selective residual dipolar couplings in cross-linked elastomers by 1h double-quantum nmr...

Ž .Solid State Nuclear Magnetic Resonance 12 1998 139–152

Selective residual dipolar couplings in cross-linked elastomers by1H double-quantum NMR spectroscopy

R. Graf, D.E. Demco, S. Hafner, H.W. Spiess )

Max-Planck-Institut fur Polymerforschung, Postfach 3148, D-55021 Mainz, Germany¨

Received 14 December 1997; revised 24 January 1998; accepted 17 February 1998

Abstract

1 Ž . Ž .H double-quantum DQ solid-state NMR spectroscopy under fast magic-angle spinning MAS is introduced as a newspectroscopic tool for the investigation of the structure and local chain dynamics of elastomers. Dipolar connectivitiesbetween the protons of the various functional groups can be directly established from the highly resolved DQ solid-state

Ž .NMR spectra as is shown for a series of cross-linked poly styrene-co-butadiene . More quantitatively, residual dipolarcouplings within and between the functional groups are evaluated selectively from the build-up curves of the double-quan-tum signals in the limit of the spin-pair approximation. In particular, the CH–CH and the CH –CH couplings of butadiene,2

which both act predominantly along the chain-segment direction, have been measured relative to the CH coupling. The2

total build-up intensity is correlated with the cross-link density. q 1998 Elsevier Science B.V. All rights reserved.

Keywords: Selective residual dipolar couplings; Cross-linked elastomers; NMR spectroscopy

1. Introduction

Ž .Multiple-quantum MQ NMR spectroscopy is well established for structural studies of liquids and highlyw xmobile solutes in liquid crystals 1–3 . In recent years there has been a sustained effort to obtain homonuclear

w x w x Ž .4–19 and heteronuclear 20,21 high-resolution multiple-quantum MQ NMR spectra of solids containingŽ .dipolar-coupled nuclei by using fast magic-angle sample spinning MAS to increase resolution and sensitivity.

The measured MQ spectra proved to be valuable tools for determining dipolar connectivities between spin-1r2w x 31nuclei, such as protons and carbons in organic solids including polymers 4–7,11,17–20 and for P in

w x Ž .crystalline or glassy phosphates 8,9,13,14,16 . More quantitatively, by analyzing double-quantum DQw xspinning sideband patterns in the spin-pair approximation 6,11 , internuclear distances, residual dipolar

w xcouplings and molecular torsion angles can be measured 10,12,21 . Thus, MQ techniques can be applied to abroad range of materials to obtain information on the local structure and the molecular dynamics which is aprerequisite for improving the material.

) Corresponding author. Fax: q49-6131-379-100

0926-2040r98r$ 19.00 q 1998 Elsevier Science B.V. All rights reserved.Ž .PII: S0926-2040 98 00058-7

( )R. Graf et al.rSolid State Nuclear Magnetic Resonance 12 1998 139–152140

w xA technologically important class of materials is represented by elastomers 22–24 , which thus have beenw x w x Žintensively investigated by various NMR techniques 25 including 2D spectroscopy 26,27 and references

.therein . From the viewpoint of NMR, cross-linked elastomers exhibit both liquid-like and solid-like features. Attemperatures well above the glass transition temperature, the time scales of molecular motions are liquid-like.However, the presence of topological constraints and permanent cross-links prevents the chain motion frombeing isotropic. Thus, anisotropic spin interactions, such as the dipole–dipole coupling are not completely

Ž w x .averaged out and give rise to solid-like properties Refs. 25–30 and references therein . Depending on thedegree of motional restriction, these residual dipolar interactions may be quite small, i.e., on the order of a few

w xpercent of those found in rigid solids 17,26,27 .Residual dipolar interactions are reflected in different ways in the various NMR parameters. For instance, the

13 1 w xshort-time behavior of C-edited transverse H relaxation curves 26,31,32 or of cross-polarization build-upw xcurves 26,33 is dominated by residual dipolar interactions within functional groups. Inter-group residual

dipolar couplings, such as the CH–CH coupling on the other hand can be investigated using one-dimensional2Ž . 1 w xand two-dimensional 2D H magnetization-exchange spectroscopy 27 . In all cases, the measured residual

couplings are found to be sensitive to the cross-link density and can be correlated with viscoelastic properties,such as the shear modulus.

In this paper, such investigations are extended by applying 1H high-resolution MQ NMR spectroscopy whichw xoffers the possibility to measure site-selective dipolar couplings between all resolved protons 34 . Because of

Ž .this selectivity, the MQ technique is an attractive tool for studying structure connectivities and dynamics inw x w xpolymer melts 17 and elastomers 4,14,15 .

