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  • colloidal particle  (2)
  • Electrostatic interaction  (1)
  • Kuhn-Tucker optimality conditions  (1)
  • 1
    ISSN: 1435-1536
    Schlagwort(e): Key words Evanescent wave ; dynamic light scattering ; particle-wall interaction ; colloidal particle ; time-correlation function
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Maschinenbau
    Notizen: Abstract  The diffusion behavior of polymer latex particles in dispersion near the quartz interface has been estimated by evanescent wave dynamic light scattering (EVDLS) technique. The diffusion coefficient of the particles was measured as a function of the distance between the particle and interface. The apparent diffusion coefficient estimated by EVDLS was small for particles near the interface and increased upon increasing the distance from the interface, and then saturated at a certain value which is close to the value expected for free-motion. The range of the distance over which diffusion was affected by interaction with the interface depended on the added salt concentration. This means that the diffusion of the particle is influenced by an electrostatic interaction between the particle and quartz interface in addition to the hydrodynamic effect near the wall. This range was found to be more than 800 nm at 0 M salt condition but about 400 nm at 10-4 and 10-3 M salt conditions. Hence it is appropriate to say that the hydrodynamic effect reaches up to 400 nm and the electrostatic effect is longer ranged, more than 800 nm, for the system studied here. The EVDLS technique is a very powerful tool for quantitative estimations of the dynamic behavior of the particle near the interface and for estimation of the range where the wall effect is dominant. EVDLS will give us an answer to the question of “where is the ‘interface’ and where is the ‘bulk’?”.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    ISSN: 1435-1536
    Schlagwort(e): Evanescent wave light scattering ; colloidal particle ; interaction potential ; thermal vibration ; particle-wall interaction
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Maschinenbau
    Notizen: Abstract The dynamic and static characteristics of a polystyrene latex particle in dispersion interacting with a glass surface were studied by the evanescent wave light-scattering microscope (EVLSM) technique originally proposed by Prieve et al. for static studies. The dynamic behavior of the thermal vibration of the particle in a potential well created by electrostatic interaction between the particle and glass and gravity was clearly and quantitatively estimated, in addition to the estimation of the potential profile itself. The potential minimum became shallower with increasing added salt concentration. It was also clearly observed that the vibrational motion of the particle in the well became large in amplitude and the probability of the occurrence of the large vibration became large with increasing salt concentration. Such information on the dynamics is essential for the correct under-standing of the interaction potential. The EVLSM method is shown to be a very powerful technique for the estimation of not only the potential profile but also dynamic characteristics.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 3
    ISSN: 1435-1536
    Schlagwort(e): Key words Evanescent wave ; Surface modification ; Light scattering ; Polystyrene latex ; Electrostatic interaction
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Maschinenbau
    Notizen: Abstract The profile of the interaction potential between polystyrene latex particle and chemically modified glass surface was estimated directly by the evanescent wave light scattering microscope (EVLSM) method; this enables us to measure the distance between particle and surface as a function of time in the order of less than a millisecond. The minimum of the potential profile, which is the result of an electrostatic repulsion and an apparent attraction by gravity between the particle and surface, was clearly observed. To change the electrostatic nature, the glass surface was chemically modified by treatment with a silanization reagent and a vinyl monomer with a sulfonate group. As the absolute value of the zeta potential of the glass surface became larger, the position of the potential minimum on the interaction potential profile shifted away from the glass surface, reflecting an increase of electrostatic repulsion between the particle and the wall. The ionic strength dependence of the potential profile was also clearly observed. In conclusion, EVLSM is a powerful tool for the quantitative estimation of particle-wall interactions.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 4
    Digitale Medien
    Digitale Medien
    Springer
    Journal of optimization theory and applications 31 (1980), S. 331-342 
    ISSN: 1573-2878
    Schlagwort(e): Minimax theorems ; Kuhn-Tucker optimality conditions ; duality theorem ; converse duality theorem ; constraint qualifications
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract For a convex-concave functionL(x, y), we define the functionf(x) which is obtained by maximizingL with respect toy over a specified set. The minimization problem with objective functionf is considered. We derive necessary conditions of optimality for this problem. Based upon these necessary conditions, we define its dual problem. Furthermore, a duality theorem and a converse duality theorem are obtained. It is made clear that these results are extensions of those derived in studies on a class of nondifferentiable mathematical programming problems.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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