Morphological Behaviour of Thermoplastic Polyurethanes During Repeated Deformation

Morphological Behaviour of Thermoplastic

Polyurethanes During Repeated Deformation

Peter R. Laity,*1 Jennifer E. Taylor,1 Steven S. Wong,2 Peck Khunkamchoo,2 Martin Cable,3

Geoffrey T. Andrews,3 Anthony F. Johnson,2 Ruth E. Cameron1

1 Department of Materials Science and Metallurgy, University of Cambridge, New Museums Site,Pembroke St. Cambridge, CB2 3QZ, UKE-mail: [email protected]

2 IRC in Polymer Science and Technology, School of Chemistry, University of Leeds, LS2 9JT, UK3 Ranier Technology Ltd. Greenhouse Park Innovation Centre, Newmarket Rd. Cambridge, CB1 5AS, UK

Received: October 6, 2005; Revised: January 12, 2006; Accepted: January 19, 2006; DOI: 10.1002/mame.200500339

Keywords: mechanical properties; morphology; polyurethanes; small-angle x-ray scattering (SAXS)

Introduction

It is generally accepted that the mechanical properties of

thermoplastic polyurethanes (TPUs) depend on their micro-

phase-separated morphologies, which develop due to immi-

scibility between ‘hard’ urethane-containing segments

(HS) and more flexible ‘soft’ segments (SS).[1–12] The HS

microdomains act as physical crosslinks and reinforcing

filler particles, while the SS microdomains impart elastic

properties.

To a first approximation, the mechanical properties

of TPUs appear ‘rubberlike’. The stress-strain curves of

softer TPUs can be fitted well using hyperelasticity

models,[11] such as that described recently by Kluppel and

Schramm:[13]

s ¼ Gcðl� l�2Þ

�(

1 � z

½1 � zðl2 þ 2l�1 � 3Þ�2� z

1 � zðl2 þ 2l�1 � 3Þ

þ Geðl�1=2 � l�2Þ)

ð1Þ

where s is the engineering stress (force divided by initial

cross-section area) and l is the extension ratio, which is

Summary: SAXS was used to investigate the morphologicalresponses of two commercial thermoplastic poly(ether-co-urethane) elastomers during repeated uniaxial extension andstress-relaxation at constant strain. Experimental data wasanalysed using a ‘globular’ morphological model, which haspreviously been shown to provide a good interpretation of theSAXS from these polymers. The results indicated thatmicrodomain rotation and fragmentation coincided withand may have contributed to the strain-softening observedduring the initial deformation cycles and stress relaxation.However, these morphological changes appeared to belargely reversed, when the material was allowed to retract;consequently, they appeared insufficient to account for thedramatic changes in mechanical properties and permanent setobserved between the first and second extension cycles. Onepossible explanation is that the mechanical properties mayhave been dominated by a few, larger microdomains that weretoo large to be observed by SAXS. Alternatively, theconsiderable changes in scattering intensity suggested a

mechanism based on the slippage of entanglements as a resultof strain-induced segmental mixing.

2D-SAXS patterns of poly(ether-co-urethane)s duringsecond uniaxial extension.

Macromol. Mater. Eng. 2006, 291, 301–324 � 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Full Paper DOI: 10.1002/mame.200500339 301

related to engineering strain (l¼ 1þ e). This model relates

the mechanical properties to the effects of permanent

crosslinks and topological constraints imposed on the

polymer chain within the tube model, which are described

by Gc and Ge respectively. The contribution from topo-

logical constraints may be significant at low strain, but

decreases as the chains become progressively less con-

voluted at higher strain. By contrast, the contributions from

permanent cross-links increase progressively with strain.

The degree of trapped entanglement (z) is expressed in

terms of the Langley trapping factor (Te)[14] divided by the

number of statistical chain segments between successive

entanglements (ne). This produces a singularity at:

ðlþ 2l�1 � 3Þ ¼ z�1 ð1aÞThe increase in s as this singularity is approached repro-

duces the observed strain hardening, which may be ascribed

to the finite extensibility of chain segments between trapped

entanglements.

The stress-strain curves of harder TPUs tend to exhibit

more pronounced ‘yielding’ or ‘strain-softening’ behav-

iour.[11] This is not described well by existing theoret-

ically-derived models, although it can be fitted using semi-

empirical models, such as those described by Meissner

and Spırkova.[8] Moreover, pre-straining causes a consid-

erable amount of residual strain or ‘permanent set’ (i.e.

the unloaded sample is elongated, compared with its

original unstrained length), while repeated straining

cycles produce significant changes in mechanical proper-

ties, similar to the work-softening of filled rubbers (the

Mullins effect). These phenomena have long been

attributed to HS microdomain fragmentation,[15] largely

by analogy with the mechanical behaviour of filled

rubbers.[8]

Figure 1. Stress-strain curves for duplicate measurements on P55D (a) and P80A (b)during first and second uniaxial extension (samples allowed to retract immediately)and curves generated using the Kluppel-Schramm model (dashed lines).