2. Theoretical background

2.1. The residual spin Hamiltonian

The rotating-frame Hamiltonian of the anisotropic couplings in a spinning sample is given by

Žk . Ž i j.H t s H q H t , 1Ž . Ž . Ž .Ý Ýz dk i-j

where the bar represents averaging due to fast molecular motions. The Zeeman Hamiltonian for magneticallyequivalent spins k is

H Žk .syDv I . 2Ž .z k k , z™ Ž .I is the total spin operator for the spins k and Dv s v qd yv, where d is the isotropic chemical shiftk k 0 k k

of the spins k, v is the Larmor frequency and v is the transmitter frequency. The chemical-shielding0

anisotropy of the protons can be neglected to a good approximation. The intra- and intergroup residual secularŽ . w xdipolar Hamiltonian for a spin pair ij under the MAS conditions can be expressed as 11

y2,2Ž i j. i j Ž2. i j Ž2. im v t i jR'H t s y 6 D D V d b e T . 3Ž . Ž . Ž . Ž .Ž .Ýd 0,ym ym ,0 M 2,0

m/0

Here b s54.78 is the magic angle of the rotor axis relative to the direction of the static magnetic field. TheMi j Ž i j i j i j. Ž .symbol V denotes the Euler angles a , b , g that relate the principal axes of each ij -dipolar-coupling

Ž .tensor which has a known relation to a polymer-chain segment to the reference frame of the rotor. For adisordered polymer, the initial rotor phase is irrelevant. The conventions used for the Wigner rotations matrices

Ž2. Ž i j. yi m a Ž2. Ž i j. yi mXg w x Ž i j.

X XD V se d b e are those defined in Ref. 35 and T are irreducible tensor operatorsm ,m m ,m 2,0w x Ž .given in Ref. 6 . The bar in Eq. 3 represents the average over the molecular reorientations which are faster

( )R. Graf et al.rSolid State Nuclear Magnetic Resonance 12 1998 139–152 141

than the spin-precession period in the rigid-lattice local dipolar field. This averaging by rapid segmental motionsw xis referred to as ‘pre-averaging’ in the literature 25 and the bars on top of the corresponding expressions

denote this pre-averaging process throughout this paper.The residual dipolar interactions can be evaluated using the scale-invariant polymer model proposed by

w x Ž .Cohen-Addad 25 and references therein . In this model, the dipolar interaction of a given spin pair is averagedŽ .over all conformations of a so-called submolecule inter-cross-link chain subject to the constraint that the

™end-to-end vector R of this submolecule is fixed. It is assumed that for the length scale of the functional groups,the reorientation of the spin-pair vectors by conformational changes is much faster than the time scale set by thestatic dipolar interaction and the rotor frequency. For a rescaled chain described by this statistics, the residual

w xdipolar coupling may be expressed as 29,36

k ™i j Ž2. i j i j i j 2 Ž2.D D V sD S R D V , 4Ž . Ž . Ž .0,ym 0,ym2 2N a

i j 2 3 2 3Ž . Ž .Ž . Ž .where the dipolar coupling constant D s m r4p g " 1rr f m r4p g "rr of the ij -pair dependsŽ .0 i j 0 i j

on the average internuclear distance r . This average must be performed because the distance between protonsi j

of different groups fluctuates due to local conformational jumps. The dipolar coupling between the CH protonand the two CH protons in the butadiene component of a styrene–butadiene rubber, for instance, is2

approximated by the dipolar coupling between the CH-proton and an effective spin 1 nucleus located at anw xaverage distance r 27 .CH – CH 2

i j i j i jw Ž .x Ž .The dynamic order parameter for a site-specific coupling is given by S sP cosu t , where u t is the2 ™™Ž .instantaneous angle between a given intramonomer dipolar coupling vector r and R. P represents thei j 2Ž .second-order Legendre polynomial averaged by fast molecular motions. The average in Eq. 4 is performed

using a simple model to describe the chain statistics, i.e., a chain of N freely jointed segments of length a fixedw xat both ends 37 . All intrachain motions are assumed to be fast enough to average elementary interactions,

w xwhereas the average positions of the junctions are static 36 .The geometrical factor k depends on the model which is adopted to describe the chain statistics and is equal

w xto 3r5 for a chain of freely jointed segments 38 . On the other hand, for a quantitative comparison with actualpolymer chains, the local geometry and dynamics as well as the limited chain flexibility have to be taken intoaccount. Therefore, the parameter N which describes the effect of the long-range structure, for instance thecross-link density, should not be strictly identified with the number of repeat units between cross-links but is

w xonly qualitatively related to it. In particular, N may be strongly biased by topological constraints 28 if theaverage chain length between them is significantly shorter than the distance between cross-links. Thus, at thispoint, all details of the spin interactions which depend on the local chemical structure of the chain monomers areincluded in the factor k.

