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Volume 23, Issue 4, 01 April 1955
23(1955); http://dx.doi.org/10.1063/1.1742065View Description Hide Description
Fluorescent emission of organic solutions in combinations of solvents is investigated in order to determine the reasons for the suitability or unsuitability of solvents for high‐energy induced fluorescence, particularly where these solvents do not influence the emission under ultraviolet irradiation. Basically two types of behavior under high‐energy radiation are found in these combined solvent solutions. In type I a considerable drop in emitted intensity occurs only when the amount of the ``poor'' solvent greatly exceeds that of the ``effective'' solvent, whereas in type II small amounts of added ``poor'' solvent produce large decreases in emitted intensity. The fluorescence depends upon the concentration of solute, larger concentrations giving greater light outputs. The results obtained are explained by assuming that energy transfer occurs from the ``poor'' solvent to the ``effective'' one. At the same time a decrease in actual lifetime of excitation in the ``effective'' solvent occurs which is induced by the presence of the ``poor'' solvent molecules. This shows up as a quenching of the gamma‐ray induced fluorescence in solutions even with solutes which are scarcely quenched at all under ultraviolet light excitation. For type I behavior this quenching is small while for type II it is considerable.
23(1955); http://dx.doi.org/10.1063/1.1742066View Description Hide Description
Empirical relationships have been found between energy of vaporization,surfaceenergy,energy of activation of viscosity, and the boiling temperature. This has been done by first considering the inert gases as the simplest type of liquid. For the simplest type of polyatomic substance the normal fluorocarbons give The normal hydrocarbons give, as expected, liquids whose properties differ from those of the normal fluorocarbons. For normal heptane it is shown that may be taken at temperatures other than Tb . Suggestions are given for theoretical reasons for these equations.
23(1955); http://dx.doi.org/10.1063/1.1742067View Description Hide Description
An exact, formal method for calculating the number of physical (as contrasted with Mayer's mathematical) clusters in an imperfect monatomic gas is developed. However, although the equations are exact, the definition of a physical cluster is somewhat arbitrary. This arbitrariness does not affect any of the purely thermodynamic properties of the gas. A particular pair‐wise definition of physical clusters is discussed in some detail and compared with Mayer's pair‐wise definition of mathematical clusters.
23(1955); http://dx.doi.org/10.1063/1.1742068View Description Hide Description
A summary of a few results of the McMillan‐Mayer solution theory is given in Sec. II, in order to have available necessary equations in a form required in later sections. It is pointed out in Sec. III that binding equilibria in a solution can in principle be discussed equally rigorously either implicitly or explicitly. The definition of ``binding'' in an explicit formulation is, strictly speaking, somewhat arbitrary but the arbitrariness disappears for practical purposes if the binding forces are very strong. However, the purely thermodynamic results are rigorously independent of the exact definition used. With the aid of Secs. II and III, it is possible to formulate in Sec. IV a general theory of protein solutions, including the effect of binding of ions or molecules on protein molecules. The discussion here is restricted to a single protein species and a single type of molecule capable of being bound, but the generalization to any number of protein or bound species is easy and will be published later. The topics discussed are osmotic pressure virial expansion, number of bound molecules per protein molecule expanded in powers of the protein concentration, distribution functions for sets of protein molecules (including the radial distribution function), potentials of average force on sets of protein molecules, superposition approximation in relation to the osmotic pressure and the Born‐Green‐Yvon integrodifferential equation for the distribution functions, and, finally, the relation to the recent Kirkwood—Shumaker theory. The theory applies equally well to polyelectrolyte,colloidal, and other solutions, but the ``protein'' language is used throughout for definiteness.
Influence of Vibration‐Rotation Interaction on Line Intensities in Vibration‐Rotation Bands of Diatomic Molecules23(1955); http://dx.doi.org/10.1063/1.1742069View Description Hide Description
The influence of vibration‐rotation interaction on line intensities in vibration‐rotation bands of diatomic molecules had been recognized and treated approximately many years ago. In the present paper matrix elements have been calculated for the P and R branches of the 0—1, 0—2 and 1—2 transitions taking into account the interaction of rotation and vibration as well as the mechanical and electrical anharmonicity. For the 0—1 and 1—2 transitions the intensities of corresponding absorption lines in the P and R branches are proportional, in first order approximation, to [1+4γθJ]J and [1—4γθ(J+1)](J+1), respectively, where J is the rotational quantum number of the initial state, γ=2Be/ω e , θ=M 0/M 1 re and M 0 and M 1 are the first two coefficients in the electric dipole moment expansion about the equilibrium internuclear distance re . Corrections to the above expressions that are proportional to γ2 have also been obtained. Formulas are given for the total integrated band intensity and for the line intensities summed over each branch taken individually. In the case of certain molecules, such as HCl for which θ≅1, it is possible to determine the magnitude of sign of θ by applying the above analyses to experimental data. For molecules such as CO, where θ≪1, the effect is negligible for the fundamental transition. A semiclassical interpretation of the influence of vibration‐rotation interaction on line intensity has also been given.
