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  • American Institute of Physics (AIP)  (6)
  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 102 (1995), S. 5077-5081 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The irreversible random adsorption of particles on a surface is guided by the available surface function φ. The relative fluctuation σ2/〈n〉 in the number of particles n in a finite region provides one characterization of the distribution of these particles on the surface. We show rigorously that the two quantities are given by the same expression to first order in the surface coverage, for any irreversible adsorption process. This is confirmed in two particular cases: for random sequential adsorption, where values for σ2/〈n〉 from numerical simulations can be compared to an analytic expression for φ, and for Ballistic deposition, where experimental values for deposition under a strong gravitational influence can also be compared to an existing analytical expression for φ. © 1995 American Institute of Physics.
    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 103 (1995), S. 8285-8295 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The statistical properties of surfaces covered by irreversibly adsorbed colloidal particles are studied as a function of the Péclet number (or equivalently as a function of their rescaled radius R*). More precisely, the radial distribution function g(r) is determined as a function of the coverage θ for five systems corresponding to different values of R*. Also measured is the reduced variance σ2/〈n〉 of the number n of adsorbed particles on surfaces of given area out of the adsorption plane. Finally, the evolution of 〈n〉 with the concentration of particles in solution during the deposition process is determined for the different systems. This allows us to obtain information on the available surface function Φ. All these parameters are compared to their expected behavior according to the random sequential adsorption (RSA) model and to the ballistic model (BM). It is found that the radial distribution function of the system of particles characterized by R*〈1 is well predicted by the RSA model whereas for R*(approximately-greater-than)3 the BM can serve as a good first approximation. On the other hand, one finds surprisingly that the available surface function Φ and the reduced variance σ2/〈n〉 vary with the coverage θ in a similar way for all the systems over the range of value of R* investigated. Their behavior corresponds, in first approximation, to the expectations from the BM. In particular, the reduced variance σ2/〈n〉 exhibits a horizontal tangent at low coverage whereas the RSA model predicts an initial slope of −4. This result is the more intriguing that σ2/〈n〉 is directly related to the radial distribution function g(r), which does vary with R*. Finally, higher order moments of the distribution of the number of particles n adsorbed on our surfaces are also determined as a function of the coverage. They behave, within experimental errors, like those of a Gaussian distribution as predicted by the central limit theorem. © 1995 American Institute of Physics.
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 6082-6085 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Scanning angle reflectometry (SAR) is used to investigate the structure of antigen/antibody layers deposited on a silica surface. The reflectivity curves are analyzed by the means of the optical invariants, which permits the determination of three structural characteristic parameters for the layer. A new invariant is constructed that yields information about the repartition of mass in the layer and thus goes beyond the usual uniform layer model. In our case, this model does not hold: the layer appears to be denser away from the adsorbing silica surface than near that surface. © 1996 American Institute of Physics.
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 1646-1653 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We investigated the suitability of reflectometry as a sizing method for polystyrene latex particles. This technique, where the particles are adsorbed at a quartz/water interface, involves the analysis of the reflection around the Brewster angle of light polarized in the plane of incidence. A computation of a full reflectivity curve containing about 20 datapoints, taking into account all electromagnetic interactions, is extremely complex and may take up to 100 h on an Indy R4600 computer (Silicon Graphics, Mountain View, CA). To use the complete electromagnetic theory for analysis of experiments therefore is impractical. We analyzed the experimental reflectivity curves using an approximate theory (free-sphere model), which neglects all electromagnetic interactions between different particles and their images in the substrate. To assess the errors introduced by neglecting these interactions, we have calculated reflectivity curves using the full electromagnetic theory for this system, and analyzed them with the free-sphere model. We found that the diameters determined with the free-sphere model deviate at most 2% from the actual values. The surface coverage determined with the free-sphere model is systematically smaller than the actual coverage. The difference can be as large as 15% at a coverage of 9%. We also show that size polydispersity of the sample plays a minor role in the analysis of the data. We illustrate the usefulness of the free-sphere model, by analyzing measurements in which polystyrene latex particles are swollen by an organic solvent that is miscible with water. © 1996 American Institute of Physics.
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 7416-7425 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: For stratified layers, it was recently demonstrated that information about the structure of thin dielectric layers could be determined from scanning angle reflectometry measurements independent of any model of the interface. A measure of the deviation of the film from uniform was defined and demonstrated to be measurable. This analysis is extended here to the case of particulate layers, where we show that the same uniformity parameter can give information about the deviation of the distribution of particles on the surface from a uniform one. Preliminary optical data on moderately sized polystyrene particles, 116 nm in diameter, suggest that the closest approach of two particles on the surface is considerably greater than their diameter. This is in agreement with direct measurements of the radial distribution functions of these particles adsorbed on surfaces under similar conditions. © 1998 American Institute of Physics.
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 3772-3785 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The perturbed Korteweg–de Vries equation is studied in a new way by a Green's function formalism without use of inverse scattering methods. The Green's function is determined by employing the Bäcklund transformation and Green's theorem. After a thorough analysis of the exact first-order solution with regard to secular terms, a two-time scale expansion leads to the adiabatic approximation and the first-order correction, in accordance with the results of Karpman and Maslov. Contrary to statements in the literature, the term tanh2 z in the expression for the modified phase of the perturbed soliton arises as a consequence of the systematically conducted first-order perturbation theory. © 1997 American Institute of Physics.
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