Index of content:
Volume 21, Issue 11, 01 November 1953
21(1953); http://dx.doi.org/10.1063/1.1698715View Description Hide Description
The magnetic anisotropy of natural rubber was measured by Krishnan's oscillation method. In the first place, the anisotropy was measured by varying the time of vulcanization and was found to decrease with the time of vulcanization. In the second place, the anisotropy was measured as a function of temperature. Similar to the breadth of nuclear magnetic resonance line, an abrupt change in the slope of the anisotropyversus temperature curve was observed at the second‐order transition temperature. Above and below this transition temperature, its change with temperature was not so strong.
21(1953); http://dx.doi.org/10.1063/1.1698716View Description Hide Description
Vapor pressureequations have proven useful in providing quantitative data on heats of vaporization but the heat capacity term, occurring in equations of the Rankine type, has been usually treated as an empirical constant. This term represents Cpvap—Cpliq for a vapor obeying the ideal gas laws and it is shown that even for a real gas the same result may be expected to hold. This conclusion is tested for twelve compounds for which data are available. The values of Cp0 calculated from the heat capacities of the liquid and the difference in heat capacities from the vapor pressureequation are in good agreement with those directly measured and would therefore be of use for thermodynamic calculations.
21(1953); http://dx.doi.org/10.1063/1.1698717View Description Hide Description
The mean square end‐to‐end separations of coiling type polymer molecules have been calculated by two different approximate methods, taking into account the effect of excluded volumes. One of the methods is the equivalent of a first‐order perturbation calculation using the unrestricted random walk as a starting approximation. The other method involves the use of certain plausible functional forms valid for large values of the chain lengths. The calculations have been carried out for three, two, and one dimensions and the results are analyzed to provide an insight into factors which might determine convergence or divergence of the quotient 〈rn 2〉Av/n (the mean‐square length divided by the number of links). It appears that the quotient converges in three (or more) dimensions, but diverges for a lower number of dimensions.
21(1953); http://dx.doi.org/10.1063/1.1698718View Description Hide Description
Static dielectric constants of solid hydrogen bromide have been measured from 186 to 70°K, and dispersion and loss below 89°K in the frequency range 15 cy to 5 Mc. Special cell designs minimized formation of cracks and voids in the polycrystalline sample, as such flaws were shown by several lines of evidence to cause serious errors. Static dielectric constants above 117°K are in quite good agreement with Onsager's equation. In phase II, stable below 113°K, the dielectric constant rises to a peak of 200 at 89°K, then falls to a value of 32 at 70°K in phase III. The principal dispersion below 89°K follows a circular arc locus with α=0.3, and a rate expression with activation energy 2.7 kcal/mole. A second dispersion is observed at much higher frequencies with energy 1.59 kcal/mole, and it is suggested that the two dispersions are a consequence of crystal anisotropy.
The Mean Amplitudes of Thermal Vibrations in Polyatomic Molecules. II. An Approximate Method for Calculating Mean Square Amplitudes21(1953); http://dx.doi.org/10.1063/1.1698719View Description Hide Description
A simple method of the calculation of the mean amplitudes of both directly bonded atom pairs and nonbonded ones is proposed by approximating the function cothx by 1/x+x/4. The enumeration of the L matrix, the most time‐consuming procedure, is replaced by the calculation of the inverse matrix F −1 from the potential energy matrix. The formulae obtained are applicable with reasonable accuracy (4 percent) to almost all the cases except the atom pairs having higher frequencies than 1200 cm−1. For the latter cases modified formulas are presented by using hyperbolic cotangent function.
It is also revealed that, if some allowance be made for the errors of the mean amplitudes, a definite value can be assigned to the mean amplitude of a given pair of atoms, without referring to the structure of the other part of the molecule. Reliable values of the mean amplitudes are computed for some typical atom pairs, by the use of the force constants of Urey‐Bradley type obtained by the analysis of the vibrational spectra.
21(1953); http://dx.doi.org/10.1063/1.1698720View Description Hide Description
This investigation deals with the normal long‐chain acetates with 18, 20, 24, and 28 carbon atoms. When crystallized from the melt, these compounds first give the transparent α‐phase which gradually changes to the white, opaque β‐phase on standing or on cooling below a certain temperature. It is found that the acetates in the α‐phase all give large dielectric absorption, whereas, in the β‐phase the absorption is small, or, in some cases, negligible.
