Showing papers in "Journal of Chemical Physics in 1945"
TL;DR: The first and second papers in this series, which make it possible to interpret entropy data in terms of a physical picture, are applied to binary solutions, and equations are derived relating energy and volume changes when a solution is formed to the entropy change for the process as discussed by the authors.
Abstract: The ideas of the first and second papers in this series, which make it possible to interpret entropy data in terms of a physical picture, are applied to binary solutions, and equations are derived relating energy and volume changes when a solution is formed to the entropy change for the process. These equations are tested against data obtained by various authors on mixtures of normal liquids, and on solutions of non‐polar gases in normal solvents. Good general agreement is found, and it is concluded that in such solutions the physical picture of molecules moving in a ``normal'' manner in each others' force fields is adequate. As would be expected, permanent gases, when dissolved in normal liquids, loosen the forces on neighboring solvent molecules producing a solvent reaction which increases the partial molal entropy of the solute.Entropies of vaporization from aqueous solutions diverge strikingly from the normal behavior established for non‐aqueous solutions. The nature of the deviations found for non‐polar solutes in water, together with the large effect of temperature upon them, leads to the idea that the water forms frozen patches or microscopic icebergs around such solute molecules, the extent of the iceberg increasing with the size of the solute molecule. Such icebergs are apparently formed also about the non‐polar parts of the molecules of polar substances such as alcohols and amines dissolved in water, in agreement with Butler's observation that the increasing insolubility of large non‐polar molecules is an entropy effect. The entropies of hydration of ions are discussed from the same point of view, and the conclusion is reached that ions, to an extent which depends on their sizes and charges, may cause a breaking down of water structure as well as a freezing or saturation of the water nearest them. Various phenomena recorded in the literature are interpreted in these terms. The influence of temperature on certain salting‐out coefficients is interpreted in terms of entropy changes. It appears that the salting‐out phenomenon is at least partly a structural effect. It is suggested that structural influences modify the distribution of ions in an electrolytesolution, and reasons are given for postulating the existence of a super‐lattice structure in solutions of LaCl3 and of EuCl3. An example is given of a possible additional influence of structural factors upon reacting tendencies in aqueous solutions.
2,572 citations
TL;DR: In this article, it was shown that for one component systems, this is a special case of a more general relation permitting the calculation of the distribution functions (and therefore the thermodynamic functions) for one fugacity set from those at another set.
Abstract: Distribution functions, Fn(z, {n}), for multicomponent systems are defined proportional to the probability density that n molecules in an infinite isothermal system of fugacity set z will occupy the configurational coordinates symbolized by {n}. All thermodynamic functions may be obtained as certain sums of integrals of these distribution functions. These sums are always convergent, but impractically slow in convergence for numerical use without further transformation. In particular, the grand‐partition function, exp [VP(z)/kT], may be expanded in a power series in the fugacities z with coefficients given by integrals of the distribution functions Fn(0, {n}) at the fugacity set 0. As has been previously demonstrated for one component systems, this is shown to be a special case of a more general relation permitting the calculation of the distribution functions (and therefore the thermodynamic functions) for one fugacity set from those at another set. The function —kT ln Fn(z, {n}) is the potential of avera...
1,637 citations
TL;DR: The principle of corresponding states in modern form has been applied to the following properties: the critical state, the virial coefficient, the Boyle point, the densities of coexistent phases, the vapor pressure of the liquid, the entropies of evaporation and of fusion, the coefficient of thermal expansion of liquid and the triple point temperature and pressure, the heat capacity of liquid, and the surface tension of liquid as mentioned in this paper.
Abstract: The principle of corresponding states in modern form has been applied to the following properties: the critical state, the virial coefficient, the Boyle point, the densities of coexistent phases, the vapor pressure of the liquid, the entropies of evaporation and of fusion, the coefficient of thermal expansion of the liquid, the triple‐point temperature and pressure, the heat capacity of the liquid, and the surface tension of the liquid It has been shown that argon, krypton, xenon, and with less accuracy neon, follow the principle with respect to all these properties It has further been shown that nitrogen, oxygen, carbon monoxide, and methane follow the principle with fair accuracy as vapors and as liquids, but not as solids The relations between surface tension, temperature, and densities have been analyzed empirically For the ``ideal'' substances under consideration Katayama's modification of Eotvos' relation holds good, but McLeod's relation does not; in the relation γ∝ (ρl—ρc)s, the exponent s is
1,056 citations
TL;DR: The instantaneous distribution of chain compositions and chain lengths in vinyl copolymers is obtained in a simple form valid for long chains as mentioned in this paper, with a standard deviation which can be calculated from experimentally observable quantities.