™w xIn a disordered polymer, the end-to-end vector R usually is assumed to obey ideal Gaussian statistics 25 .

™2 2Ž ² : . ² : w xThe statistical average denoted by of the squared end-to-end vector is R fNa 26 . Thus, theR R

Ž . y1residual dipolar coupling obtained from Eq. 4 scales as N .The dipolar tensor is partially averaged by fast intergroup rotations about the segment axis. The resulting

Ž . Ž2. Ž .average value is described in Eq. 4 by the Wigner rotation matrices D V which depend on the Euler0,ym™Ž .angles V a ,b ,g between the end-to-end chain vector R and the reference frame of the rotor.

2.2. The effectiÕe double-quantum Hamiltonian

w xThe MQ experiment, Fig. 1a, is a 2D experiment 1,35 . At first, MQ coherences are excited during a timet . Subsequently, they evolve during an evolution time t and then are reconverted to detectable single-quan-exc 1

Ž .tum SQ coherences after a reconversion time t s t . The experiment is performed under the conditions ofrec exc

fast MAS. That is, the rotor frequency v is bigger than the strongest residual dipolar coupling between twoR


Ž . ŽFig. 1. a General scheme of 2D MQ spectroscopy. During both intervals of free precession MQ coherences during t and SQ coherences1.during t dipolar decoupling can be achieved by MAS. Possible pulse sequences used for excitationrreconversion of MQ coherences are:2

Ž . w x Ž . w xb broadband BABA 8 and c C7 39 .

i jŽ . Ž .protons, i.e., v 4max D , and also bigger than the chemical-shielding interaction, i.e., v 4max d .R R k

Hence, an efficient averaging of the anisotropic spin interactions takes place during the evolution and detectionperiods and leads to liquid-like NMR spectra. During the excitation and reconversion periods of the experiment,

Ž .however, the dipolar interactions are required for the generation and reconversion of the MQ coherences. Therelevant parts of the dipolar Hamiltonian can be introduced by broadband dipolar-recoupling pulse sequences,

w x Ž . w x Ž .such as BABA 8 , see Fig. 1b , or C7 39 , see Fig. 1c . For the spin-pair approximation to be valid, we mustensure that the duration of the excitation and reconversion periods of the DQ experiments are short enough that

w xno higher-order MQ coherences are generated 6 .w x w xThe zero-order average DQ residual Hamiltonians for one rotor period for the BABA 8 and C7 39 pulse

sequences are given by

3 k ™exc i j i j 2 i j i jH s D S R sin 2b sin g T qT , 5Ž . Ž . Ž .� 4ÝDQ 2,2 2,y22 2ž /' N ap 2 ij-pairs

and

y343 k ™exc i j i j 2 ip r14 yig i j yi p r 14 ig i jH s D S R sin 2b e q i e T q e y i e T , 6Ž . Ž . Ž . Ž .� 4ÝDQ 2,2 2,y22 2ž /' N a520p 2 ij-pairs

respectively. The summation is performed over all spin pairs within or between the different functional groups.In order to compensate for the chemical-shift interaction, a super-cycle with a cycle time t s2t must bec R

w x Ž .implemented 8,39 . The norm of the BABA DQ Hamiltonian, Eq. 5 , averaged over all crystallite orientation is


Ž Ž ..approximately twice that of the C7 sequence see Eq. 6 which leads to a higher slope in the build-up curves ofthe DQ coherences.

2.3. Build-up curÕes of the double-quantum intensities

w xIn elastomers with weak residual dipolar couplings in the order of 1 kHz 27 , the fast spinning regime isfulfilled even for the relatively modest spinning frequencies of 6–10 kHz. SQ spinning sidebands thus are of alow intensity compared with the centerband and higher-order DQ spinning sidebands are even negligible. Thus,for evaluating residual dipolar couplings from DQ spectra, build-up curves of the DQ-coherence intensity mustbe analyzed.

