All Polymer Diffusion Regimes Covered by Combining Field-Cycling and Field-Gradient¹H NMR

Abstract

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.

Application of proton field‐cyclingNMRrelaxometry for studying translational diffusion in simple liquids and polymer melts

“…We only note in passing that in favourable case, when a full separation of R 1,intra ( ω ) and R 1,inter ( ω ) is achieved by isotope dilution experiments, even the mean square displacement (msd) as a function of time may be extracted from R 1,inter ( ω ), providing access to subdiffusional processes. For example, combining FC relaxometry and FG diffusometry, three subdiffusive power law regimes preceding the normal Fickian one were disclosed in the msd of several different polymer melts, and the results were found to be consistent with the Doi–Edwards tube‐reptation (TR) model . Whereas in liquids the dispersion at low frequencies is dominated by translational dynamics, rotational dynamics is reflected at high frequencies.…”

“…This was recently demonstrated in the case of the subdiffusive dynamics in polymer melts . As mentioned, the full msd as a function of time may be extracted . All in all, broadband relaxation spectra will become available that may even compete with those of standard DS and that will establish FC NMR as a method of “molecular rheology.”…”

“…Solid lines: low‐frequency behaviour according to Equation . (b) Molar mass dependence of the diffusion coefficient D of PB at T = 373 K and of polydimethylsiloxane (PDMS) at T = 292 K as obtained by FC 1 H NMR relaxometry (crosses) and by FG NMR (open symbols); solid lines: power laws with exponents as indicated; arrows mark the crossover from Rouse to entanglement dynamics.…”

Field-Cycling Relaxometry as a Molecular Rheology Technique: Common Analysis of NMR, Shear Modulus and Dielectric Loss Data of Polymers vs Dendrimers

“…For isotropic systems A p (t) does not depend on p. The correlation function (20) contains information about the dynamics of all spins and will be called the total DD correlation function. Its initial value depends on the spatial distribution of spins …”

“…Yet, this is not always a proper description when compared to experimental results. 20 This is not surprising, because the concept of Kuhn segments mainly reflects the equilibrium statistics of long polymer chains in the melt. For flexible chains the Kuhn segment roughly corresponds to a chain segment containing 3−10 monomers, which have a large number of internal degrees of freedom and internal mobility.…”