Showing papers in "Journal of Chemical Physics in 1941"

Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics

Abstract: The dispersion and absorption of a considerable number of liquid and dielectrics are represented by the empirical formula e*−e∞=(e0−e∞)/[1+(iωτ0)1−α]. In this equation, e* is the complex dielectric constant, e0 and e∞ are the ``static'' and ``infinite frequency'' dielectric constants, ω=2π times the frequency, and τ0 is a generalized relaxation time. The parameter α can assume values between 0 and 1, the former value giving the result of Debye for polar dielectrics. The expression (1) requires that the locus of the dielectric constant in the complex plane be a circular arc with end points on the axis of reals and center below this axis.If a distribution of relaxation times is assumed to account for Eq. (1), it is possible to calculate the necessary distribution function by the method of Fuoss and Kirkwood. It is, however, difficult to understand the physical significance of this formal result.If a dielectric satisfying Eq. (1) is represented by a three‐element electrical circuit, the mechanism responsible...

Granulation, Phase Change, and Microstructure Kinetics of Phase Change. III

Abstract: The theory of the preceding papers is generalized and the notation simplified. A cluster of molecules in a stable phase surrounded by an unstable phase is itself unstable until a critical size is reached, though for statistical reasons a distribution of such clusters may exist. Beyond the critical size, the cluster tends to grow steadily. The designation ``nuclei'' or ``grains'' is used according as the clusters are below or above the critical size. It is shown that a comprehensive description of the phenomena of phase change may be summarized in Phase Change, Grain Number and Microstructure Formulas or Diagrams, giving, respectively, the transformed volume, grain, and microstructure densities as a function of time, temperature, and other variables. To facilitate the deduction of formulas for these densities the related densities of the ``extended'' grain population are introduced. The extended population is that system of interpenetrating volumes that would obtain if the grains granulated and grew through each other without mutual interference. The extended densities are much more readily derivable from an analysis of the fundamental processes of granulation and growth. It is shown that, under very general circumstances, the densities of the actual grain population may be expressed simply in terms of the extended population.

Thermodynamics of High Polymer Solutions

Abstract: A statistical mechanical treatment of high polymer solutions has been carried out on the basis of an idealized model, originally proposed by Meyer, which is analogous to the one ordinarily assumed in the derivation of the ``ideal'' solution laws for molecules of equal size. There is obtained for the entropy of mixing of n solvent and N linear polymer molecules (originally disoriented), ΔS=−k[(n/β) ln v1+N ln v2] where v1 and v2 are volume fractions and β is the number of solvent molecules replaceable by a freely orienting segment of the polymer chain. This expression is similar in form to the classical expression for equal‐sized molecules, mole fractions having been replaced by volume fractions. When the disparity between the sizes of the two components is great, this expression gives entropies differing widely from the classical values, which accounts for the large deviations of high polymer solutions from ``ideal'' behavior. The entropy of disorientation of a perfectly arranged linear polymer is found t...

Some Mathematical Methods for the Study of Molecular Vibrations

Abstract: Developments which reduce the labor of calculating the vibration frequencies of complex molecules are described. In particular a vectorial scheme is given for obtaining the reciprocal of the matrix of the kinetic energy in terms of valence‐type coordinates. A general rule for writing down the coefficients of the transformation to symmetry coordinates is derived together with a method of obtaining the kinetic energy reciprocal matrix (G) in terms of symmetry coordinates with a minimum of algebra. A treatment of redundant coordinates is developed. In addition, reduction of the secular equation by the splitting out of high frequencies, a new type of isotope product rule, and the determination of normal coordinates are discussed. The molecule CH3Cl is worked out as an illustration.

