Oscillations, Waves, and Interactions - GWDG

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360 R. Pottel, J. Haller and U. Kaatze range [50]. Ion complex formation of the subgroup metal ion Cu 2+ seems to be stabilized by the Jahn-Teller effect. There are indications of an additional low-frequency relaxation term in the spectra of CuCl2 solutions which has not been covered by the measurements because transducer electrodes of the resonator cells were corroded by the samples [50]. Likely this low-frequency term reflects the equilibrium between the ion pairs and the outer-sphere complexes. Also striking is the substantial increase in the amplitude A of calcium salt solutions when chloride is substituted by nitrate (Table 3). We suppose stronger interactions of (Ca 2+ )aq with the nitrate ion, due to its lone pair electrons and its delocalized π orbital [104], than with the chloride ions with its spherical s 2 p 6 electron configuration. An unexplained result is the considerably smaller difference in the amplitudes of MgCl2 and Mg(NO3)2 solutions. 5 Conclusions Multistep associations of ions have been among the first “immeasurable fast” reactions [1] that have been effectively measured and described in detail [9,10]. Nevertheless still today much interest is directed towards these reactions. Though the Eigen- Tamm mechanism has been verified by broadband ultrasonic spectrometry of scandium sulfate solutions [17] the existence of outer-outer sphere complexes in solutions of 2:2 valent salts is still under discussion [32]. As early evaluations of experimental spectra, without any assistance from computer facilities, used a slightly incorrect high-frequency background term in the ultrasonic excess absorption spectra, a distribution of relaxation times may have been simulated. More recent broadband spectra of MnSO4 solutions (Fig. 9) reveal only two Debye-type relaxation terms within the frequency range of measurements. These terms are assigned to the coupled equilibria between completely dissociated ions and outer-sphere complexes and between the latter and contact ion pairs. Halides of second subgroup metals, such as zinc chloride, display a broad variety of ion complex structures in solution. Their spectra have indeed been discussed in terms of a complex equilibrium between stoichiometrically well-defined species [30] but have been also considered assuming fluctuating ion clusters with intra- and intercluster correlations [31]. Small-amplitude ultrasonic relaxation terms have been revealed for solutions of 2:1 valent electrolytes and have been related to the equilibrium between the complex of encounter and the outersphere complexes [34,35]. This equilibrium is of significance also for biochemistry as it may interfere with other association mechanisms, like counter ion condensation on polyelectrolytes, carbohydrate-cation interactions [107], as well as inclusion complex formation [108]. Acknowledgments We are indebted to the technicians of the institute for their continual support with precision engineering components, electronic devices, computer facilities, and figure layout.
