Volume 41, Issue 10, 15 November 1964

Occupation Probabilities in the Lattice Gas
View Description Hide DescriptionA set of relations obtained by Widom for the probabilities f_{r} that an empty cell is surrounded by r filled cells is rederived and extended. The consequences of the relations for the partition function, the correlation functions, and partially coupled systems are discussed.

Osmotic Flows in Charged Membranes. II. Thermo‐Osmosis
View Description Hide DescriptionThermo‐osmotic flow rates of an electrolyte solution through a porous charged membrane separating two solutions which are at different temperatures but have the same concentration is studied theoretically, using a capillary model for the membrane. The assumptions used are that the Debye‐Hückel approximation is applicable for the ion distribution in the double layer formed near the fixed charges on the capillary wall, and that the thickness of the double layer is much smaller than the capillary radius. The steady‐state solutions of a set of differential equations derived are obtained subject to appropriate external conditions. It is shown that plots for the flow rate of fluid against the logarithm of the concentration of the outer solution give a bell‐shaped curve. This theoretical curve follows well the Carr—Sollner data of the thermo‐osmosis for various electrolyte solutions.
The thermo‐osmosis is an electro‐osmotic flow caused by the electric field which is set up in the membrane so that no net electric charge is allowed to be transported across the membrane. The dependence of the electro‐osmotic coefficient on salt concentration is the primary cause for the characteristic behavior of the thermo‐osmosis in charged membranes. It has been shown in Part I of this series that this effect is also responsible for the anomalous osmosis.

Twinning of Monoclinic Crystals as a Function of Habit Type and Centrosymmetry
View Description Hide DescriptionTwinning in 118 species of monoclinic crystals has been surveyed. Eighty percent of such twinning occurs on planes with a k index of zero. Some of this twinning is mechanical, but most is due to a mechanism, called the SA mechanism, described in this work. It operates only in centrosymmetric crystals and in noncentrosymmetric ones that are pseudo‐orthorhombic. In most cases, SA twinning and mechanical twinning can be distinguished on the basis of the crystal's growth habit. Growth habits of monoclinic crystals can be classified into eight general types, two of which account for 75% of all monoclinic crystals. Precise criteria for pseudosymmetry are suggested.

Photolysis of Nitric Oxide
View Description Hide DescriptionElectronically excited NO (A ^{2}Σ) was produced by irradiation with the 2144‐ and 2265‐Å lines of the cadmium arc at nitric oxide pressures from 20 to 600 mm. The products were nitrogen and nitrogen dioxide. A pressure drop accompanied the reaction equivalent to the nitrogen produced. The mechanism is given. The quantum yield of nitrogen formation was independent of irradiation time and incident intensity. Its falloff with pressure was less than a factor of two, even at 20 mm. These results, when combined with the radiative lifetime measurements of Callear and Smith, show that removal of NO (A ^{2}Σ) occurs on nearly every collision.

Photolysis of Nitric Oxide in the Presence of Olefins
View Description Hide DescriptionElectronically excited nitric oxide (A ^{2}Σ) produced by irradiation with the 2265‐ and 2144‐Å lines of a cadmium arc induces the decomposition of ethylene to acetylene and hydrogen, apparently by a molecular mechanism. The acetylene, which also absorbs the radiation, photolytically reacts with the nitric oxide to give a solid deposit.

On the Connection between the Kinetic Approach and the Correlation‐Function Method for Thermal Transport Coefficients
View Description Hide DescriptionWe demonstrate the complete equivalence between the kinetic approach developed by Prigogine and co‐workers and the correlation function formalism for the calculation of linear thermal transport coefficients. We show that in both cases these transport coefficients are determined by the solution of an inhomogeneous integral equation for a one‐particle distribution function which is the generalization to strongly coupled systems of the Chapman—Enskog first approximation of the Boltzmann equation.

