Volume 45, Issue 3, 01 August 1966
Index of content:
45(1966); http://dx.doi.org/10.1063/1.1727677View Description Hide Description
The Pippard equations and the phase diagram for NH4Cl are analyzed in terms of a compressible Ising model. It is demonstrated that the Pippard relations are completely consistent with the occurrence of a first‐order transition in the immediate vicinity of a lambda point. In addition, the substantial variation in the slope of the order—disorder transition line with pressure can be well represented by this Ising model.
45(1966); http://dx.doi.org/10.1063/1.1727678View Description Hide Description
We have calculated the spin—orbit contributions to the zero‐field splitting of the NH radical and found them to be 0.496 cm−1. As this value is over 25% of the experimental ZFS, we conclude that it is not permissible to neglect spin—orbit contributions when calculating ZFS parameters.
Theoretical Depolymerization Kinetics. II. The Effect of Molecular‐Weight Distribution in Degrading Polymers Undergoing End‐Group Initiation45(1966); http://dx.doi.org/10.1063/1.1727679View Description Hide Description
It is shown that the set of coupled rate equations describing the end‐group‐initiated degradation of a polymer containing various degrees of polymerization can be transformed into a set of coupled equations describing the rate of change of the moments of the molecular‐weight distribution. These moment equations can be used as the basis for approximate but systematic treatments of degradation in systems with arbitrary initial molecular‐weight distributions. In particular, in this paper it is shown that if the Schulz—Zimm distribution is assumed to be sufficiently general to represent the molecular‐weight distribution through the course of the degradation, the moment equations allow the problem to be reduced to three simultaneous differential equations. These equations have been solved by digital computer and the sample weight, number‐average molecular weight, and distribution‐width parameter tabulated as functions of time for a wide range of kinetic parameters and initial distributions.
Theoretical Depolymerization Kinetics. III. The Effect of Molecular‐Weight Distribution in Degrading Polymers Undergoing Random‐Scission Initiation45(1966); http://dx.doi.org/10.1063/1.1727680View Description Hide Description
Differential equations describing the rate of change of the moments of the molecular‐weight distribution in the random‐scission‐initiated degradation of a heterodisperse polymer have been derived from the kinetic rate equations. These moment equations are used as the basis of an approximate treatment in which differential equations for the parameters in the Schulz—Zimm distribution are derived. These three equations have been solved by digital computer for a wide range of initial distributions and kinetic parameters. The effect of molecular‐weight distribution on this type of degradation is discussed on the basis of the above equations.
45(1966); http://dx.doi.org/10.1063/1.1727681View Description Hide Description
The reaction of oxygen in the 1Σ g +, 1Δ g , and 3Σ g − states with CO was investigated at temperatures below the point at which heterogeneous reaction is detectable. The excited oxygen was produced photochemically. In spite of moderate partial pressures of excited oxygen (about 0.25 μ), and an extremely sensitive method of analyzing for the product, no evidence of reaction was found. Upper limits for hypothetical bimolecular and termolecular rate constants are reported.
45(1966); http://dx.doi.org/10.1063/1.1727682View Description Hide Description
The matrix formalism previously introduced for the discussion of polymer dynamics is rendered more tractable by the introduction of an explicit operator representation satisfying boson commutation rules. Techniques are devised by which singular functions of segment coordinates may be expanded in a fluctuation series (containing ordered products of boson operators) around an equilibrium or nonequilibrium average. The techniques are here applied to equilibrium excluded‐volume expansions, and are shown to give good results. The detailed numerical results are presented in the following paper. The Gaussian potential is adopted for polymer chains in a theta solvent, but methods for its improvement are considered.
45(1966); http://dx.doi.org/10.1063/1.1727683View Description Hide Description
The operator techniques developed in the preceding paper are here applied to the determination of the intrinsic viscosity as a function of excluded volume and shear rate. The force constants which represent the excluded‐volume interaction are determined, at nonvanishing shear rate, by a criterion of self‐consistency. Numerical results are given for the intrinsic viscosity and the equilibrium expansion of the mean‐square end‐to‐end distance.
