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15 Dec 1965

Volume 43, Issue 12, pp. 4191-4542

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Measurement of g Values in the Electron Spin Resonance Spectra of Free Radicals

Bernice G. Segal, Michael Kaplan, and George K. Fraenkel

J. Chem. Phys. 43, 4191 (1965); http://dx.doi.org/10.1063/1.1696676 (10 pages) | Cited 113 times

Online Publication Date: 17 May 2004

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Measurements have been made of the g values in the electron spin resonance spectra of 20 aromatic free radicals with an accuracy which has not previously been attainable. The largest source of error for both absolute and relative measurements resulted from variations in the difference between the magnetic field at the ESR sample and at the proton NMR probe, located just outside the center of the microwave cavity, which was used to measure the field. Except for the p‐benzosemiquinone radical, g values were not found to depend on temperature over the range from room temperature to −100°C. The dependence of the g value on solvent and counterion was also investigated to some extent, and the g value of the perinaphthenyl radical was found to vary markedly with solvent. Agreement with Stone's theory of the g values of aromatic radicals is excellent, except for those radicals in which molecular distortions are expected according to the Jahn—Teller theorem and for radicals in which the unpaired electron is in a nonbonding molecular orbital.

Concurrent Ion—Molecule Reactions. I. Reactions in X—CD4 Mixtures

T. W. Shannon and A. G. Harrison

J. Chem. Phys. 43, 4201 (1965); http://dx.doi.org/10.1063/1.1696677 (6 pages) | Cited 14 times

Online Publication Date: 17 May 2004

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A ratio‐plot method, whereby the contribution of concurrent ion—molecule reactions to the same product ion may be estimated, has been applied to the study of the formation of the XD+ ion in X—CD4 mixtures for X=CO, N2, and CO2. It is shown that XD+ is formed by both deuteron transfer from CD4+ and by deuterium atom abstraction by X+. The cross sections for the individual reactions have been determined and compared with theory.

Concurrent Ion—Molecule Reactions. II. Reactions in X—D2 Mixtures

T. W. Shannon and A. G. Harrison

J. Chem. Phys. 43, 4206 (1965); http://dx.doi.org/10.1063/1.1696678 (7 pages) | Cited 19 times

Online Publication Date: 17 May 2004

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The formation of XD+ in X—D2 mixtures where X is CO, A, CO2, and CH3CN is shown to be the result of the two concurrent ion—molecule reactions
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The cross sections for the individual reactions have been measured and compared to theoretical predictions.

Force Fields for the Boron Trihalides

Ira W. Levin and Stanley Abramowitz

J. Chem. Phys. 43, 4213 (1965); http://dx.doi.org/10.1063/1.1696679 (10 pages) | Cited 26 times

Online Publication Date: 17 May 2004

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The method of Edgell and Moynihan for determining Coriolis zeta constants from the infrared band contours of degenerate vibrational modes was verified for selected molecules and was then applied toward computing the zeta values of the E symmetry vibrations of the boron‐trihalide molecules. Since it is not feasible to define unique potential functions for the BX3 species from only frequency data, general force fields were determined for the series by combining both the Coriolis zeta constants and the observed isotopic frequency data in a least‐squares refinement scheme. The final force fields indicate that the sensitive stretch—bend interaction constant is a significantly large negative quantity that decreases as the series progresses from BF3 to BI3.

Paramagnetic Resonance of Vanadium (II) in Ferroelectric Potassium Ferrocyanide

D. E. O'Reilly and G. E. Schacher

J. Chem. Phys. 43, 4222 (1965); http://dx.doi.org/10.1063/1.1696680 (12 pages) | Cited 34 times

Online Publication Date: 17 May 2004

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Electron paramagnetic resonance of ferroelectric potassium ferrocyanide trihydrate doped with divalent vanadium has been investigated in the temperature range −180° to 20°C. Below the ferroelectric Curie temperature (Tc=−26°C) the resonance line positions may be expressed by a spin Hamiltonian for which the fine‐structure terms D and E are linearly dependent on the spontaneous polarization. Above Tc the spin Hamiltonian is independent of temperature, D is an order of magnitude smaller than at low temperatures, E=0, and the z principal axis lies in the crystal a—c plane.
An anomaly in the linewidth of the ±math→±½ satellite resonance lines is observed in the vicinity of the ferroelectric Curie temperature. With the applied magnetic field along the z principal axis, the linewidth decreases abruptly by a factor of 2 with increase in temperature through the phase transition.
Dielectric constant and spontaneous polarization data are reported which agree with values previously given by Waku. The temperature dependence of the electron resonance is attributed to noncubic components of the crystal‐field potential at an iron site produced by the permanent dipole moments of aligned water molecules. Orientations of water molecules determined by NMR are used to calculate the fine‐structure tensor including both quartet and doublet T2g excited states. A mechanism of the anomalous line broadening due to fluctuations of the spontaneous polarization is proposed. Effects of both long‐range electrostatic and short‐range hydrogen‐bond interactions in the ferroelectric transition of KFCT are qualitatively discussed.

