NORMAL AND CROSS-LINKED POLYSTYRENE: I.HUGGINS' k′ AS A MEASURE OF NONLINEARITY

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Abstract
Polystyrene polymerized in emulsion at 55 °C. to near-complete conversion has been subjected to careful primary, secondary, and tertiary fractionation. For representative samples and fractions thereof, the intrinsic viscosity [η] and the slope constants β and k′ have been determined at 25 °C. in butanone and benzene. For intrinsic viscosities in benzene ranging from 2.10 to 8.37, the equation log [η] (in benzene) = 0.31 + 1.23 log [η] (in butanone) holds. In butanone the value of k′ is 0.40 ± 0.01, changing from 0.39 for the lower fractions ([η] in butanone <2.00) to 0.41 for the highest fractions; in benzene, the better solvent, the corresponding values of k′ are 0.02 units lower.Samples of cross-linked polystyrene were prepared by copolymerizing styrene with small proportions of divinylbenzene. Values of k′ determined for the soluble cross-linked species, both unfractionated and fractionated, varied (in butanone) all the way from the normal 0.40 to 1.14, depending on the proportion of divinylbenzene used.It is concluded that k′ is a sensitive indicator of nonlinearity in polymer molecules, and that in polystyrene as normally prepared in emulsion systems the molecules are essentially linear.