Showing papers in "Journal of Chemical Physics in 1949"
TL;DR: On the basis of the nucleation theory developed by Volmer, Becker, and co-workers, and the theory of absolute reaction rates, an expression for the absolute rate of nucleation in condensed systems was derived in this paper.
Abstract: On the basis of the nucleation theory developed by Volmer, Becker, and co‐workers, and the theory of absolute reaction rates, an expression is derived for the absolute rate of nucleation in condensed systems.
1,839 citations
TL;DR: In this article, the effect of droplet size on surface tension is given theoretical consideration with the help of results of the Gibbs thermodynamic theory of capillarity and of previous results as to the sign and magnitude of superficial densities.
Abstract: The effect of droplet size on surface tension is given theoretical consideration with the help of results of the Gibbs thermodynamic theory of capillarity and of previous results of the author as to the sign and magnitude of superficial densities. It is concluded that surface tension can be expected to decrease with decrease in droplet size over a wide range of circumstances. In addition, approximate figures are obtained for the rate at which such decreases may be expected. The decreases become significant for very small drops. The results are of interest in view of the important role of surface tension in determining the behavior of small droplets.
1,610 citations
TL;DR: In this paper, the mean square radii of various branched and ringed polymer molecules were derived under the usual assumptions regarding the statistics of chain configuration, and it was shown that the number of branches or rings can be determined from light scattering measurements.
Abstract: Formulas for the mean square radii of various branched and ringed polymer molecules are developed under the usual assumptions regarding the statistics of chain configuration. For branched molecules, the mean square radii vary less rapidly with molecular weight than for strictly linear molecules, while for systems containing only rings and unbranched chains the variation is more rapid than for the linear case. These results show that in principle the quantity of branches or of rings can be determined from light‐scattering measurements.
1,466 citations
TL;DR: In this paper, the classification of π-orbitals in a cata-condensed aromatic system is like that of the orbitals of a free electron traveling in a one-dimensional loop of constant potential around the perimeter.
Abstract: The classification of π‐orbitals in a cata‐condensed aromatic system is like that of the orbitals of a free electron traveling in a one‐dimensional loop of constant potential around the perimeter. To take into account electron interaction, certain quantities corresponding to angular momenta may be added or subtracted. Introduction of the cross‐links in the molecule removes the degeneracy. The first excited configuration in such systems gives two low frequency singlet weak absorption bands and two higher singlet strong dipole absorption bands. Selection and polarization rules are given. The levels are identified from the spectra and some of their properties are determined. An explanation is given of the regularities found by Klevens and Platt. A systematic nomenclature is given. The results agree qualitatively with LCAO theory, can be applied easily to unsymmetrical molecules, and can possibly be extended to other types of ring systems.
1,206 citations
TL;DR: In this paper, a general statistical theory of interfacial phenomena is developed and expressions are derived relating the surface tension and other superficial thermodynamic functions to the potential of intermolecular force and molecular distribution functions.
Abstract: A general statistical mechanical theory of interfacial phenomena is developed and expressions are derived relating the surface tension and other superficial thermodynamic functions to the potential of intermolecular force and molecular distribution functions. On the basis of a reasonable approximation to the superficial density of molecular pairs, the Lennard‐Jones potential and the Eisenstein‐Gingrich radial distribution function, the surface tension, surface energy, and the superficial density of matter, referred to the surface of tension, are calculated for liquid argon at 90°K and compared with experiment. The positive value which is obtained for the superficial density, referred to the surface of tension, confirms the results of Tolman's quasi‐thermodynamic theory and leads to the conclusion the surface tension of small drops decreases with increasing curvature.
1,195 citations
TL;DR: In this article, it was shown that this variation of electric field is usually simply related to the molecular electronic structure, being primarily dependent on the way in which valence electrons fill the lowest energy p-type orbits.
