Volume 30, Issue 3, 01 March 1959

Kinetics of the Thermal Decomposition of Dimethylmercury. I. Cyclopentane Inhibition
View Description Hide DescriptionThe kinetics of the pyrolysis of gaseous dimethylmercury have been studied in the presence and absence of cyclopentane inhibitor from 290–375°C for the inhibited and 265–350°C for the uninhibited reactions. The decomposition in excess cyclopentane is first order, with methane the major product (accounting for >95% of the carbon).Rate constants are dependent upon the ratio of dimethylmercury (DMM) to cyclopentane and upon total pressure. The constant for DMM loss is: k_{D} =1.1×10^{15} exp(—55 900/RT) sec^{—1}. The rate constant (from combined data on DMM loss and CH_{4} formation) extrapolated to the fully inhibited, high‐pressure limit is: k _{1}=5.0×10^{15} exp(—57 900/RT) sec^{—1}.
The data for the uninhibited decomposition agree with the literature; a partial mechanism is suggested which predicts the transition from chain to nonchain behavior with increasing temperature.
For the inhibited reaction the following mechanism is proposed: (1) Hg(CH_{3})_{2}→HgCH_{3}+CH_{3}, (2) HgCH_{3}→Hg+CH_{3}, (3) CH_{3}+Hg(CH_{3})_{2}→CH_{4}+CH_{3}HgCH_{2}, (4) CH_{3}+C_{5}H_{10}→CH_{4}+C_{5}H_{9}, (5) CH_{3}+Hg(CH_{3})_{2}→C_{2}H_{6}+HgCH_{3}, (6) 2 CH_{3}→C_{2}H_{6}, (7) CH_{3}HgCH_{2}→HgCH_{3}+CH_{2}.
Using the present value of E _{1}=57.9±1.4 kcal/mole in conjunction with known thermochemical data, E _{2}=0±3 kcal/mole. From the inhibition data, k _{3}/k _{4}=0.7±0.2 at 300°C, with a very small temperature coefficient. The inert gas pressure effect is evidence for the unimolecular nature of step (1).

Kinetics of the Thermal Decomposition of Dimethylmercury. II. Carbon‐13 Isotope Effect
View Description Hide DescriptionThe C^{13}kinetic isotope effect in the pyrolysis of gaseous dimethylmercury has been studied in the presence and absence of cyclopentane inhibitor from 290–375°C for the inhibited and 290–350°C for the uninhibited reactions. The isotopic fractionation factor (S) is defined as the ratio of rate constants for the decomposition of Hg(C^{12}H_{3})_{2} vs C^{12}H_{3}HgC^{13}H_{3}. S shows a strong dependence upon the degree of inhibition of the methyl radical chain, which, in turn, is a function of the ratio of cyclopentane to dimethylmercury. S is also a function of the total pressure.
The dependence of S upon the degree of inhibition agrees quantitatively with the predictions of the mechanism proposed in I. The pressure effect on the isotope effect is attributed to the unimolecular nature of the rate determining step (Hg–C bond rupture) and is consistent with the over‐all kinetics.
The isotope rate factor in the fully inhibited high‐pressure limit, α, is 1.034±0.002 (essentially independent of temperature over the range studied), compared to a value of 1.011±0.001 for the uninhibited (chain) decomposition.

Superposition of Configurations and Natural Spin Orbitals. Applications to the He Problem
View Description Hide DescriptionThe method of superposition of configurations is examined in its application to the helium atom in two cases: a 21×21 matrix including all configurations up to 〈6s〉^{2}, and a 20×20 matrix with all configurations up to the 4‐quantum level, including angular terms. A new radial limit is established at −2.87900±0.00003, and this is used to discuss the convergence of such expansions in Legendie functions. The variation with scale factor is discussed in detail. The wave functions are analyzed in terms of natural spin orbitals (NSO's), which seem to have many advantages. The first NSO bears a striking resemblance to the Hartree‐Fock function, and the first two together provide a close approximation to the solution of the extended Hartree‐Fock equations with different orbitals for different electrons. An energy of −2.877924 is obtained for the best (u, v) function found. An analysis of the results suggests that inner orbitals may be better represented by pure exponentials than by Hartree‐Fock orbitals whenever additional correlational degrees of freedom are permitted. Expressed in approximate NSO form, the wave function is almost invariant to choice of basis set, provided that the latter is reasonably chosen. In particular, the necessity of including continuum terms along with the discrete hydrogen‐like set is demonstrated.