Substituent Effects on Chemical Shifts and Spin—Spin Coupling Constants in Trifluorovinyl Derivatives45(1966); http://dx.doi.org/10.1063/1.1727684View Description Hide Description
Examination of the NMRspectra of a variety of trifluorovinyl derivatives of the type CF2=CFY has led to the following correlations between the fluorine NMR parameters and the nature of substituent Y: (1) the chemical shift of the fluorine atom trans to Y and the geminal F–F coupling constant both depend upon the conjugating ability of the group Y, and (2) the chemical shift of the fluorine atom attached to the same carbon as is Y and the cis F–F coupling constant both depend primarily upon the electronegativity of the directly attached atom in substituent Y. The chemical shift of the fluorine cis to Y and the trans coupling constant are not simply related to either of these properties of Y. Although the trans coupling constant is temperature‐independent, the cis and gem coupling constants increase with increasing temperature. Long‐range coupling in a trifluorovinyl thioether compared with that in trifluorovinyl ethers is consistent with d‐orbital participation in bonding of the sulfur atom in the thioether.
45(1966); http://dx.doi.org/10.1063/1.1727685View Description Hide Description
Electron spin resonance spectroscopy was used to study free‐radical formation in single crystals of cysteine HCl exposed to ultraviolet irradiation.Irradiation at 77°K and momentary warming produced the free radical S–CH2–CH(NH3Cl)COOH. Further irradiation at 77°K using longer wavelengths causes a quantitative transformation of the paramagnetic absorption which is attributed to the formation of the radical ion −S–CH2–CH–NH3Cl. The transformation is reversible and, upon warming, the initial radical is reconstituted.
45(1966); http://dx.doi.org/10.1063/1.1727686View Description Hide Description
Nuclear magnetic resonance lines of 7Li nuclei have been observed in solid,polycrystalline samples of LiNH2, LiNH, and Li3N. Protonresonance lines have also been observed in the first two samples. In LiNH2 there is a splitting of the 7Li resonance line due to first‐order quadrupole effects which indicates a coupling constant of 119±4 kHz (estimated limit to maximum error) at room temperature. In Li2NH no quadrupole effects are seen which is in agreement with the fact that the lithium nuclei in this compound are situated in sites of cubic symmetry. In Li3N both first‐ and second‐order quadrupole effects have been observed simultaneously. From these data 7Li coupling constants for Li3N have been found to be 296±4 and 200±10 kHz at room temperature. An unexplained line was also observed at low magnetic fields for this compound. These effects were found to vary with temperature and with the purity of the sample.
45(1966); http://dx.doi.org/10.1063/1.1727687View Description Hide Description
Decays of delayed luminescence in the following mixed crystals were investigated over a wide temperature range above 77°K: phenanthrene in biphenyl, naphthalene‐h 8 in biphenyl, naphthalene‐d 8 in biphenyl, and chrysene in biphenyl. It is shown that the kinetic model proposed by Sternlicht et al. explains results satisfactorily. The relationship τ P =2τ DF was found in the vicinity of the characteristic temperature, which is determined essentially by the energy difference between host triplet and guest triplet states and by the first‐order phosphorescence decay rate. The activation energies for the annihilation process were obtained from the second‐order analysis of decays observed above the characteristic temperature; this analyzing procedure differs from that used by Hirota and Hutchison.
45(1966); http://dx.doi.org/10.1063/1.1727688View Description Hide Description
Using information derived from a combination of effusion and mass‐spectrometric techniques at high temperature, the atomization energies and free energies for the reactionsGe n (gas)=n(Ge gas) (n=2, 3, 4, 5, 6, 7) have been determined. The values of the energy as obtained from the variation of the free energy of atomization with temperature (second law of thermodynamics method) are in kilocalories per mole: they are 65, 149, 238, 321, 407, and 481 for n of 2, 3, 4, 5, 6, 7, respectively. A comparison of these values with the atomization energies as calculated from the third law of thermodynamics (absolute entropy method) assuming that the geometric configuration of the molecules (n>2) is either a linear chain or a cyclic structure indicates that the former structure is to be preferred.
