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The Scaling Law between Molecular Mass and Diffusivity and its Influence on the Molecular Weight Distribution as Derived from a Stretched Exponential PGSTE NMR Response Curve
Author(s) -
Gong Xiaoliang,
Hansen E. W.,
Chen Qun
Publication year - 2012
Publication title -
macromolecular chemistry and physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.57
H-Index - 112
eISSN - 1521-3935
pISSN - 1022-1352
DOI - 10.1002/macp.201200372
Subject(s) - dispersity , exponential function , molar mass distribution , scaling , thermal diffusivity , molecular mass , laplace transform , chemistry , inverse , distribution (mathematics) , thermodynamics , physics , polymer chemistry , mathematical analysis , polymer , mathematics , geometry , organic chemistry , enzyme
The molecular weight distribution characteristics derived from an inverse Laplace transformation (ILT) of a stretched exponential PGSTE NMR response function (SEF) is discussed with reference to the scaling law between diffusivity ( D ) and molecular mass ( M ) ( D = KM −α ). Two general equations are presented, enabling the polydispersity index (PDI) and the average molecular weights ( M w , M n , and M med ) to be determined from α and the two characteristic parameters β and D 0 of the (normalized) SEF (= exp [(− D 0 t ) β ]). A detailed discussion regarding the derivation of the two equations is presented.