Solid State Nuclear Magnetic Resonance 22, 327–343 (2002)

doi:10.1006/snmr.2002.0067

b

Segmental Anisotropy in Strained Elastomers Detectedwith aPortable NMRScanner

K. Hailu, R. Fechete, D.E. Demco, and B. Bl .uumich1

Institut fur Technische Chemie und Makromolekulare Chemie, Rheinisch-Westf.aalische, Technische

Hochschule, Worringerweg 1, D-52056 Aachen, Germany

FESTSCHRIFT IN HONOR OF PROFESSOR HANS-WOLFGANG SPIESS

ON THE OCCASION OF HIS 60TH BIRTHDAY

Single-side NMR is particularly suitable for measurements of segmental anisotropy induced

in elastomers by uniaxial forces or local strain. Proton transverse nuclear magnetic relaxation

was investigated with the NMR-MOUSE1 by recording the Hahn-echo decay in cross-linked

natural rubber bands. This provided information on the dependence of the Hahn-echo decay on

the angle between the direction of the uniaxial stretching force and the axis #ZZ defined direction

perpendicular to the magnet pole faces of the NMR-scanner. The anisotropy effect on the

Hahn-echo decay is correlated with the extension ratio, and it is more evident in the liquid-like

regime of the decay. A weaker segmental anisotropy is detected by 1H solid- and Hahn-echo

decays recorded by multi-pulse sequences. A qualitative understanding of the angular

dependence is obtained by an analytical theory of the Hahn-echo decay adapted to the case

of stretched elastomers and to strongly inhomogeneous magnetic fields. Using angular-

dependent 1H residual second van Vleck moments and correlation times reported previously

[P.T. Callaghan and E.T. Samulski, Macromolecules 30, 113 (1997)] from stretched natural

rubber bands the segmental anisotropy measured in inhomogeneous magnetic fields by the

Hahn-echo decay was numerically simulated. As an example of a macroscopic distribution of

local segmental anisotropy, 1H Hahn-echo decays were measured by the NMR-MOUSE1

sensor in a stretched cross-linked natural rubber plate with a circular cut in the center. # 2002

Elsevier Science (USA)

Key Words: chain segmental anisotropy; elastomers; Hahn-echo decay; NMR in strongly

inhomogeneous magnetic fields; NMR-MOUSE.

INTRODUCTION

A well-known consequence of the theory of rubber elasticity is bond orientation[1, 2]. Elastic deformation of an elastomer induces anisotropy of the backbone bondsof the polymer coil. In recent experimental studies of rubber elasticity, themechanism of deformation and orientation of network chains has receivedincreasing attention. This has been made possible mainly by small-angle neutronscattering (SANS) by means of which changes of global chain dimensions can bestudied [3]. For the study of the chain orientation on a segmental level, nuclear

1To whom correspondence should be addressed. Tel.: 49-241-80 6420. Fax: 49-241-8888-185. E-mail:luemich@mc.rwth-aachen.de

327

0926-2040/02 $35.00# 2002 Elsevier Science (USA)

All rights reserved.

HAILU ET AL.328

magnetic resonance (NMR) appears to be a promising method. One- andtwo-dimensional NMR spectroscopy of 2H and 1H have been used intensively inthe last decade to measure homonuclear and heteronuclear residual dipolarcouplings and corresponding dynamic order parameters ([4, 5] and referencestherein).Deuterium NMR line shape analysis (splitting of the line) reveals that in the

presence of a uniaxial mechanical force, a molecular anisotropy of the chainsegments is induced in a polymer network [6–22]. The doublet structure of the 2DNMR absorption line and its angular dependence described by a second-orderLegendre polynomial P2ðcosYÞ, where Y is the angle between the uniaxial appliedforce F

*and the static magnetic field direction ~BB0, reflect uniaxiality at a local scale.

Here F*plays the role of the local symmetry axis for the reorientation of each

segment. The externally imposed uniaxial symmetry is transferred to the scale of thechain segments. When a network is deformed the line splitting seen from NMR spymolecules located on the chain segments or on the free chains dissolved in thenetwork can be accounted for by considering different mechanisms. There are twodistinct mechanisms responsible for this induced local anisotropy [13, 15, 18, 20]:(i) The anisotropy of the residual dipolar interactions is increased for each chain

due to changes in the length and orientation of the network junctions. In this‘‘phantom model’’ of a polymer network [2], the mechanism of enhanced anisotropyunder mechanical stress is independent of the interactions between the chains. Itexpresses the correlation between segmental motions and the constraints due to thejunctions and related to the end-to-end vector ~RR. The length and the orientation ofthe end-to-end vectors are affected by the applied uniaxial forces. This effect can beaccounted for by an affine deformation assumption valid for small values of theextension parameter l. Moreover, the Gaussian distribution of the end-to-endvectors is assumed to be valid. It has been shown that this mechanism of the localsegment orientation only leads to a line broadening and not to a line splitting[13, 15, 18].(ii) The second mechanism responsible for the chain anisotropy is given by the