Theory of the Transition in KH2PO4

Abstract: Potassium dihydrogen phosphate contains phosphate groups connected by hydrogen bonds. Different possible arrangements of the hydrogens result effectively in different orientations of the (H2PO4)— dipoles. Since these have the lowest energy when pointing along the axis of the crystal, there is a tendency toward spontaneous polarization along this axis, resulting in the well‐known transition, similar to Rochelle salt, with polarization below the Curie point. The theory of this transition is worked out, using statistical methods to count the number of arrangements of hydrogens consistent with each total polarization of the crystal, and deriving the free energy. It is found that the theory predicts a phase change of the first order, with sudden transition from the polarized state at low temperature to the unpolarized state at high temperature, rather than the lambda‐point transition or phase change of the second order which is observed. However, the observed transition is confined to a very narrow temperature range compared to that predicted, for instance, by the Weiss theory, so that it seems as if it might be merely a broadened transition of the first order. It is suggested that the broadening may result from the irregular shifts of transition temperatures of individual domains in the crystal on account of stresses resulting from the large piezoelectric effect and the resulting deformation of the crystal below the transition point. The susceptibility above the Curie point comes out by the theory to be 4.33 times as great as it should according to the Weiss theory, a result which seems to be in general agreement with experiment. The entropy change in the transition is given by the theory as 0.69 unit, somewhat smaller than the observed value of about 0.8 unit. No explanation is suggested for this discrepancy.

Potential Energy Functions for Diatomic Molecules

Abstract: The usual Morse functions are determined from the energy of dissociation, the equilibrium separation of the nuclei, and the fundamental vibration frequency. Two additional spectroscopic constants, ωexe and αe, are available for most of the common diatomic molecules and permit us to add a two‐parameter correction term to the Morse curve. Both the potential V/D=(1−e−x)2+cx3(1+bx)e−2x and the extended Morse curve of the Coolidge, James and Vernon type, V/D=C2(1−e−x)2+C3(1−e−x)3+C4(1−e−x)4 agree with accurate potentials in those cases where they are known. Here x = 2β(r—re)/re. The constants for the first of these potentials are easy to evaluate and are given for 25 common diatomic molecules. With only a few exceptions, the improved potentials lie above the Morse curves and the corrections for moderately large internuclear separations may amount to ten percent of the energy of dissociation. Our treatment is based on the work of Dunham and the analysis of Coolidge, James and Vernon.

Second Virial Coefficients of Polar Gases

Abstract: An equation is given for the classical second virial coefficient of a polar gas in terms of the parameters appearing in an intermolecular potential energy which includes London and dipole attraction and inverse‐power repulsion. The equation is successfully fitted to the data for H2O and NH3 with allowance for the small quantum correction, and the derived values of the London constant are in good accord with theoretical estimates. The defects of the model and its relation to the concept of the hydrogen bond are briefly discussed.

Statistical Mechanics of Fusion

Abstract: A statistical mechanical theory of fusion based upon the use of local free energies is presented. An integral equation is formulated for the distribution function of average density in a region occupied by a system of molecules. Periodic solutions characteristic of a crystalline phase are found for certain ranges of values of a set of parameters depending upon temperature and volume. When the parameters decrease below certain critical values, all terms of the Fourier series representing the distribution function vanish with the exception of the constant term. A uniform density distribution characteristic of a fluid phase is then obtained. The melting parameters of argon at several pressures are calculated with the aid of the theory and compared with experiment.

Velocity of Sound in Liquids and Chemical Constitution

Abstract: A study of the recently obtained data on the velocity of sound and density in liquids reveals a simple relation between these quantities namely the law, v⅓M/ρ = R where v is the velocity of sound in the liquid, M the molecular weight, ρ the density and R a constant independent of temperature. It is shown that the velocity of sound cannot be a proper basis of comparison in any homologous series. The result of plotting the constant R against the molecular weight of members of homologous series leads to the equation R = αM + β where α is a general constant and β a characteristic constant for any one homologous series. The difference in R for successive members of homologous series is a constant independent of the series and R is an additive function of the chemical structure. Values of R for hydrogen, carbon, oxygen, bromine, and chlorine are tabulated.