Single‐Center Expansions for One‐Electron Systems. H_{2} ^{+}
View Description Hide DescriptionThe expansion of the H_{2} ^{+}wave function in terms of the set of associated Laguerre functions of order (2l+2) based on a single point in space, the molecular midpoint, is studied by the usual variational approach. In particular, the convergence of the expansion is studied as a function of the number and type of basis functions used, the respective scaling parameters, and the internuclear distance. A peculiar behavior with respect to the scaling parameter, in which, for example, for certain optimum choices of the scale parameter for one group of basis functions no improvement is observed upon the addition of one more such function, is proved to occur generally for these functions with one‐electron Hamiltonians. This behavior emphasizes the necessity for treating such scale factors as mathematical parameters rather than as constants to be chosen by physical intuition. This single‐center expansion is concluded to be only slowly convergent and therefore, the authors feel, likely to have relatively limited use for quantitatively accurate calculations on more complex problems. Such expansions may, however, be useful for certain classes of excited states.

New Method for the Statistical Computation of Polymer Dimensions
View Description Hide DescriptionA new method is described for the generation of excluded volume random walks of contour lengths comparable to those of real polymer molecules. This work was carried out with a high‐speed electronic digital computer. An essential feature of the method is an unbiased sample enrichment process used to counteract the attrition resulting from chain intersections. Using the new method, samples were generated for chains of 800 links, a limit imposed by machine storage capacity. In principle the method could be carried even further if more storage were available.
Mean‐square end‐to‐end lengths of the chains are expressed by the equationwhere n equals the number of links and a and b are constants.

Statistical Computation of Radii of Gyration and Mean Internal Dimensions of Polymer Molecules
View Description Hide DescriptionA Monte Carlo numerical method has been employed for the computation of the mean‐square separation between pairs of elements i and j, 〈R_{ij} ^{2}〉, and the mean‐square radius of gyration, 〈S_{n} ^{2}〉, for an n‐segment coiling type polymer molecule. A restricted random walk was used as a model for the polymer, and the average dimensions in question were calculated for random samples of nonintersecting walks generated by means of a high‐speed digital computer. 〈R_{ij} ^{2}〉 has been found to be a rather complicated function of i/n and j/n, depending upon the position in the chain as well as upon the contour length of the segment between i and j. The mean‐square radius of gyration was found to be proportional to the average square end‐to‐end distance, as for simple unrestricted random walks, but the constant of proportionality differs from the value of ⅙ which is applicable in the absence of the excluded volume effect. The exact value of the ratio of the two quantities depends upon whether the molecule is constrained to 2 or 3 dimensions.

Elastic and Inelastic Scattering of Low‐Velocity Ions: Ne^{+} in A, A^{+} in Ne, and A^{+} in A
View Description Hide DescriptionElastic and charge‐exchange cross sections have been measured in the energy range 4 to 400 ev for Ne^{+} in A, A^{+} in Ne, and A^{+} in A. Charge exchange was observed only for A^{+} in A. No evidence was found for the existence of the diatomic ion NeA^{+}. Constants for empirical potential functions have been evaluated and the functions tabulated.

Thermal Conductivity of Water at High Pressures
View Description Hide DescriptionThe thermal conductivity of water has been measured between 30° and 140°C at pressures ranging up to 8000 kg/cm^{2} using Bridgman's concentric cylinder technique. At atmospheric pressure, the values obtained are about 1% less than the most probable values estimated by Powell. At higher pressures, the values agree well with Bridgman's measurements where the data overlap. The results are discussed in terms of Hall's two fluid model of water.

Optical Activity in Absorbing Media
View Description Hide DescriptionCertain dispersion formulas, relating the ellipticity and molecular rotation of optically active solutions, are derived. These are analogous to the Kramers‐Kronig transform relations between the absorption and refractive indices. Some discussion is offered of the factors influencing the respective shapes of absorption and ellipticity curves.

Molecular Configurations of Vinyl Polymers with Strictly Regular Structures and Their Mean Dimensions and Electric Moments in Dilute Solutions
View Description Hide DescriptionNeglecting the long‐range interaction between segments, general expressions for the mean dimensions and the electric moments of isotactic and syndyotactic vinyl polymers in dilute solutions are derived. For the comparison with experimental results, the following expression is employed for the potential energy of the hindered rotation around C–C links of a skeletal chain:where θ is a twisted angle from the trans position with θ_{0} as the most probable one, and E _{0} is the maximum height of the potential energy. For simplicity numerical calculations of the electric moments are restricted to vinyl polymers in which the direction of the electric moment vector of each substituted group coincides with one of four symmetry axes of tetrahedral model of carbon atom.
For isotactic polymers three cases are examined. The first: all C–C links are twisted in the same manner. The second: consecutive two C–C links are twisted to inverse directions to each other. The third: potential energies of the hindered rotation around C–C links have their minima at the same angles as in crystalline state. From consideration of the minimum distance between two adjacent substituted groups, it is concluded that, if the molecular dimension of isotactic polystyrene is not far apart from that of atactic polystyrene, the deformation of the second type would be less probable. When taken into account the collisions between different parts of the polymer molecule, the deformation of the third type or the other similar to it may be most probable. In this case when 〈R ^{2}〉/nb ^{2} is taken to be 12∼13, then 〈u ^{2}〉/Nu _{0} ^{2} should become 1.5∼1.7, N=n/2 being degree of polymerization. For syndyotactic polymers, two unknown parameters involved in the theory may be uniquely determined by measuring 〈R ^{2}〉/nb ^{2} and 〈u ^{2}〉/Nu _{0} ^{2}.