Isotropic Shifts of Some Ionic Complexes of Cobalt(II) and Nickel(II) : Evidence for Ion Pairing
View Description Hide DescriptionIsotropic proton resonance shifts have been observed for the ionic complexes, [Bu_{4}N][φ_{3}P)CoI_{3}] and [Bu_{4}N][φ_{3}P)NiI_{3}]. In addition to the phenyl (φ) proton shifts for the complex anions, isotropic shifts were observed for the cation protons as well. These shifts for the tetra‐n‐butylammonium cations are interpreted as arising solely from a pseudocontact interaction with the metal in the complex anion through partial ion pairing in the deuterochloroform solutions. From the magnitudes of the shifts for the butyl protons, an estimate is made for the relative extent of g‐tensor anisotropies for the two anionic complexes. The observed shifts for the phenyl protons are interpreted as arising from both contact and pseudocontact interactions. Based on the postulate that the unpaired spin will distribute itself in a like manner in a given ligand whether attached to cobalt or nickel, and using the estimate of the relative anisotropies of the two metals, the phenyl proton shifts are separated into their respective contact and pseudocontact contributions. The resulting unpaired spin densities on the phenyl rings compare well with those reported for the related bis(triphenylphosphine) complexes.

Mass‐Spectrometric Study of Ion—Molecule Reactions in Propane
View Description Hide DescriptionIon—molecule reactions in propane have been studied up to pressure of 0.12 Torr inside the ion source of the mass spectrometer. All but four of the propane ions followed the exponential decay law remarkably well and their total cross sections of disappearance have been determined. The major reactions of these ions lead to the formation of C_{3}H_{8} ^{+}, C_{3}H_{7} ^{+}, C_{3}H_{6} ^{+}, and C_{3}H_{5} ^{+} which, with the exception of C_{3}H_{5}, show very low reactivity. The ionic current due to purely secondary ions did not exceed few percent of the total ionic current at the highest pressure attained. The kinetics of most of the ion—molecule reactions occurring in propane have been investigated, and the pertinent cross sections have been determined.

Nuclear Magnetic Resonance Studies Concerning the Effect of Adjacent Hydrogen Atoms on the Hydrogen‐Bond Properties
View Description Hide DescriptionThe proton‐resonance absorptionspectrum has been studied in several hydrogen‐bonded solids with different O–H···O bond lengths ranging from 2.45 to 3.30 Å. The resonancelinewidth increases with the O–H···O bond length and shows a tendency to flatten out when the bond length exceeds 2.72 Å. The proton‐resonance absorptionlinewidth in molecular solids is due primarily to nuclear dipole—dipole interaction, and hence it is proportional to Σ_{ k }(r_{jk} )^{—3}, where r_{jk} is the distance between Protonsj and k, where j is any particular chosen proton. Because of the inverse‐cube dependence on r, appreciable contribution to the line broadening comes from nearest neighbors only. The dependence of the proton‐resonance linewidth on the hydrogen‐bond length, therefore, points out that the hydrogen‐bond length gets smaller when the protons are far apart and larger when they are close. This result was verified independently by calculating the nearest hydrogen—hydrogen distances for compounds where the positions of hydrogen atoms are known from neutron‐diffraction studies and in other cases by estimating these distances from the usual values of the bond lengths and bond angles. The observed result is explained by postulating that the interaction between the two O–H bonds involved in two adjacent O–H···O bonds is essentially electrostatic in origin; the interaction potential consists of attractive terms due to dipole—dipole, induced dipole, and dispersion interactions in addition to a repulsive term. The calculated interaction energy between two O–H···O hydrogen bonds is attractive up to O–H···O bond lengths of 2.80 Å and has a minimum value around 2.70 Å. The O–H···O bond length of 2.70 Å seems to be most preferred from the point of view of this energy. This is consistent with the fact that there are a large number of hydrogen‐bonded solids with bond lengths around 2.70 Å.

