Volume 40, Issue 6, 15 March 1964

Order—Disorder Transitions in Biocolloids
View Description Hide DescriptionThe author's theory of order—disorder transitions in associative colloids is tested by comparison with measurements of the viscosity of different colloidal systems as a function of temperature or concentration. The theory predicts that an order—disorder transition from a random array of monomers to a segmented one‐dimensional helical rod will occur as the temperature is reduced to the one‐dimensional freezing point or the concentration increased to the critical micelle concentration. Under these conditions as enormous increase in the solution viscosity is predicted to occur.
Semiquantitative agreement is obtained between theory and experiment for a variety of associative colloids. Fully quantitative agreement cannot be obtained because the solutions become birefringent upon aggregation of the monomers, due to the large rod lengths which are obtained. This birefringence is well known to be due to the fact that the rods bump into each other and do not have their full freedom of rotation. Although this situation more closely resembles the statistical mechanical theory which neglects rotation of the rods, there is unfortunately no adequate theory of the viscosity of such solutions and the Simha—Kuhn theory which we have used can only be approximate under these conditions.

Absorption Spectrum at 357 mμ in the Nitrogen Oxides—Water System
View Description Hide DescriptionA previously unreported ultraviolet absorptionspectrum has been observed in aged solutions of low acidity containing HNO_{2}. It is similar to that of HNO_{2} without the vibrational substructure, and its presence was detected by a differential recording technique. Possible sources of the unidentified spectrum are considered in detail. A cyclic configuration of the ion HONONO^{+}, which could be formed in the presence of NO^{+} and HNO_{2}, can satisfactorily account for the properties of the unidentified absorber, but this hypothesis has not yet been tested experimentally.

Second‐Order Perturbation Theory in Atomic and Molecular Quantum Mechanics (Application to the Electric Dipole and Quadrupole Polarizabilities and Shielding Factors of the Beryllium Atom)
View Description Hide DescriptionA new method, previously used in calculating atomic correlation energies, is shown to be applicable to a wide variety of atomic and molecular problems. Use is made of the fact that it is possible in many problems to calculate exactly the first‐order perturbation correction to uncoupled Hartree—Fock wavefunctions and also second‐order energy expressions. Particular application is made to the numerical calculation of dipole and quadrupolepolarizabilities and shielding factors for the beryllium atom.

Transient Species in the Photolysis of Anils
View Description Hide DescriptionTwo photoinduced isomerizations occur in the photolysis of ethanol solutions of the anil, o‐hydroxybenzylidene‐aniline in the temperature interval 15°—70°C. One isomerization involves the formation of a visible absorption band, λ_{max} 470 mμ, which fades in the dark with a lifetime in the millisecond region. The fading is buffer catalyzed and yields an activation energy of 3_{.5} kcal/mole for this catalysis. The second isomerization, which is observed as a change in the near ultraviolet spectrum, is about a thousand times more long‐lived and not catalyzed by the presence of buffer, activation energy: 15_{.0} kcal/mole. The two isomerizations are identified as (1) a hydrogen transfer from the ortho hydroxyl group to the nitrogen atom forming an ortho quinoid structure, (2) a cis—transisomerization around the C–N double bond.

Mass Spectrometric Studies of Reactions in Flames. I. Beam Formation and Mass Dependence in Sampling 1‐Atm Gases
View Description Hide DescriptionThe pertinence of the Kantrowitz and Grey theory of aerodynamic molecular beams to the problem of sampling high‐pressure systems with a mass spectrometer is discussed. A simple differentially pumped molecular beam system is described, which gives molecular beams of intensities of about 10^{17} molecules/cm^{2}/sec from 1‐atm sources. The behavior of this sampling system with pure gases, mixtures, and reactive systems is presented. In beams from gaseous mixtures the mass spectrometer gives a response which depends on the first power of the component molecular weight: I_{x} +=kP_{x}m_{x} .

Exponential Correlation Functions for Two‐Electron Atoms
View Description Hide DescriptionInclusion of an exponential term in r _{12} in the correlated orbital treatment of two‐electron atoms does not lead to a significant improvement in the calculated energy. However, it does cause the orbital cusp conditions to be satisfied more accurately, and at the same time, it leads to a very considerable reduction in the computing time required.

