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Volume 34, Issue 2, 01 February 1961

Heats of Mixing in Liquid Alkali Nitrate Systems
View Description Hide DescriptionThe enthalpies of mixing in binary liquid alkali nitrate systems have been measured, and are all negative. It is found that the magnitude of the molar mixing enthalpy (ΔH^{M} ) increases in a regular fashion with increasing difference in size between the two participating cations, according to the following approximate relationHere X and (1—X) are the mole fractions of the two components, U is the lattice energy of the mixture, while d _{1} and d _{2} are the interionic distances characteristic of the two pure components. The results are in accord with the view that in these systems the principal source of the enthalpy of mixing is the reduction in Coulombic repulsion between the second nearest neighbor cations. For binary systems with negative enthalpies of mixing of the order of RT there is evidence for short‐range order among the cations.

Solution at High Density to the Born‐Green Equation
View Description Hide DescriptionA solution to the Born‐Green integral equation with the Lennard‐Jones potential at v/v ^{*}=n ^{−1} a ^{−3}=0.9 is presented. Its asymptotic form is found to be 1–38.9r ^{−5} sin (2πr−2.928), and its integral over the volume τ of the system is τ−2.06. The value of E′/RT is found to be −2.6 and of pv/RT is 3.8. The magnitudes of these thermodynamic quantities are compared with those obtained by the Monte Carlo method.

Quantum Calculations of the Velocity Dependence of the Differential and Total Cross Sections for Elastic Scattering of Molecular Beams
View Description Hide DescriptionThe partial wave treatment (phase shift analysis) of the elasticscattering of molecular beams [J. Chem. Phys. 33, 795 (1960)] is applied to the calculation of the velocity dependence of the differential and total cross sections for an assumed L‐J (12, 6) potential. For most of the calculations, the ε, σ values are chosen to correspond to the H_{2}–Hg system. The range of the velocity parameter A≡kσ=μvσ/ℏ is from 3 to 30; this is equivalent to a 100‐fold variation in H_{2}beam temperature (approx 8.2–820°K). Computations of the angular distribution of the scatteringdσ(θ)/dΩ and the total cross section Q as a function of A are reported. A correlation of the interference maxima in dσ(θ)/dΩ is presented. The Massey‐Mohr approximation for Q(A) for an inverse sixth‐power attractive potential is compared with the present calculations for the L‐J (12, 6) potential. Significant undulatory deviations are noted at low A; this effect is attributed to the existence of the broad maximum in the phase shift curve η(l), which, in turn, originates from the negative repulsive phases at low l. Consideration is given to the question of the sensitivity of the scattering to the repulsive part of the potential.

Calculation of the Diamagnetic Susceptibility of N_{2}
View Description Hide DescriptionThe diamagnetic susceptibility of the nitrogen molecule has been calculated from wave functions that are constructed from gauge invariant atomic orbitals. The result is −13.539×10^{−6} which agrees satisfactorily with the average experimental value −13.3×10^{−6}.

Vibrational Relaxation in Liquids
View Description Hide DescriptionAttempts have been made to apply the binary collision theory of vibrational deactivation to the liquid phase. The change of collision frequency with density was approximately accounted for, but the transition probability per collision was assumed independent of density. This latter assumption is investigated here by an addition, to the direct intermolecular force, of the frictional and random forces of Brownian motiontheory. It is found that the frictional force has negligible effect, but the random force makes low‐energy collisions much more effective in causing transitions than is predicted for an isolated binary collision by the semiclassical theory of Zener, Landau, and Teller. As a consequence, the isolated binary collision theory cannot be applied to liquids although it should be adequate for fairly dense gases. Probably the Brownian motiontheory exaggerates the neighbor effects in liquids; the point is discussed.

Nuclear Magnetic Resonance Study of the Proton Transfer in Water
View Description Hide DescriptionMeasurements of the nuclear relaxation in water are reported. The transverse relaxation rate (1/T _{2}) of the protonresonance is pH dependent. The effect is shown to be due to a spin‐spin splitting of the protonresonance by O^{17} (spin 5/2), which is only partially averaged out by proton exchange. The increase of relaxation rate is observable in natural water (0.037% O^{17}), and becomes very appreciable in water enriched in O^{17}. Additional information can be obtained by measuring relaxation rates in the presence of an rf field H _{1}, using a method due to Solomon. A study of the width of the O^{17}resonance as a function of pH is in quantitative agreement with the results of the protonresonance. The observations provide a direct determination of the rate constants of the exchange reactions:It is found that k _{1}=(10.6±4)×10^{9} liter mole^{−1} sec^{−1} and k _{2}=(3.8±1.5)×10^{9} liter mole^{−1} sec^{−1}. The spin‐spin interaction between H and O^{17} in water is determined as 92±15 cps. In the Appendices, theoretical equations for the exchange contribution to the relaxation rate are derived.