Deuteron Magnetic Resonance of Ferroelectric Potassium Ferrocyanide Trihydrate

Tung Tsang and D. E. O'Reilly

J. Chem. Phys. 43, 4234 (1965); http://dx.doi.org/10.1063/1.1696681 (16 pages) | Cited 23 times

Online Publication Date: 17 May 2004

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The quadrupolar splittings and linewidths of the deuteron magnetic resonance of single crystals of ferroelectric K4Fe(CN)6⋅3D2O(KFCT) have been measured from −100° to 58°C. At low temperatures eight pairs of resonance lines are observed corresponding to four types of water molecules A, B, C, D, and their ac plane enantiomorphs A+, B+, C+, D+. The molecules are undergoing a fast 180° flip motion about the bisectrix of the DOD bond angle. At temperatures above the Curie temperature (−20°C) only two pairs of lines are observed which are shown to result from fast molecular reorientations within the sets A, C, A+, C+ and B, D, B+, D+. Molecular orientations are determined at low temperatures from rotation patterns and these become shifted for the C‐ and D‐type molecules in the transition to the paraelectric phase.
A structure for ferroelectric KFCT is proposed based on the deuteron resonance data. Activation energies and frequency factors for the 180° flip, AC, and AA+ averaging motions are derived and discussed. The temperature dependence of proton resonance second‐moment data and the single‐crystal spectra at 25°C are interpreted in terms of the motions deduced from the deuteron resonance experiments and compared with the results of inelastic neuteron scattering experiments.

Cluster Theory of Polyelectrolyte Solutions. I. Activity Coefficients of the Mobile Ions

Gerald S. Manning and B. H. Zimm

J. Chem. Phys. 43, 4250 (1965); http://dx.doi.org/10.1063/1.1696682 (10 pages) | Cited 38 times

Online Publication Date: 17 May 2004

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In an effort to calculate thermodynamic properties of polyelectrolyte solutions with as few assumptions as possible, we have utilized the Mayer cluster theory of ionic solutions as our starting point rather than the Poisson—Boltzmann equation. We show that the use of the Debye—Hückel screened Coulomb potential between charged sites on the polyion is an adequate first approximation for the mean activity coefficient of mobile ions, although single‐ion activity coefficients require additional terms for their description. Satisfactory agreement with experiment is obtained.

Cluster Theory of Polyelectrolyte Solutions. II. Additivity Rules, Osmotic Pressure, and Donnan Equilibrium

Gerald S. Manning

J. Chem. Phys. 43, 4260 (1965); http://dx.doi.org/10.1063/1.1696683 (8 pages) | Cited 8 times

Online Publication Date: 17 May 2004

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We apply the results of the previous paper describing the free energy of a polyelectrolyte‐added salt solution to the derivation of a relation between the osmotic coefficient and the activity coefficients of the mobile ions. From this relation, observed to be in excellent agreement with experiment, we obtain expressions resembling the empirical additivity rules. We conclude that the concept of ion binding may not be the appropriate way to interpret these rules. We also obtain an expression for the Donnan distribution of mobile ions and discuss the difficulties involved in the calculation of the Donnan osmotic pressure.

Statistical Thermodynamics of Bolaform and Dipolar Ionic Solutions by the Mayer Method

Gerald S. Manning

J. Chem. Phys. 43, 4268 (1965); http://dx.doi.org/10.1063/1.1696684 (6 pages)

Online Publication Date: 17 May 2004

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We have applied the ring‐diagram approximation of the Mayer ionic solution theory to solutions containing bolaform ions and to solutions containing dipolar ions. For the former case we derive a simple expression for the activity coefficient of the counterion to the bolaform ion. This expression has the property of increasing with the length of the bolaform ion from the Debye—Hückel limiting value for a uni‐divalent salt (zero length) to the limiting value for a uni‐univalent salt (infinite length). For dipolar ions we recover as a limiting case an expression derived by Kirkwood by classical means. We also derive a term accounting for dipolar ion—dipolar ion interactions, which is comparable to one obtained by Fuoss for a different model.

