Showing papers in "Journal of Chemical Physics in 1953"
TL;DR: In this article, a modified Monte Carlo integration over configuration space is used to investigate the properties of a two-dimensional rigid-sphere system with a set of interacting individual molecules, and the results are compared to free volume equations of state and a four-term virial coefficient expansion.
Abstract: A general method, suitable for fast computing machines, for investigating such properties as equations of state for substances consisting of interacting individual molecules is described. The method consists of a modified Monte Carlo integration over configuration space. Results for the two‐dimensional rigid‐sphere system have been obtained on the Los Alamos MANIAC and are presented here. These results are compared to the free volume equation of state and to a four‐term virial coefficient expansion.
35,161 citations
TL;DR: In this article, the resonance theory of Forster, which involves only allowed transitions, is extended to include transfer by means of forbidden transitions which, it is concluded, are responsible for the transfer in all inorganic systems yet investigated.
Abstract: The term ``sensitized luminescence'' in crystalline phosphors refers to the phenomenon whereby an impurity (activator, or emitter) is enabled to luminesce upon the absorption of light in a different type of center (sensitizer, or absorber) and upon the subsequent radiationless transfer of energy from the sensitizer to the activator The resonance theory of Forster, which involves only allowed transitions, is extended to include transfer by means of forbidden transitions which, it is concluded, are responsible for the transfer in all inorganic systems yet investigated The transfer mechanisms of importance are, in order of decreasing strength, the overlapping of the electric dipole fields of the sensitizer and the activator, the overlapping of the dipole field of the sensitizer with the quadrupole field of the activator, and exchange effects These mechanisms will give rise to ``sensitization'' of about 103−104, 102, and 30 lattice sites surrounding each sensitizer in typical systems The dependence of transfer efficiency upon sensitizer and activator concentrations and on temperature are discussed Application is made of the theory to experimental results on inorganic phosphors, and further experiments are suggested
7,635 citations
TL;DR: In this paper, the necessary coordination of the motions of different parts of a polymer molecule is made the basis of a theory of the linear viscoelastic properties of dilute solutions of coiling polymers.
Abstract: The necessary coordination of the motions of different parts of a polymer molecule is made the basis of a theory of the linear viscoelastic properties of dilute solutions of coiling polymers. This is accomplished by use of the concept of the submolecule, a portion of polymer chain long enough for the separation of its ends to approximate a Gaussian probability distribution. The configuration of a submolecule is specified in terms of the vector which corresponds to its end‐to‐end separation. The configuration of a molecule which contains N submolecules is described by the corresponding set of N vectors. The action of a velocity gradient disturbs the distribution of configurations of the polymer molecules away from its equilibrium form, storing free energy in the system. The coordinated thermal motions of the segments cause the configurations to drift toward their equilibrium distribution. The coordination is taken into account by the mathematical requirement that motions of the atom which joins two submolecules change the configurations of both submolecules. By means of an orthogonal transformation of coordinates, the coordination of all the motions of the parts of a molecule is resolved into a series of modes. Each mode has a characteristic relaxation time. The theory produces equations by means of which the relaxation times, the components of the complex viscosity, and the components of the complex rigidity can be calculated from the steady flowviscosities of the solution and the solvent, the molecular weight and concentration of the polymer, and the absolute temperature. Limitations of the theory may arise from the exclusion from consideration of (1) very rapid relaxation processes involving segments shorter than the submolecule and (2) the obstruction of the motion of a segment by other segments with which it happens to be in contact. Another possible cause of disagreement between the theory and experimental data is the polydispersity of any actual polymer; this factor is important because the calculated relaxation times increase rapidly with increasing molecular weight.
3,456 citations
TL;DR: In this article, the theory of electronic spectra and electronic structure was further developed and applied to ethylene, butadiene, benzene, pyridine, pyrimidine, pyrazine, and s-triazine.
