Bruno H. Zimm

The problem of the motions of a chain molecule diffusing in a viscous fluid under the influence of external forces or currents is considered for a particular model. This model is a chain of beads connected by ideal springs. Hydrodynamic interaction between the beads is introduced in the approximate form due to Kirkwood and Riseman. It is possible to solve this problem exactly with the use of a transformation to a set of normal coordinates. The viscosity, birefringence of flow, and dielectric and tensile relaxation behavior are calculated explicitly. The intrinsic viscosity in steady flow is somewhat different from the Kirkwood-Riseman result, and there is no change of viscosity with shear rate. The spectrum of relaxation times is similar to that found by Rouse and by F. Bueche, but has its maximum at a lower frequency than those obtained by Kuhn and Kuhn and by Kirkwood and Fuoss in other ways.

Formulas for the mean square radii of various branched and ringed polymer molecules are developed under the usual assumptions regarding the statistics of chain configuration. For branched molecules, the mean square radii vary less rapidly with molecular weight than for strictly linear molecules, while for systems containing only rings and unbranched chains the variation is more rapid than for the linear case. These results show that in principle the quantity of branches or of rings can be determined from light-scattering measurements.

A radial distribution function of polymer segments in a solution of a high polymer may be defined as a quantity proportional to the density of segments at a given distance from some given segment. An approximate expression is derived for this function for dilute solutions of chain molecules of moderate degrees of polymerization. By Fourier inversion a simple expression for the intensity of light scattering, as a function of angle and concentration, may be obtained.

A photoelectric apparatus for the measurement of the angular dependence of light scattering from solutions is described in detail and its performance is discussed. Methods of calculation for the determination of the average extension of the scattering molecules from the data are described. Data are presented for two fractions of polystyrene in various solvents, showing the effect of changing solvent power and temperature, and also confirming a theoretically derived formula for the concentration dependence of the scattering.

Abstract A theory of the electrophoresis of DNA through gels with large interfiber spacing, such as dilute agarose, is presented. We assume that the DNA molecule moves along its axis through a “tube” in a neutral gel under the influence of the electric field. The tube is random except for possible bias due to the effects of the field. When the field is small, we easily recover the inverse‐length dependence of the mobility found previously by de Gennes and by Doi and Edwards. At higher fields, a new effect appears; the tube becomes oriented because the field biases the direction of the leading end of the chain as it moves to form an extension of the tube. This leads to an increase of the mobility with increasing field by adding a field‐dependent but length‐independent term to the mobility expression. In agreement with experiment, we find that the field effect can be important at fields as low as 1 V/cm and that the effect can seriously decrease the sensitivity of the mobility to chain length. We also examine the fluctuation of the migration distance, the degree of orientation induced by the field, and the transient effects occurring when the feld direction is rotated by a right angle.