isotropic short-range orientational interactions between segments belonging todifferent chains [13, 15]. This mechanism involves the screening properties of thedeformed network chains. Under the axial deformation, the chains will produce ascreened short-range, excluded-volume interaction with an induced attractivepotential. The resulting screening potential which is common to all the bondsbecomes anisotropic and dependent on the applied deformation. The anisotropy ischaracterized by the order of N�1, where N is the number of statistical segmentsbetween the cross-link junctions. It has a nematic-like form which is linear in l2 �l�1 and inversely proportional to N for uniaxial deformations [13, 15]. This secondcontribution represents the effect of the mean orientation field, characterized by themean degree of order along the direction of the applied force.Besides 2D NMR other NMR methods used for investigation of the residual

dipolar couplings in stretched natural rubber bands are based on 1H Hahn- andsolid-echoes as well as double-quantum coherences and dipolar encoded longitudinalmagnetization [23, 24]. By measuring the residual dipolar couplings versus theextension ratio l and its dependence on the orientation angle Y, it is possible to

SEGMENTAL ANISOTROPY IN STRAINED ELASTOMERS 329

distinguish the influences from chain stretching and from chain reorientation in thedeformation process [23]. Moreover, two-dimensional 1H maps of stress distribu-tions were presented from a strained natural rubber band with a cut on one side [24].Over the last few years, a mobile NMR surface scanner called NMR-MOUSE1

(this is a registered trademark of RWTH-Aachen) has been developed for thenondestructive investigation of arbitrarily large objects [25, 26]. The NMR-MOUSE1 is a palm-size NMR device which is built up from two permanentmagnets. The magnets are mounted on an iron yoke with anti-parallel polarization toform the classical horseshoe geometry. The main direction of the polarization field B0is across the gap, and the field strength decreases rapidly with increasing distancefrom the surface. The radio-frequency (rf) field B1 is generated by a surface coilwhich is mounted in the gap. The NMR-MOUSE1 is characterized by stronginhomogeneities in the static and radio-frequency magnetic fields. Due to theseinhomogeneities, the task to implement or analyze specific NMR techniques is nottrivial. On the other hand, the orientation dependence of NMR parameters can easilybe investigated with the mobile NMR sensor for large samples on stretching devices.The aim of this paper is to investigate in how far the NMR-MOUSE1 is suitable

to measure the chain segmental anisotropy in stretched cross-linked elastomers viathe 1H Hahn-echo decay. A semi-quantitative theory of the Hahn-echo decay instrongly inhomogeneous magnetic fields is developed below to understand itsangular dependence measured with the NMR-MOUSE1. It is based on the solid-and liquid-like spin-system response of spin-1

2pairs attached to a chain segment in a

polymer network [7, 23, 27, 28]. Moreover, the possibility to detect local segmentalanisotropy is demonstrated by 1H Hahn-echo decays detected with the NMR-MOUSE1 in a stretched, cross-linked natural rubber plate with a circular cut in thecenter.

THEORY AND SIMULATIONS

Hahn-Echo Decay

In the following, the NMR response to the pulse sequence of Fig. 1 used fordetecting transverse relaxation via the Hahn-echo decay is considered for a spin-1

2

pair. This pulse sequence has pulse flip angles y=908. Therefore, the 2y pulse justpartially refocuses the evolution of the coherences under inhomogeneous spininteractions. This will give us the possibility to investigate the Hahn-echo decaywhich can be detected by the NMR-MOUSE1, i.e., in strongly inhomogeneousmagnetic fields where a distribution of pulse flip angles is present. Nevertheless, theradio-frequency pulse phases are not distributed over the sample volume.The total spin Hamiltonian in the rotating frame representation describing the free

evolution of the system belonging to the voxel at position ~rr is given by

H ð~rr; tÞ ¼ �DOð~rrÞIz þ %HHd ð~rrÞ þ D %HHd ð~rr; tÞ

¼ �DOð~rrÞT1;0 þ %oodT2;0 þ Dod ðtÞT2;0; ð1Þ

FIG. 1. Hahn-echo pulse sequence used for measuring the transverse relaxation decay with arbitrary

radio-frequency pulse flip angles y and 2y. For the NMR-MOUSE1 sensor these flip angles correspond to

a one voxel of the sensitive volume.

