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.
A formalism is presented permitting the evaluation of the relative mean-squared displacement of molecules from the intermolecular contribution to spin-lattice relaxation dispersion of dipolar coupled spins. The only condition for the applicability is the subdiffusive power law character of the time dependence of the mean-squared displacement as it is typical for the chain mode regime in polymer liquids. Using field-cycling NMR relaxometry, an effective diffusion time range from nano- to almost milliseconds can be probed. The intermolecular spin-lattice relaxation contribution can be determined with the aid of isotopic dilution, that is, mixtures of undeuterated and deuterated molecules. Experiments have been performed with melts of polyethyleneoxide and polybutadiene. The mean-squared segment displacements have been evaluated as a function of time over five decades. The data can be described by a power law. The extrapolation to the much longer time scale of ordinary field-gradient NMR diffusometry gives good coincidence with literature data. The total time range thus covers nine decades.
Field-cycling and field-gradient 1H NMR experiments
were combined to reveal the segmental mean-square displacement as
a function of time for polydimethylsiloxane (PDMS) and polybutadiene
(PB). Together, more than 10 decades in time are covered, and all
four power-law regimes of the tube-reptation (TR) model are identified
with exponents rather close to the predicted ones. Characteristic
polymer properties like the tube diameter a
0, the Kuhn length b, the mean-square end-to-end
distance ⟨R
0
2⟩, the segmental correlation time
τs(T), the entanglement time τe(T), and the disengagement time τd(T) are estimated from the measurements and
compared to results from literature. Concerning τd(T), fair agreement is found. In the case of τe, agreement with rheological data is achieved when the time
constant is extracted from the minimum in the shear modulus G″(ω). Concerning the TR predictions the molar
mass (M) dependence of τd is essentially
reproduced. Yet, calculating τe from τd for PDMS yields agreement with experimental data while for
PB it gets by 2 orders of magnitude too short. In no case τe is correctly reproduced from τs(T). Segmental and shortest Rouse times appear to coincide
for PB, while in the case of PDMS the latter turns out to be longer
by 1 decade.
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