Iso-Frictional Mass Dependence of Diffusion of Polymer Melts Revealed by¹H NMR Relaxometry

Abstract

We extract the translational diffusion coefficient D(T,M) from field cycling (FC) 1 H NMR relaxometry which provides the relaxation dispersion of poly(dimethylsiloxane), 1,4-poly(butadiene), poly(styrene), 1,4-poly(isoprene), and poly(propylene glycol) with various molecular masses M. Oligomers with very low M, nonentangled (M < M e ), and entangled (M > M e ) polymers are included. The low-frequency 1 H NMR relaxation dispersion is dominated by translational dynamics and allows extracting D via benefiting from an universal dispersion power-law characteristic of free diffusion. In order to correct for the additional mass dependence of the monomeric friction coefficient observed at low M and controlled by the M dependence of the glass transition, the segmental correlation time τ s (T,M) is taken from previous analyses of the FC susceptibility master curves. Consequently, we present the temperature independent, iso-frictional quantity Dτ s ∝ F(M), which reveals the M-dependence of the pure collective polymer dynamics. While at the lowest M the quantity Dτ s displays a trend to become M independent typical of simple liquids, it crosses over to a behavior characteristic of Rouse dynamics. In most systems, however, this crossover manifests itself in a rather narrow M interval as entanglement dynamics takes over at M > M e . Thus, pure Rouse behavior is difficult to identify, yet the approach allows one to decide when a molecule becomes a polymer, in terms of the (smallest) Rouse unit.

Proton spin dynamics in polymer melts: New perspectives for experimental investigations of polymer dynamics

“…Therefore in the limit 1 1 ωτ ≤ , the frequency dispersion of the total spin-lattice relaxation rate will always be determined by the intermolecular interactions, a fact well documented by recent experiments with polymer melts [12,13,[27][28].…”

“…Applying eq. (36) thus provides D(T,M) also for polymers [27,28]. In order to get the diffusion coefficient, equation (36) exploits the expansion of the intermolecular relaxation to lowest order in frequency.…”

“…The dynamics of the investigated systems is mainly reflected through characteristic features of nuclear spin relaxations. Important findings of recent years [7,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], affecting the understanding of the proton spin dynamics in polymer melts are the subject of discussion of this paper.…”

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

“…In Figure a, the dispersion of the relaxation rate R 1 ( ν ) of polystyrene with a rather low M value is displayed . The strong dispersion at low temperatures almost disappears at highest temperatures only apparently.…”

Determining diffusion coefficients of ionic liquids by means of field cycling nuclear magnetic resonance relaxometry

“…[11][12][13][14][15] From the corresponding slope the diffusion coefficient D can straightforwardly be obtained. We have tested this approach for molecular liquids 8 and polymers 16 comparing the obtained diffusion coefficients with results of pulsed-field-gradient NMR (PFG NMR). 8 The agreement is very good that allows us to state that FC 1 H NMR can be treated as a method complementary to PFG NMR.…”