Diffusion relaxation time

We might compare this with the rotational diffusion relaxation time of Debye (18) ... 

Theory (Odijk et al., 1977/79, Mandel et al., 1983/86) predicts that in the dilute state (c < c ) most of the parameters of the solution (intrinsic viscosity, diffusivity, relaxation times) will be functions of the molar mass, but not of the polymer concentration. In the so-called semi-diluted solution state the influence of the polymer concentration (and that of the dissolved salts) becomes very important, whereas that of the molar mass is nearly absent. Experiments have confirmed this prediction. 

Predict the changes that would occur if the PS spheres were studied in a more viscous solvent like propanol. In particular, how would the time scale needed for data acquisition change Estimate the diffusive relaxation time t for your PS spheres in propanol at 25°C (for which rj = 1.945 cP and n = 1.385). 

Two timescales can be distinguished in the adsorption process of ionic species. The first timescale is characterized by the diffusion relaxation time of the EDL, = 1 / (D,k /) see Equations 5.32 and 5.34 above. It accounts for the interplay of electrostatic interactions and diffusion. The second scale is provided by the characteristic time of the used experimental method, tgxp, that is, the minimum interfacial age that can be achieved with the given method typically,... 

We must point out that if the adsorption layer contacts with a sufficiently deep liquid, then the diffusion relaxation time can be comparable with the adsorption relaxation time. In this case, the kinetics of the adsorption layer filling, which is determined by Eqs. (7.3.3) and (7.3.4), can be diffusion-controllable for small volume concentrations of surfactants in the solution or be governed by a diffusion-kinetic mechanism for higher concentrations [274]. A pure kinetic region of the adsorption layer filling is possible only in thin layers of surfactant solutions, for example, in liquid elements of foam structures. 

Recently, Ferri and Stebe [62] proposed a scaling low in order to directly compare the adsorption dynamics of different surfactants. By plotting dynamic surface tensions in a dimensional format n( t/ToVrio, where no=y(t)-yo is the equilibrium surface pressure and the diffusion relaxation time tq is defined by the following relationship... 

The relaxation time xi is then defined in the same way as the diffusion relaxation time given in paragraph 4.2 by Eq. (4.26). 

There is one point important to note here, the experimental data plotted as y( - 1) must cross the ordinate at a value identical to the surface tension of the surfactant-free system, i.e. the surface tension of water for a water/air interface. This is often not the case, in particular for drop volume or maximum bubble pressure experiments where due to the peculiarities of the measurement an initial surfactant load of the interface exists. It has been demonstrated in the book by Joos [16] that even in these cases, assumed it is the initial period of the adsorption time, the slope of the plot y( /t) yields the diffusion relaxation time defined by Eq. (4.26) and hence information about the diffusion coefficient. For small deviation from equilibrium we have the relationship... 

Here (0 is the oscillation frequency, and the parameter cOb is the characteristic frequency, which is inverse proportinal to the diffusion relaxation time Xd given in Eq. (35). This characteristic frequency exists also for any transient relaxation processes. The interfacial response functions for a number of transient relaxations were discussed recently by Loglio et al. (2001). Among these, the trapezoidal area change is the most general perturbation which contains area changes such as the step or ramp type and the square pulse as particular cases. 

Here, (which is equal to xb. Figure 3b) denotes the distance of the energy barrier b from the energy minimum along the direction of the applied force d is the diffusive relaxation time of the bound complex. 

In [31] kinetics of the surface tension decrease was described using the model accounting for diffusion-controlled adsorption of protein molecule and for conformational changes of adsorbed molecule. The model corresponds to one proposed by Serrien [32] and describes diffusion toward a/w surface and subsequent reorientation and other changes in adsorption layer, which usually one gives a sence of conformational changes the adsorbed protein. The model yields the diffusion relaxation time (t) and (kc) - the rate constant of conformational changes. 

Equations (87)-(89) can be used to interpret data from expansion-relaxation experiments see, for example. Refs. 39, 83, and 84. Fitting the experimental data for the interfacial dilatation, one can in principle determine the Gibbs elasticity, Eq, the diffusion relaxation time, t and the dilatational surface viscosity, (or The latter is accessible to the accuracy of the aforementioned experimental techniques for high-molecular-weight surfactants and proteins sometimes, (or -qd,) can be determined also for low-molecular-weight anionic surfactants, but in the presence of multivalent counterions (like... 

Figure 9 Interfacial elasticity Eq, diffusion relaxation time t and interfacial dilatation viscosity T rf versus pH of solutions of 0.0125 wt% BSA the other phase is decane. pH is maintained by a phosphate buffer the ionic strength, I, is adjusted by NaCl. The droplet expansion method is applied. (After Ref. 84.)...

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