Volume 36, Issue 10, 15 May 1962

Ground‐State Potential Energy of Diatomic Molecules
View Description Hide DescriptionThe restrictions placed on the ground‐state potential energy of a diatomic molecule by the inequalityd ^{2}(R ^{2} E)/dR ^{2}<0 are discussed. This leads to rather weak smoothness conditions on E(R).

Sound Propagation in the Critical‐Temperature Region of Hydrogen Chloride
View Description Hide DescriptionThe velocity and absorption of ultrasonicwaves have been measured in the critical temperature region of hydrogen chloride at frequencies between 1 and 9 Mc. To explain the f ^{2} frequency dependence of the absorption on the basis of scattering by molecular ``clusters,'' one must assume that there is a correlation in the fluctuations in density between adjacent volumes of the fluid.

Heat of Formation of the CN Radical
View Description Hide DescriptionThe vapor in equilibrium with graphite and nitrogen in the temperature range 2200°—2500°K has been analyzed with a mass spectrometer. The partial pressure of CN radicals measured in this way has been used to calculate ΔH_{f} °(CN) = 109 kcal/mole, equivalent to D _{0}(CN) = 7.5±0.1_{5} ev. The results of a variety of experiments are compared with this one, and in some cases, reinterpreted. The appearance potential of CN^{+} from CN is found to be 14.2±0.3 ev. Other possible azocarbon species up to C_{6}N_{6} have been investigated and found to be much less abundant than CN.

Theory of Magnetic Rotation Spectra
View Description Hide DescriptionA general theory is developed for optical and magneto‐optical rotation in the case of resonance, that is, if the frequency v of the primary light is equal to an absorption frequency v_{k} of the system. It is concluded that for this case optical and magneto‐optical rotatory power are physically meaningless quantities since they cannot be measured; instead the total intensities of the emission lines in optical rotationspectra or magnetic rotation spectra should be considered. General formulas for these intensities are derived from the quantum theory of radiation fields by making use of a perturbation method that was introduced by Heitler and Ma for the description of damping phenomena. An important feature of the method is the introduction of a damping constant which causes our results to remain finite for v=v_{k} ; this was not the case in the older theories. The possibility of measuringoptical rotationspectra is mentioned: it is predicted that they may be observed in dilute gases of optically active molecules. No applications of the general theory to specific molecules are given.

Pressure Dependence of Fluorescence Spectra. III. Effect of Finite Pulse Length
View Description Hide DescriptionThe effect of finite lengths of square exciting pulses in vibrational relaxation experiments in gases is investigated theoretically. Taking into account the finite duration of the pulse length does not yield results drastically different from those obtained assuming instantaneous excitation, provided that the exciting pulse has a width not more than about half the mean time between 1‐to‐0 transitions.

Attachment of Low‐Energy Electrons to Oxygen
View Description Hide DescriptionThe experimental data on electron attachment in pure O_{2} and C_{2}H_{4}–O_{2}, CO_{2}–O_{2}, N_{2}–O_{2}, CH_{4}–O_{2}, and He–O_{2} mixtures are reviewed. The results have been interpreted by a mechanism which is a modification of the Hurst and Bortner extension of the Bloch and Bradbury mechanism. The rate constants in the general rate equation are estimated and the equation is shown to be in general agreement with the reaction orders which have been obtained. The CO_{2} and C_{2}H_{4} data lead to a value for the mean life of O_{2} ^{—*} against electron detachment of 1×10^{—9} sec. The various reactions are discussed in some detail. The number of collisions required to stabilize O_{2} ^{—*} has been estimated from the experimental data and compared with the theoretical estimate of the rate of vibrational deactivation for each of the molecules studied.