In the limit of fast MAS and short excitationrreconversion times, the total DQ signal is a linear superpositionw xof the DQ signals of the different spin pairs. Following the results presented in Ref. 11 , the normalized DQ

Ž .free induction decay for the ij -spin-pair is given by

3 k ™i j i j i j 2S t ; t s0 s sin D S R sin 2b cos gqv t ntŽ . Ž . Ž .DQ ,BABA 1 2 R 1 R2 2¦¦ ' N ap 2

=3 k ™i j i j 2sin D S R sin 2b cos g nt , 7Ž . Ž . Ž .R2 2 ; ;' N ap 2 R V

and

1r2343 p k ™i j 2 i j i j 2S t ; t s0 s sin 1qsin D S R sin 2b nt , 8Ž . Ž . Ž .DQ ,C7 1 2 R2 2¦ ;ž /½ 5¦ ;520p 14 N a R V

where nt is the duration of the excitation and reconversion periods expressed in units of the rotor period t . InR R

the case of C7, only the integral intensity of the DQ free-induction decay is affected by the residual dipolarŽ . i jcouplings. In Eq. 8 , the variable t in the argument of S accounts for the modulation by the chemical1 DQ,C7

shifts of the spin pair during t , the corresponding dependence, however, is not explicitly given in the formula.1Ž . Ž . Ž .The normalization factor in Eqs. 7 and 8 is the amplitude of the single-quantum FID of the ij -spin-pair.

²² : : w xThe symbol represents the ensemble average over the distribution of the end-to-end vectors 25 andR V

the powder average of the angular part of the residual dipolar coupling in the disordered elastomer.Ž .The DQ build-up curves for selectively determining the couplings between two spins i, j are obtained from

the integral intensities of the corresponding DQ peaks acquired as a function of the duration of theŽ .excitationrreconversion periods which is varied in multiples of 2t . To a good approximation, the integralR

Ž . Ž .intensity for each resolved DQ peak can be evaluated from Eqs. 7 and 8 as

3™i j 2 i j i j 2S t s0; t s0 s sin D S q sin 2b cos g nt , 9Ž . Ž . Ž . Ž .DQ , B A B A 1 2 R¦ ;¦ ;½ 5'p 2 R V

and

1r2343 p™i j 2 i j i j 2S t s0; t s0 s sin 1qsin D S q sin 2b nt , 10Ž . Ž . Ž .DQ ,C 7 1 2 s R¦ ;ž /½ 5¦ ;520p 14 R V

™™2 2 2 i jrespectively. Here we introduce q 'R rNa . The scaled dynamic order parameter is defined as S 'sŽ i j. Ž . Ž . Ž .S r N . The DQ intensity described by Eqs. 9 and 10 depends only on the effective number of statisticale

Ž . Ž .segments N ' N r k .e


In the limit of fast MAS, short excitationrreconversion times, andror weak residual dipolar couplings, thati j i j Ž . Ž .is D S nt <1, the site-selective integral intensities Eqs. 9 and 10 can be rewritten using a linears R

approximation for the sine function

6 2 2 ™i j i j i j 2 2 4² :S t s0; t s0 s D S n t q , 11Ž . Ž . Ž .Ž . RDQ ,BABA 1 2 s R25p

and2'686 2 p 2 2 ™i j i j i j 2 2 4² :S t s0; t s0 s 1qsin D S n t q , 12Ž . Ž . Ž .Ž . RDQ ,C7 1 2 s Rž /ž /' 14520p 15

™where the average over the Euler angles of the R vector is performed according to

p 2p1

² :. . . ' sinbdb dg . . . . 13Ž . Ž . Ž .H HV 4p 0 0

It is evident from the above relationships that the slope of the DQ intensity built-up curves is about fourtimes smaller for the C7 sequence than for BABA. Although at first sight this appears to be a disadvantage ofC7 it is actually advantageous for our purpose, because we confine to multiples of the rotor period in order tocompletely eliminate the chemical-shift anisotropy in the quantitative measurements described below. A slowerbuild-up of the DQ intensity allows the sampling of more points and thus a better definition of the curve.Therefore, C7 is used for our experiments. Also, we concentrate on the initial part of the build-up curves whichis less sensitive to slow motions, to the appearance of multiple-spin modes, such as high-order correlations andhigher-order multiple-quantum coherences and to pulse imperfections. Absolute values of the coupling constantscannot be determined directly from such double-quantum build-up curves for these reasons. At this stage, onethus is confined to the relative values, that is, the ratios of the coupling constants for the various couplings. This

™4² :also implies that the chain statistics used for evaluating q is unimportant since this factor does not enter theR

ratios.To estimate the absolute values of the couplings, the value of one of them is required, for instance that of the

strongest coupling, the coupling between the two protons in the CH group. This can be achieved either by a2w xrelatively sophisticated calibration of the DQ spectrum 40 or, preferably, from the analysis of the single-quan-

Ž .tum SQ spinning sideband pattern in the two-spin approximation. The normalized SQ free-induction decay ofw xa spin pair under MAS conditions is given by 6

i j i j3 D S 1s ™Ž i j. 2 'S t s cos q 2 sin 2b sin v tŽ . Ž .SQ Rž /¦¦ 2 v 2R

=1 1

2cos gq v t y sin b sin v t cos 2gqv t . 14Ž . Ž . Ž . Ž .R R Rž / ; ;2 2R V

The rotor-frequency must now be chosen such that the intragroup dipolar couplings between the protons of theCH group still lead to detectable sidebands while the weaker couplings are sufficiently reduced to justify the2

two-spin approximation and to permit resolution of the lines in the spectrum.For these conditions, a simpler relationship for the evaluation of the sideband pattern can be derived from Eq.