Thermal Decomposition of Some Tert‐Butyl Compounds at Elevated Temperatures
View Description Hide DescriptionA single‐pulse shock tube has been used to study the kinetics of the thermal decomposition of tert‐butyl chloride, bromide, alcohol, and mercaptan. The results are compared with those obtained by earlier workers who used static reaction vessels at lower temperatures. The rate constants for the unimolecular elimination reactions areThe results for the chloride and the bromide are in good agreement with those of other workers. The slight discrepancies that are present indicate that in the present work, in the temperature range 700°—950°K, the true reaction temperature behind the reflected shock is 10°—25°K lower than that computed in the usual manner.

Intrinsic Viscosity of Stiff‐Chain Macromolecules
View Description Hide DescriptionA general theory for the intrinsic viscosity of any segment distribution with cylindrical symmetry is developed. The theory avoids the substitution of a scalar for the Oseen tensor. Application is made to the wormlike coil and the weakly bending rod. The Flory φ for the random coil calculated by this method is 2.20×10^{21}. The theory is in agreement with the results of Kirkwood and Auer in the limit of the rigid rod.

Statistical Thermodynamics of Spherical Droplets
View Description Hide DescriptionThe model employed by Hill for investigating the nature of the transition region between two phases in a one‐component system is extended to spherical interfaces. The surface tension and location of Gibbs' dividing surfaces in droplets with a radius of 3 to 25 molecular diameters (the molecules are hard spheres with an attractive potential) are calculated at a reduced temperature of 0.6, providing the numerical basis for investigating the dependence of surface tension on droplet size. It is found that the surface tension in all cases is about 35% of that of a plane interface, but is almost independent of droplet size.
The values of the surface tension relative to that of a plane interface are compared with those obtained from nucleation experiments in jets, using the Becker—Doering theory of nucleation; the agreement is poor, which is not surprising, considering the rather complicated substances used for the experiment.
From the values of the surface tension at the Gibbs surface of tension, the work of formation,W/kT, of a droplet of the size in question can be calculated. Since the method here amounts to finding the critical nucleus in a supersaturated system, this quantity determines a ``critical nucleus for condensation''; from this can be found the ``critical supersaturation'' to be compared with existing cloud‐chamber measurements on low‐molecular‐weight vapors. Assuming that thermal fluctuations will suffice to initiate condensation if W/kT is less than 75, the critical nucleus for condensation is found to contain about 50 molecules, and the corresponding critical supersaturation is found to be S=2.6, in reasonable agreement with most experiments. Some questions concerning the applicability of thermodynamic concepts to microscopic droplets are briefly discussed.

Proton Mobility and Electron Exchange in Aqueous Media
View Description Hide DescriptionEvidence from several different sources is cited in support of the hypothesis that the iron (II)—(III) electron‐exchange reaction involves a Grotthuss‐type mechanism closely related to that responsible for the anomalous mobility of protons in aqueous solution. This evidence includes failure of the electron exchange to occur in the absence of water, similarity of the two processes with respect to the deuterium isotope effects, similarity of rate ratios in liquid water and ice, and similiarity of activation energies of the two processes and of their temperature dependence.

Thermal Conductivities of Gaseous H_{2}O, D_{2}O, and the Equimolar H_{2}O—D_{2}O Mixture
View Description Hide DescriptionMeasurements have been carried out over the temperature range 380°—525°K using a four‐cell hot‐wire thermal‐conductivity apparatus. At the lower temperatures the thermal conductivities of H_{2}O and D_{2}O are identical, but at the highest temperature the conductivity of D_{2}O is larger by 8–9 parts per thousand. Conductivities of the equimolar mixtures lie midway between the conductivities of the pure components. Results are analyzed to test a recent hypothesis that a resonant exchange of rotational quanta causes the thermal conductivity of a polar gas to seem anomalously low in relation to its viscosity. It is concluded that the interchange of rotational energy between neighboring dipoles may be important, but that exact resonance is probably not required, at least in the case of water vapor.