Determination of Electron‐Capture Cross Sections with Swarm‐Beam Techniques

L. G. Christophorou, R. N. Compton, G. S. Hurst, and P. W. Reinhardt

J. Chem. Phys. 43, 4273 (1965); http://dx.doi.org/10.1063/1.1696685 (9 pages) | Cited 37 times

Online Publication Date: 17 May 2004

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A method is described which combines electron‐swarm and electron‐beam techniques to obtain absolute electron‐capture cross sections as a function of electron energy. As examples of the method, data on Cl− from ortho‐chlorotoluene (approximately 1 eV) and O− from oxygen (approximately 7 eV) are presented and discussed.

Quantum Statistical Theory of Atoms in Hydroquinone Clathrates

George A. Neece and Jacques C. Poirier

J. Chem. Phys. 43, 4282 (1965); http://dx.doi.org/10.1063/1.1696686 (9 pages) | Cited 9 times

Online Publication Date: 17 May 2004

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A quantum statistical mechanical theory of clathrates is presented. This theory, like the van der Waals theory, idealizes a clathrate as (1) a lattice having properties unaffected by the extent of occupancy of its cavities by guest atoms, and (2) a system of independent cavities randomly occupied by guest atoms. Within a cavity, the guest atom is assumed to move in the cell potential
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rather than in the sphericalized Lennard‐Jones—Devonshire cell potential used in the van der Waals theory. The corresponding Schrödinger equation is exactly soluble and the energy eigenvalues are easily incorporated into a convenient quantum statistical mechanical formalism, valid at both low and high temperature, for the ``guest'' contribution to thermodynamic functions. With an assumed cubical cell symmetry, shown to be not unreasonable, one of the three parameters can be approximately determined by structural data on the β‐hydroquinone lattice. After adjusting the remaining two parameters to fit some data, the thermodynamic predictions are found to be in satisfactory agreement with all other thermodynamic data on rare‐gas hydroquinone clathrates. The energy of the transition from ground to first excited state for the motion of guest atoms is in very good agreement with experimental data.

Far‐Infrared Spectra of Gas Molecules Trapped in β‐Quinol Clathrates

J. C. Burgiel, Horst Meyer, and P. L. Richards

J. Chem. Phys. 43, 4291 (1965); http://dx.doi.org/10.1063/1.1696687 (9 pages) | Cited 31 times

Online Publication Date: 17 May 2004

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We have studied the far‐infrared spectra of 12 different gases trapped in the cages of β‐quinol clathrates. The data are most extensive for Ar, Kr, Xe, CO, N2, NO, and O2 in the frequency range from 15 to 85 cm−1. In these cases, monatomic and nonpolar diatomic gas molecules show a single absorption line, which we have assigned to translational motion of the molecule within its cage. Polar diatomic molecules show an additional line, which we have assigned to hindered rotation. These lines are an order of magnitude less intense than ordinary electric dipole transitions. The absorptions due to translational motion arise through dipole moments induced by interaction between the gas molecule and the clathrate cage. The frequencies and shapes of the infrared absorptions as a function of temperature from 1.2° to 170°K, as well as the frequencies of hindered rotation for N2 and O2 deduced from other experiments, were used to evaluate the parameters of potential‐well models for these seven gases. The specific heats associated with the enclosed molecules were computed and found to be in excellent agreement with measured specific heats. Spectra of H2, CH4, CH3F, CHF3, and NF3 clathrates and of α‐quinol are also discussed.

Classical Unimolecular Rate Theory. III. Effect of Initial Conditions on Lifetime Distributions

Roger C. Baetzold and David J. Wilson

J. Chem. Phys. 43, 4299 (1965); http://dx.doi.org/10.1063/1.1696688 (5 pages) | Cited 9 times

Online Publication Date: 17 May 2004

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The distribution of lifetimes of classical anharmonic and harmonic triatomic molecules capable of dissociation is found to depend upon the distribution of initial conditions immediately after collisional activation. Two types of collisional‐activation mechanisms are treated: one in which the density of initial points in phase space depends only upon the energy (the random mechanism), and the second in which the vibrational energy of the molecule is initially entirely kinetic (the impulsive mechanism). The random mechanism leads to a roughly exponential distribution of lifetimes for both harmonic and anharmonic molecules, in agreement with earlier work. The impulsive mechanism leads to lifetime distributions showing very marked peaks and minima for the harmonic model; this effect is much smaller for the anharmonic model.

