Area change square pulse

There is an extra oscillation module, based on direct measurements of the capillary pressure, which operates from 1 to 150 Hz. There is also an additional accessory for the PAT1 for low-frequency oscillations. The range of surface and interfacial tension is 1 to 1000 mN/m with a resolution of 0.1 mN/m. The instrument allows for transient relaxation measurements, using perturbations such as ramp, square pulse, or trapezoidal area changes. 

Fig. 6.1. Schematic of different transient area changes (solid lines) and the corresponding interfacial tension responses (dotted lines) (a) - step type, (b) - ramp type, (c) - square pulse, (d) -trapezoidal change...

It was shown by Loglio et al. (1991a) that the most useful disturbance for interfacial relaxation experiments is the trapezoidal area change. For time regimes realised in most of the transient relaxation experiments the trapezoidal area change can be approximated adequately by a square pulse. For the square pulse area change we obtain ... 

The software driven apparatus allows different types of area changes step and ramp type, square pulse and trapezoidal as well as sinusoidal area deformations. The construction ensures that area changes are almost isotropic. Area changes used in transient and harmonic relaxation experiments are of the order of 1 to 5%. The surface tension response measured via the Wilhelmy balance has an accuracy of better than 0.1 mN/m. 

Fig. 6.22 Interfacial tension relaxation of 0.02 mg/ml HA to three square pulses at 24°C at the water/decane interface a) drop area change, b) surface tension response according to Miller et al. (1993c)...

More convenient for relaxation studies are the square pulse (cf. Fig. 6.1, (c)) or its practical equivalence the trapezoidal area change (cf Fig. 6.1, (d)). The F-transforms of the respective area changes are as follows (cf Miller et al. 1991) ... 

As mentioned above the oscillating drop or bubble method, based on profile analysis tensiometry, is the most recently developed method to investigate the surface relaxation of soluble adsorption layers. By increasing/decreasing the volume of a pendent drop or bubble, a variety of area changes can be performed, such as step, square pulse, ramp type, trapezoidal, and of course harmonic area changes at low frequencies. 

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. 

The experimental results shown in Figure 12.10 demonstrate the capacity of the drop and bubble shape technique. After the adsorption process has reached an equilibrium state, over a period of time of about 6 h, some square pulses of the drop area are subsequently, produced. Such area perturbations are suitable for determining the surface dilational elasticity of the interfacial layer. Efficient dosing systems even allow a sinusoidal area change, again providing information... 

Surface diffusion can be studied with a wide variety of methods using both macroscopic and microscopic techniques of great diversity.98 Basically three methods can be used. One measures the time dependence of the concentration profile of diffusing atoms, one the time correlation of the concentration fluctuations, or the fluctuations of the number of diffusion atoms within a specified area, and one the mean square displacement, or the second moment, of a diffusing atom. When macroscopic techniques are used to study surface diffusion, diffusion parameters are usually derived from the rate of change of the shape of a sharply structured microscopic object, or from the rate of advancement of a sharply defined boundary of an adsorption layer, produced either by using a shadowed deposition method or by fast pulsed-laser thermal desorption of an area covered with an adsorbed species. The derived diffusion parameters really describe the overall effect of many different atomic steps, such as the formation of adatoms from kink sites, ledge sites... 

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