Showing papers by "DSM published in 1968"

Liquid-liquid phase separation in multicomponent polymer solutions. II. The critical state

Abstract: Theoretical and experimental evidence is put forward to prove that the determination of the phase-volume ratio as a function of temperature and concentration is a sensitive and simple means of determining the liquid–liquid critical state. Knowledge of the critical conditions permits very accurate calculations of the interaction parameter g in the free-energy function. In experiments with polystyrene–cyclohexane, g was found to depend on the concentration. The value of g and its concentration dependence agree very well with the results of osmotic measurements by Rehage and Palmen. In experiments with polyethylene–diphenyl ether, g proved to be independent of concentration in the range of measurement. The temperature function was found to be: g = −0.6086 + 482.2/T (at 137–148°C.). Gibbs' expressions for the critical conditions were worked out for a free-energy relation in the form of an extended Flory-Huggins function.

Liquid–liquid phase separation in multicomponent polymer solutions. I. Statement of the problem and description of methods of calculation

Abstract: Polymers are complex mixtures that may have widely different compositions even if they contain only components having the same chemical constitution. The effect of the chain length distribution on the phase behavior of polymer solutions in a single solvent is described qualitatively. To obtain a quantitative understanding of these phenomena a numerical calculation method is developed which is based on the Flory-Huggins relation for the free energy of mixing. Some examples are presented, and the accuracy and the reliability of the results are discussed.

Liquid–liquid phase separation in multicomponent polymer solutions. III. Cloud‐point curves

Abstract: Cloud-point curves (CPC) were calculated on the basis of the Flory-Huggins free-energy relation for various hypothetical polymer samples dissolved in a single solvent. Molecular weight distributions varying widely in shape and width were examined. The shape of the CPC reflects details of the molecular weight distribution. This appears from the location of the critical point on the right-hand branch of the CPC. The latter often shows a depression, which becomes more distinct as the Mz/Mw value increases. These theoretical results were confirmed experimentally with the system polyethylene–diphenyl ether. With the aid of the theoretical data collected it was possible to explain the remarkable agreement between the θ temperatures determined by light-scattering and by the Shultz-Flory method. The latter method is basically incorrect, since it identifies the polymer solution with a binary mixture. An explanation could also be given for the empirical relation which McIntyre et al. recently found between the shape of the top of the CPC and the width of the molecular weight distribution.

Polymer fractionation. I. The preparative problem

Abstract: The molecular weight distributions of the fractions in the two liquid phases which, in preparative fractionation, form upon a change in temperature, have been calculated for various initial concentrations and model distributions differing widely in shape and width. It was found that the normally recommended conditions do not always lead to the result desired, i.e., to a fraction with a narrow distribution. Under these conditions (dilute solution; large phase-volume ratio; small fraction, i.e., little polymer in the concentrated phase) it may even happen that the fraction has a relatively wider distribution than the parent polymer. Treatment of a single-peaked distribution will then be liable to yield a two-peak fraction distribution. These unwanted phenomena do not occur in Staverman and Overbeek's variant of the extraction fractionation method. Here, the bulk of the polymer goes into the concentrated phase, and the macromolecules left in the dilute phase constitute the fraction to be isolated. In this way, relatively narrow distributions can be obtained in one step, even at high concentrations. Moreover, the method is very well suited for use in large-scale fractionation. Fraction distribution wider than the initial distribution were found experimentally in the systems polyethylene–diphenyl ether and polystyrene–cyclohexane.

Polymer fractionation. II. The analytical problem

Abstract: Complete fractionations into 5, 10, and 20 fractions were calculated by a numerical method based on the Flory-Huggins theory in order to evaluate various procedures for determining the molecular weight distribution from fractionation data. If the initial distributions are wide, the differential distribution cannot be accurately reconstructed, not even if each fraction is characterized by two average molecular weights (instead of one, as is customary). In addition to this inadequacy in the evaluation procedure there are the experimental errors which further detract from the accuracy of the result. The integral distribution can, in some cases, be approximated fairly well by means of the Schulz method, provided that the polymer is separated into many fractions with narrow distributions. However, the integral distribution thus obtained does not reflect details in the differential distribution. Polymer fractionation does not appear to be a suitable procedure for accurate determination of the differential distribution. From the assembled material, a thermodynamic method has been derived which seems to hold out better prospects. It should enable the differential distribution to be directly determined from a detailed analysis of the liquid–liquid phase relationships, provided the free energy of mixing function of the system is known.