Abstract: Nuclear quadrupole coupling constants in molecules depend on the nuclear quadrupole moments and the variation in electrostatic field at the nucleus. It is shown that this variation of electric field is usually simply related to the molecular electronic structure, being primarily dependent on the way in which valence electrons fill the lowest‐energy p‐type orbits. Structural information which can consequently be obtained from known quadrupole coupling constants is discussed. Hybridization of the normal covalent bonds of N, Cl, and As with at least 15 percent s character is clearly shown. The alkali halides appear to be almost purely ionic; the quadrupole coupling data allow no more than 3 percent covalent character. In addition to molecular structure, some nuclear quadrupole moments are approximately evaluated by use of the theory developed here.
886 citations
Abstract: Explicit formulas and numerical tables for the overlap integral S between AO's (atomic orbitals) of two overlapping atoms a and b are given. These cover all the most important combinations of AO pairs involving ns, npσ, and npπ AO's. They are based on approximate AO's of the Slater type, each containing two parameters μ [equal to Z/(n—δ)], and n—δ, where n—δ is an effective principal quantum number. The S formulas are given as functions of two parameters p and t, where p=½(μa+μb)R/aH , R being the interatomic distance, and t=(μa—μb)/(μa+μb). Master tables of computed values of S are given over wide ranges of p and t values corresponding to actual molecules, and also including the case p=0 (intra‐atomic overlap integrals). In addition, tables of computed S values are given for several cases involving 2‐quantum s, p hybrid AO's.Hybrid S values for any desired type of hybrid can be obtained very easily from the tables as simple linear combinations of non‐hybrid S values. It is shown how S values correspondin...
868 citations
TL;DR: In this article, the average linear dimension of a polymer chain is taken proportional to a power of the chain length, that power must be greater than the value 0.50 previously deduced in the conventional ''random flight'' treatment of molecular configuration.
Abstract: The average configuration of polymer molecules in solution is markedly influenced by the obvious requirement, ordinarily disregarded in problems relating to molecular configuration, that two elements of the molecule are forbidden from occupying the same location in space. The influence of spatial ``interferences'' between different segments of the molecule on its average configuration has been investigated by statistical and thermodynamic methods.It is shown that if the average linear dimension of a polymer chain is to be taken proportional to a power of the chain length, that power must be greater than the value 0.50 previously deduced in the conventional ``random flight'' treatment of molecular configuration. This power should approach 0.60 for long chain molecules in good solvents. With increase in size of the solvent molecule, the influence of interference on molecular configuration diminishes, vanishing entirely in the extreme case of a solvent which is also a high polymer. The effect of a heat of in...
845 citations
TL;DR: In this paper, the emission lifetimes of the metastable triplet states (phosphorescent states) of a large variety of organic molecules have been measured and it is shown that the transition probabilities corresponding to shorter lifetimes are of the same magnitude as found in the light atoms of which the molecule is composed.
Abstract: The emission lifetimes of the metastable triplet states (phosphorescent states) of a large variety of organic molecules have been measured. The lifetimes are in the range from 10−4 to about 10 seconds. It is shown that the transition probabilities corresponding to the shorter lifetimes are of the same magnitude as found in the light atoms of which the molecule is composed. The longer lifetimes, on the order of seconds, are found only among the aromatic compounds. A consideration of the perturbing singlet states in aromatic compounds shows that the matrix elements for the intercombination must be very much smaller than those responsible for the intercombination in the free carbon atoms. Direct evidence that the long‐lived states of the aromatic compounds are triplet states is obtained by showing that as the atomic number of chemically similar substituents is increased (e.g. substitute Br for Cl), the transition probability increases approximately in proportion to the increase in the square of the spin‐orbit interaction energy of the substituent atom. The luminescences are usually observable only when the substance is dissolved in a rigid solvent, and the effect of such a solvent on the lifetimes is discussed. Experimental data relating singlet‐triplet absorption strength to triplet state lifetime is presented.