Abstract: The theory of electronic spectra and electronic structure, the elucidation of which was begun in the first paper of this series, is further developed and applied to ethylene, butadiene, benzene, pyridine, pyrimidine, pyrazine, and s‐triazine.A realistic and consistent LCAO‐MO π‐electron theory should allow the σ‐electrons to adjust themselves to the instantaneous positions of the mobile π‐electrons. This is accomplished in the theory by assignment of empirical values to the Coulomb electronic repulsion integrals and Coulomb penetration integrals which enter the formulas, these values being obtained in a prescribed way from valence state ionization potentials and electron affinities of atoms. Use of the empirical values in the molecular orbital theory reduces the magnitude of computed singlet‐triplet splittings and the effects of configuration interaction without complicating the mathematics. From the valence‐bond point of view, ionic structures may be said to be enhanced.The applications to hydrocarbons a...
1,514 citations
TL;DR: In this article, the incorporation of solute elements into single crystals of germanium grown from the melt is examined in terms of a simple model, which takes account of the contribution of the solute transport in the melt, owing to diffusion and fluid motion, to the over-all process of impurity incorporation during steady-state crystallization.
Abstract: The incorporation of solute elements into single crystals of germanium grown from the melt is examined in terms of a simple model. The theory takes account of the contribution of solute transport in the melt, owing to diffusion and fluid motion, to the over‐all process of impurity incorporation during steady‐state crystallization. The analysis is extended to treat the transient inclusion of solute which results when the composition of the melt is abruptly changed.
1,244 citations
TL;DR: In particular, the effects of the solvent, which is considered as an independently variable component, are taken explicitly into account in this paper, where expressions for thermodynamic equilibrium constants are set up for the ion exchange equilibria of models defined in terms of operational variables.
Abstract: Expressions for thermodynamic equilibrium constants are set up for the ion‐exchange equilibria of models defined in terms of operational variables. Formulas summarizing the methods for the computation of the requisite activity coefficients are given. In particular, the effects of the solvent, which is considered as an independently variable component, are taken explicitly into account.
791 citations
TL;DR: In this paper, the number and relative intensities of the components of a multiplet were determined by the number of and statistical weights of the various nuclear spin orientations of the nuclei causing the splitting.
Abstract: Multiple magnetic resonance lines have been observed for H1, F19, and P31 nuclei in compounds such as PH3, PF3, F2PO(OH), and BrF5, in the liquid state. The multiplets consisted of two to seven equally spaced narrow components, symmetrically placed about a central frequency, and with splittings from 0.02 to 0.8 gauss. These multiplets arise from a new variety of interaction among the nuclear moments in a molecule. Resonance lines were found to be multiple either when a nucleus interacted with a different species of nucleus or when there was interaction between nuclei of the same species with resonance frequencies separated by a chemical shift. No compounds exhibited multiplets attributable to interactions among structurally equivalent nuclei. Nor were multiplets caused by nuclei whose electric quadrupole moments were coupled to a direction fixed in the molecule.The number and relative intensities of the components of a multiplet were determined by the number and statistical weights of the various nuclear spin orientations of the nuclei causing the splitting. In a given molecule, the ratio of the multiplet splittings of the two different resonance lines was inversely proportional to the ratio of the gyromagnetic ratios of the interacting nuclei. The splittings were independent of applied magnetic field at 4180 and 6365 gauss; they were independent of temperature over ranges from 55°C to −130°C. In PF5, the one gas examined, the splitting of the doublet fluorine resonance was the same in the gas and liquid phases; also, the doublet was demonstrated to arise from coupling with the phosphorus nucleus, rather than from a chemical shift between the resonances from the apex and meridian fluorines in the bipyramidal structure, as proposed earlier.All of the above characteristics are accounted for theoretically by assuming the magnetic nuclei interact via magnetic fields inside the molecule. The qualitative aspects are predicted by coupling of the form A12μ1·μ2 between the nuclear moments μ1 and μ2. The coupling constant A12 depends upon the detailed mechanism, which must involve the molecular electrons. Second‐order perturbation theory was used to calculate the relative magnitudes of coupling via the electron orbital and the electron spin magnetic moments. The electron spin mechanism was found to give splittings ten to twenty times the orbital. Approximate calculation of the electron spin mechanism in several simpler cases gave good agreement with experiment. The influence upon the splittings of electric quadrupole coupling and spin‐lattice relaxation was considered and is discussed briefly.
