STUDIA UNIVERSITATIS BABEŞ-BOLYAI, PHYSICA, SPECIAL ISSUE, 2001
RESIDUAL DIPOLAR COUPLINGS IN CROSSLINKED
ELASTOMERS INVESTIGATED BY MAGNETIC EXCHANGE NMR
XENIA FILIP, C. FILIP1, D.E. DEMCO2
National Institute for R&D of Isotopic and Molecular Technologies,
P.O.Box 700, R-3400 Cluj-Napoca, Romania
1
Francis Bitter National Magnet Laboratory, MIT, Cambridge, Massachusetts
2
Institute of Technical Chemistry, RWTH Aachen, Germany
ABSTRACT. Solid-state one-dimensional proton magnetization-exchange is used to
investigate intergroup residual dipolar couplings in cis-1,4-polybutadiene and poly(styreneco-butadiene). A three spin model is employed, in which the CH – and CH2 – group are
considered to be coupled by residual dipolar interactions.
1. Introduction
Crosslinking of technical elastomers is of crucial importance for the
mechanical properties of rubber products. From the viewpoint of NMR, crosslinked
elastomers exhibit both solid- and liquid-like features. The presence of topological
constrains and permanent crosslinks in these materials leads to a non-zero average of
anisotropic spin interactions, such as dipole-dipole couplings. In this work one uses
solid-state NMR magnetization exchange for investigating intergroup residual dipolar
couplings in cis-1,4-polybutadiene and poly(styrene-co-butadiene) (SBR 1500)
elastomers.
2. Spin-system model
CH
CH
CH2
a)
CH2
rCH-CH
2

n
rHH
b)

R
R
Fig.1.The CH-CH2 spin system
The model which will be considered in the
following to describe the proton magnetizationexchange in cis-1,4-polybutadiene and SBR 1500
is based on the following assumptions and
properties of the polymer chain:
i) SBR 1500 is a copolymer with 23.5% styrene
units and 76.5% butadiene units distributed in a
random sequence [1]. The majority of functional
groups (a  CH2, b  CH) are arranged in a pair
sequence aabbaa…. This pair sequence is present
also in cis-1,4-polybutadiene. The alternating
sequence abab… is less frequent. The relevant
spin system is depicted in Figure 1a.
ii) Chemical crosslinks lead to restrictions of the
chain motions and hence to a non-zero average of
the dipolar interactions between the protons of
the CH2 – and CH – group along the chain.
Depending on the degree of motional averaging,
XENIA FILIP, C. FILIP, D.E. DEMCO
these residual dipolar interactions may be scaled to quite small values. They reflect
single-chain properties because the fast molecular motions of the polymer chains
effectively average the interchain dipolar interaction [2]. The validity of these
assumptions was proven by a 2D magnetization-exchange experiment performed with
a short mixing time [3].
iii) Fast anisotropic molecular motions lead to partially narrowed static proton
spectra. At room temperature, two lines are resolved in the static proton spectrum (for
cis-1,4-polybutadiene and SBR 1500). One line corresponds to the CH-groups and the
other to the CH2- groups.
iv) The dipolar couplings between two neighboring CH groups or two
neighboring CH2 groups, respectively, are not relevant with respect to measurements of
the magnetization-exchange dynamics at short mixing times [4,5].
In conclusion, the measurable exchange of longitudinal proton magnetization
predominantly takes place between the protons belonging to nearest-neighbor CH– and
CH2– groups. The spin system that has to be considered for describing this process thus
is a three-spin system in which the two strongly coupled protons of the CH2-group
interact with the remote proton of CH-group. At longer mixing times, however, a much
larger spin system along the polimer chain must be considered.
3. Magnetization-exchange observables
In the rotating-frame representation the Hamiltonian for a static sample
(characterized by the three spin system model described before) is:
CH 2
H  H zCH  H zCH 2  H d
CH CH 2
 Hd
(1)
The chemical-shift anisotropy and heteronuclear couplings are neglected. Thus the
Zeeman Hamiltonians are:
H zCH     CH I z
H zCH 2     CH 2 Fz
(2)
where i  (0   i )   , for i  CH or CH2. The spin operator for the proton of
the CH–group is denoted by I and the spin – pair represented by the methylene protons
can be replaced by a quasi-particle with spin F = 1 and o total spin operator F = I1 + I2.
The intra- and intergroup residual dipolar Hamiltonians may be expressed in secular
approximations as [6]:
CH 2
Hd
d
CH 2
CH CH 2
2
Y2, 0 () T2CH
,0 ; H d
d
CH CH 2
CH 2
Y2, 0 () T2CH
,0
(3)
j
where d (j  CH2, CH-CH2) denote the strengths of the residual dipolar couplings. The
spherical harmonics Y2,0() depend on the azimuthal angle between the local chain vector
R and the direction of the magnetic field B 0 . T2,j0 are irreducible tensor-operators. The
distance between the functional groups is fluctuating due to local conformational jumps.
Therefore, the CH-CH2 dipolar coupling of the protons is approximated by the dipolar
coupling between the CH-proton and an effective spin 1 nucleus located at an average
distance r CH CH 2 (cf. Fig.1b).
424
RESIDUAL DIPOLAR COUPLINGS IN CROSSLINKED ELASTOMERS …
In the 1D-version of the magnetization-exchange experiment, the separation of the
NMR lines enables one to apply a chemical-shift filter [7] in order to select the longitudinal
magnetization of either CH– or CH2– group. The sequence starts with an evolution period
that acts as a chemical-shift filter by an appropriate choice of the rf-irradiation frequency
and the duration t1. The remaining transverse magnetization after the second 90 pulse and
the excited multiple-quantum coherences are removed from the aquired signal by phase
cycling ant the application of a short gradient pulse of duration td, where td  tm (cf. Fig.2).
As an example, the selection of the CH signal (for cis-1,4-polybutadiene) is shown in Fig.3.
After a mixing time of tm=15ms magnetization exchange is complete and the CH2 signal is
fully recovered at the expense of the CH intensity.
The CH – or CH2 – group is selected by the conditions:
CH:
(4)
 CH (t1 )  a I z
 CH  0,  CH 2 t1   / 2
 CH 2  0,  CH t1   / 2  CH (t1 )  a cos  3 D CH t1  Fz (5)
 2



