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

Abstract

Linear poly(propylene glycol) (PPG) as well as a poly(propyleneimine) (PPI) dendrimer with different molar masses (M) are investigated by field-cycling (FC) 1 H NMR, shear rheology (G) and dielectric spectroscopy (DS). The results are compared in a reduced spectral density representation: the quantity R 1 (ωτ α )/R 1 α (0), where R 1 (ωτ α ) is the master curve of the frequency dependent spin−lattice relaxation rate with τ α denoting the local correlation time, is compared to the rescaled dynamic viscosity η′(ωτ α )/η′ α (0). The quantities R 1 α (0) and η′ α (0), respectively, are the zerofrequency limits of a simple liquid reference system. Analogously, the dielectric loss data can be included in the methodological comparison. This representation allows quantifying the sensitivity of each method with respect to the polymer-specific relaxation contribution. Introducing a "cumulative mode ratio" F i (M) for each technique i, which measures the zero-frequency plateau of the rescaled spectral density, characteristic power-law behavior F i (M) ∝ M α i is revealed. In the case of PPG, F NMR (M), F G (M), and F DS (M) essentially agree with predictions of the Rouse model yielding characteristic exponents α i . The crossover to entanglement dynamics is identified by a change in α i around M ≅ 10 kg/mol. The analysis is extended to the dendrimer which exhibits a relaxation behavior reminiscent of Rouse dynamics. Yet, clear evidence of entanglement is missing. The M-dependencies of the dendrimer diffusion coefficient D obtained by pulsed field-gradient NMR and the zero-shear viscosity are found to be D(M) ∝ M −1.6±0.2 and η(M) ∝ M 1.9±0.2 , respectively, in good agreement with our theoretical prediction η(M) ∝ M 1/3 D −1 (M). The close correspondence of R 1 (ωτ α ) with η′(ωτ α ) establishes FC NMR as a powerful tool of "molecular rheology" accessing the microscopic processes underlying macroscopic rheological behavior of complex fluids.

Slow rheological mode in glycerol and glycerol–water mixtures

“…4 of Ref. [56]. The monoalcohol as the linear polymer exhibits a clearly separated mode, while in glycerol and dendrimers there is only a shoulder.…”

“…[56] where the mechanical signature of a linear polymers is compared to that of dendrimers. While the linear polymers displayed a slow mode clearly separated from the alpha-relaxation and a distinct rubber plateau in the real part of the shear modulus, the dendrimers only display reminiscence of the Rouse dynamics in terms of a low frequency shoulder on the mechanical loss peak.…”

Spectral shape simplicity of viscous materials

“…16,17 The former two electrolytes behave as "simple" liquids, the latter two display clear evidence of chain dynamics at frequencies below wa. The type V materials are linear polymers with different chain lengths, 18,19 whereas a water solution of lithium chloride 21 is considered as type VIcorresponding to aqueous systems.…”

Local NMR Relaxation of Dendrimers in the Presence of Hydrodynamic Interactions

“…Recently, much of attention has been attracted to the local dynamics in dendrimers, both in theory (analytic theory [12,13,14] and computer simulations [15,16,17]) and experiments [18,19,20,21], see also recent review [22]. Especially the NMR relaxation experiments have remarkably advanced this field.…”