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  • pillared zirconium phosphonate  (1)
  • Γ-convergence  (1)
  • 1995-1999  (2)
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Years
  • 1995-1999  (2)
Year
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 82 (1996), S. 743-796 
    ISSN: 1572-9613
    Keywords: Interfaces ; Kac potentials ; surface tension ; Γ-convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider an Ising spin system with Kac potentials in a torus of ℤd,d〉-2, and fix the temperature below its Lebowitz-Penrose critical value. We prove that when the Kac scaling parameter γ vanishes, the log of the probability of an interface becomes proportional to its area and the surface tension, related to the proportionality constant, converges to the van der Waals surface tension. The results are based on the analysis of the rate functionals for Gibbsian large deviations and on the proof that they Γ-converge to the perimeter functional of geometric measure theory (which extends the notion of area). Our considerations include nonsmooth interfaces, proving that the Gibbsian probability of an interface depends only on its area and not on its regularity.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1573-4854
    Keywords: mesoporous zirconium phosphate ; high surface area zirconium phosphate ; layered zirconium pyrophosphate ; pillared zirconium phosphonate
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Mesoporous zirconium phosphate pyrophosphate of composition Zr(P2O7)0.81(O3POH)0.38 was obtained by calcination at 600°C of a mesoporous zirconium phosphite diphosphonate, Zr[(O3P-C6H4-PO3)0.54 (O3P-C6H4-PO3H2)0.13(O3PH)0.79]. The surface area of this completely inorganic material (215 m2/g) was lower than that of its inorgano-organic precursor (350 m2/g); however, both materials exhibited the same pore distribution, with an average pore diameter of ≈4 nm, and similar values of the mesopore volume (0.21 and 0.28 cm3/g, respectively). These results showed that the thermal treatment at 600°C leaves nearly unaltered the mesoporous structure of the precursor. 31P solid state NMR and TEM investigations were also carried out and discussed. The material obtained represents a considerable advancement in the preparation of zirconium phosphates with high surface area. Due to the good thermal stability of its surface acid groups (700–800°C), it is of interest for potential uses as an acid catalyst at high temperature.
    Type of Medium: Electronic Resource
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