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  • 1
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Analytical chemistry 57 (1985), S. 628-632 
    ISSN: 1520-6882
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 25-33 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present Raman spectroscopic measurements in the OH stretch region of water (2900 to 3800 cm−1) for the temperature range 80 to −33 °C. This latter temperature represents the homogeneous limit of nucleation for our bulk samples. We find that the temperature dependence of both our intensity and depolarization ratio measurements are well described by a two-state model in which both states have frequency dependent depolarization ratios. We argue that the hydrogen bonded mode of the spectrum begins to develop a collective nature at both its low and high frequency ends. This collective nature can explain a breakdown in isosbestic behavior at low temperature. It is suggested that these collective modes may be due to in- and out-of-phase motions of OH oscillators. Their intensity approaches those seen in amorphous solid water as the liquid is cooled to the apparent singular temperature Ts(approximately-equal-to)−45 °C, for a variety of bulk properties. We use our Raman data to make an estimate of hydrogen bond probability and show that four bonded molecules would percolate near the singularity. We then argue that the collective mode grows because clusters of four bonded molecules grow in extent until at Ts percolation occurs to yield an infinite cluster with the amorphous solid's collective spectrum.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 13-22 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We have studied the OH stretch spectrum in water to explore the effects of interoscillator coupling. Both H2O, which may have significant intra and intermolecular coupling, and dilute HOD in D2O, which is isotopically decoupled, were studied over a broad range of temperature from −33 °C to 160 °C. By adding a small amount of a calibration dopant, we obtained quantitative spectra. We found interoscillator coupling plays a large role at all temperatures. At high temperature, intramolecular coupling contributes to a downshift in the peak position for H2O as compared to HOD. Intermolecular coupling, however, still has some influence at high temperature. At low temperature, the large excess intensity below 3200 cm−1 in H2O compared to HOD we find is due to an enhanced Raman cross section due to intermolecularly coupled in-phase OH stretch oscillations. We define a degree of delocalization for coupling as the idealized number of perfectly in-phase oscillators that could cause the enhanced scattering and find N(approximately-equal-to)2 for liquid H2O at −33 °C. An exact isosbestic crossing is not found and this can be understood given the changing line shape that the intermolecular coupling can induce. All the properties of the spectrum approach those found in amorphous solid water or ice near the supercooled water anomalous temperature, Ts(approximately-equal-to)−45 °C.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 6954-6961 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present Raman data for the OD stretch mode of 10 mol % HOD in H2O for the liquid phase from −31.5 to 160 °C. We find that an exact isosbestic does not hold, but rather the crossing of isotherms slowly but uniformly changes with temperature. We present an analysis based on Boltzmann statistics which gives evidence for a distribution of deuterium hydrogen bond strengths with minimum energy near the frequency (2440 cm−1) also found in the solid ice and amorphous solid phases. This analysis also gives evidence for a band of frequencies above 2630 cm−1 due to OD oscillators all at essentially the same high energy relative to the strongest hydrogen bonds, and we interpret this band as due to broken hydrogen bonds. This allows us to calculate hydrogen bond probabilities, and we find this probability increases with decreasing temperature and approaches a value equal to the four bonded percolation threshold near the singular temperature Ts (approximately-equal-to)−45 °C for the anomalies of supercooled water. Peak frequency and full width at half-maximum of the OD stretch band are found to drop precipitously to the amorphous solid values as T→Ts implying the ultimate state of supercooled water is similar to the amorphous solid.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Biophysics and Biomolecular Structure 16 (1987), S. 423-454 
    ISSN: 0084-6589
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
    Topics: Biology , Physics
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 87 (1987), S. 4840-4845 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We have measured the density of supercooled water (H2O) in the range −33.41≤T≤−5.23 °C. Our samples were held in glass capillary tubing with an approximate inside diameter of 0.3 mm=300 μ. These samples were prepared by Mossop's method and could be cooled to their homogeneous nucleation limit before freezing. We compare our density data to other measurements using capillaries and demonstrate what appears to be an excess density in smaller capillaries which is inversely proportional to the capillary inside diameter. The origins of this excess density are unknown, but we show its effect is insignificant on our measurement. The thermal expansivities derived from our data are fit to a power law in temperature relative to a singular temperature. These results are inconclusive due to a poor knowledge of the background expansivity.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 84 (1986), S. 5085-5089 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We have measured the densities of supercooled H2O to −34.2 °C, and D2O to −19.2 °C in 25 μ i.d. glass capillaries. Because of the small size of our capillaries, some surface energy effects appear to be present in our data. Despite this we found that reasonably accurate values of the thermal expansivity could be obtained from our data. Our expansivity results support the recent contention of Leyendekkers and Hunter that previous estimates of the anomalous expansivity of supercooled water have been overestimated. The results of a power-law analysis of our expansivity were ambiguous due to the poorly known background expansivity.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Journal of Theoretical Biology 25 (1969), S. 113-126 
    ISSN: 0022-5193
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Biology
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    China Economic Review 5 (1994), S. 59-82 
    ISSN: 1043-951X
    Keywords: [JEL classification codes] J43 ; [JEL classification codes] O12
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Economics
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Advances in computational mathematics 5 (1996), S. 329-359 
    ISSN: 1572-9044
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The LambertW function is defined to be the multivalued inverse of the functionw →we w . It has many applications in pure and applied mathematics, some of which are briefly described here. We present a new discussion of the complex branches ofW, an asymptotic expansion valid for all branches, an efficient numerical procedure for evaluating the function to arbitrary precision, and a method for the symbolic integration of expressions containingW.
    Type of Medium: Electronic Resource
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