690 citations
TL;DR: In this paper, the configurational entropy of a mixture of solvent and polymer molecules composed of segments connected by flexible bonds is derived for the case in which the lattice they occupy contains limited regions of perfect order (i.e., the crystallites), which are reserved for occupancy by polymer segments exclusively.
Abstract: The configurational entropy of a mixture of solvent and polymer molecules composed of segments connected by flexible bonds has been derived for the case in which the lattice they occupy contains limited regions of perfect order (i.e., the crystallites), which are reserved for occupancy by polymer segments exclusively. Although the derivation is carried out primarily for polymer chains of uniform length, modifications required for the treatment of heterogeneous polymers are included. An expression for the free energy of fusion ΔFf of the semicrystalline mixture of polymer and solvent is derived assuming a vanLaar heat of mixing term.The equilibrium (average) crystallite length ζe, derived by differentiation of ΔFf, depends principally on the ``nucleation parameter'' D which, though it evades explicit evaluation from theory, represents the relative ease with which the first layer of a crystallite tends to form; ζe may depend to a lesser extent on the degree of crystallinity. The equilibrium degree of crysta...
558 citations
TL;DR: In this paper, a thermodynamic analysis of phase equilibria similar to that developed in Part IV when applied to the ternary system of two polymers and a solvent leads to an explanation of the usual incompatibility of different high polymers in solution.
Abstract: A thermodynamic analysis of phase equilibria similar to that developed in Part IV when applied to the ternary system of two polymers and a solvent leads to an explanation of the usual incompatibility of different high polymers in solution. Unless their heat of mixing is virtually zero or negative, two high polymers are always immiscible in the absence of a solvent; the primary role of the solvent is non‐specific, merely one of diluting the polymer mixture and decreasing the heat of interaction of the polymers. The recent experiments of Dobry and Boyer‐Kawenoki show reasonable agreement with these theoretical conclusions. Osmotic pressures of mixed polymers are discussed; such measurements would permit determination of μ12, the interaction constant of the two polymers.
TL;DR: In this paper, it was shown that the position of the absorption maxima of symmetrical polymethines and related compounds (symmetrical cyanine and oxanole dyes; Michler's hydrol blue and derivatives; malachite green and other triphenyl methane dyes, etc.) can be calculated by adopting a model of the dye molecule which is analogous to the free-electron gas model used in particular by Sommerfeld to describe the condition of metals.
Abstract: The most important organic compounds which absorb visible light can be classified into three groups typified: (a) by symmetrical polymethines, (b) by porphyrines, (c) by polyenes.Recently it was shown that the position of the absorption maxima of symmetrical polymethines and related compounds (symmetrical cyanine and oxanole dyes; Michler's hydrol blue and derivatives; malachite green and other triphenyl methane dyes; etc.) can be calculated by adopting a model of the dye molecule which is analogous to the free‐electron gas model used in particular by Sommerfeld to describe the condition of metals. The π‐electrons of the polymethine chain are considered as a one‐dimensional free‐electron gas which extends itself along the length of the chain.In the normal state the stablest energy states of the electron gas each contain two electrons in accordance with Pauli's exclusion principle. The remaining states are empty. The existence of the first absorption band is a consequence of the jump of a π‐electron from t...
TL;DR: The spectra of naphthalene, anthracene, naphthacene, phenanthrene, 1,2-benzanthrene, chrysene, and acenaphthene in n−heptane solution are extended to 1700A as mentioned in this paper.
Abstract: The spectra of naphthalene, anthracene, naphthacene, phenanthrene, 1,2‐benzanthrene, chrysene, and acenaphthene in n‐heptane solution are extended to 1700A. Electronic energy levels of 17 such cata‐condensed hydrocarbons are collected and compared. The lowest five or six excited states shift in a regular way with changes of molecular length and shape. Intensities and vibrational structures of corresponding bands are remarkably alike in the different compounds. The total oscillator strength is almost proportional to the number of π‐electrons, but the proportionality constant differs from that in polyenes. With new identifications, the positions of energy levels in naphthalene, anthracene, and azulene agree remarkably well with previous LCAO molecular orbital calculations.The lowest singlet state is of one type in benzene, naphthalene, and most non‐linear systems; of another type in anthracene and the higher linear polyacenes because of a cross‐over. This clears up some controversial questions, such as the ...
