYMER ENGINEERING AND SCIENCE, MID-AUGUST, 1979 , Vol. 19, NO. 10 671



J. Heijboer

P S M , z 200,000

Fig . 9. Tun 6 u s u func tio n of reduced frequ ency waT, t 4 1 3 K f or

PS s111.

+ PS M n = 11.000 “f , xed f l u i d

0 PS M, =20.200

l o g o , I 1 7 3 K I

/,o/

/

“/+

2 2 2 3 24 2 5

Fig. 10. Shiftfuctora,asu function ofli? ’for tan SofPS S111,

M , = 214,000, and fo r G ” of P S M , = 20,200.

absolute temperature, T . The figure also shows the shift

factor for G” vs o or the PS with M , = 20,200. Interest-

ingly, the two shift factors practically coincide. The

slope of the curve is a measure of the activation energy of

deformation. According to Gillham and Boyer, in the

whole temperature range shown, the PS with M,, =

214,000 is expected to be what they call a “fixed fluid.”

On the other hand, th e PS with M , = 20,200would be a

“fixed fluid’ at low temperatu res, and a “true liquid” at

high temperatures; the expected transition temperature

is indicated by a dashed vertical line. If this were true,one would expect a change in the activation energy at

the transition temperature. However, our data reveal no

such change.

As the measurements on PS S l l l had been taken at

large tempera tur e intervals, it was impossible to draw a

detailed curve of tan 6 (at a single frequency) as a func-

tion of temperature. However, with the aid of the mas-

ter curve (Fig. 9) and the shift factor (Fig. 10)we could

construct a reliable tan 6 vs T curve for a given fre-

quency. The curve for 0.3Hz is given inFig. 11 together

with that oftan 6 for PS M , = 194,000obtained by TBA.

(The latter data have been calculated from Fig.14

of Ref.(176)).Once more it is seen that the torsional braid gives

no reliable picture of the dependence of the losses of a

polymer melt on temperature: tan 6 (TBA) increases byonly about half a decade over a temperature range of 50K , whereas the real increase is more than 1%decades.

10

7

07

G “ I P o l

to n 6

to n 6

1

\-

\- ( K I \

\

35 0LOO

L 5 0 50 0

Fig. 11. Tun 6 und G ” of PS M , = 214,000, determined by a

cot icentr ic-cyl inderviscometer , compared wit h tan Sof P S M , =

194,000, obtained by torsional braid analysis.

Our data are in agreement with Nielsen’s ideas (190)and

with the old measurements of Cox, Isaksen and Merz

Figure 11 also shows the GI’ vs T curve of PS S l l l at

0.3 Hz. This curve has been obta ined from the reduced

loss modulus G! together with the pertinen t shift factors

(188).G! vs log w shows a flat maximum, as is usual for

monodisperse polystyrenes with a molecular weight

higher than a critical value, M, . This maximum indeedproduces a corresponding maximum in the G ” vs Tcurve, which is shown in Fig. 11 . However, it is difficult

to assume acorrelation between the latter maximum and

that obtained by TBA, because the re is a difference of at

least 40 K between their temperatures. Moreover, the

plateau in G ! vs o s not seen in polymers of lower

molecular weight, e.g., 37,000 (see Marin and Graessley

(191)),which do, however, clearly show a T , (compare

also Fig. 7; no plateau in G “ is seen).

We conclude that the torsional braid measures

neither G” nor the logarithmic decrement of the poly-

mer melt. What it does measure is not yet clear.Nevertheless, there can be no doubt about the existence

of a systematic correlation of T I [with M,. The puzzle

remains which physical quantities of the melt govern

this correlation.

As the activation energies below and above Tl1 are

practically the same, I do not think it is semantically

justified to call T l l the transition between a fixed fluid

and a true liquid.

(7).

CONCLUSIONS

In the hands of Professor Gillham and coworkers,

torsional braid analysis has proved tobe

a powerful

method, which has opened up new areas for the success-

ful application of the torsion pendulum. However, care

has to be taken in the quantitative interpretation of the

rigidity data obtained by TBA, especially in the region of

the glass transition. In addition, the technique goes

672 P O L Y M E R E N G IN E E R IN G A N D S C I E N C E , M I D - A U G U S T , 1979, V o l . 19, N O . 10




wrong if one at tem pts to use it for measuring the relative

shear modulus or relative losses of a polymer melt.

44. B. Maxwell, J . Polym. Sci., 20, 551 (1956).

45. K. Deutsch, E. A. W. Hoff, and W. Reddish,]. Polym. Sci.,

13, 565 (1954).

1.

2.

3.4.

5.

6.

7.

8.9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.39.

40.

41.

42.

43.

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