Volume 20, Issue 8, 01 August 1952

Self‐Diffusion in Solid Sodium. I
View Description Hide DescriptionMeasurements are reported for the self‐diffusion of solid sodium over the temperature range, 0°—95°C. The data fit the empirical equation D=.242 exp(−10,450/RT) with an uncertainty of ±300 cal mole^{−1} in the heat of activation. The entropy of activation calculated from the temperature coefficient of the elastic modulus is in agreement with the value based upon the vacancy mechanism.

Self‐Diffusion in Solid Sodium. II. The Effect of Pressure
View Description Hide DescriptionHydrostatic pressure is found to decrease the rate of self‐diffusion in sodium. The free energy of activation is a linear function of the melting point, and the enthalpy of activation is proportional to the melting point. For sodium and for all cubic metals (except lead and tungsten) for which diffusion data exist the enthalpy of activation is related to the latent heat of fusion by the equation ΔH = 16.5 L_{m}. The change in D _{0} for sodium with pressure is expressible in terms of the compressibility and the activation entropy change.

Photochemistry of Ferrous Ions in Aqueous Solution
View Description Hide DescriptionThe photochemistry of ferrous ions in aqueous solutions has been investigated, and it has been confirmed that irradiation in the quartz ultraviolet, in the absence of oxygen, leads to the formation of ferric salt and molecular hydrogen. It has been concluded further that the primary absorption of a light quantum results in the formation of excited ions, (Fe^{2+}·H_{2}O)^{*}, a considerable proportion of which undergo processes of deactivation, while the remaining (about one‐tenth) dissociate according to leading to the formation of hydrogen atoms. The latter can undergo back reactions of the type Investigation of the pH dependence of the quantum yield has led to the assumption that hydrogen atoms can also react according to leading to the formation of hydrated hydrogen molecular ions which intervene in this process according to the reaction
Other experimental evidence and some theoretical considerations which have led to the assumption of in aqueous solution are referred to.

Theory of Ion Exchange for Polyelectrolytes Undergoing Electrolytic Transference
View Description Hide DescriptionIt has been observed experimentally that polymeric ions generally have associated with them a large number of small ions of opposite charge. These smaller ions, which are considered bound to the polymeric ions, are capable of exchanging with free ions in solution. The rate of this exchange can be determined by certain electrolytic transference experiments involving the use of radioactive tracers. The theory of such transference experiments is worked out by formulating and solving appropriate differential equations subject to certain boundary conditions. It is then shown how results of these transference studies can be used for evaluating ion rate exchange constants.

Electrolytic Properties of Aqueous Solutions of Polyacrylic Acid and Sodium Hydroxide. III. The Rate of Sodium Ion Exchange between Polyacrylate and Free Sodium Ions
View Description Hide DescriptionThe exchange of free sodium ions with sodium ions bound to polyacrylate ion has been investigated by an electrolytic transference method. On the assumption that there is a single exchange process, rate constants have been computed and the theory has been found to provide a moderately good representation of the data. A much better correlation is obtained, however, if it is assumed that there are two exchange processes, one very rapid and the other very slow. Presumably the sodium ions that exchange rapidly belong to the polyacrylate ion atmosphere while those that exchange slowly are located within the coiled polymer ion. The distribution of sodium ions between these two groups has been computed.

Inter‐ and Intramolecular Energy Transfer Processes. I. Nitro‐Compounds and Hydrocarbons
View Description Hide DescriptionThe addition compounds of aromatic nitro‐compounds and hydrocarbons fluoresce appreciably only if the hydrocarbon component itself has a possible transition lying in the region where the nitro‐complex might be expected from its absorption to emit. The resulting emission spectrum is very similar to that of the hydrocarbon component but much more strongly allowed. This is attributed to the breaking down of the S←T selection rule as the complex dissociates.