302 P. R. Laity et al.

Macromol. Mater. Eng. 2006, 291, 301–324 www.mme-journal.de � 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

The present work investigated the morphological res-

ponses of TPUs during deformation and whether this might

provide an explanation for the observed mechanical

behaviour. Changes in morphology were observed in ‘real

time’, by small-angle X-ray scattering (SAXS) using a

synchrotron source. A common limitation of SAXS studies

is that interpretation of the observed scattering patterns is

seldom unequivocal and relies on a prior knowledge of the

morphology under investigation. In the present work, the

scattering patterns were analysed using a ‘globular’ model

consisting of dispersed HS microdomains within a mixed

HSþ SS matrix. Previous investigations have demon-

strated that this model is capable of reproducing the

scattering patterns observed from TPUs of the type studied

here and provides plausible interpretations of the morpho-

logical responses to uniaxial extension.[9–11,16,17]

Initial investigations[9] suggested that the main features

of the SAXS patterns could be explained by assuming that

the size and shape of dispersed HS microdomains remained

constant, while their centres of mass of moved according

to affine deformation of a statistical lattice. Subsequent

work[17] showed that the effective size and shape of the

dispersed microdomains were also affected when the TPUs

were deformed. Small strains caused the microdomains to

become elongated in the stretching direction and shorter in

the transverse direction. An explanation involving rotation

of anisometric microdomains was proposed, since the

modulus of the dispersed HS phase is expected to be

considerably higher than the continuous HSþ SS matrix;

however, deformation of the HS microdomains cannot be

completely ruled out. Microdomain fragmentation was also

indicated at higher strains, which implied significant stress-

transfer and suggested a tentative link to the mechanical

softening behaviour.

The present work extended this work by analysing

the morphological behaviour in four sequential stages: (i)

uniaxial extension from the virgin state to e¼ 1.5; (ii) stress

relaxation at constant strain; (iii) retraction to zero residual

stress; (iv) a second uniaxial extension. Further evidence

of microdomain fragmentation is given, while the implica-

tions of strain-induced local density variations and segmental

mixing are examined. A morphological interpretation of the

diagonal four-spot SAXS patterns exhibited by these TPUs on

retraction after the first strain cycle is also presented.

Experimental Part

Materials and Sample Preparation

Experiments were performed using Pellethane1 2363-55Dand 2363-80A poly(ether-co-urethane)s (Dow Chemical Co,Midland MI, USA), with 55% and 44% HS respectively, which

Table 1. Mechanical and morphological results for TPU samples in unstrained or relaxed states.

P55DInitial unstrained Relaxed, after holding at e¼ 1.5 for

0 min 20 min 60 min

Young’s modulus/MPa 58� 12 38 25 20Residual strain 0.23 0.32 0.38Kluppel-Schramm Gc/MPa 1.2� 0.1 5.1 4.2 4.2model Ge/MPa 27.2� 0.1 3.3 4.2 3.9

z 0.10� 0.01 0.09 0.10 0.11Strain direction d/nm (expected)a) 9.3� 0.2 9.8 (11.4) 10.3 (12.3) 10.5 (12.9)

R/nm 3.3� 0.1 3.3 3.2 3.2Transverse direction d/nm (expected)a) 9.3� 0.2 8.5 (8.4) 8.4 (8.1) 8.2 (7.9)

R/nm 3.3� 0.1 3.1 3.0 3.0I0 normalised 1.00 0.71 0.69 0.63

(expected)a) 1.00 0.90 0.87 0.85

P80A Initial unstrained Relaxed, after holding at e¼ 1.5 for

0 min 20 min 60 min

Young’s modulus/MPa 16� 1 11 12 10Residual strain 0.06 0.14 0.20Kluppel-Schramm Gc/MPa 0.6� 0.1 1.1 1.0 1.4model Ge/MPa 11.7� 0.1 5.4 4.2 3.2

z 0.08� 0.01 0.12 0.10 0.09Strain direction d/nm (expected)a) 11.7� 0.2 12.1 (12.4) 12.5 (13.3) 12.3 (14.1)

R/nm 3.7� 0.1 3.7 3.6 3.6Transverse direction d/nm (expected)a) 11.7� 0.2 11.4 (9.0) 11.1 (8.7) 10.7 (8.5)

R/nm 3.7� 0.1 3.6 3.5 3.6I0 normalised 1.00 0.91 0.77 0.76

(expected)a) 1.00 0.97 0.94 0.91

a) Expected values calculated from residual strain, assuming affine deformation of statistical lattice and no microdomain fragmentation.

Morphological Behaviour of Thermoplastic Polyurethanes During Repeated Deformation 303


Figure 2. 2D-SAXS patterns at selected strains collected during initial uniaxial extension(strain direction vertical).



were provided by Ranier Technology Ltd. Cambridge (UK).These materials (designated P55D and P80A) were selectedbecause they exhibited suitable mechanical toughness andgave well-resolved SAXS patterns. Both contained polyether

SS derived from poly(tetramethylene oxide) (PTMO) inter-spersed with short semi-aromatic urethane HS derivedfrom 4,40-methylenediphenyldiisocyanate, chain-extendedwith butane-1, 4-diol (MDIþBDO).

