Band 56, Heft 9-10

We study thermodynamics and structural properties of several liquid metals to assess the validity of the generalized non-local model potential (GNMP) of Li et al. [J. Phys. F16, 309 (1986)]. By using a new thermodynamically consistent version of the optimized random phase approx­ imation (ORPA), especially adapted to continuous reference potentials, we improve our previous results obtained within the variational approach based on the Gibbs -Bogoliubov inequality. Hinging on the unified and very accurate evaluation of structure factors and thermodynamic quantities provided by the ORPA, we find that the GNMP yields satisfactory results for the alkali metals. Those for the polyvalent metals, however, point to a substantial inadequacy of the GNMP for high valence systems.

Using an asymptotically exact reduction method based on Fourier expansion and spatiotemporal re-scaling, a new integrable system of the nonlinear partial differential equation in (2+1)-dimensions, extended Davey-Stewartson I equation, is deduced from a known (2+1)-dimensional integrable equation. The integrability of the new equation system is explicitly proved by the spectral transformation. Actually, the corresponding Lax pair of the new equations can be obtained by applying the same reduction method to the Lax pair of the original equation.

By using of the Bäcklund transformation, which is related to the standard truncated Painleve analysis, some types of significant exact soliton solutions of the (2+1)-dimensional Broer-Kaup-Kupershmidt equation are obtained. A special type of soliton solutions may be described by means of the variable coefficient heat conduction equation. Due to the entrance of infinitely many arbitrary functions in the general expressions of the soliton solution the solitons of the (2+1)- dimensional Broer-Kaup equation possess very abundant structures. By fixing the arbitrary functions appropriately, we may obtain some types of multiple straight line solitons, multiple curved line solitons, dromions, ring solitons and etc.

The phase diagram of the binary system nC 16 H 34 -nC 17 H 36 has been established at ambient pressure using DSC and crystallographic measurements. At low temperatures below the rotator phase RI there exist two crystal forms Op (about x(C 17 ) = 0.25) and Mdci (about x(C 17 ) = 0.67) which are different from the crystal structures of the pure compounds (Tp for C 16 and Oi for C 17 ). Furthermore two compositions: (a) C 16 /C 17 = 3:1 and (b) = 1:2, which correspond to the coexistence range of Op and Mdci, were chosen for high pressure DTA and pVT measurements, yielding the following findings: The specific volume of the rotator phase of C 17 is distinctly lower than those of the binary systems at the same state point. Assuming the existence of a metastable rotator phase for C 16 , an excess volume of Δ V E /V ≈ 0.01 can be estimated. Due to the very enlarged coexistence range of RI, the mixtures reach their lower transition point at considerably lower temperatures (in isobaric measurements) or higher pressures (in isothermal measurements), where the specific volume is lower than that of C 17 at its transition point. Furthermore, the volume and enthalpy changes of the Φ ord -RI transition is distinctly smaller for the binary systems than for pure C 17 . Thus the specific volumes of the phases Op and Mdci are appreciably larger than ν(spec.) of C 17 . Op and Mdci have practically the same specific volume in accordance with the crystallographic results. Enthalpy values are obtained with the aid of the Clausius-Clapeyron equation which agree well with enthalpies derived from the DSC measurements. Furthermore, pVT data have been established for the liquid and solid phases of nC 18 H 38 in the neighbourhood of the melting curve, allowing to determine volume and enthalpy changes of melting as a function of pressure.

The rotational spectra of m-xylene, (CH 3 ) 2 C 6 H 4 and of m-xylene-d 10 , (CD 3 ) 2 C 6 D 4 have been recorded between 6 and 26.5 GHz using pulsed beam Fourier transform microwave spectroscopy. The clue for the assignment of the internal rotation multiplets was the inertial defect derived from the A 1 A 1 species transitions. The rotational constants for m-xylene and m-xylene-d 10 are A = 3572.1117(1) MHz / 2896.1195(17) MHz, B = 1761.8621(1) MHz / 1446.0236(15) MHz, C =1197.3943(2) MHz / 988.2357(7) MHz, the barrier to internal rotation of the two methyl groups are V 3 = 53.7(16) J/mol / 39.8(5) J/mol, their moments of inertia were assumed to be I ∞ = 3.14 uÅ 2 / 6.28 uÅ 2 .