CH2:
2
2
where i (t1) (i = CH, CH2) are the density operators at the beginning of the mixing
period, a is the prefactor of the density operator of thermal equilibrium in the highfield/high
temperature
approximation,
D
CH 2
d
CH 2
Y2,0 () .
The
symbol
... represents the statistical ensemble average [7] of the space part of the dipolar
coupling in the disordered elastomer.
900 900
900
1
3
2
AQ
t1
tm
t1
t2 timp
Gz
td
Fig.2.
timp
Basic scheme for magnetic-exchange
spectroscopy
Fig.3. Proton spectra of cis-1,4-polybutadiene
recorded in D magnetization-exchange
experiments
The NMR observables of the 1D magnetization-exchange experiment with
chemical-shift filter are:
425
XENIA FILIP, C. FILIP, D.E. DEMCO

Tr I z  CH (t m  t1 )
Tr I z  CH (t1 )

I z (t m )



;
Fz (t m ) 
which, in the limit of short mixing time, 3 D
 1
I z (t m )
CH CH 2
where D
D
1
2
 d
CH CH 2
CH CH 2

CH 2

2
t m2 ;

Tr Fz  CH 2 (t m  t1 )
Tr Fz  CH 2 (t1 )



(6)
  tm  1 transforms to:

 1
Fz (t m )
D
1
4

CH CH 2
2
t m2 (7)
Y2, 0() . In this short mixing time, the initial decay rates
depend only on the intergroup residual dipolar coupling. The longitudinal
magnetization transfer from CH to CH2 is twice as fast as that from CH2 to CH.
4. Experimental results
The investigated elastomers systems are based on a cis-1,4-polybutadiene and
SBR 1500 synthetic rubbers. The NMR experiments were performed at a 1H frequnecy
of 300 MHz on a Bruker MSL spectrometer using a variable temperature probe.
1.00
1.00
0.98
M ( tm ) / M 0
M ( tm ) / M 0
0.95
0.90
0.96
0.94
0.92
0.85
0.90
0.80
1
2
3
4
5
tm [ 10  s ]
2
Fig.4.
5
2
6
7
0
1
2
3
4
tm [ 10  s ]
2
5
2
The initial decay of proton magnetization Fig.5. The initial decay of proton magnetization
for cis-1,4-polybutadiene
for SBR 1500
The decay of the longitudinal magnetization M(tm) normalized to the value M0
that corresponds to zero mixing time, is recorded for short mixing times using the CH
chemical-shift filter. According to Eq.(7), the magnetization-exchange dynamics
should show an initial quadratic dependence on tm. This dependence indeed is found in
the experiments and is shown in Fig.4 (cis-1,4-polybutadine) and Fig.5 (SBR 1500).
The solid-like behavior of the magnetization decay is valid for mixing times
tm  3 D

426
CH 2
1
  . This expression can be estimate using data of protonic spectrum

RESIDUAL DIPOLAR COUPLINGS IN CROSSLINKED ELASTOMERS …
(the line width at half-intensity and the distance from lines). A deviation from the tm2
dependence is expected for mixing times tm > 500 s (for cis-1,4-polybutadiene) and
tm > 400 s (for SBR 1500). This deviation is confirmed by experiments (Figs. 4 and 5).
Defining the efective dipolar coupling constant
0.0

CH CH 2
as Deff
 D
-0.1
CH CH 2

2
1/ 2
, this can be
-0.2
ln ( Deff
CH-CH2
)
evaluate from the initial magnetization
decays in the 1D exchange experiments.
CH CH 2
The measuremnets of Deff
versus
-0.3
-0.4
-0.5
-0.6
-0.7
3.5
3.6
3.7
3.8
3.9
-1
1000 / T [ K ]
Fig.6.
4.0
4.1
temperature (for cis-1,4-polybutadiene) is
presented in Fig.6. In the investigated temperature range 245-285 K, the temperature
dependence can be in a good approximation
fitted with an exponential function. Finally
based on a gaussian distribution [8] of
CH CH 2
polymer chains where Deff
 N-1 [7],
one can readily extract the temperature
dependence of the crosslink density, N.
5. Conclusions
In this work it was shown that proton NMR magnetization exchange
experimets are very well suited to probe small intergroup rezidual dipolar couplings in
elastomers. For the investigated systems it was demonstarted that in the short mixingtime limit the measurable exchange of longitudinal proton magnetization predominantly
takes place between the protons belonging to nearest-neighbor CH– and CH2– groups.
Within this regime the residual dipolar couplings and hence the cross link density in
cis-1,4-polybutadiene and poly(styrene-co-butadiene) were accurately determined. At
longer mixing times, however, a much larger spin system along the polymer chain must
be considered.
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[2]
[3]
[4]
[5]
[6]
[7]
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427