Figure 2. (Continued)



Sample preparation was as described previously.[17] Thinfilms (approximately 0.35 to 0.4 mm thickness) were obtainedby hot-pressing at 220 8C and quenching in iced water.Rectangular specimens (approximately 10� 40 mm) werecut using a scalpel and steel rule, then annealed at 135 8C for 4 hto develop the microphase-separated morphologies.

Mechanical Deformation Experiments

Stress-strain measurements were performed using a ‘Minimat’miniature materials testing apparatus (Polymer Labs. Shrop-shire, UK). Specimen thickness (s), width (w) and gauge lengthbetween the Minimat jaws (L0) were measured using caliperswith a vernier scale. Engineering stress (s) and strain (e) were

calculated from the measured force (F) and jaw displacement(x) from the starting position, according to:

s ¼ F

s � w ð2aÞ

e ¼ x

L0

ð2bÞ

The specimens were initially deformed in uniaxial extensionunder ambient condition, to e¼ 1.5, at a strain rate of de/dt¼0.15 min�1. In some cases, the specimens were allowed toretract immediately, by releasing one of the jaws. In othercases, stress relaxation measurements were made while thespecimens were maintianed at e¼ 1.5, for 20 or 60 min before

Figure 3. Meridional (a and c) and equatorial (b and d) 1D-scans through 2D-SAXSdata collected during first uniaxial extension.



being allowed to retract. The gauge lengths of the retractedspecimens (LR) were measured, in order to calculate theresidual strain due to permanent set:

eR ¼ LR � L0

L0

ð3Þ

Then, the sample was subjected to a second uniaxialextension to e¼ 1.5.

SAXS Measurements and Interpretation

Two-dimensional scattering measurements (2D-SAXS) wereperformed during deformation experiments at station 16.1 ofthe synchrotron radiation source (SRS), Daresbury. Methods ofdata acquisition and correction for background scattering wereas described previously.[16,17]

The SAXS data was analysed using a ‘globular’ scatteringmodel, which is described in more detail elsewhere.[9–11,16,17]

This model treated the scattering as the product of a particlefunction and a structure factor:

IðqÞ ¼ I0 � PðqÞ � SðqÞ ð4Þ

where q is the modulus of the scattering vector:

q ¼ 4po

sin y ð4aÞ

where 2y is the scattering angle ando is the X-ray wavelength.I0 was regarded as a scaling factor, which depended on theintensity of the X-ray illumination, acquisition time andilluminated sample volume, as well as the volume fraction (f)and electron density contrast (Dr) between scatterers. It should




be noted that this model refers to the effective distributionsof size, shape, orientation and spacings for populations ofscatterers and not individual microdomains.

To a first approximation, the population of HS micro-domains in isotropic samples may be treated as a collection ofmonodispersed spheres with effective radius, R:

PðqÞ ¼ 9 � sinðqRÞ � qR cosðqRÞðqRÞ3

( )2

ð5Þ

In mechanically deformed samples, however, the popu-lation of scatterers became oriented with their longer axespredominantly towards the stretching direction. This wasincorporated into the model by allowing R(j) to depend on theangle j between the scattering vector and direction of appliedstrain.

The structure factor may be described equally well assuminga distorted one-dimensional statistical lattice (Zernike-Prins,ZP model) or using a more sophisticated description of liquid-like structure (Percus-Yevick, PY model).[16,17] The deriva-

tions of these models are somewhat different: the former isbased on simple geometric assumptions, while the latterattempts to incorporate thermodynamic interactions. Never-theless, the essential difference between them lies in theunderlying distributions of interdomain spacings. For thepurposes of the work presented here, the description providedby the ZP model in terms of an average projected distance (d)was considered to be more useful, although it is not certainwhether the resulting lengths are absolutely correct. For aGaussian distribution of interdomain spacings, with standarddeviation (d), Hosemann[18,19] showed that:

SðqÞ ¼ 1 � A2

1 � 2A � cosðqdÞ þ A2ð6Þ

where:

A ¼ exp � q2d2

2

� �ð6aÞ

Figure 4. Morphological responses during first uniaxial extension; continuous linesindicate the expected values based on pure affine deformation, the different shadings ofthe symbols represent measurements from duplicate experiments.



Results

Stress-strain curves for P55D and P80A during a first uniaxial

extension from the virgin state and a second deformation

cycle (after immediate retraction) are compared in Figure 1,

along with curves generated using the Kluppel-Schramm

model [Equation (1)]. For ease of comparison, the strain in

both deformation cycles is calculated with respect to the

initial unstrained sample length.

During the initial measurements, the stress increased

relatively steeply at low strain, followed by a broad strain-

softening zone and an almost linear region of lower slope at

intermediate strain. Differences in composition between the

two materials used were reflected in Young’s moduli

(obtained from the approximately linear region below

e¼ 0.03, which are given in Table 1) and the relative heights

of the stress-strain curves.

