Volume 15, Issue 6, 01 June 1947

On the Concentration Dependence of the Rates of Sedimentation and Diffusion of Macromolecules in Solution. Preliminary
View Description Hide DescriptionThe concentration dependence of the osmotic pressure, rate of diffusion, and sedimentation velocity for solutions of high molecular weight solutes, on the basis of certain assumptions, have been shown to be interrelated. Experimental confirmation, however, has been lacking. Preliminary data are given in this article which satisfy these interrelationships, with fractions of cellulose acetate in acetone; however, more cooperative osmotic pressure,diffusion, and sedimentation experiments on a variety of well‐defined systems are necessary to confirm the hypothesis.
If and when this additional confirmation is produced, the assumptions involved in the hypothesis may be considered correct; these are: (1) that the frictional coefficient in diffusion is the same (barring special cases of orientation during transport) as the frictional coefficient in sedimentation; and (2) that the driving force of diffusion is the gradient of the free energy of dilution of the system.
For solutions with no heat of mixing, the slight dependence of the diffusion constant on concentration has its molecular basis in the fact that the size and shape of the molecules affect the thermodynamic and hydrodynamic contributions to the variation of the diffusion rate to a comparable extent, and these contributions partially cancel one another. This is quantitatively so in the simple case of rigid spheres in an athermal solution.

The Non‐Degenerate Vibrations of Dimethylacetylene, Diacetylene, and Dimethyldiacetylene
View Description Hide DescriptionBy using force constants obtained from the observed non‐degenerate frequencies of dimethylacetylene and diacetylene, the non‐degenerate frequencies of dimethyldiacetylene were calculated. It was found that when several of these force constants were modified, agreement to within 2 percent of the observed values of the frequencies was possible. In order to check the values of the modified force constants the non‐degenerate frequencies of diacetylene were recalculated. The central C–C stretching force constant was found to have a value of 3.234_{2}×10^{5} dynes/cm which is much less than the normal value (5×10^{5} dynes/cm) for a C–C stretching force constant. Finally, the previous tentative assignment of the observed Raman frequencies of dimethyldiacetylene has been revised as a result of the calculations.

The Entropy of Mixing of Binary Liquid Mixtures
View Description Hide DescriptionThree factors which may contribute to the excess entropy of mixing of binary solutions have been explored. These are the relative volumes of the molecules, the spatial distribution of the molecules about a given reference molecule, and the lack of randomness of the orientational distribution of the molecules about a reference molecule. Of these, the spatial distribution, which depends upon the energy of mixing, is the smallest. It yields a negative value for the excess entropy and becomes zero at infinite dilution. The effect of differences in the volumes of the molecules of the components is positive and may be appreciable. The greatest effect is obtained from the orientational distribution. An estimation of the lack of randomness in this distribution for the pure components is obtained from the differences of the entropies of evaporation of the components and that of argon compared under corresponding conditions. This difference is positive and is comparable, at least in order of magnitude, to the observed partial molal excess entropy of mixing at constant pressure and at infinite dilution for the six binary mixtures composed of benzene, carbon tetrachloride, cyclohexane, and methanol. The contribution of the change in the orientational distribution of the components to the partial molal excess entropy at infinite dilution is then considered to be caused by two effects, one in which the orientational distribution of the solute becomes completely random when dissolved in a solvent at infinite dilution and the other in which the orientational distribution of the solvent is changed by the substitution of a solute molecule for a solvent molecule. The individual behavior of each solvent is very evident and is consistent with its molecular structure.

Comparative Thermodynamic Properties of the Restricted Rotator and the Harmonic Oscillator
View Description Hide DescriptionThe differences between the thermodynamic properties of the restricted internal rotator and a defined harmonic oscillator are expressed within narrow limits as a function of the single variableV/RT, where V is the height of the restricting potential barrier. As a result, a single table with one column for each of the four thermodynamic functions can be used in conjunction with standard harmonic oscillator tables to give the restricted rotator properties. This approximation is accurate within 0.02 cal./mole/deg. for nearly all cases to which it might be applied, and it is shown to be improbable that rotators will be found for which the error would rise appreciably above this limit. The harmonic oscillator chosen for comparison has a slightly lower frequency than the limiting one approached by the restricted rotator at very high values of V/RT.

Intermolecular Forces and Energies of Vaporization of Liquids
View Description Hide DescriptionBy using a ``smoothed potential'' model for the liquid state and assuming isotropic, homogeneous expansion with temperature which involves no change in coordination, it is shown that it is possible to reduce the expression for the configurational energy of the liquid to a function of a single parameter, the density. If the intermolecular forces can be put into a polynomial form then the expression for the configurational energy can be factored, resulting in an algebraic equation of the form:in which D is the molar density and the B's are constants independent of temperature. For the distances occurring in liquids, the last three terms can be either dropped or combined with the first, leaving as an approximation: E_{c}=AD^{x}/3. The energy of vaporization is given by: E_{v}=A(D _{1} ^{ x/3}—D_{g} ^{x}/3 ). Values calculated from this last equation show excellent agreement with experimental values for a large number of both normal and ``abnormal'' liquids. Values of x=5 or 6 both work, the latter being better up to the critical temperature.

