The effect of pressure on the formation of alkali metal borate ion pairs at 25°C

Pressure dependent UV-visible spectrophotometric measurements were used to determine \(\Delta \bar V^ * \) and \(\Delta \bar \kappa ^ * \) for the formation of alkali metal borate ion pairs. The association constant for each ion pair was measured at 25°C and at ionic strengths of 0.1 and 1.0m over a pressure range of 1 to 2000 atm. The pressure dependence of the apparent association constants, K _A (P)/K _A (1), have been fitted to $$[RT/(P - 1)]ln[K_A (P)]/[K_A (1)] = - \Delta \bar V^0 + \Delta \bar \kappa ^0 [(P - 1)/2]$$ to determine \(\Delta \bar V^0 and \Delta \bar \kappa ^0 \) . The \(\Delta \bar V^0 \) for the alkali metal borate ion pairs range from 5–9 cm³-mol^?1. The association constants were also measured as a function of ionic strength at 1 atm. Extrapolation to I=0 yielded K _A of 2.12, 0.66, 0.76 and 1.12 for [LiB(OH)₄], [KB(OH)₄], [RbB(OH)₄] and [CsB(OH)₄], respectively. The trend generally indicates less ion pairing and a smaller volume change for the ion pair formation as the size of the cation increases. The concept of localized hydrolysis is used to explain the trend observed in the equilibrium constant of the ion pair as the cation size is changed.     

Heat capacity and density of potassium iodide solutions in mixed N-methylpyrrolidone-water solvent at 298.15 K

The heat capacity and density of potassium iodide solutions in a mixed N-methylpyrrolidone (MP)-water solvent with a low content of the organic component are measured via calorimetry and densimetry at 298.15 K. Standard partial molal heat capacities \(\bar C_{p,2}^ \circ \) and volumes \(\bar V_2^ \circ \) of potassium iodide in MP-water mixtures are calculated. Standard heat capacities \(\bar C_{p,i}^ \circ \) and volumes \(\bar V_i^ \circ \) of potassium and iodide ions are determined. The character of the changes in heat capacity and volume are discussed on the basis of calculating additivity coefficients δ _c and δ _v upon the mixing of isomolal binary solutions KI-MP and KI-water, depending on the composition of the MP-H₂O mixture and the concentration of the electrolyte.     

The thermodynamic properties and solvation of lithium halides in N-methylpyrrolidone at 298.15 K

The heat capacity and density of solutions of lithium chloride, bromide, and iodide in N-methylpyrrolidone (I) were determined by calorimetry and densimetry techniques. The standard partial molar heat capacities and volumes ( $\overline {C^\circ _{p2} } $ and $\overline {V^\circ _2 } $ ) of lithium halides in I were calculated. The $\overline {C^\circ _{pi} } $ and $\overline {V^\circ _i } $ values for halogen and lithium ions in I were determined. The coordination numbers of the Li⁺, Cl^?, Br^?, and I^? ions in solutions in I at 298.15 K were calculated.     

Half-width and asymmetry of glow peaks and their consistent analytical representation

The kinetic equation which describes many electronic as well as atomic or chemical reactions under the condition of a steadily linear raise of the temperature, is considered in a mathematically exact and straightforward way. Therefore, the equation has been transformed into a dimensionsless form, using with profit the maximum condition for the intensity peak. The two temperatures T₁ and T₂, corresponding to the half-height of the intensity peak, are found as unique polynomials of the small argument \(\bar y \equiv {{k\bar T} \mathord{\left/ {\vphantom {{k\bar T} E}} \right. \kern-0em} E}\) only ( \(\bar T\) =temperature of peak maximum). Thereupon, further combinations give half-widthδ, peak asymmetryA=δ₂/δ₁ or \(\tilde A = {{\bar C} \mathord{\left/ {\vphantom {{\bar C} {(1 - \bar C)}}} \right. \kern-0em} {(1 - \bar C)}}\) and the maximum of the intensity peakJ; they again all depend only on¯y. In some cases this dependence is weak, so that e.g. it is deduced that the half-width energy product divided by \(\bar T^2 \) is an invariant, different for every kinetic orderπ: $$\frac{{\delta \cdot E[eV]}}{{\bar T^2 }} = \left\{ {\begin{array}{*{20}c} {{1 \mathord{\left/ {\vphantom {1 {4998 K for monomolecular process}}} \right. \kern-\nulldelimiterspace} {4998 K for monomolecular process}}} \\ {{1 \mathord{\left/ {\vphantom {1 {3542 K for bimolecular process}}} \right. \kern-\nulldelimiterspace} {3542 K for bimolecular process}}} \\ {{1 \mathord{\left/ {\vphantom {1 {2872 K for trimolecular process}}} \right. \kern-\nulldelimiterspace} {2872 K for trimolecular process}}} \\ \end{array} } \right.$$ By means of these correlations, activation energy valuesE [eV] can be determined accurately to within 0.5 %, so that for most experiments the inaccuracy of theδ values becomes dominant and limiting. A special nomogram for the express estimation ofE from experimentally observedδ and \(\bar T\) is demonstrated.     