A General Thermodynamic Theory of the Spreading of Liquids to Form Duplex Films and of Liquids or Solids to Form Monolayers

Abstract: A comprehensive thermodynamic theory is developed for the spreading of any liquid or solid b over the surface of any liquid a. Spreading is considered to occur by two types of processes: (A) duplex film or D spreading, and (B) non‐duplex or M spreading. A duplex film is always unstable, and transforms into a non‐duplex film and a lens. Every non‐duplex film of known structure is a monolayer (M). Either type of film may spread if its formation involves a decrease of free energy. The free surface energy of mercury at 20°C is 476 erg cm—2, and the spreading of water or any organic liquid on the surface as either a duplex film or a monolayer, gives a decrease of free surface energy, so all such liquids spread on mercury. On water all organic liquids spread as monolayers; an organic solid also spreads as a monolayer unless it is too non‐volatile in the two‐dimensional system. A liquid b will spread over the surface of a liquid a as a duplex film if the initial spreading coefficient Sb/a = WA — WCb is positive, that is if the work of adhesion WA between the two liquids is greater than the work of cohesion (WCb) in b. If b is saturated with a, then Sb′/a is designated as the semi‐initial spreading coefficient, which has almost the value of the initial coefficient. If the liquids are mutually saturated the final spreading coefficient, Sb′/a′, is always negative. Thus a liquid b will never spread over its own monolayer, and if the whole surface of water in any vessel is covered by a duplex film, it is certain that a monolayer has not spread over any part of it. After a definite period, the length of which is dependent on many factors, a duplex film begins to segregate into a monolayer, patches of thicker duplex film, and lenses, and finally into a monolayer and a lens. The film pressure πe of a monolayer of b in equilibrium with a lens of b is equal to the difference between the semi‐initial and the final spreading coefficient, or πe = Sb′/a — Sb′/a′. Since Sb′/a′ is always negative, the equilibrium film pressure is always greater than the semi‐initial coefficient. Hydrocarbons of not too high molecular weight are found to spread on water as either duplex films or monolayers. Thus many nonpolar oils spread on water to form either type of film. Benzene, which according to one of the most prominent theories does not spread at all, spreads readily, and exhibits the following values, which are almost the same as those for isopentane: initial coefficient 8.94, semi‐initial 8.90, and equilibrium film pressure 10.6, in erg cm—2. Carbon disulfide (nonpolar) and methylene iodide (highly polar) have initial coefficients —7.3 and —23.8, and therefore do not give duplex films, but they vaporize in the two‐dimensional surface, and give equilibrium film pressures of 2.3 and 0.6 dyne cm—1, respectively. Presumably their monolayers are gaseous. In general for liquids which spread as duplex films, it takes less work (i.e., the increase of free energy is less) to pull a liquid away from its equilibrium monolayer than to pull it away from itself. For benzene the difference is 1.7 and for n‐heptyl alcohol, 5.4 erg cm—2. An oil which is non‐spreading in the sense of duplex film formation, may be caused to spread as a duplex film by the addition of an oil of sufficiently high initial spreading coefficient. This also increases the equilibrium film pressure of the monolayer. The oils added for this purpose are, in general, of the polar‐nonpolar type, such as stearic acid. With such mixtures the values of the thermodynamic spreading coefficients, or the free energy levels, are highly dependent upon the nature and the concentration of the oil added. If the aqueous subphase is alkaline, stearic, or another similar acid is converted into a salt, and if the positive ions have a charge of two or higher, this has a pronounced effect upon the spreading coefficients and the film pressure.

Anomalous Dispersion and Dielectric Loss in Polar Polymers

Abstract: A theory of dielectric loss of polar polymers at high dilution in a nonpolar plasticizer is developed. The theory leads to a broad distribution in relaxation times, associated with the internal rotatory Brownian motion of the hydrocarbon chain. An approximate relation between the degree of polymerization, the frequency of maximum loss, and the viscosity coefficient of a polar plastic is obtained. The loss factor is calculated from the theoretical relaxation time distribution for a mono‐disperse polymer and for a poly‐disperse polymer with an exponential distribution in chain length. The theoretical loss factor is compared with the experimental loss factor of polyvinyl chloride plasticized with diphenyl. The agreement with experiment is semi‐quantitative.

