Segmental motion of entangled random coil polymers studied by pulsed gradient spin echo nuclear magnetic resonance

Characterizing diffusion of gases and liquids within pores is important in understanding numerous transport processes and affects a wide range of practical applications. Previous measurements of the pulsed gradient stimulated echo (PGSTE) signal attenuation, E(q), of water within nerves and impermeable cylindrical microcapillary tubes showed it to be exquisitely sensitive to the orientation of the applied wave vector, q, with respect to the tube axis in the high-q regime. Here, we provide a simple three-dimensional model to explain this angular dependence by decomposing the average propagator, which describes the net displacement of water molecules, into components parallel and perpendicular to the tube wall, in which axial diffusion is free and radial diffusion is restricted. The model faithfully predicts the experimental data, not only the observed diffraction peaks in E(q) when the diffusion gradients are approximately normal to the tube wall, but their sudden disappearance when the gradient orientation possesses a small axial component. The model also successfully predicts the dependence of E(q) on gradient pulse duration and on gradient strength as well as tube inner diameter. To account for the deviation from the narrow pulse approximation in the PGSTE sequence, we use Callaghan's matrix operator framework, which this study validates experimentally for the first time. We also show how to combine average propagators derived for classical one-dimensional and two-dimensional models of restricted diffusion (e.g. between plates, within cylinders) to construct composite three-dimensional models of diffusion in complex media containing pores (e.g. rectangular prisms and/or capped cylinders) having a distribution of orientations, sizes, and aspect ratios. This three-dimensional modeling framework should aid in describing diffusion in numerous biological systems and in a myriad of materials sciences applications.

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“…using hyperpolarized noble gases in the lung) to nanometers [e.g. using protons residing on long-chain polymers (25)]. …”

Section: Introductionmentioning

confidence: 99%

Three‐dimensional water diffusion in impermeable cylindrical tubes: theory versus experiments

et al. 2008

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“…Other techniques measure directly the early-time di usion of labelled monomers on the chain. Both incoherent neutron spin echo and pulsed gradient spin echo NMR [45] have identi®ed dynamics of ¿ n …t †ˆh‰R…n; t † ¡ R…n; 0 †Š 2 i that are sub-di usive, a consequence of chain connectivity predicted by theory.…”

Section: Nmr Magnetic Relaxationmentioning

confidence: 99%

“…However, time and spatial scales relevant to entangled dynamics have recently been explored by two other variants of this very adaptable technique. Field-gradient NMR (FGNMR) is essentially a method of spin-labelling monomers to extract information on spatial di usion [45], so will be deferred to the next section. A direct measure of local orientational dynamics, on the other hand, capable of accessing timescales up to 100 ms or more is provided by the transverse magnetic relaxation, often referred-to as T 2 '.…”

Section: Nmr Magnetic Relaxationmentioning

confidence: 99%

Tube theory of entangled polymer dynamics

McLeish

2002

Advances in Physics

827

1,122

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The dynamics of entangled¯exible polymers is dominated by physics general to many chemical systems. It is an appealing interdisciplinary ®eld where experimental and theoretical physics can work closely with chemistry and chemical engineering. The role of topological interactions is particularly important, and has given rise to a successful theoretical framework: the`tube model'. Progress over the last 30 years is reviewed in the light of specially-synthesized model materials, an increasing palette of experimental techniques, simulation and both linear and nonlinear rheological response. Our current understanding of a series of processes in entangled dynamics:`reptation',`contour length¯uctuation' and`constraintrelease' are set in the context of remaining serious challenges. Especial attention is paid to the phenomena associated with polymers of complex topology or`long chain branching'.

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“…Thus, D min may be as small as 10 -14 m 2 s -1 . In reality, however, 94 J. Kärger these limiting values are only attained in exceptional cases [65,66], and realistic lower limits are of the order of 300 nm and 10 -13 m 2 s -1 , respectively. It may easily be deduced from Eqs.…”

Section: Range Of Applicability and Limitationsmentioning

confidence: 95%

Diffusion Measurements by NMR Techniques

Kärger

Molecular Sieves

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Segmental motion of entangled random coil polymers studied by pulsed gradient spin echo nuclear magnetic resonance

Cited by 46 publications

References 81 publications

Three‐dimensional water diffusion in impermeable cylindrical tubes: theory versus experiments

Three‐dimensional water diffusion in impermeable cylindrical tubes: theory versus experiments

Tube theory of entangled polymer dynamics

Diffusion Measurements by NMR Techniques

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