Ž . w x14 by performing a series expansion followed by an analytical powder average 40 . One obtains

20 ISB™4 i j i j² :( q D S s v , for I -0.01 I , 15Ž . Ž .(R s R SB CB(3 ICB

where I is the intensity of the centerband and I is the intensity of one of the two first-order sidebands.CB SB


i j Ž .The determination of S from the residual dipolar couplings, Eq. 15 , now requires the calculation of thes™i j 4² :static couplings D from the known proton distances and the evaluation of the average value q . This isR

usually performed assuming Gaussian statistics of the end-to-end vectors and results in

1r2`6 3 1

™ ™ ™4 2 4² :q s exp y q q dqs . 16Ž .R H ½ 5ž /p 2 30

Within the validity of Gaussian statistics, the values of the order parameters can thus be determined.

3. Experimental

3.1. Samples

Ž .The investigated elastomer system is based on the synthetic rubber BUNA 1924 S25 Bayer, Leverkusen , aŽ . Ž .poly styrene-co-butadiene rubber polymerized from solution. It is composed of 23.4% styrene units wt.%’s

and 76.6% butadiene units distributed in a random sequence. The distributions of the different configurations ofŽ . Ž . Ž .the butadiene units is: 40.2% trans or 30.8% including the styrene , 33.9% 26% vinyl and 25.9% 19.8%

cis-butadiene. The glass transition temperature is T s226 K. The investigated samples of the cross-linkinggŽ .series contain 3 phr parts-per-hundred rubber ZnO and 1 phr stearic acid. The sulfur and accelerator content

are shown for the different samples in Table 1.After mixing the compounds in a laboratory mixer at 508C, the vulcanization was performed at 1508C in a

vulcameter. The cross-link densities of samples A–E were controlled by measuring the stress s that has tols2Ž .be applied for drawing the sample to an elongation of ls2 see Fig. 5b, below . This quantity is often used in

tire industry for such a purpose.

3.2. NMR measurements

The NMR experiments were performed on a Bruker ASX 500 NMR spectrometer operating at a 1Hfrequency of 500.13 MHz. A standard Bruker 4 mm MAS probe was used which allows a maximum spinningfrequency of 15 kHz. A 908 pulse length of about 4 ms was applied in the experiments. DQ coherences were

w xexcited and reconverted with the C7 pulse sequence 39 following the general scheme of 2D multiple-quantumspectroscopy shown in Fig. 1. The increment in the indirect dimension t was 15 ms. The over-all pulse phases1

for the excitation period were phase cycled according to the time-proportional phase-incrementation procedurew x Ž .for recording DQ spectra 1–3 . The measurements were performed at room temperature Ts293 K which

corresponds to TfT q70 K for the investigated elastomer series.g

Table 1The SBR cross-linking series

Ž . Ž .Sample Sulfur phr Accelerator phr

A 0.8 0.8B 1.2 1.2C 1.6 1.6D 2.0 2.0E 2.4 2.4


4. Results and discussion

4.1. Dipolar connectiÕities from the high-resolution 1H DQ MAS spectrum

A prerequisite for the analysis of DQ spectra is the resolution of chemically distinct sites. As a demonstrationof the resolution that can be obtained by MAS in elastomers, Fig. 2 shows the 1H SQ spectra of the sample with

Ž . Ž .the highest a and the lowest b cross-link density acquired at a spinning frequency of 15 kHz. Comparing thetwo spectra, almost no indication of different cross-link densities is found because the dipolar couplings areaveraged out nearly completely by MAS for both cases. The resolution provided by MAS is comparable to that

Žfound in solution spectra of the unvulcanized material. This allows the assignment of all major signals see. w xFig. 2 and the evaluation of the percentage of the vinyl butadiene, which was found to be 26.6% 41 in

Ž .agreement with the value provided for the synthetic rubber BUNA 1924 S25 by the producer 26.0% . Note,that the evaluation of this value from the MAS spectra can be performed on the final product, that is, on thefully cross-linked sample.

Fig. 3b shows the 1H DQ spectrum of the least cross-linked sample which has been acquired at a spinningfrequency of 10 kHz. On top of the 2D spectrum, the single-quantum projection is shown. The minor deviationsof this spectrum from the two spectra of Fig. 2 not only result from the lower rotor frequency but also from DQfiltration due to the excitation and reconversion parts of the 2D sequence which favors more strongly coupledprotons.