HAILU ET AL.330

where DOð~rrÞ is the local off-resonance Hamiltonian [29] and T1;0 is the irreducibletensor operator [30] corresponding to the spin operator Iz. D %HHd ð~rr; tÞ ¼ Hd ð~rr; tÞ �%HHd ð~rrÞ is the part of the dipolar Hamiltonian fluctuating around the residual partgiven by [13, 15]

%HHd ¼ð�

ffiffiffi6

pÞ

2DSs

1

Na2ð~RR0Þ2P2ðcos b

0Þ þ KP2ðcosYÞðl2 � l�1Þ� �

T2;0; ð2Þ

where the first and the second term in the curly bracket of Eq. (2) correspond to themechanisms (i) and (ii) of induced segmental anisotropy described above. Thedynamic order parameter is given by S � %PP2½cos b

ijðtÞ, where bijðtÞ is theinstantaneous angle between a given internuclear vector ~rrij and end-to-end vector~RR [4]. A scaled dynamic order parameter can be defined as Ss � S

Ne, where the effective

number of statistical segments is Ne � Nk . The geometrical factor k depends on the

model which is adopted to describe the chain statistics and is equal to 35for a chain of

freely jointed segments [30]. For a strained elastomer, the stretched end-to-endvector is denoted by ~RR0 and the angle b0 describing the orientation of the ~RR0 vectorrelative to the static magnetic field ~BB0. Both quantities have a complicateddependence on the orientation angle Y which includes second-order Legendrepolynomial P2ðcosYÞ and other trigonometric functions. Therefore, the orientationdependence of the residual dipolar Hamiltonian cannot be described simply by aP2ðcosYÞ function. K is an effective interaction parameter describing short-range,excluded-volume interactions [13, 15]. The residual dipolar coupling constant %ood isgiven by the prefactor to the irreducible tensor operator T2;0 in Eq. (2). The dipolarcoupling fluctuating around the residual values is denoted by Dod ðtÞ. For a spin-12

SEGMENTAL ANISOTROPY IN STRAINED ELASTOMERS 331

pair all the terms of the Hamiltonian described by Eq. (1) commute with each other,which allows to obtain an exact evaluation of the spin-system response.The propagators describing the spin-system evolution are given as follows: P ¼

expfiyIxg for a hard radio-frequency y pulse along the x-axis; Eðt; 0Þ ¼ expf�iDOIztg expfi %HHdtg expfiD %HHd ðt; 0Þg for the first free evolution period (cf. Fig. 1), whereD %HHdðt; 0Þ ¼

R t0 D %HHd ðtÞ dt, and Eð2t; tÞ ¼ expf�iDOIztg expfi %HHdtg expfiD %HHd ð2t; tÞg

for the second free evolution period, where D %HHd ð2t; tÞ ¼R 2tt D %HHd ðtÞ dt.

The reduced density operator at the Hahn-echo time 2t is given by the followingcanonic quantum-mechanical transformations:

sð2tÞ ¼ #EEð2t; tÞ #PP2 #EEðt; 0Þ #PPsð0Þ; ð3Þ

where the Liouville operator #OO is defined by #OOs � OsO�1. The initial densityoperator describes the state of thermodynamic equilibrium, i.e., sð0Þ / Iz, where~IIðIx; Iy ; IzÞ is the total spin vector operator for the spin-pair system. The spin-systemresponse described by Eq. (3) is complicated by the presence of the off-resonanceHamiltonian and radio-frequency pulses with arbitrary flip angles as well as thepartially refocusing character of the 2y pulse. To evaluate this response, thecanonical quantum-mechanical transformations corresponding to various Hamilto-nians in the irreducible tensor representation were taken from Bowden andHutchinson [30]. A computer program was written to implement the chain of thesetransformations to generate various multipolar spin states [31, 32] of the densityoperator at time 2t. They are represented by longitudinal magnetization, single-quantum coherences, anti-phase single-quantum coherences, dipolar order, anddouble-quantum coherences. Single-quantum coherences which lead to a Hahn-echosignal are described by Ix ¼ �1ffiffi

2p ½T11 � T1�1 and Iy ¼ 1 ffiffi

2p ½T11 þ T1�1, where

T1 1 ¼ �1ffiffi2

p ðIx iIyÞ, [30]. The density operator terms responsible for the real and

imaginary parts of the Hahn-echo signal contain oscillatory trigonometric functionsof the form sin½DOð~rrÞ; cos½DOð~rrÞ; sin½2DOð~rrÞ; sin2½DOð~rrÞ, and cos2½DOð~rrÞ. Thedestructive interference which takes place because of the static magnetic fielddistribution inside each macroscopic voxel leads to hsin½DOð~rrÞiDO � hcos½DOð~rrÞiDO � hsin½2DOð~rrÞiDO � 0, and hsin2½DOð~rrÞiDO � hcos2½DOð~rrÞiDO � 1