The bond‐dissociation energies (process Ge n =Ge n−1+Ge) as obtained from the second law are 75, 86, 83, 89, 84, and 65 kcal/mole for n of 7, 6, 5, 4, 3, and 2, respectively.
45(1966); http://dx.doi.org/10.1063/1.1727689View Description Hide Description
A three‐parameter potential‐energy function for diatomic molecules proposed by Varshni and Shukla, has been modified to improve its accuracy. The modified function is , where De is the molecular dissociation energy,re is the equilibrium internuclear distance, and , where Δ=½kere 2/De, ke being the force constant. This function appears to be more accurate than previously proposed three‐parameter functions.
Electronic Spectra and Coordination Geometry in Molten Mixtures of CsCl and NiCl2 Containing up to 60 Mole% NiCl245(1966); http://dx.doi.org/10.1063/1.1727690View Description Hide Description
Optical absorptionspectra (5–26 kK) of fused mixtures of CsCl and NiCl2 containing 2–60 mole % NiCl2 were measured at about 860°C and a mixture containing 20 mole % NiCl2 was studied at 560°—862°C. Up to 20 mole % NiCl2 the Bouguer—Beer law was accurately obeyed, and each nickel was tetrahedrally coordinated to four chlorides. At higher NiCl2 contents, nickel coordination was partitioned between tetrahedral and other (unidentified) geometries. The fraction with tetrahedral coordination progressively decreased with increasing NiCl2 content but was still appreciable at 60 mole % NiCl2. The most prominent feature of the spectrum associated with the unidentified geometries was a band between 18 and 19 kK. These results indicate that nickel has very similar coordination geometries in the liquid and crystalline phases of Cs3NiCl5 but very different coordination geometries in crystalline and liquid CsNiCl3.
45(1966); http://dx.doi.org/10.1063/1.1727691View Description Hide Description
Solid hydrogen (normal and para), deuterium, and the systems neon—hydrogen and neon—deuterium were studied by x‐ray diffraction at various temperatures with and without prior plastic deformation. Under most conditions D2 freezes from the liquid phase as hexagonal close packed (hcp) and is stable in this form against plastic deformation; similarly H2 usually freezes in the hcp form. When gold foil with a cube texture is present, D2, normal H2 and para‐H2 freeze in the face‐centered‐cubic (fcc) form. Plastic deformation at about 3° and 4.2° causes the addition of fcc reflections to the hcp diffraction pattern with samples of normal H2 that previously had shown only hcp.
It is concluded that normal H2 is metastable in the hcp structure at these temperatures, and that the spontaneous transformation to cubic on cooling may often be incomplete.
It was found that, in concentrations between 0.25% and 99.5% Ne, Ne and the hydrogens are immiscible.
45(1966); http://dx.doi.org/10.1063/1.1727692View Description Hide Description
The second and fourth moments 〈r 2〉 and 〈r 4〉 of the end‐to‐end distance r of the polyethylene chain of length n are calculated, based on expressions previously derived. The model employed is the familiar three‐state [trans (θ(T)=0°), gauche (θ(G)=120°), and gauche prime (θ(G′)=−120°)] rotational—isomeric model. An approximate expression for the reduced distribution function, which is readily obtainable from 〈r 2〉 and 〈r 4〉, is calculated as a function of the reduced end‐to‐end distance ξ=〈r 2〉* −½ r. Here Wn (r) is the distribution function in the usual sense and(An asterisked quantity denotes the corresponding Gaussian analog.) Approximate expressions for Wn (0)/Wn* (0) and 〈r −1〉/〈r −1〉* are also calculated as functions of n.