Ž . Ž .Fig. 2. High-resolution proton SQ MAS spectra of the SBR samples with the highest cross-link density a sample E and lowest cross-linkŽ . Ž . Ž . Ž .density b sample A , acquired at a rotor frequency of 15 kHz. The peaks marked by a – f correspond to the various functional groups of

Ž .the butadiene and styrene monomers see Fig. 3a .


Ž .Fig. 3. Proton DQ MAS spectrum of the SBR sample with the lowest cross-link density Table 1 . The rotor frequency was 10 kHz and thet increment was 15 ms. The diagonal peaks and the cross peaks of the functional groups are assigned as indicated.1

Various peaks are found in the DQ spectrum. They correspond to double-quantum coherences between twospins which must be relatively close neighbors in space in order to contribute significantly to the peak intensityas follows from the strong distance dependence of the dipolar coupling. From the existence of the correspondingpeaks therefore through-space dipolar connectiÕities can be established. The assignment of the peaks is shown

Ž .along the v dimension by pairs of letters a–f see Fig. 3a which indicate the functional groups that are1

involved in the generation of the corresponding DQ peaks.Some conclusions can be drawn from a simple qualitative inspection of the DQ spectrum. When comparing

Ž .the intensities, however, one should keep in mind that also the relative number of the protons of thecorresponding functional group has to be taken into account as well as the molecular dynamics. Nevertheless,from Fig. 3b, it can be seen that there are dipolar connectivities between practically all functional groups. The

Ž .strongest DQ signals are found between protons of the polybutadiene PB groups, but also DQ peaks ofconsiderable intensity are visible between the PB protons and the aromatic protons of the styrene units. Thisindicates a good mixture of the different functional groups on the nanometer length scale as is found forinstance in the case of a statistical copolymer. Only the protons of the vinyl configuration of polybutadieneŽ .labelled by the letter c in Fig. 3a produce DQ signal exclusively with themselves apart from a weak coupling

Ž .to the CH group of the same unit. The dynamics of the corresponding side chain see Fig. 3a obviously issufficient to average out the couplings between these CH protons and other functional groups leaving only the2

intragroup CH coupling. This shows that in mobile polymers not only structural parameters but also the2

mobility of the corresponding group determines the DQ intensity. Also, other deviations are found whencomparing the measured peak intensities with those that are expected by only considering structural parameters.For instance, if only structural parameters are considered, the peak ee that results from intragroup coherences


should have a much stronger intensity compared to the others due to the comparatively small distance betweenthe CH protons. Thus, even by qualitative inspection, it is evident that local molecular dynamics plays an2

important role in such DQ spectra. In Section 4.2, we will attempt to evaluate this more quantitatively byanalyzing the build-up curves.

4.2. Site-selectiÕe double-quantum build-up curÕes

The experimental site-selective proton DQ build-up curves for the SBR samples with the lowest and theŽ .highest cross-link densities sample A and E, see Table 1 are presented in Fig. 4. After an initial parabolic

dependence on the excitationrreconversion time nt , the build-up curves reach maxima and then decay withRw xdifferent rates. Simulations of these build-up curve for an isolated spin-pair, on the other hand, show 11 that

after an initial parabolic rise period the DQ intensity should oscillate about a saturation level. This, however, isnot found in the experiments. Instead, a decay of the DQ build-up curves takes place for longer excitation times.This decay is related to the relaxation of DQ coherences by the chain motions, the pumping of higher-ordercoherences and the accumulation of radio-frequency pulse imperfections. From Fig. 4a and b, it is evident thatthe proton DQ coherences corresponding to the CH groups decay faster than those of the CH –CH and2 2

Ž . Ž .Fig. 4. Site-selective proton DQ build-up curves for the lowest and highest cross-linked samples, A a and E b , respectively. The build-upŽ . Ž . Ž .curves have been recorded using the C7 pulse sequence see Fig. 1c . The DQ signals correspond to the –CH – B , CH –CH– ' and2 2

Ž .CH–CH coherences v . The vertical dashed lines mark the excitation times for the maximum signal for the methylene protons, whichdiffers for the two cases.