Statistical Mechanics of Nearest Neighbor Systems

Abstract: In many solids the intermolecular forces are sufficiently short ranged so that practically the entire potential energy of the system results from interactions between nearest neighbors. The thermodynamic properties of a solid with respect to a given coordinate, α, (for example, in a ferromagnetic system α might represent the excess unpaired electron spin at a given lattice point; or in a substitutional binary alloy α might denote which of the two possible kinds of atoms are at a given lattice point) can be found from the factor of the partition function which averages over all possible configurations of α at all lattice points.Here the evaluation of such a factor of the partition function is reduced to the calculation of the largest characteristic value of a linear homogeneous operator equation involving the potential energy between two adjacent layers of lattice points in the solid. By assuming that all possible configurations of a layer are equally probable, a lower bound for the partition function for ...

The Long Wave‐Length Spectra of Aldehydes and Ketones Part II. Conjugated Aldehydes and Ketones

Abstract: An interpretation of the long wave‐length absorption regions of conjugated aldehydes and ketones is given. The strong regions can be assigned to transitions of the N→V1 type known to produce the intense long wave‐length absorption in polyenes. The weak absorption regions, which are characteristic of the carbonyl group, can be explained as arising from the type of transition previously proposed to explain the weak carbonyl absorption in saturated aldehydes and ketones. This transition involves the excitation of a loosely bound electron occupying a nonbonding orbital lying in the molecular plane and across the C–O direction, to an excited molecular orbital with a node in this plane. In conjugated molecules several of these excited MO's exist and transitions to them all are predicted. The longest wave‐length carbonyl absorption represents a transition to the lowest of these MO's and the observed shift of this absorption toward longer wave‐lengths with each addition to the number of conjugated bonds in the ch...

The Influence of Intramolecular Atomic Motion on Electron Diffraction Diagrams

Abstract: A discussion of the influence of atomic vibrations and of free or hindered rotations of molecular groups in molecules on their scattering properties. The radial distribution curve is calculated and the results which may be expected from an analysis of this curve are indicated.

Erratum: Spectroscopic Evidence for Hydrogen Bonds: Comparison of Proton‐Attracting Properties of Liquids. IV

Abstract: The strengths of deuterium bridges formed between heavy water and forty‐two different basic solvents are compared by measurements of the perturbations which the solvents produce on the OD vibrational band of heavy water which occurs at 3.59 μ in heavy water vapor and at 4.00 μ in liquid heavy water. The solvents were selected from the following classes: ketones, ethers, esters, glycols, nitriles, amides, ketoximes and amines. The proton‐attracting properties of twenty‐five solvents are compared by measurement of the strengths of the hydrogen bonds which they form by sharing the proton of hydrogen chloride. Heavy water was found more satisfactory for strong and moderately weak bases; hydrogen chloride, for extremely weak bases. The shifts which the different liquids produce upon the D2O band and the HCl band are compared with the shifts which the same solvents produce on the OD vibrational band of CH3OD. A linear relation was found in each case, with frequent but small variations from linearity. Basicity constants were known from other measurements for nineteen of the solvents used with D2O. The shifts which these solvents produce on the D2O band were found to be directly proportional to the logarithms of their basicity constants. The method used here promises to be practical for comparing basicities of numerous types of compounds. The close relation existing between the hydrogen bond theory and modern theories of acids and bases is discussed.

Infra‐Red and Raman Spectra of Polyatomic Molecules XIII. Nitromethane

Abstract: The infra‐red spectrum of gaseous nitromethane has been studied over the wave‐length range from 3 to 25 μ. The Raman work of Pendl, Reitz and Sabathy has been checked. These data together with a partial normal coordinate treatment enable us to make an assignment of the observed lines and bands which accounts for all the fundamental frequencies except the torsion around the C–N bond. The fundamental frequencies for the gas are 476, 599, 647, 921, 1097, 1153, 1384, 1413, 1449, 1488, 1582, 2965, 3048 (2). No decision regarding the potential barrier restricting the internal rotation of the methyl group can be made until at least one thermo dynamic quantity has been measured. The present results are compatible with the usual structure CH3NO2.