Abstract: The instantaneous distribution of chain compositions and chain lengths in vinyl copolymers is obtained in a simple form valid for long chains. The compositions of chains of a given length are normally distributed about the mean value, with a standard deviation which can be calculated from experimentally observable quantities. The distribution of chain lengths intimately resembles that for simple polymers.
228 citations
TL;DR: In this article, a general molecular theory describing the behavior of matter under stress is discussed and related to previous investigations and to experimental observations, where results on relaxation and creep of rubbers are interpreted in terms of modern structural concepts.
Abstract: Actual substances exhibit a very complicated behavior under mechanical stresses which cannot be described by classical elasticity theory nor by the classical theory of the hydrodynamics of viscous fluids. A general molecular theory describing the behavior of matter under stress is discussed and related to previous investigations and to experimental observations. Particular attention is devoted to rubberlike substances for which the classical theories are definitely inadequate. Experimental results on relaxation and creep of rubbers are interpreted in terms of modern structural concepts. It is found that these substances exhibit three regions of stress‐temperature‐time dependence. At intermediate temperatures there exists a region of relative stability in which the statistical‐thermodynamic theory of rubber elasticity is valid. At elevated temperatures relaxation and creep are caused by chemical changes involving the rupture and formation of primary valence bonds. These chemical changes, which are responsible for the aging of rubber, can be isolated and studied by appropriate experimental techniques. At low temperatures relaxation and creep are caused by the slipping of secondary interchain bonds which are breaking and reforming in times comparable to experimental times of measurement. Theories are advanced to explain the observed stress‐temperature‐time behavior of rubbers over the entire temperature range studied.
184 citations
TL;DR: In this article, a comparison between theory and experiment in dilute solutions reveals a large discrepancy between the calculated and the observed departures from the ideal entropy of dilution, and the assumption of random occupancy of lattice sites by polymer segments, which is employed in previous treatments, is at fault.
Abstract: Whereas extensive efforts have been directed recently toward improving the mathematical exactness of the statistical mechanical theory of polymer solutions, fundamental limitations set by the nature of the physical approximations have not received adequate attention. A careful comparison between theory and experiment in dilute solutions reveals a large discrepancy between the calculated and the observed departures from the ideal entropy of dilution. The assumption of random occupancy of lattice sites by polymer segments, which is employed in previous treatments, is at fault. In very dilute solutions of high polymers the solution is microscopically discontinuous. Two regions of the volume can be distinguished: one is totally unoccupied by segments of polymer molecules; the other consists of regions encompassed by the irregularly coiled polymer molecules. In the latter the concentration of lattice cells occupied by polymer segments is determined by the configuration of the polymer molecule, being independen...
109 citations
TL;DR: In this article, a molecular theory of the scattering of light by fluids of isotropic molecules is developed, utilizing recent advances in the statistical mechanics of condensed phases, and the results are shown to be the same in first approximation as those of the continuous theory based on fluctuations originally proposed by Smoluchowski and Einstein.
Abstract: A molecular theory of the scattering of light by fluids of isotropic molecules is developed, utilizing recent advances in the statistical mechanics of condensed phases. The results are shown to be the same in first approximation as those of the continuous theory based on fluctuations originally proposed by Smoluchowski and Einstein. Higher approximations of the molecular theory are especially applicable to the study of critical opalescence and fluids consisting of very large molecules.
106 citations
TL;DR: In this article, the theory of Flory and Huggins for the free energy of mixing a homogeneous chain polymer of uniform molecular weight with a single uniform solvent was extended to the case of a polymer mixture of varying chain lengths with a mixture of solvents.
