Volume 20, Issue 9, 01 September 1952
Index of content:
20(1952); http://dx.doi.org/10.1063/1.1700760View Description Hide Description
A previously reported discrepancy between the predicted and observed infrared spectrum of crystalline carbon dioxide is shown to arise from the presence of two peaks due to C13O2, a combination band involving a lattice frequency near 110 cm−1 and two reflection peaks. The infrared spectrum was studied at − 190°C and aside from the previous features shows one component from ν3 and two from ν2, shifted very little from the gas frequencies. The difficulties encountered in interpreting the spectrum of this simple crystal occur quite generally in the spectra of more complicated substances.
20(1952); http://dx.doi.org/10.1063/1.1700761View Description Hide Description
It is shown that the contribution of a set of equivalent nuclei to the zeta‐sum for the fundamental vibrations of any symmetry species in a molecule possessing only one multiple axis of symmetry is zero unless the nuclei are situated on the axis. In the latter case the contribution of the set of equivalent nuclei to the zeta‐sum in any species is one unit for every degree of freedom the set contributes to that species. With the help of these theorems a table is worked out from which the zeta‐sums can be determined immediately for any axially symmetrical molecule of known structure. Use of the table is illustrated with several simple examples.
20(1952); http://dx.doi.org/10.1063/1.1700762View Description Hide Description
The statistical treatment of a lattice of classical dipoles, electric or magnetic, has been intractable because of the ``strong'' condition that all dipoles have a fixed length. The spherical model consists in replacing the above strong condition by the weaker condition that the sum of the squares of the dipole vectors have the correct value, thus permitting some, but not much, fluctuation from the true situation.
The previous work of Berlin and Thomsen using the spherical model and nearest neighbor interactions is generalized to include a mixture of long and short range interactions. The evaluation of the partition sum in the presence of long‐range forces requires care because some of the eigenvalues depend on specimen shape. A formula has been derived for the susceptibility, however, in which the shape dependence is explicitly shown to cancel. In fact, it is proven that in the spherical model a permanent dipole lattice is equivalent to an induced dipole lattice with a certain effective polarizability. Expansion of this polarizability in inverse powers of the temperature shows precise agreement to terms of order (1/T)3 with an exact evaluation of the corresponding expansion coefficients.
All qualitative results are in agreement with those of Berlin and Thomsen. One‐ and two‐dimensional lattices show no transition. A simple cubic lattice (the case they treat) shows an antiferroelectric transition bounded by a critical field curve E=Ec [1—(T/Tc )]½.
The effective field and its application to an elementary quantum mechanical treatment of the ferromagnetic problem are described.
20(1952); http://dx.doi.org/10.1063/1.1700763View Description Hide Description
The ``random flight'' distribution function for the relative positions of two segments of a linear polymer chain is based on the assumption that the space occupied by a single polymer segment is relatively small and may be neglected. In this paper, the space requirements of a real polymer chain are taken into account. A generalized Fokker‐Planck equation is formulated, and the distribution function, the average square distance, and the average inverse distance between two chain segments are calculated.
20(1952); http://dx.doi.org/10.1063/1.1700764View Description Hide Description
A mathematical model, the spherical model, of electric dipole‐dipole interaction in simple lattices is discussed. The partition function for the system, assuming just nearest neighbor interaction, is evaluated for one‐ and three‐dimensional simple lattices. Only the three‐dimensional lattice exhibits a phase transition. The transition is discussed. The transition behavior in the presence of an external field is also analyzed, and the electric susceptibility is computed.
20(1952); http://dx.doi.org/10.1063/1.1700765View Description Hide Description
The fluorescencespectrum of naphthalene vapor has been photographed and found, under suitable conditions, to consist of a number of discrete bands. Thirty‐nine bands were measured and a vibrational analysis was carried out making use of assignments of infrared and Raman fundamentals. The analysis indicates that the transition observed is forbidden by symmetry and made weakly allowed by a molecular vibration of frequency 478 cm−1 belonging to the representation b2 u . This indicates that the wave function of the lowest excited singlet state of naphthalene belongs to the irreducible representation Ag or B1 g of the point group D2 h .
20(1952); http://dx.doi.org/10.1063/1.1700766View Description Hide Description
The inner cone of the acetylene‐oxygen flame burning lean (1:5), stoichiometric (2:5), and rich (4:5) at atmospheric pressure has been studied spectroscopically with the object of gaining some information about the elementary processes occurring in this flame. The rotational, vibrational, and electronic distributions of OH(2Σ+) have been determined for each fuel mixture. The analysis of the data showed a rotational Maxwell‐Boltzmann distribution with a rotational ``temperature'' several hundred degrees higher than the adiabatic flame temperature. The vibrational distribution of OH(2Σ+) was distinctly nonequilibrium with an excess population in the level v′=3 analogous to that observed for the hydrogen‐oxygen flame. This is attributed to the interaction of the 2Σ+ and 2Σ− states of OH. The analysis of the electronic distribution of OH indicated that OH(2Σ+) is present in its thermal equilibrium concentration in the flame at atmospheric pressure. The results of this study in conjunction with the work of Gaydon and Wolfhard on the low pressure acetylene‐oxygen flame indicate that the radiation of OH(2Σ+) is to a large extent chemiluminescence so that a considerable fraction of the excited hydroxyl radicals must have been formed in the 2Σ+ state by a chemical reaction (or reactions).