2. The sym-

bol hð� � �ÞiDO denotes the average over the off-resonance values inside each voxel atposition ~rr.The normalized Hahn-echo signal originating from the sample voxel ~rr, in

quadrature with the first radio-frequency excitation pulse (cf. Fig. 1), can beevaluated based on the above considerations and the final result is given by

Syð~rr; 2tÞSyð~rr; 0Þ

¼

*fcos2½ð %MM2Þ

1=2t þ p sin2½ð %MM2Þ1=2tg

� cos

ffiffiffi3

2

r Z t

0

dt0Dodðt0Þ

" #cos

ffiffiffi3

2

r Z 2t

tdt00Dod ðt00Þ

" #* +sa

HAILU ET AL.332

þ fsin2½ð %MM2Þ1=2t þ p cos2½ð %MM2Þ

1=2tg

� sin

ffiffiffi3

2

r Z t

0

dt0Dod ðt0Þ

" #sin

ffiffiffi3

2

r Z 2t

tdt00Dodðt00Þ

" #* +sa

+; ð4Þ

where %MM2 is the second van Vleck moment for a well-defined end-to-end vectorlength and orientation. The general expression for the second van Vleck moment [33]is given by

%MM2 ¼ �Trf½ %HHd ; T11ðaÞ2g

TrfðT11ðaÞÞ2g

; ð5Þ

where %HHd is given by Eq. (2) and T11ðaÞ is the anti-symmetric irreducible tensoroperator [30]. The averaged residual second moment hð %MM2Þi has a complexdependence on the orientation angle Y which is not described by the ðP2ðcosYÞÞ2

function. The average hð� � �Þi � hh i~RR0ib0 includes two separate averages, one overthe length of the reduced end-to-end vector ~RR0 denoted by hð� � �Þi~RR0 and the otherover the azimuthal angle b0 denoted by hð� � �Þib0 .The function p in Eq. (4) depends on the pulse flip angle y and is given by

p ¼ cos 2y�cos 4y2 sin2 y

. The symbol hð� � �Þisa denotes a statistical average over the thermallyfluctuating part of the residual dipolar Hamiltonian. The sine and cosine correlationfunctions [32, 34] in Eq. (4) are stationary and independent of the voxel position forthe homogeneous sample. It can be shown that the Hahn-echo signal in phase withthe first pulse vanishes.It is clear from the above equations that the Hahn-echo signal cannot be written as

a simple product of solid- and liquid-like contributions like in the case of the freeinduction decay [28]. Only in homogeneous magnetic fields for a pulse flip angley ¼ 908, i.e., for p ¼ �1, this separation of the contributions takes place.We can estimate the total Hahn-echo decay signal for the entire sample for the

particular case of a NMR-MOUSE1 sensor by considering the distribution over thepulse flip angle y in the sensitive volume. Using the results of Balibanu et al. [35] weget

Psensitivevolume

pðyÞ � �0:287. Moreover, the sine and cosine correlation functions inEq. (4) can be evaluated using the exponential correlation functions forhhDoðt00ÞDoðt0Þii [34, 36]. In the limit h %MM2i1=2t � 1, we finally get from Eq. (4)

Syð2tÞSyð0Þ

/hfcos2½ð %MM2Þ1=2t � 0:287 sin2½ð %MM2Þ

1=2tg

� exp½�2 %MM2t2cðe�t=tc � 1þ t=tcÞ

� cosh½2 %MM2t2cð1� 2e�t=tc þ e�2t=tc Þi; ð6Þ

SEGMENTAL ANISOTROPY IN STRAINED ELASTOMERS 333

where tc is the correlation time of the segmental motions. In the limit of short Hahn-echo time, the above equation can be approximated by

Syð2tÞSyð0Þ

/fcos2½h %MM2i1=2t � 0:287 sin2½h %MM2i1=2tg

� exp½�2h %MM2it2cðe�t=tc � 1þ t=tcÞ

� cosh½2h %MM2it2cð1� 2e�t=tc þ e�2t=tc Þ: ð7Þ

The presence of the residual second van Vleck moment in the argument of thetrigonometric functions and exponentials will finally lead to a complicateddependence on the orientation angle Y. Moreover, at the magic angle valueYm ¼ 54:748, i.e., for P2ðcosYmÞ ¼ 0 when the residual second moment reaches aminimum value which is different from zero, the Hahn-echo signal will be maximumfor a given t value.