The Lowest Triplet Levels of Aromatic Hydrocarbons
View Description Hide DescriptionNew data for anthracene and naphthacene suggest that the lowest triplet levels of polyacenes are of species ^{3} L_{b}. This makes the 39,000 cm^{−1} singlet band of benzene of symmetry B _{2u } as was originally proposed and not B _{1u } as was later suggested.

The Statistical Mechanical Theory of Irreversible Condensation. I
View Description Hide DescriptionA theory of nucleation, based on statistical mechanics, is presented. The problem reduces to the computation of the multiple occupation, by molecules, of cells, this being accomplished through the evaluation of the configuration integral for a supersaturated assembly. The new theory does not consider the first fragments of the stable phase formed to be spherical liquid drops. In no place (not even at the nucleus) is it necessary to to consider explicitly phase equilibrium between an embryo and the mother phase. The manifold difficulties connected with this point (in view of the small dimensions of typical nuclei) are therefore obviated. Furthermore, it is possible to define an embryo unambiguously, and in such a manner that its energetic properties can, in principle, be computed. This is not possible in the classical theory.
Certain limitations on the application of Einstein fluctuation theory to supersaturated systems are demonstrated.

Rotational Isomerism and the Vibrational Spectrum of Sym‐Dideuterodibromoethane
View Description Hide DescriptionTrans‐ethylene‐d _{2} was brominated by two methods, which involved different stereochemical paths, to give 95 percent meso‐BrDHC‐CHDBr as one product and a mixture of meso‐ and racemic‐BrDHC‐CHDBr as the other. Liquid phase Raman spectra and liquid and solid phase infrared spectra of these materials have been obtained and a tentative assignment of the vibrational frequencies of BrDHC‐CHDBr to the trans and skew configurations of the meso and racemic compounds has been made.

Interdiffusion of Polyvinyl Acetate with a Series of Solvents
View Description Hide DescriptionThe Lamm scale method has been used to follow the interdiffusion of polyvinyl acetate with ethyl acetate, propyl acetate, isopropyl acetate, butyl acetate, and triacetin at 30°C, and with acetone at 20°, 30°, and 40°C. For all these systems the mutual diffusion coefficient attains a maximum value at intermediate polymer concentrations. At a given concentration and temperature the D(c) values are largest with acetone and much the smallest with triacetin, although the relative variation in D(c) over the concentration range is actually largest with the latter. The general variation of D(c) with concentration can be plausibly interpreted in terms of the mass flow‐intrinsic diffusion concept introduced by Hartley. For the system acetone—polyvinyl acetate the calculated energy of activation for the diffusion is nearly constant at 1 kcal in the concentration range 0 to 40 grams polymer per 100 cc of solution but then rises rapidly to 10 kcal at 90 grams polymer per 100 cc.

The Rotation‐Vibration Spectra of Allene and Allene‐d _{4}
View Description Hide DescriptionThe infrared absorption spectra of allene and allene‐d _{4} vapor have been measured over the spectral range 250–5000 cm^{−1} with a prismspectrometer. The infrared data, together with previously obtained Raman spectra, enable a complete vibrational analysis that satisfies the product rule well for all vibrational species. The torsional vibration is located at 865 cm^{−1} in allene and 615 cm^{−1} in allene‐d _{4}. Fine structure was resolved for all perpendicular fundamental bands except that of the lowest frequency in both compounds. With help of the zeta‐sum rule, a modified equation of H. H. Nielsen and the statistical weights of the rotational levels, the fine structure is analyzed to yield a complete set of zeta‐values for both molecules and a moderately accurate value for the moment of inertia about the figure axis. The latter gives for the HCH angle the figure 113°±1° if one assumes a C–H distance of 1.071A.