Attempts to fit the stress-strain data using the Kluppel-

Schramm model were partially successful. It was found that

the model could be fitted to the P80A data very well

(Figure 1b), although this may not be particularly

significant due to the limited strain range used. However,

close examination of the P55D data showed that the model

was unable to exactly reproduce the more pronounced

strain-softening behaviour of the harder formulation (as

indicated in Figure 1a). Similar discrepancies at low strain

have been reported previously for comparable TPUs.[11]

Furthermore, it was shown that fitting the Kluppel-

Schramm model to experimental data above the strain

softening zone resulted in a discrepancy at low strain, which

increased with the HS content and was attributed to an

additional work of deformation component that was not

included in the model. The values of the parameters

obtained by curve-fitting the model to the initial deforma-

tion cycle data are given in Table 1, indicating that tube-

constraint effects dominated the mechanical behaviour of

the virgin samples.

Repeated experiments showed reasonably good reprodu-

cibility. Consequently the changes observed in the mechanical

behaviour from the first to the second extension cycles were




highly significant. Both TPUs exhibited considerable perma-

nent set, causing the origins of the second stress-strain curves

to be displaced along the strain axis. The pre-strained samples

exhibited considerably smaller Young’s moduli, compared

with the virgin materials, and appeared to undergo stress-

softening almost immediately, during the second extension

cycles. These effects appeared greater with the harder TPU

formulation and increased with stress-relaxation times, as

shown in Table 1.

However, after the relatively slow initial stress increase

and subsequent softening observed in the second exten-

sions, the samples exhibited considerable strain-hardening

above e¼ 0.8, such that the second extension curves inter-

cepted the initial curves around e¼ 1.5. These results

appeared consistent with recent work by Meissner and

Spırkova,[8] who showed that the stress-strain curves

for first and second deformation cycles converged

beyond the ‘pre-strain’. The Kluppel-Schramm model

was able to fit the stress-strain data from second

deformation cycles fairly well, up to the point where they

intercepted the initial curves, although any attempts to

model the convergence beyond the pre-strain were

unsuccessful.

The parameters obtained during the second extension

cycles are also shown in Table 1. The degree of trapped

entanglements appeared largely similar during the first and

second extension cycles; however, Ge decreased signifi-

cantly while Gc increased for the pre-strained, relaxed

samples. This was more pronounced for the P55D material,

where the effects of Gc appeared to dominate the second

deformation. These results suggested that the tube-

constraints were decreased by the first deformation cycle,

while the effects of cross-links became more important. In

the theory presented by Kluppel and Schramm,[13] Gc

and Ge are inversely proportional to the chain length

between cross-links and the tube radius respectively. An

Figure 5. Changes in scaling factor during first uniaxial extension; data normalisedusing values for unstrained samples to remove differences due to initial samplethickness.



interpretation of the present observations within this

framework is not clear, however.

Morphological Changes DuringInitial Deformation

Selected frames of 2D-SAXS data collected during the

initial deformation cycles for P55D and P80A are compared

in Figure 2. (The narrow horizontal lines observable across

the lower part of some frames were artefacts caused by an

electronic fault on the detector, which did not affect the rest

of the data and were omitted from subsequent analyses.)

The circular rings of highest intensity exhibited by un-

deformed samples indicated isotropic morphologies. The

only significant difference between P55D and P80A was

that the intensity maximum appeared at lowerq in the latter,

indicating larger average microdomain spacing in the softer

formulation.

Similar changes were observed for P55D and P80A at

low strain: the meridional intensity (i.e. in the stretching

direction) increased and the peak moved towards lower q,

while the equatorial scattering (i.e. transverse direction)

decreased and the peak moved to higher q. Hence, the locus

of highest intensity changed from a circle to an ellipse, then

separated into two crescents. These observations were

consistent with previous reports.[9–12,15,17,20]

At higher strain, the SAXS intensities from both mate-

rials decreased. However, while the meridional scattering

from the P55D specimens remained in the form of a single

peak, careful examination of the P80A data revealed

bimodal peaks for e> 1.1. Although bimodal peaks have

been observed for some TPUs under static conditions,[21]

Figure 6. Stress-relaxation after uniaxial extension to e¼ 1.5.



we are not aware of any previous reports describing similar

behaviour during deformation.

Meridional and equatorial 1D-scans corresponding to

selected frames of 2D-SAXS data are presented in Figure 3,

which demonstrate the changes in peak intensity and

position during deformation. The development of bimodal

peaks is clearly evident in the meridional 1D-scans for

P80A (Figure 3c).

The morphological responses to uniaxial extension were

analysed by curve fitting the ZP model [Equation (4)–(6)]

to meridional and equatorial scans, as described previ-

ously.[16,17] Results from samples prior to deformation are

presented in Table 1; subsequent changes in d and R during

the first deformation cycle are presented in Figure 4.

The dispersed HS microdomains appeared to be somewhat

larger and more widely separated in the softer P80A

formulation, compared with P55D. Nevertheless, the two

TPUs exhibited qualitatively similar behaviour during

deformation. At small extentions, the HS microdomains

appeared to become elongated in the strain direction

(Figure 4a and 4c) and to be displaced following approx-

imately affine deformation of the statistical lattice (Figure 4b

and 4d). R and d continued to decrease progressively in the

transverse direction, up to e¼ 1.5. By contrast, significant

changes were observed in the strain direction behaviour for

e> 0.4: the effective radius appeared to peak, then decline

slightly, while d exhibited significant deviations from

expectations based on affine deformation. Similar behaviour

in the strain direction results has been reported previ-

ously,[11,17] which was attributed to microdomain fragmen-

tation, with the fragments bisecting the expected distances

between the original scatterers.