Ion-molecular interactions in solutions of potassium and cadmium thiocyanates in N-methylpyrrolidone at 298.15 k, according to calorimetry and densitometry data

The heat capacity and density of KNCS-N-methylpyrrolidone (MP), Cd(NCS)₂-MP, and KNCS-Cd(NCS)₂-MP solutions at 298.15 K are studied by means of calorimetry and densitometry. Standard partial molar heat capacities and volumes ( $\bar C^\circ _{p,2} $ and $\bar V^\circ _2 $ ) of the studied electrolytes in MP are calculated. Standard values of heat capacity $\bar C^\circ _{p,i} $ and volume $\bar V^\circ _i $ of NCS^? ions in MP at 298.15 K are determined. Values of the heat capacity and volume changes upon the formation of the three-component system KNCS-Cd(NCS)₂-MP from binary solutions are obtained and discussed.     

A topological index for the totalπ-electron energy

A modified topological index \(\tilde Z_G \) is proposed to be defined as $$\tilde Z_G = \sum\limits_{k = 0}^{[N/2]} {( - 1)^k } a_{2k} $$ for characterising theπ-electronic system of a conjugated hydrocarbonG withN carbon atoms, wherea _2k is the coefficient of the characteristic polynomial ofG defined as $$P_G (X) = ( - 1)^N \det |A - XE| = \sum\limits_{k = 0}^N { a_k X^{N - k} } $$ with an adjacency matrixA and the unit matrixE. \(\tilde Z_G \) is identical toZ _G for a tree graph, or a chain hydrocarbon.Z _G increases with a (4n+2)-membered ring formation and decreases with a 4n-membered ring formation. The totalπ-electron energyE _π of the Hückel molecular orbital is shown to be related with \(\tilde Z_G \) asE _π =Cln \(\tilde Z_G \) . With this relation generalised and extended Hückel rules for predicting the stability of an arbitrary network are proved.     

The effective resonance energy\overline {E_r } as a parameter for the correction of resonance integrals in 1/E1+α epithermal neutron spectra; tabulation of\overline {E_r } -values for 96 isotopesfor 96 isotopes

The present paper shows that the effective resonance energy \(\overline {E_r } \) introduced by RYVES, is a useful parameter for the correction of resonance integrals in non-ideal epithermal neutron spectra, which can be approximated by a 1/E^1+α-flux distribution. The definition, the characteristics and the calculation of \(\overline {E_r } \) are discussed thoroughly. Tabulations are included, giving \(\overline {E_r } \) for 96 isotopes.     

Doppelnebenklassen als Klassenbegriff und Nomenklaturprinzip für Isomere und ihre AbzÄhlung

The general principle of classifying molecules of a common gross formula according to “configurations” is founded on the combination of two abstractions among rigid molecular models with a common molecular frame, numbered places for ligands, and numbered ligands. It is shown that the various points of view, which can be taken for the classification are determined by two accordingly chosen subgroups \(\mathfrak{A}\) and \(\mathfrak{B}\) of a permutation group \(\mathfrak{S}\) , the configurations being defined by the double cosets of the product \(\mathfrak{A}\mathfrak{B}\) . Just as the irreducible representations of the symmetry group of an observable furnish the nomenclature for different types of eingenfunctions the double cosets here provide a nomenclature for the configurations. The special principle of classification is given by the choice of \(\mathfrak{A}\) , \(\mathfrak{B}\) and \(\mathfrak{S}\) . Thus, the enumeration of configuration leads to the generalised problem of enumerating double cosets. For this, three formulas are derived. In case of the special group \(\mathfrak{S} = \mathfrak{S}_n \) G. Pólya found a formula of enumeration which is shown to reduce to our formulas in the appendix.     