Ligand‐Field Treatment of the Jahn—Teller Distortion in VCl4

C. J. Ballhausen and J. De Heer

J. Chem. Phys. 43, 4304 (1965); http://dx.doi.org/10.1063/1.1696689 (11 pages) | Cited 21 times

Online Publication Date: 17 May 2004

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A ligand‐field treatment of the Jahn—Teller distortion in VCl4 is developed using perturbation methods. Several of the results are at variance with those obtained earlier by means of the electrostatic crystal field model, and are in substantial agreement with some recent molecular orbital calculations. It is found that distortions are of the same order of magnitude as the relevant zero‐point vibrational energies so that no ``static'' effect can be expected. This is in accordance with the available experimental evidence. Our results suggest certain splittings in the infrared and Raman spectrum of VCl4. On the basis of the present experimental evidence the consequences of such a ``dynamic'' Jahn—Teller effect can neither be confirmed nor contradicted with certainty.

ESR Study of NO3 and NO2 Produced on uv Irradiation of HNO3 Solutions at 77°K

E. Hayon and E. Saito

J. Chem. Phys. 43, 4314 (1965); http://dx.doi.org/10.1063/1.1696690 (5 pages) | Cited 6 times

Online Publication Date: 17 May 2004

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The paramagnetic species produced on uv photolysis of nitric acid at 77°K were studied using electron spin resonance. The primary photochemical process HNO3→OH+NO2 is followed by OH+HNO3→H2O+NO3. Three species are observed. One species is a triplet and is characteristic of the NO2 spectrum. The second is a singlet in H14NO3 (g=2.018) and a nonfully resolved doublet in H15NO3. On the basis of its blue color, absorption spectrum, photodecomposition on irradiation in its wave bands, competitive elimination on addition of OH radical scavengers, and hyperfine structure it is identified as the NO3 radical. The third species (g=2.0075), is produced as a product of the photodecomposition of NO3, and is tentatively assigned to NO.

Dielectric Relaxation in Liquid Polypropylene Oxides

M. E. Baur and W. H. Stockmayer

J. Chem. Phys. 43, 4319 (1965); http://dx.doi.org/10.1063/1.1696691 (7 pages) | Cited 73 times

Online Publication Date: 17 May 2004

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The dielectric properties of undiluted liquid atactic polypropyleneoxide have been studied as functions of temperature and molecular weight. The principal dispersion occurs at essentially the same frequency for all molecular weights at a given temperature, but at ower frequencies there is a small secondary loss peak that depends strongly on molecular weight. This secondary dispersion is shown to result from relaxation of a ``cumulative'' dipole, about 0.18 D per monomer unit, whose resultant magnitude depends on the long‐range conformation of the chain molecule. Experimental relaxation times for the secondary dispersion agree well with predictions based on Rouse—Bueche—Zimm theory. The main dispersion shifts with temperature according to the WLF equation.

Proton Magnetic Resonance Studies of Solid Triethylenediamine—Molecular Structure and Motions

George W. Smith

J. Chem. Phys. 43, 4325 (1965); http://dx.doi.org/10.1063/1.1696692 (12 pages) | Cited 29 times

Online Publication Date: 17 May 2004

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Proton magnetic resonance (PMR) studies of solid triethylenediamine (TEDA) were made between 77° and 420°K. Measurements of linewidth, second moment, and spin—lattice relaxation time were determined. Rigid‐lattice second moments yielded a C☒H distance of 1.09±0.02 Å but could not distinguish between the D3h and D3 molecular configurations. A line narrowing at about 190°K was explained in terms of a restricted molecular reorientation about the N☒N axis plus a wobbling of the axis, the activation energy being about 7 kcal/mole. At the temperature of transition to a plastic crystal (351°K) the second moment dropped discontinuously to a value characteristic of general molecular reorientation. Simultaneously, molecular self‐diffusion became effective as a line‐narrowing agent. The activation energy for diffusion was found to be 16.2 kcal/mole, in good agreement with the lattice energy of 14.8 kcal/mole, as estimated from the heat of sublimation. A high‐resolution experiment failed to reveal any interconversion between the D3 and D3h molecular configurations. Theoretical expressions for the second moment for isotropic molecular reorientation are given in terms of the density, the molecular mass, and the number of protons per molecule for simple cubic, fcc, bcc, and hcp structures. Within 0.5% the expressions are the same for the last three lattices, and the simple cubic lattice expression is only 13% larger.