It was assumed that the bimodal meridional scans

exhibited by P80A beyond e¼ 1.1 were due to some kind

Figure 7. Changes in meridional scattering during stress relaxation at e¼ 1.5.



Figure 8. 2D-SAXS data after retraction to zero stress, showing ‘diagonal’ 4-spot patterns.



of mixed binary morphology. This was analysed using an

extended scattering model:

IðqÞ¼ I0A � PðqRAÞ � Sðq; dA; dAÞþ I0B � PðqRBÞ � Sðq; dB; dBÞ

ð7Þ

where the functions are as described in Equation (4) to

(6) and the subscripts refer to individual populations of

scatterers. Values of I0, R and d were permitted to change

independently for each population In order to facilitate

curve fitting, however, the same level of lattice distortion

was assumed for both populations. This improved the

reliability of convergence of the model to the data, although

the assumption may not have been strictly valid. The results

for P80A using the extended model are shown in Figure 4c

and 4d beyond, e¼ 1.1. It appeared that the effective radius

of the larger scatterers was slightly less than twice the value

of the smaller scatterers, while the larger d-spacings

(assumed to correspond to the larger scatterers) were

roughly 1.5 times the smaller d-spacings.

It may be significant that extrapolation from the initial

strain direction behaviour fell close to the larger values of d

and R given by this analysis; moreover, extrapolating the

curve describing low-strain results appeared to bisect the

high-strain bimodal data. This behaviour appeared to be

consistent with some HS microdomains fragmenting early

in the deformation experiments, even though bimodal meri-

dional scattering peaks were not evident below e¼ 1.1.

It should be noted that the original ZP scattering model

Figure 9. Morphological data for relaxed P55D (&) and P80A (&) samples (afteruniaxial extension, stress relaxation at e¼ 1.5 over 20 min and subsequent retractionto s¼ 0).



(as well as each component of the binary model)

yield average morphological values; whereas, polydis-

persed HS microdomain sizes and interdomain spacings

are expected in the TPU samples. Consequently, a picture

emerges of some elongated microdomains remaining

intact and being oriented in the stretching direction,

giving the larger values of R and d, while others

broke into fragments that subdivided the original inter-

domain spacing and gave the smaller values of R and d.

Although the particle function used [Equation (5)] can

only give effective average values of R, the results during

uniaxial extension suggest that the HS microdomains were

significantly elongated. Hence, the clear indication of

bimodal scattering peaks during the first uniaxial extension

of P80A may be attributable to longer HS microdomains in

this material compared with P55D. Moreover, the differ-

ence in behaviour between the materials studied appeared

to be only one of degree; evidence of bimodal scattering in

P55D also emerged at later stages of the deformation

experiments, as described below.

The geometric changes in R and d presented in Figure 4

appeared to explain the main features of the observed 2D-

SAXS patterns. However, an examination of the changes in

I0 presented in Figure 5 revealed an additional level of

complexity in the morphological response to strain. Pure

affine deformation was expected to reduce sample thick-

ness, causing a reduction in I0 inversely proportional to

(1þ e)1/2, which should act equally in the meridional and

equatorial scattering. This is represented by the continuous

lines in Figure 5a and 5b. However, the experimental results

from both materials showed considerable deviations from

these expectations. The strain direction scaling factor

initially increased substantially, with a maximum around

e¼ 0.4, before decreasing at higher strain. The break in the




Figure 10. 2D-SAXS patterns, at selected strains collected during second uniaxialextension (after stress-relaxation at e¼ 1.5 for 60 min and retraction to s¼ 0; values ofstrain given with respect to the retracted length).



strain direction data at e¼ 1.1 for P80A (Figure 5b)

corresponded to the onset of the bimodal meridional

scattering, with the smaller scattering bodies giving the

lower values of I0. The apparent conjunction of the peak in

the strain direction scaling factor with strain softening

and the point at which the behaviour of R and d indicated

the onset of microdomain fragmentation suggested that

these effects might be connected. By contrast, I0 was signi-




ficantly smaller for the transverse direction scattering

and decreased progressively with strain, well below the

expected values.

Stress Relaxation

The stress relaxation behaviour of P55D and P80A at

e¼ 1.5 is compared in Figure 6. Although the starting

values of s reflected the different compositions, P55D and

P80A exhibited qualitatively similar behaviour. The rapid

initial decrease in stress became progressively slower with

time, although significant changes could still be observed at

1 h. This decrease in s appeared approximately logarithmic

with time, as demonstrated in Figure 6b.

Stress relaxation was accompanied by significant

changes in the meridional scattering, as demonstrated in

Figure 7. The single peak exhibited by P55D at the end of

the deformation stage decreased in height and became

distinctly bimodal, with a shoulder at higher q growing in

prominence during stress relaxation. The scattering peak

exhibited by P80A was already distinctly bimodal by the

end of the deformation stage, but the higher q component

became dominant during stress relaxation. In both materi-

als, these changes occurred through a pronounced decrease

in the intensity of the lower q component in the 1D-scans,

while the scattering at higher q increased slightly. Analysis

of the meridional scattering data using Equation (7) found

no significant changes in R or d within the individual

populations. However, the relative decrease in the propor-

tion of larger, more widely spaced scatterers was consistent

with microdomain fragmentation.

