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Volume 20, Issue 7, 01 July 1952
20(1952); http://dx.doi.org/10.1063/1.1700666View Description Hide Description
Equations are written for the binding energy of a finite number of ions at fixed coordinate positions. Each ion is assumed to have a lowest nondegenerate (closed shell) configuration. In the Heitler‐London approximation the state of the assembly is assumed to be: (a) a properly antisymmetrized sum of products of one‐electron functions, and, (b) the constituent one‐electron functions are assumed to be linear combinations of only the one‐electron functions composing the ground states of the isolated ions. We use, for each ion a, its density matrixwith , the coordinates, including spin, of a single electron, and the sum including all filled one‐electron functions, ψνa , of the ground state of ion a. The binding energy, consistent with the two assumptions (a) and (b) is then derived and found to be expressible in a reasonably compact exact form, using this density matrix. By making use of an approximate expression for the density matrix the integrations occurring in the energy expression are tractable.
20(1952); http://dx.doi.org/10.1063/1.1700667View Description Hide Description
By combining Slater's classical treatment for the adiabatic decomposition of an unstable molecule with the Lindemann mechanism for collisional activation it is possible to make a uniform and consistent treatment of kinetic processes of all orders. The high pressurerate constants may then be represented bywhere is a root mean square average of the ``n'' normal modes of vibration of the activated complex, E * is the minimum energy required for reaction, α is a ``transmission coefficient'' which is unity for unimolecular processes and between ½ and 1 for higher order reactions, and K # can be interpreted in terms of an entropy of activation. A more complicated expression is obtained for lower pressures in the case of unimolecular reactions.
The theory is sufficiently detailed to allow predictions on the relation of molecular structure to the pressure region in which collisional activation becomes a limiting rate factor for unimolecular reactions. Similarly predictions may be made concerning the nature of recombination processes and their pressure and temperature dependence. It is shown that recombination processes will have a negative temperature coefficient and in addition the mean life of the activated complex will vary inversely with some power of the strength of the bond being formed. As a result of this, recombination will be more efficient in photochemical or, more generally, low temperature chain reactions than in pyrolytic reactions and consequently chain lengths will be longer in the latter.
Application of Eller's Optical Machine to the Determination of the Molecular Structure of Gases by Electron Diffraction20(1952); http://dx.doi.org/10.1063/1.1700668View Description Hide Description
20(1952); http://dx.doi.org/10.1063/1.1700669View Description Hide Description
The theory of ``Conductance in Polarizable Media'' developed by one of the authors is modified in such a way as to be applicable to electrolytic solutions. This is achieved by the introduction of a new set of boundary conditions. In their original form they expressed the fact that the polarizing ions could not carry any current through the boundary. Now it is assumed that the discharge at the electrodes is a rate process of the first order, characterized by a rate constant ξ. In Sec. II the case of an applied ac voltage is treated. The expressions for the equivalent parallel conductance and capacitance of the polarization layer 1/Rp and Cp are derived by the same method, and to the same extent, as in the older theory. If ξ tends to zero, the previous results are obtained (``completely blocked electrode''). If ξ increases, the ``polarizationcapacitance'' and the ``excess resistance'' both decrease until they vanish for ξ=∞ (``open electrode''). The dependence on frequency remains similar for all finite values of ξ, and is represented in Figs. 1 and 2. Subsequently, in Sec. III, the older theory is improved by a determination of the thickness of the polarization layer. Reduced values of 1/Rp and Cp can be represented as universal functions of one reduced variable, which is proportional to the frequency. The two universal functions are tabulated to some extent in Table I. Finally the theory is extended to the case where several groups of ions of different mobilities are present in the electrolyte.
20(1952); http://dx.doi.org/10.1063/1.1700670View Description Hide Description
The object of the present investigation was to supply material for testing the theory given in the preceding paper. Therefore, the ``polarizationcapacitance'' and the ``excess resistance'' of electrolytic solutions were measured over wide ranges of frequency and concentration, and for different plate distances. Also the material of the electrodes was modified, and some temperature coefficients were measured.
