N. Fatkullin et R. Kimmich, THEORY OF FIELD-GRADIENT NMR DIFFUSOMETRY OF POLYMER SEGMENT DISPLACEMENTS IN THE TUBE-REPTATION MODEL, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 52(3), 1995, pp. 3273-3276
The spin-echo attenuation in NMR field-gradient diffusometry experimen
ts is treated for the tube model in a time scale longer than the entan
glement time tau(e). The theory comprises the Doi-Edwards [M. Doi and
S. F. Edwards. The Theory of Polymer Dynamics (Clarendon, Oxford, 1986
)] limits of the (anomalous) segment displacement as well as the (ordi
nary) center-of-mass diffusion. This formalism is to be distinguished
from formalisms for anomalous diffusion on fractal networks: The repta
tion mechanism implies an intrinsically different character of the dis
placement probability density. It is shown that the expressions usuall
y applied in NMR diffusometry are inadequate for the reptation problem
and can cause misinterpretations. Applications of the formalism to po
lymer chains in bulk and confined in porous media are discussed.