Volume 28, Issue 5, 01 May 1958
Index of content:
28(1958); http://dx.doi.org/10.1063/1.1744264View Description Hide Description
A new method for the determination of the equilibrium composition of complex mixtures is described. The general method, which is based on the minimization of free energy, states the problem with unusual simplicity, avoiding many of the usual difficulties of description and computation. Two specific computation procedures are shown, one using a steepest descent technique applied to a quadratic fit, the other making use of linear programing.
28(1958); http://dx.doi.org/10.1063/1.1744265View Description Hide Description
On the basis of a rigorous statistical mechanical approach it is shown that the treatments of the configuration of a polyelectrolyte molecule given by Katchalsky and Lifson and by Krieger are equivalent to retaining only the first‐order term of the high temperature expansion of the free energy. Katchalsky's and Lifson's more accurate calculation is exact in the limit of a ``continuous'' chain but the neglected correction terms are shown to be significant. Krieger's approximate expression for the first‐order term is only valid for highly stretched chains and it predicts incorrect results when the interaction potential is appreciable near the origin.
28(1958); http://dx.doi.org/10.1063/1.1744266View Description Hide Description
The absorptionspectrum of single sublimation flakes of anthracene has been redetermined with a view to investigating the b polarized absorption edge. From measurements at room temperature on crystals of known thickness and also from spectra at 77° and 4°K it has been established that the major part of this absorption takes place in a region of about 50 layers below the crystal surface. The crystal energy levels are then split to a much greater extent than in the main body of the crystal, and it is suggested that this occurs because of some slight crystal structure modification. The weaker absorption lines which also occur on the absorption edge are taken to represent transitions in molecules located near or at imperfections.
28(1958); http://dx.doi.org/10.1063/1.1744267View Description Hide Description
The absorption and fluorescence spectra of crystalline pyrene have been measured at room temperature and 77°K. Only the first absorption region could be studied because of crystal thickness but a Davydov splitting of about 18 cm—1 was detected with the apolarization at higher energy than the bpolarization. Calculations of the splitting (dipole‐dipole approximation for the intermolecular potential) give 23 and 13 cm—1, respectively, for the B 2u and B 3u levels with the observed sense, and so it is not possible to decide between two possible assignments from theory. The polarization ratio shows that mixing with a higher level of opposite polarization is present and this is consistent with the only theoretical prediction of energy levels in the molecule.
The fluorescence is displaced to long wavelengths from the absorptionspectrum and is a broad band with a maximum which is further displaced on cooling the crystal. The band has been interpreted as a charge‐transfer transition involving the molecules grouped in pairs in the crystal.
28(1958); http://dx.doi.org/10.1063/1.1744268View Description Hide Description
A model is proposed from which energies of activation and potential energy surfaces of three atom reactions may be calculated. The method makes use of internuclear attractive and repulsive potential functions which have been derived from a quantum mechanical delta‐function model. The energy of activation of the ortho‐para hydrogen reaction was calculated and found to have a value of 8.5 kcal in agreement with the experimental value. The model predicts the presence of a slightly stable H3 complex. This complex, however, is asymmetric, located at a minimum in the potential curve just before the barrier, and is stable by an energy of about 1 kcal.
The method may be classified as semiempirical. However, all parameters used are obtained theoretically from the proposed model. One advantage of the method is that the main points of interest on the potential energy surface may be calculated without calculating a complete potential energy surface.
28(1958); http://dx.doi.org/10.1063/1.1744269View Description Hide Description
28(1958); http://dx.doi.org/10.1063/1.1744270View Description Hide Description
Contrary to previously published values, the characteristic B–C asymmetric stretching mode in trialkylboranes is assigned to the 1116 to 1150 cm—1 range. The basis for the assignment of the various characteristic bond vibrations is the comparison of the infrared spectrum of trimethylborane‐b 10 with the infrared and Raman spectra of isotopically normal trimethylborane. The new values lead to better consistency with spectra of other trialkylboranes and alkyldiboranes.
28(1958); http://dx.doi.org/10.1063/1.1744271View Description Hide Description
The infrared spectra of isotopically normal and triethylborane b 10 are reported, and the major bands are assigned to the characteristic bond vibrations of the molecules. Analogous to trimethylborane, the asymmetric B–C stretching frequency is placed at ca 1120 cm—1. In view of the complexity of the molecule a more complete assignment is not feasible at this time.