608 citations
TL;DR: In this paper, a theoretical analysis of the relation between the magnetic absorption line shape and the chemical exchange frequency suggests that rather short chemical lifetimes can be measured; at least one can infer from the appearance of a single or complex resonance that the average lifetime is greater or less than a determinable value in a range about 10−2 to 10−4 sec.
Abstract: The position of the proton magnetic resonance is concentration dependent in aqueous solutions of electrolytes yielding hydrogen containing ions. Chemical exchange averages the chemical shifts in the proton resonance position over the different chemical species. The averaged shifts observed are correlated with dissociation of the solute, and evidence is obtained in very concentrated solutions for the incomplete dissociation of HNO3, HClO4, and H2SO4 and for the formation of ion pairs of Na+OH−. A theoretical analysis of the relation between the magnetic absorption line shape and the chemical exchange frequency suggests that rather short chemical lifetimes can be measured; at least one can infer from the appearance of a single or complex resonance that the average lifetime is greater or less, respectively, than a determinable value in a range about 10−2 to 10−4 sec.
412 citations
TL;DR: The variability of the Ag/S ratio in silver sulfide has been studied with the help of electrochemical measurements as mentioned in this paper, and it is shown that the variability of Ag2S at 160°C is of the order of 3×10−5 g−atom Ag/mole Ag 2S.
Abstract: The variability of the Ag/S ratio in silver sulfide has been studied with the help of electrochemical measurements. Silver sulfide coexisting with metallic silver at 200°C contains a silver excess of 2.0×10−3 g‐atom Ag/mole Ag2S, whereas silver sulfide coexisting with liquid sulfur has very nearly ideal stoichiometric composition. The variability of the Ag/S ratio in β Ag2S at 160°C is of the order of 3×10−5 g‐atom Ag/mole Ag2S.The interdiffusion coefficient of silver in Ag2S at 220°C is about 3×103 times greater than the self‐diffusion coefficient of silver in Ag2S.A thermodynamic calculation gives the result that the transformation temperature of Ag2S coexisting with metallic silver is about 1.7°C lower than the transformation temperature of Ag2S coexisting with liquid sulfur in accordance with observations made by Kracek.
386 citations
325 citations
TL;DR: In this paper, the free-electron model for conjugated systems is consistently developed as the limiting case of a three-dimensional quantum-mechanical treatment of the π electrons in such systems.
Abstract: The free‐electron model for conjugated systems is consistently developed as the limiting case of a three‐dimensional quantum‐mechanical treatment of the π electrons in such systems. Joint conditions (for branching points) and boundary conditions (for free end points) are derived and the hermiticity of the Hamiltonian is shown. A matrix formulation of the theory is established which makes the application to large systems feasible, and at the same time leads to a close analogy with the LCAO model (LCAO MO treatment considering only nearest neighbor interactions). Quantities analogous to the quantities q (the charge in an atomic orbital) and p (the bond order) are defined, and special attention is given to alternant conjugated systems for which a population theorem, analogous to the one in LCAO theory, is valid.
TL;DR: The theory of hindered rotation in methyl alcohol developed by Burkhard and Dennison has been extended to include the second-order Stark effect as well as a detailed discussion of K-type doubling as discussed by the authors.
Abstract: The theory of hindered rotation in methyl alcohol developed by Burkhard and Dennison has been extended to include the second‐order Stark effect as well as a detailed discussion of K‐type doubling. It has been applied to an interpretation of the microwave spectrum of normal methanol and of two isotopic molecules, C13H3O16H and C12H3O18H3 recently measured by Hughes, Good, and Coles. A very convincing fit between the predicted and observed lines is obtained which serves to determine many of the molecular constants, as well as providing a substantial number of self‐consistency checks.The height of the potential barrier (on the assumption of a sinusoidal potential) is found to be 374.8 cm−1. The CH distance in the methyl group cannot be obtained with any accuracy from the present data but is consistent with the CH distance in methane, namely, 1.093A, and has been taken to have this value. The remaining dimensions are, however, well determined and are: OH distance=0.937A, CO distance=1.434A, COH angle=105°56′,...