23(1955); http://dx.doi.org/10.1063/1.1742070View Description Hide Description
The 2900—2500 A region of absorption in both light and heavy naphthalene is interpreted as an allowed A 1g –B 2u transition, and the bands at 35 910 and 36 040 cm—1 are assigned as the respective 0,0 bands. Upper‐state frequencies of 485, 710, 995, 1390, 1520, and 1600 cm—1 and the ground‐state frequencies of 495, 755, 1024, and 1380 cm—1 in the ordinary naphthalene spectrum are correlated with previously reported Raman frequencies. A corresponding interpretation is given for the vibrational frequencies occurring in the spectrum of deuterated naphthalene. The general appearance of the spectrum is compared with recent absorption curves in solid solution by Passerini and Ross, and with crystal data obtained with polarized light. Possible occurrence of vibrationally induced ``forbidden'' bands is discussed.
23(1955); http://dx.doi.org/10.1063/1.1742071View Description Hide Description
The general configuration of the emission spectrum of synthetic NaCl crystals which had been irradiated with 7 × 105 r of x‐rays at room temperature and were then permitted to luminesce at 500°K was determined, and bands were located with maxima at 362, 418, 432, and 525 millimicrons. The glow curves for NaCl crystals irradiated with x‐rays or ultraviolet light were investigated, and eight bursts of light (glow peaks) were found with peaks at temperatures between 334 and 625°K. The relative contribution of the different bursts to the total glow curve was determined as a function of the amount of x‐ray irradiation. The activation energies for five of the bursts were measured and in each case turned out to be about 1.25 ev. It is suggested that these results indicate that the thermoluminescence takes place by means of a two‐stage process of the following sort. The first stage, which is the same for all the bursts and is thermally activated with the measured activation energy, takes place when trapped electrons are raised from F‐centers into the conduction band. In the second stage, electrons in the conduction band fall into different empty energy levels, there being one type of level for each burst. The large observed differences between the peak temperatures of the different bursts is then due to large variations in the probabilities of this second process for different levels.
23(1955); http://dx.doi.org/10.1063/1.1742072View Description Hide Description
The self‐diffusion coefficient of CCl4 has been measured over a range of temperature between 25° and 50°C and at 1 and 200 atmospheres. The results can be expressed by the equations: for 1 atmos, D=325 exp (—3300/RT), for 200 atmos, D=264 exp (—3300/RT). The activation energy for constant volume is 1070 Cal. These activation energies are identical with those previously found for the diffusion of I2 in CCl4. The temperature coefficient of diffusion at constant volume parallels in both cases the increase of kinetic energy. Dη/T is constant within 7 percent in the range studied, where η denotes viscosity. These results are discussed in relation to various theories for the mechanism of diffusion.
23(1955); http://dx.doi.org/10.1063/1.1742073View Description Hide Description
The infrared spectra of crystalline HCl, HBr, and HI have been studied at —205°C. The fundamental vibrations were observed in HCl at 2704 and 2746 cm—1, in HBr at 2404 and 2438 cm—1, and in HI at 2120 cm—1. In addition, low‐frequency bands associated with torsional lattice vibrations were observed directly and in combination with the fundamental vibrations of the molecules. It is concluded that in the low‐temperature crystalline phases both HCl and HBr form zigzag hydrogen‐bonded chains, the angle between adjacent molecules being about 107° in HCl and 97° in HBr. The crystalline potential function is investigated for all three molecules.
23(1955); http://dx.doi.org/10.1063/1.1742074View Description Hide Description
A proof of Wulff's theorem for the equilibrium shape of a two‐dimensional crystal has been given by Burton, Cabrera, and Frank. This has been extended to three dimensions in the present note and an expression has been derived for the principal radii of curvature of the crystal.