Spectroscopic Studies in the Near Ultraviolet of the Three Isomeric Dimethylbenzene Vapors. II. Absorption Spectra of Meta and Ortho Dimethylbenzene
View Description Hide DescriptionThe vapor absorption spectra of meta‐ and ortho‐xylene were obtained with a 3‐meter gratingspectrograph. The m‐xylene spectrum has the least number of bands and the most diffuse appearance. Its 0, 0 band is located at 36955 cm^{−1}. The o‐xylene spectrum consists of many very sharp bands, several of which must be assigned to v—v transitions. Its 0, 0 band is found at 37308 cm^{−1}. Vibrational frequencies of 965, 675 and 470 cm^{−1} are found in the upper level of the meta‐spectrum and are correlated with the ground‐state frequencies of 995, 725, and 510 cm^{−1}. In the ortho spectrum ground‐state vibrational frequencies of 1233, 1054, and 736 cm^{−1} are correlated with the excited state values 1195, 939, and 692 cm^{−1}, respectively. Assignments of the different frequencies are discussed. The Tesla luminescencespectrum of meta‐xylene is interpreted along with the absorptionspectrum.

Some Statistical Mechanical Models of Elastic Polyelectrolytes and Proteins
View Description Hide DescriptionThree statistical mechanical models are developed for use in connection with the problem of muscle action. In addition, the models should apply to certain other systems, for example, polyelectrolyte fibers or gels, fibrous proteins in general, and ion exchange resins.
The first model is a statistical mechanical version of the ``autone'' model of Varga, Szent‐Gyorgyi, Gergely, and Laki, but we extend the theory to include the effect of an adsorbed substance (e.g., ATP) on the length of the elastic element.
The second model is a charged rubber‐like cylindrical fiber. The charges on the molecular chains of the network may be permanent or may result from the adsorption of ions from solution (e.g., hydrogen ions, or ATP). The approximate free energy of the system is computed by combining the Flory‐Rehner swelling theory, the Fowler‐Langmuir adsorptionmodel, and an electrostatic free energy based on a ``smeared'' uniform charge density inside the fiber (electrolyte is also present), as suggested by the work of Hermans and Overbeeck. If the radius of the cylinder is large compared to the radius of the Debye‐Hückel ionic atmosphere, it is not necessary to linearize the Boltzmann factor in the Poisson‐Boltzmann equation. From the free energy of the system one obtains the interconnected pressure‐volume, length‐tension and adsorption isotherm relations. Important special cases are isotropic swelling (zero tension) with the gel under pressure or not, and the elasticity of the fiber (with adsorption) under zero pressure. When the fiber is constrained to a constant radius, it is possible to get a phase change in the length‐tension curve (see below).
The third model is an equilibrium statistical theory of the well‐known α—β transformation in fibrous proteins (such as keratin and myosin). Adsorption of ions from solution and electrostatic effects can be included here as well as in the preceding model, but the discussion is concerned primarily with an analysis of the elasticity of a sheet of polypeptide chains with α‐ and β‐units statistically scrambled, taking into account as a nearest‐neighbor problem in statistical mechanics (using the quasi‐chemical method) lateral β—β hydrogen bonds and vertical α—α hydrogen bonds. From the theory it would appear that critical phenomena, phase changes (for example, a considerable increase in length at constant tension, representing a phase change from primarily vertical α—α crystallization to primarily lateral β—β crystallization) and hysteresis are to be expected. These phenomena are observed experimentally, though modified in most cases by superimposed non equilibrium effects. It is pointed out that a fiber operating (on stretching and retraction) between the two ``ends'' of a phase change would be particularly suitable in the muscle problem, because of the sensitivity of the length of the fiber at constant tension to small changes in environment (e.g., pH).
Although a few illustrative examples are given, further applications are reserved for a later paper.

The Quantum‐Mechanical Partition Function
View Description Hide DescriptionAn exact evaluation is attempted of the quantum‐mechanical partition function for an assembly of similar particles with central interaction. Quantum‐mechanical analogs of the classical cluster integrals are derived and evaluated as far as required to determine the virial coefficients. It is shown that the results are particularly well adapted for computation at very low temperatures.