By contrast, relatively little change in the equatorial

scattering or the corresponding morphological data was

observable during stress relaxation. Overall, the samples

retained a significant level of anisometry, with significantly

smaller values of R and d in the transverse direction.

Morphology After Retraction

2D-SAXS patterns from retracted samples are presented in

Figure 8. Both materials exhibited diagonal four-spot

Figure 11. Changes in R and d for P55D (a and b) and P80A (c and d) during second uniaxialextension, (after stress-relaxation for 60 min at e¼ 1.5 and retraction; continuous lines representtrends during initial deformation).



patterns, which were most pronounced for those samples

allowed to relax at e¼ 1.5 for 20 min before retraction.

These appeared similar to the patterns observed previously

from strained TPUs by Blundell et al.[9] 1D-scans were

obtained from the 2D-SAXS data at 108 intervals from the

strain to transverse directions, and analysed by curve-fitting

the ZP model; the results are presented in Figure 9.

Morphological data in the strain and transverse directions

for virgin and strained, retracted samples is also compared

in Table 1.

The anisometry in microdomain size that developed

during the initial straining and persisted during stress

relaxation was lost on retraction. No significant angular

dependence of R was observable in the retracted sam-

ples. This probably occurred by elongated HS micro-

domains rotating back into random orientations, effectively

reversing the process by which anisometry developed

during uniaxial extension, although some shape-changing

cannot be ruled out. Moreover, no significant differences in

the values of R could be observed between virgin and

retracted samples, suggesting that HS microdomain frag-

ments may have re-united, when the stress was released.

Some angular dependence persisted in the interdomain

spacings of retracted samples; values of d within 208 from

the strain direction were about 10% longer than in the

transverse direction. However, these observed differences

were significantly less than expected on the basis of the

residual strain after retraction causing a corresponding

displacement of microdomains on the ‘statistical lattice’.

This suggested that a certain amount of microdomain

redistribution may have occurred during uniaxial extension

and retraction.

The residual anisotropy in d would account for the slight

ellipticity in the 2D-SAXS patterns of the retracted samples

and favour stronger scattering close to the strain direction.

But it does not explain the ‘off-axis’ maxima of the four-spot

patterns. In this respect, variations in I0 and d/d appeared to

be more important. The scaling factors exhibited peaks

around 108 to 308 and minima around 608 to 708 from the

strain direction, for P80A and P55D respectively




(Figure 9c). This suggested angular variations in scattering

contrast, possibly as a result of localised segmental mixing

or density variations around the HS microdomains. The

shallow minimum in the lattice distortion around 408 to 608would also favour sharper scattering curves, with slightly

greater intensity close to the diagonals of the 2D-SAXS

patterns.

Morphological Changes DuringSecond Deformation

Typical 2D-SAXS patterns collected during the second

extension cycles for P55D and P80A are compared in

Figure 10. The four-spot patterns exhibited by either TPU

initially appeared to intensify at low strain, generally

becoming clearest around e¼ 0.3 (with respect to the

retracted sample length). At higher strain, the spots moved

slightly towards the meridian and became weaker, although

feint traces were still discernible at e¼ 0.7. Above about

e¼ 1.3, the 2D-SAXS patterns from the first and second

deformation cycles appeared similar, although the former

were generally more intense.

Changes in R and d obtained by curve-fitting meridional

and equatorial scans during the second deformation cycle

are presented in Figure 11. For comparison, the trends from

the first deformations are also shown. P55D and P80A

exhibited similar results, becoming distinctly anisotropic

Figure 12. Changes in scaling factor for P55D (a) and P80A (b) during second uniaxialextension, after stress-relaxation for 60 min at e¼ 1.5 and retraction (continuous linesrepresent trends during initial deformation).



at low strains, with both materials developing bimodal

meridional scattering populations above e¼ 1.1 and 0.9

respectively. Although this represented further evidence

of microdomain fragmentation, comparison with the data

from the first deformation cycles suggested that the

changes in R and d from the virgin state were relatively

minor. Consequently, although microdomain re-orientation

and fragmentation clearly occurred during the deformation

experiments, these processes seem unable to provide a

complete explanation for the considerable changes observed

in mechanical properties.

Both materials exhibited considerable decreases in

scaling factor between the first and second deformation

cycles, as demonstrated in Figure 12. This may be attributed

to strain-induced segmental mixing during the initial

deformation cycle that was not recovered on retraction.

Possible connections between the underlying molecular

changes responsible for the decrease in scattering intensity

and the stress-strain behaviour are discussed below.