Rendements de fission cumulatifs du252Cf

The cumulative yields of 28 isotopes have been measured in the spontaneous fission of²⁵²Cf. Measurements were made by Ge(Li) gamma-spectrometry. An average number of neutrons per fission \(\bar V:3.71\) was derived from the mass distribution. Using Terrell's method, and with the mass distribution before neutron emission, measured in an other laboratory and with our results, the mass-dependent variation of \(\bar V\) was also deduced.     

Röntgenkleinwinkeluntersuchungen der strahleninduzierten Aggregation von Ribonuclease,Lactat-Dehydrogenase,Glycerinaldehyd-3-phosphat-Dehydrogenase und Serumalbumin. Ein Vergleich mit Malatsynthase

The X-ray induced aggregation of ribonuclease, lactate dehydrogenase (LDH), glyceraldehyde-3-phosphate dehydrogenase (GAPDH) and serum albumin in aqueous solution was monitored in situ by means of small-angle X-ray scattering. The time dependence of several molecular parameters viz. the apparent radius of gyration \(\tilde R\) , the maximum visible diameterD, the mean degree of aggregation \(\bar x\) , and the mean radius of gyration \(\bar R\) was used to compare the various proteins with each other and with malate synthase which has been studied previously (P. Zipper andH. Durchschlag, Radiat. and Environm. Biophys., 1980). Measurements carried out with ribonuclease,LDH and serum albumin in the absence of dithiothreitol (DTT) and withGAPDH in the presence of 0.2mM DTT established the following series for the rates of aggregation of the proteins under these conditions: ribonuclease>LDH>GAPDH>serum albumin. The rate of aggregation ofGAPDH was found to be of similar magnitude as that obtained for malate synthase under comparable experimental conditions (presence of 0.2mM DTT, similar X-ray intensity) in our previous study. Within six hours from the beginning of irradiation (i.e. about the time required for the exposure of one complete scattering curve under the conditions of our experiments) the following increases of \(\tilde R\) resulted: ribonuclease 9%,LDH 7%,GAPDH 4%, serum albumin<1%. Changes of \(\tilde R\) exceeding 1% are, of course, too high to be tolerated in conventional scattering experiments.     

Auswertung von EMK-Messungen zur Bestimmung thermodynamischer Exzeßgrößen im System Silberchlorid—Lithiumchlorid

The partial molar excessGibbs energies \(\Delta \overline G _{AgCl}^E \) of AgCl in the binary system AgCl?LiCl have been measured over the entire composition range at temperatures between 923.15K and 1175.15K in steps of 50K, using the reversible formation cell $${{Ag\left( s \right)} \mathord{\left/ {\vphantom {{Ag\left( s \right)} {AgCl\left( l \right)}}} \right. \kern-\nulldelimiterspace} {AgCl\left( l \right)}}---LiCl\left( l \right)/C,Cl_2 $$ The measured \(\Delta \overline G _{AgCl}^E \) values were fitted by the use of theRedlich-Kister-Ansatz for thermodynamic excess functions. The evaluatedRedlich-Kister parameters have been used to calculate the molar excessGibbs energies ΔG ^E and the partial molar excessGibbs energies \(\Delta \overline G _{LiCl}^E \) of LiCl. From the temperature dependence of theRedlich-Kister parameters for ΔG ^E the partial and integral molar heats of mixing and excess entropies were calculated. For 1073 K and the mole fractionx=0.5 the following values were obtained: $$\Delta G^E = 2130\left[ {J mol^{ - 1} } \right], \Delta H^E = 1994\left[ {J mol^{ - 1} } \right], \Delta S^E = 0.127 \left[ {J mol^{ - 1} K^{ - 1} } \right]$$      

Spectral variational principle for Green's functions

For a suitable approximation \(\tilde K\) (q, q′, τ) to the Dirac-Feynman Green's function of a quantummechanical system, the parameter \({\mathcal{L}\tilde K}\) is defined, where ?≡i?/?τ??. It is shown thatΔ≧0 andΔ→0 asK→K, the exact Green's function, thus providing a criterion on approximate Green's functions analogous in its role to the variational principle for wavefunctions. A second somewhat weaker criterion is also proposed, based on \(\Sigma \equiv \left[ {tr\tilde K*tr\mathcal{L}^2 \tilde K - |tr\mathcal{L}\tilde K|^2 } \right]_{\tau avg} \geqq 0\) . Recipes are given for projecting out continuum contributions toΔ or∑ and for analyzing for the discrete eigen-value spectrum.     