28(1958); http://dx.doi.org/10.1063/1.1744272View Description Hide Description
A statistical theory of the excluded volume effect in a polymer molecule is developed, making use of a pearl necklace model with a continuous medium approximation. For the mean square end‐to‐end distance 〈R 2〉 and the mean square radius of gyration 〈S 2〉, the theory leads to the same expressions as Zimm, Stockmayer, and Fixman's. Taking solutions of polystyrene in cyclohexane as an example, it is illustrated that, in the vicinity of the Flory temperature, the expression for 〈S 2〉 enables to give a complete quantitative interpretation to light scattering data. The distribution function for distance Rkl between segments k and l, its 2mth moment 〈Rkl 2m 〉, and the mean square distance 〈Sk 2〉 between segment k and the center of molecular mass are also calculated to make clear the nature of the excluded volume effect. Finally, the influence of the volume effect upon light scatteringmeasurement is discussed somewhat in detail.
28(1958); http://dx.doi.org/10.1063/1.1744273View Description Hide Description
Two methods are described for mass spectrometric determination of the electron affinitiesE(X) of electronegative atoms X. Both methods were used to determine the electron affinity of fluorine, E(F), the best measured value being E(F)=82.1±2.1 kcal/mole. In the first method the ratio of numbers of X‐ negative ions to M+ positive ions emitted from a hot tungsten filament in MX salt vapor is measured. From this the equilibrium constant for the attachment reaction X+e ‐=X‐, and hence E(X), may be calculated. In the second method, the difference in electron affinities,E(Y)‐E(X), is calculated from a measurement of the ratio of numbers of Y‐ to X‐ ions emitted from a hot filament surrounded by X m Y n gas. Measurements were also made for the other halogens; these gave E(Cl)=86.6±2.0 kcal/mole, E(Br)=80.9±1.5 kcal/mole, and E(I)=73.2±1.7 kcal/mole.
28(1958); http://dx.doi.org/10.1063/1.1744274View Description Hide Description
Phosphorescence of toluene has been studied at 4°K and 77°K in its solid phases (crystalline and amorphous) and in solid solution (EPA) at 77°K. The spectrum of the crystal at 4°K (3460‐4530 A) consists of sharp bands, and weaker diffuse bands which resemble in arrangement the rigid glass spectrum at 77°K. This emission has a lifetime of about 8 sec. The spectrum of solid toluene at 77°K (3950‐4900 A) has broad diffuse bands, and an estimated lifetime of ∼10‐2‐10‐3 sec. Its vibrational structure differs from that of the spectra at 4°K and in EPA, but resembles much the structure of the phosphorescence spectrum of benzaldehyde. The origin of the various spectra and the differences between them are discussed. The suggestion is made that benzaldehyde is produced photochemically and that its spectrum appears by a process of sensitization.
28(1958); http://dx.doi.org/10.1063/1.1744275View Description Hide Description
General formulas for the thermodynamic properties of amorphouspolymer phases are obtained from statistical mechanics, with the aid of the lattice model, in a manner which avoids the use of restrictive assumptions concerning the nature of the individual polymer chains.
Certain results, such as prediction of a second‐order transition for systems of semiflexible chains and the Flory‐Huggins formula for the entropy of mixing with monomeric solvent, are thus shown to be independent of the precise nature of the model assumed for the polymer chains.
More complete information may be obtained by application of the general formulas to models descriptive of the molecular chains in question. As an example, the results of Flory for semiflexible linear chains whose stiffness arises exclusively from intramolecular nearest neighbors are obtained as a special case. (The conventional thermodynamic properties of polydisperse systems of chains of this type are shown to depend on the number average molecular weight.)
28(1958); http://dx.doi.org/10.1063/1.1744276View Description Hide Description
The expression : where k′S are the force constants of the bondsAA, AB, and BB of given type and Δ, an ionic contribution term, has been suggested. For single bonds, the value for √Δ corresponds to the difference in the electronegativities of the atoms A and B in their valence states. In the case of multiple bonds the value for √Δ leads to proper value for the percentage ionic character of the bond. Force constant has been shown to be proportional to the product of the strengths of the bond orbitals, the magnitude of a bond orbital in its angular dependence being defined as the strength with value 1 for an s orbital and 1.732 for a p orbital. The value for the sp 3 orbital has been found to be about 2 but for sp 2 and sp orbitals, values differing from those suggested by Pauling have been obtained. Among s—pbonds, digonal bonds have been shown to be the strongest followed by trigonal and tetrahedral bonds. In alkali metals, the bonds have been shown to be s—pbonds with strength 1.732. Force constant has been shown to be linearly related to bond order. Finally, values for the force constants of various covalent bonds have been assigned.