23(1955); http://dx.doi.org/10.1063/1.1742075View Description Hide Description
By means of Wheland's method of treating systems with hetero‐atoms three possible isomers of porphyrin and five of dihydroporphyrin are studied from the viewpoint of the energies of the ground states and the transition energies to the lowest lying excited states. In the case of porphyrin it is found that, within the limits of accuracy of the method used, two of the structures, PA (porphyrin‐adjacently bonded hydrogens) and PO (porphyrin‐oppositely bonded hydrogens), have identical ground state energies. In the case of dihydroporphyrin the DHP‐AI (DHP‐A—dihydroporphyrin‐adjacently bonded hydrogens) isomer is most stable and the DHP‐AII and DHP‐OII (DHP‐O—dihydroporphyrin‐oppositely bonded hydrogens) isomers are more energetic by 1.06 and 1.20 kcal/mole, respectively. With respect to the transition energies and the resulting spectra it is possible that the peaks in the spectrum of porphyrin are not due mainly to vibrational fine structure of a single electronic transition, as is proposed by Rabinowitch, but rather are the combination of the electronic spectra of the PA and PO isomers. The dihydroporphyrin spectral analysis, however, indicates that several of the peaks are probably vibrational fine structure of a single electronic transition. The calculated bond orders are given for the various structures discussed.
23(1955); http://dx.doi.org/10.1063/1.1742076View Description Hide Description
An interaction potential of the form A/R 10—B/R 6 for two argon atoms is assumed. The values of A and B are evaluated using the heat of sublimation and the lattice constant at temperature T=0°K and pressurep=0. By assuming that each atom moves in a potential field because of all the other atoms at rest in their mean positions, a theory is developed for anharmonic vibrations using the perturbation theory for a harmonic oscillator. The partition function for each argon atom is obtained and the equation of state is calculated. The specific‐heat equation obtained represents a correction of the Einstein form. The specific heats at constant pressure are calculated as a function of temperature and deviate from the experimental ones by only 3 percent at low temperatures (15°K—30°K) and only 1 percent at higher temperatures. The isothermal elastic coefficients C 11, C 12, and C 44 are calculated by Born's method without neglecting the part played by the thermal energy. The Cauchy relation is found to be invalid, C 44 being about twice C 12 at the higher temperatures.
23(1955); http://dx.doi.org/10.1063/1.1742077View Description Hide Description
An effort was made to observe the structure of the reaction zone for a detonation in a gas. Detonations in a 50 percent H2:50 percent O2 mixture at 0.035 atmos pressure containing 1 percent I2 were initiated by shock waves in a shock tube. Because of ignition delays and the short length of tube available, the detonations did not settle down to a steady state and were of unexpectedly high velocity. The iodine served as a colorimetric indicator for the shock front. The light output of the detonation is a step function of time with a front coincident with the shock front within 2—3 μsec. The experiment indicates that the reaction zone is less than 104 collisions thick. A crude theoretical estimate of the reaction zone thickness of 1000—4000 collisions is made. Possible chain initiating steps are also considered.
23(1955); http://dx.doi.org/10.1063/1.1742078View Description Hide Description
Experimental measurements of the kinetics of thermal decomposition of ammonium nitrate have been made in the temperature range from 443 to 553°K. The results indicate that the degradation of ammonium nitrate is an autocatalytic liquid‐phase reaction, the rate of which is proportional to the product of the mass of salt and the concentration of acid. The activation energy for this process is found to be 31.4 kcal. Adjustment of the concentration of acid present offers an effective means for the control of the rate of thermal degradation of ammonium nitrate.
23(1955); http://dx.doi.org/10.1063/1.1742079View Description Hide Description
The potential at zero charge for an ideal polarized electrode, as measured with respect to some reference electrode, varies linearly with the work function of the metal, while this potential for a reversible electrode is independent of the nature of the electrode. This observation is verified experimentally for Ag, Cd, Cu, Ga, Hg,Ni,Pb, Pt, and Tl in the case of ideal polarized electrodes and for Ag,Au, Bi, Cu,Hg, and Pt for reversible electrodes. It is shown that the difference between the Volta potentials from electrode to solution for an ideal polarized electrode at zero charge is approximately —0.33 volt, and that the difference between the Galvani potentials is equal to the surface potential of the electrode. The difference of Volta potentials for a reversible electrode at zero charge varies linearly with the electronic work function of the metal.
