Change of translational-rotational coupling in liquids revealed by field-cycling 1H NMR

Abstract

Applying the field-cycling nuclear magnetic resonance technique, the frequency dependence of the (1)H spin-lattice relaxation rate, R1ω=T1(-1)ω, is measured for propylene glycol (PG) which is increasingly diluted with deuterated chloroform. A frequency range of 10 kHz-20 MHz and a broad temperature interval from 220 to about 100 K are covered. The results are compared to those of experiments, where glycerol and o-terphenyl are diluted with their deuterated counter-part. Reflecting intra- as well as intermolecular relaxation, the dispersion curves R1ω,x (x denotes mole fraction PG) allow to extract the rotational time constant τrot(T, x) and the self-diffusion coefficient D(T, x) in a single experiment. The Stokes-Einstein-Debye (SED) relation is tested in terms of the quantity D(T, x) τrot(T, x) which provides a measure of an effective hydrodynamic radius or equivalently of the spectral separation of the translational and the rotational relaxation contribution. In contrast to o-terphenyl, glycerol and PG show a spectral separation much larger than suggested by the SED relation. In the case of PG/chloroform mixtures, not only an acceleration of the PG dynamics is observed with increasing dilution but also the spectral separation of rotational and translational relaxation contributions continuously decreases. Finally, following a behavior similar to that of o-terphenyl already at about x = 0.6; i.e., while D(T, x) τrot(T, x) in the mixture is essentially temperature independent, it strongly increases with x signaling thus a change of translational-rotational coupling. This directly reflects the dissolution of the hydrogen-bond network and thus a change of solution structure.

Application of proton field‐cycling NMR relaxometry for studying translational diffusion in simple liquids and polymer melts

“…As discussed, a separation parameter r = 9 follows from the SED relations . Thus, they clearly fail in the case of glycerol and its homologues (see Figure a) that was explained by the strong 3D hydrogen bond network in such poly‐alcohols . As a consequence of the failure of SED, the hydrodynamic radius calculated from Dτ rot (Equation ) becomes unphysically small.…”

“…Figure b). Furthermore, FC NMR relaxometry allows to determine τ rot from the high‐frequency dispersion and assuming SED the product yields an estimate of the hydrodynamic radius R H …”

“…In the past, such experiments were done at few frequencies only, and the interpretation was often elusive. Only recently, comprehensive 1 H FC NMR experiments were performed in which the rates R 1, intra ( ω ) and R 1, inter ( ω ) over broader ranges . However, as translational and rotational contributions are more or less separated in frequency and display different low‐frequency limits, this offers the opportunity to determine D and τ rot by FC 1 H NMR even without performing an isotope dilution experiment.…”

Dynamics of a Paradigmatic Linear Polymer: A Proton Field-Cycling NMR Relaxometry Study on Poly(ethylene–propylene)

“…Correspondingly, the total relaxation rate in the low-frequency limit is described by a universal relaxation law, explicitly R 1 (ω) = R 1 (0) – cω 1/2 . From the parameter c , the diffusion coefficient can be derived, an approach which was only recently applied for simple liquids as well as polymer systematically. ,− In the case of polymers with their different subdiffusive regimes, by separating R 1 inter (ω) from R 1 (ω) one may even extract the time dependence of the msd, as mentioned. ,, …”

“…It is not an ease to attribute both parts, which additively contribute to the total 1 H relaxation R 1 (ω). Yet, at low frequencies the dispersion of the total relaxation is dominated by intermolecular relaxation which is mediated by translational diffusion. − This allows extraction of the diffusion coefficient. , The separation of R 1 intra (ω) and R 1 inter (ω) is achieved by the application of the isotope dilution technique. , Diluting protonated molecules in a matrix composed by deuterated analogues supresses the intermolecular relaxation. Not only the diffusion coefficient but also the subdiffusive segmental mean square displacement (msd) ⟨ r 2 ( t )⟩ of polymers as a function of time can be extracted after singling out R 1 inter (ω). , Recently, such ⟨ r 2 ( t )⟩ data was combined with that of field-gradient NMR, and all four regimes of segmental diffusion of linear entangled chains predicted by the tube-reptation (TR) model were identified in polybutadiene (PB) as well as in poly­(dimethylsiloxane) (PDMS).…”