Electronic Structure of Nitric Oxide
View Description Hide DescriptionThe self‐consistent field (SCF) molecular orbitals for nitric oxide have been calculated in the linear‐combination‐of‐atomic‐orbitals molecular orbital approximation (LCAO‐MO) using 1s, 2s, and 2p Slater atomic functions. Three different calculations have been made.
(1) An ``incomplete treatment'' in which mixing between the inner orbitals, which contain only 1s functions, and outer orbitals, which contain orthogonalized 2s and 2p functions, is neglected.
(2) A similar calculation, but here the outer orbitals are forced to be orthogonal to the inner orbitals.
(3) The ``complete treatment'' in which all orbitals are combinations of 1s, 2s, and 2p functions. The single Slater determinant wave function built from the orbitals calculated from the complete treatment gives a negative binding energy, but a limited configuration interaction calculation accounts for 26% of the observed binding energy. The agreement between the calculated and observed first ionization potential is very good. Certain aspects of the uv spectra seem to be reasonably well explained from this calculation. The dipole moment is calculated to be 0.5 D (N^{‐}O^{+}) as compared to an observed value of 0.16 D with undetermined sign. Following Mulliken, atomic and overlap populations have been calculated.

General Approach to the Study of Electrical Conductance and Its Relation to Mass Transport Phenomena
View Description Hide DescriptionA method of writing phenomenological equations for the description of electrical and mass transport, based on approaches of Onsager and of Klemm, is shown to give rise to a set of coefficients defined in a particularly useful and economical way. Conceptually akin to friction coefficients, these quantities are shown to tie together the results of such very different measurements as electrical conductance, transference numbers, and diffusion coefficients in such a way that a single type of physical concept can be applied in interpreting the results of all three. The characteristics of the phenomenological friction coefficients are examined for three different classes of electrolyte:electrolyticsolutions, ionic crystals, and molten salts. Known limiting relations, such as the Nernst‐Einstein relation, are shown to follow from the macroscopic treatment in cases where they are experimentally valid. In certain cases it is shown how the macroscopic treatment can be made more consistent with a microscopic model through alternative selection of the entities to be taken as components. Some macroscopic criteria are offered as bases for such selection in cases where more than one possibility seems reasonable.

Molecule Formation in the Inert Gases
View Description Hide DescriptionThe Schrödinger energy eigenvalue equation for the relative motion of two inert gas atoms is solved approximately by fitting a Morse interatomic potential to the generally accepted Lennard‐Jones 12–6 interatomic potential. A condition for binding is derived involving the phenomenological parameters present in the 12–6 potential; from the empirical values of these parameters one can then conclude that all the inert gases, except helium, do form stable diatomic molecules. A qualitative argument is presented showing that an hexatomic helium molecule may be stable. The vibration‐rotation energy spectrum of the stable inert gas diatomic molecule is discussed. Finally, the partition function for the diatomic molecule is evaluated in an approximate way, whence, using the standard form for the equilibrium constant in terms of partition functions, it follows that at reasonable values of temperature and pressure several percent of the atoms are associated in the form of diatomic molecules.

Irradiation Effects in Simple Organic Solids
View Description Hide DescriptionThe color centers and free radicals produced in irradiated solid alcohols, ketones, ethers, and other compounds have been examined experimentally by means of optical absorption and EPRspectroscopy to obtain information regarding the products of ionization and the associated electronic processes. At liquid nitrogen temperature these products of electron or x‐ray bombardment are stable; however, the color centers are photosensitive and can be bleached both optically and thermally. The alcohols also show an increase in absorption near the characteristic uv bands. Removing the visible color centers increases the EPR hfs, but bleaching in the uv band markedly reduces or changes the hfs. In methanol and ethanol, free radicals are formed with good efficiency requiring about 18 and 12 ev per radical, respectively. Saturation concentrations of 2×10^{19} and 9×10^{19} spins per cc were produced in acetone and methanol, respectively. The hfs of ethanol and methanol indicate an alkyl hydrogen is missing from the radicals produced by irradiating these materials. No sign of the atomic hydrogen doublet was observed at liquid nitrogen temperature. Support for the α—β hypothesis was found in the hfs displayed by the irradiated alcohols, paraffins, ketones, and ethers.

