Debye plateau

In Markovian approximation (zj =0) this quantity approaches the famous Debye plateau shown in Fig. 2.3 whereas non-Markovian absorption coefficient (2.56) tends to 0 when ft) — 0 as it is in reality. This is an advantage of the Rocard formula that eliminates the discrepancy between theory and experiment by taking into account inertial effects. As is seen from Eq. (2.56) and the Hubbard relation (2.28)... 

Debye phenomenon and theory 59-60, 198 dense media see orientational relaxation in dense media orientational diffusion 70 Debye plateau 6, 73, 81 dephasing see adiabatic dephasing detailed balance principle, spectral collapse 137... 

In the spirit of Eq. 3.39 and neglecting the ongoing decay of Schain(Q>0 due to local reptation, from the heights of the achieved plateaus we may obtain a first estimate for the amount of confinement. Identifying the plateau levels with a Debye-Waller factor describing the confinement we get d=44 A, a value that is a lower estimate for the true tube diameter since S ° (Q,t) is not fully relaxed. The horizontal bars in Fig. 3.16 are the predictions from this Debye-Waller factor estimate. 

Figure 5(a) shows the static structure factor of Rouse chains with N = 16, 32, 64 plotted against normalized scattering vector (fb /R. In this representation, S Debye function/(y ) (solid line) for q[Pg.143]

So, Debye s treatment leads to a plateau for the potential o, at high c. However, it is observed experimentally that some salts do not exhibit any plateau, but rather a continuously decreasing pattern. As the frequency is typically on the order of 100 kHz for a wave lenght of 1 cm and a pressure amplitude around 0.1 Atm in water, absorption effect or the ionic association could not explain this decreasing. The consideration of non ideal terms gives an explanation of this behaviour. 

The range of the self-similar internal structure ends when r approaches Rq. Around q l/Jf o the curve deviates from the plateau and decays to zero. As mentioned earlier, universal behavior is also limited towards small distances. Specific polymer properties emerge, if one approaches distances in the order of the persistence length. For this reason, for polymers at higher s deviations from the Debye-structure function show up, beginning around q As indicated in Fig. 2.10, one observes an increase in the slope, and... 

Unlike the cylindrical case of Eq. [265], this expression is not a function of Koa alone. We have plotted this fraction in Figure 36 for two values of the Debye constant (0.01 and 0.1 and for two different sphere radii (10 and 20 A). For micelles of radius 20 A, there is a noticeable difference between Kd = 0.01 and 0.1 A in the rate at which the limiting fraction plateau is reached. The condensation radius determined from Eq. [269] and the corresponding potential as a function of the scaled charge density are displayed in Figures 29 and 30, respectively, and compared with those for the plane and cylinder. Comments follow those given earlier for a charged cylinder. 

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