Out‐of‐Plane CH_{2} Bending Potential Functions of Diazomethane, Ketene, and Related Molecules
View Description Hide DescriptionThe unusually low out‐of‐plane CH_{2} bending potential constants of ketene and diazomethane are discussed in terms of a valence bond comparison of their electronic structures to those of ethylene and ammonia. The anharmonic energy levels of the CH_{2} out‐of‐plane bending in diazomethane are fitted with an harmonic‐quartic potential function. V(γ)=(½(2.74)·Δγ^{2}+0.651·Δγ^{ 4} × 10^{—13} erg. A model is developed in which potential constants are transferred from the ethylene and ammonia molecules to the two valence‐bond structures usually considered for the ketene and diazomethane molecules. The unusually high intensities of the bending overtones are found to be a necessary consequence of this treatment. A further experimental test may be found in the expected large change in dipole moment with vibrational state. The model provides a basis for understanding the potential functions of ketene and diazomethane, and for making qualitative predictions about other molecules such as cyanamide and CF_{2}N_{2}.

Discreteness‐of‐Charge Adsorption Micropotentials. I. Infinite Imaging
View Description Hide DescriptionThe Ershler infinite imaging model for adsorption of ions from electrolytes is discussed in detail. An incorrect derivation of the basic equations for the micropotential is critically examined, and a correct derivation provided. The potential arising from discrete adions and their images is determined exactly based upon a method which heretofore has only been applied to crystal field problems. Finally, the accurate results obtained using a digital computer are compared with the approximate results of other treatments.

Diffusion and Reaction of Water in Additively Colored KCl
View Description Hide DescriptionAdditively colored KCl single crystals heated in the presence of water vapor developed a colorless region around the surface of the crystal. This bleaching effect is found to be described by a model in which water, or fragments from the dissociation of water, diffuses into the crystal and reacts with the excess potassium to form a colorless, photochemically sensitive reaction product, possibly KH or KOH. Using this model, an order‐of‐magnitude estimate of the diffusion coefficient of water in colored KCl is

ESR Study of NO_{2} and NO_{3} in Irradiated Lead Nitrate
View Description Hide DescriptionLead nitrate crystals have been irradiated with electrons at room temperature and their electron spin resonance spectra examined at 77°K to reveal three paramagnetic species. One species shows no hyperfine structure and has an isotropic gtensor with a g value at the free spin value: little can be said of its nature. The others are located, by their spectral anisotropy, at nitrate sites in the crystal with the axes of their axially symmetric gtensors parallel to the nitrate triad axes. One of these species is interpreted as NO_{3}: it shows no nitrogen hyperfine structure but a slight interaction with ^{207}Pb. The other is identified as NO_{2} rotating in the plane of the nitrate site. Theoretical predictions are in accord with these assignments.
Various conclusions are drawn for the radiation chemistry. Other species than the NO_{2} ^{—} and O_{2}, revealed by chemical analysis, are significant products. The particular lattice determines the nature of these products, their stability and, in the case of NO_{2}, its mechanism of formation. The annealing kinetics of NO_{2} and NO_{3} differ from that of the NO_{2} ^{—}: Mechanisms previously postulated for the latter are almost certainly too simple.