Discussion

It has been demonstrated previously[9–11,16,17] that the

SAXS patterns from TPUs such as those studied here could

be interpreted using a two-phase model comprising

elongated, globular HS microdomains dispersed within a

mixed HSþ SS matrix. Studies using DSC and wide-angle

X-ray scattering (WAXS), to be reported elsewhere,

have effectively excluded any significant scattering from

SS crystallites in the TPUs used here. Although it is

acknowledged that PTMO is prone to crystallisation,

previous work by Van Bogart et al.[22] showed that this

required SS molecular weights above 1 000 Da. Since the

P55D and P80A samples used here are believed to have SS

molecular weights of approximately 600 to 650 and 1 000

Da respectively,[16,23] this explains the absence of SS

crystallites. Moreover, since WAXS did not reveal any

significant peaks associated with HS crystallites in these

TPUs, this suggests that the HS microdomains were essen-

tially glassy. Again, this is consistent with the short HS and

HS lengths in P55D and P80A,[16] which is also likely to

produce significant HSþ SS mixing.

A common problem in the interpretation of SAXS is that

similar patterns may be given by different morphologies.

Ideally, the morphology present should be confirmed by

independent methods, such as transmission electron micro-

scopy (TEM) or atomic force microscopy (AFM). A

number of published studies of TPUs and related poly-

mers[23–33] have indicated morphologies composed of

elongated HS microdomains within a SS matrix, roughly

consistent with the ‘globular’ scattering model used here.

The publications by McLean and Sauer[32] and Christenson

et al.[33] appears particularly relevant, since they included

polymers very similar to those used in the present work.

Nevertheless, these techniques are not without their

own problems; our attempts to study P55D and P80A

using TEM[34] appeared to indicate mixtures of weakly-

contrasting globular or lamellar HS microdomains, but also

demonstrated a considerable risk of artefacts due to in-

appropriate sample cutting, staining methods and viewing

conditions. It is possible that the weak TEM contrast (even

using heavy metal stains) may have been linked to consi-

derable SS and HS mixing in these materials, which is a key

element of the SAXS interpretation presented here.

There are likely to be some subtle morphological details,

such as local composition or density fluctuations within

microphases, the nature of the interfaces and the exact

shapes of dispersed HS microdomains that are not

encompassed by the two-phase globular model. It is also

expected that some combinations of TPU formulations and

processing conditions could give morphologies beyond the

scope of this simple scattering model. In particular, formu-

lations with longer or less miscible SS and HS will be more

strongly microphase-separated, which could lead to larger

microdomains, bi-continuous morphologies, the possibility

of semicrystalline microphases and spherulites. Never-

theless, we believe that these features are absent in the TPUs

studied here and there are no substantial arguements against

interpreting the SAXS from copolymers of this type using

the two-phase globular model.

The ZP model generally appeared well able to fit the

changes in scattering intensities observed during uniaxial

extension experiments, in line with previous work.[9–

11,16,17] Moreover, the experiments reported here extended

this analysis to stress relaxation at constant strain (e¼ 1.5),

retraction to zero stress and a second uniaxial extension.

It has been noted that the volume fractions of dispersed

microdomains indicated by the PY model were generally

lower than corresponding estimates from the ZP model.[16,17]

These discrepancies are thought to be caused by the

underlying distributions of interdomain distances inherent

in each model. Since the distribution exhibited by the TPUs is

not known at present, the values of d obtained by curve-fitting

the ZP model may not be absolutely correct and should

be treated with some caution. Further uncertainty in the

SAXS interpretation was introduced by the extended model

used to model the bimodal intensity curves exhibited

by strained materials under some conditions in the present

work.

Although analyses of SAXS data using the ZP model may

not be relied on to give a quantitatively accurate interpre-

tation, it indicated a combination of strain-induced dis-

placement, rotation and fragmentation of the dispersed HS

microdomains during uniaxial extension. This was broadly

in agreement with previous studies of mechanically

deformed TPUs, using SAXS[2,9–12,16,17,20,22] and other

techniques.[2,3,5,33,35–37] It should be noted that the ob-

served changes in R during uniaxial extension are assumed

to be attributable to microdomain rotation. Deformation



is thought to be less likely, due to the considerably

higher modulus expected for HS microdomains compared

with the HSþ SS matrix; this possibility cannot be

totally excluded, however, since the expected difference

in modulus may be reduced by incomplete segmental

demixing.

It appeared that microdomain rotation, the onset of

fragmentation and stress softening occurred roughly

concurrently in the first deformation cycles, which implied

that these effects may be connected. The strain-softening

observed with some TPUs has often been attributed to

fragmentation and a decrease in interconnectivity amongst

HS microdomains.[8,15,23,33,35] This hypothesis may be well

justified for copolymers with a large volume fraction of

considerably elongated or interconnected HS microdo-

mains; morphologies such as these have been reported

recently by Klinedinst et al.[38] for poly(alkylurethane-co-

urea), where the SS and HS compositions are expected to

cause stronger and more extensive microphase separation.

However, the materials used in the present study are

expected to be less strongly microphase-separated, with

smaller volume fractions of relatively short HS micro-

domains. Moreover, the morphological changes during the

first deformation cycle appeared to be largely reversed on

retraction to zero stress. Hence, while fragmentation and re-

orientation of dispersed HS microdomains during uniaxial

extension may be contributory factors, they appear unable

to fully explain the dramatic reduction in mechanical

properties from the first to second deformation cycles for

the materials studied here.