Simulation of the Hahn-Echo Decay Anisotropy

The results presented above allow us to simulate the dependence of the Hahn-echodecay on the angle Y for a uniaxially stretched elastomer. To simplify the numericalcomputations only the voxels for which ~BB0 vectors are parallel to the directionperpendicular to the faces of the permanent magnets of the NMR-MOUSE1 weretaken into account.For a natural rubber band stretched to l � 5, the residual second van

Vleck moment averaged over the Y angle is h %MM2i1=2 � 1:8� 103 s�1 [23].Using this value for t ¼ 300 ms, we get h %MM2i1=2t � 0:5. Therefore, Eq. (7) can beused to estimate the decay and anisotropy of the Hahn-echo decay up to this echotime.Simulations of the Hahn-echo decays in the initial time regime for a natural rubber

band for three orientation anglesY are shown in Fig. 2a. The 1H residual second vanVleck moments and correlation times for a natural rubber band with the extensionratio l � 5 measured for three orientation angles Y are taken from Ref. [23] (cf.Table 1). As expected at the magic angle Ym ¼ 54:78, the reduction in the strength ofthe residual dipolar couplings will lead to a smaller attenuation of the Hahn-echodecay.The anisotropy of the Hahn-echo decay defined as SyðYÞ=SyðY ¼ 08Þ,

where SyðYÞ is given by Eq. (7) with the orientation-dependent residualsecond moments from reference [23], is shown in Fig. 2b. It is evident fromthese simulations that the anisotropy is very weak for decay times belowt � 100 ms. The anisotropy effect increases strongly for the longer Hahn-echodecay times.

FIG. 2. (a) Normalized Hahn-echo decay evaluated numerically from Eq. (7) for three different

orientation anglesY. The 1H residual second van Vleck moments and correlation times measured for threeorientation angles Y are taken from Ref. [23] (cf. Table 1) for a natural rubber band with the extension

ratio l � 5. The dashed lines correspond to the echo times at which the values of the signals were taken for

the evaluation of the anisotropy. (b) Anisotropy of the Hahn-echo decay SyðYÞ=SyðY ¼ 08Þ evaluated atdifferent echo times.

TABLE 1

Angular Dependence of the 1H Residual Dipolar van Vleck Moment, h %MM2i, and the Correlation Time,tc, of the Natural Rubber Band with the Extension Ratio l � 5 from Ref. [23]

Y h %MM2i ðHzÞ2 tc (ms)

08 4:34� 106 0.12

558 2:81� 106 0.14

908 2:99� 106 0.14

HAILU ET AL.334

SEGMENTAL ANISOTROPY IN STRAINED ELASTOMERS 335

EXPERIMENTAL

Materials

The elastomer samples investigated are from commercially availablenatural rubber (NR) SMR10 (Malaysia). The additives were 3 phr (parts-per-hundred-rubber) ZnO and 2 phr stearic acid. The sulfur and accelerator contents are1:5 phr each. The accelerator is of the standard sulfenamide type(TBBS, benzothiazyl-2-tert-butyl-sulfenamide). After mixing the compounds in alaboratory mixer at 508C, the samples were vulcanized at 1608C in a MonsantoMDR-2000-E vulcameter. The degree of cross-linking was measured by the low-frequency shear modulus at a temperature of 1608C in the vulcameter directly aftervulcanization. The measurements were performed with an oscillation amplitude of 0:58 and a frequency of 1:67 Hz. The samples were supplied (Dunlop GmbH,Hanau) in sheets of 2 mm thickness. For the NMR experiments under uniaxialstretching conditions, NR bands of 25 mm� 115 mm were used. For the spatiallylocalized anisotropy measurements, the relaxed NR band had dimensions of 115mm� 115 mm with a circular cut in the middle of the band with a diameter of14 mm.

NMR Measurements

The 1H NMR experiments in inhomogeneous fields were performed withan NMR-MOUSE1 sensor driven by a Bruker minispec spectrometer operatingat a carrier frequency of 20:0 MHz. The coil geometry produces a sensitivevolume of about 9 mm� 4 mm in the plane and 0:5 mm in depth. Furtherdetails are published in Ref. [25]. The length of the radio-frequency pulses of theHahn-echo pulse sequence (cf. Fig. 1) was 2:7 ms, and the recycle delay was 0:25 s.The echo time 2t was varied from 0.05 to 7 ms for the stretched NR bands and from0.05 to 15 ms for the relaxed NR sample. The Hahn-echo decay has a complexnonexponential dependence on the pulse sequence parameter t as discussed above.Nevertheless, in order to simplify the analysis of the anisotropy effect we fit theHahn-echo decay with an exponential function of the general formAþ B expð�2t=T2eff Þ. The effective Hahn-echo decay time T2eff is a global transversemagnetization relaxation parameter which is affected by the polymer chain segmentorientation via solid- and liquid-like contributions. Moreover, in order to comparethe measurements with the simulations, the normalized Hahn-echo signalswere measured versus the orientation angle Y for different values of the decaytime t.For the experiments performed under mechanical stress, a simple home

build stretching device was used. The NMR-MOUSE1 was positioned belowthe rubber band in contact with the surface of the rubber band. The width ofthe band was larger than the diameter of the radio-frequency coil of 8 mm. Thesamples were rotated on the NMR-MOUSE1 in steps of 108 and near the magicangle in steps of 58. All measurements were carried out at the room temperature22 18C.

