Height fluctuations

If the height fluctuations for a specified laser beam area a are uncorrelated and characterized by a standard deviation Aha, then the standard error on N measurements of spot height is simply / mln = Ah, j /N. To express this in terms of the total scanned area A of a protein layer, it becomes... 

To quantitatively characterize the surface roughness of the Pt films, the rms roughness cr of the electrodes was evaluated and the resulting values are indicated in Figures 10a, 10b and 10c, respectively. From the comparison between [Pg.379]

Fourier component of height fluctuation of gel surface dimensionless parameter dependent on q defined by Eq. (4.43)... 

We may also predict pretransitional enhancement of the height fluctuation. By assuming that ( ) has the profile of the Rayleigh wave, we may calculate the excess free energy in terms of the height deviation h, Eq. (7.3), in the form,... 

Fytas et al. [18[ observed polymer dynamics associated with height fluctuations of PEO-PS copolymers attached to glass in toluene. Some of the measured normalized autocorrelation functions are shown in Fig. 8. The data was well represented by a single exponential function with a decay constant that exhibited minimal dependence on q. There is no calculation of the structure factor for such a system, but it is possible to rationalize the dependence of the decay constant on the 5/3 power of the chain density and the cube of the number of monomers in the PS segment. 

When f = 0, if the film thickness/(x,0) is uniform enough for our analysis, the initial surface-height fluctuation can be denoted as follows using Equation 5.1 (Note the origin of the height axis is variable). 

The dynamic scaling theory [38] considers the development of a rough surface on a flat ID surface of size L at time t = 0 (Fig. 15). It is assumed that the growth of the rough surface takes place in a well defined direction so that the instantaneous surface height can be described by the function h x t). The surface width in the z-direction, (T,t), taken as a measure of the surface roughness, is defined by the root mean square of the height fluctuations,... 

The fixed-position roll is motor-driven to establish the line speed. Since the line speed (nip speed) is a primary control determining film thickness, bubble diameter, and frost-line height, fluctuations in the motor speed should be minimized, generally less than 1% full scale. 

The photomultiplier, as shown in Fig. 6, is almost universally used as a photon counter, that is, the internal electron multiplication produces an output electrical pulse whose voltage is large compared with the output electric circuit noise. Each pulse in turn is the result of an individual photoexcited electron. The numbered electrodes, 1-8, called dynodes, are each successively biased about 100 V positive with respect to the preceding electrode, and an accelerated electron typically produces about 5 secondary electrons as it impacts the dynode. The final current pulse collected at the output electrode, the anode, would in this case contain 5 400,000 electrons. The secondary emission multiplication process is random, the value of the dynode multiplication factor is close to Poisson distributed from electron to electron. The output pulse amplitude thus fluctuates. For a secondary emission ratio of = 5, the rms fractional pulse height fluctuation is 1 /V<5 — 1 = 0.5. Since the mean pulse height can be well above the output circuit noise, the threshold for a pulse count may be... 

Another way to reduce finite size effects is to study closed vesicles. The first simulations on closed vesicles ( = 0) were by Komura and Baumgartner. For a closed vesicle in the flat phase, all three eigenvalues of M should scale linearly with N and a new measure of the height fluctuations and C are needed. At first thought, one might try to measure from the fluctuations in the mean-square radius of gyration, ... 

A quantitative comparison of our results with experiments should be possible for Van der Waals (non-polar) liquids such as PDMS (silicone oil) spreaded on various preprepared rough surfaces like etched glass, fused silica and mica. In a grazing incidence X-ray diffraction experiment the ratio of intensities scattered from the liquid and solid surfaces lL q)/Is q) is proportional to the ratio of the -component of the mean-squared height fluctuations of the two surfaces, (Ci( ))/(Cs( ))... 

In an approximation which ignores height fluctuations in region (3), a simple linear stability analysis about the interface separating regions (1) and (3) indicates that the flow is unstable to perturbations in the position of the interface or in the local surface tension. The stability analysis does not include the... 

Let us take a water-oil interface in the x-y plane separated by surfactant molecules as shown in Fig. 2. We consider a surface of total area A consisting of Ng surfactants each with an area per polar head of S so (A - NgS), For now we ignore deviations (height fluctuations) of the interface from the x-y plane. Following DeGennes and Taupin we can write down a simple expression for the free energy of the interface ... 

Figure 4.2d). Also, surfaces can become rough above a critical temperature because of atomic height fluctuations. 

Also for surfactant micelles, such roughening of the surface due to height fluctuations was observed by dynamic small-angle neutron scattering [1298]. 

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