Biochemie und Chemie
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The relations of the theory of real gases which have first been derived by Mayer and his co-workers can be obtained in a simple way by the functional method. In this case the assumption of the pairwise additivity of the intermolecular potential can be dropped. Apart from some new relations for distributions functions the expansion of the direct correlation functions is obtained as a power series in density with coefficients consisting of integrals over Husimi functions.
Es werden allgemeine Gleichungen zur Berechnung der Verteilung der Nullstellen von der großen kanonischen Verteilungsfunktion Ξ (y) eines Gittergases in der komplexen Ebene der Fugazität y in Bethescher Näherung angegeben, die nach einem graphischen Verfahren gelöst werden können. Für das zweidimensionale, quadratische Gitter und das dreidimensionale, kubische Gitter werden die Bestimmungsgleichungen für die Nullstellenverteilung mit Hilfe des graphischen Verfahrens explizit gelöst. Die Nullstellenverteilung von Ξ (y) des eindimensionalen Gittergases wird in geschlossener Form angegeben.
The cooperative problem for a lattice gas on a plane, square lattice and on a simple cubic lattice is solved by a system of two coupled, transcendental equations, derived by a combinatorial method, which describes a homogeneous or periodical particle density on the lattice as a function of the temperature and the chemical potential of the lattice-gas.
For the particle interaction a Hard-Core potential (nearest neighbour exclusion) with a soft long-range tail is assumed. The zero-component of the Fourier-transform of this long-range interaction part can be positive or negative.
The system of transcendental equations is solved by a graphic method. As a result, the complete pressure-density state diagram and the pressure-temperature phase diagram can be drawn.
The lattice-gas exists in three stable phases: gas, liquid and solid. Three phase changes are possible: condensation, crystallization and sublimation.
Critical points of condensation and freezing are examined. The number of possible phases and phase changes at a fixed temperature depends on the geometric structure of the particle interaction.
Die „Selbstenergien“ Gn in 1 wurden durch näherungsweise Auswertung einer größeren Klasse von Selbstenergiediagrammen approximativ berechnet. Das Gleichungssystem (3.3) in 1 für die renormierten Semiinvarianten wurde umgeformt und durch zusätzliche Näherungsannahmen vereinfacht. Durch Näherungsansätze für die Semiinvarianten M2, M3,... konnten einfache Gleichungen für die Magnetisierung M1 hergeleitet werden. Diese Gleichungen wurden numerisch gelöst. Auf der Grundlage der Beziehungen (3.5) und (4.8) in 1 wurden ferner die innere Energie, die freie Energie und die Atomwärme des zweidimensionalen Ising-Ferromagneten sowie die Druck-Dichte-Isothermen des zweidimensionalen Gittergases numerisch ausgerechnet.
Die FOURIER-Nullkomponente der Bindungsmatrix Gij G(0) in 1 Beziehung (5.16) wurde durch Summation spezieller Diagramme in der sogen. „Kettenapproximation“ und der „Wassermelonenapproximation“ näherungsweise berechnet. Auf der Basis von (5.16) in 1 wurde in der Kettenapproximation und der Wassermelonenapproximation die magnetische Suszeptibilität und die Magnetisierung des dreidimensionalen ISING-Modells bestimmt. In der Kettenapproximation wurden ferner die freie Energie, die innere Energie und die Atomwärme des dreidimensionalen ISING-Ferromagneten sowie die Druck-Dichte-Isothermen des dreidimensionalen Gittergases ausgerechnet.
A theory of the luminescence lifetime of a radiation-damped classical electrical point dipole near a plane interface to a medium with different optical constants is given. The influence of the interface on the lifetime of the dipole is calculated in first approximation with the methods of molecular optics. Theoretical and experimental results for a purely dielectric interface are compared.
Excitation of CO molecules into the lowest vibrational level of the B1Σ+ electronic state by absorption of the (B 1Σ+υ′=0 →X 1Σ+ ,υ′′=0) resonance band at 1150 Å has been studied under various experimental conditions by observing the steady state fluorescence of the (B 1Σ+→A1Π) Angstrom bands. Stern-Volmer plots of the fluorescence intensities at the addition of various foreign gases yielded straight lines whose slopes k̃qм = kqм · τeff were strongly dependent on the CO sample pressure. This effect was found to be due to changes of the effective radiative lifetime of the B 1Σ+υ′=0 because of resonance trapping of the (0,0) band of the (B → X) fluorescence. The CO(B 1Σ+υ′=0) molecules are found to be quenched by He, Ne, Ar, H2 and D2 with effective collision cross sections of 0.23, 0.48, 22.4, 10.7, and 11.4 Å2, respectively, at 298 °K. In addition, an approximate value for the ratio ABA/ (ABA+ABX)of the radiative transition probabilities of the (B → A) and (B → X) transitions could be derived from the measurements.
The mass spectra and the ion molecule reactions of methylphosphine, dimethylphosphine and dimethyldeuterophosphine have been studied by ion cyclotron resonance spectrometry. About 50 ion molecule reaction are observed for each compound. The product ions can be classified as ions with two phosphorus atoms: P2R5+, P2R3+, P2R2+ and P2R+ (R = CH3 or H), as phosphonium and phosphinium ions and ions resulting from collision dissociations and charge exchange reactions. Tertiary ions with three phosphorus atoms like CH3P3H2+ (from CH3PH2) and (CH3)4P3H2 (from (CH3)2PH) have also been detected. The mechanisms of the ion molecule reactions, rearrangements, P -H- and C-H-reactivities and product ion structures are discussed, using in the case of dimethylphosphine the results obtained with the deuterated compound. Rate constants of formation of the more abundant product ions from the molecular ion and the CH3P+ ion, both odd electron particles, have been determined. The reactions with dimethylphosphine have much smaller rate constants than the reactions with methylphosphine.