HAILU ET AL.336

RESULTS AND DISCUSSION

Segmental Anisotropy

Experimental data measured with the NMR-MOUSE1 sensor showing theeffective rate 1=T2eff of the Hahn-echo decay versus extension ratio l for a uniaxiallystretched natural rubber band are depicted in Fig. 3. An upturn in the values of the1=T2eff versus l was detected in the region of l ¼ 2–2.5. This effect was reportedpreviously for natural rubber by Callaghan and Samulski [23] in their measurementsof the 1H residual second van Vleck moment and by Schneider et al. [24] using 1Hresidual dipolar couplings measured by double-quantum build-up curves and thefull-widths at half height of NMR multiple-quantum filtered spectra. All thesemeasurements were performed in homogeneous magnetic fields. It is well known thata wide class of networks which include natural rubber exhibit strain-inducedcrystallization, where well-defined crystallites form and grow during an anisotropicdeformation [2]. Therefore, we consider that this upturn is related to stress-inducedcrystallization.The experimentally determined anisotropy of 1=T2eff which reflects segmental

orientation induced by the uniaxial stretching force is shown for the angle Y in therange 0–3608 in Fig. 4 using polar and Cartesian coordinates. The relevant range ofthe angles Y is 0–908. A periodic change in the 1=T2eff was detected with the periodof 908. Moreover, the relaxation rate shows a minimum near the value of the magicangleYm ¼ 54:78, which is repeated periodically. The anisotropy of 1=T2eff is difficultto detect for l42. It increases with the elongation ratio l. The relative anisotropycontrast defined by b1=T2eff ðY ¼ 08Þ � 1=T2eff ðYmÞc=1=T2eff ðY ¼ 08Þ reaches a valueof about 33% for l ¼ 11 (cf. Fig. 4b). The minimum of 1=T2eff ðYÞ around the magicangle Y ¼ Ym ¼ 54:78 is mainly related to the presence of the Legendre polynomial

Θ = 0°

1 2 3 4 5 6 7 8 9 10 11 12

1.8

1.6

1.4

1.2

1.0

0.8

0.6

T 2eff

-1[m

s-1]

λ

FIG. 3. Effective 1H Hahn-echo decay rate 1=T2eff measured with the NMR-MOUSE1 versus the

extension ratio l for a uniaxially stretched natural rubber band.

T [

ms

]2e

ff

- 1- 1

[°]Θ

0 50 150 250 300200100 350 4000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8λ =

11.62.34811

T [

ms

]2 e

ff-1

-1

(a)

0.0

0.4

0.8

1.2

1.6

030

60

90

120

150180

210

240

270

300

330

0.0

0.4

0.8

1.2

1.6

λ =11.62.34811

(b)

FIG. 4. Anisotropy of the 1=T2eff rate for different elongation ratios l shown in polar (a) andCartesian (b) coordinates for a uniaxial stretched natural rubber band measured with the NMR-

MOUSE1.

SEGMENTAL ANISOTROPY IN STRAINED ELASTOMERS 337

of the second-order P2ðcosYÞ in the expression of the residual second van Vleckmoment which occurs in the Hahn-echo signal given by Eq. (7), together withEqs. (5) and (2).An attempt to compare the simulation of the anisotropy of the Hahn-echo decay

discussed above (cf. Fig. 2) to the data obtained from a stretched NR band is basedon the measured normalized decay signal anisotropy (Fig. 5). It is evident that therelative anisotropy increases with the Hahn-echo decay time and the extension ratio(cf. Figs. 5a and 5b). It has its maximum value near the magic angle where thestrength of the residual dipolar coupling has the smallest value. For the Hahn-echodecay time of t ¼ 100 ms and for l ¼ 5, the maximum change in the normalizedsignal takes place at the magic angle and is of the order of 0.1 (cf. Fig. 5b). Thesimulation made for the same extension ratio gives a value of about 0.05 (cf. Fig. 2b).

0 10 20 30 40 50 60 70 80 90 100

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

1.04

1.00

1.08

1.12

1.16

1.20

1.24

1.28

1.32

1.36

norm

aliz

ed e

cho

ampl

itude

norm

aliz

ed e

cho

ampl

itude

0 10 20 30 40 50 60 70 80 90

Θ[°]

Θ[°]

τ = 25 µs

τ = 100 µs

τ = 300 µs

τ = 50 µs

τ = 300 µs

τ = 600 µs

5=λ

2.3=λ

(b)

(a)

FIG. 5. Anisotropy of the 1H Hahn-echo signal normalized to the signal for the orientation angle

Y ¼ 08 for three values of the decay time t measured for a natural rubber band with the NMR-MOUSE1

sensor for extension ratios l ¼ 2:3 (a) and l ¼ 5 (b).

