Macromolecules, Vol.48, No.20, 7521-7534, 2015
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 (PC) H-1 NMR, shear rheology (G) and dielectric spectroscopy (DS). The results are compared in a reduced spectral density representation: the quantity R-1(omega tau(alpha))/R-1(alpha)(0), where R-1(omega tau(alpha)) is the master curve of the frequency dependent spin lattice relaxation rate with tau(alpha) denoting the local correlation time, is compared to the rescaled dynamic viscosity eta'(omega tau(alpha))/eta'(alpha)(0). The quantities R-1(alpha)(0) and eta'(alpha)(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) proportional to M-alpha 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 alpha(i). The crossover to entanglement dynamics is identified by a change in alpha(i) around M congruent to 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) proportional to M-1.6 +/- 0.2 and eta(M) proportional to M-1.9 +/- 0.2, respectively, in good agreement with our theoretical prediction eta(M) proportional to M-1/3 D-1(M). The close correspondence of R-1(omega tau(alpha)) with eta'(omega tau(alpha)) establishes PC NMR as a powerful tool of "molecular theology" accessing the microscopic processes underlying macroscopic rheological behavior of complex fluids.