Systematic Approach to Explanation of the Rigid Disk Phase Transition
View Description Hide DescriptionBy classifying particle center positions with a hexagonal grid, evaluation of the two‐dimensional rigid sphere partition function is reduced to a special lattice statistics problem, with precisely defined nearest‐neighbor effective pair interactions. The hexagonal cell size is chosen to be the maximum consistent with no more than double occupancy. Since the resulting lattice partition function (with three states per site) contains a collectively determined many‐cell effective interaction Δ^{*}, as well as nearest‐neighbor contributions, it becomes necessary to examine in detail the statistical geometry of available phase space for the original spheres, under varying restraints of nearest‐neighbor cell distribution. Accordingly, we obtain for the first time an unambiguous definition of ``random close‐packed'' or ``glassy'' arrangements of spheres (which however are not themselves equilibrium states), and to relations between properties of these arrangements, and of Δ^{*}. The key features which subsequently allow description of rigid sphere order—disorder behavior are: (1) the observation that certain nearest‐neighbor cell pairs which occur in the glassy state (both unoccupied and both doubly occupied) are geometrically excluded completely in the ordered, close‐packed arrangement; (2) Δ^{*} sensitively depends upon these pair distributions. In spite of the fact that Δ^{*} is thereby assigned a specially generalized free‐volume form, the theory leads to a proper virial series development at low density.
In addition, we report some preliminary results for the effective cell interactions, for glassy state parameters, and some calculations designed to reveal the structure of Δ^{*}.
Although this analysis does not yet represent a full quantitative theory of the two‐dimensional rigid disk system, it does lead to a novel qualitative explanation of how a fluid—solid transition can occur, and suggestions are given for completing the quantification.

Residual Entropy of Ice
View Description Hide DescriptionWe examine the problem of evaluation of residual hydrogen‐bond entropy in ice, first noting by way of introduction the results of applying certain well‐known approximate lattice theory combinatorial techniques (mean field, Bethe, Kikuchi approximations). Subsequently, a general matrix method is introduced for evaluation of the residual entropy in the square planar lattice analog of ice, in terms of a series of contributions, each of which corresponds to a connected cluster diagram. The leading term in this latter method is the Pauling estimate, and two successive orders of terms are evaluated explicitly to indicate rate of convergence. In the real three‐dimensional case the generalization of the matrix method indicates that the Pauling estimate is roughly 1% low.

Role of Hard‐Core Collisions with Large Angle Deflections in the Kinetic Theory of Dense Fluids
View Description Hide DescriptionThe validity of the Fokker—Planck equation is discussed within the framework of Kirkwood's time smoothing formalism. It is shown that the equation is equivalent to the Boltzmann equation for a dilute homogeneous system in which grazing binary collisions predominate. Using this as a mathematical prescription, the Rice—Allnatt equation is modified by replacing the Boltzmann collision integral by a Fokker—Planck operator, but leaving the excluded volume term unchanged. The kinetic and collisional transport coefficients derived from the modified equation are compared with those derived from the Chapman—Enskog equation, the Rice—Allnatt equation, and the Fokker—Planck equation. It is concluded that the role of hard core collisions in the theory is to emphasize the importance of large angle deflections, which are not important in a dilute gas.

Infrared Spectrum of ν_{2} of Dichloroborane and Dichloroborane‐d
View Description Hide DescriptionThe ν_{2} fundamental of HBCl_{2} and DBCl_{2} has been observed under high resolution. A series of evenly spaced lines occurs, which has the appearance of a ⊥ band of a symmetric top molecule. Analysis of the spectra gives an approximate value for the smallest moment of inertia, from which the following molecular dimensions are calculated: B–H bond length=1.13±0.2 Å and Cl–B–Cl bond angle=119.7±3°. The position of the band center, 2616.9 cm^{—1}, for HBCl_{2}, has also been determined.

Orbital Following in the Methyl Radical
View Description Hide DescriptionIncomplete orbital following of the molecular vibrations in the methyl radical is examined through its relationship to the hyperfine splittings observed in the ESRspectrum. A semiempirical nonionic valence‐bond theory with different degrees of carbon sigma‐orbital following is used to estimate the proton and C^{13} splitting constants as a function of the nuclear positions that correspond to the out‐of‐plane bending mode. It is found that a considerable ``lag'' in the orbital motion with respect to that of the nuclei is required to achieve a consistent interpretation of the hyperfine spectrum in the methyl radical and its isotopic analogs. A variety of additional factors (i.e., integral parameter variation, breakdown of Born—Oppenheimer approximation, ionic contributions, other vibrations) are also investigated to determine their effects on the hyperfine splittings. Although some of the factors are found to be significant (particularly the choice of integral parameters), it appears that they cannot serve to explain the hyperfine data in the presence of complete following. Comparisons of the present conclusions with other studies of hyperfine splittings and related investigations of orbital following are presented.