Molecular weight dependence of the second virial coefficient. Solutions of styrene dimers up to high polymers and other systems

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Abstract
The second virial coefficient B or A2 has been calculated from cryoscopic measurements in naphthalene of polymers of styrene from dimers up of high polymers. The B‐degree of polymerization curve has a maximum in the range of the tetramer. The portion of the curve showing the increase to a maximum is explained as a “macromolecule effect” of rigid rods according to the theory of Flory and Huggins. The A2–P (or B–P) curves investigated so far are described by the equation, A2 = (a/M1/2) + b. It is assumed that the shape of a macromolecular coil in solution depends upon the fact whether the main chain skeleton and its sidegroups have the same or opposite affinity to the solvent. In the case of polystyrene in naphthalene it is assumed that the CC chain behaves as a lyophobe and the benzene groups as a lyophil. This leads to an increased density of the benzene sidegroups in the surface of the macromolecular coil. The interaction potential between the coils as a whole is therefore different from that in the interior. This effect is realized by splitting the excluded volume into two parts and leads to the reciprocal square root dependence of A2. This equation has been tested for many endothermal and exothermal systems. The constants a and b are zero at the θ‐temperature and can be determined therefrom.