Abstract: The theories of Flory and Huggins for the free energy of mixing of a homogeneous chain polymer of uniform molecular weight with a single uniform solvent have been extended to the case of a polymer mixture of varying chain lengths with a mixture of solvents. By making the similar assumptions as those of Huggins, and utilizing familiar statistical mechanical methods, the partial molal free energy of mixing of the solvent is found to be ΔF0¯=RT[ln φ0+(1−φ0)(1–1/mN)+μ(1−φ0)2], where φ0 is the volume fraction of solvent, mN a simple function of the number average molecular weight, and μ a constant characteristic of the polymer‐solvent mixture (consisting largely of a heat term, but also including γ, the coordination number of the rubber segments). By assuming that a mixture of two solvents behaves like a new homogeneous liquid a method of calculating μ for such mixtures is developed. Applications of these formulas to solubility and fractionation are shown in a subsequent article.
105 citations
TL;DR: In this article, the results of the first paper of this series, and a generalization of a method due to Eyring, are used to obtain an expression for the free volume of a liquid, Vf=fb3g3/h3n3×[RT/ΔEv]3, and an equation for the entropy of vaporization.
Abstract: The results of the first paper of this series, and a generalization of a method due to Eyring, are used to obtain an expression for the free volume of a liquid, Vf=fb3g3/h3n3×[RT/ΔEv]3, and an equation for the entropy of vaporization. ΔS=R[ln Vg−lnVl−ln β+3lnβ+3ln(ΔH/RT−1)]. Here β=γfb3g3/h3n3, where γ measures the interference in the liquid with the internal motions (rotations, vibrations) of the molecule, and f, b, g, h, n are quantities which depend on the geometry of the liquid and the energetic and dynamic interaction of the molecules. The rule of Barclay and Butler, that the 25°C value of ΔS for various pure liquids has a rough linear relationship to the corresponding ΔH of vaporization, is shown to imply a general tendency for a liquid to have a smaller β the larger its ΔH of vaporization. In many cases this means a smaller γ, resulting from increased interference with rotation of the molecules in the liquid. Pitzer's perfect liquid has a value β = 16, sensibly independent of ΔH. This is taken to m...
97 citations
90 citations
TL;DR: In this paper, the quasi-chemical method in the investigation of the equilibrium distribution of atoms in the pairs of neighboring sites in a superlattice is generalized by considering groups containing large numbers of sites.
Abstract: The quasi‐chemical method in the investigation of the equilibrium distribution of atoms in the pairs of neighboring sites in a superlattice is generalized by considering groups containing large numbers of sites. The generalized method may be used to obtain successive approximations of the free energy of the crystal. The labor of integration is avoided by the introduction of a Legendre transformation. In order to analyze the fundamental assumption underlying the method more closely, the number of arrangements of the atoms for given long‐distance order is calculated and the hypothesis of the non‐interference of local configurations discussed. The method is applied to the calculation of the free energy in the different approximations discussed in this paper, including Bethe's second approximation and a simple approximation for the face‐centered cubic crystal Cu3Au.
TL;DR: In this paper, the authors proposed the concept of fluctuation entropy, which is a contribution to the entropy of the system, and the name "fluctuation entropy" is proposed for it, including what has been called ''communal entropy'' as well as a term due to the temperature variability of cell sizes.
Abstract: In a system of atoms whose motions are classically excited, the change in entropy in any isothermal process can be written R ln (Vf2/Vf1) per mole, one such term for each kind of atom in the system. The free volume Vf used in this expression is the effective volume accessible to the centers of gravity of the atoms, corrected for fluctuation effects. Corresponding expressions can be written for the classical (translational or rotational) part of the motions of polyatomic molecules in real liquids and solids. In solids the free volume can be written Vf = Nvf, where v is a box, or cage, volume accessible to one particle, and f, the fluctuation factor, has a numerical value which depends on the way in which the box is defined. R ln f is a contribution to the entropy of the system, and the name ``fluctuation entropy'' is proposed for it. The fluctuation entropy includes what has been called ``communal entropy'' as well as a term due to the temperature variability of cell sizes. The free volume in a monatomic c...
TL;DR: In this article, an interpretation of the modified Staudinger rule is offered, which relates the exponent a of the molecular weight to a flexibility parameter p of the chain in a given solvent, varying between zero and one.