References Multistep association of cations and anions 361 [1] M. Eigen, Nobel Lecture, 1967. [2] K. Tamm and G. Kurtze, ‘Absorption of Sound in Aqueous Solutions of Electrolytes’, Nature 168, 346 (1951). [3] G. Kurtze, ‘Untersuchung der Schallabsorption in wäßrigen Elektrolytlösungen im Frequenzbereich 3 bis 100 MHz’, Nachr. Akad. Wiss. Gött. Math.-Phys.-Chem. Kl., 57 (1952). [4] K. Tamm, ‘Schallabsorptionsmessungen in Wasser und in wässerigen Elektrolytlösungen im Frequenzbereich 5 kHz bis 1 MHz’, Nachr. Akad. Wiss. Gött. Math.- Phys.-Chem. Kl., 81 (1952). [5] G. Kurtze and K. Tamm, ‘Measurements of Sound Absorption in Water and in Aqueous Solutions of Electrolytes’, Acustica 3, 33 (1953). [6] K. Tamm, G. Kurtze, and R. Kaiser, Measurements of Sound Absorption in Aqueous Solutions of Electrolytes, Acustica 4, 280 (1954). [7] K. Tamm, in Handbuch der Physik 11.I, edited by S. Flügge (Springer, Berlin, 1961). [8] M. Eigen, G. Kurtze, and K. Tamm, ‘Zum Reaktionsmechanismus der Ultraschallabsorption in wäßrigen Elektrolytlösungen’, Z. Elektrochem. Ber. Bunsenges. Phys. Chem. 57, 103 (1953). [9] M. Eigen and K. Tamm, ‘Schallabsorption in Elektrolytlösungen als Folge chemischer Relaxation I. Relaxationstheorie der mehrstufigen Dissoziation’, Z. Elektrochem. Ber. Bunsenges. Phys. Chem. 66, 93 (1962). [10] M. Eigen and K. Tamm, ‘Schallabsorption in Elektrolytlösungen als Folge chemischer Relaxation II. Meßergebnisse und Relaxationsmechanismen für 2-2-wertige Elektrolyte’, Z. Elektrochem. Ber. Bunsenges. Phys. Chem. 66, 107 (1962). [11] K. G. Plaßand A. Kehl, ‘Schallabsorption in Lösungen 2-2-wertiger Elektrolyte im Frequenzbereich 0.3 GHz bis 2.8 GHz’, Acustica 20, 360 (1968). [12] L. G. Jackopin and E. Yeager, ‘Ultrasonic Relaxation in Manganese Sulfate Solutions’, J. Phys. Chem. 74, 3766 (1970). [13] K. Fritsch, C. J. Montrose, J. L. Hunter, and J. P. Dill, ‘Relaxation Phenomena in Electrolytic Solutions’, J. Chem. Phys. 52, 2242 (1970). [14] D. P. Fay and N. Purdi, ‘Ultrasonic Absorption in Aqueous Salts of the Lanthanides III. Temperature Dependence of LnSO4 Complexation’, J. Phys. Chem. 74, 1160 (1970). [15] A. Bechtler, K. G. Breitschwerdt, and K. Tamm, ‘Ultrasonic Relaxation Studies in Aqueous Solutions of 2-2-Electrolytes’, J. Chem. Phys. 52, 2975 (1970). [16] P. Hemmer, ‘The Volume Changes in Ionic Association Reactions’, J. Phys. Chem. 76, 895 (1972). [17] A. Bonsen, W. Knoche, W. Berger, K. Giese, and S. Petrucci, ‘Ultrasonic Relaxation Studies in Aqueous Solutions of Aluminium Sulphate and Scandium Sulphate’, Ber. Bunsenges. Phys. Chem. 82, 678 (1978). [18] R. Pottel, ‘Die komplexe Dielektrizitätskonstante wäßriger Lösungen einiger 2-2wertiger Elektrolyte im Frequenzbereich 0.1 bis 38 GHz’, Ber. Bunsenges. Phys. Chem. 69, 363 (1965). [19] R. Pottel, in Chemical Physics of Ionic Solutions, edited by B. E. Conway and R. G. Barradas (Wiley, New York, 1966). [20] U. Kaatze and K. Giese, ‘Dielectric Spectroscopy on Some Aqueous Solutions of 3:2 Valent Electrolytes. A Combined Frequency and Time Domain Study’, J. Mol. Liq. 36, 15 (1987). [21] U. Kaatze, ‘Dielectric Effects in Aqueous Solutions of 1:1, 2:1, and 3:1 Valent Elec-
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Thomas Kurz, Ulrich Parlitz, and Ud
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erschienen im Universitätsverlag G
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Bibliographische Information der De
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iv Contents Laser speckle metrology
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Oscillations, Waves and Interaction
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Applied physics at the “Dritte”
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noise component [GNE] 5 4 3 2 1 can
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3.4 Transfer to running speech Spee
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3.4.2 Analysis of running speech Sp
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Speech research 33 Area [Pixels] 60
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82 D. Ronneberger et al. Figure 8.