The coordination capability of Cl and Br in halogenocadmate(II) complexes is estimated by a solution of the structure of 1,3-propanediammonium dibromodichlorocadmate(II). The compound crystallizes as a layered anion structure with Cl bridges and Br terminals at 293 K: Imma, a = 741.56(7), b = 1869.5(5), and c -771.55(8) pm, Z = 4. In order to explain the stronger tendency of halogenocadmate(II) complexes to form layered structures as compared to halogenozincate(II), ab-initio calculations were performed. The stability of MX 5 3- (M = Cd, Zn; X = Cl, Br) is compared. Isolated ZnX 5 3- and CdBr 5 3- ions are not stable. On the other hand a trigonal bipyramid CdCl 5 3- ion is considered to be subtly stable in the crystal mainly due to Coulomb attractive interactions between the positively charged metal cation Cd 2+ in a CdCl 3- fragment and two Cl - ions.

The temperature and enthalpy of the phase transition and fusion of EuCl 2 were determined and found to be 1014 K, 11.5 kJ mol -1 and 1125 K, 18.7 kJ mol -1 , respectively. Addition­ ally, the heat capacity of solid EuCl 2 was measured by Differential Scanning Calorimetry in the temperature range 306 -1085 K. The results were fitted to the linear equation C 0 p,m = (68.27 + 0.0255 T/K) J mol -1 K -1 in the temperature range 306 -900 K. Due to discrepancies in the liter­ ature on the temperature of fusion of EuCl 2 , the determination of the NaCl-EuCl 2 phase diagram was repeated. It consists of a simple eutectic equilibrium at T eut = 847 K with x(EuCl 2 ) = 0.49.

The molar enthalpies of mixing (Δ mix H m ) of MCl-EuCl 2 (M = Na, K, Rb) liquid binary systems were measured at 1138 K over the whole composition range by direct calorimetry. A Calvet type calorimeter was used, and mixing of the two liquid components was achieved by the ampoule break-off technique under argon at atmospheric pressure. The enthalpy of mixing of these systems is negative over the whole composition range with a minimum of approximately -0.5, -3.5 and -4.5 kJ mol -1 for M = Na, K, Rb, respectively. The least-squares coefficients A, B, C in the equation A (kJ mol -1 ) = A + B x + C x 2 , where λ is an interaction parameter, are reported. From the trend observed in these MCl-EuCl 2 systems it was possible to estimate the mixing enthalpy of the CsCl-EuCl 2 system.

Thermodynamic measurements have been carried out on the binary system of a swallow-tailed liquid crystal A = bis{[2,2-di(n-hexyloxycarbonyl)ethenyl]phenyl} biphenyl-4,4'-dicarboxylate (4DS6) and B = 4-n-octyloxyphenyl 4-rc-pentyloxybenzoate (5O/O8). A filled smectic A phase is induced in the concentration range 0.11 < x A < 0.75. The maximum of the SmA-N transition temperature (365 K) is observed for x A = 0.33. Dilatometric measurements show that the packing density in the filled phases is increased. High-pressure DTA is employed in order to investigate the coexistence range of the liquid crystalline phases and the slopes of the transition lines. The slopes of the melting curves for the mixtures are significantly smaller than those for the pure components. The slopes for the smectic - nematic - isotropic transitions are considerably larger. The coexistence range for the (smectic + nematic) phases does not seem to be pressure-limited, rather it increases with pressure.

We apply a recently introduced cognitive system for dynamics recognition to a two-dimensional array of coupled oscillators. The cognitive system allows for both the control and the adaptation of spatio-temporal patterns of that array of oscillators. One array that shows Turing-pattems in a self-organizational manner is viewed as an externally presented dynamics (stimulus) which is mapped onto a mirror dynamics, whereby the latter is capable to simulate (simulus). Two of the parameters of the stimulus are thereby regarded to be unknown and have to be estimated by the cognitive system. The cognitive system itself consists of dynamical modules that are stimulated by the external dynamics in the sense of Pyragas' external force control mechanism and thereby yield measures of how good they match the stimulus. These measures are used as weights to construct the simulus. The adaptation process is performed "on the fly", i. e., without the storage of data. The proposed cognitive system, therefore, is a prominent candidate for the construction of a control device for a permanent real time observation of an external dynamical system in order to interfere instantaneously when necessary.

The conductivities of the binary room-temperature molten salt systems AlCl 3 -N-n-butylpyridinium chloride (BPC), AlCl 3 -l-ethyl-3-methylimidazolium chloride (EMIC) and AlCl 3 -benzyltriethylammo-nium chloride (BTEAC) have been measured at different temperatures and compositions by a d.c. four-probes method. There is a maximum of the conductivity at 50 mol% AlCl 3 in the AlCl 3 -BPC and AlCl 3 -EMIC systems at 40 to 80 °C, their activation energies being relatively low (20.79 and 14.76 kJ/mol, respec­ tively). As to the A1C13-BTEAC system, there is an irregular change in the conductivity at 40-70 mol% AlCl 3 in the temperature range 50 to 80 °C. The conductivities of the three RTMS are in the order AlCl 3 -EMIC > AlCl 3 -BPC > AlCl 3 -BTEAC, the reason being discussed.