Of the long‐chain compounds so far investigated, the acetates in the α‐phase are unique in giving two absorption regions which appear to be the result of the rotational transitions of complete molecules. The maxima for the two regions are separated by about 7 decades in frequency. Measurements of the lower frequency absorption at various temperatures show that the associated energy barrier is very large compared with previous values for compounds of similar chain‐length. To explain these results it is suggested that a molecule rotating in the crystal lattice of a long‐chain compound possesses four positions of equilibrium instead of two, as previously proposed.
In addition to the two absorption regions mentioned above, the long‐chain acetates in the α‐phase give further absorption at still higher frequencies, which is probably caused by independent orientation of the polar groups near the ends of the molecular chains.
21(1953); http://dx.doi.org/10.1063/1.1698721View Description Hide Description
The Kstructure in the P and R branches of the 2ν1 band of CHD3 has been resolved permitting the determination of the following molecular constants: ν0=5865.02, B″=3.2777, B′=3.2396, A′—A″=−0.0181, DJ =3.9×10−5, and DJK =−4×10−5 cm−1. The Q branch is synthesized from these data and compared with the spectrometer trace of that branch.
21(1953); http://dx.doi.org/10.1063/1.1698722View Description Hide Description
The static dielectric constants of n‐butyl alcohol, t‐butyl alcohol, n‐butyl chloride, n‐butyl bromide, t‐butyl chloride, and water were experimentally determined over a temperature range of 14° to 50°C and over a pressure range of 1 to 200 atmos. In addition, for glycerol, both the static dielectric constant from −18° to 14°C and the dielectric relaxation data at 0°C and up to 1.5 mc were obtained over the same pressure interval. The theory of dielectric polarization was then applied to these measurements to determine the molecular interaction. On the basis of the molecular interaction,structures and structure changes with temperature and pressure have been proposed for the various liquids studied.
21(1953); http://dx.doi.org/10.1063/1.1698723View Description Hide Description
The infrared spectrum of gaseous F2C:CFCl has been reinvestigated in greater detail and over a more extensive region than in earlier work. Three hitherto unobserved bands have been found at 369, 338, and 194 cm−1. These data, together with the previously available Raman spectrum, have made possible the achievement of a new and more satisfactory fundamental assignment: 1792 (ν CC), 1336 (ν CF), 1215 (ν CF), 1058 (ν CF), 689 (ν CCl), 517 (δ CF2), 463 (ρ CF2), 338 (δ CFCl), 194 (ρ CFCl) for the planar vibrations; and 538 (β CF2), 369 (β CFCl), 158 (τ) for the out‐of‐plane modes. The ideal‐gas entropy value based on the present assignment agrees with that obtained calorimetrically.
21(1953); http://dx.doi.org/10.1063/1.1698724View Description Hide Description
A crude calculation of the frequency spectrum and heat capacity has been made for a simple model of a large crystal composed of long parallel polymer chains. The heat capacity is very unlike that of a cubic crystal but can be represented quite well with a simple two‐parameter equation recently proposed by Tarasov.
21(1953); http://dx.doi.org/10.1063/1.1698725View Description Hide Description
Paramagneticresonance absorption in solutions of K and Na in liquid NH3 has been investigated. The resonance has been studied at a frequency of approximately 7.0·106 cycle sec−1 and a magnetic field of 2.5 gauss. The measurements have been made at 240°K, 274°K, and 298°K and over a concentration range from 0.004 M to 0.7 M. The intensities and susceptibilities,spectroscopic splitting factors, widths, shapes, and extents of saturation of the resonances have been determined. The paramagnetic parts of the magnetic susceptibilities in static fields have been calculated from the rf data and have been compared with the susceptibilitiesmeasured in static fields by other investigators. The relations of the trapped electron model of such solutions to these quantitative measurements on the paramagneticresonance absorption have been considered.
21(1953); http://dx.doi.org/10.1063/1.1698726View Description Hide Description
It is shown that the theoretical equation for the ratio of the rate constants of isotopic molecules is essentially independent of whether the crossing of the barrier is treated as a translation or a vibration. The temperature independent factor in this equation is evaluated for the case of substitution or displacement reactions. Calculations are presented for several cases involving the isotopes of carbon where there is simultaneous bond rupture and bond formation.