Linewidths of the Microwave Inversion Spectrum of Ammonia

Robert L. Legan, James A. Roberts, Edgar A. Rinehart, and Chun C. Lin

J. Chem. Phys. 43, 4337 (1965); http://dx.doi.org/10.1063/1.1696693 (9 pages) | Cited 60 times

Online Publication Date: 17 May 2004

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The linewidths of some 25 inversion spectral lines of ammonia in the frequency region of 18–29 kMc/sec have been measured. Corrections due to various effects such as source modulation, cell‐length broadening, and Doppler shift were applied to the experimental data to evaluate the linewidth parameters. Self‐broadening and foreign‐gas broadening by some 15 different gases have been studied. In the case of self‐broadening of the series of lines with J=K for which the effect of rotational resonance is negligible, the width parameters determined experimentally agree well with those calculated by Anderson's theory from (2, 2) to (5, 5), but appreciable deviations are found at higher J. For the lines with J≠K, the discrepancy becomes larger and increases with increasing difference between J and K. The quantum number dependence of the foreign‐gas broadening by methyl chloride and by carbon dioxide has been investigated in detail. For methyl chloride broadening the theoretical and measured widths agree with each other to about the same extent as in self‐broadening, whereas the agreement is somewhat less satisfactory in the case of carbon dioxide. An alternative formulation of the collision theory of line broadening is presented. Here the theory of radiation interruption is treated as a problem of multichannel collision. The essential feature of this formulation is that it includes the higher‐order effects of the collision process rather than just the usual first‐order terms. This analysis leads to suggestions as to possible directions of improving the calculations.

Absolute Intensities of the Discrete and Continuous Absorption Bands of Oxygen Gas at 1.26 and 1.065 μ and the Radiative Lifetime of the 1Δg State of Oxygen

Richard M. Badger, Alan C. Wright, and Rodger F. Whitlock

J. Chem. Phys. 43, 4345 (1965); http://dx.doi.org/10.1063/1.1696694 (6 pages) | Cited 145 times

Online Publication Date: 17 May 2004

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Laboratory measurements have been made of the absolute intensities of the discrete‐line absorption band at 1.26 μ, and of the continuous bands at 1.26 and 1.065 μ in oxygen gas at pressures up to 4.3 atm. It has been shown that discrete and continuous absorptions are quite independent features, the one being a measure of the intrinsic transition probability in isolated molecules, the other of its enhancement in collision complexes. In the former the lines show significant pressure broadening, but the integral molecular absorption coefficients are constant; in the latter they are proportional to pressure and continuous absorption dominates in the 1.26‐μ region at about ☒ atm oxygen pressure.
The radiative half‐life of isolated 1Δg oxygen molecules is estimated to be 45 min, and the effect of gas pressure on the rate of decay has been predicted.

Polarization of CaF2:Sm3+ Fluorescence

T. F. Ewanizky, P. J. Caplan, and J. R. Pastore

J. Chem. Phys. 43, 4351 (1965); http://dx.doi.org/10.1063/1.1696695 (4 pages) | Cited 3 times

Online Publication Date: 17 May 2004

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The particular environments which produce two different types of CaF2:Sm3+ fluorescence were deduced from study of the polarization of each spectrum. Either trigonal or tetragonal symmetry was observed and attributed to the local charge compensator associated with each spectral type. Depolarization mechanisms and the effects of secondary impurities on the activator ions are discussed.

On the Limiting Shape of the Distribution Function of Lengths of a Single Polymer Molecule with Excluded‐Volume Effects

Jacob Mazur

J. Chem. Phys. 43, 4354 (1965); http://dx.doi.org/10.1063/1.1696696 (3 pages) | Cited 23 times

Online Publication Date: 17 May 2004

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The distribution of the lengths of the polymer molecule is estimated from the computed reduced moments with the excluded‐volume effect being taken into consideration. It is found that the probability distribution function for chain ends can be fitted reasonably well by an exponentially decaying function, raised to the power of t, where t, the shape factor, exceeds its Gaussian value of 2. As a result of the excluded‐volume effect, the distribution of the lengths of a single polymeric molecule results in the chain assuming a more uniform conformation, as compared with the Gaussian coil model.

