Programmed polymer light-scattering data

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Abstract

An ALGOL computer program has been devised to manipulate light-scattering data from the Brice-Phoenix photometer. The input consist of experimental values of the galvanometer deflections and filter factors used for each concentration c and angle of measurement θ. These are transformed to the appropriate variables in the fundamental equation including the particle scattering factor, viz: c/Qθ = (W/K*)w−1[1 + (16/3) × π2n12λ〈S2〉 sin2 (θ/2)] + (W/K*)2A2c + (W/K*)3A3c2 in which Qθ is a corrected from of the Rayleigh ratio and (W/K*) is a composite constant term for the instrument and polymer–solvent system. By writing ij for the variable c/Qθ at θi and cj, a function X is found by least squares to fit ij, thus X = l + m sin (θ/2) + ncj + bcj2. The equations arising from minimizing ΣiK=1 ΣjL=1 (Xijij)2 are solved by the computer to yield the best-fitting coefficients l, m, n, and b. These can then be related simply to the molecular weight, root-mean-square radius of gyration, second and third virial coefficients, respectively. The final portion of the program is designed to check the fit of these coefficients. It yields a table of the differences between all experimental c/Qθ values and the coressponding ones obtained by inserting the derived l, m, n, and b into the fundamental equation. The procedure has been tested satisfactorily by using a well-standardized sample of polystyrene in toluene at 30°C. and a wavelength of 436 mμ.

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