Table VIII. Ratio of Elution Volumes for Polystyrenes with Molecular Weights of 1 X lo6 and 2 X l o 3 to the Elution Volume at Molecular Weight of 1.8 X lo6 Ratio of elution volumes, Ve(2)/Ve(l) Calculated Observed PS PS a1 1 x 105 2 x 103 PS 1 x 10s p s 2 x 103 (1.02-1.09) (1.095-1.14) Av. 1.065 Av 1.111 al = ro 1 . 1 3 1.46 al = 0 . 5 r o 1.38 1.60 al = 0 . 1~ 1.14 1.19 ai = O.O1ro 1.02 1.02Assuming the effective radius, al, of polystyrene having molecular weight 1.8 X 106, to be successively a1 = ro, a1 = 0.5 ro, a1 = 0.1 ro and a1 = 0.01 ro, we calculated the ratios of elution volumes of polystyrenes having molecular weight 1 X lo5 and 2 X lo3 to that of 1.8 X lo6 using Equations 4 and 8. The results are shown in Table VIII.End-to-end distances of polystyrenes calculated by D. F.Alliet and J. M. Pacco (7) are 1490 8, (PS 1.8 X 106 mol wt), 280 8, (1 X lo5 mol wt), and 35.2 8, (2 X lo3 mol wt). If half of these values are considered to be equal to the effective radius of the polymers, then the value of a1 falls between 0.106 ro and 0.166 ro. Comparison of the calculated and observed values at a1 = 0.1 ro shows that the experimental results are in reasonable agreement with theory.For estimation purposes, we have assumed values of K = 1 X and 01 = 0.75, then (S2)'/' = 4.65 x 10-2@*58d-1/3An effective radius for the polymer molecule is expressed by Equation 8 obtained by combining Equations 3 and 7
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