Determination of perturbed angular correlation parameter\overline {G_{22} } for111In in hydrochloric acid solutions by the sum peak methodfor111In in hydrochloric acid solutions by the sum peak method

Application of the sum peak method to indium solutions in hydrochloric acid has been studied. A calibration line to determine a PAC parameter \(\overline {G_{22} } \) has been adopted using two samples with known values of \(\overline {G_{22} } \) . The results show feasibility of the method because of its simplicity and of smaller amounts of radioactivity required in the measurement compared to the ordinary PAC method.     

Effects of dissolved electrolytes on the solubility and partial molar volume of helium in water from 50 to 400 atmospheres at 25°C

The solubility of helium in water and aqueous CsCl, NaCl and MgCl₂ solutions at concentrations up to 3.380 molal has been measured at 50 atm intervals from 50 to 400 atm at 25°C. Setschenow coefficients for helium are practically invariant with pressure in each solution, decrease significantly with increasing electrolyte concentration and vary with the type of electrolyte in a fashion identical to that observed for the low pressure solubilities of other gases. The pressure dependence of the helium solubility in each solution follows a form of Henry's law in which the helium partial molar volume at infinite dilution \(\bar V^{_{He}^o } \) is independent of pressure. Values of \(\bar V^{_{He}^o } \) , computed from Henry's law, are smaller for the electrolyte solutions than for water and vary systematically with the type and concentration of dissolved electrolyte. This result is explained qualitatively in terms of ion hydration and its influence on the ability of the intrinsic configurational volume in each liquid to accommodate the relatively small helium molecules. It is concluded that intrinsic solvent structure is an important factor governing the partial molar volume of helium and the pressure dependence of helium solubility in water and aqueous electrolytes.     

Thermodynamics of bolaform electrolytes. III. Partial and apparent molal volumes in H2O and D2O

The apparent,φ _v, and partial, \(\bar V\) ₂, molal volumes of a series of homologousbis-tetraalkylammonium bromides have been determined in H₂O and D₂O at 25°C from precision density measurements carried out with a buoyancy densimeter and a dilatometer. The Debye-Hückel theoretical limiting slope forφ _v and \(\bar V\) ₂ as a function of the square root of molar concentration is approached for all of the salts studied. the concentration dependence ofφ _v and \(\bar V\) ₂ is anomalously large and negative in both solvents, with the deviations being less negative in D₂O than in H₂O. The bolaform salts have larger \(\bar V\) ₂ ^o values in H₂O than in D₂O, contrary to the observed behavior of R₄NX salts. Possible origins of the solvent isotope effects observed are discussed in terms of structural and cavity contributions to the measured volumes. A comparison of thermodynamic transfer functions (H₂O→D₂O) for Et₄N Br and the corresponding bolaform analog appropriate in the consideration of cation-cation pairing of Et₄N⁺ ions shows inconclusive evidence for the support of the cation pair theory.     

The effect of pressure on the ionization of boric acid in aqueous solutions from molal-volume data

The apparent, φ _v , and partial, \(\bar V_2 \) molal volumes of dilute (0.02 to 0.7m) aqueous boric acid, B(OH)₃, and sodium borate, NaB(OH)₄, solutions have been determined from 0 to 50° C from precision density measurements. The φ _v of boric acid is a linear function of the first power of concentration. For sodium borate, the Debye-Hückel theoretical limiting law slope for the φ _v as a function of the square root of molar concentration is approached at all temperatures studied. The positive deviations at higher concentrations increase with decreasing temperature. The infinite-dilution volume properties of both B(OH)₃ and NaB(OH)₄ indicate that these solutes behave like “structure breakers” between 0 and 50°C (that is ?²φ _v ^° /?T² is negative). The volume change for the ionization of boric acid in water \(\Delta \bar V^\circ \) , is calculated from the volume data at various temperatures. This volume change has been used to estimate the effect of pressure on the ionization of boric acid solutions from 0 to 50°C and 0 to 1000 bars. The calculated effect of pressure on the ionization is in good agreement with direct measurements.     