Virial Coefficients for Square‐Well Potentials
View Description Hide DescriptionA comparatively simple method for evaluating virial coefficients for square‐well potentials is investigated. The method is based on the fact that a square‐well function can be expressed as a sum of step functions. Calculations are made for the third virial coefficient and for the fourth virial coefficient. The results for the third virial coefficient are in agreement with published values but the calculated fourth virial coefficients differ from those in the literature. Our values are confirmed by comparison with values derived by an entirely different method which we describe elsewhere. Critical constants are calculated on the assumption that fifth and higher virial coefficients may be neglected at the critical density.

Fourth Virial Coefficients for the 12–6 Potential
View Description Hide DescriptionA satisfactory numerical method for evaluating fourth virial coefficients for angle‐independent intermolecular potential energy functions is developed. The method is based on an expansion in Legendre polynomials which reduces the numerical problem from sixfold integration to triple integration, thus bringing it within the capacity of modern computers. The method is tested by some calculations for square‐well potentials and then used to calculate fourth virial coefficients for the Lennard‐Jones 12–6 potential. Using the fourth virial coefficients, critical constants for a 12–6 fluid are calculated and compared with experimental values for argon. The calculated and experimental critical temperatures and pressures agree to within 5% and the critical volumes to within 15%.

Thermal Properties Based upon Heat Capacity and Decomposition Pressure of Tetramethylammonium Hydrogen Dichloride. Nature of the Hydrogen Bond in the [Cl–H–Cl]^{—} Ion
View Description Hide DescriptionThe heat capacity of tetramethylammonium hydrogen dichloride was determined from 5° to 350°K by adiabatic calorimetry and the derived thermodynamic properties were calculated. No thermal anomalies were found. Molal values of heat capacity,entropy, and free‐energy function at 298.15°K are 49.07, 60.63, and —31.72 cal mole^{—1} °K^{—1}, respectively. The decomposition pressure of tetramethylammonium hydrogen dichloride, measured from 340° to 380°K with a Bourdon gauge as the null indicator, can be represented by the equation log_{10} P _{mm}=—28.4677–1698.5 T ^{—1}+15.502 log_{10} T—0.012256 T. Extrapolated values at 298.15° and 410.8°K are 1.8 and 760 mm Hg, respectively. Entropy increments for the decomposition reaction were calculated from the equilibrium data and compared with third‐law entropy increment values derived from the thermal data. Excellent agreement was obtained. This provides strong support for the location of the equilibrium position of the hydrogen ion midway between the two chloride ions.

Extrapolation of the Orthorhombic n‐Paraffin Melting Properties to Very Long Chain Lengths
View Description Hide DescriptionAn analysis of the equation T_{M} =T _{0} (n+a) / (n+b) is made in order to determine the convergence temperature T _{0} of the melting temperatures of the n‐paraffins from C _{44} to C _{100}. A good fit is obtained using T _{0}=414.3°K, a=—1.5, and b=5.0. This value of T _{0} (414.3°K=141.1°C) has an estimated total uncertainty of ±2.4°K and is proposed as the correct value of the equilibrium melting temperature of polyethylene. It is shown that presently available data do not permit accurate extrapolation of the n‐paraffin heats and entropies of fusion to the polymer limit.

Shock‐Tube Study of the Kinetics of Nitric Oxide at High Temperatures
View Description Hide DescriptionA shock‐tube program was carried out in which the NO concentration was followed as a function of time behind the shock front by absorption of 1270 A radiation, where ground vibrational state O_{2} and N_{2} are essentially transparent. The absorption coefficients of the species NO, O_{2}, and N_{2} as functions of the respective vibrational temperatures were determined by measuring the absorption by the shock‐heated gas at a point in the time history corresponding to complete vibrational relaxation but before the onset of dissociation.
Time history analyses were made on a total of 42 shock‐tube runs covering a temperature range of 3000°—8000°K on the following six mixtures: ½% NO, ½% NO+¼% O_{2}, 10% NO, 50% NO, 20% air, and 100% air—the diluent in all cases being argon.
An IBM 704 computer was programmed to integrate the vibrational and chemical rate equations as a function of time behind the shock front, subject to the constraints of the conservation equations. The pertinent rate constants were varied in a systematic trial‐and‐error manner in order to get the best fit to all the data.