Vibrational—Rotational Spectrum of Difluoroborane and Difluoroborane‐d

L. Lynds and C. D. Bass

J. Chem. Phys. 43, 4357 (1965); http://dx.doi.org/10.1063/1.1696697 (8 pages) | Cited 8 times

Online Publication Date: 17 May 2004

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Four HBF2 and two DBF2 fundamentals have been resolved into their fine structure under medium dispersion. The three A1 modes, v1, v2, and v3 are characterized by a series of evenly spaced lines having the general appearance of a ⊥ band of a symmetric‐top molecule. The B2 modes, v6, have a strong Q branch in addition to a well‐defined subband system and have the appearance of Type‐C bands near the prolate limit. Using a symmetric‐top approximation, an analysis of the spectra provided six independent measurements for the smallest moment of inertia from which the average apex angle F☒B☒F was calculated to be 117.4±2° assuming the BH(BD) bond distance to be 1.20 Å. In HBF2, interband agreement of the rotational constant A, associated with the smallest moment of inertia, was quite good. It was possible to assign K values to the individual lines and to determine the position of the band centers for the resolvable fundamentals v1, v2, v3, and v6.

Interaction Potentials of Simple Nonpolar Molecules with Boron Nitride

A. D. Crowell and Chai Ok Chang

J. Chem. Phys. 43, 4364 (1965); http://dx.doi.org/10.1063/1.1696698 (4 pages) | Cited 6 times

Online Publication Date: 17 May 2004

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The interaction energies of Ne, Ar, Kr, Xe, N2, and CH4 near a semi‐infinite hexagonal boron nitride lattice at the potential minimum have been calculated using lattice sums of a (6–12) potential. Potential constants were obtained from empirical values corresponding to like‐molecule interactions and by the use of combination rules. Literature values for the gas‐molecule parameters were used, and the necessary constants for boron nitride were found from its solid‐state physical properties. Comparisons are made with other calculations and with experimental results.

Fluorescence and Defect Fluorescence of Anthracene at 4.2°K

W. Helfrich and F. R. Lipsett

J. Chem. Phys. 43, 4368 (1965); http://dx.doi.org/10.1063/1.1696699 (9 pages) | Cited 68 times

Online Publication Date: 17 May 2004

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Previous measurements of space‐charge‐limited hole currents have shown that anthracene crystals, even if very pure, contain large numbers of hole traps distributed exponentially in depth. Arguments are presented that these defects, if structural, should also act as singlet excitation states below the singlet exciton band. In order to detect such excitation states, the following experiments were carried out at 4.2°K: (1) observation of fluorescence with ordinary excitation within the singlet absorption band (vexc>v0☒0) to check the purity of the anthracene crystals, (2) observation of fluorescence with defect excitation (vexc<v0☒0), (3) observation of both kinds of fluorescence after the crystals were annealed at 130°C.
Some of the ordinary fluorescence spectra showed sharper lines than spectra previously reported. These lines appeared as doublets. Three kinds of defect fluorescence, which depended on the crystal used and on vexc, were observed: (a) fluorescence without structure in its excitation and emission spectra, (b) fluorescence with structured emission spectrum, (c) strong background emission in the ordinary fluorescence. No indications of chemical impurities were found. The results indicate that disordered regions, point defects, and dislocations play a significant role in the fluorescence process.

Monte Carlo Equation of State for a Mixture of Hard Spheres

A. Rotenberg

J. Chem. Phys. 43, 4377 (1965); http://dx.doi.org/10.1063/1.1696700 (5 pages) | Cited 53 times

Online Publication Date: 17 May 2004

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The equation of state for an equimolar binary mixture of hard spheres has been calculated by the Monte Carlo method for the case where the ratio of diameters is 1.1 to 1. The contact values of the three radial distribution functions are compared with those obtained from the solution of the Percus—Yevick equation as well as with an approximation obtained from scaled particle theory and are found to be in good agreement for densities below the phase transition. The density at which the phase transition occurs is about the same as the corresponding density for the one‐component system. At higher densities the contact value of the radial distribution function between pairs of small spheres remains essentially constant.
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