Centre of mass diffusion in polymer liquids

Because of its sensitivity to self-motion of the labelled chain, as indicated in equation (9.7), PGSE NMR has proven of especial value in studying the 

In many polymer systems, polydispersity is a feature that must be accounted for in analysing the results of PGSE NMR measurements. Allowing for both relaxation time and diffusion coefficient dependence on molar mass, the echo attenuation expression in equation (9.6) must be modified to read 

One particularly useful depiction of P(M) is the log-normal distribution for which 

L being ln(M). Lq and a are the centre and standard deviations, respectively, of the log normal distribution. In this case, allowing that scales with molar mass as M , yields a simple power series evaluation of equation (9.11) whose leading term is determined by the mass-averaged diffusion coefficient to be [112] 

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