Abstract: Expressions for the mean square separation of chain ends and modifications of the formula for an ideal coil are discussed. On the basis of these and of the hydrodynamic theory of intrinsic viscosity, an interpretation of the modified Staudinger rule is offered. It relates the exponent a of the molecular weight to a flexibility parameter p of the chain in a given solvent, varying between zero and one (Eq. (4), (5)). Recent data on polystyrene and on cellulose nitrate are analyzed in greater detail. By means of the frictional ratio f/f0, the sedimentation constant s and the diffusion constant D, respectively, are connected with the degree of polymerization in terms of p (Eq. (9)). The limiting dependence of sedimentation and diffusion rate upon molecular weight for a straight chain and an ideal coil is also found in this manner. A comparison shows satisfactory agreement between values for p found from intrinsic viscosity and those determined from sedimentation or diffusion rates, for certain cellulose ester...
TL;DR: The free energy relations for heterogeneous molecular weight distributions developed in Part I, are applied to problems of solubility and fractionation in this paper, and critical conditions for solubilities are obtained.
Abstract: The free energy relations for heterogeneous molecular weight distributions developed in Part I, are applied to problems of solubility and fractionation. Critical conditions for solubility are obtained. A rigorous expression for the solubility is derived, although certain approximations are made to facilitate calculation, and to permit extension to polymers which are part ``gel.'' Following the same methods the thermodynamic equilibria involved in fractionation are described by mathematical expressions which permit a comparison of the extraction and precipitation methods. The effectiveness of fractionation is shown to be strongly dependent upon concentration.
TL;DR: In this article, the conductance of aqueous solutions of potassium chloride, sodium chloride, and potassium bromide has been determined by the direct-current method at temperatures from 15° to 45°C.
Abstract: The conductance of aqueous solutions of potassium chloride, sodium chloride, and potassium bromide has been redetermined by the direct‐current method at temperatures from 15° to 45°C. It is found that on the whole the present measurements satisfactorily confirm the earlier work reported from this laboratory; however, there were apparently slight errors in the temperature scale at 35° and 45° corresponding to a few hundredth's of a percent in the conductance. Revised values of the conductance, of the limiting ionic conductance and its temperature coefficient, and of the coefficients in the Onsager‐Shedlovsky equation are tabulated.
TL;DR: In this article, x-ray data from crystalline selenium and tellurium and from stretched sulfur (amorphous), polyethylene, polyisobutylene, polyvinyl alcohol and polyphosphonitrile chloride are compared.
Abstract: Published x‐ray data from crystalline selenium and tellurium and from stretched sulfur (amorphous), polyethylene, polyisobutylene, polyvinyl alcohol, polyvinyl chloride, polyvinylidine chloride, polyoxymethylene, polyoxyethylene, polyethylene disulfide, polyethylene tetrasulfide, and polyphosphonitrile chloride are compared. In most cases the experimental identity distance in the direction of the chain axes and the expected interatomic distances and interbond angles are found to be in agreement with the assumption that the chain atoms form a regular spiral, unidirectional in each chain and of uniform pitch. Apparent exceptions are briefly discussed.
TL;DR: In this article, it was shown that, contrary to Mache's model of the progressive extinction of a flame from the burner rim, a combustion zone cannot vanish within a combustible stream and the depth of penetration of the quenching of the explosive reaction by the burner wall is calculated from values of burning velocity and critical boundary velocity gradient for flashback.
Abstract: It is shown that, contrary to Mache's model of the progressive extinction of a flame from the burner rim, a combustion zone cannot vanish within a combustible stream. The depth of penetration of the quenching of the explosive reaction by the burner wall is calculated from values of burning velocity and critical boundary velocity gradient for flashback; it is compared with the limiting distance between plane‐parallel plates and the limiting tube diameter for flame propagation. The thermal expansion of the gas normal and parallel to the combustion zone is discussed. An experimental analysis and discussion of partial entrance of the combustion zone into the burner tube (tilted flame) and partial attachment to the burner rim are given. New data have been obtained on hydrogen and acetylene flames. For instantaneous flashback, the boundary velocity gradients are independent of tube diameter, as expected; these gradients are not a satisfactory criterion for flame stability because flashback can be readily induce...