20(1952); http://dx.doi.org/10.1063/1.1700767View Description Hide Description
Two dispersion regions in the liquid in addition to the primary dispersion have been measured at audio‐and radiofrequencies below −120°C, which make small but significant contributions to the dielectric constant. Both move rapidly to lower frequencies with decreasing temperature and the relaxation times of the intermediate dispersion are 200 times smaller than for the primary one. The temperature and frequency dependences are those to be expected for orientation rather than induced polarization.
20(1952); http://dx.doi.org/10.1063/1.1700768View Description Hide Description
The sedimentation constants s 0 at infinite dilution and the intrinsic viscosities [η] of five fractions of polyisobutylene have been determined in cyclohexane, a good solvent. Their osmotic molecular weights ranged from 3.1×104 to 1.4×106. Under the assumption that the effective hydrodynamic radii vary as the average linear dimensions of the molecule, f 0/η0=P(〈r 2〉)½ and , where f 0 is the frictional coefficient, η0 is the viscosity of the solvent, 〈r 2〉 is the mean‐square end‐to‐end distance of the molecule, and P and Φ are constants. In confirmation, s 0[η]⅓/M ⅔ is constant throughout the molecular weight range investigated. Furthermore, Φ⅓ P −1=2.5×106. The close agreement of this quantity with values for four other systems reported in the literature indicates that P, like Φ, is a universal constant for flexible chain molecules. It follows also that the observed proportionality of s 0 (or of M/f 0) to M 0.42 instead of to M ½ occurs because of intramolecular interactions which cause the molecule in solution to be expanded by a factor α which increases with molecular weight.
The above theory accounts for both the sedimentation and intrinsic viscosity behavior of flexible chain molecules in a satisfactory manner. Neither the Kirkwood‐Riseman nor the Debye‐Bueche theories succeeds in doing so.
20(1952); http://dx.doi.org/10.1063/1.1700769View Description Hide Description
The interatomic spacings as obtained from the radial distribution method of analysis of electron diffraction patterns are given for vitreous silica, Vycor, and Pyrex glasses. The results are in general agreement with the x‐ray diffraction results published by others.
20(1952); http://dx.doi.org/10.1063/1.1700770View Description Hide Description
The exchange equilibrium PH2D(g)+H2O(l)=PH3(g)+HDO(l) has been measured at 25°C by the use of dilute sulfuric acid and buffer solutions as a catalyst. From this measurement and the ratio of the vapor pressures of H2O and HDO the equilibrium constant for the exchange PH2D(g)+H2O(g)=PH3(g)+HDO(g) is calculated to be 1.52 at 25°C. The latter experimental value is combined with a theoretical computation of the temperature independent factor of the equilibrium constant to evaluate the difference in the zero point energies of PH3 and PH2D. This leads to the equation, which is valid up to about 500°K, K g =0.781e 198/T . This equation is in good agreement with calculations based on the spectra of PH3 and PD3 and the rule of the geometric mean.
20(1952); http://dx.doi.org/10.1063/1.1700771View Description Hide Description
Considering only collisions of the ``billiard ball'' type the total retention is obtained as a sum of partial retentions for an infinite number of collisions. Expressions are derived which give the retention as a function of the initial energy of the recoil atom. The calculation shows that it is not possible to determine the initial recoil energy by the retention.
20(1952); http://dx.doi.org/10.1063/1.1700772View Description Hide Description
A study of proposed explanations for the forces governing the interaction of hydrogen‐bonded molecules has been made by investigating various models for the intermolecular potential function for H2O. Implications of the models concerning the known properties of H2O have been examined.
1. After a survey of existing views and data on hydrogen bonding, the electrostatic model is chosen for further study. The criterion selected to winnow the proposed models is their ability to correlate second virial data and the energy of sublimation of ice.
2. The dipolar energy of ice is calculated after Ewald and Kornfeld. Although the dipole approximation fails to pass test No. 1, it is sufficient for interesting observations on some crystal properties of ice.
3. The consistency of the dipole model with Pauling's explanation of the entropy discrepancy is examined.
4. Point charge models are discussed and a multipole calculation made for the icestructure with the highest dipole‐dipole energy.
5. Calculations made suggest that a properly chosen point charge model may suffice for the correlation of gas and crystal data.