Shock‐Tube Study of the Vibrational Relaxation of Nitric Oxide
View Description Hide DescriptionThe vibrational relaxation time of nitric oxide in NO–Ar mixtures was determined over the temperature range 1500°—7000°K. An ultraviolet absorption technique using 1270‐A radiation was employed to monitor the vibrational temperature as a function of time after these mixtures were shock heated to high translational temperatures. P _{10}, the transition probability per oscillator per collision for transition between vibrational levels 1 and 0 calculated from the measuredrelaxation times ranged from 1.0×10^{—3} at 1500°K to 2.8×10^{—2} at 7000°K for NO–NO collisions. Argon is about 1/50 as efficient as NO. The results are compared with the lower temperature (400°—1500°K) work of Robben and with the adiabatic theory of Schwartz, Slawsky, and Herzfeld and the nonadiabatictheory of Nikitin.

Homogeneous Nucleation in a Miscibility Gap System. A Critical Test of Nucleation Theory
View Description Hide DescriptionA critical test of the classical nucleationtheory applied to condensed phases has been carried out for the liquid miscibility gap system, methylcyclohexane‐perfluoromethylcyclohexane (C_{7}H_{14}–C_{7}F_{14}). The densities of, and the interfacial free energies between the coexisting liquid phases have been measured as a function of temperature. The interfacial free energy is found to vary as the power of the critical temperature T_{c} , less the experimental temperature, and these data are used to calculate the gradient energy parameter κ in the Cahn‐Hilliard theory of nucleation. The magnitudes of the relevant parameters are such that the Cahn‐Hilliard theory reduces to the classical theory for the present system.
These data, together with literature data on the thermodynamic properties of the bulk solutions, enable the degree of undercooling for a sensible nucleation rate to be calculated from classical theory. The experimentally determined undercoolings necessary to nucleate the C_{7}H_{14}‐rich phase from the solution are found to be much greater than those predicted by the classical theory by factors ranging from 8.5 at 10 deg below T_{c} to 340 at 0.3 deg below T_{c} . These very large discrepancies are attributable to the breakdown of the traditional approximation in the classical nucleationtheory that the number of molecules involved in the embryo population is a negligible fraction of the number of molecules in the system. When this approximation is avoided, the very complicated expression that results can be evaluated for the present case, leading to reasonable agreement between the predicted and the observed undercoolings. This is believed to constitute a satisfactory verification of the ``corrected'' classical theory of nucleation for condensed systems. The ``embryo population'' factor can be neglected in homogeneous nucleation in solidification and condensation (except near the critical temperature) and in most of the corresponding cases of heterogeneous nucleation. However, it is extremely important for nucleation in miscibility gap systems, or in any system in which the properties of the parent and daughter phases become identical at a critical temperature.

Studies on Mutual Diffusion of Polar‐Nonpolar Gas Mixtures
View Description Hide DescriptionThe two‐bulb technique of Ney and Armistead was employed for the measurement of the diffusion coefficient of binary mixtures of ammonia with argon and krypton in the temperature range —20° to 60°C. Diffusion was allowed to take place through a precision capillary tube connecting the two diffusion bulbs, and a previously calibrated thermal conductivityanalyser was used for analyzing the gas samples at different times.
A least‐square method was employed for determining the unlike interaction parameters of the Lennard—Jones (12:6) potential from the experimental D _{12} values at different temperatures. The combination rules for such systems and the force constants of pure components were also used for calculating the unlike interaction parameters. It has been concluded that the combination rules for polar‐nonpolar interactions are reasonably satisfactory but not sufficiently precise for accurate work.