TL;DR: In this paper, the lower excited energy levels of diphenyl were calculated by the method of antisymmetrized products of molecular orbitals, and the wave functions for diphensyl were constructed from linear combinations of benzene molecular orbital and the perturbation of the original energy levels caused by the presence of the second benzene ring in Diphenyl.
Abstract: The lower excited energy levels of the molecule diphenyl are calculated by the method of antisymmetrized products of molecular orbitals. The wave functions for diphenyl are constructed from linear combinations of benzene molecular orbitals and the perturbation of the original energy levels of benzene caused by the presence of the second benzene ring in diphenyl is computed. The theory predicts the splitting of the two non‐degenerate singlet levels and the one degenerate singlet level of benzene into eight levels, four of which give allowed electronic transitions to the ground state and four of which do not. Experimentally three strong structureless bands are observed, one between λ = 2200A and λ = 2800A, one at about λ = 1900A, and one below λ = 1700A. The calculated spectrum has allowed transitions at about 2400A, 1900A, 1500A, and 1400A, and thus is in good agreement with the experimental observations.
TL;DR: In this article, a quantitative treatment of the effect of cross-linked polymer deswelling is given in terms of the Flory-Rehner theory of the thermodynamic properties of gels, and the flory-Huggins theory of thermodynamics of high polymer solutions.
Abstract: When a cross‐linked polymer initially swelled to its equilibrium volume in pure solvent is transferred to a solution of a high polymer in the same solvent and at the same temperature, the gel deswells. A quantitative treatment of this effect is given in terms of the Flory‐Rehner theory of the thermodynamic properties of gels, and the Flory‐Huggins theory of thermodynamics of high polymer solutions. The extent of deswelling depends on the molecular weight and concentration of the solute, on the solvent‐polymer interactions, and on the degree of cross‐linking in the gel. It thus offers in principle a new method for determination of the number average molecular weight of the solute. Various calculations are presented to show the extent of deswelling under given conditions. Finally, some experimental data is offered to demonstrate determinations of molecular weights, using styrene‐divinyl‐benzene copolymer gels and polystyrene solutions.
TL;DR: The general theory of the adsorption of solutes from solutions which are treated by a process similar to that employed in chromatography is presented in this paper, assuming a chemical equilibrium between adsorbed material and the solution.
Abstract: The general theory of the adsorption of solutes from solutions which are treated by a process similar to that employed in chromatography is presented. By assuming a chemical equilibrium between adsorbed material and the solution, the adsorption equations can be solved explicitly. A detailed discussion of the two‐component problem is given; the many‐component problem and the extension of the theory to more general adsorption isotherms are considered briefly.
TL;DR: In this article, a change of spectral absorption of certain dyes as between water and organic solvents is shown to appear in aqueous solutions of gelatin or of the colloidal detergent, cetyl pyridinium chloride.
Abstract: A characteristic change of spectral absorption of certain dyes as between water and organic solvents is shown to appear in aqueous solutions of gelatin or of the colloidal detergent, cetyl pyridinium chloride. This behavior is attributed to a bilateral character of lamellar micelles of such bodies, the elementary lamellae being polar and hydrophile on one side, non‐polar and organophile on the reverse side. The possibility is indicated of diagnosing such amphipathic characteristics by comparative spectrophotometric measurements with suitable dyes.
TL;DR: In this paper, the turbidity of the solution and the change in index of refraction with concentration of a solution were measured and compared with a comparison between molecular weights measured by this method and other methods.
Abstract: The determination of the molecular weights of large molecules by measuring the turbidity of the solution and the change in index of refraction with concentration is discussed. The apparatus, its calibration, and the technique used are treated together with a comparison between molecular weights measured by this method and other methods. The effect of polymolecularity is also presented.
TL;DR: In this article, the absorption of iodine by cuprous iodide has been studied by means of a quartz microbalance, and the concentration of absorbed iodine varies as the square root of the pressure of iodine vapor in equilibrium with the sample.
