Debye-Bueche theory

Tables IV and V show the dimensions calculated from the various theories of viscosity and sedimentation, respectively, in comparison with those obtained from light-scattering. It will be seen that, in the case of the viscosity data, the agreement between the calculated and experimental values is, with the exception of the Brinkman-Debye-Bueche theory, very reasonable. The values of (ro) calculated from sedimentation data are not, in general, in such good agreement with the light-scattering results.

The Debye-Bueche theory, on the other hand, considers the partially draining coil as a sphere that is more or less permeable, within which a number of smaller beads is homogeneously distributed. The beads correspond to the monomeric units. The drag which one bead produces on the others is calculated, and this resistance is then expressed in terms of a length L, which corresponds to the distance from the surface of the sphere to where the flow rate of the solvent is reduced to 1 /e times what it is at the surface of this sphere. The shielding ratio, or shielding factor, is given by... 

Debye-Bueche Theory Debye and Bueche (1948) criticize the theory of Kirkwood and Riseman as being unrealistic in assuming that the hydrodynamic... 

Equation (2.61) predicts a 3.5-power dependence of viscosity on molecular weight, amazingly close to the observed 3.4-power dependence. In this respect the model is a success. Unfortunately, there are other mechanical properties of highly entangled molecules in which the agreement between the Bueche theory and experiment are less satisfactory. Since we have not established the basis for these other criteria, we shall not go into specific details. It is informative to recognize that Eq. (2.61) contains many of the same factors as Eq. (2.56), the Debye expression for viscosity, which we symbolize t . If we factor the Bueche expression so as to separate the Debye terms, we obtain... 

Eine von Peterlin (P 6, 7, 8) angegcbene Variante der Viscositats-theorie von Brinkman-Debye-Bueche (B 16, D /) ermoglicht die Bc-rechnung von R auch fiir Nicht-GauBsche Knauel. 

Calculated from theories of Brinkman, and Debye-Bueche. Calculated from Kirkwood-Riseman theory. Calculated from Kuhn-Kuhn theory, using values in Ref. 155. Caleulated from theory of Peterlin. Calculated from Flory-Fox theory, using values in Ref. 155. (See pp. 381-385.)... 

Our approach in this chapter is to alternate between experimental results and theoretical models to acquire familiarity with both the phenomena and the theories proposed to explain them. We shall consider a model for viscous flow due to Eyring which is based on the migration of vacancies or holes in the liquid. A theory developed by Debye will give a first view of the molecular weight dependence of viscosity an equation derived by Bueche will extend that view. Finally, a model for the snakelike wiggling of a polymer chain through an array of other molecules, due to deGennes, Doi, and Edwards, will be taken up. 

Affected by multiple scattering are, in particular, porous materials with high electron density (e.g., graphite, carbon fibers). The multiple scattering of isotropic two-phase materials is treated by Luzatti [81] based on the Fourier transform theory. Perret and Ruland [31,82] generalize his theory and describe how to quantify the effect. For the simple structural model of Debye and Bueche [17], Ruland and Tompa [83] compute the effect of the inevitable multiple scattering on determined structural parameters of the studied material. 

Meyerhoff (182)] but also in the short-chain region [Marzolph and Schulz (176)]. The decrease in the slope of the double-logarithmic plot at low molecular weights is naturally and faithfully reproduced. This would be equally true of the Flory-Fox theory, as represented by Eqs. (5) to (8). There seems to be absolutely no evidence for partial draining of the solvent through the polymer coils, such as would be predicted by the theories of Brinkman (45 ), Debye and Bueche (79), Kirkwood and... 

Comparisons of the data with predictions based on the theory of Brinkman (45) and Debye and Bueche (79) or on the model experiments of Kuhn and Kuhn (153) lead to very similar conclusions. 

The viscosities of many binary liquid systems display minima as functions of composition at constant temperature, so that negative values of D are also possible. Yajnik and his coworkers (265 ) long ago observed that very frequently an extremum in the isothermal vapor pressure-composition curve is accompanied by an extremum of the opposite sense in the viscosity-concentration curve. Data are apparently not available for solutions of very low-molecular-weight paraffins in carbon tetrachloride, but minima are found for the viscosities of solutions of CC14 with ethyl iodide, ethyl acetate and acetone, so that a minimum appears quite probable for mixtures of small aliphatic hydrocarbons with carbon tetrachloride. If this were true, the downward trend of the Meyer-Van der Wyk data on C17—C31 paraffins, earlier discussed in connection with the polyethylene plots of Fig. 14, would be understood. It will be recognized that such a trend is also precisely what is to be expected from the draining effect of the hydrodynamic theories of Debye and Bueche (79), Brinkman (45 ) and Kirkwood and Riseman (139). However, the absence of such a trend in the case of polyethylene... 

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