DISTRIBUTION OF GAUSSIAN DECAY FUNCTIONS AND ITS REPRESENTATION BY A COMPRESSED EXPONENTIAL FUNCTION (NMR HAHN-ECHO ANALYSIS OF PPC-COMPOSITES)

It is well known that a stretched exponential function   q t r Exp r q t SEF R ) * ( ) * , ; (   for 0 < q < 1 can be expressed by a continuous distribution ) , ( q x SEF P of single exponential decay functions, i.e.;  dx t xr Exp q x SEF P r q t SEF R * ) , ( 0 ) * , ; (     with  dx sx q q x Exp q q x q s SEF P      0 ) cos( )) sin( sin( / 1 ) : (    . In a recent paper (Hansen et al., Macromol. Chem. Phys. 2013, DOI: 10.1002/macp.201200715) it was suggested that a corresponding compressed exponential function (CEF)   q t r Exp r q t CEF R ) * ( ) * , ; (   with 1 < q < 2 can represent a corresponding distribution ) , ( q x PCEF of Gaussian decay functions;  dx t xr Exp CEF P r q t CEF R 2 ) * ( 0 ) * , ; (     with ) 2 / ; 2 ( 2 ) , ( q x SEF xP q x CEF P  . Further support and legitimacy of this latter relation is exemplified by numerical calculations (0 < q < 2) and its applicability is illustrated by examining the NMR Hahn echo relaxation response of some composite materials of polypropylene carbonates and graphite nano-platelets.