TL;DR: In this paper, it was shown that an electric potential exists between the surface and the bulk of ionic crystals and the potential is expressed in terms of the energies necessary for formation of lattice defects.
Abstract: It is shown that an electric potential exists between the surface and the bulk of ionic crystals. The potential is expressed in terms of the energies necessary for formation of lattice defects. The distribution of the potential and of lattice defects near the surface is calculated. The difference between the concentration of lattice defects near the surface and that in the bulk leads to a ``surface conduction.'' The magnitude of the potential, the thickness of the space‐charge layer near the surface and the ``surface conduction'' are calculated for NaCl crystals using numerical values, calculated by Mott and Littleton [N. F. Mott and M. J. Littleton, Trans. Faraday Soc. 34, 485 (1938)] for the energies of formation of lattice defects. The effect of charged impurities in the crystals on the surface potential is discussed. The importance of the surface potential on diffusion, photoelectric effect, and photographic effect is mentioned.
TL;DR: In this article, the absorption coefficients of oxygen were measured at several hundred wavelengths in the region 1050-1900A with a one-meter vacuum monochromator and a phosphor-coated photomultiplier as detector.
Abstract: Absorption coefficients of oxygen were measured at several hundred wavelengths in the region 1050–1900A with a one‐meter vacuum monochromator and a phosphor‐coated photomultiplier as detector. The absorption intensity of the Schumann‐Runge continuum was found to be somewhat less than previous results, and the intensity distribution was less symmetrical. The 19–0 and 20–0 bands of the Schumann‐Runge progression were observed and the dissociation limit of the B3Σu− state was 57140±60 cm−1. Several other bands and continua were found at shorter wavelengths.
TL;DR: In this article, a model for the geometrical effects in the radiolysis of water as a result of the diffusion of free radicals is presented, and the motion of secondary electrons immediately following the passage of the ionizing particle is discussed in an appendix.
Abstract: A model is presented which describes the geometrical effects in the radiolysis of water as a result of the diffusion of free radicals. The motion of secondary electrons immediately following the passage of the ionizing particle is discussed in an appendix, and it is concluded that radicals are most likely formed in pairs at the approximate sites of the original ionizations. Models for the diffusion of these radicals are shown to result in a definite fraction of radicals which undergo initial recombination for gamma‐ and fast beta‐rays, for which the spurs are considered as diffusing independently. For alpha‐rays a connected‐track model is used. For the intermediate case of tritium beta‐rays, a two‐stage model is constructed. In each case the comparative yields of the ``forward'' and ``radical'' reactions (GF and GR) are calculated. Subsequent chemical effects in pure water and solutions are also considered briefly.
TL;DR: In this article, the relationship between transition moment direction and dichroic ratio was derived for perfectly and imperfectly oriented fibers, and the effects of reflection losses, form dichroism, and convergence were considered.
Abstract: The increasing use of infrared dichroism measurements in studying the molecular structure of fibrous proteins necessitates a critical examination of its interpretation. Relationships between transition moment direction and dichroic ratio are derived for perfectly and imperfectly oriented fibers, and the effects of reflection losses, form dichroism, and convergence are considered. Uncertainties in the assignment of the transition moment directions associated with the principal vibrations of the —CO·NH— group are discussed.
TL;DR: In this paper, the spectral properties of pyridine and its derivatives were analyzed with the help of the product rule and by analogy with the fundamental frequencies of benzene and benzene-d6.
Abstract: Pyridine‐d5 has been prepared by exchange between pyridine vapor and heavy water in the presence of a palladium catalyst. Infrared and Raman spectra are reported for pyridine and pyridine‐d5 over the spectral range 300–4000 cm−1. Interpretation of the spectra with the help of the product rule and by analogy with the fundamental frequencies of benzene and benzene‐d6 leads to complete sets of frequencies for the 27 vibrational degrees of freedom of pyridine and of pyridine‐d5. The frequency assignment for pyridine does not differ greatly from previous ones, but is believed to be more reliable because of the additional spectroscopic data.