Choice of Parameters for the Hückel π‐Electronic Structure of Furan: Tentative Extension to Pyrrole and Thiophene
View Description Hide DescriptionA comparison of the experimental bond lengths of furan with empirical bond length/bond energy relations for carbon‐oxygen bonds leads to the conclusion that the ratio of the carbon‐oxygen resonance integral to the carbon‐carbon resonance integral of furan is between about 0.1 to 0.3. Use of this value along with a Coulombic integral parameter based upon the ultraviolet absorptionspectrum of furan leads to a Hückel molecular orbital picture of the π‐electronic structure of furan which is compatible with the known chemical reactivity of the molecule. The same approach is used to suggest resonance and Coulombic parameters for the Hückel molecular orbital treatment of pyrrole and thiophene. The treatment yields atom localization energies and para‐localization energies consistent with the relative chemistries of furan, pyrrole, and thiophene.

Interpretation of Viscosity Data for Concentrated Polymer Solutions
View Description Hide DescriptionAn empirical viscosity vs concentration relation for concentrated polymer solutions is derived in terms of a simple free volume theory, and its applicability is tested with some available data for amorphous polymer+solvent systems. It is found that the derived relation fits well those data over the range of polymer concentrations so concentrated that interchain entanglements occur to form a weak network structure throughout the solution. In the region of relative low polymer concentrations, however, it shows deviation of a common feature from the experimental results. Two temperature‐dependent parameters are contained in the viscosity equation derived; one is characteristic of the polymer species and the other is dependent upon the particular combination of polymer and diluent. These parameters are evaluated from comparisons with experimental data, and their variations with temperature are discussed.

Zero‐Field Splitting of Molecular Zeeman Levels
View Description Hide DescriptionElectron spin‐spin coupling, responsible for zero‐field splitting of Zeeman levels, may be discussed very generally by means of a ``coupling anisotropy function'' defined in terms of the components of the two‐electron density matrix. The properties of this function are fully discussed elsewhere: the present note is concerned with zero‐field splitting of triplet levels and with the series of approximations which lead from the general results to simple (orbital theory) approximations. A numerical calculation on the phosphorescent triplet states of naphthalene gives reasonable agreement with experiment.

Valence Bond Treatment on the B State of the Hydrogen Molecule
View Description Hide DescriptionThe potential energy of the lowest ^{1} Σ_{ u } ^{+} state of the hydrogen molecule is given as a function of the internuclear distance. Calculations were carried out by the valence bond method using Slater 1s and 2p atomic orbitals. Both ionic and covalent structures were considered. The 1s orbitals of the ionic and covalent functions included a variational parameter but the orbital exponent of the 2p orbital was kept constant. It is found that the introduction of the 2p orbital into the wave function results in a considerable improvement of the dissociation energy and that further the state is essentially covalent in character rather than ionic, as previously reported.

Theory of Light Scattering by Thin Rodlike Macromolecules in a Liquid Subjected to Shear
View Description Hide DescriptionThe light scattering by thin rodlike particles in a liquid subjected to shear is calculated on the basis of the Rayleigh‐Gans treatment. The calculations are made for both unidirectional laminary flow and for flow of periodically alternating direction. The calculation is carried out by two methods: the interference factor P is expressed in terms of a power series of G/D, where G and D are the rate of shear and the rotatory diffusion constant, respectively, of the rod rotating around its minor axis. This treatment is applicable to sufficiently low G/D values. The result for a very wide range of rate of shear is obtained by using the Peterlin distribution function of particle axis. Numerical calculation shows that both results agree in a region of G/D below about two if the axial ratio is large enough. The theoretical results appear to agree with the experimental ones.

Approximate Theory of Transport in Simple Dense Fluid Mixtures
View Description Hide DescriptionThe theory of transport proposed by Rice and Kirkwood is extended to the case of multicomponent systems. As in the previous case, the intermolecular force contributions to the shear and bulk viscosities and the thermal conductance are displayed as functions of the diffusion coefficient and the thermodynamic properties of the mixture. The self‐diffusion coefficient is related to the intermolecular forces and molecular distribution function, thereby completing the molecular basis of the computation. Formulas are also given for the thermal diffusion factor and the heat of transport. The reader is referred to Eqs. (91), (104), (106), and (109). The theory presented predicts a form of volume fraction mixing. For example, the shear viscosity becomeswith v _{1} ^{*} and v _{2} ^{*} the volume of N _{1} molecules of component one and of N _{2} molecules of component two, respectively, at the same temperature and pressure as the mixture. The quantities η_{1} ^{*}, η_{2} ^{*}, η_{12} ^{*} are composition dependent so that the predicted mixing law is not pure volume fraction mixing except in the case of an ideal solution. The theory is compared with experimental measurements of the viscosity of benzene—carbon tetrachloride mixtures, and good agreement is found. The agreement between theory and experiment is discussed with reference to the mechanism of irreversibility.