One possible explanation may be that the mechanical

properties of P55D and P80A were dominated by the

behaviour of a few much larger (probably elongated) HS

microdomains. These microdomains would scatter at very

low q, outside the range of the present SAXS measure-

ments, although their fragmentation might contribute to the

observed increase in meridional intensity at low strain.

Fragmentation of these microdomains could account for

strain softening and the considerable modulus decrease

from the virgin to pre-strained state. However, this hypo-

thesis does not easily explain the significant strain harden-

ing observed above e¼ 0.8 during the second extension

cycles or the convergence with the initial deformation

stress-strain curves above the ‘pre-strain’, which was report-

ed by Meissner and Spırkova.[8]

Any explanation based purely on microdomain rotation

and fragmentation also overlooks the considerable strain-

induced changes and angular dependence observed in the

scaling factor. No adequate explanation for these observa-

tions can be envisaged at present based on purely ‘geo-

metric’ changes in microdomain orientation or distribution;

whereas, several possible mechanisms providing explan-

ations based on variations in scattering contrast due to

localised composition or density changes appear possible.

Dilatational effects during polymer deformation have been

discussed by Naqui and Robinson.[39] Although it is gen-

erally expected that rubbery polymers deform at approx-

imately constant volume, this may not preclude local

density fluctuations on a nanometre scale, due to the mod-

ulus difference between dispersed HS microdomains and

the softer, mixed HSþ SS continuous phase. This may be

regarded as an extension to the nanometre scale of local

stress variations in composites, which have been discussed

extensively by Hull and Clyne.[40] Based on the analysis

Figure 13. Suggested mechanisms producing local variations inscattering contrast.



method developed by Eshelby,[41,42] uniaxial extension of

the TPU is initially expected to produce dilation in the

continuous phase adjacent to HS microdomains in the strain

direction and compression in the transverse direction. Since

the mixed HSþ SS phase is expected to have a lower

electron density than the dispersed HS microdomains, this

would explain the angular dependence in I0 at low strain.

The subsequent general decrease in scattering intensity at

higher strain may be attributed to strain-induced segmental

mixing, with HS being pulled from microdomains in the

strain direction. These mechanisms are represented di-

agrammatically in Figure 13.

HS pull-out and strain-induced segmental mixing sug-

gests an alternative explanation for the observed mechan-

ical behaviour. The HS microdomains are usually assumed

to act as physical crosslinks; however, the chain movement

implied by segmental mixing could provide a mechanism

for relieving the stresses associated with strained macro-

molecular entanglements. Entanglements play a key part in

models of rubber-like elasticity, such as those described by

Kluppel and Schramm,[13] Edwards and Vilgis[43,44] and

others.[45] A distinction is made between ‘slip links’ that

can move relatively freely at low strain and ‘trapped

entanglements’ that contribute to load-bearing. According

to the present hypothesis, HS pull-out and chain diffusion

through HS microdomains may permit the release of

entanglements and stress-relief, giving rise to the observed

strain softening. Strain hardening during subsequent

extension cycles can then be attributed to chain segments

that had slackened through HS pull-out becoming taught

again, as the previous maximum strain is approached and

exceeded.

It was suggested previously[11] that the slower segmental

motion within HS micodomains might impede but not

completely stop the movement of entanglements. In support

of this hypothesis, NMR studies by Schmidt-Rohr and

Spiess,[46] Robertson et al.[47] and Miyoshi et al.[48] pre-

sented evidence of chain diffusion through polymer

crystals. Moreover, van der Schuur and Gaymans[49]

recently reported considerable differences in the mechan-

ical behaviour of segmented block copolymers with similar

compositions but containing different amounts of covalent

crosslinks. The suggested dependence of mechanical

properties on a combination of freely moving and trapped

entanglements in the TPUs studied is expected to cause a

strong dependence on temperature and strain rate; this is

under investigation and will be reported subsequently.

It may be possible to observe strain-induced segmental

mixing by changes in thermal behaviour, by DSC

or dynamic mechanical thermal analysis. Segmental

mixing and chain movement may also be investigated

by neutron scattering with deuterium labelled materials,

along the lines previously used by Naylor et al.[50] to

study the thermal behaviour and microphase mixing in

TPUs.

Conclusion

The SAXS patterns from two commercial TPUs undergoing

repeated uniaxial extension and stress relaxation were

analysed in terms of ‘globular’ morphologies. The results

indicated some strain-induced microdomain displacement,

reorientation and fragmentation, but the net changes

appeared incommensurate with the observed decrease in

mechanical properties from the first to second deformation

cycles.

Considerably more pronounced variations in the SAXS

scaling factor were observed, which were attributed to local

density changes and strain-induced segmental mixing. It is

suggested that the associated chain movement could

provide a mechanism for relieving the stress associated

with strained macromolecular entanglements, which has a

greater effect on the mechanical properties.

Acknowledgements: This work was funded by RanierTechnology Ltd, DTI and EPSRC. The help of A. Gleeson forsetting up station 16.1, at the SRS is gratefully acknowledged. Theauthors would especially like to thank A. Renouf, A. Kamvari, S.Freeburn, A. Lynn, J. Sandler, S. Pegler and P.Werner, who helpedto perform the experiments on which this paper is based.

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