After the general introduction (Sec. I) the method used is described in Sec. II; it is essentially a Jones bridge method, with suitable modifications. In Sec. III the cell is described. Section IV deals with the general scope of the measurements and with the procedure in performing them. The range of frequencies was, as a rule, from 18 to 18,000 cps; the molar concentrations varied from 10−4 to 10−2 g‐eq/liter. In addition to solutions of KCl and MgSo4, conductance water was investigated. Electrodes of Al, Ni,Au, and Pt were used. In Sec. V a survey of the results, independent of any theory is given. Finally, in Sec. VI the results are compared with those of the theory, by analyzing completely several series of measurements referring to water and KCl solutions. A quantitative agreement can be realized, if (a) the effect of the solvent is taken into account, and if (b) it is admitted that there are, in ``conductance water,'' ions of considerably (about 100 times) lower mobility than the ordinary electrolytic ions. With these assumptions the concentrations and the mobilities of the ions can be determined. Finally, the rate constants which are characteristic of the presented theory can be evaluated.
20(1952); http://dx.doi.org/10.1063/1.1700671View Description Hide Description
By assuming that the activation energy for flow in associated liquids is proportional to the inverse square of the absolute temperature, an empirical expression for the viscosity is obtained, which fits the data well. An empirical expression for the activation energy of mixtures of associated liquids is also proposed.
20(1952); http://dx.doi.org/10.1063/1.1700672View Description Hide Description
The infrared absorption spectra of gaseous and liquid CF2:CHCl have been obtained in the regions 2–22μ and 2–38μ, respectively, with the aid of LiF, NaCl, KBr, and KRS‐5 prisms. The Raman spectrum of the liquid phase has been photographed with a three‐prism glass spectrograph of linear dispersion 15 A/mm at 4358A. Relative intensities and depolarization ratios have been measured for the stronger Raman bands. A complete assignment of fundamental vibration frequencies is given, the spectra are interpreted in detail, and thermodynamic functions are calculated for the temperature range 253–600°K.
Transition Probabilities III. Dipole Velocity Computations for C2 and N2 +. The Question of Degree of Hybridization20(1952); http://dx.doi.org/10.1063/1.1700673View Description Hide Description
Previous computations of transition probabilities for hydrogen using the dipole velocity operator are here extended to the diatomic molecules C2 and N2 + with particular reference to the former. Whereas previous calculations have shown the dipole length method to be relatively insensitive to the effective nuclear charge, the present computations show great sensitivity of the dipole velocity method to the ratio of the effective Z of the bonding orbital to that of the antibonding orbital. The results are less sensitive to the absolute magnitude of the Z's. The results are discussed with respect to reasonable assignments for the degree of s and pσ‐hybridization of the respective orbitals and with respect to reasonable choices for the effective Z values. It is concluded that the degree of hybridization is most probably considerably higher than previously estimated. The dipole velocity method is a promising one for further development.
20(1952); http://dx.doi.org/10.1063/1.1700674View Description Hide Description
A general sum‐over‐states form of the Lindemann theory of unimolecular reactions is analyzed with respect to properties in the high concentration region, and results are compared with similar deductions found in the low concentration region. In a general form the theory can set a limit on the low concentration rate constant from data taken in the high concentration region alone, and it can set a limit on the high concentration rate constant from data taken in the low concentration region alone. If there are data at both the low and high concentration regions, one can compute two dimensionless parameters which are useful in interpreting kinetic data. In particular, these parameters may be used to select the number of oscillators and their frequency in the Rice‐Ramsperger‐Kassel form of the theory. These methods are applied to nitrogen pentoxide and nitrous oxide.