Diffusion and Viscosity in a Spherical Cavity
View Description Hide DescriptionA system consisting of two, in principle concentric, spherical surfaces separated by a fluid, is considered. The torque and force required to rotate and translate the inner sphere is calculated, as well as the work necessary to maintain fluid flow around it, the flowpattern at the outer sphere being specified. Using this, general expressions for the diffusion constants for rotation and translation for the inner sphere and for the effective viscosity of the bulk liquid are obtained. The inner sphere (a) can be viscous, its surface may slip or adsorb fluid. The effect of a perturbation in the flowpattern at the outer surface (R) is examined. For a small value of a/R, the expressions become those given by Stokes and Einstein for dilute solutions.
For the ratio a/R≈1, the expressions apply to liquids flowing through membranes or porous media. Rotational diffusion of paramagnetic hydrates in diamagnetic environment, translational diffusion of ions through membranes, the viscosity of concentrated suspensions and fluid flow through porous media are discussed.

Electron Coupling of Nuclear Spins. II. Molecular Orbital Interpretation of Coupling Constants Observed in Fluorobenzenes
View Description Hide DescriptionThe H–H, H–F, and F–F coupling constants and relative signs determined previously in high resolution NMR experiments are considered in terms of molecular orbital theory. The data, including the dependence of the coupling upon the relative positions of the atoms in the benzene ring, are sufficient to indicate which of the various interactions contribute most to the coupling. In general, the largest contribution is that carried by s electrons through the Fermi contact interaction. However, there are significant one‐electron terms. The H–F and F–F coupling constants suggest that there is about 5% fluorine 2s character in the C–F bond.

Curve‐Matching Method for Quasi‐Unimolecular Reactions
View Description Hide DescriptionA graphical method is presented for evaluating the high‐pressure limiting rate, the low‐pressure limiting rate, and the parabolic exponent from data on quasi‐unimolecular reactions. A logarithmic plot of k _{1} against k _{2}, the apparent first‐order and second‐order rate constants, is matched against a family of theoretical curves. Computations for plotting the theoretical curves are tabulated. The technique is illustrated with data from the literature on cyclopropane and other cyclic molecules, nitrogen pentoxide, and nitrous oxide.

Destruction of Metastable Helium Atoms in Binary Collisions
View Description Hide DescriptionA calculation of the cross section for the reaction He′+He′=He+He^{+}+e (destruction of the metastable 2^{3} S state by ionization) has been performed by means of the perturbed stationary state method. The cross section obtained is of the order of magnitude 10^{—18} cm^{2} at room temperature and increases slowly with decreasing kinetic energy of the colliding particles. The magnitude of the cross section fits well with a tentative scheme which considers processes of the type A′+B=A+B ^{+}+e as being intermediate between true resonance collisions and nonresonance collisions. It disagrees by 4 orders of magnitude with experimental findings [A. V. Phelps and J. P. Molnar, Phys. Rev. 89, 1202 (1953)]. The reason for this discrepancy is not known.

Unimolecular Decomposition of Chemically Activated sec‐Butyl Radicals from H Atoms plus cis‐Butene‐2
View Description Hide DescriptionChemically activated sec‐butyl radicals have been produced at temperatures between —103° and 25°C by reaction of H atoms with cis‐butene‐2. H atoms were allowed to effuse through a molecular slit into a spherical reactor containing olefine at low pressure. The system resembles the Polanyi diffusionflame, and some solutions for the radial distribution functions of the species involved are given. Disproportionation‐recombination ratios for sec‐butyl radicals, and for methyl plus butyl radicals, were measured as 0.94 and 0.30 respectively. The ratios of stabilization vs decomposition by C–C rupture for the energized butyl radicals were measured as a function of pressure and temperature. Hydrogen and helium were also used as inert gases. k_{a} the observed rate constant for decomposition is ∼10^{7} sec^{—1}. The energized butyl radicals are closely monoenergetic. The unimolecular decomposition behavior is compared with theory wherein expressions due to Marcus are employed. All vibrational degrees of freedom may be taken as active.

Mobility of Molecules in Liquids near the Glass Temperature
View Description Hide DescriptionA theory for the molecular motion in liquids is formulated. It treats the system as a series of molecular shells bound elastically to each other and to a central molecule. The vibrations of this system are analyzed approximately in an effort to find the probability that the central molecule will be left in a hole large enough so it can move to a new position. It is found that the jump frequency of the molecules obeys an equation of the form exp (—E/kT) at high temperatures but conforms to the WLF equation at low temperatures. The anomalous behavior of liquids near the glass temperature is shown to result from the fact that a great deal of cooperation among adjacent molecules must occur if a molecule is to move at low temperatures. The molecular parameters needed to fit the experimental data available are found to be of reasonable magnitude. The influence of various factors such as molecular size, weight and attraction are also discussed. It is concluded that the glass transition is similar in high and low molecular weight substances and is not a property peculiar to macromolecules.