Differential scanning calorimetry on (Li 1-x K x ) 2 SO 4 mixed crystals, where x = 0.01, 0.1, 0.3 and 0.5, revealed that, as the potassium content increases, the first high temperature phase of the intermediate LiKSO 4 phase at T - 432 °C grows and shifts to higher temperature, and a double-phase mixture consisting of LiKSO 4 and Li 2 SO 4 exists for x< 0.5. Ionic conductivity measurements on (Li 1-x K x ) 2 SO 4 mixed crystals for x < 0.5 did show that the electrical conductivity increases as the Li 2 SO 4 concentration increases, with an average activation energy of 0.9 eV. The enhanced electrical conductivity is primarily a result of the increase in the Li + ion (charge carriers) concentration and/or the formation of a diffuse space charge layer at the interface between the two phases.

A value of the finestructure constant at the unification eneigy is obtained by a dimensional analysis of quantum gravity and fluid dynamics. The derivation assumes that the vacuum is a superfluid made up of positive and negative Planck mass particles obeying an exactly nonrelativistic law of motion with Lorentz invariance a low energy approximation. The dimensional analysis presented gives a value for the finestructure constant in good agreement with the empirical value 1/α = 25.

New intermolecular H-bonded liquid crystalline complexes, viz., 2-(p-n-heptyloxybenzylidene imi-no)-5-chloro-pyridine:p-/z-alkoxybenzoic acid; (HICP:nABA) (where n denotes the alkoxy carbon num­ bers 3 to 10 and 12) exhibiting smectic-F (n = 12) and smectic-G phases have been synthesized and char­ acterized by Thermal Microscopy and Differential Scanning Calorimetry (DSC). Detailed IR (solid and solution states) analysis confirms the existence of intermolecular H-bonding between the pyridyl nitro­ gen and the COOH group of the p-n-alkoxybenzoic acid moiety. The phase behaviour of the series is discussed in the light of reported data on free p-n-alkoxybenzoic acids. The crystallization kinetics of a representative complex, using the DSC technique, is discussed. The mechanism of the crystal growth of the new crystalline smectic-G phase is computed with the Avrami equation.

Two novel intermolecular hydrogen bonding mesogenic series comprising two distinct structural iso­ mers nABA:R:nABA and «ABA:H:«ABA (where R = resorcinol; H = hydroquinone; nABA = p-n-al-kyloxybenzoic acid with the alkyl carbon number varying from propyl-to decyl-and dodecyl-) have been synthesized using resorcinol and hydroquinone as central bent and linear cores, respectively. The thermal and phase behaviour of these complexes is studied by thermal microscopy and differential scan­ ning calorimetry. The IR spectral data confirm the formation of intermolecular hydrogen bonding between the OH group of the non-mesogen and -COOH group of the nABA moiety. Thermal studies reveal the existence of new phases: smectic-A and smectic-G. Comparative phase transition studies sug­gest that these isomers exhibit a different trend of mesomorphism.

27 AI NMR spectra of pure crystalline and molten A1C13 and of RECI3-AICI3 (RE = Y, La) glass form­ ing binary mixtures have been obtained. Compositions corresponding mainly to YC13/A1C13 = 1/3 and LaCiyAlC^ = 1/3.7 have been studied from the glassy and crystalline state up to the melt. The 27A1 spectra can be unambiguously assigned to four-coordinated Al-species, such as A12C16, 'A1C14', and 'A12C17\ The chemical shifts lie between 95 and 110 ppm, very well separated with the -1.6 ppm giv­ en by the 'A1C16' coordination in solid A1C13. From the temperature evolution of the 27Al NMR spec­ tra, a description for the dynamic behaviour of these systems is proposed.

Rates of Heck-type reactions, catalysed by a Pd-catalyst with benzothiazole carbene as ligands, are strongly influenced by tetrabutylammonium bromide utilized as solvent.

An apparatus has been manufactured to measure the density of molten KHF 2 . A linear dependence of the density on temperature is found in the range of 280-450 °C.

We show that particular solutions of certain nonlinear field equations can be constructed using Bäcklund transformations, recursion and Bessel functions.