Dynamics of PPI Dendrimers: A Study by Dielectric and2H NMR Spectroscopy and by Field-Cycling1H NMR Relaxometry

Abstract

We investigate bulk poly(propyleneimine) dendrimers of generation (G) 2–5 by dielectric spectroscopy (DS), solid-state 2H NMR, and field-cycling 1H NMR relaxometry (FC 1H NMR) in a large temperature range (120–400 K). Three relaxation processes are identified by DS: a main (α-) relaxation (T > Tg) and two secondary processes (T < Tg). The α-process exhibits a super-Arrhenius temperature dependence typical of glass-forming liquids and changes only weakly with G, yielding Tg ∼ 200 K. The temperature dependence of the secondary relaxations is governed by an Arrhenius law. While one secondary process exhibits features characteristic for glasses, the other is atypical. Its time constant is virtually independent of G, and its spectral width does not increase with lowering temperature as is usually observed for sub-Tg relaxations. Regarding FC 1H NMR probing the dispersion of the spin–lattice rate R1 in the frequency range 200 Hz–30 MHz, transformation to the susceptibility representation, χ″(ω) ≡ ωR1(ω), and applying frequency–temperature superposition, an effective frequency range of 9 decades is covered by a master curve χ″(ωτα). In addition to the segmental time τα(T), which complements the results from DS up to high temperatures, a longer terminal relaxation τt(T) is identified. In between, an intermediate power-law regime is observed in χ″(ωτα) with an exponent of about 0.8. The broad relaxation spectrum is attributed to local dynamics, breathing modes, and overall tumbling and diffusion of the dendrimer molecule. In the low-frequency limit, R1(ω) is determined by intermolecular relaxation from which the molar mass dependence of the translational diffusion coefficient can be estimated. We find D(M) ∝ M–1.2±0.2.