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 wa...
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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 800nm at OM 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'?".
Successive band-splitting transitions occur in the one-dimensional map xi+1=g(xi),i=0, 1, 2,... withg(x)=αx, (0 ⩽x⩽ 1/2) −αx +α, (1/2<x⩽ 1) as the parameterαis changed from 2 to 1. The transition point fromN(=2...
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Successive band-splitting transitions occur in the one-dimensional map xi+1=g(xi),i=0, 1, 2,... withg(x)=αx, (0 ⩽x⩽ 1/2) −αx +α, (1/2time-correlation functionξi=〈δxiδx0〉/〈(δx0)2,δxi≡ xi−〈xi〉 is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition pointα=√2,ξi−[(10−4√2)/17] δi,0-[(10√2-8)/51]δi,1+ [(7 + 4√2)/17](−1)ie−yi, whereγ≡√2(α−√2) is the damping constant and vanishes atα=√2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly atα=√2. The asymptotic expression forξihas been obtained by deriving an analytic form ofξifor a sequence ofαwhich accumulates to √2 from the above. Near the transition pointα=(√2)1/N, the damping constant ofξifori⩾Nis given byγN=√2(αN-√2)/N. Numerical calculation is al
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