Atomic Distributions in Liquid Elements

Abstract: Monochromatic x‐ray diffraction patterns of liquid chlorine, tin, indium, zinc, cadmium, aluminum, and lithium were obtained, using Mo Kα radiation. The effect of temperature change on the patterns was determined for tin and indium. Fourier analyses of these patterns led to the determination of atomic distribution curves for each element. Each atom in liquid chlorine has one nearest neighbor, which means that chlorine is diatomic in the liquid state. The distribution curves for liquid tin, zinc and aluminum agree very well with the distributions in the corresponding crystals. The distribution curves for indium, cadmium, and lithium do not agree very well with distributions in the corresponding crystals.

Statistical Mechanics of Imperfect Gases

Abstract: The application of statistical mechanical equations to the calculation of thermodynamic properties of imperfect gases has been hindered by the occurrence of highly multiple integrals in these equations. By observing that some of these multiple integrals are related to the iterated kernels of an integral equation involving the potential energy function of a pair of molecules, a technique is developed which expresses these integrals in terms of the characteristic values of the integral equation. This technique is applied to the calculation of third virial coefficients and the molecular distribution function (which is essentially the probability of finding two specified molecules in two small volume elements a distance r from each other) at various temperatures for imperfect gases with Lennard‐Jones potential energy functions.

Semi‐Empirical Calculations of Activation Energies

Abstract: The predictions of the Eyring semi‐empirical scheme for calculating activation energies are compared with the existing experimental data. It is found that in most cases this agreement is satisfactory. However, the experimental data are not sufficiently accurate to make this scheme appear unique. The experimental activation energies seem to be functions only of the binding energies and do not depend in an important way on either the size of the atoms or on the diatomic force constants. If the reaction a+bc→ab+c is exothermic, it is found that the activation energy is 0.055D′bc, where D′bc is the energy of the bond bc. This formula is derived from the semi‐empirical scheme on the assumption that the attraction between the distant atoms a and c is zero. For exothermic four atom reactions ab+cd→ac+bd, it is found that the activation energy is 0.28(D′ab+D′cd). The numerical factor was adjusted to fit the H2+I2 reaction and although, in most cases, this gives activation energies in agreement with the semiempiri...

Remarks on the Fluorescence, Phosphorescence and Photochemistry of Dyestuffs

Abstract: Many of the apparently conflicting facts of the photochemistry as well as of the phosphorescence and of the fluorescence quenching of dyes can be given a rational and unified interpretation if it be assumed that an electronically excited dye molecule can go over, by a process of internal conversion, to the electronic ground state of a reactive energy‐rich tautomer. The endothermic reversion of such a tautomer to the electronically excited state of the original molecule would explain the weak, temperature dependent phosphorescence observed in some systems. In the presence of a suitable reducing agent the reactive tautomer may be reduced to a semiquinone. This process and the likely subsequent reactions are sufficient to explain the majority of dye‐sensitized photo‐oxidations as well as the photo‐bleaching of dyes by reducing agents. In the case of chlorophyll, and possibly a few other dyes, it appears to be necessary to assume that the tautomer and a normal dye molecule can undergo a process of disproportionation. The assumption of this step leads directly and simply to an explanation of the rapid reversible bleaching of chlorophyll which is consistent with the other known photochemical and optical properties of this substance. In addition to the more familiar reaction steps which have been assumed as follow reactions in setting up the various mechanisms, it is necessary to include a step in which the HO2 radical reduces a partially oxidized dye molecule (i.e., radical) back to the normal state. The several reaction steps assumed in these various schemes appear to be energetically feasible.

Determination of Diffusion Coefficients

Abstract: Diffusion equations derived from Fick's law are discussed and applied to experimental data in the literature on the diffusion of oxygen in copper and on reaction rates for chemical reactions in the solid phase. Previous limitations on the applicability of the formulae are removed by the use of a simple graphical method so that the theory can be applied to data to which it was previously inapplicable. It is pointed out that the exact solution to Fick's law obtained is equivalent to the parabolic law in the early stages of the diffusion process. The activation energy for the diffusion of oxygen in copper is found to be 50.5 kcal. per g‐atom.