TL;DR: In this paper, an extension of the work of Chapman and Cowling is presented, showing that the variational principle of the Enskog procedure can be justified on the basis of variational principles for a large class of problems.
Abstract: Equations are derived for the viscosity, ordinary (pressure) diffusion, and thermal diffusion of multicomponent mixtures of gases. The ordinary diffusion velocities are expressed in terms of the usual diffusion coefficients for binary mixtures. The analysis is an extension of the work of Chapman and Cowling. It is shown that the Chapman‐Cowling and Enskog procedure can be justified on the basis of a variational principle. This variational principle should be generally applicable to a large class of problems.
TL;DR: In this article, the rate constants for competitive reactions of isotopic molecules are considered from the theory of ''absolute rates'' and the collision theory, and the conditions for the rate constant of the heavy molecule to exceed that of the light one are formulated.
Abstract: The rate constants for competitive reactions of isotopic molecules are considered from the theory of ``absolute rates'' and the collision theory. Formulas are derived for the ratio of the rate constants and the difference in the activation energies for reactions of isotopic molecules. The difficulties in the a priori calculation of relative rates are pointed out and discussed.In general the rate constant for the light molecule will be greater than that of the heavy molecule. It is shown that the maximum ratio in the rates occurs when the isotopic atom is essentially free in the activated complex. The conditions for the rate constant of the heavy molecule to exceed that of the light one are formulated.It is shown that the difference in activation energies covers the range from zero to the difference in the differences in the zero‐point energies of the reacting molecules and their respective activated complexes.
TL;DR: In this article, a method of setting up the vibrational secular equation for polyatomic molecules of ''Urey-Bradley field'' type is described, and 102 fundamental frequencies calculated using 28 distinct force constants are in satisfactory agreement with the observed, with a mean deviation of 1.4 percent.
Abstract: A method of setting up the vibrational secular equation for polyatomic molecules of ``Urey‐Bradley field'' type is described. By this method the vibration frequencies of CCl4, CBr4, CH4, CD4, CCl3Br, CCl2Br2, CClBr3, CCl3H, CCl2H2, CClH3, CCl3D, CCl2D2, CClD3, CH3D, CH2D2, and CHD3 molecules have been calculated. The 102 fundamental frequencies calculated using 28 distinct force constants are in satisfactory agreement with the observed, with a mean deviation of 1.4 percent.
TL;DR: In this article, the thermodynamics of an adsorbate on an inert adsorbent are discussed in some detail, and the heat of adsorption is investigated in an attempt to clarify and extend the available methods in this field.
Abstract: The thermodynamics of an adsorbate on an inert adsorbent is discussed in some detail. Heats of adsorption are given particular attention in an attempt to clarify and extend the available methods in this field. It is found that the true equilibrium ΔH=TΔS of adsorption for adsorbate molecules is given by (∂ lnp/∂T)[open phi]=−ΔH/RT2, where [open phi] is the two‐dimensional spreading pressure.The relation of the work of Rowley and Innes to the present paper is considered.
TL;DR: In this paper, a classification of the motions of a crystal is made on the basis of space symmetry, with the aid of the Born-Karman boundary conditions, and the selection rules for fundamentals arising from this classification are the same as those derived by the unit cell analysis of Bhagavantam and Venkatarayudu.
Abstract: A classification of the motions of a crystal is made on the basis of space symmetry, with the aid of the Born‐Karman boundary conditions. It is shown that the selection rules for fundamentals arising from this classification are the same as those derived by the unit cell analysis of Bhagavantam and Venkatarayudu. A relation between the unit cell and site analyses is investigated which makes it possible to obtain the unit cell results by means of the usually simpler site method. A space symmetry criterion for the appearance of composite transitions is established, and some of the effects expected on the basis of this criterion are discussed. The character tables for space groups are described.
