Topology of High Free Volume Regions from Pulsed Field Gradient Diffusion Studies of Penetrant Motion in Perfluorodioxole Copolymer

Meresi, Ghirmai; Wang, Yingzi; Cardoza, Job D.; Wen, Wen Yang; Jones, Alan A.; Inglefield, Paul T.

doi:10.1021/ma0009395

Cited by 14 publications

(29 citation statements)

References 9 publications

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“…This is a very permeable polymer at temperatures well below the glass transition. [14][15][16][17][18][19][20] The fractional free volume in this high-perme- ability polymer is ∼0.3, whereas the fractional free volume [17][18][19][20] associated with the larger free-volume elements is considered to be ∼0.03. Thus, 10% of the free volume is associated with the large-free-volume elements.…”

Section: Comparison To Experimental Resultsmentioning

confidence: 99%

A Lattice Model for the Simulation of Diffusion in Heterogeneous Polymer Systems. Simulation of Apparent Diffusion Constants as Determined by Pulse-Field-Gradient Nuclear Magnetic Resonance

et al. 2003

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The diffusion of molecules through heterogeneous media is not simple Fickian diffusion on the length scale of the heterogeneities. Pulse-field-gradient (PFG) NMR measurements of diffusion reflect this by yielding apparent diffusion constants that are dependent on the time over which diffusion is observed. Equations for simple cases of tortuous diffusion and restricted diffusion are available where some fraction of the medium is assumed to be permeable and some fraction is impermeable. In many polymer systems, the medium has domains that are more permeable and less permeable. In the limit of long times and above the percolation threshold, diffusion in such systems can be characterized with effective medium theory (EMT). To characterize diffusion as a function of time in heterogeneous media and at all compositions, a lattice model is presented based on an approach developed by Ediger. The lattice model gives results that match EMT at long times and produces tortuous and restricted diffusion above and below the percolation limit when one domain is made impenetrable. It also shows a wide range of behavior of the apparent diffusion constant, relative to observation time, which is intermediate between tortuous diffusion and restricted diffusion. The intermediate behavior arises for various ratios of the diffusion constant in the more-and less-permeable domains and for various ratios of solubility between the more-and less-permeable domains. Brief comparisons are made with PFG NMR data on a heterogeneous, high-permeability copolymer and on a polymer blend composed of more-and less-permeable constituents. The model demonstrates that apparent diffusion data from PFG NMR provide a new structural view of the heterogeneities in systems with more-and less-permeable domains.

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Section: Comparison To Experimental Resultsmentioning

confidence: 99%

A Lattice Model for the Simulation of Diffusion in Heterogeneous Polymer Systems. Simulation of Apparent Diffusion Constants as Determined by Pulse-Field-Gradient Nuclear Magnetic Resonance

et al. 2003

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“…It was noticed that the product of the slower diffusion constant and ∆ was constant for large values of ∆. Estimates of the slower diffusion constant could also be obtained by simply fitting the last part of the decay curves at large ∆, 9 and values similar E(q) ) P fast exp(-4π 2 q 2 D fast ∆) + P slow exp(-4π 2 q 2 D slow ∆) (1) to those from in the double exponential fits were obtained. Again, for values of ∆ between 100 and 1000 ms, the product of the slower diffusion constant and ∆ was constant.…”

Section: Resultsmentioning

confidence: 99%

“…The size of the domain over which restricted diffusion occurs can be estimated from the formula This leads to a value of a ) 0.7 µm, which differs only slightly from the estimate of 0.6 µm made from the value of the diffusion constants at large ∆ in the initial report. 9 Equation 2 assumes a spherical geometry.…”

Section: Discussionmentioning

confidence: 99%

“…Such behavior is observed for pentane and decafluoropentane in TFE/BDD copolymer and indicates the presence of structural features influencing diffusion on a micron length scale. 9,10 The apparent diffusion constant for pentane in this polymer decreases to a constant value as the time scale of the experiment increases, which is characteristic of diffusion in a porous material. For decafluoropentane, more complex behavior was noted.…”

Section: Introductionmentioning

confidence: 88%

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Diffusion of Decafluoropentane in Amorphous Glassy Perfluorodioxole Copolymer by Pulse Field Gradient NMR Spectroscopy

et al. 2001

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Pulse field gradient diffusion measurements were made on the decafluoropentane molecule, CF3CHFCHFCF2CF3, in the copolymer of tetrafluoroethylene (TFE) and 2,2-bis(trifluoromethyl)-4,5-difluoro-1,3-dioxole (BDD). The proton spectrum consisted of two overlapping line shapes, and the decay of the echo amplitude with increasing gradient required the use of two apparent diffusion constants. The two apparent diffusion constants differed by 1.5-3 orders of magnitude depending on the length of time over which diffusion occurred. Both apparent diffusion constants were also functions of the diffusion time, indicating the presence of structure in this system that obstructs the translational motion of the penetrant molecules. The slower diffusion process ranged from 10 -8 to 10 -10 cm 2 s -1 , while the faster diffusion process ranged from 10 -6 to 10 -8 cm 2 s -1 . The product of the slower diffusion constant and the diffusion time was constant within experimental error, which is typical of restricted diffusion. Assuming a spherical geometry, the length scale was 0.7 µm. The fast diffusion constant appeared to decrease toward a plateau at large diffusion times, which is typical of tortuous diffusion in a porous medium. The slower diffusion process was considered to involve molecules in low-free-volume regions as this process was associated with the broader proton resonance and a longer spin-lattice relaxation time. The faster diffusion process was considered to involve penetrant molecules in high-free-volume regions that were interconnected. A narrower resonance with a shorter spin-lattice relaxation time was associated with this process.

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“…Many of these materials have important permeation‐selective properties. A number of papers dealt with changing the timescale of the gradient experiment and hence examining diffusion over differing length scales,10, 11 important when dealing with systems with such complex morphologies.…”

Section: Illustrationmentioning

confidence: 99%

Alan A. Jones (1944–2006)

Colby¹,

Ediger²,

Inglefield³

2006

J Polym Sci B Polym Phys

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Topology of High Free Volume Regions from Pulsed Field Gradient Diffusion Studies of Penetrant Motion in Perfluorodioxole Copolymer

Cited by 14 publications

References 9 publications

A Lattice Model for the Simulation of Diffusion in Heterogeneous Polymer Systems. Simulation of Apparent Diffusion Constants as Determined by Pulse-Field-Gradient Nuclear Magnetic Resonance

A Lattice Model for the Simulation of Diffusion in Heterogeneous Polymer Systems. Simulation of Apparent Diffusion Constants as Determined by Pulse-Field-Gradient Nuclear Magnetic Resonance

Diffusion of Decafluoropentane in Amorphous Glassy Perfluorodioxole Copolymer by Pulse Field Gradient NMR Spectroscopy

Alan A. Jones (1944–2006)

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