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Starting from Onsager's theory and an extension of it given by Bottcher a method is given for computing dipole moments from data of diluted solutions in non-polar solvents. The dipole moments determined in this way agree rather well with those computed from gas data.

A method for the calculation of the polarisabilities and radii of ions in solution previously developed by one of the authors is applied to solutions of salts in mixtures of water and glycerol, to aqueous solutions of KF and to solutions of aluminium chloride in dilute hydrochloric acid. From the results of the measurements a further discussion of the method is given.

On the basis of the Smoluchowski-Einstein-Zernike theory, it is shown that light-scattering measurements on mixtures can, in general, yield information about the second derivatives of the free enthalpy (Gibbs free energy) of mixing with respect to the concentrations. This method can be applied to concentrated solutions of polydisperse polymers or polymer mixtures. Integration of the appropriate experimental data yields the chemical potentials and the interaction parameters. From the same theory it follows that plotting of the reciprocal of the scattered-light intensity versus the temperature for a number of compositions, and extrapolation to zero yields the spinodal. This procedure does not initiate from any particular molecular model. It can be applied to simple polymer solutions, but equally well to more complicated systems such as two polymers in one solvent or a mixture of two or more polymers. Spinodals have been determined for solutions in cyclohexane of three polystyrene samples with the same weight-average molecular weight but differing in their width of distribution.

The reduction in molecular dimensions due to the presence of short side chains in otherwise linear polyolefins can very simply by calculated by assuming that the configuration of the main chain is not influenced by the side chains. This enables us to express the intrinsic viscosity–molar mass relationship as a function of the mass fraction of side chains (S): [η] = (1 − S)α+1KPEMνα and, with use of the universal calibration principle, to convert the GPC calibration for purely linear polymers samples into the calibration for short-chain branched polymers: M* = (1 − S)M. Experimental data from literature on short-chain branched poly-ethylenes, and our own data on ethylene–propylene copolymers are used to verify the above assumption. It appears that the experimentally found relations between [η], Mw and M*w (GPC) within the usual accuracy justify this approach.

In gel permeation chromatography on long-chain branched polymers, calibration with linear samples leads to incorrect results. There are, however, several ways in which the data can be treated correctly. All of them call for the use of extra experimental information, such as viscosity or light scattering data of the whole polymer or the GPC eluent. The Drott—Mendelson method, using [η] of the whole polymer and GPC data, has been employed for analysing three low density polyethylene samples. The potentialities of viscometry and light-scattering measurements in the GPC effluent have also been examined. From [η], Mw and GPC data the long-chain branching index g′ can be derived in three ways, although it should be stated that the average g′-values so found for polydisperse samples are different.

It is demonstrated that, although addition of n-propanol to aqueous poly(vinyl alcohol) solutions prevents their aging, the polymer is not present in a molecularly dispersed form. Further, it is shown that viscometry is not a suitable method to study the degree of dispersion of poly(vinyl alcohol) in water or water/n-propanol solution. The results of turbidity measurements as a function of poly(vinyl alcohol) concentration, n-propanol concentration and time suggest that it is a change of solvent quality rather than a specific interaction between polymer and n-propanol that is responsible for the suppression of aging effects.

With the aid of a modified Sofica light-scattering apparatus an investigation was carried out of the crystallization of polyolefines from dilute solutions in several solvents. The intensity of the light scattered at various angles was determined as a function of time in the initial period of crystallization. Both linear polyethylene and polypropylene in p-xylene and in 1-chloronaphthalene showed the formation of disk-shaped crystals, which, after their formation, rapidly grew.

For determination of mol. wt. distribution from sedimentation-diffusion equilibria, the concentrations or the concentration gradients are measured in a number of places in the solution column for equilibria at various rotor speeds. The mol. wt. distribution is represented by a given series of mol. wts. Using a method of linear programming, a digital computer is made to find the weight fractions of the mol. wts. in the sample which fit best with the experimental data. A method of quadratic programming (least squares method) can be used just as well. From a three-peak polystyrene sample (a mixture of three polystyrene samples with narrow distribution), the mol. wt. distribution has been determined in this way. The mol. wt. distribution of the same sample has also been determined by sedimentation velocity analysis at the temperature where the sedimentation coefficient is independent of the concentration. The distributions obtained by these two methods agree well with each other and with the distribution obtained by gel permeation chromatography. The average mol. wts. M a , M w , M z and M z + 1 calculated from these distributions also agree well with the values calculated from the average mol. wts. of the three original samples.

From the intensities of light scattered from dilute and concentrated solutions of a given polymer, the chemical potential of the polymer and the solvent can be determined. Experiments have been carried out with solutions of monodisperse polystyrenes of different molecular weights in a poor solvent (cyclohexane) and in a good solvent (toluene) at different temperatures and at concentrations up to 30 per cent by weight. For all concentrations, the interaction parameter χ appears to be slightly dependent on the molecular weight. The results are compared with those determined by equilibrium ultracentrifugation and critical miscibility measurements.

Sedimentation equilibrium in the ultracentrifuge means that there is such a distribution of molecular species throughout the cell, that the centrifugal forces are balanced by differences in the activities. This provides a method for determination of the activities and the chemical potentials in polymer solutions which, in principle, is very simple and reliable. A complication is caused by polydispersity of the dissolved polymer. If one assumes that the interaction parameter depends on concentration and temperature, but not on molecular weight, it is possible to determine the chemical potential of polymer and solvent from the ultracentrifugal data. Experiments have been carried out on the systems polystyrene–toluene and polystyrene–cyclohexane at different temperatures and in the concentration range 0–80 wt-%. The results are expressed in the data for the chemical potential of the solvent, the number average chemical potential of the polymer and the interaction parameter χ.