TL;DR: In this article, the dipole moments of fulvene and azulene have been calculated theoretically by the LCAO MO method, and have been obtained from experimental data.
Abstract: The dipole moments of fulvene and azulene have been calculated theoretically by the LCAO MO method, and have been obtained from experimental data. The experimental results support the theoretical predictions.
TL;DR: In this paper, the authors compared two approximate methods of calculating equilibrium phase diagrams in ternary systems of polymer and mixed liquids, compared with exact phase diagrams based upon the Flory-Huggins equations.
Abstract: Two approximate methods of calculating equilibrium phase diagrams in ternary systems of polymer and mixed liquids have been compared with exact phase diagrams based upon the Flory‐Huggins equations. Both a ``single liquid approximation'' and a ``complete immiscibility approximation'' are worthless except for the crudest qualitative considerations. Analytical expressions for the plait points of such ternary systems (a maximum of ten) have been derived. A consideration of the solubility of polymers in mixed solvents leads to the conclusion that a polymer may be completely soluble in certain mixtures of non‐solvents if its internal pressure (cohesive energy density) lies between those of the two liquids and if the two liquids are themselves completely miscible. The position of the phase boundary is nearly independent of the molecular weight of the polymer for molecular weights above 10,000. Osmotic pressures in mixed solvents are discussed, and Gee's suggestion that the osmotic pressure is zero at the critical solubility limit is confirmed.
TL;DR: In this paper, a molecular theory of the coefficients of shear and bulk viscosity of monatomic liquids is developed on the basis of the general theory of transport processes presented in the first article of this series.
Abstract: A molecular theory of the coefficients of shear and bulk viscosity of monatomic liquids is developed on the basis of the general theory of transport processes presented in the first article of this series. With the use of the Lennard-Jones potential and a reasonable analytic approximation to the experimental radial distribution function, calculations of the coefficients of shear and bulk viscosity of liquid argon at 89°K have been carried out. The theory leads explicitly to ratios of the coefficients to the friction constant of the theory of Brownian motion. With a preliminary estimate of the friction constant, a value of the shear viscosity of liquid argon in moderately good agreement with experiment is obtained.
TL;DR: In this paper, the infra-red spectrum of crystalline benzene has been studied at −12°C, −65°C and −170°C as well as the liquid at 28°C.
Abstract: The infra‐red spectrum of crystalline benzene has been studied at −12°C, −65°C and −170°C as well as the liquid at 28°C. The lines are extremely sharp, the mean line width for fundamentals being 7 cm−1 in the crystal. In three cases, it is less than the spectral slit width. All out‐of‐plane degenerate modes are split by about 10 cm−1. Selection rules are obeyed and agree with the reported x‐ray structure. All ungerade fundamentals are observed directly, some for the first time. Fifty‐two combination bands are observed. The frequency assignments of Ingold et al. are confirmed except for the B2u species. Evidence is cited for re‐assigning ν14 from 1648 cm−1 to 1310 cm−1 and ν15 from 1110 cm−1 to 1150 cm−1. Ingold's isotopic data does not conflict with this change. Combination frequencies involving torsional lattice modes are apparently observed at −170°C.
TL;DR: In this paper, a method for calculating the elements of the kinetic energy matrix for rotation for any molecule is given, which includes the effects due to any number of linked rotating groups, balanced or unbalanced.
Abstract: A method is given for calculating the elements of the kinetic energy matrix for rotation for any molecule. The treatment includes the effects due to any number of linked rotating groups, balanced or unbalanced. In a simple case these equations reduce to the simpler ones of the two previous papers of this series. This rotational matrix is then converted into the matrix of the internal rotations. The reduced moments of inertia that form the latter are then used with the methods of the previous papers of this series to calculate energy levels and thermodynamic functions.