For the GG′‐eliminated trans‐preferred chain with reasonable values for parameters, which approximates the polyethylene chain: (i) 〈r 2〉 and 〈r 4〉 are smaller than their respective Gaussian analogs, the deviation being more pronounced with the latter, (ii) the approximate distribution function becomes sharp and somewhat shifted toward ξ=0 compared with the Gaussian distribution, and (iii) as n decreases from infinity, both Wn (0)/Wn* (0) and 〈r −1〉/〈r −1〉* first decrease gradually from unity, then pass through minima, and subsequently increase rapidly, largely exceeding unity. The GG′‐eliminated gauche‐preferred chain behaves like the chain just mentioned above in all respects. For the gauche‐preferred independent‐rotation chain, the opposite trends result for Items (i) and (ii) above; for Item (iii), both quantities monotonously decrease as n decreases. It is shown that for the polyethylene chain, Kuhn's equivalent random chain does not correctly predict (considerably underestimates) the departure from the Gaussian distribution.
45(1966); http://dx.doi.org/10.1063/1.1727693View Description Hide Description
The photolysis of (CH3)2CDCH2CH3, (CH3)2CHCH2CD3, and of equimolar mixtures has been investigated in the presence of NO at 1470 Å (8.4 eV), 1236 Å (10 eV) and at 1048–1067 Å (11.54–11.72 eV). Furthermore, in order to obtain quantitative information concerning the free radicals produced in the fragmentation processes, (CD3)2CDCD2CD3 has been photolyzed at 1236 Å in the presence of various concentrations of H2S.
Fragmentation of the excited isopentane molecule produced at 8.4 or 10 eV, as well as of the superexcited molecule formed at 11.54–11.72 eV, yields mainly olefinic products and the following radicals, in order of decreasing yield: H>CH3>C2H5>C3H7. In addition, on the basis of the various isotopically labeled products, it is concluded that methane, ethane, and propane are split off from the excited isopentane molecule by formation of (a) the corresponding carbene (1,2 elimination), or (b) the corresponding olefin (1,3 elimination). When the energy of the photon is increased from 8.4 to 10.0 eV, the 1,2‐elimination processes become more important relative to the 1,3‐elimination processes in all cases. At 11.54–11.72 eV, the parent ion decomposes to form methane and ethane mainly by a 1,3‐elimination mechanism. It is derived from the results that, in addition to the C4H8 + and C3H6 + ions formed by the latter fragmentation processes, the ions C4H9 + and C3H7 + are produced with ion‐pair yields (M/N) of 0.15 and 0.06, respectively. The ion‐pair yield of the parent ion is estimated to be 0.35. In contrast to observations derived from an earlier investigation of photoionization of n‐butane at 11.54–11.72 eV, an increase in pressure from 0.15 to 15 torr has only a minor effect on the fragmentation of the parent ion.
45(1966); http://dx.doi.org/10.1063/1.1727694View Description Hide Description
A special parallel‐plate microwave spectrometer has been constructed and the effect of deuteration on the dipole moment in the ground vibrational state of seven different molecules has been measured. The molecules studied were: methylacetylene, propane, methyl fluoride, fluoroform, vinylidene fluoride, methylsilane, and methylgermane. With the exception of fluoroform, where an effect of 0.001 D was observed, the magnitude of the isotope effect was found to be of the order of 0.01 D. A simplified interpretation of the isotope effects leads to information about the signs of the dipole moments in these molecules.
45(1966); http://dx.doi.org/10.1063/1.1727695View Description Hide Description
Absolute cross sections for single ionization of the atomic elements have been calculated using the classical method of Gryzinski. They are in good agreement with experimental cross sections. They differ significantly, however, from certain of the values of Otvos and Stevenson.
Polarization of the Lowest‐Energy Allowed Transition of β‐Ionylidene Crotonic Acid and the Electronic Structure of the Polyenes45(1966); http://dx.doi.org/10.1063/1.1727696View Description Hide Description
Polarized specular reflection spectra have been obtained for two faces of the all‐trans β‐ionylidene crotonic acidsingle crystal in the 700‐to‐220‐mμ region. Visual inspection of these results leads to the assignment of the absolute polarization of the lowest allowed transition, which is believed to be the first accurate absolute assignment for a polyene‐related compound. The polarization is confirmed by the integrated intensities of the absorption bands derived through a Kramers—Kronig analysis of the reflection data. The relationship between the experimental polarization and that predicted by various zero‐order theories that have been applied to the polyenes is examined and the effect of refinements in these theories on the direction and magnitude of the transition moment explored.