28(1958); http://dx.doi.org/10.1063/1.1744278View Description Hide Description
The optical density of a flame fusion single crystal plate of CaTiO3 is reported. The refractive indices for the visible region are given, with nD = 2.403±0.02. The results of dielectric constant and loss measurements over the temperature range from 90 to 430°K reveal no unusual behavior. A room‐temperature dielectric constant of 190 is reported.
28(1958); http://dx.doi.org/10.1063/1.1744279View Description Hide Description
The preparation and handling of high purity boron tribromide (BBr3) and boron triiodide (BI3) are described. The infrared absorption spectra of BBr3 in the gas, liquid, and CS2‐solution phases and of BI3 in the gas, CS2‐solution, and solid phases at room temperature are presented and analyzed. The observed BI3spectrum is consistent with the expected planar configuration. The hitherto unpublished fundamental vibrational frequencies for BI3 are used along with those for BF3, BCl3, and BBr3 in a uniform force constant calculation based on a modified valence force potential. The fundamental frequencies for these four molecules should prove useful in testing various potential functions and the force constants should be valuable in predicting the vibrational fundamental frequencies in molecules such as BClI2 and BBr2I. The bond stretching force constant for the boron‐iodine bond is 1.95×105 dynes/cm. The boron‐iodine distance in BI3 is discussed and a tentative value of 2.10 A is proposed.
28(1958); http://dx.doi.org/10.1063/1.1744280View Description Hide Description
The internal rotation of hydrogen peroxide molecule is treated on the assumption that the hindering potential is approximately expressed by the two‐term Fourier expansion: . The doublet structure of the infrared absorptionspectrum is considered to be caused by the existence of a double minimum in the hindering potential. The available experimental data on the microwave spectra and on the infrared combination bands yield the result of V 1=244 cm—1 (700 cal/mole) and V 2=319 cm—1 (910 cal/mole). Thus it is concluded that the cis barrier (452 cm—1 or 1290 cal/mole) is definitely higher than the trans one (208 cm—1 or 590 cal/mole).
28(1958); http://dx.doi.org/10.1063/1.1744281View Description Hide Description
The statistical mechanical theory of solutions is applied to reaction kinetics and the effect on reaction order is calculated. It is found that the rate constant is multiplied by an exponential function of the concentration of addend, solvent, product, or reactant. The theory is then applied to data obtained by Ingold and others from studies of nucleophilic substitution on saturated carbon atoms. The exponential dependence predicted by theory is observed.
28(1958); http://dx.doi.org/10.1063/1.1744282View Description Hide Description
The intensity of the low fundamental of C2F6 at 219 cm—1 was measured using a CsI prism. This completed earlier studies on the other fundamentals, and permits extension and revision of the interpretation. Effective bond moments are compared with those of other fluorocarbons.
28(1958); http://dx.doi.org/10.1063/1.1744283View Description Hide Description
Two new photonuclear reactions are reported, Br79(γ,2n)Br77 and Br79(γ,3n)Br76.
The organic retention following the Br81(γ,n)Br80m reaction in liquidn‐ and isopropyl bromides was found to be 47 and 36%, respectively, appreciably higher than reported values following the Br79(n,γ)Br80m reaction. Higher retentions were also noted for irradiations of the solid bromides. The relative yields of individual organic products were determined for irradiations of both liquid and solid and were in many respects in striking agreement with data from activation by (n,γ) reaction and isomeric transition. In solidn‐propyl bromide the (γ,n) and (γ,3n) reactions gave the same ratio of parent compound to total organic yield.
Data on the scavenger effect show that thermal recombination reactions occur in both liquid and solid. Marked increases are shown in the thermal organic yield with only slight increases in the nonthermal retention for both bromides for (γ,n) compared to (n,γ) activation. The reasons for these increases are discussed.
In general, the data indicate that elastic collision mechanisms are unimportant compared to random fragmentation as an explanation of the results.