TL;DR: The distribution of matter within the transition layer between the two phases of a fluid system is considered in this article, where approximate values are obtained for the superficial density of matter Γ, calculated with reference to the Gibbs surface of tension as the dividing surface between the phases.
Abstract: The distribution of matter within the transition layer between the two phases of a fluid system is considered. Approximate values are obtained for the superficial density of matter Γ, calculated with reference to the Gibbs surface of tension as the dividing surface between the phases.
TL;DR: In this article, the failure of certain LCAO molecular orbital calculations of the spectrum of porphine was attributed to the incorrect assumption of complete aromaticity, and a division of the π-electron system into noninteracting parts was supported by the fact that the dynamical properties of the divided system, as calculated by the freeelectron model, are in approximate agreement with experiment.
Abstract: The failure of certain LCAO molecular orbital calculations of the spectrum of porphine is attributed to the incorrect assumption of complete ``aromaticity.'' A division of the π‐electron system into non‐interacting parts is supported by the fact that the dynamical properties of the divided system, as calculated by the free‐electron model, are in approximate agreement with experiment. A proof of the equivalency of the LCAO method (with overlap neglected) and an approximation to the free‐electron method is indicated for certain dynamical systems.
TL;DR: In this article, the theory for computing radial distribution curves has been extended to permit accurate curves to be obtained from scattering data covering only a restricted range of angle, which obviates the necessity for visual examination of the diffraction photographs.
Abstract: A procedure has been developed for the determination of molecular structure by electron diffraction which yields accurate intensity data and obviates the necessity for visual examination of the diffraction photographs. The theory for computing radial distribution curves has been extended to permit accurate curves to be obtained from scattering data covering only a restricted range of angle. From this method, it is possible to obtain not only equilibrium distances but also the probability distributions for the vibrational motion between pairs of atoms in a molecule. The procedure has been applied to CCl4 and CO2 and when comparisons may be made with spectroscopic results, satisfactory agreement is obtained.
TL;DR: In this paper, the Urey Bradley field for various chemical structures, stretching, bending and repulsive force constants were determined so as to give the best fit with the observed vibration frequencies.
Abstract: Assuming the Urey‐Bradley field for various chemical structures, stretching, bending and repulsive force constants were determined so as to give the best fit with the observed vibration frequencies The magnitude of these force constants, especially of repulsive constants, was discussed
TL;DR: In this paper, the authors generalized the Langmuir isotherm for localized unimolecular adsorption on a heterogeneous surface, with and without interactions between adsorbed molecules.
Abstract: The Langmuir isotherm for localized unimolecular adsorption is generalized (using statistical methods) in order to discuss adsorption on a heterogeneous surface, with and without interactions between adsorbed molecules. The configurational entropy, and the nature of the phase changes on a random heterogeneous surface are discussed. In particular, on this type of surface, the theory predicts, at least for one special case, that condensation will occur in two steps (instead of the customary one step) at low enough temperatures.
TL;DR: In this paper, the second moment of the absorption line in a rigid lattice has been used to determine structural parameters from the experimental line shapes of 1.2-dichloroethane.
Abstract: Experimental absorption line shapes at nuclear magnetic resonance are given for several simple assemblies of nuclei, with spin ½, in the solid state at temperatures between 90° and 95°K. Analysis of these data is facilitated by the theory of Van Vleck which relates the second moment of the absorption line in a rigid lattice to nuclear spins, gyromagnetic ratios, and internuclear distances, and which provides, therefore, an objective and general method for determining structural parameters from the experimental line shapes.1,2‐dichloroethane exhibits a proton resonance with line structure characteristic of nuclear magnetic moments interacting in pairs to produce the broadening of the absorption line. Consideration of both fine structure and second moment leads to an inferred H–H distance of 1.71±0.02A in the —CH2Cl group. In conjunction with the expected C–H bond distance of from 1.09A to 1.10A, this implies that the H–C–H bond angle is between 4° 30′ and 9° less than tetrahedral. Absorption line shapes fo...