Mixtures of protonated and deuterated polybutadiene and
polydimethylsiloxane are studied by means of field-cycling (FC) 1H NMR relaxometry in order to analyze the intra- and intermolecular
contributions to spin–lattice relaxation. They reflect reorientational
and translational dynamics, respectively. Master curves in the susceptibility
representation χ″(ωτs) are constructed
by employing frequency–temperature superposition with τs denoting the segmental correlation time. The intermolecular
contribution is dominating at low frequencies and allows extracting
the segmental mean square displacement ⟨R
2(t)⟩, which reveals two power-law
regimes. The one at short times agrees with t
0.5 predicted for the free Rouse regime and at long times a
lower exponent is observed in fair agreement with t
0.25 expected for the constrained Rouse regime of the
tube-reptation model. Concomitantly the reorientational rank-two correlation
function C
2(t/τs) is obtained from the intramolecular part.
Again two power-law regimes t
–ε are identified for polybutadiene. The first agrees with t
–1 of free Rouse dynamics whereas at
long times ε = 0.49 is obtained. The latter is corroborated
by the 2H relaxation of deuterated polybutadiene, yet,
it does not agree with ε = 0.25 predicted for constrained Rouse
dynamics. Thus, the relation C
2(t) ∝ ⟨R
2(t)⟩–1 as assumed by the tube-reptation model
is not confirmed.
The segmental dynamics of 1,4-polybutadiene is investigated
by
means of electronic field cycling 1H NMR. The frequency
dependence (dispersion) of the spin–lattice relaxation time
is probed over a broad range of temperature (223–408 K), molecular
mass (355 ≤ M (g/mol) ≤ 441 000),
and frequency (200 Hz–30 MHz). The extremely low frequencies
are accessed by employing a home-built compensation for earth and
stray fields extending prior reports about 2 decades to lower frequencies.
Applying frequency–temperature superposition yields master
curves over 10 decades in frequency (or time), and after Fourier transform
the full dipolar correlation function is traced over up to 8 decades
in amplitude. Several relaxation regimes can be identified, and their
power-law exponents are compared to the predictions of the Doi–Edwards
tube-reptation model, namely the free Rouse (I) and the constrained
Rouse regime (II). Whereas the predicted value of the power-law exponent
of regime II is 0.25, we find that it depends on M and levels off at 0.32 for very high M = 441 000
≈ 220M
e (M
e: entanglement molecular mass). This is in good agreement
with recent results from double quantum 1H NMR and indicates
that the actual onset of full reptation dynamics is strongly protracted.
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