CH–CH groups. Since this decay is directly correlated with the strength of the corresponding residual dipolarcouplings, it is probably dominated by relaxation due to fluctuations of the local dipolar fields. At this stage, wedescribe this decay approximately by an ad hoc exponential function with an effective relaxation rate T . Thus,eff

Ž .from Eq. 12 we can write

t2 exc™i j i j i j 4 2² :S t s0; t s0 fA D S q t exp y , 17Ž . Ž .Ž . RDQ ,C7 1 2 s exc i jž /Teff

where t snt is the duration of the excitation or reconversion periods and A is a factor that describes theexc R

efficiency of the recoupling pulse sequence and instrumental parameters. Fitting the experimental DQ built-upŽ . Ž .curves for the different DQ peaks using Eq. 17 see Fig. 4 allows to determine the ratio of the corresponding

CH CH CH – CH CH – CH CH – CH CH – CH i j2 2 2 2Ž . Ž . Ž .couplings, i.e., D S : D S : D S , where D represents a preaveraged dipolars s s

coupling constant and Si j the corresponding order parameter. As an example, ratios of the different couplings

constants have been determined for the samples with the lowest and the highest cross-link densities and aregiven in Table 2.

The fact that residual dipolar couplings changes with the cross-link density can also be seen qualitativelyŽ .from Fig. 4. In the build-up curve of the sample with the lowest cross-link density Fig. 4a, sample A , the DQ

intensity of the methylene protons reaches the maximum value after a longer excitation time compared with thatŽ . Ž .of the curve corresponding to sample E Fig. 4b which has the highest cross-link density see Table 1 .

Ž .So far, only the relative couplings have been evaluated since some of the factors in Eq. 17 , such as thefactor A or the actual relaxation time are not known. As outlined before, the absolute values can be determined

Ž .by evaluating the CH residual dipolar coupling from SQ MAS spinning-sideband patterns using Eq. 15 . In2

practice, however, this is difficult since the sidebands are of a relatively low intensity at the rotor frequenciesthat are necessary to achieve a sufficient separation of the lines and to fulfil the two-spin approximation. Foreach sample, therefore, several measurements have been performed at rotor frequencies between 4–6 kHz, andthe average values have been determined. At these frequencies, only first-order spinning sidebands show

Ž .significant intensities and the evaluation can be performed conveniently using Eq. 15 . Because of the relativelylow intensities of the sidebands which are on the order of the wings of the centerband lines, the resulting valuesonly give an estimation of the strength of the CH coupling which is accurate to around 10%.2

The resulting values for the highest and lowest cross-linked samples are given in Table 2 together with theratio of the couplings, so that the absolute values of all couplings can be determined from Table 2. From theseabsolute values, the scaled dynamic order parameters Si j can be evaluated taking into account the geometricals

w xparameters of the configurations of the polybutadiene 42 and assuming a Gaussian distribution of theŽ Ž .. Ž . CH 2 Ž .end-to-end vectors Eq. 16 . The values for the samples A and E in brackets are S s0.083 0.092 ands

CH 2 – C H Ž . CH 2 – CHS s0.092 0.104 , respectively. The order parameters S thus are found to be close to the values s

SCH 2 – CH s0.1 that has been estimated for a different series of SBR samples by magnetization-exchangesw x CH – CHexperiments 27 . For determining the order parameter S for the line connecting two CH protons, thes

Table 2The ratios of the residual dipolar couplings and order parameters of the different functional groups for the SBR samples A and E of thecross-linking series

Sample A E

CH CH CH – CH CH – CH CH – CH CH – CH2 2 2 2Ž . Ž . Ž .D S : D S : D S 1:0.41:0.60 1:0.38:0.60s s sCH CH – C H CH – CH2 2Ž . Ž . Ž .S : S : S 1:1.11:1.88 1:1.13:1.88s s s

™4 CH CH2 2² :' q D S 1.0 kHz 1.1 kHzR s

The absolute values of the CH residual dipolar coupling are also given for the calibration of the other couplings. The value has been2Ž .determined from SQ sideband pattern, Eq. 15 .


Ž .percentage of the different configurations has to be taken into account see Section 3.1 . The average values forCH – CH Ž .the two samples are given by S s0.156 0.173 .s

Note, however, that these values of the dynamic order parameters are not determined directly from thedouble-quantum intensities but rely on the accuracy of the measurement of the CH coupling from the2

sidebands. Also, they have been evaluated assuming a Gaussian distribution of the end-to-end vectors. Thus, inTable 2, only the ratios of the order parameters are given since they are independent of the assumed statisticsand nevertheless allow the comparison of the different groups and samples. Within the experimental errors, thecross-linking appears to affect the dynamic order parameters of different functional groups in the same way.