Slow-brittle-fracture transition in polymethylmethacrylate

A slow crack growth was achieved in initially edge-cracked specimens made of a high-molecular weight PMMA by regulating the cross-head speed of loading by a computer-driven testing machine. The strain rate \(\dot \varepsilon \) used during the tests varied between \(\dot \varepsilon \) =1× l0^?6 s^?1 and 1×10^?4 s^?1. It was shown that, in this zone of slow quasi-static loading of brittle polymethylmethacrylate specimens under conditions of plane stress, the crack initiated for a critical value of loading, at some characteristic zone of strain-rate variation at the crack tip. It was established that for strain rate between \(\dot \varepsilon \) =0.18×10^?5 s^?1 and \(\dot \varepsilon \) =0.45×10^?4 s^?1 brittle cracks were propagating always slowly with velocities in the range ofc=3 to 5×10^?2 m/s. For values ofv _s outside this transition zone fracture was typically brittle with high crack-propagation velocities. As the strain rate was varying beyond the stable low-velocity region, a two-step crack velocity pattern was operative, where the one step took always low values, and the other step corresponded to crack-propagation velocities significantly higher than these limits, tending to typical brittle-fracture velocities of the material. Oscillations of the velocityc at the transition zones, or, in many cases all over the zone of slow propagation of the crack, indicated the unstable character of crack propagation, influenced by different stress raisers and especially by the opposite longitudinal boundary of the specimen. Stress intensity factor values during crack propagation, evaluated from the front (cuspoid) and the rear (external) caustic, which remained alwaysk _g-dominant, were following similar trends as the variation of the crack propagation velocity.     

Volumetric and Viscometric Studies in Binary Liquid Mixtures of 2-Methyl-2-propanol with Some Ketones at Different Temperatures

Densities, ??, and viscosities, ??, of binary mixtures of 2-methyl-2-propanol with acetone (AC), ethyl methyl ketone (EMK) and acetophenone (AP), including those of the pure liquids, were measured over the entire composition range at 298.15, 303.15 and 308.15?K. From these experimental data, the excess molar volume $V_{\mathrm{m}}^{\mathrm{E}}$ , deviation in viscosity ????, partial and apparent molar volumes ( $\overline{V}_{\mathrm{m},1}^{\,\circ }$ , $\overline{V}_{\mathrm{m},2}^{\,\circ }$ , $\overline{V}_{\phi ,1}^{\,\circ}$ and $\overline{V}_{\phi,2}^{\,\circ} $ ), and their excess values ( $\overline{V}_{\mathrm{m},1}^{\,\circ \mathrm{E}}$ , $\overline{V}_{\mathrm{m,2}}^{\,\circ \mathrm{ E}}$ , $\overline {V}_{\phi \mathrm{,1}}^{\,\circ \mathrm{ E}}$ and $\overline{V}_{\phi \mathrm{,2}}^{\,\circ \mathrm{ E}}$ ) of the components at infinite dilution were calculated. The interaction between the component molecules follows the order of AP > AC > EMK.     

Electromagnetic structure of lighter antiprotonic atoms

The electric and magnetic fine structures of \(\bar p\) -atoms are tabulated up toZ=20. They are calculated perturbatively to second order in the Uehling potential, to first order in relativity and to all orders in recoil.     

PCILO method for excited states

In the scope of building a PCILO method for excited states, one builds and tests excitonic zeroth order wave-functions. For \(\left( {_\pi ^{\pi ^ * } } \right)\) transitions, the (σ+π) excitonic and purely (π) excitonic wave functions are compared, showing that theσ-π coupling between \(\left( {_\pi ^{\pi ^ * } } \right)\) and \(\left( {_\sigma ^{\sigma ^ * } } \right)\) single excitations may be considered as a perturbation. The excited state wave-functions are analyzed in terms of neutral and ionic structures, and the fluctuation of the charges in the two-electrons loges are studied, showing that theσ-π coupling favours the neutral structures and diminishes the charge-fluctuations.