Nonequilibrium Thermodynamics of Canonically Invariant Relaxation Processes
View Description Hide DescriptionA relaxation process in which a dilute system is in weak interaction with a heat bath is termed canonically invariant if the time‐dependent system distribution function maintains its canonical form throughout the relaxation process and is thus characterized by a time‐dependent temperature. We discuss here the nonequilibrium (i.e., time‐dependent) thermodynamics of such canonically invariant relaxation processes. Explicit analytic forms are obtained for the partition functions Q(t), the system thermodynamic propertiesE(t), A(t), S(t), and C _{v}(t), the global free energy and entropya(t) and s(t), and their time derivatives for both classical and quantum systems. For quantum systems with a finite number of discrete energy levels, the above treatment is extended to include canonically invariant processes at negative absolute temperatures. Finally, we demonstrate that an initial canonical distribution for a fixed S(0) extremizes the entropy production of systems exhibiting canonically invariant relaxation processes.

Spin Splittings and Rotational Structure of Nonlinear Molecules in Doublet and Triplet Electronic States
View Description Hide DescriptionMatrix elements are presented for the Hamiltonian of a nonlinear, nonrigid polyatomic molecule in a multiplet electronic state. Their use is only appropriate for electronic and vibrational spectra since hyperfineinteractions involving nuclear spins and nuclear quadrupole moments are not considered. For the most general case, nine parameters are required to take full account of spin—rotation interactions, and five are required for spin—spin interactions. For molecules of orthorhombic symmetry only three spin—rotation parameters and two spin—spin parameters are nonzero. For nonlinear molecules in doublet and triplet electronic states, explicit formulas are presented for (a) the rotational term values of symmetric rotors and (b) spin splittings of asymmetric rotors possessing orthorhombic symmetry. All these formulas reduce to well‐known expressions for diatomic molecules in ^{2}Σ and ^{3}Σ states when K‐dependent terms are ignored. Application of the above formulas to the results of Dressler and Ramsay on the ^{2} B _{1}ground states of NH_{2} and ND_{2} permits the determination of the spin—rotation parameters of these molecules. All five spin parameters of formaldehyde in its lowest ^{3} A _{2} state are given together with curves of spin splittings in the lower K levels. The spin parameters of HCHO, NH_{2}, and ND_{2} are compared with those of NO_{2} and ClO_{2} found by recent microwave studies. For a triplet state of an orthorhombic molecule, the spin—spin constants determined by band spectroscopy are simply related to the spin constants D and E determined from zero field splittings in electron spin resonance spectroscopy. The surprisingly small value of D=0.42 cm^{—1} for the lowest triplet state of formaldehyde is briefly discussed in terms of a breakdown of the orbital approximation for this prototype ``n—π^{*} state.''

Infrared Spectrum of HCO
View Description Hide DescriptionHCO and DCO have been prepared by the photolysis of HI (DI) and of H_{2}S (D_{2}S) in a CO matrix at 14° and at 20°K. The earlier infrared spectroscopic identification of these species has been confirmed. The C=O stretching frequency of DCO has been revised to 1800 cm^{—1}. Unusually low C–H and C—D stretching frequencies, 2488 and 1937 cm^{—1}, respectively, are obtained. Observations on H^{13}CO and D^{13}CO support these assignments. Spectroscopic, kinetic, and electron spin resonance data all suggest that the C–H bond is exceptionally weak. Fermi resonance may occur between the C—D and C=O stretching modes of DCO. Evidence is presented suggesting that considerable activation energy is required for the reaction of H atoms with CO.

Radiationless Intermolecular Energy Transfer. I. Singlet→Singlet Transfer
View Description Hide DescriptionRadiationless energy transfer between unlike molecules has been studied under conditions where the interaction described in the ``Förster'' formulation may be expected to dominate other effects. Primary emphasis is placed on a direct observation of the effect of energy transfer on the excited‐state lifetime of the donor. These results are related through the theory with other spectroscopic measurements. Good agreement is found with the predictions of Förster based on a long‐range (25–50 Å) dipole—dipole interaction leading to an R ^{—6} distance dependence of the transition probability between donor and acceptor.