Substituted Methanes. XXI. Calculated and Observed Wave Numbers, and Calculated Thermodynamic Properties, for Bromodeuteromethane and Bromodideuteromethane23(1955); http://dx.doi.org/10.1063/1.1742080View Description Hide Description
Using potential energy constants obtained from CH3Br and CD3Br, wave numbers (fundamentals) for CH2DBr and CHD2Br were calculated by means of the Wilson FG matrix method with a potential energy function containing all possible second degree terms. The calculated values of the wave numbers were then used to assign existing infrared and Raman spectral data for these molecules. Then the heat content, free energy,entropy, and heat capacity for the ideal gaseous state at 1 atmos pressure were calculated for 12 temperatures from 100 to 1000°K with a rigid rotator, harmonic oscillator approximation.
Substituted Methanes. XXV. Potential Constants and Calculated Thermodynamic Properties of Dibromofluoromethane23(1955); http://dx.doi.org/10.1063/1.1742081View Description Hide Description
On the basis of previous Raman data, a reasonable set of potential constants was calculated for CHFBr2 by the Wilson method, assuming a most general quadratic potential energy function. The thermodynamic properties—heat content, free energy,entropy, and heat capacity—for the ideal gaseous state at 1 atmos pressure were computed for 12 temperatures from 100 to 1000°K.
23(1955); http://dx.doi.org/10.1063/1.1742082View Description Hide Description
The pure quadrupoleresonances of Cl35 in acid chlorides of some aliphatic dicarboxylic acids have been observed. No resonances have been found in acid chlorides of aliphatic monocarboxylic acids which retain the unsubstituted CH3 configuration at the chain end not occupied by the COCl group. This absence of resonances is attributed to possible randomness in the crystal structure or thermally activated low‐frequency reorientations of groups within the molecule.
Resonances have also been measured in several chlorates, sulfuryl chloride, iodine monochloride, iodine trichloride, and selenium tetrachloride. Structural and bonding discussions are given for the latter two compounds.
23(1955); http://dx.doi.org/10.1063/1.1742083View Description Hide Description
A mathematical expression for the helical configuration of a polymer chain has been derived as a function of the bond lengths, bond angles, and internal rotation angles. The result of the calculation has been applied to the determination of stable configurations of several polymer chains.
23(1955); http://dx.doi.org/10.1063/1.1742084View Description Hide Description
A previously given theory of the electronic spectra and electronic structure of complex unsaturated molecules is applied to ethylene‐like molecules, molecules such as ethylene itself, propylene or formaldehyde, which have two π electrons and two atomic π orbitals available for π‐bond formation. Relations are derived among electronic excitation energies, intensities of electronic transitions, extra‐ionic resonanceenergies and dipole moments of such molecules. Relative electronegativities are shown to play an important role in these relations, where the effective electro‐negativity of an atom is Mulliken's electronegativity (the mean of the appropriate atomic valence‐state ionization potential and electron affinity) plus the total attraction of the valence electron of the atom for all other atoms in the molecule.
The analysis yields the result that the dipole moment due to a slight bond heteropolarity is proportional to the electronegativity difference of the bonded atoms, the extra‐ionic resonanceenergy to its square. Proportionality factors are given absolutely by the theory. It is pointed out that the theory of a two‐electron σ bond is formally the same, moreover, so that a derivation is provided for the familiar electronegativity relations of Pauling. Theoretical and empirical values for the proportionality factors are found to agree reasonably well for both π bonds and σ bonds.
The formulas given cover multiple perturbations of any type which may be considered not to add (or subtract) π electrons or π orbitals. They thus provide a scheme for quantitative evaluation of inductive effects in ethylene‐like molecules. Systematic consideration of mesomeric effects is deferred, but an outline of the procedure which may be used for their study is given, using mono‐substituted ethylene as an example.
To illustrate the use of the formulas, to bring out the relationships between the method and the work of other authors, and to see whether the method has promise for σ‐electron systems, calculations are made of the electronic spectrum of ethylene, the twisting force constant of ethylene, the ionization potential and electron affinity of ethylene, the electronic spectrum and dipole moment of formaldehyde, and the electronic spectrum,ionization potential, and binding energy of the hydrogen molecule.