Markoff Random Processes and the Statistical Mechanics of Time‐Dependent Phenomena
View Description Hide DescriptionTwo principles of a statistical mechanics of time‐dependent phenomena are proposed and argued for. The first states that the proper mathematical object to describe the physical situation is the stationary random process specified by the ensemble of time seriesa_{i} (X_{t} )i=1···s and the distribution ρ(X). The set phase functions a_{i} (X)i=1···s represent the set of grossly observable features of the system. X_{t} is the image of the phase X after time t. ρ(X) is a stationary distribution. The second principle is concerned with the very common case in which the phenomenological equations are of the first order in time and states that in this case the random process in question is a Markoff process. A Fokker‐Planck equation is derived for the process, and an entropy is defined and is shown always to increase. Phenomenological equations are derived as a first approximation to the Markoff process. These involve a certain matrix ξ_{ ij } which is shown to satisfy symmetry relations which are a generalization of Onsager's. The theory is applied to the uniformization of the direction of momentum of a particle on a two‐dimensional torus subject to a small perturbing potential.

Viscosities of Some Lower Aliphatic Alcohols at Constant Volume
View Description Hide DescriptionFrom an analysis of all the published experimental data for methyl, ethyl, n‐propyl, isobutyl, and n‐octadecyl alcohols, it is shown that, even for these compounds, at constant volume logη is a rectilinear function of 1/T and the general pattern of behavior is similar to that described previously. , the energy of activation of viscous flow at constant volume, is plotted as a function of volume, and the curve for ethyl alcohol shows an apparently anomalous minimum.

The X‐Ray K Absorption Edges of Covalently Bonded Cr, Mn, Fe, and Ni
View Description Hide DescriptionWe discuss some recently measured absorption edges of covalent nickel complexes and edges of Cr, Mn, and Fe in similar complexes already in the literature. Low energy absorption (generally resolved as a line) is observed in all complexes where empty 4p orbital is expected from chemical or magnetic data. From the position of the line it is concluded that the metal ion is near neutral in the covalent complex. Where the 4p orbital is completely used in bonding, no low energy absorption line is observed. The method may be useful as an additional experimental check on the assignment of bonding orbitals.

A Calculation of the Static Dielectric Constant of Ice
View Description Hide DescriptionA calculation is made of the static dielectric constant of ice using only simple molecular data and with well‐defined assumptions as to the possibilities of molecular movement in the crystal. The paper serves as an illustration of the procedure for calculating static dielectric constants, and it results in a numerical value of this quantity for ice which is in reasonable agreement with experiment.

Dielectric Properties of Ice and Solid D_{2}O
View Description Hide DescriptionComplex dielectric constants have been measured for ice from the melting point to −65°C, and for solid D_{2}O to −35°C, by a combination of bridge and transient methods. For both, the dispersion is described by the simple Debye formula, and the relaxation times τ by the simple rate expression τ = A exp(B/RT). For ice,A = 5.3×10^{−16} sec, B = 13.2 kcal/mole; and for solid D_{2}O, A = 7.7×10^{−16} sec, B = 13.4 kcal/mole. The equilibrium dielectric constant for ice is 91.5 at 0°C and increases at lower temperatures; the values for solid D_{2}O are only slightly smaller. Measures taken to minimize errors from voids in the sample and direct current conductance are discussed.

The Absolute Quantum Yields of the Fluorescence of Chlorophyll Solutions
View Description Hide DescriptionAn integrating sphere has been adapted to the measurement of the quantum yield of the fluorescence of solutions of pigments. The intensities of the fluorescence and of the absorbed light were determined separately with a thermopile.
Chlorophylls a and b dissolved in various solvents have been studied with this apparatus over a range of concentrations, and the measured yields corrected for autoabsorption. The yield for chlorophyll a is 0.25 and is in general independent of solvent and excitation wavelength. The yield for chlorophyll b is 0.11 for ether solutions and 0.06 for methanol solutions. The absolute fluorescent yields of solutions of fluorescein, eosine, magdala red, and rubrene were also measured. These results are in reasonable agreement with the published values of the yields for the same compounds.