Programmed polymer light‐scattering data

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 / Q θ = ( W / K * ) M̄ w −1 [1 + (16/3) × π 2 n 1 2 λ〈 S 2 〉 sin 2 (θ/2)] + ( W / K * )2 A 2 c + ( W / K * )3 A 3 c 2 in which Q θ 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 X̄ ij for the variable c / Q θ at θ i and c j , a function X is found by least squares to fit X̄ ij , thus X = l + m sin (θ/2) + nc j + bc j 2 . The equations arising from minimizing Σ i K =1 Σ j L =1 ( X ij − X̄ ij ) 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/Q θ 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 m μ.