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  • Title: A lattice model for the simulation of one and two dimensional 129Xe exchange spectra produced by translational diffusion.
    Author: Lin G, Jones AA.
    Journal: Solid State Nucl Magn Reson; 2004 Sep; 26(2):87-98. PubMed ID: 15276639.
    Abstract:
    Xenon-129 spectra in some heterogeneous polymer systems consist of two resonances which collapse to a single resonance as a function of temperature. Two different resonances arise from spatially separated, distinct sorption environments and spectral collapse occurs when xenon atoms diffuse from one environment to the other at a sufficiently fast rate. This exchange mechanism involves a distribution of time constants and a two domain lattice model is used to generate a realistic distribution of correlation times resulting from diffusion in a heterogeneous matrix. The distribution of correlation times is inhomogeneous in the sense that different xenon atoms would exchange between the two domains or environments with a variety of time constants and the resulting spectrum is a superposition of spectra associated with each of the time constants. To demonstrate the nature of exchange according to this model, diffusion out of a sphere is simulated which corresponds to a progressive saturation experiment used to determine the diffusion constant of xenon in polystyrene. Then the model is used to demonstrate the difference between homogeneous and heterogeneous spectral collapse in one- and two-dimensional examples. Lastly, the simulation model is used to interpret one- and two- dimensional xenon-129 line shape changes for xenon sorbed into poly(2,6-dimethyl-1,4-phenylene oxide) as a function of temperature. Two broad resonances are observed at low temperatures in this polymer corresponding to xenon-129 sorbed in high free volume and low free volume domains. Exchange between the two main resonances collapses the spectrum to a single peak at higher temperatures. Both the collapse in one dimension and exchange in two dimensions as a function of mixing time can be simulated using the distribution from the lattice model. An average domain size of 70 nm is estimated by combining the simulation of the exchange experiment with the results of a one-dimensional progressive saturation experiment. The size of the sites sorbing individual xenon atoms has been reported from positron annihilation lifetime spectroscopy as 1.4 nm for the high free volume sites and 0.3 nm for the low free volume sites. The domain size is more than an order of magnitude larger than the individual sorption site indicating that domains consist of many sites as assumed in the lattice model description.
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