Chemical Forms Assumed by C^{14} Produced by Neutron Irradiation of Beryllium Nitride
View Description Hide DescriptionThe nature of the radioactive compounds formed in the production of C^{14} by neutron irradiation of beryllium nitride has been investigated. Solution of the irradiated powder gave activities corresponding to methane,carbon monoxide, carbon dioxide, hydrogen cyanide, methanol, and formic acid. Formaldehyde was not found. The distribution of activities is not affected by the acidity of the solvent. The results are considered in the light of earlier work.

Photoelectric Intensity Measurements of Raman Spectra
View Description Hide DescriptionAn instrument for the direct photoelectric recording of Raman spectra of liquids is described together with the results obtained for CCl_{4}, CHCl_{3}, CH_{2}Cl_{2}, and C_{6}H_{6}. The precision of the results was tested by eight recorded spectrograms of CHCl_{3}. The intensity ratios of anti‐Stokes to Stokes lines were found to be in good agreement with theoretical values. Approximate values of the change of the bondpolarizability of the C–Cl bond in CCl_{4} and the C–H bond in C_{6}H_{6} caused by valence vibrations are calculated from the intensity data.

A Potentiometric Secular Equation Computer
View Description Hide DescriptionAn electrical computer for solving secular equations is described. The technique makes use of the linear equations from which the secular equation is derived. Each of the linear equations is successively represented by a potentiometric circuit. A series of successive approximations is carried out to arrive at the desired solutions.

Multilayer Gas Adsorption on Composite Surfaces
View Description Hide DescriptionThe equation of Brunauer, Emmett, and Teller (BET) for the adsorption of a gas on a free plane homogeneous surface is extended to the case of a mixture of two such surfaces, in an attempt to explain the observed deviations below one monolayer. The resulting equation may be greatly simplified for the case that the adsorption energy parameter, c, for each component surface, is large with respect to unity, as is usually the case in low temperatureadsorptions of nitrogen, argon, etc. This approximate form of the equation is applied to the nitrogen isotherm on an inorganic salt and gives substantially better agreement with experiment than does the simple BET equation. The region of agreement between the experimental and BET isotherms is discussed on the basis of a two‐component surface, and conditions are given under which one might obtain two distinct regions of the isotherm which are fitted by the BET equation by the use of two sets of parameters. It is suggested that it is the lower of these two regions which gives rise to the occasionally observed ``saturation adsorption'' values corresponding to only small fractions of a monolayer.

Thermodynamics of Crystallization in High Polymers. I. Crystallization Induced by Stretching
View Description Hide DescriptionA theory of oriented crystallization in elongated polymers having network structures (e.g., in vulcanized rubber) is developed through the application of statistical mechanical procedures similar to those employed in rubberelasticity theory. Expressions are derived which, within the limitation imposed by the simplifying assumptions, relate the incipient crystallization temperature with the elongation, the degree of crystallinity with the elongation and temperature, and the retractive force at crystallization equilibrium with the elongation at constant temperature. The reciprocal of the absolute temperature for incipient crystallization is predicted to decrease linearly with a simple function of the elongation and the average number of chain segments between cross linkages. Only moderate degrees of crystallinity are predicted at equilibrium. In conformity with requirements of the second law of thermodynamics, equilibrium crystallization decreases the tension in the stretched specimen.
Apparent discrepancies between some of these predictions and various observations are attributed to severe departure from equilibrium crystallization when the polymer undergoes crystallizationduring the stretching process. A better approach to equilibrium should be achieved by stretching under conditions which prevent crystallization (e.g., at elevated temperature), then allowing crystallization to proceed at fixed elongation. Few experiments have been performed in this manner, but such results as are available confirm qualitatively the predictions of the theory.
Reasons for the rapid increase in tension which is observed when crystallization occurs during ordinary stretching of rubber are discussed. It is pointed out that crystalline and amorphous regions preferably should not be regarded as separate phases. Likewise, the conversion of amorphous to crystalline polymer does not conform to the definition of a phase transition.

On the Mass Spectra of Hydrogen and Deuterium
View Description Hide DescriptionOn the basis of reasonable assumptions with regard to the probabilities of electron‐impact induced transitions of hydrogen and deuterium, it is calculated that the relative intensity of H^{+} in the mass spectrum of hydrogen should be 2.3 times greater than that of D^{+} in the mass spectrum of deuterium for ionization by electrons of less than 35‐volt energy. This value is compared with experimental values 2.8 (22‐v energy), 1.5 (30‐v energy), 1.9 (50‐v energy), and 2.2 (100‐v energy).

Average Square Length and Radius of Unbranched Long‐Chain Molecules with Restricted Internal Rotation
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 LETTERS TO THE EDITOR


Dye Sensitization of Photographic Emulsions and the Triplet State
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An X‐Ray Examination of Cyclooctatetraene
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A New Refinement Technique for X‐Ray Structure Analysis
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Upper Limit to the Tritium Content of Ordinary Water
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Patterson‐Harker Maps of Molecular Crystals
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Application of Radioactive Isotopes to the Problem of Diffusion of Electrolytes in Aqueous Solutions
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Propagation of Ultrasonic Waves Through Liquid Mixtures and the Dynamics of Their Molecular Interaction
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Influence of Neighbor Bonds on Additive Bond Properties in Paraffins
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