20(1952); http://dx.doi.org/10.1063/1.1700675View Description Hide Description
On the basis of considerable experimental evidence, a particular form for the dielectric loss factor, ε″, is assumed to hold for many materials exhibiting a distribution of relaxation times. The dielectric constant, ε′, corresponding to the assumed form of ε″ is then computed by means of the Kronig‐Kramers relations and tabulated as a function of log frequency and of the distribution function half‐width parameter, α. Using these results, experimental ε′ and ε″ curves can be easily tested for mutual consistency and can be fitted individually. In conclusion, a brief discussion of other methods of dealing with the many‐relaxation‐time dispersion problem is given.
20(1952); http://dx.doi.org/10.1063/1.1700676View Description Hide Description
Microwave spectroscopicmeasurements on the partially deuterated forms of CH3Cl, CH3Br, and CH3I allow a determination of the structural parameters which is less subject to zero‐point vibration errors than other methods. In addition, examination of all measured isotopic species reveals that the C—D distance is shorter than C–H by 0.009A, and the D—C—D angle greater than that for H–C–H by about 12 minutes. Best values of structural parameters for the species containing the light isotope of hydrogen only are C–Cl distance 1.781, C–Br 1.939, C–I 2.139, C–H 1.11 (same for all halides), H–C–H angle 110°31′ for CH3Cl, 111°14′ for CH3Br, and 111°25′ for CH3I. Deuteration not only gives a change in the C–H bond but also a well‐correlated change in the quadrupole coupling constant of the halogen.
20(1952); http://dx.doi.org/10.1063/1.1700678View Description Hide Description
20(1952); http://dx.doi.org/10.1063/1.1700679View Description Hide Description
Monochromatic x‐ray diffraction patterns were taken of liquid alloys of sodium and potassium of seven different compositions at 115°C. Contrary to previous results, the present work does not show in a plot of position of main peak vs composition an inflection which had been taken as evidence for the existence of Na2K molecules in the liquid.Fourier analyses made for five of the alloys gave distribution curves which prove that there are no compact molecules in these liquid alloys, though they do not rule out the possibility that there may be weakly associated groups of atoms.
Microwave Absorption and Molecular Structure in Liquids. IX. Measurement in Organic Halides at 10‐Cm Wavelength20(1952); http://dx.doi.org/10.1063/1.1700680View Description Hide Description
The results of a systematic investigation of dielectric dispersion and absorption in the microwave region are discussed. Simple relations between the complex dielectric constant of an absorptive medium and the complex propagation constant of an electromagnetic wave within the medium are discussed in connection with a new interferometric method for measuring wavelength and absorption index directly within the medium. Results of measurements made at 10 cm wavelength by this method on twenty‐five liquid organic halides are reported. The data of the present and previous measurements on these compounds are discussed in terms of distributions of relaxation times and, on the basis of absolute rate theory, the processes of dipole orientation and viscous flow in these liquids are compared.
20(1952); http://dx.doi.org/10.1063/1.1700681View Description Hide Description
Changes in the potential of an electrode with time during electrolysis at constant current are controlled by two factors: (1) the charging and discharging of the double layercapacitor (causing ``capacitive'' changes) and (2) alteration of the composition and other properties of the electrode and the adjacent solution (causing ``non‐capacitive'' changes). Equations are derived for the capacitive changes in potential, assuming that the current‐voltage relation across the electrodesurface is given by Tafel's law.
An experimental study has been made of the potential accompanying the evolution of oxygen from 1N KOH at a platinumanode. When the current was held constant the potential increased slowly with time. When the current was interrupted the potential rapidly decreased, the decay being faster the higher the initial potential. The decay generally followed the above‐mentioned equations for a capacitive change in potential, thus making it possible to evaluate effective Tafel constants of the electrode at various stages during electrolysis. These constants were found to depend very much on the time and on the current density, indicating that the electrodesurface undergoes important changes. The behavior of the potential on increasing or decreasing the current has also been studied. This too reflects changes in the electrodesurface.