The Effect of the Rotation of Groups about Bonds on Optical Rotatory Power

Abstract: It is shown that the numerical value of the optical activity of an optically active compound is markedly reduced if the groups surrounding the asymmetric atoms in the compound possess a threefold axial symmetry about the bonds connecting them with the asymmetric atoms. This threefold symmetry may be either inherent in the groups themselves, or it may be acquired by them through the free rotation of the groups about these bonds or by their orienting themselves to equal extents in each of the three possible equilibrium positions about each bond. The order of magnitude of the numerical value of the optical activity is thus a measure of the freedom of orientation about single bonds of the groups in an asymmetric molecule. That this effect is actually a dominant factor in determining the order of magnitude of the optical activity is proved by the contrast in the optical activities of cyclic and open chain compounds. It is shown to have an important effect on the temperature coefficient of optical activity and ...

The Effect of Electrostatic Forces on Electrokinetic Potentials

Abstract: Assuming that the ions in solution near a charged wall are subjected only to electrostatic and kinetic forces, it is shown that the potential gradient normal to the wall is determined principally by the valence and concentration of the ion of opposite charge to the wall. Assuming that the valence and concentration of this ion determine the effect of the salt on the electrokinetic potential of the wall, the surface potential of the wall and the thickness of the immobilized liquid layer are calculated from electrokinetic potential data. Salts of ``normal'' ions (NaCl, BaCl2, etc.) cause relatively small changes in the surface potential and thickness of the immobilized layer at a glass surface and these changes occur only at very low salt concentrations. Salts containing ``abnormal'' ions (H+, OH—, La+++, etc.) produce larger changes and the change continues over a much wider concentration range. The extreme effectiveness of salts like AlCl3 and ThCl4 in lowering negative electrokinetic potentials cannot be accounted for by the higher valence of the ions.

Force Constants in Some Organic Molecules

Abstract: Consistent normal coordinate treatments, involving force‐constants which are related to bond structures and which may be transferred from one molecule to another, are applied to hydrogen cyanide, methyl cyanide, and the methyl halides. The connection with previous treatments of acetylene, ethane, and methyl and dimethyl acetylene is discussed. A method of setting up such a consistent treatment is described, and a table of force constants for a number of bond structures is given. The structural significance of these force constants is briefly discussed.

Thermodynamic Properties of Binary Solid Solutions on the Basis of the Nearest Neighbor Approximation

Abstract: An approximate method of computing the partition function of a binary solid solution is formulated. If the only constraints are on the mean energy and mean composition, it is shown that no metastable phase is predicted. The partition function is shown to be obtainable from the largest eigenvalue of a quadratic form and the condition for a phase transition is shown to be related to the degeneracy of the largest eigenvalue. The physical interpretation of the eigenfunction is shown to be related to the probability of surface configuration, while the square of the eigenfunction is related to the probability of a configuration on the interior of the crystal. Some simple examples are discussed which are related to the effect of coordination number on phase transitions.

Electric Polarization of Carboxylic Acids in Dilute Solutions of Nonpolar Solvents I. The Relation of Electric Polarization to the Association of Carboxylic Acids in Hydrocarbon Solvents

Abstract: The association and polar character of various carboxylic acids have been studied in the solvents benzene and heptane by means of measurements of the electric polarization in very dilute solutions. The data have been analyzed by assuming an equilibrium between dimers and monomers of the acid molecules. A rather large anomalous contribution to the polarization of the dimer has been found. Possible origins of this polarization have been briefly considered.

Theory of Some van der Waals Molecules

Abstract: Using a potential function of the form V(R)=A(ρ)e−R/ρ−c1R6−c2R8−c3R10−c4R12, the vibrational wave number and energy of dissociation of the molecules HgHe, HgNe, HgA, HgKr, HgXe, Hg2, (O2)2 and (NO)2 in the normal state are calculated. It is found that, if the single value ρ=0.28A is chosen, satisfactory agreement is obtained with experimental data except in the case of (NO)2. The latter structure is believed to owe its binding partly to first‐order attractive forces.