P. Debye

Scattering by an Inhomogeneous Solid

A general treatment of the scattering of radiation by an inhomogeneous material is developed. It is shown how scattering measurements can be used to obtain the average square of the fluctuations in refractive index or electron density and a correlation function which measures the degree of correlation between two fluctuations as a function of their distance of separation.The scattering of visible light by Lucite and two glass samples has been investigated. The data are analyzed in terms of the quantities mentioned above. It is found that the extensions in space of the inhomogeneities in the Lucite sample are much greater than those in the optical glass samples investigated. The magnitudes of the fluctuations in refractive index are found to be dependent on the composition of the sample.

Scattering by an Inhomogeneous Solid. II. The Correlation Function and Its Application

Experiments on the angular intensity distribution of x‐rays scattered by porous materials (hole structures) in the range of small angles are described. It is shown that the scattering can be characterized by an exponential correlation function in the case of a distribution of holes of random shape and size in solid; a theoretical derivation of the exponential function is given for this case. When the correlation function is an exponential, the rule holds that the reciprocal square root of the scattered intensity is a linear function of the square of the scattering angle. The specific surface of the material is determined by the slope of this straight line. Specific surfaces of a number of compositions are calculated from their experimental correlation functions and compared to surfaces based on adsorption measurements.

Intrinsic Viscosity, Diffusion, and Sedimentation Rate of Polymers in Solution

Intrinsic viscosity, diffusion and sedimentation rate of polymers in solution is calculated by a generalization of Einsteins theory for impermeable spheres. For the coiled polymer molecule a sphere is substituted which hinders the liquid flow through its interior only to a degree depending on the average density in space of the polymer molecule in solution. The amount of shielding of the liquid flow which is introduced in this way determines the exponent in the customary exponential relation between intrinsic viscosity, diffusion, or sedimentation rate and molecular weight. This relation is shown to have only the merits of an interpolation formula. It is shown how the dimensions of the molecular coil can be derived from the experimental data on viscosity, and these dimensions are compared with those derived from interference measurements. The point is stressed that the relation between intrinsic viscosity and molecular weight is rather indirect and depends essentially on the type of polymer molecule unde...

Angular Dissymmetry of the Critical Opalescence in Liquid Mixtures

Visible light scattered by a one‐component homogeneous liquid in the vicinity of its critical point or by a homogeneous mixture of two liquids in the vicinity of their critical mixing temperature shows angular dissymmetry which becomes the more pronounced the nearer the temperature comes to the critical temperature. It is shown how this dissymmetry can be used as a measure for the range of molecular forces in the case of ordinary molecules. In the case of polymer molecules, observation of the dissymmetry provides a method for measuring the size of polymer coils in a size range too small to be measured by the usual dissymmetry method applied to diluted solutions.

The Influence of Intramolecular Atomic Motion on Electron Diffraction Diagrams

A discussion of the influence of atomic vibrations and of free or hindered rotations of molecular groups in molecules on their scattering properties. The radial distribution curve is calculated and the results which may be expected from an analysis of this curve are indicated.

The Determination of Polymeric Molecular Weights by Light Scattering in Solvent‐Precipitant Systems

The theory of scattering by an inhomogeneous dielectric medium has been extended so as to account for the turbidimetric behavior of polymer solutions in solvent‐precipitant mixtures. It is predicted by this theory and verified by experiment that correct values of molecular weight are obtained by the usual interpretation of turbidity measurements if and only if the solvent and precipitant have the same refractive index. The practical utility of turbidimetry in high polymer solutions is shown to be greatly increased by the proper use of solvent‐precipitant mixtures. If the solvent and precipitant have different refractive indices, scattering measurements give information about the extent of selective absorption of solvent by the polymer.

Long‐Lifetime Phosphorescence and the Diffusion Process

The long‐lifetime phosphorescence of certain, easily oxidizable organic compounds in rigid media at the temperature of liquid nitrogen has been found to decay by an inverse power function of the time. Decay kinetics of this type have been observed previously in inorganic phosphors. Employing the diffusion equation and the observed rate law, a distribution function for electrons in the solid media is derived. Data from the experiments are discussed in relation to this theoretical treatment.

Flow of Liquid Hydrocarbons in Porous Vycor

Experimental investigation of the flow rates of normal paraffins in porous Vycor glass shows that there are deviations from the viscosity dependence required by Poiseuilles law. A discussion of the application of capillary models to describe flow in porous media in terms of the measured porosity and surface‐to‐volume ratio points out that such models are not generally applicable, though they give useful results for some purposes. An estimate of the permeability predicted by Poiseuilles law is made by an empirical method which uses gas flow measurements in the Knudsen flow region. The equations of slip flow as derived for gases do not explain the experimental deviations from Poiseuille flow. The concept of a slipping adsorbed layer of molecular thickness at the wall of a capillary is combined with the usual Poiseuille treatment for the interior to give a result which is compatible with experiment.

The Measurement of Self‐Diffusion in Solid Polymers

The self‐diffusion constant of the macromolecules in plasticized polystyrene and pure poly‐n‐butyl acrylate has been measured over a wide variety of conditions by a radioactive tracer technique. Well‐characterized polymer fractions were used throughout. Simultaneous measurements of the bulk viscosity were also made. From the data obtained one is able to show that within experimental error the product of the self‐diffusion constant and the bulk viscosity is equal to a constant. This constant has been predicted by theory, and the agreement with the experimental value is good. Therefore, it appears possible to obtain diffusion constants directly from bulk viscosity data.

Electrical Field Effect on the Critical Opalescence

The free energy involved in the concentration fluctuations of a liquid mixture is changed by an electric field. The effect becomes observable near the critical point. It increases with decreasing distance from the critical temperature and it is proportional to the square of the field intensity and to the second derivative of the dielectric constant with respect to the concentration. Temperature as well as field strength dependence are in agreement with a theory built along classical lines. The effect can be interpreted as a shift of the critical temperature and the sign of this shift is also predicted correctly. Experiments performed with a field intensity of 45 000 V/cm on the system nitrobenzene‐2,2,4‐trimethylpentane give a value of 0.015° for this shift (which is a depression), while the theory predicts the same.