Results are given of a number of measurements of the refractive index, dielectric constant and density of some normal alkanes at different temperatures. From the data obtained the radii and the polarisabilities of the molecules are evaluated.

From the sedimentation-diffusion equilibria of some polymer solutions the average molecular weights Mn, Mw, Mz, and Mz+1 have been determined in different ways. In particular, the applicability of Fujita's method, which utilizes concentration gradient values at the midpoint of the solution column at a number of rotor speeds, was examined. It appears that if the gradients at some other places in the column are also used, a smaller range of rotor speeds suffices. This method is generally applicable for determining the average molecular weights specified above.

Proceeding from the work of Zimm and Stockmayer and of Benoit, a general formula is derived for the calculation of the radius of gyration of block and graft copolymers. It appears that with linear block copolymers the ratio of the mean-square radius of gyration and the mean-square end-to-end distance is usually not far from 1/6. With a great number of blocks the difference from 1/6 can entirely be neglected. Also the influence of the composition of the molecules on the scattered light intensity has been considered.

In sedimentation-equilibrium experiments, especially at high temperatures, convection distrubances often occur. Regularities are given with regard to the appearance of these disturbances. The convections are caused both by the main heating and by the temperature control heating. Putting some plates in the rotor chamber, so as to prevent the direct heat radiation from the heating elements reaching the cell, eliminates these disturbances to a great extent. Bei Sedimentationsgleichgewichts versuchen treten, besonders bei hoheren Temperaturen, oft Konvektionsstorungen auf. Es werden in bezug auf das Auftreten dieser Storungen Gesetzmasigkeiten gegeben. Sowohl die Haupterwarmung als auch die Reguliererwarmung fuhren diese Konvektionen herbei. Durch Einbau einiger Platten in die Rotorkammer, welche die direkte Warmestrahlung von den Heizelementen zu den Zellen verhindern, lassen sich diese Storungen weitgehend vermeiden.

Determination of the sedimentation–diffusion equilibrium is one of the methods furnishing data on the thermodynamic parameters of polymer solutions. By means of this procedure measurements can be performed over a considerable range of concentrations. The equilibria in the ultracentrifuge have been determined for five polystyrene samples of narrow distribution covering the molecular weight range 2 × 104 to 2 × 106, at concentrations up to 40 wt-% and at temperatures of 30, 45 and 65 °C. The results are expressed in the data for the chemical potential of the solvent, the number-average chemical potential of the polymer and the interaction parameter ξ. The results are compared with those obtained from osmotic pressure, light scattering and critical miscibility measurements. At very low concentrations the molecular weight dependence of the interaction parameter is in agreement with literature values derived from osmotic pressure and light scattering figures. At higher concentrations this molecular-weight dependence decreases sharply but remains noticeable up to 40% concentration.

Starting from the Lorentz-Lorenz equation, Heller, a few years ago, advanced a method for calculating the partial specific volume of a substance in a dilute solution from the refractive index increment of the solution and the specific refraction of the solute. It is shown that this method, based on graphical extrapolation, can be considerably simplified. Further, a method is indicated by which the partial specific volume of a substance over the whole range of concentrations can be calculated in an analogous manner. The method is checked and elucidated with reference to some experimental examples.

The determination of long-chain branching (LCB) of polymers is in most cases performed by evaluation of both molecular dimensions and molar mass. Several experimental techniques, e.g. light scattering, diffusion, sedimentation, viscometry and gel permeation chromatography, can furnish the necessary data. Indices of LCB in use are the ratios for branched and linear macromolecules of the mean square radii of gyration (g), of the hydrodynamic radii (h) and of the intrinsic viscosities (g’). A survey is given of how these indices can be determined from the experiments, how they are interrelated, and how they are connected with the LCB structure and the number of long side chains. The complications occurring with samples polydispersed in molar mass and in degree of branching are also considered.

The combination of size exclusion chromatography (SEC) and high performance precipitation liquid chromatography (HPPLC) of the SEC fractions is performed on a mixture of five styrene-acrylonitrile copolymers (SAN) of strongly different composition and on a commercial SAN sample. HPPLC has proved to give a good separation by chemical composition. The cross-fractionation method has proved to be able to detect the combined molar mass- and chemical composition distribution very accurately. Conditions for an accurate and reliable application of this method are described. Results for the average composition of a commercial SAN as a function of molar mass are compared with those from SEC with dual detection and SEC with pyrolysis gas chromatography.

From the scattered light intensities of polydisperse polymer solutions, the thermodynamic parameters of the system, i.e. the chemical potentials of the solvent and the polymer and the interaction parameter in the Flory and Huggins equation, can be determined. The maxima of the scattered light intensity (as a function of concentration) and of the quotient of scattered light intensity and concentration (as a function of concentration) give information on these thermodynamic parameters, and localize the maximum of the spinodal. The spinodal itself can be determined from data in the stable region by means of an extrapolation procedure. These thermodynamic parameters can be determined also from sedimentation-diffusion equilibrium data, even over a considerable range of concentrations.