Abstract: The absorption of iodine by cuprous iodide has been studied by means of a quartz micro‐balance. At 132.1°C the concentration of absorbed iodine varies as the square root of the pressure of iodine vapor in equilibrium with the sample. The temperature dependence of the the reaction at constant iodine vapor pressure indicates a heat of reaction of 0.24 ev per atom absorbed. The electrical conductivity of cuprous iodide at 132.1°C varies approximately as the 4/3 power of the concentration of the absorbed iodine.
TL;DR: In this paper, a method for obtaining depolarization factors of Raman lines is described in which a 90° split-field Polaroid disk is placed in contact with the window of the Raman tube and is focused upon the slit of the spectrograph by means of a condensing lens.
Abstract: A method for obtaining depolarization factors of Raman lines is described in which a 90°, split‐field Polaroid disk is placed in contact with the window of the Raman tube and is focused upon the slit of the spectrograph by means of a condensing lens. Corrections for real or apparent polarization owing to the spectrograph, reciprocity failure of the plates, and convergence errors are made. The precision of the results was tested by measurements on five different spectrograms of CCl4. The results indicated that the method is equal in precision to the method of Reitz. Intensities were obtained by use of a Gaertner microdensitometer. Depolarization factors for toluene were also obtained. It is shown that, for this method, a reasonable working rule is to regard those Raman lines having observed depolarization factors equal to or greater than 0.78 as depolarized, all others as polarized.
TL;DR: In this paper, the zeta potential of vitreous silica capillaries in contact with three dilute solutions of potassium chloride (10−3, 10−4, 10 −5N) was determined.
Abstract: Improvements in the technique for the determination of the electric potential at the interface between a non‐conducting solid and an aqueous solution of an electrolyte (commonly called the zeta‐potential) have been developed and are described in detail. Zeta‐potentials of vitreous silica capillaries in contact with three dilute solutions of potassium chloride (10−3, 10−4, 10−5N) have been determined. These data have been used for the interpretation of the surface tension data of Jones and Ray by using Langmuir's theory for the thickness of wetting films as a function of the zeta‐potential.
TL;DR: The specific heat of α and γ-manganese were measured in the temperature range 52° to 298°K, with the peak of the ''hump'' occurring about 95°K.
Abstract: The specific heats of α‐ and γ‐manganese were measured in the temperature range 52° to 298°K The specific heat curve of α‐manganese exhibited a small ``hump,'' extending over the temperature range 63°—103°K, with the peak of the ``hump'' occurring about 95°K No anomaly appeared in the specific heat curve of γ‐manganese The computed heat contents and entropies per gram‐atom are as follows: α‐manganese, H°29816—H°0=1193±4 cal, and S°29816=759±004 EU; γ‐manganese, H°29816—H°0=1221±4 cal, and S°29816=772±004 EU
TL;DR: The process of chromatographic adsorption from the kinetic viewpoint was studied in this article, assuming a bimolecular reaction between adsorbent and solute, and the time of passage of the solution through the column is greater than the half-life of the reaction by a factor of at least one hundred.
Abstract: The process of chromatographic adsorption is studied from the kinetic viewpoint, assuming a bimolecular reaction between adsorbent and solute. Boundaries characteristic of equilibrium adsorption are obtained only if the time of passage of the solution through the column is greater than the half‐life of the reaction by a factor of at least one hundred.
TL;DR: In this article, the potential energy of the triatomic isosceles triatomic molecule YX2 was analyzed and the number of force constants reduced to four (c1, c2, c3, c4, and c4) from three experimentally determined fundamental frequencies.
Abstract: In the general expression of the potential energy of the triatomic molecule XYZ there are six force constants c1, c1′ (valence bond), c2 (angle deformation), c3, c3′ (angle bond interaction), and c4 (bond‐bond interaction), of which only three can be calculated from the three experimentally determined fundamental frequencies. For the isosceles triatomic molecule YX2 the number of force constants reduces to four (c1, c2, c3, and c4). From a study of all the real values of these four force constants, it is seen that they are related to one another by ellipses and straight lines. The graphs of these ellipses indicate the possibility of choosing a certain singular point (near one end of the major axis) which gives the following relation between the force constants: dc4/dc2=0 or dc4/dc3=0. This condition and the equations usually obtained from the theory of small vibrations permit the calculation of a singular set of four force constants of the isosceles triatomic molecule. When these force constants are app...