HAILU ET AL.338

Taking into account the simplified assumptions employed in the development of thetheory and the errors in the measured residual van Vleck moments, the agreement issatisfactory. Moreover, for the Hahn-echo decay time t ¼ 300 ms the simulationgives a maximum anisotropy change of 0.33 which compares well with the measuredvalue of 0.34.The segmental anisotropy of networks induced by uniaxial stretching was also

investigated by the Ostroff–Waugh [36] (OW4: yx � t� ðyy � t� echo� tÞn) andCarr–Purcell–Meiboom–Gill (CPMG: yx � t� ð2yy � t� echo� tÞn) pulse se-quences, and the results were compared with those from the Hahn-echo pulsesequence. The data are summarized in Fig. 6 in terms of effective transverserelaxation rates 1=T2eff . The highest sensitivity to the segmental anisotropy isobtained for the Hahn-echo pulse sequence (Fig. 6a). This can be explained by thefact that the train of the solid echoes generated by the OW4 pulse sequence partially

0.14

0.16

0.18

0.20

0.22

0.24

0.26

OW4CPMG

0.0

0.2

0.4

0.6

0.8

1.1

1.2

1.4

1.6

1/T 2e

ff[m

s-1]

1/T 2e

ff[m

s-1]

OW4CPMGHahn echo

0 10 20 30 40 50 60 70 80 90 100Θ [°]

0 10 20 30 40 50 60 70 80 90 100Θ [°]

(b)

(a)

FIG. 6. (a) Anisotropy of the effective relaxation rate 1=T2eff for OW4, CPMG and Hahn-echo pulsesequences. (b) A small anisotropy was also detected with the OW4 and CPMG pulse sequences. All the

data were recorded with the NMR-MOUSE1 for a uniaxially stretched natural band at an elongation

ratio l ¼ 8.

SEGMENTAL ANISOTROPY IN STRAINED ELASTOMERS 339

refocuses the residual dipolar couplings. At the same time, in the long decay timeregime the train of the Hahn-echoes for the CPMG pulse sequence is more sensitiveto the liquid-like contribution to the spin dynamics which is less affected by thesegmental anisotropy. Nevertheless, the data recorded with the NMR-MOUSE1

and shown in Fig. 6b reveal a small chain segmental anisotropy.

Spatial Distribution of the Segmental Anisotropy

The one-sided sensitive volume of the NMR-MOUSE1 sensor allows us to easilyperform measurements of the segmental anisotropy induced by a spatial distributionof strain in elastomers. This is demonstrated in Fig. 7 for a natural rubber band witha circular cut in the center. The band was uniaxially stretched to l ¼ 2:9. The circularcut changes to the shape of an ellipse. A distribution of the strain around theperiphery of the ellipse is expected to occur similar to that which was investigated fora natural rubber band with a cut on one side by measuring various 1H spinmultipolar state filtered parameter maps in high magnetic field [24]. The effective

0.18

0.14

0.11

0.14

0.13

0.19

0.14

0.11

8

7

3

12

4

65

FIG. 7. Sketch of the shape of a natural rubber band uniaxially stretched at l ¼ 2:9 with a circular cutin the center. The measurement positions of the segmental anisotropy contrast Dð1=T2eff Þ=1=T2eff ðY ¼ 08Þby 1H Hahn-echo decays are marked by numbers. The contrast values are shown underneath the position

numbers. The direction of the stretching force ~FF is also shown.

HAILU ET AL.340

TABLE 2

Effective Proton Hahn-Echo Decay Rates 1=T2eff , Anisotropy Dð1=T2eff Þ ¼ 1=T2effðY ¼ 08Þ � 1=T2eff ðY ¼ 908Þ and Relative Anisotropy Dð1=T2eff Þ=ð1=T2eff ðY ¼ 08ÞÞ Measured by the

NMR-MOUSE1 at the Locations Shown in Fig. 7 for a Natural Rubber Band with a Central Circular

Cut and an Extension of l ¼ 2:9

Position 1=T2eff ðY ¼ 08Þa 1=T2eff ðY ¼ 908Þa Dð1=T2eff Þa D=ð1=T2eff ðY ¼ 08ÞÞb

ðms�1Þ ðms�1Þ ðms�1Þ

1 1.09 0.89 0.20 0.18

2 1.08 0.88 0.20 0.19

3 0.85 0.73 0.12 0.14

4 0.84 0.72 0.12 0.14

5 0.97 0.86 0.11 0.11

6 0.99 0.86 0.13 0.13

7 0.95 0.82 0.13 0.14

8 0.95 0.85 0.10 0.11

aUncertainties are lower than 10%.bUncertainties are lower than 20%.

