A small-angle scattering experiment on a dilute polymer solution gives the following…

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Condensed Matter, Materials & Soft Matter · Data analysis and model fitting in the laboratory

Soft Matter at the Thermal Scale, Ch The size and shape of a polymer chain

Problem

A small-angle scattering experiment on a dilute polymer solution gives the following normalised intensities. Data: at q=0.010,0.030,0.060,0.090 nm−1q = 0.010, 0.030, 0.060, 0.090\,\mathrm{nm^{-1}} the ratio I(q)/I(0)I(q)/I(0) is 0.9925,0.9358,0.7769,0.59260.9925, 0.9358, 0.7769, 0.5926 respectively. ((a)) Using the Guinier law I(q)/I(0)=1−q2Rg2/3+⋯≈e−q2Rg2/3I(q)/I(0) = 1 - q^2R_g^2/3 + \dots \approx e^{-q^2R_g^2/3}, plot ln⁡[I(q)/I(0)]\ln[I(q)/I(0)] against q2q^2 and use the two lowest-qq points, where the Guinier criterion qRg<1qR_g < 1 is most safely met, to extract the slope and hence RgR_g. ((b)) Using your value of RgR_g, find qRgqR_g for the largest-qq point, compare its measured intensity with the value the Guinier line predicts there, and state whether that point should have been included in the fit.

Browse the problem library