TL;DR: In this article, the distortion constants ταβγδ are expressed in terms of inverse force constants and of the derivatives of the inertia tensor with respect to interatomic parameters.
Abstract: The distortion constants ταβγδ are expressed in terms of inverse force constants and of the derivatives of the inertia tensor with respect to interatomic parameters. Harmonic potential functions are assumed. Relations that simplify the procedure for obtaining the required derivatives are obtained. Furthermore, rules are given that enable one to write down directly the derivatives with respect to certain common internal displacement coordinates. Group theoretical considerations are used to obtain some knowledge of the distortion constants.
TL;DR: In this paper, the boundary layer theory was applied to derive the form of relationships for the extent, heats, and rates of chemisorption and some consequences with respect to catalysis.
Abstract: When chemisorption on a semiconductive solid is accompanied by electronic charge transfer between adsorbate and solid, an electronic boundary layer analogous to that in rectifying junctions may develop and polarization of charges in the solid may result. These phenomena may limit or control the chemisorption characteristics. The boundary layer theory developed for electrical contacts and elementary considerations concerning the effect of the polarization potential are applied to derive the form of relationships for the extent, heats, and rates of chemisorption and some consequences with respect to catalysis. An attempt is made to illustrate the detailed physical processes in order to examine the meaning of ``heterogeneity'' and ``active centers'' in cases of this type of chemisorption.
TL;DR: In this paper, the components of charge and capacity in the diffuse double layer at a plane interface for electrolytes of the 1:2 and 2:1 valence types were derived.
Abstract: Equations are derived for the variation of potential with distance and for the components of charge and capacity in the diffuse double layer at a plane interface for electrolytes of the 1:2 and 2:1 valence types. Some additional relations are also deduced for other valence types.
TL;DR: In this paper, exact expressions for the molecular distribution functions in a one-dimensional fluid whose particles interact with a nearest neighbor pair potential were derived for rigid spheres and the superposition principle was found to be exact in such a fluid.
Abstract: Exact expressions are derived for the molecular distribution functions in a one‐dimensional fluid whose particles interact with a nearest neighbor pair potential. The pair distribution function for rigid spheres is found to be identical with Frenkel's result. The one‐dimensional form of a new set of integral equations for the molecular distribution functions is examined. The superposition principle is found to be exact in a one‐dimensional fluid with nearest neighbor interactions.
TL;DR: In this paper, the intensity and wavelength of the charge transfer transitions of a large number of molecular complexes in solution are examined in terms of possible theoretical interpretations of the transition transitions, and it was shown that the wavelengths of these transitions show an excellent correlation with the ionization potentials of the electron donor partners of the complexes.
Abstract: The intense so‐called ``intermolecular charge‐transfer spectra'' shown by a large number of molecular complexes in solution are found to exhibit certain regularities in regard to wavelength and intensity. The wavelengths of these transitions show an excellent correlation with the ionization potentials of the electron donor partners of the complexes. The intensities of the charge‐transfer transitions are markedly dependent on the electron acceptor partner of the complex. These results are examined in terms of possible theoretical interpretations of the charge‐transfer transitions.
TL;DR: A series of approximations for the statistical mechanics of order disorder, proposed by Bethe, Takagi, Yang, Li, Hill, and Kikuchi, are investigated in detail in two ways as mentioned in this paper.
Abstract: A series of approximations for the statistical mechanics of order‐disorder, proposed by Bethe, Takagi, Yang‐Li‐Hill, Kikuchi, and others, are investigated in detail in two ways. (1) A new interpretation of the method for constructing the combinatory factor is presented in order to give a better understanding of the nature of approximations. (2) The partition functions with approximate combinatory factors are expanded to compare with the rigorous expansion and the discrepancies between them are investigated in detail. One of the conclusions is that in order to obtain a higher approximation, it is necessary to use the basic figure ``closed'' with respect to the cluster of the preceding approximation. In appendices, an improved treatment of the body‐centered cubic lattice (Ising model) is given, and Bethe's fundamental assumptions are derived from our scheme.