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104 D. Ronneberger et al. [4] J. Br
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106 D. Ronneberger et al. strömung
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108 D. Guicking synchronised tuning
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110 D. Guicking primary noise micro
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112 D. Guicking primary sensor desi
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114 D. Guicking by an antiphase sou
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116 D. Guicking R L C C + + 1 1−C
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118 D. Guicking More involved than
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120 D. Guicking In the 1980s, longi
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122 D. Guicking with electrodynamic
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124 D. Guicking 3.6 Noise reduction
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126 D. Guicking the turbulence of a
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128 D. Guicking References [1] Lord
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130 D. Guicking [44] Falcke, H.,
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132 D. Guicking [84] J. Melcher,
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134 D. Guicking [125] D. Heyland et
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136 D. Guicking [166] S. Zommer et
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138 D. Guicking [212] M. L. Post an
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140 W. Lauterborn et al. liquid κ
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142 W. Lauterborn et al. Figure 2.
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144 W. Lauterborn et al. nator, and
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158 W. Lauterborn et al. laser puls
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168 W. Lauterborn et al. R [µ m] 1
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170 W. Lauterborn et al. [17] M. P.
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172 R. Mettin (a) (b) Figure 1. Bub
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174 R. Mettin 0 ms 2 mm 1 ms 2 ms 3
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176 R. Mettin important quantity ch
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178 R. Mettin 100 kPa 200 kPa | | F
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180 R. Mettin Figure 7. Trapped sin
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182 R. Mettin concentration of spec
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184 R. Mettin which is called the p
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186 R. Mettin R 02 [µm] R 02 [µm]
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188 R. Mettin constant to M a = 2π
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190 R. Mettin (a) p a [Pa] 140 120
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192 R. Mettin z [mm] 5 4 3 2 1 0 -1
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198 R. Mettin [52] R. Mettin, C.-D.
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260 K. D. Hinsch Generally, any of
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262 K. D. Hinsch Figure 1. Monitori
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264 K. D. Hinsch Figure 3. ESPI stu
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266 K. D. Hinsch Figure 4. Deterior
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268 K. D. Hinsch Often, in-plane mo
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270 K. D. Hinsch Figure 7. Optical
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272 K. D. Hinsch Figure 9. Humidity
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276 K. D. Hinsch Figure 13. Map of
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278 K. D. Hinsch References [1] D.
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280 Schreiber not moving along with
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282 Schreiber These properties made
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284 Schreiber Figure 3. The G ring
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286 Schreiber Rotation Rate [rad/s]
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290 Schreiber n1 D A B n Figure 8.
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292 Schreiber Beamwalk [µm] 80.0 7
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294 Schreiber ∆ Perimeter [*10e12
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296 Schreiber and the last term acc
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298 Schreiber Δf [µHz] 100 50 0 -
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300 Schreiber formation of a new wo
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302 Schreiber PSD [*10 16 (rad/s) 2
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304 Schreiber 7.2 The ring laser co
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308 Schreiber Est. Phase Vel. (m/s)
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410 U. Parlitz 4 10 5 5 (a) (b) (c)
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412 U. Parlitz two-parameter studie
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414 U. Parlitz GN differential opti
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416 U. Parlitz P 1 P 2 P 3 S P 1 P
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418 U. Parlitz Figure 9. Correlatio
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420 U. Parlitz series” where for
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422 U. Parlitz current state future
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424 U. Parlitz tion [69] of two uni
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426 U. Parlitz LD1 LD2 M BS1 BS2 OD
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428 U. Parlitz with a clear tendenc
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430 U. Parlitz (a) y (c) y 40 20 È
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432 U. Parlitz [29] P. Grassberger,
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434 U. Parlitz [76] H. D. I. Abarba
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436 S. Lakämper and C. F. Schmidt
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462 Index basin of attraction, 144
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464 Index cone bubble structure, 19
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466 Index turbulent, 111, 126 fluct
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468 Index LPC, 29 luminescence of b
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470 Index peak factor, 38, 43 Peier
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472 Index laser-induced bubble, 152
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474 Index ultraharmonic resonance,
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