The Microwave Spectra, Structure, Dipole Moment, and Chlorine Nuclear Quadrupole Coupling Constants of Methylene Chloride20(1952); http://dx.doi.org/10.1063/1.1700773View Description Hide Description
The microwave spectra of CH2Cl2 35, CH2Cl35Cl37, CH2Cl2 37, CDHCl2 35, CDHCl35Cl37, CD2Cl2 35, and CD2Cl35Cl37 have been examined and effective moments of inertia have been determined for these seven isotopic species. From these data the effective bond distances and angles were determined as C–Cl distance=1.7724±0.0005A, Cl–C–Cl angle=111°47′±1′, C–H distance=1.068±0.005A (average of all species), or 1.082A (extrapolated to infinite hydrogen mass), and H–C–H angle=112°0′±20′ (average of all species) or 112°58′ (extrapolated to infinite hydrogen mass). The best value for the dipole moment of methylene chloride was found from the Stark splitting to be 1.62±0.02×10−18 esu. The chlorine nuclear quadrupole coupling constants were also determined and their relationship to the structure is discussed.
Fluorescence Studies of Some Simple Benzene Derivatives in the Near Ultraviolet. III. Benzotrifluoride20(1952); http://dx.doi.org/10.1063/1.1700774View Description Hide Description
The fluorescencespectrum of benzotrifluoride has been studied using various sources of excitation. The spectrum consists of about 36 bands for which assignments are given according to the symmetry properties of the molecule. The analysis is in agreement with that of the absorptionspectrum. In the region of overlap, fluorescence and absorption bands show close coincidence.
20(1952); http://dx.doi.org/10.1063/1.1700775View Description Hide Description
The low velocityscattering of H+, H2 +, and H3 + in both ethane and propane have been measured at ion velocities of less than 150 volts. Ion neutralization was detected and measured for all three ions in both hydrocarbons and elasticscattering potential functions evaluated for all six interactions. The scattering of hydrogen ions in the first four members of the series of straight chain saturated hydrocarbons can now be compared, and it is shown that they change in a systematic manner.
20(1952); http://dx.doi.org/10.1063/1.1700776View Description Hide Description
The 003, 103, and 004 rotation‐vibration bands of HC13N have been observed in the photographic infrared region of the spectrum. In addition, the Raman spectrum of the liquid was obtained with sufficient dispersion to measure the isotopic shift of ν1. Values are given for B′, B″, D′, and D″ of the three infrared bands as well as for α1 and α3.
The average values of B″=1.44006 is in excellent agreement with B″=1.44008 calculated from microwave data and the velocity of light as c=299,776 km/sec.
The Properties of the Interstitial Compounds of Graphite. II. The Structure and Stability of Graphite Residue Compounds20(1952); http://dx.doi.org/10.1063/1.1700777View Description Hide Description
1. Controlled decomposition of lamellar compounds of graphite produces substances intermediate in composition between graphite and lamellar compounds. These intermediate compounds have been termed residue compounds. They are much more resistant to decomposition than the lamellar compounds.
2. The x‐ray pattern of residue compounds shows a very slight increase in the c spacing of the graphite lattice. The increase is entirely insufficient to account for the trapped reactant. Consequently, the bulk of the trapped reactant is believed to be situated at crystal imperfections.
3. Quantitative studies of the composition of graphite bromide residue compounds have shown that their composition is strongly dependent on the type and subdivision of the graphite used and the temperature to which the compounds have been heated.
The Properties of the Interstitial Compounds of Graphite. III. The Electrical Properties of the Halogen Compounds of Graphite20(1952); http://dx.doi.org/10.1063/1.1700778View Description Hide Description
The presence of lamellar or of residual bromine in artificial graphite reduces the resistance, the absolute magnitude of its temperature coefficient near room temperature, and the magneto resistance. The Hall coefficient increases and eventually changes from negative to positive values. The changes resemble very closely those obtained in the oxidation of graphite in sulfuric acid. This similarity in properties suggests that the electron acceptors in these compounds are only weak scattering centers for conduction electrons.
Since the electrical properties of graphite bisulfate and of graphite bromide are very similar, it may be assumed that both compounds are of a similar type. Since the bisulfate compound is ionic in nature, the bromine in graphite bromide is also probably ionized. On this assumption the graphite bromides have the formulas C n Br·3 Br2 for the lamellar and C n Br·2.25 Br2 for the residue compounds.
Chlorine reacts with graphite at low temperatures only. The properties of the compounds of chlorine and graphite resemble in all respects those of the compounds of bromine and graphite. Attempts to react iodine and graphite have failed. Iodine chloride, however, reacts rapidly with graphite.
20(1952); http://dx.doi.org/10.1063/1.1700779View Description Hide Description
A potential energy curve for the mercury hydride molecule is constructed which takes into account the fact that the molecule can change from a structure bonded by exchange forces below about 2.65A, to a quasi‐molecule held together by London dispersion forces at larger distances. The breaking off of certain bands can be understood on the basis of maxima in vibrational‐rotational energy curves.