Most of these variations can be understood if it is assumed that the electrodesurface is non‐uniform, the current being carried by relatively few active centers. The non‐uniformity is similar to that encountered in ordinary catalysis, but is more complex since the same centers may not be active at all potentials. A simple graphical method of dealing with such a non‐uniformity has been developed. It is based on the assumption that Tafel's law is valid for each microscopic element of the surface, and allows the Tafel constants to vary from one element to another. The electrode as a whole may then no longer obey Tafel's law. The concepts of poisoning and promotion, so important in catalysis, are readily incorporated and explain most of the observed results in a direct manner.
20(1952); http://dx.doi.org/10.1063/1.1700682View Description Hide Description
The aim of this paper is to develop a selfconsistent theory of rubber‐like materials consisting of networks of non‐Gaussian chain molecules. Three kinds of series developments are derived for the distribution function of perfectly flexible single chains from the Fourier integral solution of Rayleigh; namely, (1) long chains with actual extension much less than the maximum extension, (2) long chains with actual extension comparable to the maximum extension, and (3) short chains. In the non‐Gaussian network theory, the leading term of the series (2) is used as the starting point for the individual chains of the network. Calculations are made for the case where the free junctions are moving with no restriction, and for the case where the free junctions are assumed to be at their most probable positions. The final expressions of the elastic energy for the two cases are compared, and it is shown that the percentage difference of the two expressions is of the order 1/n (n being the average number of links per chain), which is negligible for sufficiently large n. Finally an expression of the elastic energy is obtained with the assumption that all junctions are fixed and is shown to be, in general, a function of three strain invariants. The interdependence of the coefficients of the invariants is shown. Comparison of theory and experiment is given. Because of the interdependence of the coefficients only part of the observed deviations from Gaussian theory can be explained by our molecular theory. The remaining discrepancies must be ascribed to van der Waals forces. This should show up in the (not yet investigated) temperature dependence of these discrepancies.
20(1952); http://dx.doi.org/10.1063/1.1700683View Description Hide Description
Vapor pressures of pure ozone have been measured over the range −183°C to −30°C with an estimated accuracy of ±3 percent and are represented by the equationThe normal boiling point is −111.9°C±0.3°C. The critical temperature has been determined experimentally and found to be −12.1°C±0.1°C. The critical pressure derived from this critical temperature and the vapor pressure equation is 54.6 atmospheres absolute. Results are, in general, in good agreement with the meager data in the literature. The precision of the vapor pressure data is limited by the unstable nature of ozone and the necessarily small samples which must be used for measurements in the interests in the interests of safety.
20(1952); http://dx.doi.org/10.1063/1.1700684View Description Hide Description
The Onsager and Kirkwood theories of polar liquids have been used to analyze the available experimental data on the pressure dependence of the dielectric constant. It is found necessary in most cases to assume an appreciable decrease in the dipole moment arising from intramolecular distortion which may be large enough in some cases to more than compensate for the increase in effective moment caused by intermolecular compression. Quantitative estimates of these two factors are given, and their influence on binding energy and compressibility is discussed.
20(1952); http://dx.doi.org/10.1063/1.1700685View Description Hide Description
The absorption of thiocyanate, chloride, bromide, and iodide ions are markedly altered on complexing with nickelous or cobaltous ions in isopropyl alcohol solution, new peaks appearing at longer wavelengths. In the case of iodide ion, the absorption spectra of the complexes with nickelous ion, cobaltous ion, and iodine (the ``tri‐iodide'' complex) are practically distinguishable only by their extinction coefficients. A characteristic feature of the modified iodide spectrum is the pair of peaks, found at shorter wavelengths in the spectra of the free iodide ion, and in other forms. The cobaltous complexes with bromide and chloride ions show analogous splittings, but the absorption of the trihalide ions show single peaks which agree in wavelength with the longer‐wavelength peak of the cobalt‐complexed ion. The nickelous complexes absorb at shorter wavelengths.