21(1953); http://dx.doi.org/10.1063/1.1698727View Description Hide Description
The body‐centered and face‐centered cubic monatomic metals are represented by a model consisting of an ion point lattice embedded in an electron gas. The Born‐von Kármán lattice dynamics are modified to include the role which the conduction electrons play in acoustical wave motion. This leads to relations connecting the dynamic parameters with the elastic constants, and yields the Fuchs relations in an elementary manner. The discrepancy in the Cauchy relation is shown to be just the bulk modulus of the electron gas.
In studying the contribution of the conduction electrons to the thermal motion, two extreme cases are treated: 1.—the electron gas does not partake of the thermal motion appreciably; 2.—the electron gas follows the ion motion almost exactly. The secular equations are given for both cases. The Debye characteristic temperature in the T 3 region of atomic heat is computed analytically for both cases when the departure of the elastic constants from the isotropy condition is not too large.
21(1953); http://dx.doi.org/10.1063/1.1698728View Description Hide Description
The incorporation of solute elements into single crystals of germaniumgrown from the melt is examined in terms of a simple model. The theory takes account of the contribution of solute transport in the melt, owing to diffusion and fluid motion, to the over‐all process of impurity incorporation during steady‐state crystallization. The analysis is extended to treat the transient inclusion of solute which results when the composition of the melt is abruptly changed.
21(1953); http://dx.doi.org/10.1063/1.1698729View Description Hide Description
Experiments have been performed on the distribution coefficients of a number of solute elements in germanium crystals grown from the melt. The variation of distribution coefficient with conditions of crystallization is examined in the light of the theory of Part I. The incorporation of solute elements into the crystal is shown to depend critically upon the transport processes occurring in the melt.
21(1953); http://dx.doi.org/10.1063/1.1698730View Description Hide Description
The infrared spectra of the series SiCl4 through SiMe4 have been obtained in the gas phase over the range 2–25 microns using CaF2, NaCl, and KBr prisms. The spectra are compared with Raman data for these compounds, and vibrational assignments are made. The methyl band at about 8 microns is shown to be associated with the symmetrical CH3 deformation, the bands around 12 microns with the methyl rocking and Si–C stretching vibrations, and the bands between 16 and 25 microns with the SiCl stretching modes. A comparison of frequencies for the members of the series has made it possible to assign fundamentals for all motions except those involving torsion of the Me group around its axis.
21(1953); http://dx.doi.org/10.1063/1.1698731View Description Hide Description
The vibration potential functions of electronic ground and excited states of molecules of C2v and D6h symmetry are computed and compared. From this, quantitative characteristics of the molecular orbitals belonging to the correlated angular molecules and to a negative ion are deduced and, in this connection, the structure of the CF2 and CH2 radicals is discussed. The behavior of the interaction terms is examined, and a rule concerned with their sign is obtained in the case of n→π* and π→π* transitions. Various other effects, such as the σ—π resonance and the part played by the lone‐pair electrons, are studied.
21(1953); http://dx.doi.org/10.1063/1.1698732View Description Hide Description
Data are given for the absolute intensities, in chloroform and carbon tetrachloride solutions and in the vapor state, of the carbonyl infrared absorption bands of a number of compounds in which the carbonyl group is conjugated by varying amounts. The absolute intensity differs in the different solvents and in the vapor, but the increase in intensity of a conjugated carbonyl over that of a simple ketone or aldehyde seems to be independent of the state. For most of these compounds a simple relation is shown to exist between this increase in carbonyl intensity with conjugation and the resonance energy of conjugation. This relation is expected from a consideration of the electronic configurations available to the normal and distorted molecule. That such compounds as the amides do not necessarily fit this trend is attributed to the geometric requirements on the molecule of these electronic configurations.
21(1953); http://dx.doi.org/10.1063/1.1698733View Description Hide Description
21(1953); http://dx.doi.org/10.1063/1.1698734View Description Hide Description
The Schroedinger equation for a particle moving in a perturbed periodic potential is transformed into a representation called the ``Crystal momentum representation.'' It is shown that by use of this representation previous approximate ``effective mass''equations can be readily derived and extended to arbitrarily high approximation. A theorem concerning weak space dependent perturbations is discussed.