SEGMENTAL ANISOTROPY IN STRAINED ELASTOMERS 341

relaxation rate for the 1H Hahn-echo decay was measured for two NMR-MOUSE1

orientations relative to the direction of the stretching force, i.e., for Y ¼ 08 andY ¼ 908 for the positions 1–8 marked on the natural rubber band in Fig. 7. Thevalues of the effective relaxation rates 1=T2eff ðY ¼ 08Þ and 1=T2eff ðY ¼ 908Þmeasured for those positions are given in Table 2. The anisotropy parameterdefined by Dð1=T2eff Þ � 1=T2eff ðY ¼ 08Þ � 1=T2eff ðY ¼ 908Þ and the values of theanisotropy contrast defined by Dð1=T2eff Þ=1=T2eff ðY ¼ 08Þ are shown in Fig. 7. Thelargest anisotropy was detected for locations 1 and 2 compared to locations 3 and 4.Within the limit of experimental error, the anisotropy contrast assumes the samevalues for the locations symmetrically situated around the cut. This picture isconsistent with the results reported previously in Ref. [24] where a ‘‘butterfly’’-shaped distribution of strain in the areas surrounding the cut can clearly be identifiedand the highest strain is located at the center of the one-sided cut. Moreover, thelowest chain segmental anisotropy was detected at location 8 (cf. Fig. 7). This is,again, in agreement with the results previously reported [24].

CONCLUSIONS

A semi-quantitative theoretical expression for the Hahn-echo decay was derivedfor the case of the spin-system response in strongly inhomogeneous magnetic fields.The model is based on an isolated two-spin 1

2system. Nevertheless, the multi-spin

dipolar interactions mainly along the polymer chain and at high elongations alsobetween the neighboring chains have to be taken into account. The existence of anintrachain dipolar network in poly(styrene-co-butadiene) [37] and 1,4-cis-polyiso-prene [38] was proved directly by two-dimensional double-quantum MAS NMRspectroscopy. Moreover, the methyl group present in the monomer unit of naturalrubber cannot be described by spin-1

2pairs [38], and the correlation time describing

HAILU ET AL.342

slow chain motions is supposed to be not distributed, which is a crudeapproximation for polymers [39]. Also, the stress-induced crystallization which ispresent for natural rubber at high elongations [2] was not taken into account.The results incorporate the case of Hahn-echo decays detected in homogeneous

magnetic fields. It was shown that in contrast to the latter case, the spin-systemresponse in inhomogeneous fields cannot be written in general as a product of solid-and liquid-like contributions. For the case of the NMR-MOUSE1 sensor, anevaluation of the anisotropy of the Hahn-echo decay was presented for naturalrubber using simplifying assumptions related to the spatial distribution of themagnetic fields. It was shown that the relaxation rate anisotropy increases with theelongation ratio and the Hahn-echo decay time in agreement with the measurementsmade on stretched natural rubber bands.The strain effect and the influence of stress-induced crystallization produced by the

elongation of a natural rubber band due to uniaxial stretching was convenientlydetected with the NMR-MOUSE1. Even though a distribution of the orientation ofthe static magnetic field exists for this NMR sensor, the anisotropy of the Hahn-echodecay reflecting the segmental anisotropy induced by the stretching force wasdemonstrated. Furthermore, the anisotropy contrast defined as the differencebetween an NMR parameter (relaxation rate or signal intensity) characterizing theHahn-echo decay measured Y ¼ 08, and at the magic angle or Y ¼ 908 is smallercompared to that recorded in homogeneous magnetic fields. The larger sensitivity tothe chain segmental anisotropy is offered by the Hahn-echo pulse sequence as aresult of more efficient encoding of the residual dipolar couplings compared to theOW4 and CPMG pulse sequences. The spatial distribution of the segmentalanisotropy contrast for a stretched rubber band with a circular cut in the center wasalso mapped by the NMR-MOUSE1. This parameter map is in agreement with theprevious results employing other NMR parameters [24]. Therefore, the NMR-MOUSE1 can be used for investigations of the local segmental anisotropy in largeelastomer samples.

ACKNOWLEDGMENTS

This work was supported by a Grant (DE 780/1-1) from the Deutsche Forschungsgemeinschaft (DFG).

The authors are grateful to Dr. K. Unseld and V. Hermann, Dunlop GmbH, Hanau, for providing the

samples and helpful information. The authors acknowledge stimulating discussions with Dr. Ralf Eymael.

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