On the Reduction of Certain Multiplicative Chemical Equilibrium Systems to Mathematically Equivalent Additive Systems
View Description Hide DescriptionThe vectorial formulation of the chemical equilibrium problem, represented by tableaux, provides a concise method for consolidating a large amount of fact and hypothesis relating to large chemical systems involving reactions and states of complex molecules. This formulation plus the associated techniques for minimizing the free energy of the entire system allows equilibrium states under varying conditions to be calculated in a rapid and efficient manner on electronic computers. In biological systems involving hemoglobin, for example, it is possible to account for and to compute the effects of simultaneous changes in pH, CO_{2}, O_{2}, and metabolite concentrations on the oxygenation of hemoglobin. The effects of changes in temperature and total pressure may also be introduced into the model in a convenient fashion. A subsequent paper will present the results of such numerical calculations using the approach developed in this paper.

Nuclear Magnetic Resonance Spectra of Silicon Hydrides and Derivatives. I. Coupling Constants Involving Hydrogen
View Description Hide DescriptionMeasurements of the H–H, H–Si, H–F and Si–F coupling constants for the halogen‐substituted monosilanes, disiloxane, disilyl sulfide and trisilylamine are described. The failure of the simple valence‐bond calculation to interpret the H–H coupling constants as a function of the H–Si–H angle is attributed to the d orbitals of silicon. A comparison of the H–H and H–Si coupling constants is also presented.

Infrared Spectra and Structures of the Crystalline Phases of CH_{4} and CD_{4}
View Description Hide DescriptionInfrared spectra of CH_{4} and CD_{4}, in the region of the fundamentals ν_{3} and ν_{4}, have been obtained in all of their crystalline phases at temperatures ranging from 5° to 40°K. In addition, the spectra of dilute solutions of CH_{4} and CD_{4} in one another have been studied through the same temperature range. The spectra of the dilute solutions consist of single sharp lines for both fundamentals, demonstrating that the barriers to molecular rotation are high in all the phases. The fine structure observed in the low‐temperature phases of the pure crystals is inconsistent with any of the structural models heretofore proposed but a model for phase II is suggested which is consistent with the spectra and which shows very efficient packing. Phase III of CD_{4} is probably complex and of low symmetry. Phase I is probably disordered.

Tunneling Model for Electron Transport and Its Temperature Dependence in Crystals of Low Carrier Mobility. Example: Anthracene
View Description Hide DescriptionA tunnelingmodel is used to explain electron transport in crystals of low carrier mobility. Temperature is incorporated into the model by allowing the barrier width to vary sinusoidally as a result of lattice vibrations. The maximum amplitude of vibration is proportional to T ^{½}. The resulting expression for the mobility exhibits a linear temperature dependence. The model can also be used to estimate the width of the conduction band. The calculated results are compared with experimental results on anthracene, and the agreement is quite good for the mobility but not as good for the temperature dependence.

Empirical Method for Estimating Diamagnetic Anisotropy Effects in NMR Spectroscopy, Based upon the Use of C^{13}–H Coupling Constants
View Description Hide DescriptionAn empirical method is described for the estimation of diamagneticanisotropyeffects in nuclear magnetic resonance spectroscopy, based upon correlations between protonchemical shifts and C^{13}–H coupling constants. This method has been applied to obtain anisotropyeffects for benzene, thiophene, acetylene, allene, and chlorine. The results are supported by internal consistency and comparisons with other available estimates.

Unimolecular Decomposition of Vibrationally Excited Ethane and Ethyl Radicals
View Description Hide DescriptionH or D atoms and ethyl radicals were concurrently produced by the mercury sensitized photolysis of mixtures of H_{2} (or D_{2}) and diethyl ketone. Combination of an ethyl radical with a hydrogen atom produces vibrationally excited ethane molecules. Their rate of dissociation into methyl radicals relative to stabilization to ethane was studied as a function of pressure of ketone for both H and D.
Similar studies were made of the mercury sensitized reactions of mixtures of D_{2} or H_{2} and ethylene, which permitted the measurement of the maximum rates of decomposition of excited ethyl radical and of excited ethane both as a function of pressure and of temperature.
Our results show that vibrational energy is not used in overcoming the barrier for alkyl radical addition to an olefin bond.