Polydispersity effects in polymer self‐diffusion measured by small‐angle neutron scattering

Abstract

The small‐angle neutron scattering (SANS) method for measuring the self‐diffusion coefficient D has been analyzed for effects of polydispersity in degree of polymerization for the case of linear polymers diffusing by reptation. Polydispersities corresponding to Mw/Mn = 1.0−10 were considered. It is shown that in all cases a meaningful effective diffusion coefficient De can be obtained from the short time recovery of the SANS intensity. This quantity De ≤ 1.3 D(Mw), where D(Mw) is the diffusion coefficient of a monodisperse polymer having molecular weight M = Mw. The method relies on SANS intensities extrapolated to zero scattering angle; realistic extrapolation is shown to give rise to quite acceptable errors on the order of 0.05 De.

A Reconsideration of the Measurement of Polymer Interdiffusion by Fluorescence Nonradiative Energy Transfer

“…Diffusion of macromolecules across polymer-polymer interfaces has been an active area of study for well over a decade. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] Technologically, interest has arisen from issues related to polymer welding, crack healing, coextrusion, etc.1-4•20"22 Experimentally, many of the techniques employed in measuring diffusion coefficients of polymers have involved the use of interfaces, either imposed on bulk samples through some photochemical or similar means23-25 or by joining two distinct polymer films5-18 and annealing at temperatures exceeding the glass transition temperature, Tg. Scientifically, by employing experimental systems involving interfaces, it may be possible to test many important issues ranging from determining the appropriate combination of dynamic and thermodynamic models26-29 for describing mutual diffusion of either chemically identical polymers of different molecular weight (MW) or chemically different polymers to testing some of the basic tenets of reptation theory15•30 using chemically identical polymers of like MW.…”

Study on interdiffusion of polystyrenes of high molecular weight by SANS

“…Extension of the discussion of Finerman & Crist (1987) to include the interaction parameter 2' gives the coherent scattering cross section of a monodisperse sandwich sample as with the contrast factor K = n2(bH-bD) 2, n is the number of exchanged protons in the monomer, N is the total number of monomers (scatterers), bH and bD are the scattering lengths of thermal neutrons for hydrogen and deuterium and d is the thickness of the sample. For amorphous polystyrene, the chain conformation is well described by a Gaussian coil and the form is given by Debye's function (Debye, 1947 have a slight positive offset from the origin.…”

“…If the scattering intensity is normalized to the final state, the q dependence of the -7-" 150 signal cancels and the shape of the coherent scat-E tering function l(q,t) does not change with time (Finerman & Crist, 1987): ~ 100…”