Radiationless Intermolecular Energy Transfer. II. Triplet→Singlet Transfer
View Description Hide DescriptionThe time dependence of the de‐excitation of the phosphorescent state of phenanthrene‐d _{10} by radiationless energy transfer to the fluorescent state of rhodamine B is observed. Good agreement is found with predictions based on the long‐range dipole—dipole interaction described by Förster.

Radiationless Intermolecular Energy Transfer. III. Determination of Phosphorescence Efficiencies
View Description Hide DescriptionLong‐range radiationless energy transfer from the triplet states of aromatic hydrocarbons to the singlet states of fluorescent dyes (10^{—3} M) is used to measure the efficiencies of energy dissipation (φ_{ F }, φ_{ IS }, φ_{ P }) for triphenylene, phenanthrene, p‐terphenyl, chrysene, naphthalene, and/or their deuterated counterparts. Rhodamine B, rhodamine 6G, acriflavin, and fluorescein were found to be suitable acceptors. By measuring phosphorescence efficiencies directly, reliable estimates of T→S radiative rate constants can be obtained.

Radiationless Intermolecular Energy Transfer. IV. Triplet—Triplet Annihilation
View Description Hide DescriptionPhosphorescence quenching for phenanthrene‐d _{10} has been observed in solid solution. The quenching efficiency is dependent on the triplet concentration η_{ T } with a threshold at η_{ T }∼10^{—3} M. It is interpreted to occur by the process T _{1}+T _{1}→S _{0}+T _{2}, involving a radiationless transfer of one triplet excitation to the triplet—triplet absorption band of the other. The necessary conditions described by Förster for dipole—dipole radiationless energy transfer are shown to be satisfied.

Radiationless Intermolecular Energy Transfer. V. Singlet→Triplet Transfer
View Description Hide DescriptionThe quenching of the fluorescent state of perylene by radiationless energy transfer into the triplet manifold of phenanthrene‐d _{10} is observed, viz., S _{1} ^{D}+T _{1} ^{A}→S _{0} ^{D}+T _{2} ^{A}. The variation of perylene fluorescence intensity as a function of phenanthrene‐d _{10} triplet concentration is predicted quantitatively by the Förster theory.

Electronic Energy Levels at a Crystal Surface as Observed by Electron Diffraction
View Description Hide DescriptionA cleavage face (104) of calcite was charged with electrons. This charged surface was studied by electron diffraction. Average energy of the electrons on the surface was estimated to be about 5 eV from the diffraction pattern obtained.

Critical Opalescence of Binary Mixtures: Perfluorotributylamine Isopentane
View Description Hide DescriptionCritical opalescence of the binary liquid mixture perfluorotributylamine and isopentane is investigated. By combining light scattering and x‐ray scattering measurements, data over a broad range of values of s/λ[s=2 sin (Θ/2), λ is wavelength] are obtained. The second moment of the averaged intermolecular pair potential is determined. It is shown how deviations from straight line behavior in plots of reciprocal intensity versus (s/λ)^{2} are determined by the shape of the intermolecular pair potential curve.

Formation of NH from Shock‐Heated Ammonia
View Description Hide DescriptionMixtures of ammonia in xenon were shock heated to temperatures in the range 2900° to 9600°K and the radiation from NH was monitored at 3360 Å. It was found that the production of NH (A ^{3}II) was second order in initial ammonia concentration within experimental error, and could be described by a rate constant K=4×10^{—14} exp ( —54 000/T) cm^{3} molecule^{—1}·sec^{—1}. Significant changes in shape of the radiation profiles were observed at different temperatures; in particular it was found that NH normally decayed at two different rates, one being half as great as the other. The results are discussed and compared with recent measurements made by other authors, revealing some discrepancies that could not be explained.