4.3. Correlation with the cross-link density

Residual dipolar couplings between the CH and CH protons show a linear dependence on the cross-link2w xdensity 27 . From a series of DQ experiments the behavior of all site-selective couplings could be investigated

in principle. For a series of differently cross-linked samples, however, this is very time-consuming. A lessdetailed but also less time-consuming method for probing the correlation of residual dipolar couplings with the

Žcross-link density or viscoelastic properties is the measurement of the integral DQ-filtered signal normalized to.the integrated SQ-signal . In the limit of short excitationrreconversion times this quantity is composed of the

Ž . 1 Ž .Fig. 5. a The square root of the normalized integrated H DQ signal for the SBR cross-linking series samples A–E, see Table 1 as aŽ .function of the sulfur-accelerator content. The residual dipolar couplings are dominated by topological constraints. b Stress s requiredls2

Ž . Žfor drawing samples A–E to twice their length ls2 as a function of the cross-link density sulfur-accelerator content in parts per hundred.rubber . It increases with the cross-link density and assures that the cross-linking of the series was successful.


contributions from the site-selective residual dipolar couplings. In Fig. 5a the square root of the total DQŽ .intensity is plotted vs. the cross-link density sulfur-accelerator content . The dependence is approximately

Ž .linear and only sample E smallest cross-link density deviates slightly from this behavior which might reflectw xthe increasing importance of topological constrains for lower cross-link densities 17,28 . As noted before

w x26,27 , residual dipolar couplings in moderately cross-linked SBR rubbers at temperatures 50–80 K above TgŽ w x.are dominated by topological constraints that are already present in the melt see also 17 . This is evident from

Fig. 5a where the DQ intensity extrapolated to zero cross-link density is much larger than the differencebetween this intercept and the value for the highest cross-linked sample E. The techniques thus is not a sensitivemeasure of the cross-link density as relaxation processes, such as T are, but is a rather sensitive and selective1 r

probe for local dynamic chain order.In order to assure that the vulcanization of the cross-linking series was successful, Fig. 5b shows the increase

of the stress required for drawing samples of the cross-linking series to twice their length as a function of thesulfur-accelerator content.

5. Conclusions

The spectroscopically resolved 1H DQ technique provides supplementary information to that accessible byw x w xpreviously reported methods using spin echoes 25,28,30 , heteronuclear local dipolar field measurements 32

w xand magnetization exchange 27 .Proton dipolar connectivities between functional groups can be investigated by a qualitative analysis of a

highly resolved solid-state DQ spectrum. Useful information on phase-separation and sample composition isdirectly accessible from such a spectrum. Also, DQ spectroscopy can help one to assign lines in a SQ spectrumby providing connectivities between unknown lines and already assigned lines. However, care has to be takenwith such a qualitative interpretation of DQ spectra, in particular in the case of unknown samples. All availablesupplementary information must be taken into account as well. For instance, a rough estimate of the molecularmobility can be made from the linewidth of the corresponding SQ spectrum while the relative number of spinsbelonging to chemically different sites can be obtained from the integration of the lines.

Performing such an investigation in a more quantitative way, 1H-DQ-NMR spectroscopy permits site-selec-tive measurement of residual dipolar couplings between protons belonging to the same or to different functionalgroups. In principle, the latter case can be also investigated by 2D magnetization-exchange spectroscopyperformed in the short mixing-time regime. However, for evaluating the data, a model of the spin topology isrequired while DQ MAS spectroscopy allows a model-free access to the ratio of the site-selective couplings

w xwhen the spin pair approximation is valid 14 . Another possibility for the direct measurement of such couplingsw x 13has recently been reported 32 . It exploits the indirect observation of protons through C resonances in a 2D

w xWISE experiment 35,31 . The advantage of proton MQ experiments compared with this conceptually relativelysimple technique is that the acquisition of the signal from low abundance isotopes is avoided.

From the absolute values of the residual dipolar couplings, order parameters could be determined. Thedetermined values depend on the assumed distribution of the end-to-end vectors. Such an assumption can beavoided by considering ratios of the order parameters. A different degree of motional averaging was found forthe different functional groups. The order parameter corresponding to the CH–CH coupling provides the bestmeasure for the chain dynamics since this coupling is predominantly aligned along the segmental axis.

The evaluation of site-selective couplings is relatively time-consuming especially when a series of sampleshas to be evaluated. In this case, overall residual dipolar couplings can be recorded using MQ filtration. Whilethis substantially reduces the measuring time it does so at the cost of site selectivity. Which variant of thetechnique is actually chosen thus depends on the nature of the investigated problem, that is, how muchinformation is desired and how much measuring time is available.


Acknowledgements

The authors acknowledge financial support from the Volkswagen-Stiftung. We would like to thank Dr. G.Heinrich and Dr. H. Dumler, Continental, for providing the samples and for helpful discussions. We would alsolike to thank Prof. Dr. R. Kimmich, Prof. B. Blumich, Dr. A. Dardin and Dr. S. De Paul for stimulating¨discussions.

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