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

Linear poly(propylene glycol) (PPG) as well as a poly(propyleneimine) (PPI) dendrimer with different molar masses (M) are investigated by field-cycling (FC) ¹H NMR, shear rheology (G) and dielectric spectroscopy (DS). The results are compared in a reduced spectral density representation: the quantity R₁(ωα_α)/R1α(0), where R₁(ωα_α) is the master curve of the frequency dependent spin-lattice relaxation rate with α_α denoting the local correlation time, is compared to the rescaled dynamic viscosity n′(ωα_α)/n′_α(0). The quantities R1α(0) and n′_α(0), respectively, are the zero-frequency 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 (M) M^1.9±0.2, respectively, in good agreement with our theoretical prediction n(M) M^1/3 D^-1(M). The close correspondence of R₁(ωα_α) with n′(ωα_α) establishes FC NMR as a powerful tool of "molecular rheology" accessing the microscopic processes underlying macroscopic rheological behavior of complex fluids.