Spectroscopy of Fluorine Flames. I. Hydrogen‐Fluorine Flame and the Vibration‐Rotation Emission Spectrum of HF
View Description Hide DescriptionThe hydrogen fluoride vibration‐rotation emission spectrum from a hydrogen‐fluorine diffusionflame has been studied under high dispersion from 3200 cm^{−1} in the infrared to about 5500 A in the visible. Measurements were made on the rotational lines in 23 bands including (1–0), (2–1), and (3–2) of the Δv=1 sequence; (2–0), (3–1), (4–2), (5–3), and (6–4) of Δv=2; (3–0), (4–1), (5–2), and (6–3) of Δv=3; (4–0), (5–1), (6–2), (7–3), (8–4), and (9–5) of Δv=4; and (5–0), (6–1), (7–2), (8–3), and (9–4) of Δv=5. Complete rotational and vibrational analyses were carried out. The constants B_{v}, D_{v}, and H_{v} are given for v=0 to 9. The data were extensive and precise enough to warrant an extended Dunham treatment from which 18 coefficients could be determined, including those for terms in (v+½)^{5} and J ^{4}(J+1)^{4}. Band centers for 22 bands and the vibrational term values E_{v} for v=0 to 9 are given.

Quasi‐Lattice Model of Reciprocal Salt Systems. A Generalized Calculation
View Description Hide DescriptionA generalized statistical‐mechanical calculation of the solution thermodynamics of the reciprocal molten salt system A ^{+}, B ^{+}, C ^{−}, and D ^{−} dilute in A ^{+} ions has been made. The calculation is based on the quasi‐lattice model of reciprocal salt systems and treats the problem as an order‐disorder problem. Associations of the A ^{+} and C ^{−} ions as are taken into account. In terms of the conventional equilibrium constantsK _{1}, K _{2}, and K _{3} for (A), (B), and (C), respectively, where Z is the quasi‐lattice coordination number, β _{j} =exp(—ΔA_{j}/kT) and ΔA_{j} may be termed a specific bondfree energy of the jth C ^{−} ion and is the specific Helmholtz free energy change for the formation of the jth bond. Equations (1), (2), and (3) demonstrate the surprising fact that the higher order association constants are dependent on the magnitude of the lower order association constants not only through the factor containing Z but also through the values of the β_{ i } for the lower association constants. If β_{1}=β_{2}=β_{3}=··· etc., the equations reduce to the statistical ratios of Bjerrum. The higher association constants can be shown to be smaller for a case in which the bonding is directional (e.g., linear AC _{2} ^{−}), than if they are nondirectional, as in Eqs. (2) and (3), even if the bondfree energies are equal in the two cases.

Effect of Solvent and Solute Structure on Scintillator Pulse Heights. I. Correlation of Pulse Heights for Ring Substituted Styrene Plastic Scintillators with Hammett Substituent Constants
View Description Hide DescriptionA group of different ring substituted styrene plastic scintillators were prepared with a constant concentration of p‐terphenyl as the fluor and POPOP as the waveshifter. The effect of this variation in the structure of the polymer phase on pulse‐height response to β and γ radiation was determined. It was found that correlations exist between the relative pulse height and the Hammett (δ) and Taft (δ_{ I }) substituent constants for the substituted polystyrenes. Pulse heights increase with an increase in the negative value of the substituent constant, i.e., with an increase in the electron‐donating power of the ring substituent on the polystyrene. It was found that markedly lower relative pulse heights were obtained for a series of styrene plastics in which the α‐hydrogen in the backbone chain was substituted by a methyl group. This suggests that an α‐hydrogen in the backbone chain is required for an efficient plastic solvent.