TL;DR: The Matano Boltzmann method of graphical calculation of diffusion coefficients in solutions is replaced by an analytical method in certain systems, such as copper-nickel as discussed by the authors, which enables accurate calculation of the diffusion coefficients near the concentration extremes.
Abstract: The Matano‐Boltzmann method of graphical calculation of diffusion coefficients in solutions is replaced by an analytical method in certain systems. This procedure enables accurate calculation of diffusion coefficients near the concentration extremes. An equation is derived for the diffusion coefficient D as a function of concentration c. The equation predicts a variation of D with c which is not exponential in metallic systems, contrary to the proposal of Wagner. Comparison of D values with those obtained graphically, for the system copper‐nickel, indicates that the graphical values may be appreciably in error at that extreme where the diffusion coefficient is greatest.
TL;DR: In this article, the effects of the change of the (geometrical) configuration of the intermediate reaction complex during reaction and of the electronic vibrational coupling on these correlations have been considered in detail.
Abstract: Adiabatic orbital and spin correlation rules applicable to a detailed study of elementary chemical reactions involving nonlinear polyatomic intermediate complexes have been formulated and are presented together with some pertinent correlation tables. These correlation rules and tables permit the determination of the adiabatically allowed term manifold of reaction products from the states of the separated reactants without reference to their detailed electronic configurations. The formulation presented here utilizes group theoretical arguments relating to the symmetry properties of the reactants, the intermediate reaction complex, and the products and is based principally upon the results obtained previously by Mulliken for the resolution of species into those of point groups of lower symmetry. The effects of the change of the (geometrical) configuration of the intermediate reaction complex during reaction and of the electronic‐vibrational coupling on these correlations have been considered in detail. It i...
TL;DR: In this paper, the authors discussed the relation of the relaxation time τ of a dielectric to the measured decay time of polarization T and proposed a new expression for the internal field in a Dielectric subjected to an alternating field.
Abstract: The paper discusses the relation of the relaxation time τ of a dielectric to the measured decay time of polarization T and proposes a new expression for the internal field in a dielectric subjected to an alternating field. It is found for this expression that 1
TL;DR: In this article, a general formulation of the excluded volume effect in polymer chains is set up and compared with the theory of Markoff processes, and the results of preliminary numerical calculations for the relation between the mean square radius of the chain and the second virial coefficient, in good agreement with experiment, are given.
Abstract: This discussion is concerned with the excluded volume effect in polymer chains, i.e., the mathematical problem of random flights with correlations between the flights, which is of importance in relating the mean size of a chain to its structure. A general formulation of the problem is set up and compared with the theory of Markoff processes. It is shown that although an integral equation of the Markoff form for the distribution function exists, it contains a complicated function whose exact evaluation is difficult. Since the same function occurs in the problem of the osmotic second virial coefficient, it is natural to relate the excluded volume effect to the second virial coefficient. The results of preliminary numerical calculations for the relation between the mean square radius of the chain and the second virial coefficient, in good agreement with experiment, are given. It is concluded that the volume effect is certainly not negligible for real chains, except when the second virial coefficient is zero, and that the effect increases with increasing chain length.
TL;DR: In this paper, the specific heat of high purity Acheson graphite was measured from 13° to 300°K and the derived thermodynamic functions, entropy, enthalpy, and free energy, were determined by graphical integration and tabulated at integral values of temperature up to 300.
Abstract: The specific heat of high‐purity Acheson graphite prepared by the National Carbon Company has been measured from 13° to 300°K. In the region 13° to 54°K the Cp data follows a T2 dependence quite accurately in agreement with previous experimental work and recent theoretical investigations of specific heat in strongly anisotropic solids.On the basis of some recent studies for other highly anisotropic solids, it is suggested that the specific heat of graphite will eventually follow a T3 dependence at still lower temperatures.The derived thermodynamic functions, entropy, enthalpy, and free energy, have been determined by graphical integration and tabulated at integral values of temperature up to 300°K. The entropy of graphite at 298.16°K is 1.372±0.005 cal/g‐atom deg, of which 0.004 is extrapolated from 13° to 0°K assuming the third law and the T2 dependence.