Effect of Solvent and Solute Structure on Scintillator Pulse Heights. II. Correlation of Pulse Heights for Aromatic Liquid Organic Scintillators with Hammett Substituent Constants
View Description Hide DescriptionIt has been found that numerous data in the literature on aromatic organic liquid scintillators could be interpreted in terms of the resonance and polarity of the constituent solvents and fluors. The resonance and polarity of the ring substituted aromatic compounds were characterized quantitatively by Hammett substituent constants (δ). For a number of liquid scintillator systems in which the fluor composition was kept constant and the structure of the aromatic solvent was varied, pulse heights increased approximately linearly with increasing electron donating (negative δ values) power of the substituents on the aromatic molecule. This correlation held for nine different fluors in each of seven different aromatic solvents. A similar correlation was found for a series of fluors consisting of substituted 2,5‐diphenyl‐1,3,4‐oxadiazoles and 2,5‐diphenyl 1,3‐oxazoles in which toluene was used as the sole solvent. Pulse heights varied much more with a change in substituent groups on the solvent than with a similar change in the fluors. The observed correlation affords a means of organizing a large body of data and of gaining a further insight into the mechanism of scintillation.

Vibration Relaxation in Oxygen‐Argon Mixtures
View Description Hide DescriptionThis paper and the one following [M. Camac and A. Vaughan, J. Chem. Phys. 34, 459 (1961)] discuss the use of a new experi‐mental technique for the determination of vibration and dissociation rates. The concentration of in the ground vibrational state can be inferred from measurements of ultraviolet light transmission at 1470 A. has a strong continuous absorption band in this vacuum ultraviolet region. The vibrational relaxation rate of in shock‐heated mixtures was obtained from 1200 °K to 7000 °K. For collisions, the measuredrelaxation time t, can be fit by the Landau‐Teller theory [L. Landau and E. Teller, Physik. Z. Sowjetunion 10, 34 (1936)] , where n is the number of particles/cc and T is the temperature in °K. and The observed vibrational relaxation time for collisions is times faster than that for collisions. The experimental results are compared to the theoretical predictions of Schwartz and Herzfeld [R. N. Schwartz, Z. I. Slawsky, and K. F. Herzfeld, J. Chem. Phys. 20, 1591 (1952); R. N. Schwartz and K. F. Herzfeld, ibid. 22, 767 (1954)]. At the lower temperatures, the rates given by Blackman [V. H. Blackman, J. Fluid Mech. 1, 61 (1956)] have a different temperature dependence than the rates obtained in this experiment.

Dissociation Rates Mixtures
View Description Hide DescriptionExperimental measurements of the dissociation rate in shock‐heated oxygen‐argon mixtures were obtained with the ultraviolet light absorption technique described in the preceding article. The dissociationrate constant for the reaction can be fit over the temperature range from 3400 °K to 7500 °K by the theoretical formula where and is the oxygen dissociation energy;R is the gas constant; and T is the temperature. This result is compared with the classical collision theory and the theories of Wigner and Keck. The rates for the dissociation of by O and were also determined; compared to the argon rate constant Our experimental results are compared with those of Byron and Matthews. The relaxation times for dissociation and vibration are observed to be comparable at about 8000 °K. The experimental data indicate that the dissociation rate above 8000 °K is at least a factor of two less than the expected rate when the vibration is not in equilibrium (the vibrational temperature being less than the translational temperature) during dissociation.

Electron Spin Resonance Study of p‐Phenylene‐Diamine Positive Ion
View Description Hide DescriptionThe mono‐positive radical ion of p‐phenylene diamine has been prepared by controlled potential electrolysis and studied by electron spin resonance. This ion has been formed in acetonitrile solution with sodium perchlorate as supporting electrolyte and the controlled potential electrolysis has been carried out in the microwave cavity of the ESRspectrometer. The ion exhibits a complex hyperfine structure in dilute solution; the observed spectrum consists of about 75 hyperfine components. Isotropic hyperfine coupling constants have been assigned for the three types of interacting nuclei: the aromatic ring protons, amine protons, and the nitrogen nuclei. The large nitrogen hyperfineinteraction observed is in marked contrast to Würster’s Blue cation, for which this interaction is vanishingly small. ESR spectra of deuterated derivatives have been obtained and employed in making the assignment. The magnitude of the nitrogen hyperfineinteraction relative to that of the amine protons is shown to be consistent with the mechanism of a electron exchange interaction on the nitrogen atom. Electrochemical generation allows the study of the relatively unstable ion‐radical, whereas other methods of preparation have been less successful.

Infrared Spectra of Alkyldiboranes. IV. 1,1‐Dimethyl‐ and 1,1‐Diethyldiboranes
View Description Hide DescriptionThe infrared spectra of five isotopic variants of two 1,1‐dialkyldiboranes, viz., and and the corresponding diethyl compounds, are reported and frequency assignments are made. A method for purification of these compounds also is described. The intensity ratio of the 923 to bands in served as a simple preliminary criterion.for the absence of other alkyldiboranes. The strong bridge‐stretching frequencies of the 1,1dialkyldiboranes at are unique in being ca lower than corresponding bands in other alkyldiboranes. Another absorption, at is quite intense compared with other alkyldiboranes.